Compute the probability of event E if the odds in favor of E are 28 to 29.

Using the probability concept, considering complementary probabilities, there is a 0.12 = 12% probability that the integer is of 20 or more.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

If two events are complementary, the sum of their probabilities is of 1. In this problem, we have that an integer being less than 20 is complementary to an integer being 20 or more.

We have that:

These events are complementary, hence:

0.88 + x = 1

x = 1 - 0.88

x = 0.12

There is a 0.12 = 12% probability that the integer is of 20 or more.

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The rational roots of f(x) = 3x^3 + 2x^2 + 3x + 6 are ±(1, 2, 3, 6, 1/3, 2/3)

The function is given as:

f(x) = 3x^3 + 2x^2 + 3x + 6

For a function P(x) such that

P(x) = ax^n +...... + b

The rational roots of the function p(x) are

Rational roots = ± Possible factors of b/Possible factors of a

In the function f(x), we have:

a = 3

b = 6

The factors of 3 and 6 are

a = 1 and 3

b = 1, 2, 3 and 6

So, we have:

Rational roots = ±(1, 2, 3, 6)/(1, 3)

Split the expression

Rational roots = ±(1, 2, 3, 6)/1 and ±(1, 2, 3, 6)/3

Evaluate the quotient

Rational roots = ±(1, 2, 3, 6, 1/3, 2/3, 1, 2)

Remove the repetition

Rational roots = ±(1, 2, 3, 6, 1/3, 2/3)

Hence, the rational roots of f(x) = 3x^3 + 2x^2 + 3x + 6 are ±(1, 2, 3, 6, 1/3, 2/3)

The complete parameters are:

The function is given as:

f(x) = 3x^3 + 2x^2 + 3x + 6

The rational roots of f(x) = 3x^3 + 2x^2 + 3x + 6 are ±(1, 2, 3, 6, 1/3, 2/3)

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Answer:

f(x) = g(x) + 9 because it is shifted 9 to the right

Answer: square of 459 is 210681

The conclusion that can be made based on the hypothesis is:

1. It's a valid conclusion.

2. It is a valid conclusion.

3. It is a valid conclusion.

According to the law of detachment, when the conditional and the hypothesis are true, the conclusion will be true.

Therefore, if 6x < 42, the value of x will also be less than 6. This is valid.

When an angle is more than 90°, it's an obtuse angle and since A is 103°, it's valid.

Also, the statement about the violin being a string instrument is logically valid.

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The balance that Cody earned after 20 years is 891.57. Using the compound interest formula, the required value is calculated.

The compound interest is calculated by

[tex]A = P(1 + \frac{r}{n} )^n^t[/tex]

Where,

A - Total amount (Future value)

P - Principal amount (Initial value)

r - The rate of interest

n - Number of times compounded per 't'

t - Total number of years the money is invested

It is given that,

P = 600

r = 2% = 0.02

t = 20 years

n = 1 (since the amount is compounded annually)

Then,

[tex]A=600(1+\frac{0.02}{1})^1^*^2^0[/tex]

   = 600 (1 + 0.02)²⁰

   = 600 (1.02)²⁰

   = 891.57

Therefore, the balance after 20 years is 891.57.

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Answer:

84,08964 [gr.].

Step-by-step explanation:

for more details see in the attachment.

Answer:

answer 0.8

Step-by-step explanation:

Solution

0.396 has 3 significant digits

0.5      has 1 significant digit.

Therefore the answer should be 1 significant digit.

0.396 / 0.5 = 0.792

Rounded to 1 sig dig, the answer = 0.8

Answer:

we write in form of (a x 10^n)

5.702 x 10⁷

Answer:

5.702 x 10^7

Step-by-step explanation:

In scientific notation, a number in the ones place is raised to a power of 10: the power will be positive if the original number is huge, and negative if the original number is small.

The number 57,020,000 is a huge number. We simply move the decimal 7 places to the left to get 5.072, and since we moved the decimal 7 places, 10 is raised to the power of 7.

Brainliest, please :) Hope this helps!

Using the normal distribution, there is a 0.1894 = 18.94% probability that the sample average will exceed $75.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 70, \sigma = 40, n = 50, s = \frac{40}{\sqrt{50}} = 5.66[/tex]

The probability that the sample average will exceed $75 is one subtracted by the p-value of Z when X = 75, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (75 - 70)/5.66

Z = 0.88

Z = 0.88 has a p-value of 0.8106.

1 - 0.8106 = 0.1894.

0.1894 = 18.94% probability that the sample average will exceed $75.

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The equation of the ellipse in standard form is (x + 3)² / 100 + (y - 2)² / 64 = 1. (Correct choice: B)

By analytical geometry we know that foci are along the major axis of ellipses and beside the statement we find that such axis is parallel to the x-axis of Cartesian plane. Then, the standard form of the equation of the ellipse is of the following form:

(x - h)² / a² + (y - k)² / b² = 1, where a > b     (1)

Where:

Now, we proceed to find the vertex and the lengths of the semiaxes:

a = 10 units.

b = 8 units.

Vertex

V(x, y) = 0.5 · F₁(x, y) + 0.5 · F₂(x, y)

V(x, y) = 0.5 · (3, 2) + 0.5 · (- 9, 2)

V(x, y) = (1.5, 1) + (- 4.5, 1)

V(x, y) = (- 3, 2)

The equation of the ellipse in standard form is (x + 3)² / 100 + (y - 2)² / 64 = 1. (Correct choice: B)

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Using the addition rule of the Sine function and the Cosine function, we obtain [tex]\cos\dfrac{x+y}{2}=\dfrac{b}{\sqrt{a^2+b^2}}[/tex].

Given that

[tex]\sin x + \sin y = a\\\cos x + \cos y = b[/tex]

Then using the above formulas, we get:

[tex]2\sin\frac{x+y}{2}\cos\frac{x-y}{2}=a[/tex]       (1)

[tex]2\cos\frac{x+y}{2}\cos\frac{x-y}{2}=b[/tex]       (2)

Dividing the equation (1) by (2), we get:

[tex]\dfrac{\sin\dfrac{x+y}{2}}{\cos\frac{x-y}{2}}=\dfrac{a}{b}\\\Longrightarrow \tan\dfrac{x+y}{2}=\dfrac{a}{b}[/tex]             (3)

Now, we know that  [tex]\cos\theta=\dfrac{1}{\sqrt{1+\tan^2\theta}}[/tex].

Thus, using the above formula, we get from (3):

[tex]\cos\dfrac{x+y}{2}=\dfrac{1}{\sqrt{1+\tan^2\dfrac{x+y}{2}}}\\\Longrightarrow \cos\dfrac{x+y}{2}=\dfrac{1}{\sqrt{1+\dfrac{a^2}{b^2}}}\\\Longrightarrow \cos\dfrac{x+y}{2}=\dfrac{b}{\sqrt{a^2+b^2}}[/tex]

Therefore, using the addition rule of the Sine function and the Cosine function, we obtain [tex]\cos\dfrac{x+y}{2}=\dfrac{b}{\sqrt{a^2+b^2}}[/tex].

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The value of the median, lower and upper quartile

The minimum value = 10

The maximum value = 38

The median is the value that is found in the center of the data when it is ordered from lowest to highest. In the event that there is no value that precisely corresponds to the center, the value will be determined by taking the average of the values that are located on each side of the middle.

10  11  12  15  19  24  27  29  33  38

Median = 21.5

The intermediate value of the data that is located to the left of the median is known as the lower quartile.

10  11  12  15  19

lower quartile = 12

The intermediate value of the data that is located to the right of the median is known as the upper quartile.

24  27  29  33  38

upper quartile = 29

In conclusion, the 5 number summary is 10, 12, 21.5, 29, 38 → A

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Answer: minimum 10 first quartile 11.5 median 12.5 third quartile 16 maximum 20

Step-by-step explanation:

Answer:

11/12

Step-by-step explanation:

no of sample space=12

number of 7 to occur is 1/12

number of not 7:

since the total probability is 1

so 1-1/12=11/12

Answer: She started with 28 pieces of candy.

Step-by-step explanation: In the beginning of the question it says that heather took 8 pieces. Then she divided the rest evenly amongst her 5 kids. Each received 4, so that make the equation 8+(5x4) which gives us 8+(20). Or 8+20 which is 28.

Answer:

She started with 28 candies.

Explanation:

Let the total amount of candies be c

Build equation:

→ remaining: c - 8

→ each gets: (c - 8)/5

Here given each gets 4 candies

So,

(c - 8)/5 = 4

c - 8 = 5(4)

c - 8 = 20

c = 20 + 8

c = 28

Answer: $3.2a

Step-by-step explanation: We need to decrease $8a by 60 percent because $8a is the price after a 60% increase. 8 x 6/10 is 48/10 which as a mixed number is 4 8/10 or 4.8. Now, we subtract 4.8 from 8 which yields our answer of 3.2.

Answer:

Equation of a line has a form as below:

y=ax+b

Given:

b ( the y intercept)= -5

a ( the slope)= -3

so, y= -3x -5 is the equation of the line.

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By Euler's method the numerical approximate solution of the definite integral is 4.189 648.

In this problem we must make use of Euler's method to estimate the upper bound of a definite integral. Euler's method is a multi-step method, related to Runge-Kutta methods, used to estimate integral values numerically. By integral theorems of calculus we know that definite integrals are defined as follows:

∫ f(x) dx = F(b) - F(a)     (1)

The steps of Euler's method are summarized below:

The table for x, f(xₙ, yₙ) and y is shown in the image attached below. By direct subtraction we find that the numerical approximation of the definite integral is:

y(4) ≈ 4.189 648 - 0

y(4) ≈ 4.189 648

By Euler's method the numerical approximate solution of the definite integral is 4.189 648.

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The given operation is not a vector space because it fails axiom 8 ("distributivity of scalar multiplication with respect to field addition").

A vector space can be defined as a space (set) which comprises vectors, whose elements can be added under the associative and commutative operation, and can be multiplied by scalars under the associative and distributive operation.

This ultimately implies that, a vector space must be comprised of at least one element, which is generally regarded as its zero vector and the smallest possible vector space.

For every element {u, v and w} in vector (V), and element {a and b} in vector (F), this 8th axiom must be satisfied in order to have a vector space:

(k + m)u = ku + mu

Note: The above axiom (k + m)u = ku + mu is generally referred to as the "distributivity of scalar multiplication with respect to field addition."

Given the following vector:

k(x, y, z) = {k²x, k²y, k²z}

If x₁ · x₂ ≥ 0, then, (kx₁) · (kx₁) = k²x₁y₁ ≥ 0 [Closed in scalar multiplication].

If x₁ · x₂ ≥ 0, x₂ · y₂ ≥ 0, then (x₁ + x₂) · (y₁ + y₂):

x₁y₁ + x₂y₂ + x₁y₂ + x₂y₁ < 0

x₁y₁ + x₂y₂ < -(x₁y₂ + x₂y₁) [Not closed in vector addition].

In conclusion, we can infer and logically deduce that the given operation is not a vector space because it fails axiom 8 ("distributivity of scalar multiplication with respect to field addition").

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Complete Question:

Determine whether each set equipped with the given operations is a vector space. For those that are not vector spaces identify the vector space axioms that fail.

The set of all triples of real numbers with the standard vector addition but with scalar multiplication defined by k(x, y, z) = {k²x, k²y, k²z}.

Esto significa que debemos tener 58 páginas de plástico para contener las 517 tarjetas.´

Sabemos que cada página puede almacenar hasta 9 cartas.

Entonces queremos ver cuantos grupos de 9 cartas hay en el conjunto de 517, para ver esto tomamos el cociente entre 517 y 9.

N = 517/9  = 57.44

Y no podemos tener un numero racional, así que debemos redondear al proximo número entero, que es 58.

Esto significa que debemos tener 58 páginas de plástico para contener las 517 tarjetas.

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Answer:

Step-by-step explanation:

Answer:

1/7

Step-by-step explanation:

Lets start with the probability of flipping tails, 1/2.

Then the probability of the day starting with the letter s, 2/7.

Calculate the final probability by multiplying the two together.

[tex]\frac{1}{2}*\frac{2}{7}=\frac{2}{14}[/tex]

You can simplify 2/14 down to 1/7

Answer: C

Step-by-step explanation: The y-intercept is 1/5 since the point on the y-axis is (0, 1/5). The slope is 2/3 because the other coordinate is up 2 and right 3 from (0, 1/5) *remember rise over run*. The shading means that the answer (y) must be less than or equal to 2/3x + 1/5, hence it being underneath the line.

Answer:

$15666.83 (2dp)

Step-by-step explanation:

Mean = Total of all values / Number of Values

= [tex]\frac{17484+14978+13521+14500+18540+14978}{6}[/tex]

=[tex]\frac{94001}{6}[/tex]

= $15666.83 (2dp)

Answer: y = 5.4

Step-by-step explanation: This is a proportional statement. So we can set up a system of proportions.

So we know when x is 5, y is 3. Thus, we can set up a proportion [tex]\frac{x}{y}[/tex] such that substituting will give [tex]\frac{5}{3}[/tex].

Now, we know when x is 9, y is some unknown number. So we can set up the second proportion as [tex]\frac{9}{y}[/tex].

Since 5/3 and 9/y are directly proportional, these 2 expressions are therefore equal. So we have [tex]\frac{5}3}[/tex] [tex]= \frac{9}{y}[/tex].

Cross multiplying, we get [tex]5y = 27[/tex].

Dividing by 5, we get [tex]y = 5.4[/tex]

Hope this helped!

Answer:

5.3333333 or 5 [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

30 divided by 2 equals 15.

80 divided by 15 equals 5.3333333 or 5 [tex]\frac{1}{3}[/tex].

it should be 70 percent

Step-by-step explanation:

100 subtract by 30 is 70 percent

Answer:

d = [tex]\sqrt{29}[/tex]

Step-by-step explanation:

The distance between two points is given by

d = [tex]\sqrt{ ( x2 - x1) ^2 - ( y2-y1)^2}[/tex]  where ( x1,y1) and ( x2,y2) are the two points

d = [tex]\sqrt{( 0 - -5) ^2 + (4 - 2) ^2}[/tex]

d = [tex]\sqrt{5^2 + 2^2}[/tex]

d = [tex]\sqrt{25 +4}[/tex]

d = [tex]\sqrt{29}[/tex]

Answer: [tex]\Large\boxed{Distance=\sqrt{29} }[/tex]

Step-by-step explanation:

Given information

[tex](x_1,~y_1)=(-5,~2)[/tex]

[tex](x_2,~y_2)=(0,~4)[/tex]

Given the distance formula

[tex]Distance =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Substitute values into the formula

[tex]Distance =\sqrt{((0)-(-5))^2+((4)-(2))^2}[/tex]

Simplify values in the parenthesis

[tex]Distance =\sqrt{(0+5)^2+(4-2)^2}[/tex]

[tex]Distance =\sqrt{(5)^2+(2)^2}[/tex]

Simplify the exponents

[tex]Distance =\sqrt{25+4}[/tex]

Simplify values in the radical sign

[tex]\Large\boxed{Distance =\sqrt{29}\approx5.4}[/tex]

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The dividends per share on each class of stock for each of the four years for Seventy-Two Inc. are as follows:

                                            Year 1       Year 2        Year 3           Year 4

Distributed Dividends    $32,000    $40,000    $36,000        $36,000

Outstanding shares          60,000      60,000      60,000           60,000

Dividend per share           $0.53       $0.67          $0.60             $0.60

                                          Year 1       Year 2        Year 3           Year 4

Distributed Dividends    $0              $32,000     $44,000       $64,000

Outstanding shares        400,000    400,000     400,000       400,000

Dividend per share        $0              $0.08            $0.11              $0.16

                              3% Cumulative Preferred       Common Stock

Outstanding shares          60,000                        400,000

Par Value                            $20                              $25

Total value                       $1,200,000              $10,000,000

Annual dividend            $36,000 ($1,200,000 x 3%)

                                            Year 1       Year 2        Year 3           Year 4

Distributed Dividends    $32,000    $72,000    $80,000       $100,000

Cumulative Preferred      $32,000    $40,000    $36,000        $36,000

Common Stock                $0              $32,000    $44,000        $64,000

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