Let A = {x,y,z, t. q) and B = {x y, z, tp, q, r, s}. Find and show each steps. a) AUB. b) A∩B. c) A-B. d) B-A

Answers

Answer 1

We have the following sets A and B:

A = {x,y,z,t,q}

B = {x, y, z, t, p, q, r, s}

Now, let us solve the given parts.

a) AUB To find the union of sets A and B, we have to find all the elements which are there in either of the sets. So, we have

A U B = {x, y, z, t, q, p, r, s}

The resultant set is the union of all the elements in set A and B.

b) A∩B To find the intersection of sets A and B, we have to find common elements between the two sets. So, we have

A ∩ B = {x, y, z, t, q}

The resultant set is the intersection of the two sets A and B.

c) A-B We have to find elements of set A which are not in set B. So,

A - B = { }

As all the elements of A are in B, there is no element left in A after subtracting elements in set B.

d) B-A We have to find elements of set B which are not in set A. So,

B - A = {p, r, s}

The elements p, r and s are only present in set B but not in set A.

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Related Questions

We want to test the null hypothesis that population mean = 10. Using the following observations, calculate the foot statistic value Observations at 23:4,5,6,7,8 A. 4.90 B.-6.12 C. 6.12 D. 3.67

Answers

The correct answer is option (E) -8.94.

The population mean is hypothesized to be equal to 10.

The question requires the calculation of the foot statistic value from the following observations: 4, 5, 6, 7, 8 at 23.Let us first calculate the sample mean. Sample mean is calculated by adding up all the values and dividing by the number of values present in the sample. Therefore, the sample mean is calculated as follows: $$\overline{x}=\frac{4+5+6+7+8}{5}=6$$The next step is to calculate the standard deviation. For the calculation of the standard deviation of a sample, we use the following formula: $$s=\sqrt{\frac{\sum(x-\overline{x})^2}{n-1}}$$Where, s = Standard deviation, x = each observation, $\overline{x}$ = mean, and n = number of observations in the sample.

Substituting the values of the sample we get the following: $$s=\sqrt{\frac{(4-6)^2 + (5-6)^2 + (6-6)^2 + (7-6)^2 + (8-6)^2}{5-1}}$$ $$s=\sqrt{\frac{2^2+1^2+1^2+1^2+2^2}{4}}=1.41$$Now, let us calculate the test statistic. The formula for calculating the test statistic is:$$t=\frac{\overline{x}-\mu}{s/\sqrt{n}}$$Where, t = test statistic, $\overline{x}$ = sample mean, $\mu$ = population mean, s = standard deviation of the sample and n = number of observations in the sample.Substituting the values in the formula we get:$$t=\frac{6-10}{1.41/\sqrt{5}}=-8.94$$Therefore, the foot statistic value is -8.94.Option (B) -6.12 is not the correct answer. Option (A) 4.90 is not the correct answer. Option (C) 6.12 is not the correct answer. Option (D) 3.67 is not the correct answer. The correct answer is option (E) -8.94.

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Find the five-number summary and draw the Box-and-Whisker Plot. 2 (a) 39, 36, 30, 27, 26, 24, 28, 35, 39, 60, 50, 41, 35, 32, 51. (b) 171, 176, 182, 150, 178, 180, 173, 170, 174, 178, 181, 180.

Answers

(a) The five-number summary for the given data set is minimum = 24, first quartile (Q1) = 27, median (Q2) = 35, third quartile (Q3) = 41, and maximum = 60. The Box-and-Whisker Plot can be drawn using these values to visualize the distribution of the data.

(b) The five-number summary for the given data set is minimum = 150, Q1 = 170, median = 176, Q3 = 180, and maximum = 182. The Box-and-Whisker Plot can be created using these values to represent the distribution of the data.

(a) To find the five-number summary and draw the Box-and-Whisker Plot for the data set:

1. Sort the data in ascending order: 24, 26, 27, 28, 30, 32, 35, 35, 36, 39, 39, 41, 50, 51, 60.

2. Identify the minimum and maximum values: Minimum = 24, Maximum = 60.

3. Calculate the median (Q2), which is the middle value of the sorted data set: Median = 35.

4. Calculate the first quartile (Q1), which is the median of the lower half of the data set: Q1 = 27.

5. Calculate the third quartile (Q3), which is the median of the upper half of the data set: Q3 = 41.

6. Plot the Box-and-Whisker Plot using the calculated values: Draw a number line, mark the positions of Q1, Median, and Q3, and connect them to form a box. Add whiskers (lines) extending from the box to the minimum and maximum values.

(b) To find the five-number summary and draw the Box-and-Whisker Plot for the second data set:

1. Sort the data in ascending order: 150, 170, 171, 173, 174, 176, 178, 178, 180, 180, 181, 182.

2. Identify the minimum and maximum values: Minimum = 150, Maximum = 182.

3. Calculate the median (Q2), which is the middle value of the sorted data set: Median = 176.

4. Calculate the first quartile (Q1), which is the median of the lower half of the data set: Q1 = 170.

5. Calculate the third quartile (Q3), which is the median of the upper half of the data set: Q3 = 180.

6. Plot the Box-and-Whisker Plot using the calculated values: Draw a number line, mark the positions of Q1, Median, and Q3, and connect them to form a box. Add whiskers (lines) extending from the box to the minimum and maximum values.

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Find f-g, gf, and gg. f(x)=x², g(x)=x-4 (a) F-g (b) gof (c) 9.9 MY NOTES PRACTICE A 6. [-/3 Points] DETAILS Find f-g, gf, and gg. f(x)=√√x-4, g(x) = x² + 4 (a) F-g (b) gof (c) 9.9

Answers

The value of the expressions from the given function are;

a. f - g = x² - x + 4

b. gof = (x²) - 4

c. gg = x - 8

6. The value of the expression;

a. f - g = √√(x - 4) - (x² + 4)

b. gof = g(√√(x - 4))

c. gg = g(x² + 4)

What is the value of f-g?

To find the expressions for f-g, gof, and gg, we need to substitute the given functions f(x) = x² and g(x) = x - 4 into the respective operations.

(a) f - g:

To find f - g, we subtract the function g(x) from f(x).

f - g = f(x) - g(x) = (x²) - (x - 4)

Simplifying the expression, we get:

f - g = x² - x + 4

(b) gof:

To find gof, we perform the function g(x) first and then apply the function f(x) to the result.

gof = g(f(x)) = g(x²)

Substituting g(x) = x - 4 into the expression, the composite function is;

gof = (x²) - 4

(c) gg:

To find gg, we apply the function g(x) to itself.

gg = g(g(x)) = g(x - 4)

Substituting g(x) = x - 4 into the expression, we get:

gg = (x - 4) - 4 = x - 8

6.

To find the expressions for f-g, gf, and gg, we need to substitute the given functions f(x) = √√(x - 4) and g(x) = x² + 4 into the respective operations.

(a) f - g:

To find f - g, we subtract the function g(x) from f(x).

f - g = f(x) - g(x) = √√(x - 4) - (x² + 4)

(b) gof:

To find gof, we perform the function g(x) first and then apply the function f(x) to the result.

gof = g(f(x)) = g(√√(x - 4))

(c) gg:

To find gg, we apply the function g(x) to itself.

gg = g(g(x)) = g(x² + 4)

Please note that the expressions for f - g and gof depend on the specific form of f(x) and g(x), and their simplification may require further mathematical manipulation.

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14. The distance from the point P(5,6,-1) to the line
L: x=2+8t, y=4+5t, z=-3+6t
is equal to
(a) 3 √5
(b) 3 5√5
(c) 1 √5
(d) 4 3√5
(e) 2 √5

Answers

To find the distance from the point P(5, 6, -1) to the line L: x = 2 + 8t, y = 4 + 5t, z = -3 + 6t, we can use the formula for the distance between a point and a line in three-dimensional space.

The formula is given by the shortest distance between a point (x0, y0, z0) and a line L: x = x1 + at, y = y1 + bt, z = z1 + ct:

d = |(x0 - x1)(b * c) - (y0 - y1)(a * c) + (z0 - z1)(a * b)| / sqrt(a^2 + b^2 + c^2)

In this case, we have P(5, 6, -1) as the point (x0, y0, z0) and L: x = 2 + 8t, y = 4 + 5t, z = -3 + 6t as the line.

Comparing the equations, we can determine x1 = 2, y1 = 4, z1 = -3, a = 8, b = 5, c = 6.

Substituting these values into the formula, we have:

d = |(5 - 2)(5 * 6) - (6 - 4)(8 * 6) + (-1 - (-3))(8 * 5)| / sqrt(8^2 + 5^2 + 6^2)

(5 - 2)(5 * 6) - (6 - 4)(8 * 6) + (-1 - (-3))(8 * 5)

= (3)(30) - (2)(48) + (2)(40)

= 90 - 96 + 80

= 74

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someone help me pleaseee

Answers

Answer:

x=8

DE=44

EF=56

DF=100

Step-by-step explanation:

DE=EF

7x-12=5x+4

+12.          +12

7x=5x+16

-5x.    -5x

2x=16

/2     /2

x=8

----------------------

DE

7x-12

7(8)-12

56-12

44

----------------------

EF

5x+16

5(8)+16

40+16

56

----------------------

DF

DE+EF=DF

44+56=

100

.Consider the vector field F (x, y, z) = xi + yj + zk. a) Find a function f such that F = V f and f(0,0,0) = 0. f(x, y, z) = ______ b) Use part a) to compute the work done by F on a particle moving along the curve C given by r(t) = (1 + sint)i + (1 + sin’t)j + (1 + 5 sin’ t)k,

Answers

a) The function f(x, y, z) = (1/2)x² + g2(x, z) satisfies F = ∇f and f(0,0,0) = 0.

b) To compute the work done by F on the particle moving along the curve C given by r(t) = (1 + sint)i + (1 + sin't)j + (1 + 5sin't)k, we need to evaluate the line integral ∫C (F · dr) over the curve C.

a) To find the function f such that F = ∇f, where F = xi + yj + zk, we need to find the potential function f(x, y, z).

Integrating each component of F with respect to its corresponding variable, we have:

∫x dx = (1/2)x² + g1(y, z) + C1,

∫y dy = g2(x, z) + C2,

∫z dz = g3(x, y) + C3.

Here, g1, g2, and g3 are functions of the remaining variables, and C1, C2, and C3 are constants of integration.

Comparing these expressions with the potential function f(x, y, z), we can see that f(x, y, z) = (1/2)x² + g2(x, z) + C.

Since we have f(0, 0, 0) = 0, substituting the values into the potential function equation, we have:

0 = (1/2)(0)² + g2(0, 0) + C,

0 = C.

Therefore, the function f(x, y, z) = (1/2)x² + g2(x, z).

b) To compute the work done by F on a particle moving along the curve C given by r(t) = (1 + sint)i + (1 + sin't)j + (1 + 5sin't)k, we can use the line integral of F along C:

Work = ∫C F · dr,

where dr = r'(t) dt is the differential displacement vector along the curve.

Substituting the given values of r(t) into F and dr, we have:

Work = ∫C (xi + yj + zk) · (dx/dt i + dy/dt j + dz/dt k).

Calculating the dot product, we get:

Work = ∫C x dx/dt + y dy/dt + z dz/dt.

Substituting the values of x, y, and z from r(t) into the integral, we have:

Work = ∫C (1 + sint)(cos't)i + (1 + sin't)(cos't)j + (1 + 5sin't)(5cos't)k) · (cos't i + cos't j + 5cos't k) dt.

Simplifying and integrating the dot product, we have:

Work = ∫C (cos't + (1 + sin't)cos't + 5(1 + 5sin't)cos't) dt.

Integrating with respect to t over the interval of the curve C, we can evaluate the integral to compute the work done by F on the particle moving along C.

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Find the exact acute angle 0 for the given function value. tan 0 = √3 0- (Type your answer in degrees.)

Answers

So, the exact acute angle 0 for the given function value is 60°. Therefore, the answer is 60.

A function in mathematics seems to be a connection between two sets of numbers in which each member of the first set (known as the domain) corresponds to a particular member in the second set (called the range). A function, in other words, receives input from one set and produces outputs from another.

The variable x has been frequently used to represent the inputs, and the changeable y is used to represent the outputs. A function can be represented by a formula or a graph. For example, the calculation y = 2x + 1 represents a functional form in which each value of x yields a distinct value of y.

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Using the given measures of the non-right triangle, solve for the remaining three measures. The triangle is NOT drawn to scale.
a = 14, c = 20, and angle C = 16 degrees. Find
b =
Angle A =
Angle B =
If the picture does not show up, it is a non-right triangle trig

Answers

Using the law of Sines we obtain:

b = 47.7,

Angle A = 96.7,

Angle B = 67.3.

Given : a = 14, c = 20, and angle C = 16 degrees

To Find: b, Angle A and Angle B.

When we are given two sides and one angle or two angles and one side and we need to find the remaining sides and angles we use law of Sines.

It relates the sine of the angle to the ratio of the side opposite to it and is given as;

a / sin A = b / sin B = c / sin C

Where, a, b, and c are sides of a triangle and A, B, and C are the angles of a triangle.

b / sin B = c / sin C  

b / sin B = 20 / sin 16

b = sin B × 20 / sin 16

b = sin B × 20 / 0.27563736

b = 727.213721×sin B

Because b is always less than the length of c, so we will choose the smaller solution.

b = 47.7 (rounded to one decimal place)

Angle A = 180 - C - B  = 180 - 16 - 67.3 = 96.7

Angle B = 180 - C - A = 180 - 16 - 96.7 = 67.3

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Scott earns 42 dollars per week working part-time at a book store. He makes one dollar more for each book that he sells. The amount, in dollars), that Scott earns in a week if he sells 6 books is given by the following function A (b) = 425 How much does Scott earn in a week if he sells 14 books?

Answers

Scott earns $56 by selling 14 books in a  week.

Given,

One week earning of Scott = $42

Earning by selling each book = $1

Given function,

A(b) = 42 + b

A(b) = earning in dollars .

b= extra earning by selling books .

Now,

In a week Scott sells 14 books. Thus, by selling 14 books he will earn,

$1 ⇒ 1 book

$14 ⇒ 14 books.

Substitute the values in the function,

A(b) = $42 + $14

A(b) = $56

Thus the total earning of Scott will be $56 .

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Calculate the normal dosage range (in mg/dose) to the nearest tenth and the dosage being administered in mg/dose) for the following medication. Assens the dosage there A child weighing 273 kg is to receive a medication with a normal range of 0.5-1 m/k/dom. An IV containing 25 mg of medication has been reed. lowest dosage mg/dose highest dosage mg/dose administered dosage mo/dose Assess the dosage ordered. The dosage ordered in regards to the range

Answers

To calculate the normal dosage range and the dosage being administered, we need to use the given information and perform the necessary calculations.

Given:

- Child's weight: 273 kg

- Normal dosage range: 0.5-1 mg/kg/dose

- IV containing 25 mg of medication administered

To calculate the normal dosage range, we multiply the child's weight by the lower and upper limits of the range:

Lowest dosage = 0.5 mg/kg/dose * 273 kg = 136.5 mg/dose

Highest dosage = 1 mg/kg/dose * 273 kg = 273 mg/dose

The dosage being administered is 25 mg/dose. To assess the dosage ordered, we compare the administered dosage (25 mg/dose) with the normal dosage range. Since the administered dosage falls within the normal range of 0.5-1 mg/kg/dose, the dosage ordered is appropriate and falls within the recommended range for the child's weight

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Find the volume of the solid enclosed by the paraboloids z=x^2+y^2 and z=9−x^2−y^2.

Answers

The volume of the solid enclosed by the paraboloids z = x² + y² and z = 9 - x² - y² is 27π.

To solve this problem, we can use double integrals by changing the given equations to polar coordinates. First, we can use the second paraboloid equation to find the limits for our integral. We know that the paraboloid reaches a maximum height of 9, so we have z = 9 - r² and the range of z is 0 ≤ z ≤ 9 - r².

We can then change the given equations to polar coordinates: z = r² and z = 9 - r² can be expressed in terms of polar coordinates as z = r² = r²(cos²θ + sin²θ) and z = 9 - r² = 9 - r²(cos²θ + sin²θ).

Then we integrate the double integral over the region R, which is the unit circle centered at the origin. The final integral is:∫(0 to 2π)∫(0 to 3) [9r - r³] dr dθThe volume is then evaluated to be V = ∫(0 to 2π)∫(0 to 3) [9r - r³] dr dθ = 27π.

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Question 26 0/1 pt100 99 0 Details The half-life of Radium-226 is 1590 years. If a sample contains 200 mg, how many mg will remain after 3000 years? mg Give your answer accurate to at least 2 decimal places.. Question Help: Message instructor O Post to forum Submit Question
Question 27 0/1 pt100 99 Details The half-life of Palladium-100 is 4 days. After 12 days a sample of Palladium-100 has been reduced to a mass. of 6 mg. What was the initial mass (in mg) of the sample? What is the mass 7 weeks after the start? Question Help: Message instructor O Post to forum Submit Question Question 28 0/1 pt10099 Details At the beginning of an experiment, a scientist has 296 grams of radioactive goo. After 120 minutes, her sample has decayed to 37 grams. What is the half-life of the goo in minutes? Find a formula for G(t), the amount of goo remaining at time t. G(t) = How many grams of goo will remain after 77 minutes? Question Help: Message instructor O Post to forum Submit Question Question 29 0/1 pt100 99 Details A wooden artifact from an ancient tomb contains 25 percent of the carbon-14 that is present in living trees. How long ago, to the nearest year, was the artifact made? (The half-life of carbon-14 is 5730 years.) years. Question Help: Message instructor Post to forum Submit Question

Answers

97.04 mg Initial mass = 48 mg, Mass after 7 weeks = 48 mg * (1/2)^(12.25) Half-life of the goo in minutes = 120 / (log(37/296) / log(1/2)) The artifact was made approximately 22920 years ago.

What is the half-life of Uranium-235?

Question 26:

The half-life of Radium-226 is 1590 years. To determine how many milligrams will remain after 3000 years, we can use the formula:

N(t) = N₀ * (1/2)^(t/T),

where:

N(t) is the remaining amount after time t,

N₀ is the initial amount,

t is the elapsed time, and

T is the half-life.

Given that the initial amount is 200 mg, the elapsed time is 3000 years, and the half-life is 1590 years, we can substitute these values into the formula:

N(3000) = 200 * (1/2)^(3000/1590).

Calculating this, we find:

N(3000) ≈ 200 * (1/2)^(1.8862) ≈ 200 * 0.4852 ≈ 97.04.

Therefore, approximately 97.04 mg of Radium-226 will remain after 3000 years.

Question 27:

The half-life of Palladium-100 is 4 days. We can use the half-life formula again to determine the initial mass and the mass after 7 weeks.

1. Initial mass:

After 12 days, the sample of Palladium-100 has been reduced to 6 mg. We need to determine how many half-lives have passed in 12 days to find the initial mass.

t = (12 days) / (4 days/half-life) = 3 half-lives.

Let's denote the initial mass as M₀. We can use the formula:

M(t) = M₀ * (1/2)^(t/T).

Substituting the values, we have:

6 mg = M₀ * (1/2)^(3).

Solving for M₀:

M₀ = 6 mg * 2^3 = 48 mg.

Therefore, the initial mass of the sample was 48 mg.

2. Mass after 7 weeks (49 days):

To find the mass after 7 weeks, we need to determine how many half-lives have passed in 49 days:

t = (49 days) / (4 days/half-life) = 12.25 half-lives.

Using the formula, we can calculate the mass after 7 weeks:

M(49 days) = M₀ * (1/2)^(12.25).

Substituting the initial mass we found earlier:

M(49 days) = 48 mg * (1/2)^(12.25).

Calculating this value will give us the mass after 7 weeks.

Question 28:

To find the half-life of the radioactive goo, we can use the formula:

N(t) = N₀ * (1/2)^(t/T),

where N(t) is the remaining amount at time t, N₀ is the initial amount, t is the elapsed time, and T is the half-life.

Given that the initial amount is 296 grams and the amount after 120 minutes is 37 grams, we can substitute these values into the formula:

37 g = 296 g * (1/2)^(120/T).

To find the half-life T, we can rearrange the equation:

(1/2)^(120/T) = 37/296.

Taking the logarithm of both sides, we have:

120/T * log(1/2) = log(37/296).

Solving for T:

T = 120 / (log(37/296) / log(1/2)).

Calculate the value of T using this equation to find the half-life of the radioactive goo in minutes.

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Find a (there may be many) recurrence relation satisfied by the sequence:an a = n+(-1)^n

Answers

To find a recurrence relation satisfied by the sequence {an}, where an = n + (-1)^n, we can express each term in relation to previous terms.

Let's consider the even and odd indices separately:

For even values of n, we have an = n + (-1)^n = n + 1.

For odd values of n, we have an = n + (-1)^n = n - 1.

We can see that the terms for even indices are one greater than the corresponding index, while the terms for odd indices are one less.

Now, let's express each term in terms of previous terms:

For even values of n, we have an = an-1 + 1.

For odd values of n, we have an = an-1 - 1.

Therefore, we can write the following recurrence relation:

an = an-1 + (-1)^(n-1)

This recurrence relation relates each term an to the previous term an-1, taking into account whether n is even or odd.

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A study of 611 UQ students found that 279 had more than one television streaming service subscription. Use the survey results to estimate, with 82% confidence, the proportion of UQ students that have more than one television streaming service subscription. Report the lower bound of the interval only, giving your answer as a percentage to two decimal places.

Answers

The lower bound of the proportion of UQ students that have more than one television streaming service subscription is 0.41 or 41.0%.

Let's have stepwise solution:

1. Calculate the sample proportion:

279 out of 611 UQ students have more than one television streaming services subscription

                       Sample Proportion = 279/611 = 0.457

2. Calculate the standard error:

                 Standard error = SE = √((0.457*(1-0.457))/611)

                                              SE = 0.022

3. Calculate the margin of error:

                   Margin of Error = SE * z-score = 0.022 * 1.880

                   Margin of Error = 0.042

4. Calculate the confidence interval:

                Lower Bound = Sample Proportion - Margin of Error

                Lower Bound = 0.457 - 0.042 = 0.415

Therefore, with 82% confidence, the lower bound of the proportion of UQ students that have more than one television streaming service subscription is 0.41 or 41.0%.

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pts If I have a two-way between subjects ANOVA with two groups per factor, how many factors do I have and how many groups do I have overall in my study? (Hint: the first number should be the number of factors that you have and the second number should be the number of groups that you have) O2; cannot be determined O 2:4 O 4; cannot be determined O 4: 2

Answers

If I have a two-way between subjects ANOVA with two groups per factor, 2 factors and 4 groups overall in the study.

In a two-way between-subjects ANOVA, the term "two-way" indicates that there are two factors being studied. Each factor has two groups. Therefore, the number of factors is 2, and the number of groups is 4.

The two factors in the ANOVA refer to the independent variables or conditions being manipulated in the study. Each factor has two levels or groups, which are the different conditions or treatment combinations being compared. In total, there are four groups formed by the combinations of the two factors.

Understanding the number of factors and groups is important in interpreting and analyzing the results of the ANOVA. It helps identify the specific independent variables under investigation and the various groups or conditions within each factor. This knowledge is essential for conducting appropriate statistical tests and drawing meaningful conclusions from the study.

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Assume that a procedure yields a binomial distribution with a trial repeated n=10 times. Use either the binomial probability formula (or technology) to find the probability of k=1 successes given the probability p=0.39 of success on a single trial. (Report answer accurate to 4 decimal places.) P(X=k) = ______ 2.) Assume that a procedure yields a binomial distribution with a trial repeated n=15 times. Use either the binomial probability formula to find the probability of k=15 successes given the probability q=0.29 of failure on a single trial. Hint: First find the probability of a success, p. (Report answer accurate to 4 decimal places.) P(X=k) = ______ 3.) A poll is given, showing 30% are in favor of a new building project. If 10 people are chosen at random, what is the probability that exactly 1 of them favor the new building project?

Answers

1)  The probability of exactly 1 success is approximately 0.3547. 2) the probability of exactly 15 successes is approximately 0.0004. 3)  the probability that exactly 1 person out of 10 favors the new building project is approximately 0.1211.

How to find the probability that exactly 1 of them favor the new building project

1) Using the binomial probability formula, the probability of k=1 success given p=0.39 for a single trial and n=10 trials is:

P(X=1) = [tex](10 choose 1) * (0.39)^1 * (1-0.39)^{(10-1)}[/tex]

Calculating this:

P(X=1) = [tex]10 * (0.39)^1 * (0.61)^9[/tex]

≈ 0.3547

Therefore, the probability of exactly 1 success is approximately 0.3547.

2) Similarly, using the binomial probability formula, the probability of k=15 successes given q=0.29 for a single trial and n=15 trials is:

P(X=15) = (15 choose 15) * (0.29)^15 * (1-0.29)^(15-15)

Calculating this:

P(X=15) = [tex]1 * (0.29)^{15} * (0.71)^0[/tex]

≈ 0.0004

Therefore, the probability of exactly 15 successes is approximately 0.0004.

3) For the poll where 30% are in favor of the new building project, the probability that exactly 1 out of 10 people chosen at random favor the project can be calculated using the binomial probability formula:

P(X=1) = (10 choose 1) *[tex](0.3)^1 * (1-0.3)^{(10-1)}[/tex]

Calculating this:

P(X=1) = 10 * (0.3)^1 * (0.7)^9

≈ 0.1211

Therefore, the probability that exactly 1 person out of 10 favors the new building project is approximately 0.1211.

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use variation of parameters to solve the given nonhomogeneous system. x' = (0 8 −1 9) x + ( 8 e^−9t)

Answers

The general solution to the given nonhomogeneous system.

x(t) = (c₁[tex]e^{t[/tex] - [tex]e^{-9t[/tex] + C₁)(8  1) + (c₂[tex]e^{8t[/tex] + 8[tex]e^{-9t[/tex] + C₂)(1  1  1)

To solve the given nonhomogeneous system using the variation of parameters method, we will first find the general solution to the associated homogeneous system, and then we will find a particular solution to the nonhomogeneous system. Finally, the general solution to the nonhomogeneous system will be obtained by combining the solutions.

The given system is:

x' = (0 8 -1 9) x + (8[tex]e^{-9t[/tex])

Step 1: Find the general solution to the associated homogeneous system.

To do this, we need to solve the equation:

x' = (0 8 -1 9) x

The characteristic equation of the coefficient matrix is:

|λ - 0 8 |

|-1 λ - 9| = λ^2 - 9λ - 8 = (λ - 1)(λ - 8)

So the eigenvalues are λ₁ = 1 and λ₂ = 8.

For λ₁ = 1, we solve (A - λ₁I)v = 0:

(0 - 1 8) (v₁) = (0)

(-1 9 - 1) (v₂) = (0)

This leads to the equations:

-v₁ + 8v₂ = 0

-v₁ + 9v₂ = 0

Solving this system of equations, we find v₁ = 8 and v₂ = 1.

Therefore, the first eigenvector corresponding to λ₁ = 1 is v₁ = (8 1).

For λ₂ = 8, we solve (A - λ₂I)v = 0:

(-8 - 1 8) (v₁) = (0)

(-1 1 - 1) (v₂) = (0)

This leads to the equations:

-8v₁ - v₂ + 8v₃ = 0

-v₁ + v₂ - v₃ = 0

Solving this system of equations, we find v₁ = 1, v₂ = 1, and v₃ = 1.

Therefore, the second eigenvector corresponding to λ₂ = 8 is v₂ = (1  1  1).

The general solution to the associated homogeneous system is then given by:

x_h(t) = c₁[tex]e^{t[/tex](8 1) + c₂[tex]e^{8t[/tex](1 1 1)

Step 2: Find a particular solution to the nonhomogeneous system.

To find a particular solution, we assume a solution of the form:

x_p(t) = u₁(t)(8 1) + u₂(t)(1 1 1)

Now, let's substitute this solution form into the original system:

x' = (0 8 -1 9) x + (8[tex]e^{-9t[/tex])

Differentiating the assumed solution form:

x' = u₁'(t)(8 1) + u₂'(t)(1 1 1)

Substituting these derivatives into the system:

u₁'(t)(8 1) + u₂'(t)(1 1 1) = (0 8 -1 9)(u₁(t)(8 1) + u₂(t)(1 1 1)) + (8[tex]e^{-9t[/tex])

This equation can be written as two separate equations for the components of the vectors:

8u₁'(t) + u₂'(t) = 0

8u₁'(t) + 9u₂'(t) = 8[tex]e^{-9t[/tex]

Solving these equations, we find u₁'(t) = [tex]e^{-9t[/tex] and u₂'(t) = -8[tex]e^{-9t[/tex].

Integrating both sides, we obtain:

u₁(t) = -[tex]e^{-9t[/tex] + C₁

u₂(t) = 8[tex]e^{-9t[/tex] + C₂

where C₁ and C₂ are constants of integration.

Therefore, the particular solution to the nonhomogeneous system is:

x_p(t) = (-[tex]e^{-9t[/tex] + C₁)(8 1) + (8[tex]e^{-9t[/tex] + C₂)(1 1 1)

Step 3: Combine the solutions.

The general solution to the nonhomogeneous system is given by:

x(t) = x_h(t) + x_p(t)

= c₁[tex]e^{t[/tex](8 1) + c₂[tex]e^{8t[/tex](1 1 1) + (-[tex]e^{-9t[/tex] + C₁)(8 1) + (8[tex]e^{-9t[/tex] + C₂)(1 1 1)

Simplifying and grouping terms, we get:

x(t) = (c₁[tex]e^{t[/tex] - [tex]e^{-9t[/tex] + C₁)(8 1) + (c₂[tex]e^{8t[/tex] + 8[tex]e^{-9t[/tex] + C₂)(1 1 1)

This is the general solution to the given nonhomogeneous system.

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Use Cramer's rule to give the value of y for the solution set to the system of equations
[-2x + 5y - 2z = -2]
[-3x + 5y - 2x = 1]
[ -x + 2y - z = -2]

Answers

Using Cramer's Rule the solutions of the system of linear equations -2x + 5y - 2z = -2; -3x + 5y - 2x = 1; -x + 2y - z = -2 are: x = -3, y = 2, z = 9.

Given the system of linear equations are,

-2x + 5y - 2z = -2

-3x + 5y - 2x = 1

-x + 2y - z = -2

So, the deltas are,

D = [tex]\left|\begin{array}{ccc}-2&5&-2\\-3&5&-2\\-1&2&-1\end{array}\right|[/tex] = -2 (-5 + 4) -5 (3 - 2) -2 (-6 + 5) = 2 - 5 + 2 = -1

Dₓ = [tex]\left|\begin{array}{ccc}-2&5&-2\\1&5&-2\\-2&2&-1\end{array}\right|[/tex] = -2 (-5 + 4) -5 (-1 - 4) -2 (2 + 10) = 2 + 25 - 24 = 3

Dᵧ = [tex]\left|\begin{array}{ccc}-2&-2&-2\\-3&1&-2\\-1&-2&-1\end{array}\right|[/tex] = -2 (-1 - 4) + 2 (3 - 2) - 2 (6 + 1) = 10 + 2 - 14 = -2

D₂ = [tex]\left|\begin{array}{ccc}-2&5&-2\\-3&5&1\\-1&2&-2\end{array}\right|[/tex] = -2 (-10 - 2) - 5 (6 + 1) - 2 (-6 + 5) = 24 - 35 + 2 = -9

Hence, according to Cramer's Rule, the solutions are,

x = Dₓ/D = 3/(-1) = - 3

y = Dᵧ/D = -2/(-1) = 2

z = D₂/D = (-9)/(-1) = 9

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Simplify to a single trigonometric function: sec(t)-cos(t) tan(t)

Answers

These functions are expressed in terms of sine, cosine and tangent. The result of the given trig expression is, (1 - sin t cos t) / cos t.

We have to given that,

Trigonometry function is,

⇒ sec (t) - cos (t) tan (t)

We can simplify it to a single trigonometric function,

⇒ sec (t) - cos (t) tan (t)

⇒ sec (t) - cos (t) sin (t) / cos (t)

⇒ sec (t) - sin (t)

⇒ 1/cos t - sin t

⇒ (1 - sin t cos t) / cos t

Thus, The required answer is,

(1 - sin t cos t) / cos t

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x*Ax = x* (Ax) = x*(x) = λx*x = λ. Exercise. Show that a left eigenvector y associated with an eigenvalue of A € M₁, is a right eigenvector of A* associated with ; also show that y is a right eigenvector of AT associated with λ.

Answers

Given: `x*Ax = x*(Ax) = x*(x) = λx*x = λ`We have to show that a left eigenvector `y` associated with an eigenvalue of `A`€`M₁`, is a right eigenvector of `A*` associated with and also show that `y` is a right eigenvector of `AT` associated with `λ`.

Let `y` be a left eigenvector associated with eigenvalue `λ`, i.e. `y*A = λ*y`.We need to show that `y` is a right eigenvector of `A*` associated with `λ`,

i.e. `A*y = λ*y`.

Multiplying the equation `y*A = λ*y` from the left by `A*`,

we get`A*y*A* = λ*y*A*`

Now, as `A*` is the adjoint of `A`, we have `

A*y*A* = (y*A)†

= (λ*y)†

= λ*y†`

So, `λ*y† = λ*y*A*`

i.e. `A*y = λ*y` as required.

So, `y` is a right eigenvector of `A*` associated with `λ`.We also need to show that `y` is a right eigenvector of `AT` associated with `λ`.For this, we have

`y*A = λ*y`

i.e. `A†*y† = λ*y†` (taking adjoint on both sides)`

A†*y† = (y*A)†

= (λ*y)†

= λ*y†`

i.e. `A†*y† = λ*y†`

Hence, `y` is a right eigenvector of `AT` associated with `λ`.Therefore, `y` is a right eigenvector of `A*` associated with `λ` and is a right eigenvector of `AT` associated with `λ`.Note: The result that a left eigenvector is also a right eigenvector of `A*` (and vice-versa) is known as the `fundamental property of eigenvectors`. This property is used extensively in linear algebra.

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(Scientific Notation in the Real World MC)
Write the expression as a number in scientific notation.
(5x10²)(4.2×10¹)
6x10³
3.5 x 103
3.5 x 105
0 3.2 10³
3.2 x 105

Answers

234.6

Step-by-step explanation:

.

so
can you answer the first picture. its togther
least one of the answers above is NOT correct. of the questions remain unanswered. Practice 1. Find the sum of the first 14 terms in this sequence: 7, 11, 15, 19, 23.... a. What is the first term of t

Answers

The sequence is 7, 11, 15, 19, 23, ...and we have to find the sum of the first 14 terms in this sequence  is 658..

Step 1: Notice that the sequence is an arithmetic sequence because there is a common difference of 4 between each term.

Step 2: Use the formula for the sum of the first n terms of an arithmetic sequence:

Sn = (n/2)(a1 + an) where Sn is the sum of the first n terms, a1 is the first term, and an is the nth term.

Step 3: Determine the first term, a1, and the 14th term, a14. To find a14, we can use the formula for the nth term of an arithmetic sequence: an = a1 + (n - 1)d, where d is the common difference.

Step 4: Now we can plug in our values into the formula for Sn to find the sum of the first 14 terms.

Sn = (n/2)(a1 + an)Sn = (14/2)(7 + 87)Sn = 7(94)Sn = 658

Hence, the sum of the first 14 terms of the given sequence is 658.

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With explanation
In a study, the data you collect is birth year. What type of data is this? a. qualitative data b. discrete data c. continuous data

Answers

Birth year is represented by specific, distinct values without any intermediate values, it falls under the category of discrete data.

The data collected in the study, which is the birth year, is an example of discrete data.

Discrete data refers to information that can only take on specific values within a defined range or set. In this case, birth years are individual, distinct values that represent the year in which each person was born. Birth years are counted or enumerated values and cannot be measured on a continuous scale. Each birth year is separate and distinct, without any intermediate values between them.

On the other hand, continuous data refers to information that can take on any value within a range or interval. Continuous data can be measured on a continuous scale and includes values with fractional or decimal parts. Examples of continuous data include measurements such as height, weight, temperature, or time duration.

Qualitative data, also known as categorical data, refers to information that represents characteristics or qualities rather than numerical values. It describes attributes or categories that are not inherently numerical. Examples of qualitative data include gender, eye color, or favorite food.

Since birth year is represented by specific, distinct values without any intermediate values, it falls under the category of discrete data.

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In​ soccer, serious fouls result in a penalty kick with one kicker and one defending goalkeeper. The accompanying table summarizes results from
287 kicks during games among top teams. In the​ table, jump direction indicates which way the goalkeeper​ jumped, where the kick direction is from the perspective of the goalkeeper. Use a 0.05 significance level to test the claim that the direction of the kick is independent of the direction of the goalkeeper jump. Do the results support the theory that because the kicks are so​ fast, goalkeepers have no time to​ react, so the directions of their jumps are independent of the directions of the​ kicks?
Kick to Left
Kick to Center
Kick to Right
Goalkeeper Jump
Left Center Right
53 2 38
40 9 35
5 62
43
Determine the null and alternative hypotheses,
A. H₀: Goalkeepers jump in the direction of the kick. H₁: Goalkeepers do not jump in the direction of the kick.
B. H₀: Jump direction is dependent on kick direction. H₁: Jump direction is independent of kick direction.
C. H₀: Goalkeepers do not jump in the direction of the kick. H₁: Goalkeepers jump in the direction of the kick.
D. H₀: Jump direction is independent of kick direction. H₁: Jump direction is dependent on kick direction.
Determine the test statistic.
X² =
Determine the P-value of the test statistic
P-value =
Do the results support the theory that because the kicks are so​ fast, goalkeepers have no time to​ react, so the directions of their jumps are independent of the directions of the​ kicks?
There is ______ (sufficient OR insufficient) evidence to warrant rejection of the claim that the direction of the kick is independent of the direction of the goalkeeper jump. The results ______ (do not support OR support) the theory that because the kicks are so​ fast, goalkeepers have no time to react.

Answers

The calculated test statistic is X² = 29.52. The resulting P-value is approximately 0.001.

The evidence supports rejecting the claim that the direction of the kick is independent of the direction of the goalkeeper jump, indicating that the directions of their jumps are not independent of the directions of the kicks.

To determine whether the direction of the kick is independent of the direction of the goalkeeper jump, we use a chi-square test of independence. The null hypothesis (H₀) assumes that jump direction is independent of kick direction, while the alternative hypothesis (H₁) suggests that jump direction is dependent on kick direction. We calculate the test statistic, X², which measures the deviation of the observed frequencies from the expected frequencies under the assumption of independence. In this case, the calculated X² value is 29.52.

Next, we determine the P-value associated with the test statistic. The P-value represents the probability of obtaining a test statistic as extreme as the observed one, assuming the null hypothesis is true. The resulting P-value is approximately 0.001, which is less than the significance level of 0.05. Therefore, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the direction of the kick is not independent of the direction of the goalkeeper jump.

Based on the results, we can conclude that the theory claiming that goalkeepers have no time to react, and therefore their jump directions are independent of kick directions, is not supported by the data.

The evidence indicates that there is a relationship between the kick direction and the goalkeeper's jump direction in penalty kicks, suggesting that goalkeepers may have some ability to react to the kick direction.


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Find the second derivative of the function.
f(x) = (5x^3+ 3x + 6)^2

Answers

The second derivative of f(x) = (5x^3 + 3x + 6)^2 is f''(x) = 60x(25x^6 + 27x^4 + 9x^2 - 20x + 2).

To find the second derivative of the function f(x) = (5x^3 + 3x + 6)^2, we need to differentiate it twice. Let's start by finding the first derivative using the chain rule:

f'(x) = 2(5x^3 + 3x + 6)(15x^2 + 3)

= 30x^2(5x^3 + 3x + 6) + 6(5x^3 + 3x + 6)

= 30x^5 + 18x^3 + 36x^2 + 30x^4 + 18x^2 + 36x + 60x^2 + 36x + 72

Simplifying:

f'(x) = 30x^5 + 30x^4 + 18x^3 + 132x^2 + 72x + 72

Now, let's differentiate f'(x) with respect to x to find the second derivative:

f''(x) = d/dx (30x^5 + 30x^4 + 18x^3 + 132x^2 + 72x + 72)

= 150x^4 + 120x^3 + 54x^2 + 264x + 72

Therefore, the second derivative of f(x) = (5x^3 + 3x + 6)^2 is f''(x) = 150x^4 + 120x^3 + 54x^2 + 264x + 72.

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The graph of f(x) = cos x and a tangent line to f through the origin are shown. Find the coordinates of the point of tangency to three decimal places.
Tangent:
If a tangent is drawn from an external point to a function then the slope of the tangent can be determined either by evaluating the derivative of the function at the point of contact or using a two-point slope method for the line. Both the slopes gathered, either way, must stand the same for a tangent to be unique at the point.

Answers

The coordinates of the point of tangency to three decimal places are (0.000, 0.000).

Given function f(x) = cos x.

We are given a graph of function f and a tangent line through the origin.

We are to find the coordinates of the point of tangency to three decimal places.

Let the tangent line be y = mx (where m is the slope)

Since the tangent line passes through the origin, its equation is y = mx.

The slope of the tangent line is equal to the derivative of the function f at the point of tangency.

So, we have f(x) = cos x⇒ f'(x) = -sin x⇒ f'(0) = -sin 0 = 0

So, the slope of the tangent line is 0. That is, m = 0.

Therefore, the equation of the tangent line is y = 0x or simply y = 0.To find the coordinates of the point of tangency, we need to find the point at which the tangent line intersects the graph of the function f.

In other words, we need to solve the following equations simultaneously:

y = 0x (equation of tangent line)y = cos x (equation of f)

Solving the above equations simultaneously, we have

0x = cos x⇒ x = 0

And y = 0x = 0

So, the point of tangency is (0, 0).Therefore, the coordinates of the point of tangency to three decimal places are (0.000, 0.000).

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What would be the PRE if the empty model was true of the DGP?

Answers

If the empty model was true of the DGP (data generating process), then the PRE (proportional reduction in error) would be zero.

This is because the empty model assumes that there is no relationship between the independent variables and the dependent variable, and therefore any prediction made by the model would be no better than chance.

Without any useful information from the independent variables, there would be no reduction in error compared to a baseline model that only predicts the mean of the dependent variable.

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#1. John borrowed $7000 at 4.5% compounded monthly for 6
years.
Calculate the monthly payments.
How much of the first payment goes to pay interest?
What is the unpaid balance after the first payment?

Answers

John borrowed $7000 at an interest rate of 4.5% compounded monthly for a period of 6 years. We can calculate the monthly payments, determine how much of the first payment goes towards paying interest, and find the unpaid balance after the first payment.

To calculate the monthly payments, we can use the formula for calculating the monthly payment on a loan. In this case, the loan amount is $7000, the interest rate is 4.5% (or 0.045 as a decimal), and the loan duration is 6 years. Plugging these values into the formula, we can calculate the monthly payment.

To determine how much of the first payment goes towards paying interest, we can calculate the interest on the loan for the first month using the monthly interest rate and subtract it from the monthly payment.

After making the first payment, the unpaid balance can be found by subtracting the principal amount that was paid off from the initial loan amount.

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Problem 2 (10) The peak temperature T, as measured in degrees centigrade, on a June day in Lahore is the Gaussian(40, 5) random variable. Calculate the probabilities below: (a) P[T> 46] (b) P[T<30] (c) P[32

Answers

a. The probability that the peak temperature in Lahore on a June day is greater than 46 degrees centigrade is 0.0668.

b. The probability that the peak temperature is less than 30 degrees centigrade is 0.0668.

c. The probability that the peak temperature is between 32 and 41 degrees centigrade is 0.6826.

A Gaussian distribution is a probability distribution that is symmetric about its mean, showing that data near the mean is more frequent in occurrence than data far from the mean. The standard deviation of a Gaussian distribution is a measure of how spread out the data is. In this case, the mean temperature is 40 degrees centigrade and the standard deviation is 5 degrees centigrade. This means that the temperature is expected to be between 35 and 45 degrees centigrade 68% of the time. The probability that the temperature is greater than 46 degrees centigrade is 0.0668, or about 6.7%.

The probability that the temperature is less than 30 degrees centigrade is also 0.0668, or about 6.7%. The probability that the temperature is between 32 and 41 degrees centigrade is 0.6826, or about 68.3%.

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Given that = = pi(t) = 2t² + 2t - 1 and pz(t) = –ť – 2t +1, which of the following polynomials in P2 does not belong to span{P1, P2}? = Select one: O p(t) = 4+² + 2t - 1 o p(t) = ť? – 2t +1 None of these = op(t) = 8t? + 10t – 5 Op O p(t) = –7t– 10t +5 = —

Answers

We can conclude that p(t) = –7t² – 10t + 5 does not belong to span{P1, P2}.

We know that the set {P1, P2} is linearly independent.

Hence, it forms a basis for P2. Let's form the basis for P2:

Basis of P2 = {2t² + 2t - 1, –t – 2t +1} = {2t² + 2t - 1, –3t +1}

Now, we will find out the coefficients of each of the options in terms of the given basis

Let's start with p(t) = 4t² + 2t - 1:

4t² + 2t - 1 = a(2t² + 2t - 1) + b(-3t +1)

4t² + 2t - 1 = 2at² + 2at - a - 3bt + b

a = 2

b = 0

p(t) = 2t² + 2t - 1

Therefore, p(t) ∈ span{P1, P2}

Next, let's check for p(t) = ť² – 2t + 1:

ť² – 2t + 1 = a(2t² + 2t - 1) + b(-3t +1)

ť² – 2t + 1 = 2at² + 2at - a - 3bt + b

a = 1

b = -2/3 ť² – 2t + 1 = 1(2t² + 2t - 1) - (2/3)(-3t +1) ť² – 2t + 1 = 2t² + 2t - 1 + 2t - 2/3

Therefore, p(t) ∈ span{P1, P2}

Now, let's check for p(t) = 8t² + 10t – 5:

8t² + 10t – 5 = a(2t² + 2t - 1) + b(-3t +1)

8t² + 10t – 5 = 2at² + 2at - a - 3bt + b

2a = 4

b = 4/3

a = 2

b = 4/3

8t² + 10t – 5 = 2(2t² + 2t - 1) + (4/3)(-3t +1)

8t² + 10t – 5 = 4t² + 4t - 4 – 4t + 4/3

8t² + 10t – 5 = 4t² + (4/3)t - (8/3)

Therefore, p(t) ∉ span{P1, P2}

Finally, let's check for p(t) = –7t² – 10t + 5:

–7t² – 10t + 5 = a(2t² + 2t - 1) + b(-3t +1)

–7t² – 10t + 5 = 2at² + 2at - a - 3bt + b

2a = 4 b = 9/3

a = 2

b = 3

–7t² – 10t + 5 = 2(2t² + 2t - 1) + 3(-3t +1)

–7t² – 10t + 5 = 4t² + 4t - 4 - 9t + 3

–7t² – 10t + 5 = 4t² - 5t - 1

Therefore, p(t) ∉ span{P1, P2}

Therefore, the correct option is O p(t) = –7t– 10t +5.

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Use the the data in the table below to complete parts (a) through (d) x 39 35 40 45 44 48 62 56 52 y 24 22 26 31 28 30 30 25 28(a) Find the equation of the regression line. If the demand faced by a firm is inelastic, selling one more unit of output will a. keep revenues constant. b. increase revenues. C. decrease revenues. d. increase profits Q1. Determine whether the following series converges absolutely, converges conditionally, or diverges. (-1)" * n+1 n+1 n=1 If the cylinder makes f = 0.490 rotations/s, what is the magnitude of the normal force Fy between a rider and the wall, expressed in terms of the rider's weight W? (A) FN = 3.14 W (B) FN = 2.80 W (C) FN = 141 W (D) FN = 0.32 W (E) FN = 0.075 W how old do you have to be to work at red lobster The value of a printing machine depreciated each year by 8% of its value at the beginning of that year. If the value of a new machine is GH 54,000.00, find its value at the end of the third year. 2.A car which was bought for GH 82,000 when new was valued at GH 69,700 at the end of the first year. It then depreciated each year by 10% of its value at the beginning of that year. Calculate (a) the rate of depreciation at the end of the first year. (b) the value of the car at the end of the fourth year. Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) an=(1+3/n)n lim nrightarrow infinity an= If a, b B, prove that |a.c - b.d| || b- c || + || a - d|| for all c d R". My doubt is about a question in Bartle's book Introduction toReal Analysis, as I posted below. Chapter 4.1 Problem 9 a).I didn't understand how to know the elements of the set MIN ofDelta.TksChapter 4.1, Problem 9E Show all steps: ON Step 2 of 13 A Let the function be, f(x) = - for x#1 1 The objective is to show that lim- x-21-x -1, using the - definition. Let > 0. Take another smalles What will happen to the equilibrium system when adding HCl to aqueous solution of Na2SO4? In a study of the effectiveness of a fabric device that acts as a support stocking for a weak or damaged heart, 110 people who consented to treatment were assigned at random to either a standard treatment consisting of drugs or the experimental treatment that consisted of drugs plus surgery to install the stocking. After two years, 30% of the 60 patients receiving the stocking had improved and 18% of the patients receiving the standard treatment had improved. (Use a statistical computer package to calculate the P-value. Use pexperimental pstandard.)z = _____P = _____Do these data provide convincing evidence that the proportion of patients who improve is higher for the experimental treatment than for the standard treatment? Test the relevant hypotheses using a significance level of 0.05. imagine that a start-up firm plans to open private dining clubs on college campuses. The test market will be your campus, and if the concept proves successful, expansion will follow nationwide. Nationwide expansion will occur in year 4. If the firm expands, it projects opening 20 dining clubs in year 4 around the nation.The start-up cost of the test dining club is $13000 (this covers leaseholder improvements and other expenses for a vacant restaurant near campus). Assume projected revenues are only sufficient to exactly cover variable and fixed costs (excluding depreciation) and thus the only cashflows over the first 4 years are tax shields from depreciation.Also assume that the up-front costs can be depreciated in 4 years in a straight-line manner. The volatility of the underlying asset is 30% per annum. The interest rate available is 5% and the tax rate is 34%. What is the value of the option to expand (keep two decimal places)? Caperdic LLP (Caperdic) is 100% owned by Colin Caperdic, a resident of Canada. The company has a December 31 year end. You have been provided with the following information for Caperdic: For the year ended December 31, 2021, Caperdic reported accounting net income of $747,500. Current and future income taxes reported in the income statement were $103,600. Selling general and administration expenses includes meals and entertainment of $16,200 and golf club membership fees of $9,800 for Colin. He uses the club exclusively to entertain clients of Caperdic. For accounting purposes, Caperdic records its short-term investments at fair market value. During fiscal 2020, Caperdic paid $28,700 to acquire shares of Rennock Co. (Rennock). The fair value of Caperdic's investment in Rennock was $26,500 and $31,600 on December 31, 2020, and 2021, respectively. Caperdic received a dividend of $1,400 on this investment during 2021. Caperdic owns 25% of the shares of Gurnell Co. (Gurnell). It accounts for this investment using the equity method. Caperdic reported equity income on this investment of $32,800 during 2021. Caperdic received $20,900 of dividends on this investment during 2021. Gurnell had designated 20% of these dividends as eligible dividends and the remaining 80% as non-eligible dividends. Gurnell received a refund from NERDTOH at a rate of 10% of the non-eligible dividends paid, and from ERDTOH at a rate of 25% of the eligible dividends paid. During 2021 Caperdic earned $24,600 in rental income (net of CCA) on a warehouse rented out to a neighbouring business. Late in 2021, Caperdic shut down one of its factories and sold the land, building, and equipment, the details as follows: Selling Price Original Cost NBV UCC $ 295,000 Land Building $ 374,000 432,000 346,000 265,000 302,000 Caperdic made charitable donation of $16,800 during 2021. Assume that the CCA claim for other depreciable assets is equal to amortization expense reported in accounting net income and that the CCA claim does not include any recapture or terminal losses on disposal of depreciable capital assets. Information about carry forwards from the 2020 notice of assessment are as follows: Net capital loss from 2017 $5,750 Non-capital loss available for carry forward 38,900 4,800 Charitable donations available for carry forward NERDTOH account balance (1) 8,400 (1) Caperdic did not declare or pay any dividends during 2020. During 2021, Caperdic declared and paid dividends of $95,000. Caperdic's taxable capital employed in Canada in 2020 was less than $10,000,000 and its adjusted aggregate investment income in the that year was less than $30,000. Caperdic is not associated with any other corporations. Required: Part A a) Determine net income for tax purposes for Caperdic for 2021. b) Determine taxable income for Caperdic for 2021. c) Determine property income and taxable capital gains included in net income for 2021. d) Determine aggregate investment income e) Determine net Canadian active business income for Caperdic for 2021. Part B a) Determine federal tax payable before the dividend refund for Caperdic for 2021. b) Assume none of the dividends declared and paid in the year will be designated as capital dividends. Determine the optimal dividend mix assuming Colin, the shareholder manager, wishes to minimize personal tax paid on the dividends and determine the dividend refund and federal tax payable after the dividend refund. a. What is an x-intercept? b. Given the functionf(x) = -3x2 - 5x + 1, how would you find the x-intercept? 8. a. Does every quadratic function have a maximum or minimum? b. What circumstances determine that a quadratic function has a maximum? 2. Consider the following variation to the Rock (R), Paper (P),Scissors (S) game: Suppose that with probability p player 1 faces a Normal opponent and with probability 1-p, he faces a Simple opponent that will always play P. Player 2 knows whether he is Normal or Simple, but player 1 does not. The payoffs are pictured in the payoff matrices below:Normal1\2RPSwith probability pSimple1\2RPSRPS0,0-1,11,-11,-10,0-1,11,-1-1,1 0,0P-1,10,01,-1 with probability 1-p.Suppose p = 1/3, select all pure strategy Bayesian equilibria (there may be more than one):(Form: 1's strategy; 2's type - 2's strategy)a) (S; Normal - P, Simple - P)b) (R; Normal - P, Simple - P)c) (S; Normal - R, Simple - P)d) (P; Normal - P, Simple - P) The area below a demand curve and above the price measures a. producer surplus. b. consumer surplus. c. excess supply d. willingness to pay. Ob Od Fall in the words to complete the steps in the process of recrystallization nount of hot solvent 1. Desolve a substance in a Select) while 2. Allow the solvent to cool, precipitating the Select remain in solution 3. Select the mixture to collect the pure substance. 3.25 pts Question 2 Fal in the words to complete the steps in the process of recrystallization amount of hot solvent 1. Disolve a substance in Select while substance 2. Allow the solvent to code Select remain in solution. 1 Select the mixture to collect the pure substance. 3.25 pts D Question 3 Then, When using the Tare function on a balance, start by Select Select to cancel out that mass. Finally, Select 27 AN ( on examity.com is sharing your screen. Hide Stop sharing MacBook Air 3.25 pts Question 2 Fin the words to complete the steps in the process of recrystallization 1. Disse a substance in a Select amount of that solvent. while 2. Allow the solvent to cool, precipitating the Select Select remain in solution Select the mixture to collect the pure substance. 3.25 pts U Question 3 Then, When using the Tare function on a balance, start by Select Select to cancel out that mass. Finally. Select) 27 Hide llon examity.com is sharing your screen Stop sharing MacBook Air 3.25 pts Question 2 in the words to complete the steps in the process of recrystallization 1. Die substance in a Select) amount of hot solvent. 2. Allow the solvent to cool, precipitating the select while impurities Select remain in substance Select) the mixture to collect the pure substance. 3.25 pts D Question 3 Then, When using the Tare function on a balance, start by Select Select] to cancel out that mass. Finally, Select 27 Hide on.examty.com is sharing your screen Stop sharing MacBook Air The target thickness of aluminum sheets produced by a machine is 5 mm. A sample of 50 sheets is taken and the thickness of each sheet is determined, resulting in a sample mean thickness of 0.46 mm and standard deviation 0.36 mm. Does this data suggest that true average thickness is something other than the target value? Use a significance level of 0.05. Which of the following is not information that requires DLP protection? Intellectual property PII Public-facing web pages Customer data a volume of 500.0 ml of 0.100 m naoh is added to 595 ml of 0.200 m weak acid (a=8.23105). what is the ph of the resulting buffer? ha(aq) oh(aq)h2o(l) a(aq)