if x is a random variable having a binomial distribution with n = 20 and p = 0.4, and y is a transformed version of x, where y = 2x 3, what is the expected value of y?

if Craig is painting the foul line area on the high school

basketball court, the value of the area he needs to paint is 114ft².

Option J) is the correct answer.

A rectangle is a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.

Area of a rectangle is expressed as;

A = length × breadth

Given the the foul line area is in the shape of a rectangle.

We substitute the values into the above equation.

A = length × breadth

A = 19ft × 6ft

A = 114ft²

Therefore, if Craig is painting the foul line area on the high school

basketball court, the value of the area he needs to paint is 114ft².

Option J) is the correct answer.

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Answer:

374 °F

Step-by-step explanation:

Data obtained from the question include the following:

Temperature (°C) = 190 °C

Temperature (°F) =?

Recall:

The conversion scale of temperature from °F to °C is given by the following equation:

C = 5/9(F – 32)

Next, we shall make F the subject of the formula. This can be obtained as follow:

C = 5/9(F – 32)

Cross multiply

5(F – 32) = 9C

Divide both side by 5

F – 32 = 9C/5

Rearrange

F = 9C/5 + 32

With the above formula, we can convert 190 °C to °F as follow:

Temperature (°C) = 190 °C

Temperature (°F) =?

F = 9C/5 + 32

F = 9 × 190/5 + 32

F = 1710/5 + 32

F = 342 + 32

F = 374 °F

Therefore, Teo will set the oven to 374 °F

The pentagonal prism with volume 360 in³ and height of 3 inches have a base area of 120 in²

A pentagonal prism is a prism that has two pentagonal bases like top and bottom and five rectangular sides.

Given that, the volume of a pentagonal prism is 360 in³, with a height of 3 inches,

We need to find the area of the base,

We know that, the volume of a pentagonal prism is =

V = 1/4 √(5(5+2√5)·a²h

Where a is the base edge and h is the height,

360 = 1/4·3 √(5(5+2√5)·a²

1/4·√(5(5+2√5)·a² = 120

Since, the base of a pentagonal prism is a pentagon, and the area of a pentagon = 1/4 √(5(5+2√5)·a²

And we have,

1/4 √(5(5+2√5)·a² = 120

Therefore, the base area is 120 in²

Hence, the pentagonal prism with volume 360 in³ and height of 3 inches have a base area of 120 in²

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The rate of change of the height of the top of the ladder above the ground at the instant when the base of the ladder is 30 ft. from the base of the building is -3 ft./min.

The rate of change of the height of the top of the ladder above the ground at the instant when the base of the ladder is 30 ft. from the base of the building is -3 ft./min. This rate takes into account the fact that the ladder is slipping at a rate of 3 ft./min. As the base of the ladder is slipping away from the building, the top of the ladder is moving down, hence the negative rate of change. This rate of change will remain the same until the base of the ladder has slipped the full 50 ft. from the base of the building. At this point, the rate of the change of the height of the top of the ladder will be 0, since the ladder will no longer be slipping.

The rate of change can be calculated as follows:

Rate of change = Change in height / Change in time

Change in height = Initial height - Final height

Initial height = 50 ft.

Final height = 50 ft. - 30 ft. = 20 ft.

Change in time = 30 ft. / 3 ft./min. = 10 min.

Rate of change = (50 ft. - 20 ft.) / 10 min. = -3 ft./min.

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B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

To determine the possible values for the length of the third side of a triangle, we need to consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given that two sides have lengths 6 and 9, we can analyze the possibilities:

6 + 9 > x

x > 15 - The sum of the two known sides is greater than any possible third side.

6 + x > 9

x > 3 - The length of the unknown side must be greater than the difference between the two known sides.

9 + x > 6

x > -3 - Since the length of a side cannot be negative, this inequality is always satisfied.

Based on the analysis, the possible values for the length of the third side are:

A. 7

C. 4

□E. 10

O F. 12

B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

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Answer:

X=9

Step-by-step explanation:

3x+3=2x+12

3x-2x=12-3

x=9

To work out the size of angle x, we need to use the fact that the angles in a straight line add up to 180 degrees. Looking at the diagram, we can see that angle x is one of three angles that make up this straight line.

Therefore, we can set up an equation: x + angle B + angle C = 180. We don't know the size of angles B and C, but we do know that angle B is vertically opposite to angle A (which is marked as 68 degrees), so angle B must also be 68 degrees. And since angle C is alternate angles with angle A, which means they are equal, angle C must also be 68 degrees. Now we can substitute these values into our equation: x + 68 + 68 = 180
Simplifying this, we get: x + 136 = 180
Subtracting 136 from both sides gives: x = 44

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An appropriate cautious reading of a receipt entail making sure that the

items charged are the same as the items received and checking to see if all

of the discounts were applied properly,

When an item is bought, a receipt is usually issued which confirms that

payment has been made for the goods or services. Receipt however should

be properly checked to detect any error in the course of the transaction.

Making sure that the items charged are the same as the items received and

checking to see if all of the discounts were applied properly should be done

to avoid shortages of the resources of the parties involved.

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Answer:

c

Step-by-step explanation:

Steps to solve:

3x - 5y = 20

~Subtract 3x to both sides

-5y = 20 - 3x

~Divide everything by -5

y = -4 + 3/5x

Best of Luck!

The equivalent value of the expression is y = ( 3x - 20 ) / 5

Given data ,

Let the equation be represented as A

Now , the value of A is

3x - 5y = 20

On simplifying the equation , we get

3x - 5y = 20

So , the left hand side of the equation is equated to the right hand side by the value of 20

Adding 5y on both sides , we get

3x = 20 + 5y

Subtracting 20 on both sides , we get

5y = 3x - 20

Divide by 5 on both sides , we get

y = ( 3x - 20 ) / 5

Therefore , the value of y = ( 3x - 20 ) / 5

Hence , the expression is y = ( 3x - 20 ) / 5

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The correct simplification of the expression is c12 (option c).

The expression (c^4)^3 can be simplified using the exponent rules for powers of a power, which states that when a power is raised to another power, we can multiply the exponents.

Thus, we have:

(c^4)^3 = c^(43) [Using the rule (a^m)^n = a^(mn)]

Simplifying the exponent 4*3, we get:

c^(4*3) = c^12

Therefore, the correct simplification of the expression is c^12.

Option (c) is the correct answer as it correctly represents the simplified form of the given expression. Option (a) c^-1, option (b) c^7, and option (d) c^64 are not correct because they do not follow the exponent rules used to simplify the expression.

In summary, the expression (c^4)^3 simplifies to c^12, which is option (c) in the given options.

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The solution to the linear programming problem is:

Maximum value of z = 120

x₁ = 0, x₂ = 6

To solve the given linear programming problem using the graphical method, we first need to plot the feasible region determined by the constraints and then identify the optimal solution.

The constraints are:

x₁ + x₂ ≥ 12

x₁ + x₂ ≤ 6

x₁, x₂ ≥ 0

Let's plot these constraints on a graph:

The line x₁ + x₂ = 12:

Plotting this line on the graph, we find that it passes through the points (12, 0) and (0, 12). Shade the region above this line.

The line x₁ + x₂ = 6:

Plotting this line on the graph, we find that it passes through the points (6, 0) and (0, 6). Shade the region below this line.

The x-axis (x₁ ≥ 0) and y-axis (x₂ ≥ 0):

Shade the region in the first quadrant of the graph.

The feasible region is the overlapping shaded region determined by all the constraints.

Next, we need to find the corner points of the feasible region by finding the intersection points of the lines. In this case, the corner points are (6, 0), (4, 2), (0, 6), and (0, 0).

Now, we evaluate the objective function z = 15x₁ + 20x₂ at each corner point:

For (6, 0): z = 15(6) + 20(0) = 90

For (4, 2): z = 15(4) + 20(2) = 100

For (0, 6): z = 15(0) + 20(6) = 120

For (0, 0): z = 15(0) + 20(0) = 0

From the evaluations, we can see that the maximum value of z is 120, which occurs at the corner point (0, 6).

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Answer:

600 tulips

Step-by-step explanation:

The number of tulips used will be the number of tulips per vase multiplied by the number of vases. That's \(20*30=600\).

Answer:

600 tulips

Step-by-step explanation:

You have to multiply the number of vases by the number of tulips in each vase.

20 times 30 is equal to 600.

Answer:

-12x = -60

Step-by-step explanation:

-12x = -79+19

-12x = -60

Answer:

Step-by-step explanation:

HOW MUHPOINTS U GON GIVE ME?

Answer:

definatly fan, i do not know about the water heater if it blows air then i think its true  last 2 i would select

Step-by-step explanation:

Answer:

it's a fan cause a turbine is currently a fan

James will earn approximately $6,639.12 in interest after 10 years.

What is simple interest?

Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.

To solve this problem, we can use the formula for compound interest:

\(A = P(1 + r/n)^{(nt)}\)

where:

A is the final amount (including interest)

P is the principal amount (initial deposit)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the time (in years)

Plugging in the given values, we get:

\(A = 10000(1 + 0.055/2)^{(2*10)}\)

\(A = 10000(1.0275)^{20}\)

A = 10000(1.664)

A ≈ 16639.12

To find the amount of interest earned, we subtract the principal amount from the final amount:

Interest = A - P

Interest = 16639.12 - 10000

Interest ≈ 6639.12

Therefore, James will earn approximately $6,639.12 in interest after 10 years.

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Answer:

Δy = 9

Δx = -6

Slope = -3/2

Step-by-step explanation:

The slope formula is the change in y (Δy) over change in x (Δx).

Δy = \(y_2-y_1\)

Δx = \(x_2-x_1\)

We are given the points of (5,-3) and (-1,6).

\(m=\frac{6-(-3)}{-1-5}=\frac{9}{-6}=\boxed{-\frac{3}{2}}\)

The slope is -3/2.

Hope this helps.

A. The total differential of the utility function U(X,Y) = X^αY^β is dU = αX^(α-1)Y^β dX + βX^αY^(β-1) dY.

B. The total differential of the utility function U(X, Y) = X^2 + Y^3 + XY is dU = (2X + Y) dX + (3Y^2 + X) dY.

A. The total differential of a function represents the small change in the function caused by infinitesimally small changes in its variables. In this case, we are given the utility function U(X, Y) = X^αY^β, where α and β are constants.

To find the total differential, we differentiate the utility function partially with respect to X and Y, and multiply the derivatives by the differentials dX and dY, respectively.

For the partial derivative with respect to X, we treat Y as a constant and differentiate X^α with respect to X, which gives αX^(α-1). We then multiply it by the differential dX.

Similarly, for the partial derivative with respect to Y, we treat X as a constant and differentiate Y^β with respect to Y, resulting in βY^(β-1). We then multiply it by the differential dY.

Adding these two terms together, we obtain the total differential of the utility function:

dU = αX^(α-1)Y^β dX + βX^αY^(β-1) dY.

This expression represents how a small change in X (dX) and a small change in Y (dY) affect the utility U(X, Y).

B. To find the total differential of the utility function U(X, Y) = X^2 + Y^3 + XY, we differentiate each term of the function with respect to X and Y, and multiply the derivatives by the differentials dX and dY, respectively.

For the first term, X^2, we differentiate it with respect to X, resulting in 2X, which is then multiplied by dX. For the second term, Y^3, we differentiate it with respect to Y, resulting in 3Y^2, which is multiplied by dY. Finally, for the third term, XY, we differentiate it with respect to X and Y separately, resulting in X (multiplied by dY) and Y (multiplied by dX).

Adding these three terms together, we obtain the total differential of the utility function:

dU = (2X + Y) dX + (3Y^2 + X) dY.

This expression represents how a small change in X (dX) and a small change in Y (dY) affect the utility U(X, Y).

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Answer:

The slope: 2/5

The point is on the graph below

Step-by-step explanation:

y−4=2/5(x+3)

y - 4 = 2/5x + 3

y = 2/5x + 7

The equation is y = mx + b

m = the slope

m = 2/5

Answer:

\(point=(-3,4)\\\\slope=\frac{2}{5}\)

Step-by-step explanation:

\(y-y_0=m(x-x_0)\)

\(y_o:y-point\\x_o:x-point\\m=slope\)

\(y-4=\frac{2}{5}(x+3) \\\\y_0=4\\x_0=-3\\\\slope=\frac{2}{5}\)

Answer:

Horizontal, 0, y

Step-by-step explanation:

Answer:

the multiplacative inverse of ⅔ is 3/2 because when we multiply them both it returns 1

2/3 x 3/2 = 1

a) The mean for crimes against persons 47.

b) The standard deviation for crimes involving vandalism 307

c) The number of crimes according to the histogram for hate crimes against persons shows that 31 of the 50 states is 9

d)  The histogram for hate crimes involving vandalism shows that 31 of the 50 states had fewer than 10 crimes

a. To determine which histogram represents hate crimes against persons, we need to identify the distribution with a mean of 47. The histogram with a mean of 47 is likely to correspond to the hate crimes against persons since these types of crimes are typically less severe and may occur more frequently than crimes involving destruction of property.

b. Similarly, to determine which histogram represents hate crimes involving vandalism, we need to identify the distribution with a standard deviation of 307.

The histogram with a standard deviation of 307 is likely to correspond to hate crimes involving vandalism since these types of crimes are more severe and may vary widely in their degree of destruction.

c. To answer this question, we need to examine the histogram for hate crimes against persons and identify the bin that represents the number of reported crimes below the desired threshold

We are told that 31 of the 50 states had fewer than the desired threshold. This means that we need to find the bin that includes the 31st state when the states are arranged in ascending order of the reported hate crimes against persons.

d. We are told that 31 of the 50 states had fewer than the desired threshold, so we need to find the appropriate bin and determine the upper limit of the bin to find the maximum number of reported hate crimes below the threshold.

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Complete Question:

The number of reported hate crimes committed against persons, as well as the number of reported hate crimes involving destruction of property (such as vandalism), were recorded by the federal government for each of the 50 states in the year 2002, with results displayed in these histograms.

a. One of the distributions has a mean of 47 and the other has a mean of 177. Which is the mean for crimes against persons?

b. One of the distributions has a standard deviation of 78 and the other has a standard deviation of 307. Which is the standard deviation for crimes involving vandalism?

c. The histogram for hate crimes against persons shows that 31 of the 50 states had fewer than how many such crimes?

d. The histogram for hate crimes involving vandalism shows that 31 of the 50 states had fewer than how many such crimes?

Based on a critical value of 21.026, we would fail to reject the null hypothesis because it's greater than the absolute value of the test statistic (10.600).

A critical value can be defined as a measurement which is used to calculate the margin of error that exists in a data set. Mathematically, it is expressed as follows:

Critical value (p*) = 1 - (α/2)

Critical value (p*) = 1 - (0.05/2)

Critical value (p*) = 1 - 0.025

Critical value (p*) = 0.975.

Also, the degrees of freedom (df) is given by:

Degrees of freedom (df) = n - 1

Degrees of freedom (df) = 13 - 1

Degrees of freedom (df) = 12.

From the Chi-square distribution table, a critical value at t₀.₀₅, ₁₂ = 21.026.

Note: If the critical value (21.026) is lesser than the absolute value of the test statistic (10.600), then we would reject the null hypothesis.

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364

I hope it helps you ❤️❤️❤️

Here's a sample program in C++ that satisfies your requirements:

```
#include
using namespace std;

int main() {
 int num;
 cout << "Enter an integer between 0 and 35: ";
 cin >> num;

 if (num <= 9) {
   cout << num << endl;
 } else if (num >= 10 && num <= 35) {
   char letter = static_cast('A' + num - 10);
   cout << letter << endl;
 } else {
   cout << "Invalid input." << endl;
 }

 return 0;
}
```

- The program prompts the user to input an integer between 0 and 35 using the `cout` and `cin` statements.
- The `if` statement checks whether the number is less than or equal to 9. If it is, it outputs the number using the `cout` statement.
- The `else if` statement checks whether the number is between 10 and 35 (inclusive). If it is, it calculates the corresponding letter using the ASCII value for 'A' and the given number. The `static_cast` statement converts the calculated value to a character. Finally, the program outputs the letter using the `cout` statement.
- The `else` statement handles the case when the input is outside the range of 0 to 35. It outputs an error message using the `cout` statement.
- The program ends with the `return 0` statement.

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Answer:

Step-by-step explanation:

Here is the workings

2x+4y+6+2y-5+3x  combine like terms

2x+3x+4y+2y+6-5

Step 2

2x+3x+4y+2y+6-5   Add the similar exponents

5x+4y+2y+6-5

5x+6y+6-5

Step 3

5x+6y+6-5  Add and subtract

Your answer would be 5x+6y+1

Answer:

(d + 9)  ÷ 2

Step-by-step explanation:

because you have D witch is increased by 9 so D+9 then you have divided by 2 witch would make it (d + 9)  ÷ 2

The statement "When two events A and B are independent, the joint probability of the events can be found by multiplying the probabilities of the individual events" is true.

When two events A and B are independent, it means that the occurrence of one event does not affect the probability of the other event. In such cases, the joint probability of both events can be found by multiplying their individual probabilities. Mathematically, this can be expressed as P(A ∩ B) = P(A) * P(B). This rule holds true for independent events and is a fundamental concept in probability theory.

Now, let's examine the other statements:

1. The probability of the union of two events can exceed one:

This statement is false. The probability of an event is always between 0 and 1, inclusive. When you consider the union of two events, the probability of their combined occurrence cannot exceed 1. It is possible for the sum of the individual probabilities of the two events to exceed 1, but the probability of their union will never be greater than 1.

2. When events A and B are mutually exclusive, then P(A ∩ B) = P(A) + P(B):

This statement is false. Mutually exclusive events are events that cannot occur at the same time. If events A and B are mutually exclusive, their intersection (A ∩ B) will be an empty set, and therefore, the probability of their intersection is 0 (P(A ∩ B) = 0). The correct statement for mutually exclusive events is P(A ∪ B) = P(A) + P(B), where P(A ∪ B) represents the probability of the union of events A and B.

3. The union of events A and B consists of all outcomes in the sample space that are contained in both event A and B:

This statement is false. The union of events A and B, denoted as A ∪ B, consists of all outcomes that belong to either event A or event B or both. In other words, it includes all outcomes that are in A, in B, or in both A and B. The intersection of events A and B (A ∩ B) represents the outcomes that are contained in both A and B.

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Answer:

$113. 35

Step-by-step explanation:

first multiply 99.99 by 0.09 and then add that to 99.99

after that multiply 108.99 by 0.04 and you get 113.35