The drama club is selling tickets to their play to raise money for the show's expenses:

Each student ticket sells for $5 and each adult ticket sells for $7.50

The auditorium can hold no more than 75 people.

The drama club must make a minimum of $450 from ticket sales to cover the show's costs.

If x represents the number of student tickets sold and y represents the number of adult tickets sold, write and solve a system of inequalities graphically and determine one possible solution.

The correct answer is Wednesday, January 26, at 4 p.m when your subject-matter expert informs you that she believes it will take her 40 hours to finish the work.

Given that,

Your subject-matter expert informs you that she believes it will take her 40 hours to finish the work. The project begins on January 20 at 8 a.m. The staff only works throughout the weekdays, eight hours a day.

We have to find when will the assignment be completed.

We know that,

This simple table explains the answer

Thursday, January 20, at 4 p.m. - 8 hours worked

Friday, January 21, at 4 p.m. - 16 hours worked

Monday, January 24, at 4 p.m. - 24 hours worked

Tuesday, January 25, at 4 p.m. - 32 hours worked

Wednesday, January 26, at 4 p.m. - 40 hours worked

Therefore, The correct answer is Wednesday, January 26, at 4 p.m when your subject-matter expert informs you that she believes it will take her 40 hours to finish the work.

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The number of subs in the order is 8 or 9

Let's call the number of subs in the order "x".

Since the cost of 3 subs is $20, the cost per sub is $20 / 3 = $6.67.

And since the cost of 4 subs is $26, the cost per sub is $26 / 4 = $6.50.

So the cost per sub is between $6.50 and $6.67.

If the total cost is $56, then the cost per sub must be $56 / x.

So:

x = 56/6.5 or x = 56/6.67

Evalutate

x = 8.6 or x = 8.4

Approximate

x = 9 or 8

Hence, the subs is 8 to 9

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Answer:

D

Step-by-step explanation:

you have it right :)

The function with the coordinates (1, 8) and (0, 2) is \(f(x)=2\times(4)^x\). Therefore, option D is the correct answer.

Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).

From the given graph, the coordinate points are (1, 8) and (0, 2)

Using the formula \(y=a\times(b)^x\)

Where, a is x-intercept

Substitute, a=2 and (x, y)=(1, 8) in \(y=a\times(b)^x\), we get

\(8=2\times(b)^1\)

⇒ b=4

Substitute a=2 and b=4 in \(y=a\times(b)^x\), we get

\(y=2\times(4)^x\)

⇒ \(f(x)=2\times(4)^x\)

Therefore, the function for the given coordinates is \(f(x)=2\times(4)^x\).

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Answer:

when v increases w tends to increase

Step-by-step explanation:

the solution to the given system of linear equations using matrix inversion is x = 1.5 and y = -1.5.

To solve the given system of linear equations using matrix inversion, we can represent the system in matrix form as follows:

AX = B

where A is the coefficient matrix, X is the column matrix of variables (x and y), and B is the column matrix of constants.

The given system of equations is:

x + y = 4    ...(Equation 1)

x - y = 1    ...(Equation 2)

In matrix form, this becomes:

⎡ 1  1 ⎤   ⎡ x ⎤   ⎡ 4 ⎤

⎢      ⎥ * ⎢   ⎥ = ⎢   ⎥

⎣ 1 -1 ⎦   ⎣ y ⎦   ⎣ 1 ⎦

To find the solution, we need to calculate the inverse of the coefficient matrix A and multiply it by the constant matrix B. The solution is given by:

X = A^(-1) * B

To proceed, let's find the inverse of matrix A:

A = ⎡ 1  1 ⎤

     ⎣ 1 -1 ⎦

To find the inverse of A, we can use the formula for a 2x2 matrix:

A^(-1) = (1/det(A)) * adj(A)

where det(A) is the determinant of A and adj(A) is the adjugate of A.

Calculating the determinant of A:

det(A) = (1*(-1)) - (1*1) = -1 - 1 = -2

Now, let's find the adjugate of A:

adj(A) = ⎡ -1  1 ⎤

             ⎣  1  1 ⎦

Using these values, we can find the inverse of A:

A^(-1) = (1/det(A)) * adj(A) = (1/-2) * ⎡ -1  1 ⎤ = ⎡ 1/2  -1/2 ⎤

                                                                     ⎣ -1/2 1/2 ⎦

Next, we multiply A^(-1) with the constant matrix B:

⎡ 1/2  -1/2 ⎤   ⎡ 4 ⎤   ⎡ (1/2)*4 + (-1/2)*1 ⎤   ⎡ 2 - 1/2 ⎤

⎢           ⎥ * ⎢  ⎥ = ⎢                   ⎥ = ⎢         ⎥

⎣ -1/2 1/2  ⎦   ⎣ 1 ⎦   ⎣ (-1/2)*4 + (1/2)*1 ⎦   ⎣ -2 + 1/2 ⎦

Calculating the resulting values:

X = ⎡ 2 - 1/2 ⎤ = ⎡ 3/2 ⎤ = ⎡ 1.5 ⎤

   ⎣ -2 + 1/2 ⎦   ⎣ -3/2 ⎦   ⎣ -1.5 ⎦

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Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

cosa = \(\frac{1}{seca}\) , sina = \(\frac{1}{coseca}\) , sin²a + cos²a = 1

Consider the left side

\(\frac{1}{sec^2a}\) + \(\frac{1}{cosec^2a}\)

= cos²a + sin²a

= 1 = right side ⇒ verified

Answer: The one on the left.

Step-by-step explanation:

There is no file, but the panda on the left is bigger.

Number of students need to be sampled = 610

A study to determine the true average number of alcoholic drinks consumed by Greek students is conducted.

Standard Deviation, σ = 6.3

Margin Error of population mean, E = 0.5

Probability = 95% = 0.95

The p-value corresponding to 0.95 probability = (1+0.95)/2 = 0.975

The z-score corresponding to this p-value = 1.96 [from the z-tables]

Now, The margin error, E = zσ/√n, where n is the sample size

⇒ n = (zσ/E)²

⇒ n = (1.96 x 6.3/0.5)²

⇒ n ≈ 610

Hence 610 students need to be sampled.

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Answer:

Irrational

Step-by-step explanation:

root of 5 = 2.23606797749978969640917366873127623544061835961152572427089…

This number never ends. Another term for it would be a recurring decimal, but it is not exact. Anyway, the square root of 5 is irrational since it is not defined to stop. Even if it was rounded, it would not be exact.

Hope this Helps.

To calculate Mark and Diane's property tax, we need to first convert the millage rate to a decimal. To do this, we divide the millage rate by 1,000, so 43.7 mills becomes 0.0437.

We then multiply this decimal by the assessed value of their home, which is $74,000.

0.0437 x $74,000 = $3,233.80

Therefore, Mark and Diane's property tax is $3,233.80. It's important to note that the millage rate can vary depending on the location and local tax laws, and the assessed value of the property may also change over time due to changes in the real estate market or improvements made to the home. Property tax is used to fund local government services, such as schools, roads, and public safety.

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The point (1, 1) does not satisfy the given inequality system.

Given is the inequality system as -

y < 2x - 1

y > x - 1

Refer to the graph of the inequalities attached. The points in the shaded region represents the solution coordinates for the given system of equations. The point (1, 1) lies on the dotted line. So, this does not satisfy the given inequality system.

Therefore, the point (1, 1) does not satisfy the given inequality system.

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We have to form differential equations that represent various families of curves. We need to find the differential equations and to eliminate arbitrary constants from given equations to form differential equations.

1. To form the differential equation representing the family of curves y = A cos(mx + B), we need to differentiate both sides with respect to x. Taking the derivative, we get -A m sin(mx + B) = y'. Therefore, the differential equation is y' = -A m sin(mx + B).

2. For the equation y = Cx + D, the differential equation can be found by taking the derivative of both sides. Differentiating y = Cx + D with respect to x gives us y' = C. Therefore, the differential equation is y' = C.

3. To form the differential equation representing the family of curves y = Ae^(-3x) + Be^(sx), where A and B are constants, we differentiate both sides with respect to x. Taking the derivative, we get \(y' = -3Ae^{(-3x)} + Bse^{(sx)\). Thus, the differential equation is \(y' = -3Ae^{-3x} + Bse^{sx}\).

4. For the equation y = A sin(5x) + B cos(5x), where A and B are constants, we differentiate both sides. The derivative of y with respect to x gives us y' = 5A cos(5x) - 5B sin(5x). Hence, the differential equation is y' = 5A cos(5x) - 5B sin(5x).

5. To form the differential equation representing the family of curves \(y^2 - 2ay + x^2 = a^2\), where a is a constant, we differentiate both sides. Taking the derivative, we obtain 2yy' - 2ay' + 2x = 0. Rearranging, we get y' = (a - y)/(x). Therefore, the differential equation is y' = (a - y)/(x).

6. The given equation is \(y^2 = Ax + 3x^2 - A^2.\) To eliminate the arbitrary constant A, we differentiate both sides with respect to x. Taking the derivative, we get 2yy' = A + 6x - 0. Simplifying, we have yy' = 6x - A. This is the differential equation formed by eliminating the arbitrary constant A from the given equation.

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The -value of the test is 1.90. This indicates that the mean processing time is significantly greater than 5.5 hours, supporting the manufacturer's desire to set a standard time required by employees to complete a certain process

The t-value will be equal to 1.39 for the given statistics.

To test if the mean processing time exceeds 5.5 hours, we can use a one-sample t-test.

The null hypothesis is that the mean processing time is less than or equal to 5.5 hours:

H0: µ ≤ 5.5

The alternative hypothesis is that the mean processing time is greater than 5.5 hours:

Ha: µ > 5.5

We will use a significance level of 0.05.

The formula for the t-test statistic is:

t = (X - µ) / (s / √n)

Where:

X = sample mean

µ = hypothesized population mean

s = sample standard deviation

n = sample size

Substituting the given values, we get:

t = (6 - 5.5) / (2 / √21) = 1.386

The degree of freedom for the t-test is n-1 = 20.

Using a t-table or calculator, the p-value associated with a t-value of 1.386 and 20 degrees of freedom is 0.093.

Since the p-value (0.093) is greater than the significance level (0.05), we fail to reject the null hypothesis. Therefore, there is not enough evidence to suggest that the mean processing time exceeds 5.5 hours.

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Using the slope formula, it is found that the value of j is 12.

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line. The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given;

A line with a slope of -1/10 passes through the points (-2,6) and (j,5).

Now,

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

-1/10= 5-6/j+2

-1/10= -1/j+2

10=j+2

j=12

Therefore, by the given slope j will be 12.

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s + p <= 50

2s + 5p >= 100

The inequality for the number of tickets they can sell is:

s + p <= 50

Where s represents the number of student tickets and p represents the number of parent tickets. This inequality shows that the total number of tickets sold cannot exceed 50.

The inequality for the amount of money they need to earn is:

2s + 5p >= 100

Where s represents the number of student tickets and p represents the number of parent tickets. This inequality shows that the total amount of money earned from selling tickets must be at least $100.

The left side of the inequality represents the total amount of money earned from selling student tickets (2s) and parent tickets (5p). The right side of the inequality represents the minimum amount of money they need to earn ($100).

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Answer:

Sonya would need to serve 1500 meals

Step-by-step explanation:

425=15%(x)+200 or 425=.15(x)+200

solve for x

425=.15x+200 distribute

subtract 200 from both sides

225=.15x

divide both sides by .15 to isolate x

1500=x or x=1500

Given statement solution is :- a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

Set A: {apple, banana}, Set B: {cat, dog}

Power set of A: {{}, {apple}, {banana}, {apple, banana}}

Power set of B: {{}, {cat}, {dog}, {cat, dog}}

Set A: {red, blue}, Set B: {circle, square}

Power set of A: {{}, {red}, {blue}, {red, blue}}

Power set of B: {{}, {circle}, {square}, {circle, square}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

Set A: {apple, banana, orange}, Set B: {cat, dog, elephant}

Power set of A: {{}, {apple}, {banana}, {orange}, {apple, banana}, {apple, orange}, {banana, orange}, {apple, banana, orange}}

Power set of B: {{}, {cat}, {dog}, {elephant}, {cat, dog}, {cat, elephant}, {dog, elephant}, {cat, dog, elephant}}

Set A: {red, blue, green}, Set B: {circle, square, triangle}

Power set of A: {{}, {red}, {blue}, {green}, {red, blue}, {red, green}, {blue, green}, {red, blue, green}}

Power set of B: {{}, {circle}, {square}, {triangle}, {circle, square}, {circle, triangle}, {square, triangle}, {circle, square, triangle}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

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(a) Mean = (9 + 15 + 18 + 11 + 12) / 5 = 65 / 5 = 13

(b) Mean of the sample = (9 + 15) / 2 = 24 / 2 = 12

(c) The means of the samples vary, but they tend to be close to the population mean of 13.

(d) Since the problem does not provide the values for the 25 x values, we cannot construct a density histogram or determine if most of the values are near the population mean.

(a) The mean of the population is calculated by summing all the values and dividing by the total number of values:

Mean = (9 + 15 + 18 + 11 + 12) / 5 = 65 / 5 = 13

(b) To calculate the mean for a random sample of size 2, we randomly select two values from the population and calculate their mean:

Random sample: 9, 15

Mean of the sample = (9 + 15) / 2 = 24 / 2 = 12

(c) Repeatedly selecting random samples of size 2 and calculating the mean for each sample:

Here are the means for 25 random samples of size 2 (selected without replacement):

Sample 1: 9, 18 -> Mean = (9 + 18) / 2 = 27 / 2 = 13.5

Sample 2: 11, 9 -> Mean = (11 + 9) / 2 = 20 / 2 = 10

Sample 3: 15, 12 -> Mean = (15 + 12) / 2 = 27 / 2 = 13.5

...

Sample 25: 12, 15 -> Mean = (12 + 15) / 2 = 27 / 2 = 13.5

The means of the samples vary, but they tend to be close to the population mean of 13.

(d) Constructing a density histogram using the 25 x values:

Since the problem does not provide the values for the 25 x values, we cannot construct a density histogram or determine if most of the values are near the population mean.

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Answer:

m = 903

Step-by-step explanation:

99+m=1002

Subtract 99 from both sides.

m=1002−99

Subtract 99 from 1002 to get 903.

m=903

Answer:

M=903 pls mark brainliest(little crown)

Step-by-step explanation:

Subtract 99 from both sides.

m=1002−99

Subtract 99 from 1002 to get 903.

m=903

Answer:

K is -1 12/55

Step-by-step explanation:

You take 3 2/11 minus 4 2/5 to get -1 12/55. If you want to make sure, you add 4 2/5 and -1 12/55. The answer will be 3 2/11

Answer:

33.82

Step-by-step explanation:

8.9 x 3.8 would be 33.82

make brainliest if u want

Hope this helped :)

The net annual percentage growth rate of the city population is 0.4%

To calculate the net annual percentage growth rate of a population, we can use the following formula:

Net Annual Percentage Growth Rate = ((Births + Immigrants) - (Deaths + Emigrants)) / Initial Population x 100%

Plugging in the given values, we get:

Net Annual Percentage Growth Rate =\(((100 + 10) - (40 + 30)) / 10,000 x 100%\)

Net Annual Percentage Growth Rate = \((40 / 10,000) x 100%\)

Net Annual Percentage Growth Rate =\(0.4%\)

The net annual percentage growth rate of the city population is 0.4%

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Answer:

3/2

Step-by-step explanation:

Slope formula

\( \frac{ - 14 - - 2}{ - 15 - - 7} \\ \frac{ - 14 + 2}{ - 15 + 7} \\ \frac{ - 12}{ - 8} \\ \frac{3}{2} \)

The slope of the line is 3/2 which passes through the points (-7,-2) and (-15, -14) the answer is 3/2.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\)

It is given that:

The slope of the line that passes through the points (-7,-2) and (-15, -14):

Using the slope formula:

\(\rm m =\dfrac{-14-(-2)}{-15-(-7)}\)

m = -12/(-8)

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

m = 12/8

m = 3/2

Thus, the slope of the line is 3/2 which passes through the points (-7,-2) and (-15, -14) the answer is 3/2.

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Answer:

I think Quadrant 1. I;m not trying to just answer for the points

Step-by-step explanation:

Answer: 6 inches

Step-by-step explanation:

2 inches = 35 miles, so, 105 divided by 35 which is three, then 3 x 2  = 6

you're welcome

The required answers are:

1. Level of significance of hypothesis testing: 0.01

2. Area of the sampling distribution corresponding to the P-value: The area of the sampling distribution is to the left of −2.463 and to the right of 2.463.

1. State the hypotheses:

Null hypothesis (H0): The dividend yield of all Australian bank stocks is not higher than 7.5%.

Alternative hypothesis (H1): The dividend yield of all Australian bank stocks is higher than 7.5%.

Set the significance level:

α = 0.01

Calculate the test statistic:

Since the population standard deviation (σ) is known and the sample size is small (n = 19), we can use a z-test.

Calculate the z-score using the formula: \(z = (x^- - \mu) / (\sigma / \sqrt n)\), 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, \(x^-\) = 6.33%, μ = 7.5%, σ = 2.0%, and n = 19.

Compute the z-score.

Determine the critical value:

Since the alternative hypothesis is one-tailed (we are testing for "greater than"), we need to find the critical value corresponding to a significance level of α = 0.01 from the standard normal distribution.

Find the z-value that corresponds to a cumulative probability of 1 - α = 0.99.

Compare the test statistic with the critical value:

If the test statistic (z-score) is greater than the critical value, we reject the null hypothesis.

If the test statistic is less than or equal to the critical value, we fail to reject the null hypothesis.

Therefore,

If we reject the null hypothesis, it indicates that the dividend yield of all Australian bank stocks is higher than 7.5% with a significance level of 0.01.

If we fail to reject the null hypothesis, there is not enough evidence to conclude that the dividend yield is higher than 7.5%.

2. State the hypotheses:

Null hypothesis (H0): The hay fever rate in the age group over 50 is not lower than the hay fever rate in the age group under 25.

Alternative hypothesis (H1): The hay fever rate in the age group over 50 is lower than the hay fever rate in the age group under 25.

Set the significance level:

α = 0.05

Calculate the test statistic:

Since the sample sizes are small and the standard deviation is unknown, we can use the t-test.

Calculate the t-score using the formula:

\(t = (x^-_1- x^-_2) / \sqrt{(s_1^2 / n_1) + (s_2^2 / n_2)}\),

where \(x^-_1\) and \(x^-_2\) are the sample means,\(s_1\)and \(s_2\) are the sample standard deviations, and \(n_1 , n_2\) are the sample sizes.

In this case, we have \(x^-_1, x^-_2, s_1, s_2, n_1, n_2\) values.

Determine the critical value:

Since the alternative hypothesis is one-tailed (we are testing for "lower than"), we need to find the critical value corresponding to a significance level of α = 0.05 from the t-distribution.

Find the t-value that corresponds to a cumulative probability of α = 0.05 with the appropriate degrees of freedom.

Compare the test statistic with the critical value:

If the test statistic (t-score) is less than the critical value, we reject the null hypothesis.

If the test statistic is greater than or equal to the critical value, we fail to reject the null hypothesis.

Therefore,

If we reject the null hypothesis, it indicates that the age group over 50 has a lower hay fever rate than the age group under 25 with a significance level of 0.05.

If we fail to reject the null hypothesis, there is not enough evidence to conclude that the age group over 50 has a lower hay fever rate.

Note: The step-by-step explanation provided above assumes you are familiar with hypothesis testing concepts and the appropriate test statistic selection based on the given information.

Therefore, the required answers are:

1. Level of significance of hypothesis testing: 0.01

2. Area of the sampling distribution corresponding to the P-value: The area of the sampling distribution is to the left of −2.463 and to the right of 2.463.

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Answer:

72 \(ft^{2}\)

Step-by-step explanation:

a = 1/2(24)(6)

a = 72