at state college last term, 53 of the students in a physics course earned a's, 81 earned b's, 106 got c's, 85 were issued d's, and 64 failed the course. if this grade distribution was graphed on pie chart, how many degrees would be used to indicate the a region?

Answer:

x = 13

Step-by-step explanation:

m∠A + m∠B = 90° complementary angles = 90°

m∠A = 23°

m∠B = (4x + 15)°

23 + 4x + 15 = 90

- 15 - 23 both sides = cancel out to make 4x the subject

4x = 52

÷ 4 both sides = get rid of coefficient (make x alone)

x = 13

Answer:

B) x = 13

Step-by-step explanation:

Complementary angles means that, when combined, they add up to 90°. In this case, the given Angles A & B are complementary, ∴

∠A + ∠B = 90°

It is given that:

m∠A = 23°

m∠B = (4x + 15)°

Plug in the corresponding terms to the corresponding variables:

m∠A + m∠B = 90°

(23)° + (4x + 15)° = 90°

First, combine like terms. Like terms are terms that share the same amount of the same variables:

4x + 15 + 23 = 90

4x + (15 + 23) = 90

4x + 38 = 90

Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

~

First, subtract 38 from both sides of the equation:

4x + 38 = 90

4x + 38 (-38) = 90 (-38)

4x = 90 - 38

4x = 52

Next, divide 4 from both sides of the equation:

(4x)/4 = (52)/4

x = 52/4

x = 13.

B) x = 13 is your answer.

Check: Plug in 13 for x in the given angle measurements, and combine the angles to obtain the measurement 90° (complementary):

m∠B = (4x + 15)

m∠B = (4 * 13) + 15

m∠B = 52 + 15

m∠B = 67°

m∠A + m∠B = 90°

m∠A + (67) = 90°

m∠A + 67 (-67) = 90 (-67)

m∠A = 90 - 67

m∠A = 23°

~

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To find the marginal pdf of a joint pdf, you must first integrate the joint pdf over the appropriate marginal domain.

To find the marginal pdf of a joint pdf, you need to integrate the joint pdf over all possible values of the other variable(s) in the joint distribution. For example, if you have a joint pdf for two variables X and Y, to find the marginal pdf of X, you integrate the joint pdf over all possible values of Y.

This will give you the pdf of X alone. Similarly, to find the marginal pdf of Y, you integrate the joint pdf over all possible values of X. This approach works for any number of variables in the joint distribution, and can be used to obtain the pdf of each variable individually.

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Answer:

Below in bold.

Step-by-step explanation:

We have a right triangle here with the hypotenuse = 2 and the legs are 1 and √3.

If tan A > 0 then the opposite side to < A  in the triangle is greater than the adjacent so the leg opposite angle A is √3 and the adjacent side = 1.

So cos A = adj/hyp = 1/2.

She would need 32 1-quart containers because 8 gallons is 32 quarts.

She would need 64 cups because there are 62 pints in 8 gallons.

Answer:

Q=L

Step-by-step explanation:

Answer:A

Step-by-step explanation:

The probability that an adult over 40 years of age is diagnosed with the disease is approximately 0.314.

To find the probability that an adult over 40 years of age is diagnosed with the disease, we can use Bayes' theorem.

Let's define the events:

A: An adult over 40 years of age has the disease.

B: An adult over 40 years of age is diagnosed with the disease.

We are given the following probabilities:

P(A) = 0.04 (probability of an adult over 40 having the disease)

P(B|A) = 0.78 (probability of correctly diagnosing a person with the disease)

P(B|A') = 0.05 (probability of incorrectly diagnosing a person without the disease)

We want to find P(A|B), the probability of an adult over 40 having the disease given that they are diagnosed with the disease.

According to Bayes' theorem:

P(A|B) = (P(B|A) * P(A)) / P(B)

To calculate P(B), we can use the law of total probability:

P(B) = P(B|A) * P(A) + P(B|A') * P(A')

Since P(A') = 1 - P(A) (probability of not having the disease), we can substitute it into the equation:

P(B) = P(B|A) * P(A) + P(B|A') * (1 - P(A))

Plugging in the given values:

P(B) = 0.78 * 0.04 + 0.05 * (1 - 0.04)

Now we can calculate P(A|B) using Bayes' theorem:

P(A|B) = (P(B|A) * P(A)) / P(B)

P(A|B) = (0.78 * 0.04) / P(B)

Substituting the value of P(B) we calculated earlier:

P(A|B) = (0.78 * 0.04) / (0.78 * 0.04 + 0.05 * (1 - 0.04))

Calculating this expression:

P(A|B) ≈ 0.314

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Answer:

So, I solved it and I got this:

Simplify the expression.

24 x^ 4

Step-by-step explanation:

hope this helps! have a great day!

The correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are given below.Option A. V = -(0.25)x - 4 Option B. V = − (0.25)x+4

A function can be defined as a special relation where each input has exactly one output. The set of values that a function takes as input is known as the domain of the function. The set of all output values that are obtained by evaluating a function is known as the range of the function.

From the given options, only option A and option B are the functions that satisfy the condition.Both of the options are linear equations and graph of linear equation is always a straight line. By solving both of the given options, we will get the range as (-∞, 4) and domain as (-∞, 0).Hence, the correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are option A and option B.

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Answer:

1/3

Step-by-step explanation:

\(g(f(x))=x \\ \\ g'(f(x))f'(x)=1 \\ \\ g'(f(x))=\frac{1}{f'(x)} \\ \\ g'(f(x))=\frac{1}{\cos x+2} \\ \\ g'(f(0))=\frac{1}{\cos(0)+2} \\ \\ g'(1)=\frac{1}{3}\)

Answer:

He made Rs.500

He gave Rs.250 to the orphanage

Sharing

It is expected that 300 participants out of the 900 who participate in the survey would receive a coupon for sleigh rides.

To determine the number of participants expected to receive a coupon for sleigh rides, we need to divide the total number of participants (900) by the number of coupon options (3) since each option has an equal chance of being received.

The expected number of participants receiving a coupon for sleigh rides can be calculated as follows:

Total participants / Number of coupon options = Expected number of participants receiving a sleigh ride coupon

900 participants / 3 coupon options = 300 participants.

Therefore, it is expected that 300 participants out of the 900 who participate in the survey would receive a coupon for sleigh rides.

It's important to note that this calculation assumes an equal chance of receiving each type of coupon and does not consider any specific preferences or biases that participants may have.

The calculation is based on the assumption of a random distribution of coupons among the participants.

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For this study, what is the response variable is b. Whether or not a student graduates from college.

The outcome of an experiment in which the explanatory variable is altered is the response variable. It is a variable whose variation can be accounted for by other variables. It is also known as the outcome variable or the dependent variable. As an illustration, the students wish to utilise height to predict age; hence, height is the explanatory variable and age is the response variable.

Whether a student in the example graduates from college. The university official is interested in examining this variable to see whether it has any associations with the predictor variable, which is whether students declare their majors before their junior year. A is the predictor variable. if a student chooses a major prior to entering their junior year.

Complete Question:

A university official wants to determine if a relationship exists between whether students choose their majors before their junior year and whether they graduate from college. For this study, what is the response variable?

a. Whether a student decides on his/her major before their junior year

b. Whether or not a student graduates from college.

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Answer:

Step-by-step explanation:

17

To understand the relationship between the location on the ramp where the rolls are released and the distance they travel, Priya can gather data by conducting an experiment. She can release rolls from different locations on the ramp and measure the distance they travel in meters.

She can repeat this process multiple times for each location to ensure accuracy and gather enough data for analysis.

To make the experiment more controlled, Priya can keep the release force constant for each roll and use the same type of rolls throughout the experiment. Additionally, she can use a measuring tape or ruler to measure the distance traveled by each roll.

Once Priya gathers all the data, she can analyze it by creating a graph or chart to visually represent the relationship between the release location and the distance traveled. This will help her identify any patterns or trends and draw conclusions about the relationship.

Priya can set up an experiment following these steps:

1. Set up the ramp on a flat surface and ensure it is stable.
2. Use a measuring tape or ruler to measure and mark specific locations on the ramp in meters (e.g., every 0.5 meters). These will serve as the release points for the ball.
3. Choose a ball of consistent size and weight to roll down the ramp.
4. Begin by releasing the ball from the first marked location on the ramp (e.g., 0.5 meters). As the ball rolls, make sure to track its distance from the bottom of the ramp.
5. Use a measuring tape or ruler to measure the distance the ball traveled from the base of the ramp in meters. Record this measurement in a data table or notebook.
6. Repeat the experiment for the other marked locations on the ramp, carefully measuring and recording the distance the ball travels each time.
7. Conduct multiple trials at each release location to account for any variability in the data.
8. Analyze the data by comparing the release location (in meters) to the corresponding distance the ball traveled. This will help Priya understand the relationship between the ball's release location on the ramp and the distance it rolls.

Overall, conducting an experiment to gather data is an effective way for Priya to understand the relationship between the location on the ramp where rolls are released and the distance they travel in meters.

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Step-by-step explanation:

Horizontal asymptote is the same and vertical asymptote at x = 6 (B).

The area of the walkway is 24π square meters.

To find the area of the walkway, we need to subtract the area of the inner circle from the area of the outer circle.

The inner circle has a radius of 5 meters, so its area can be calculated using the formula for the area of a circle: A_inner = π * \((r_inner)^{2}\).

A_inner = π * \(5^{2}\) = 25π square meters.

The outer circle has a radius equal to the sum of the inner radius and the width of the walkway. In this case, the outer radius is 5 + 2 = 7 meters.

The area of the outer circle can be calculated in the same way: A_outer = π * \((r_outer)^{2}\).

A_outer = π * \(7^{2}\) = 49π square meters.

Now, we can find the area of the walkway by subtracting the area of the inner circle from the area of the outer circle: A_walkway = A_outer - A_inner.

A_walkway = 49π - 25π = 24π square meters.

The area of the walkway is 24π square meters, where π (pi) is a mathematical constant approximately equal to 3.14159.

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Answer:

17

Step-by-step explanation:

for f(6).

\(f(6) = - 3 \times 6 + 1 = 17\)

Answer:

17

Step-by-step explanation:

As per the question, All four students A, B, C, and D are loss-averse over money and have the same value function as below:v(x dollars)={√x     x ≥ 0   {-2√-x  x < 0They are also loss averse over mugs and have the same value function.

v(y mugs)={3y y ≥ 0
        {4y y < 0
Now, we have to find the values of a, b, c and d as below:
- Student A owns a mug and is willing to sell it for a price of a dollars or more. i.e v(a) = v(0) + v(a-A), where A is the initial endowment of A. According to the given function, v(0) = 0, v(a-A) = 3, and v(A) = 4.
So, a ≥ A+3/2
- Student B does not own a mug and is willing to pay up to b dollars for buying it. i.e v(B-b) = v(B) - v(0), where B is the initial endowment of B. According to the given function, v(0) = 0, v(B-b) = -4, and v(B) = -3.
So, b ≤ B+1/2
- Student C does not own a mug and is indifferent between getting a mug and getting c dollars. i.e v(c) = v(0) + v(c), where C is the initial endowment of C. According to the given function, v(0) = 0, v(c) = 3.
So, c = C/2
- Student D is indifferent between losing a mug and losing d dollars. i.e v(D-d) = v(D) - v(0), where D is the initial endowment of D. According to the given function, v(0) = 0, v(D-d) = -3.
So, d = D/2
2) In this case, value function for money changes to:v(x dollars)={√x     x ≥ 0
            {-√-x   x < 0
However, the value function for mugs remains the same:v(y mugs)={3y y ≥ 0
         {4y y < 0
Therefore, values for a, b, c, and d will remain the same as calculated in part (1).
3) In this case, students are not loss-averse. Value function for money:v(x dollars)={√x     x ≥ 0
            {-√-x   x < 0
Value function for mugs:v(y mugs)={3y y ≥ 0
The reference point is the status quo, i.e initial endowment. So,
- Student A owns a mug and is willing to sell it for a price of a dollars or more. The value of mug for A is 3 initially and he would sell it for 3 or more.
So, a ≥ A+3/2
- Student B does not own a mug and is willing to pay up to b dollars for buying it. The value of mug for B is 3 initially and he would buy it for 3 or less.
So, b ≤ B+3/2
- Student C does not own a mug and is indifferent between getting a mug and getting c dollars. The value of the mug for C is 3 initially.
So, c = 3
- Student D is indifferent between losing a mug and losing d dollars. The value of the mug for D is 3 initially.
So, d = 3
4) In this case, value function for money:v(x dollars)={√x     x ≥ 0
            {-√-x   x < 0
Value function for mugs: Mug will have a value of 4 for someone who owns it and 3 for someone who does not own it.
The reference point is the status quo, i.e initial endowment. So,
- Student A owns a mug and is willing to sell it for a price of a dollars or more. The value of mug for A is 4 initially and he would sell it for 4 or more.
So, a ≥ A+2
- Student B does not own a mug and is willing to pay up to b dollars for buying it. The value of mug for B is 3 initially and he would buy it for 3 or less.
So, b ≤ B+3/2
- Student C does not own a mug and is indifferent between getting a mug and getting c dollars. The value of the mug for C is 3 initially and he would like to buy it for 3.
So, c = 3
- Student D is indifferent between losing a mug and losing d dollars. The value of the mug for D is 3 initially.
So, d = 3.

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A relation in math is a set of ordered pairs containing two elements, one from each set. The first element is from the domain and the second from the range.

Relations can be expressed as a set of ordered pairs, as a graph, or as a mapping diagram. A function is a special type of relation in which, for every element in the domain, there is one and only one element in the range. This is expressed mathematically by stating that for every x in the domain, there is one and only one y in the range such that y = f(x). To calculate a relation, the domain and range values are paired with each other, and the ordered pairs are written down. For example, if the domain is {2,3,4,5} and the range is {7,8,9,10}, then the relation would be {(2,7),(3,8),(4,9),(5,10)}.

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Answer:

A. B = 5

Step-by-step explanation:

Joe:

J(b) = 14b + 7

Will:

W(b) = 7b + 42

Where,

b = number of hamburgers cooked

J(b) and W(b) = amount of time each cook takes in minutes respectively

At what value of b will their cooking time be equivalent?

Equate both functions

Joe = Will

14b + 7 = 7b + 42

Collect like terms

14b - 7b = 42 - 7

7b = 35

Divide both sides by 7

b = 35 / 7

= 5

b = 5

The answer is

A. B = 5

Slope is  $0.15 of the equation of cost  C=$0.15t+$35.00.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Given that A cell phone company uses the equation C=$0.15t+$35.00

C is the total cost for a month of service.

t is the number of text messages.

We have to find the slope of the equation.

slope is 0.15 and 35.00 is the y intercept of the equation given.

Hence, slope is  $0.15 of the equation of cost  C=$0.15t+$35.00.

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The solution to the question \(-7 \frac{2}{3} + (-5\frac{1}{2} ) + 8\frac{3}{4}\) is \(-4\frac{5}{12}\).

To solve this problem, we need to add up all the given numbers. To make the addition process easier, we can convert all the mixed numbers into improper fractions first.

\(-7\frac{2}{3}\) =\(-(\frac{21+2}{3} )\)= \(-\frac{23}{3}\)

\(-5\frac{1}{2}\) = \(-(\frac{10+1}{2} )\)= \(-\frac{11}{2}\)

\(8\frac{3}{4}\) = \(\frac{32+3}{4}\) = \(\frac{35}{4}\)

Now we can add up the three fractions:

\(-\frac{23}{3}+ -\frac{11}{2}+\frac{35}{4}\)

We must choose a common denominator so that we can sum up these fractions. The smallest common multiple of 3, 2, and 4 is 12.

Therefore,

\(\frac{(-23*4)+(-11*6)+(35*3)}{12}\)

\(\frac{-92-66+105}{12} \\\frac{-53}{12}\)

Therefore, the solution is \(\frac{-53}{12}\). We can also convert this back into a mixed number if required:

\(\frac{-53}{12}\) = \(-\frac{(4*8+5)}{12}\) =\(-4\frac{5}{12}\).

So the final answer is \(-4\frac{5}{12}\).

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The Zeller’s congruence is an algorithm developed to calculate the day of the week is given below.

We know that Zeller's congruence is an algorithm that determines the day of the week for any given date.

First Take the month and subtract two from it if the month is January or February. Otherwise, leave the month unchanged.

Then Divide the result from step 1 by 12 and round down to the nearest integer. Call this value "C".

Divide the year by 4 and round down to the nearest integer. Call this value "Y".

Divide the year by 100 and round down to the nearest integer. Call this value "Z".

Divide the year by 400 and round down to the nearest integer. Call this value "X".

To Calculate the day of the week

(day + ((13 * A) - 1) / 5 + Y + Y / 4 + Z / 4 - 2 * Z + X) % 7

Where A is the result from step 1.

This formula will give a number between 0 and 6, where 0 represents Saturday, 1 represents Sunday, 2 represents Monday, and so on.

To print a calendar using Zeller's algorithm, we can first calculate the start day of the month using the algorithm above, and then use that information to print out the calendar for the entire month.

Tuesday Wednesday Thursday Friday Saturday Sunday Monday

1 2 3 4 5 6 7

8 9 10 11 12 13 14

15 16 17 18 19 20 21

22 23 24 25 26 27 28

29 30 31

This calendar shows the days of the week along the top row and the dates of the month in the corresponding columns.

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Answer:

Line a. goes to table 3, line b. goes to table 2, and line c. goes to table 1.

Step-by-step explanation:

Here are the 3 lines graphed (I even labeled each for you) so you can have a bit of a visual.

Hopefully you can find the points on each graph.

(Hint: The x row represents the x coordinate of an ordered pair, and the y row represents the y coordinate of an ordered pair.)

Ordered pairs look like this btw (x,y)

Hope this helps :)