In a class of students, the following data table summarizes how many students play an instrument or a sport. What is the probability that a student chosen randomly from the class plays neither a sport nor an instrument? Plays an instrument Does not play an instrument Plays a sport 3 2 Does not play a sport 7 15

(a)   g(x) = 2f(x) + 3.

b.)

the inverse functions are:

f-1(x) = x/2

g¹(x) = (x - 3)/2

c.)

g¹(x) = 2*f-1(x+3).

d. ) we obtain the graph of g¹(x) = 2f-1(x+3). and  g(x) = 2f(x) + 3.

(b) The inverse function of f(x) = 2*x is f-1(x) = x/2.

We found the  inverse function of g(x) = 2f(x) + 3 = 2(x) + 3, by isolating f(x):

g(x) = 2*f(x) + 3

(g(x) - 3)/2 = f(x)

f-1(x) = (x - 3)/2

(d)   we work on this graph f-1(x) and g¹(x),  by graphing f(x) = 2x and y = x/2 on the same set of axes.

shift the graph of f(x) to the right by 3 units to obtain the graph of f-1(x+3), and stretch it vertically by a factor of 2 to obtain the graph of g¹(x) = 2f-1(x+3).

The resulting graph should have a horizontal asymptote at y = 3 and pass through the points (0, -1.5) and (6, 4.5).

To produce g(x) from f(x), we will use  a vertical stretch by a factor of 2, which results in 2f(x). Then, we shift the graph 3 units upward, which results in g(x) = 2f(x) + 3.

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The measure of the minor arc m∡rv = 111°

Recall that according to the principle of angle of intersecting secants, (a-b)/2 = c

Where a = ∡RV
b = ∡SU = 37°:

and c = ∠T (the angle between intersecting secants.

Thus, if (a-b)/2 = c, and b = c = 37 degrees, then we can substitute these values into the equation to get:

(a - 37) / 2 = 37

Multiplying both sides by 2 gives:

a - 37 = 74

Adding 37 to both sides gives:

a = 111

Therefore, a is equal to  m∡rv = 111°.

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Both the inequalities are true when we substitute x = -1 and y = 0, so (-1, 0) satisfies the system of inequalities.

An inequality expresses a relationship between two values, indicating whether one is greater than, less than, or greater than or equal to or less than or equal to the other.

To check whether the point (-1, 0) is a solution of the system of inequalities:

-7x + 3y > -1

5x - 9y > -6

We need to substitute x = -1 and y = 0 into both inequalities and check whether the resulting expressions are true or false:

-7(-1) + 3(0) > -1

==> 7 > -1 (true)

5(-1) - 9(0) > -6

==> -5 > -6 (true)

Both the inequalities are true when we substitute x = -1 and y = 0, so (-1, 0) satisfies the system of inequalities. Therefore, the answer is: option A) Yes.

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Jim needs a cardboard sheet with an area of at least 1440 square inches to make the box.

What is a rectangular prism?

A rectangular prism is a three-dimensional shape with six rectangular faces. It is also known as a rectangular parallelepiped or a rectangular cuboid.

To find out how much cardboard Jim needs to make the box, we need to calculate the total surface area of the box.

The rectangular prism has six faces, and we need to cut out each of these faces from the cardboard sheet.

The top and bottom faces are both 12x20 inches, so they have a combined area of 2(12x20) = 480 square inches.

The two side faces are both 12x15 inches, so they have a combined area of 2(12x15) = 360 square inches.

Finally, the front and back faces are both 15x20 inches, so they have a combined area of 2(15x20) = 600 square inches.

Therefore, the total surface area of the box is 480 + 360 + 600 = 1440 square inches.

Therefore, Jim needs a cardboard sheet with an area of at least 1440 square inches to make the box.

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Step-by-step explanation:

To perform polynomial division of x^3 + 10x^2 + x + 10 by (x+1), we get the coefficients 1, 10-i, and -10i. This means that:

x^3 + 10x^2 + x + 10 = (x+1)(x^2 + (10-i)x - 10i)

Now we need to divide x^2 + (10-i)x - 10i by (x-1). We can use polynomial long division:

x + 11 - i

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

x - 1 | x^2 + (10-i)x - 10i

- x^2 + x

-----------

(9-i)x - 10i

(9-i)x + 9-i

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

-i

Therefore, the resulting reduced polynomial is x - i.

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The unit rate for points per game is determined by dividing the total points scored by the number of games played. In this case, 62 points  3 games = 20.67 points per game (rounded to two decimal places).

To determine the unit rate for points per game, we need to divide the total number of points scored by the number of games played. In this case, Pedro scored 62 points over the last 3 basketball games.

The unit rate for points per game is found by dividing the total points scored by the number of games played. In this case, Pedro scored 62 points over 3 basketball games, so the unit rate for points per game is:

62 points ÷ 3 games = 20.67 points per game (rounded to two decimal places)

So, none of the given options is correct. The correct answer is 62 over 3 points per game, which is equivalent to 20.67 points per game when rounded to two decimal places.

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Answer:

62.01 i took the test

Step-by-step explanation:

The value of the set for the given value of set complement is n(X ∩ Y) = 92.

In set theory, a set's complement The set of all U elements that are not in A is known as A. In other words, all the components that are in U but not in A are in A'. A' is the set of odd numbers, for instance, if U is the set of integers and A is the set of even integers. In many mathematical and computational applications, the complement of a set is a crucial idea in set theory.

Given that, n(U) = 100, n(X) = 51, n(Y) = 63 and n(XUY)' = 8.

Using the formula of union of two sets we have:

n(XUY)' = n(U) - n(X ∩ Y)

Substituting the values we have:

8 = 100 - n(X ∩ Y)

n(X ∩ Y) = 100 - 8

n(X ∩ Y) = 92

Hence, the value of the set for the given value of set complement is n(X ∩ Y) = 92.

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Answer:

[tex]\frac{9}{7}[/tex]

Step-by-step explanation:

[tex]\frac{6}{7}[/tex] ÷ [tex]\frac{2}{3}[/tex] = [tex]\frac{6}{7}[/tex] · [tex]\frac{3}{2}[/tex] = [tex]\frac{18}{14}[/tex] = [tex]\frac{9}{7}[/tex]

So, the answer is  [tex]\frac{9}{7}[/tex]

Answer:

[tex]m = \frac{10 - 3}{6 - 2} = \frac{7}{4} [/tex]

Answer:

7/4.

Step-by-step explanation:

Slope = rise / run

= (10-3)/(6-2)

= 7/4.

Answer:

600/7% OR 85.71%

Step-by-step explanation:

increase in speed =v-u

I=115-85

I=30km/h

percentage increase =(I/u) ×100

30/85 ×100

6/17×100

600/7%

Answer:

80π square feet

Step-by-step explanation:

The 95% confidence interval for the average interval of violations per lawbreaker is (11.12, 18.88) and other solutions are below

a) To estimate the average interval of violations per lawbreaker, we need to calculate the sample mean and standard deviation of the 15 offenders.

Mean = (15+20+10+25+5+22+8+12+18+7+23+6+24+19+11)/15 = 15

Sample standard deviation, s = 7.01

To calculate the 95% confidence interval, we can use the formula:

CI = x ± t(α/2, n-1)*(s/√(n))

where, α= 1 - confidence level = 0.05 (for 95% confidence level)

t(a/2, n-1) = t(0.025, 14) = 2.145 (from t-table)

CI = 15 ± 2.145*(7.01/√(15))

CI = 15 ± 3.88

CI = (11.12, 18.88)

Therefore, the 95% confidence interval for the average interval of violations per lawbreaker is (11.12, 18.88)

b) To make the interval estimate of the proportion of offenders who violate the law exceed 20 times, we need to calculate the sample proportion and standard error.

Sample proportion,

p = number of offenders who violate the law more than 20 times / sample size

p = 4/15

Sample standard error,

SE = √(p*(1-p)/n)

SE = √(4/15 * 11/15 / 15) = 0.114

To calculate the 90% confidence interval, we can use the formula:

CI = p ± z(a/2)*SE

where, a= 1 - confidence level = 0.1 (for 90% confidence level)

z(a/2) = z(0.05) = 1.645 (from z-table)

CI = 4/15 ± 1.645*0.114

CI = (0.079, 0.455)

Therefore, the 90% confidence interval for the proportion of offenders who violate the law more than 20 times is (0.079, 0.455)

Using a graphing tool, we have

y = 0.89x - 0.69

r^2 = 0.9964

We can use the t-test.

The formula for the t-test is:

t = r*√(n-2) / √(1-r^2)

Also, we have

r^2 = 1 - (SSres/SStot)

Since r^2 = 0.9964, we can estimate

SSres/SStot = 0.0036

SStot = SSres/0.0036

Using these values, we can calculate the t-statistic:

t = r*√(n-2) / √(1-r^2)

t = 0.9964*√(6-2) / √(1-0.9964^2)

t = 23.51

Using a two-tailed test and a significance level of 0.05, the critical t-value with 4 degrees of freedom is ±2.101.

Since the calculated t-value (23.51) is greater than the critical t-value (2.101), we reject the null hypothesis and conclude that there is a significant correlation between the percentage increase in the number of lawyers and the percentage increase in revenue from the attorney's office.

Therefore, it is possible to predict Y using the equation y = 0.89x - 0.69. The equation is in the form of y = a + bx, where a is the y-intercept (-0.69) and b is the slope (0.89).

The equation tells us that for every 1% increase in the number of lawyers, there will be a predicted 0.89% increase in revenue from the attorney's office.

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The area of the region below y = x^2 + x + 4 and above y = 2 for 2 <= x <= 6 is 93.33 square units.

To find the area of the region below y = x^2 + x + 4 and above y = 2 for 2 <= x <= 6, we need to integrate the difference between the two functions with respect to x over the given interval.

The lower boundary of the region is y = 2, and the upper boundary is y = x^2 + x + 4. So, we can write the integral as:

∫[2,6] [(x^2 + x + 4) - 2] dx

Simplifying the integrand, we get:

∫[2,6] (x^2 + x + 2) dx

Integrating with respect to x, we get:

[(1/3)x^3 + (1/2)x^2 + 2x] evaluated from 2 to 6

Plugging in the upper and lower limits, we get:

[(1/3)(6^3) + (1/2)(6^2) + 2(6)] - [(1/3)(2^3) + (1/2)(2^2) + 2(2)]

Simplifying the expression, we get:

93

Therefore, the area of the region is 93.33 square units.

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Answer:

The interest portion of the first payment is $433.20.

Step-by-step explanation:

To find out how much of your first payment will go to interest, we need to calculate the monthly interest rate and then use it to calculate the interest portion of the monthly payment.

First, we need to calculate the monthly interest rate by dividing the annual interest rate by 12. 

Annual interest rate = 13%

Monthly interest rate = 13%/12 = 0.01083

Next, we can use the monthly payment amount and the monthly interest rate to calculate the interest portion of the payment:

Interest portion of payment = Monthly interest rate x Remaining loan balance

To calculate the remaining loan balance after the first payment, we can use the formula for the present value of an ordinary annuity:

Remaining loan balance = Present value of remaining payments

Present value of remaining payments = Monthly payment x (1 - (1 + monthly interest rate)^-n) / monthly interest rate

where n is the total number of payments over the term of the loan.

n = 12 years x 12 months/year = 144 payments

Present value of remaining payments = $450 x (1 - (1 + 0.01083)^-144) / 0.01083 = $44,373.68

Remaining loan balance after first payment = $44,373.68 - $40,000 = $4,373.68

Finally, we can calculate the interest portion of the first payment:

Interest portion of payment = 0.01083 x $40,000 = $433.20

Therefore, the interest portion of the first payment is $433.20.

The measure of BC is 110°

Semicircle is defined as a half circle formed by cutting the circle into two halves. It is formed when a line passes through the center and touches the two ends of the circle. This line is called the diameter of the circle.

line AB is the diameter of the circle and thus, AB gives a semi circle.

This means that, since angle Ina semi circle is 180°, the sum of AC and BC is 180°

therefore, 2x-30+x = 180°

3x = 180+30

3x = 210

divide both sides by 3

x = 210/3 = 70°

therefore BC = 2x-30

= 2×70-30

= 140-30

= 110

therefore the measure of BC is 110°

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Answer: For each hour spent driving, the distance increases by 59.3

miles.

Step-by-step explanation:

Your welcome!

Answer:

C)  For each hour spent driving, the distance increases by 59.3 miles.

Step-by-step explanation:

In the function f(x) = 59.3x + 58.3, the coefficient of x is 59.3.

This coefficient represents the rate of change or slope of the linear relationship between distance traveled (in miles) and time (in hours).

Specifically, it represents the speed of the car in miles per hour (mph).

This means that for each hour spent driving (each unit increase in time), the car travels an additional 59.3 miles, so its distance increases by 59.3 miles each hour. Hence, the car is traveling at a speed of 59.3 mph.

The vertex of the graph of this equation y = x² - x - 2 is equal to -2.25.

In this exercise, you are required to determine the vertex form of a quadratic function h(x) that is written in standard form. Mathematically, the vertex form of a quadratic equation is given by this formula:

y = a(x - h)² + k

Where:

For the given quadratic function y = x² - x - 2 in question 9, the axis of symmetry can be calculated as follows:

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(-1)/2(1)

Axis of symmetry, Xmax = 1/2

Axis of symmetry, Xmax = 1/2.

Next, we would determine the vertex when x = 1/2 as follows;

y = x² - x - 2

y = (1/2)² - 1/2 - 2

y = 1/4 - 1/2 - 2

y = 0.25 - 0.5 - 2

y = -2.25.

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Answer: 3.2 or 16/5

Step-by-step explanation:

the mixed number would be 3 1/5

Option C is correct. probability of choosing man and non drinker is given s 0.932

Probability is a branch of mathematics that deals with the study of random events or experiments, and the likelihood or chance of certain outcomes occurring. It is concerned with quantifying the uncertainty of events and helps us make predictions or informed decisions in situations where the outcome is not certain.

probability of choosing man and non drinker= 209 / 425 + 322 / 425 - 135 / 425

= 0.4917 +0.7576 - 0.3176

= 0.9317

this is approximately 0.932

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Answer:

3 days

Step-by-step explanation:

set up an equation 40+28x=124

solve for x

x=2,-13

Hope this helps

After answering the presented question, standard deviation t Lower bound = X - [tex](t * (s/\sqrt(n))) = 1271.89 - (1.860 * (34.753/\sqrt(9))) = 1238.94[/tex]

A statistic that expresses the variability or variation of a bunch of values is the standard deviation. A high standard deviation indicates that the values are more distributed, whereas a low standard deviation indicates that the numbers are closer to the set mean. The standard deviation is a measure of how far the data are from the mean (or ). When the standard deviation is small, the data tends to cluster around the mean; when it is great, the data is more spread. The standard deviation represents the average variability of the data collection. It displays the average deviation from the mean of each score.

Next, we need to find the t-value for a 90% confidence interval with 8 degrees of freedom (n-1):

t = t(0.05, 8) = 1.860

Now we can calculate the lower and upper bounds of the confidence interval:

Lower bound = X - [tex](t * (s/\sqrt(n))) = 1271.89 - (1.860 * (34.753/\sqrt(9))) = 1238.94[/tex]

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The value of 0.52 represents the ratio of male babies to female babies born in the affected region in the seven years following the 1977 dioxin spill.

To conduct a hypothesis test to determine whether this ratio is different from the earlier ratio, we can set up the null and alternative hypotheses as follows:

Null hypothesis (H0): The ratio of male babies to female babies in the affected region did not change significantly after the 1977 dioxin spill.

Alternative hypothesis (Ha): The ratio of male babies to female babies in the affected region changed significantly after the 1977 dioxin spill.

We can use a one-sample proportion test to test this hypothesis. The test statistic is calculated as:

z = (p - P₀) / √(P₀ * (1 - P₀) / n)

where p is the sample proportion (0.52), P0 is the hypothesized population proportion (0.51), and n is the sample size (123).

Using a significance level of 0.05, we can compare the calculated test statistic to the critical value from the standard normal distribution. If the calculated test statistic falls outside the critical values, we reject the null hypothesis in favor of the alternative hypothesis.

A type II error in this context would occur if we fail to reject the null hypothesis when it is actually false. In other words, we would conclude that the ratio of male babies to female babies did not change significantly after the dioxin spill, when in fact it did. This means that we would fail to detect a real effect of dioxin exposure on the ratio of male to female births, which could have important implications for public health and environmental policy.

Steps:

1) State the null and alternative hypotheses

2) Choose a significance level (alpha)

3) Calculate the test statistic

4) Determine the critical value from the standard normal distribution based on the chosen alpha level

5) Compare the calculated test statistic to the critical value

6) Make a decision to either reject or fail to reject the null hypothesis

7) Interpret the results and draw conclusions, including the possibility of a type II error.

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Question:

In a study of the effects of a 1977 dioxin spell in Italy on the ratio of male babies to female babies born to humans, researchers wanted to know whether dioxin exposure affected the ratio in the seven years following the spill the researchers found that the of the 123 babies born to parents in the affected region 51 warm out the ratio of males to females in previous period during which exposure to dioxin was pretty presume to be absent.

What is 0.52 for the researchers conducted the hypothesis test to determine whether the later ratio is different from the earlier ratio? What does making a type two error mean in the context of this hypothesis test?

a)The term 1-16t²represents the effect of gravity on the apple, which causes it to fall with increasing speed. The constant term 36 represents the initial height of the apple

b)Interpreting the domain, we can say that h(t) makes sense only for non-negative values of t. In other words, we can use the function h(t)to find the height of the apple at any time t a

what is gravity ?

Gravity is a fundamental force of nature that causes objects with mass to attract each other. It is the force that keeps planets in orbit around stars, and stars in orbit around the center of their galaxies.

In the given question,

a. The function h(t)=-16t²+36 represents the height of an apple above the ground at time t after falling off a tree. The term1 -16t² represents the effect of gravity on the apple, which causes it to fall with increasing speed. The constant term 36 represents the initial height of the apple when it fell off the tree.

b. The domain of h(t) in this situation is the set of all possible values of t that make sense in the context of the problem. Since h(t) represents the height of the apple at time t after it fell off the tree, the domain of h(t)is the set of all non-negative real numbers, or [0,\infty) This is because time cannot be negative, and the apple cannot fall for an infinite amount of time.

Interpreting the domain, we can say that h(t)makes sense only for non-negative values of t. In other words, we can use the function h(t) to find the height of the apple at any time t after it fell off the tree, as long as t is non-negative..

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The total number of copies sold to date is approximately 369,767.

An equation can be described mathematically as a statement that supports the equality of two expressions joined by the equals sign "=". For instance, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. "=" is the sign that connects these two expressions.

Let's assume the total number of copies sold to date as x.

We know that the number of copies sold in the first month is 31,800, which is 8.6% of the total number of copies sold to date.

So we can set up an equation as follows:

31,800 = 0.086x

To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides by 0.086:

x = 31,800 / 0.086

x = 369,767.44

Therefore, the total number of copies sold to date is approximately 369,767.

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Answer:

Step-by-step explanation:

Answer: -78

-5(11)-23=?
-55-23= -78

Answer:

-78

Step-by-step explanation:

n = 11

Replace n with its given value in this expression:

[tex] - 5n - 23[/tex]

[tex] - 5 \times 11 - 23 = - 55 - 23 = - 78[/tex]

Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{x}\\ a=\stackrel{adjacent}{3}\\ o=\stackrel{opposite}{4} \end{cases} \\\\\\ x=\sqrt{ 3^2 + 4^2}\implies x=\sqrt{ 9 + 16 } \implies x=\sqrt{ 25 }\implies x=5[/tex]