10. If the mine winch drum diameter is 6M, calculate how far the counterweight will lift for each single rotation of the drum.​

Answer:

-0.1, -0.02, \(\frac{5}{6}\), \(|\frac{9}{8}|\), 10

Step-by-step explanation:

Tthe surface area of the rectangular prism is 62 square centimeters.

(a) To visualize the net of the rectangular prism, two possible nets are shown.

(b) Using the net from part (a), we can determine the surface area of the prism.

Explanation:

(a) Unfortunately, as a text-based AI, I am unable to see or interact with images. However, the net of a rectangular prism consists of six connected rectangles that can be folded to form the prism. Each rectangle represents one face of the prism. To obtain the net, you can imagine unfolding the prism and flattening it out.

(b) The rectangular prism has three pairs of faces that have the same dimensions: the top and bottom faces, the front and back faces, and the left and right faces. The area of each pair of faces can be found by multiplying the length and width. The surface area of the prism is the sum of the areas of all six faces.

Given that the length is 5 centimeters, the width is 2 centimeters, and the height is 3 centimeters, we can calculate the surface area as follows:

- Area of the top and bottom faces: 5 cm * 2 cm = 10 cm² each

- Area of the front and back faces: 5 cm * 3 cm = 15 cm² each

- Area of the left and right faces: 2 cm * 3 cm = 6 cm² each

Adding up the areas of all six faces, we get:

10 cm² + 10 cm² + 15 cm² + 15 cm² + 6 cm² + 6 cm² = 62 cm²

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a. A

b. C

A is a right triangle

C compared & matched : 2 angles in that triangle are the same number of degrees

Answer:

\((a)\ Area = 3765.32\)

\((b)\ Area = 4773\)

Step-by-step explanation:

Given

\(A_1 = 169in^2\) --- area of each square

\(Shade = 4in\)

See attachment for window

Solving (a): Area of the window

First, we calculate the dimension of each square

Let the length be L;

So:

\(L^2 = A_1\)

\(L^2 = 169\)

\(L = \sqrt{169\)

\(L=13\)

The length of two squares make up the radius of the semicircle.

So:

\(r = 2 * L\)

\(r = 2*13\)

\(r = 26\)

The window is made up of a larger square and a semi-circle

Next, calculate the area of the larger square.

16 small squares made up the larger square.

So, the area is:

\(A_2 = 16 * 169\)

\(A_2 = 2704\)

The area of the semicircle is:

\(A_3 = \frac{\pi r^2}{2}\)

\(A_3 = \frac{3.14 * 26^2}{2}\)

\(A_3 = 1061.32\)

So, the area of the window is:

\(Area = A_2 + A_3\)

\(Area = 2704 + 1061.32\)

\(Area = 3765.32\)

Solving (b): Area of the shade

The shade extends 4 inches beyond the window.

This means that;

The bottom length is now; Initial length + 8

And the height is: Initial height + 4

In (a), the length of each square is calculated as: 13in

4 squares make up the length and the height.

So, the new dimension is:

\(Length = 4 * 13 + 8\)

\(Length = 60\)

\(Height = 4*13 + 4\)

\(Height = 56\)

The area is:

\(A_1 = 60 * 56 = 3360\)

The radius of the semicircle becomes initial radius + 4

\(r = 26 + 4 = 30\)

The area is:

\(A_2 = \frac{3.14 * 30^2}{2} = 1413\)

The area of the shade is:

\(Area = A_1 + A_2\)

\(Area = 3360 + 1413\)

\(Area = 4773\)

The correct option is option (C) .

Cluster Sampling is a type of probability sampling and other options are non- probability sampling examples .

Sampling :

Sampling is defined as a technique that selects individual members or subsets from a population to help determine characteristics of the population as a whole.

Croach and Housden postulate that a sample is a finite number taken from a large group for testing and analysis, and that the sample can be taken as representative of the group as a whole.

There are two main types of sampling:

i) probability sampling

ii) Non-probability sampling

A) probability sampling:

It is defined as the sampling technique which researchers use a related method to draw probability theory samples from a larger population.

The most important requirement for probabilistic sampling is that everyone in the population has a known equal chance of being selected.

Probability Samples:

1. Stratified Sampling: Stratified sampling is a type of sampling technique that divides the total population into smaller groups or strata to complete the sampling process. Hierarchies are formed based on some common characteristics of demographic data.

2. Cluster Sampling: Cluster sampling is a probabilistic sampling technique in which researchers divide a population into multiple groups (clusters) for research purposes. Researchers then select random groups using simple sampling techniques for data collection and data analysis.

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========================================================

Explanation:

There are two approaches

Method 1

25% of 79 = 0.25*79 = 19.75

Mary saves $19.75 and the price before tax is 79 - 19.75 = 59.25

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

Method 2

She saves 25% so she must pay the remaining 75%

75% of 79 = 0.75*79 = 59.25

This is a slight shortcut, and it's very useful when it comes to chaining multiple discounts together.

Consumption of resources at a 3.0 planet rate indicates that a country needs to reduce its resource consumption by 2/3 to be sustainable.

Humans will be benefited from two types of resources namely renewable and non-renewable resources. The former can be utilized for the long term but the latter needs to be handled carefully.

But, they are misused by humans which leads to a lack of resources for us. Common example of non-renewable resources includes natural gas, coal, oil, etc.

The consumption of resources at a given planet rate indicates the rate of utilization of resources. With the increased consumption of resources, pollution on the planet increases. It is accompanied by numerous health issues.

It additionally requires alternatives to the resources that we will consume completely.

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Answer:

(1/6)

Step-by-step explanation:

ℎ 1/6

b. 31.5

Step-by-step explanation:

AREA OF RHOMBUS = a=pq/2

a=9×7/2

63/2

=31.5

The total number of free throws she attempted is 1700.

Given,

Latanya misses 4% of the free throws she attempts in a season.

Missed throws are 68.

We need to find how many total free throws she attempted.

Total is always considered as 100%

If,

28 = total

100% = 28 and 50% = 14

We have,

4% = 68

Now total throws are 100%.

So,

If 4% = 68

Then,

4% = 68

Multiply both sides by 25.

25 x 4% = 25 x 68

100% =  1700

We see that 1700 is the total number of throws.

Thus the total number of free throws she attempted is 1700.

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Answer:

Step-by-step explanation:

area = pi*radius*radius -> Radius =  \(\sqrt{\frac{area}{pi} }\)

area: 63.585 m2

   -> radius = \(\sqrt{\frac{63.585}{3.14} }\) = 4.5 m

area: 28.26m2

  -> radius = \(\sqrt{\frac{28.26}{3.14} }\) = 3m

   -> diameter = 6m

area: 120.7016m2

  -> radius = \(\sqrt{\frac{120.7016}{3.14} }\) = 6.2m

   -> diameter = 12.4m

area: 12.56m2

   -> radius = \(\sqrt{\frac{12.56}{3.14} }\) = 2m

area: 482.8064m2

   ->radius = \(\sqrt{\frac{482.8064}{3.14} }\) = 12.4m

area: 113.04 m2

   ->radius = \(\sqrt{\frac{113.04}{3.14} }\) = 6m

Answer:

No

Step-by-step explanation:

When \(x=2\), \(y=-6(2)=-12\), not \(4\).

To determine under what conditions Chris would choose not to buy any Red Bulls, further information or constraints are needed. The marginal utility per dollar spent can be calculated for each item, providing insights into their relative importance in maximizing utility.

To determine under what conditions Chris would choose not to buy any Red Bulls, we need additional information such as the price of Red Bulls and Chris's preferences and budget constraints specifically related to Red Bulls. Without such information, it is not possible to ascertain the conditions under which Chris would choose not to buy any Red Bulls.

Moving on to the utility function and expenditure question, given the utility function U = 6ln(b) + 2ln(c) + ln(s) + x, where b represents loaves of bread, c represents kilos of cheese, s represents kilos of salami, and x represents dollars left over to spend on other goods and services, the consumer aims to maximize utility.

To determine the optimal bundle, the consumer will allocate their budget of $160 to purchase specific quantities of bread, cheese, and salami while leaving a portion for other goods and services. The specific amounts purchased will depend on the prices of bread, cheese, and salami and their respective marginal utilities.

Calculating the marginal utility per dollar spent on bread, cheese, salami, and other goods and services will reveal the relative importance of each item in maximizing utility. By comparing these values, we can identify which goods provide the highest marginal utility per dollar spent and are, therefore, the most beneficial in terms of utility maximization.

Please note that the calculations for the optimal bundle and marginal utility per dollar spent require specific numerical values for prices and quantities to provide a more detailed answer.

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To order the given expressions from least to greatest, we need to find the values of each expression. However, since we do not have the function p(x), we cannot find the values of p′(1), p′(3), p′(6), p′(7), p′(9), and p′(10). Therefore, we cannot order the expressions from least to greatest.

It is important to note that the sign of each expression will depend on the function p(x) and its derivative p′(x). If p′(x) is positive, then the function p(x) is increasing at that point. If p′(x) is negative, then the function p(x) is decreasing at that point. Without the function p(x), we cannot determine the sign of each expression and therefore cannot order them from least to greatest.

In conclusion, without the function p(x), we cannot order the expressions p′(1), p′(3), p′(6), p′(7), p′(9), and p′(10) from least to greatest.

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dy/dt = 10/3 when x = 1, y = 2, and dx/dt = 5. We can calculate it in tis manner:

Given that x and y are functions of t. The values of dx/dt, x = 1 and y = 2 are given. Also, y³ = 2x⁴ + 6

We have to find dy/dt.

Let's find the value of x at t = 1, using dx/dt=5∴ (d/dt)x = 5⇒ (d/dt)x = (d/dt)(1) = 5

Integrating both sides w.r.t t, we get,⇒ ∫(d/dt)x dt = ∫5 dt⇒ x = 5t + C1

Where C1 is the constant of integration. Given that x = 1 at t = 0. So, substituting these values in the above equation, we get,1 = 5(0) + C1⇒ C1 = 1So, x = 5t + 1

Also, we are given that y³ = 2x⁴ + 6By differentiating w.r.t t on both sides, we get,⇒ (d/dt)y³ = (d/dt)(2x⁴ + 6)⇒ 3y² (d/dt)y = 8x³ (d/dt)x⇒ (d/dt)y = 8x³ (d/dt)x / 3y²Now, we know that (d/dt)x = 5 and x = 1, y = 2.

So, substituting these values in the above equation, we get,(d/dt)y = 8(1³)(5) / 3(2²)⇒ (d/dt)y = 20/12⇒ (d/dt)y = 5/3

Therefore, dy/dt = 5/3
To find dy/dt, first differentiate the given equation y^3 = 2x^4 + 6 with respect to t using the chain rule.

Differentiating both sides with respect to t, we get:

3y^2(dy/dt) = 8x^3(dx/dt)

Now, substitute the given values x = 1, y = 2, and dx/dt = 5 into the equation:

3(2)²(dy/dt) = 8(1)^3(5)

12(dy/dt) = 40

Solve for dy/dt:

dy/dt = 40/12

Simplify the fraction:

dy/dt = 10/3

Therefore, dy/dt = 10/3 when x = 1, y = 2, and dx/dt = 5.

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Answer:

105 Degrees

Step-by-step explanation:

Angle 3 is 105 degrees because it is cut in half on a striaght line. A   line is 180 degrees so you subtract 75 from 180 and you get 105

Answer:

105°

Step-by-step explanation:

To find an exterior angle, subtract the interior angle from 180.

180 - 75 = 105

Therefore, angle 3 is 105°.

Let me know if I did something wrong.

The distance between the point P and the line ℓ is 24 / √(74) units.

To find the distance between a point P and a line ℓ, we need to use the coordinates of both the point and the line. In this case, we have the coordinates of the point P, which is (−1, 1), and two points on the line ℓ, which are (11, −1) and (−3, −11).

The first step is to find the equation of the line ℓ. We can use the two points on the line to find the slope of the line, which is:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points on the line. Substituting the given coordinates, we get:

m = (-11 - (-1)) / (-3 - 11) = -10 / (-14) = 5 / 7

Now we can use the point-slope form of the equation of a line to find the equation of line ℓ:

y - y₁ = m(x - x₁)

where (x₁, y₁) is any point on the line. We can choose either of the given points, let's choose (11, −1):

y - (-1) = (5 / 7)(x - 11)

Simplifying this equation, we get:

y = (5 / 7)x - 36 / 7

So, the equation of line ℓ is y = (5 / 7)x - 36 / 7.

Now we can use the formula for the distance between a point and a line:

distance = |ax + by + c| / √(a² + b²)

where a, b, and c are the coefficients of the equation of the line, and x and y are the coordinates of the point. In this case, the coefficients of the equation of line ℓ are a = 5 / 7, b = -1, and c = -36 / 7. Substituting the coordinates of the point P, we get:

distance = |(5 / 7)(-1) - 1 + (-36 / 7)| / √((5 / 7)² + (-1)²)

Simplifying this equation, we get:

distance = 24 / √(74)

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Answer:

Step-by-step explanation:

Here we see regrouping of the multiplied numbers.

Relevant property is given below

Answer:

Your answer is C

Step-by-step explanation:

Answer:

the answer to the question is online if you

Answer: \(x+y=45\\\\1000 x + 500y = $2500\)

Step-by-step explanation:

Let x =  Number of employees taking technology training

y= Number of employees taking customer service training

Given, The technology training costs $1,000 per person. The customer service training costs $500 per person.

Total cost = 1000 x + 500y

Since, Total cost = $25,000 and total employee to attend training= 45 .

That means , the required equations are:

\(x+y=45\\\\1000 x + 500y = $2500\)

Answer:

1,000x + 500y = 45

x + y =45

Step-by-step explanation:

So that means answer b is the correct answer, also I took the test.

Over 10.144 years of age are found in 75% of firm employees' autos.

We need to identify the z-score that corresponds to the age of the cars driven by firm employees that are 75% older than the other cars of 75th percentile of the normal distribution.

A normal distribution calculator or statistical software programme can be used to find this z-score. As an alternative, we can look for the value using a z-distribution table.

The formula for the z-score is:

z = (x - μ) / σ

If x is the value we are looking for, is the distribution's mean, and is its standard deviation.

We can use the common normal distribution table or a calculator with a built-in function to determine the z-score corresponding to the 75th percentile  to a cumulative probability of 0.75. The table value is 0.67.

As a result, we can determine the age of the company vehicles that are approximately 75% older than the others as follows:

x = μ + zσ

= 8 + (0.67)(3.2)

= 10.144

As a result, more than 75% of the cars that firm employees drive are older than 10.144 years.

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Rounded to the nearest hundredth, the football will hit the ground in approximately 0.03 seconds.

a. To find the initial height of the football, we can plug in x = 0 into the equation:

y = -16(0)^2 + 64(0) + 2

= 2

Therefore, the initial height of the football is 2 feet.

b. To find the height of the football after 1 second, we plug in x = 1 into the equation:

y = -16(1)^2 + 64(1) + 2

= -16 + 64 + 2

= 50

The height of the football after 1 second is 50 feet.

c. To find the height of the football after 3 seconds, we plug in x = 3 into the equation:

y = -16(3)^2 + 64(3) + 2

= -16(9) + 64(3) + 2

= -144 + 192 + 2

= 50

The height of the football after 3 seconds is 50 feet.

d. The maximum height of the football can be found using the formula x = -b / (2a), where the equation is in the form y = ax^2 + bx + c.

In this case, a = -16 and b = 64.

x = -64 / (2(-16))

= -64 / (-32)

= 2

Therefore, it will take 2 seconds for the football to reach its maximum height.

e. To find the maximum height of the football, we substitute the value of x = 2 into the equation:

y = -16(2)^2 + 64(2) + 2

= -16(4) + 128 + 2

= -64 + 128 + 2

= 66

The maximum height of the football is 66 feet.

f. To find the time it takes for the football to hit the ground, we set y = 0 and solve for x:

-16x^2 + 64x + 2 = 0

This quadratic equation can be solved using the quadratic formula. Applying the formula, we get:

x = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values a = -16, b = 64, and c = 2 into the formula, we have:

x = (-64 ± √(64^2 - 4(-16)(2))) / (2(-16))

= (-64 ± √(4096 + 128)) / (-32)

= (-64 ± √4224) / (-32)

Simplifying further:

x ≈ (-64 ± 65.07) / (-32)

We ignore the negative solution since time cannot be negative in this context:

x ≈ (-64 + 65.07) / (-32)

≈ 1.07 / (-32)

≈ -0.033

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Answer:

\(-3\leq x\) < 6

third answer choice

Step-by-step explanation:

Answer:

y=90x+2,000

y=mx+b

Answer: $50

Step-by-step explanation:

The calculated z-score (0.745) is within the range -1.96 to +1.96, we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that the GPAs earned by RTC students.

To find the mean GPA for the RTC students in the sample, we need to calculate the average of the given GPAs:

GPA for RTC Students:

3.70, 2.60, 3.10, 3.00, 3.10, 3.80, 2.60, 3.40, 3.00, 2.80

Mean GPA = (3.70 + 2.60 + 3.10 + 3.00 + 3.10 + 3.80 + 2.60 + 3.40 + 3.00 + 2.80) / 10

Mean GPA = 31.10 / 10 = 3.11

Therefore, the mean GPA for the RTC students in the sample is 3.11.

The null and alternative hypotheses are statements about the population based on the given data. In this case, the null hypothesis (H0) assumes no significant difference in the GPAs of RTC students compared to the population, while the alternative hypothesis (Ha) assumes a significant difference.

Null Hypothesis (H0): The mean GPA of RTC students is equal to the mean GPA of the population (μ = 2.90).

Alternative Hypothesis (Ha): The mean GPA of RTC students is different from the mean GPA of the population (μ ≠ 2.90).

To determine if the GPAs earned by RTC students differ significantly from the population, a statistical test can be conducted. The most common test for this situation is the t-test, which compares the means of two groups. By comparing the mean GPA of the RTC students to the population mean, we can determine if there is a significant difference.

However, since the population standard deviation is known (0.89), we can use a one-sample z-test instead. The z-test compares the sample mean to the population mean when the population standard deviation is known. By calculating the z-score and comparing it to the critical value, we can determine if the difference is statistically significant.

To perform the z-test, we calculate the z-score using the formula:

z = (X - μ) / (σ / √n)

where X is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, X (sample mean) is 3.11, μ (population mean) is 2.90, σ (population standard deviation) is 0.89, and n (sample size) is 10.

Plugging in the values, we get:

z = (3.11 - 2.90) / (0.89 / √10)

Calculating the numerator and denominator separately:

Numerator: 3.11 - 2.90 = 0.21

Denominator: 0.89 / √10 ≈ 0.2818

Dividing the numerator by the denominator:

z ≈ 0.21 / 0.2818 ≈ 0.745

To determine if the GPAs earned by RTC students differ significantly from the population, we compare the calculated z-score to the critical value for the desired level of significance (e.g., α = 0.05).

By looking up the critical value in the standard normal distribution table for α = 0.05 (two-tailed test), we find that the critical z-value is approximately ±1.96.

Therefore, the calculated z-score (0.745) is within the range -1.96 to +1.96, we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that the GPAs earned by RTC students.

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Incomplete question:

An educational psychologist is interested in seeing if Return To College (RTC) students—that is, students who have not attended school for more than 4 years in order to work or raise a family—are more motivated to achieve higher grades than students who have not taken a break in their education. She knows that the distribution of grade point averages (GPAs) for students at her college who have not interrupted their education is normally distributed with a mean of 2.90 and a standard deviation of 0.89. She collects the following sample of GPAs for 10 RTC students. Use the data in Table 9.6 to answer the following questions.

GPA for RTC Students

GPA

3.70

2.60

3.10

3.00

3.10

3.80

2.60

3.40

3.00

2.80

Use the data to answer the following questions--MUST SHOW WORK TO RECEIVE CREDIT:

Find the mean GPA for the RTC students in the sample.

Determine the null and alternative hypotheses.

Decide if the GPAs earned by RTC students differ significantly from the population.

The calculated z-score (0.745) is within the range -1.96 to +1.96, we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that the GPAs earned by RTC students.

To find the mean GPA for the RTC students in the sample, we need to calculate the average of the given GPAs:

GPA for RTC Students:

3.70, 2.60, 3.10, 3.00, 3.10, 3.80, 2.60, 3.40, 3.00, 2.80

Mean GPA = (3.70 + 2.60 + 3.10 + 3.00 + 3.10 + 3.80 + 2.60 + 3.40 + 3.00 + 2.80) / 10

Mean GPA = 31.10 / 10 = 3.11

Therefore, the mean GPA for the RTC students in the sample is 3.11.

The null and alternative hypotheses are statements about the population based on the given data. In this case, the null hypothesis (H0) assumes no significant difference in the GPAs of RTC students compared to the population, while the alternative hypothesis (Ha) assumes a significant difference.

Null Hypothesis (H0): The mean GPA of RTC students is equal to the mean GPA of the population (μ = 2.90).

Alternative Hypothesis (Ha): The mean GPA of RTC students is different from the mean GPA of the population (μ ≠ 2.90).

To determine if the GPAs earned by RTC students differ significantly from the population, a statistical test can be conducted. The most common test for this situation is the t-test, which compares the means of two groups. By comparing the mean GPA of the RTC students to the population mean, we can determine if there is a significant difference.

However, since the population standard deviation is known (0.89), we can use a one-sample z-test instead. The z-test compares the sample mean to the population mean when the population standard deviation is known. By calculating the z-score and comparing it to the critical value, we can determine if the difference is statistically significant.

To perform the z-test, we calculate the z-score using the formula:

z = (X - μ) / (σ / √n)

where X is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, X (sample mean) is 3.11, μ (population mean) is 2.90, σ (population standard deviation) is 0.89, and n (sample size) is 10.

Plugging in the values, we get:

z = (3.11 - 2.90) / (0.89 / √10)

Calculating the numerator and denominator separately:

Numerator: 3.11 - 2.90 = 0.21

Denominator: 0.89 / √10 ≈ 0.2818

Dividing the numerator by the denominator:

z ≈ 0.21 / 0.2818 ≈ 0.745

To determine if the GPAs earned by RTC students differ significantly from the population, we compare the calculated z-score to the critical value for the desired level of significance (e.g., α = 0.05).

By looking up the critical value in the standard normal distribution table for α = 0.05 (two-tailed test), we find that the critical z-value is approximately ±1.96.

Therefore, the calculated z-score (0.745) is within the range -1.96 to +1.96, we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that the GPAs earned by RTC students.

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Incomplete question:

An educational psychologist is interested in seeing if Return To College (RTC) students—that is, students who have not attended school for more than 4 years in order to work or raise a family—are more motivated to achieve higher grades than students who have not taken a break in their education. She knows that the distribution of grade point averages (GPAs) for students at her college who have not interrupted their education is normally distributed with a mean of 2.90 and a standard deviation of 0.89. She collects the following sample of GPAs for 10 RTC students. Use the data in Table 9.6 to answer the following questions.

GPA for RTC Students

GPA

3.70

2.60

3.10

3.00

3.10

3.80

2.60

3.40

3.00

2.80

Use the data to answer the following questions--MUST SHOW WORK TO RECEIVE CREDIT:

Find the mean GPA for the RTC students in the sample.

Determine the null and alternative hypotheses.

Decide if the GPAs earned by RTC students differ significantly from the population.