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One wall in Mr. Parker’s attic is shaped like a trapezoid. He wants to cover the wall with insulation that is sold by the square foot. How many square feet of insulation will he need to cover the wall if it measures 14 feet wide at the top, 36 feet wide at the bottom, and has a height of 8 feet?



200 ft2



400 ft2



504 ft2



654 ft2

Answer:

2 squared - 7 + -4

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

Answer:

Step-by-step explanation:I found the answer on this web\(^{}\)site. It seems correct! Link Below!ly/3fcEdSx

bit.\(^{}\)

Answer:

800

Step-by-step explanation:

Answer:

≈ 11.78 in

Step-by-step explanation:

The arc length is calculated as

arc = circumference of circle × fraction of circle

     = 2πr × \(\frac{\frac{\pi }{4} }{2\pi }\) ( cancel 2π on numerator/ denominator )

     = 15 × \(\frac{\pi }{4}\)

     = \(\frac{15\pi }{4}\)

     ≈ 11.78 in ( to 2 dec. places )

In this case, the preferred alternative is Alternative 1, since it has a present value of $60,623.

An investment is the use of money to buy assets or take part in activities with the expectation of a financial gain or other benefit in the future. It can take many forms, such as purchasing shares, bonds, mutual funds, real estate, artwork, or antiques.

The present value of an investment can be calculated by taking the amount of the future cash flow and discounting it by an appropriate rate of return. In this case, the appropriate rate of return is 15%. The present value of Alternative 1 can be calculated by taking the total cash flows of $105,000 and discounting them by 15%:

Present Value of Alternative 1 = $105,000 / (1 + 0.15)3 + (1 + 0.15)7 = $60,623

The present value of Alternative 2 can be calculated in the same manner:

Present Value of Alternative 2 = $8,000 / (1 + 0.15)7 = $4,923

The discounted cash flow criterion states that the preferred alternative is the one with the higher present value. Therefore, in this case, the preferred alternative is Alternative 1, since it has a present value of $60,623 compared to the present value of Alternative 2, which is $4,923.

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The Coalition for Airline Passengers Rights, Health, and Safety averages 400 calls a day to help stranded travelers deal with airlines. The hotline is staffed for 16 hours a day.

To calculate the average number of calls in different time intervals and the probability of different events related to these calls.

Part 1:

a. 60-minute interval average number of calls: 400/16 = 25 calls

30-minute interval average number of calls: 25/2 = 12.5 calls

15-minute interval average number of calls: 12.5/2 = 6.25 calls

Part 2:

b. To find the probability of exactly 6 calls in a 15-minute interval, we can use the Poisson distribution formula. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of exactly 6 calls in a 15-minute interval is:

P(6 calls) = (e^-6.25)*(6.25^6)/6! = 0.0686

c. To find the probability of no calls in a 15-minute interval, we can use the Poisson distribution formula. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of no calls in a 15-minute interval is:

P(0 calls) = e^-6.25 = 0.0047

d. To find the probability of at least two calls in a 15-minute interval, we can use the cumulative distribution function of the Poisson distribution. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of at least two calls in a 15-minute interval is:

P(X >= 2) = 1 - P(0 calls) - P(1 call) = 1 - 0.0047 - (e^-6.25)*(6.25^1)/1! = 0.9906

Thus, the average number of calls in a 60-minute interval is 25, in a 30-minute interval is 12.5, and in a 15-minute interval is 6.25. The probability of exactly 6 calls in a 15-minute interval is 0.0686, the probability of no calls in a 15-minute interval is 0.0047, and the probability of at least two calls in a 15-minute interval is 0.9906.

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Answer:

THE ANSWER IS 81/16 OR C

Answer:

The number of positive solutions to this equation is one

Step-by-step explanation:

The number of solutions of a given quadratic equation is determine by the discriminant.

Answer: 5/2

Step-by-step explanation:

slope equation: (y2-y1)/(x2-x1)

13-3/5-1 = 10/4 or 5/2

Answer:

2.5

Step-by-step explanation:

Gradient (slope) =

\(m = \frac{y2 - y1}{x2 - x1} = \frac{13 - 3}{5 - 1} = \frac{10}{4} = 2 \frac{1}{2} \)

Answer:

60

Step-by-step explanation:

The dividends per share for preferred stock for each year are: Year 1 - $1.25, Year 2 - $2.25, Year 3 - $3.25. The dividends per share for common stock for each year are all $0.

To determine the dividends per share for preferred and common stock for each year, we need to divide the total dividends by the number of shares for each type of stock.

Preferred Stock:

Dividends per share of preferred stock = Total dividends for preferred stock / Number of preferred shares

Year 1:

Dividends per share of preferred stock for Year 1 = $50,000 / 40,000 shares = $1.25

Year 2:

Dividends per share of preferred stock for Year 2 = $90,000 / 40,000 shares = $2.25

Year 3:

Dividends per share of preferred stock for Year 3 = $130,000 / 40,000 shares = $3.25

Common Stock:

Dividends per share of common stock = Total dividends for common stock / Number of common shares

Year 1:

Dividends per share of common stock for Year 1 = ($50,000 - Total dividends for preferred stock) / 100,000 shares = ($50,000 - $50,000) / 100,000 shares = $0

Year 2:

Dividends per share of common stock for Year 2 = ($90,000 - Total dividends for preferred stock) / 100,000 shares = ($90,000 - $90,000) / 100,000 shares = $0

Year 3:

Dividends per share of common stock for Year 3 = ($130,000 - Total dividends for preferred stock) / 100,000 shares = ($130,000 - $130,000) / 100,000 shares = $0

The dividends per share for preferred stock for each year are: Year 1 - $1.25, Year 2 - $2.25, Year 3 - $3.25. The dividends per share for common stock for each year are all $0.

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Answer:

sorry

Step-by-step explanation:

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a. The x-coordinate of the vertex (2) represents the time it takes for the ball to reach its maximum height, and the y-coordinate (182) represents the maximum height itself.

b. The tennis ball is initially at a height of 126 feet above the ground.

a. The x-coordinate of the vertex is 2. To find the y-coordinate, we substitute this value back into the equation:

h(2) = -14(2)² + 56(2) + 126

h(2) = -14(4) + 112 + 126

h(2) = -56 + 112 + 126

h(2) = 182

Therefore, the vertex of the equation is (2, 182). In this context, the vertex represents the highest point reached by the tennis ball during its trajectory. The x-coordinate of the vertex (2) represents the time it takes for the ball to reach its maximum height, and the y-coordinate (182) represents the maximum height itself.

b. In order to find the y-intercept, we set t equal to zero and evaluate h(t):

h(0) = -14(0)² + 56(0) + 126

h(0) = 126

The y-intercept is 126. In this context, the y-intercept represents the initial height of the ball when it is thrown. Therefore, the tennis ball is initially at a height of 126 feet above the ground.

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Step-by-step explanation:

A drought is an event of prolonged shortages in the water supply, whether atmospheric, surface water or ground water. A drought can last for months or years, or may be declared after as few as 15 days.

Answer:

B. They are not parallel because their slopes are not equal.

Step-by-step explanation:

Find the slope of the line that runs through points (6, 3) and (-1, 5):

\( slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 3}{-1 - 6} \)

\( slope (m) = \frac{2}{-7} = -\frac{2}{7} \)

Since the slope of the line that passes through points (6, 3) and (-1, 5) is not the same with line that has a slope of ¾, therefore, both lines cannot be parallel.

The answer is "B. They are not parallel because their slopes are not equal."

If Gavin contributes towards a Pension fund (7,5% of his Basic Salary), then his net salary will be reduced by the amount he contributed towards pension fund i.e. R652.5.

1.1 Name of employee is Gavin Pillay. 1.2 UIF stands for Unemployment Insurance Fund. UIF is a benefit to provide short-term relief to workers who lose their jobs, or can't work due to illness, maternity or adoption leave. 1.3 The UIF paid by Gavin is calculated correctly.

Firstly, we need to calculate Gross Salary of Gavin, which is given as: Basic Salary + Overtime + M = R8700 + R1200 + R3201 = R13101Then, calculate total deductions from gross salary.

Total Deductions = PAYE + UIF = R1200 + 87 = R1287Hence, Gavin's net salary = Gross salary - Total Deductions = R13101 - R1287 = R11814Therefore, UIF paid by Gavin is calculated correctly as R87.1.4 This payslip is for the month of May i.e.

31/05/2023.1.5 Basic salary of Gavin = R8700. Deduct 7.5% of his basic salary to calculate his pension fund contribution. Pension Fund Contribution = 7.5/100 x R8700 = R652.5.1.6

Total deductions of Gavin includes PAYE, UIF and pension fund contribution.

Therefore, Total Deductions = PAYE + UIF + Pension Fund Contribution = R1200 + R87 + R652.5 = R1939.5.1.7

Gavin's age can not be determined as his date of birth is not provided.1.8 Address of Gavin's workplace is 21 Halsted Road, Pietermaritzburg?

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Answer:

Step-by-step explanation:

its c

Answer:

vertex point is (4,-6)

and it opens upwards as the coefficient of x is positive.

I assume B is the correct answer, good luck!

Option A correctly describes the area of the graph of the function.

How is an area of the graph calculated?

The area of a graph is the area under the function curve enclosed within the X-axis of the graph. Thus, it is the area of the figure formed by enclosing the function graph with the X-axis.

It is the integration of the function polynomial of the possible values of x that the function curve lies in.

Here the function equation is : \(f(x) = ( 25 - x^{2} )\)

From the figure, we can see that the value of x varies from -5 to 5.

Initial x-value of integration = minimum value of x

                                          = -5

Final x-value of integration = maximum value of x

                                          = 5

Thus, the area of the graph can be correctly calculated as. :

               \(Area = \int\limits^{maxX}_ {minX} \, f(x)dx\)

               \(Area = \int\limits^5_ {-5} \, (25-x^{2} )dx\)

Hence, Option A correctly calculates the area of the graph given.

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Answer:

\(15 \times 2.205 = 33.0693 \: lb\)

Unit conversion is a way of converting some common units into another without changing their real value. The Weight of Jackson's backpack is 33.075 pounds.

Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimetre is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.

Since 1 kg is equal to 2.205 pounds. Therefore, the Weight of Jackson's backpack is,

15 kg = 2.205 × 15 kg = 33.075 pounds

Hence, the Weight of Jackson's backpack is 33.075 pounds.

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Answer:

If the width of the compass changed, it would make the arc smaller or larger. This would then make the line segment to be drawn smaller or larger, so it would not match the original.

Step-by-step explanation:

We assume your construction is trying to copy the length of a line segment. That length is "measured" by the width of the compass. If it is changed, it no longer matches the length of the segment you're trying to copy, so you will not get the copy you want.

Answer:

Let's assume the original price of the stock was x.

When the company announced it overestimated demand, the stock price fell by 40%.

So, the new price of the stock after the first decline was:

x - 0.4x = 0.6x

A few weeks later, when the seats were recalled, the stock price fell again by 60% from the new lower price of 0.6x.

So, the new price of the stock after the second decline was:

0.6x - 0.6(0.6x) = 0.24x

Given that the current stock price is $2.40, we can set up the equation:

0.24x = 2.40

Solving for x, we get:

x = 10

Therefore, the stock was originally selling for $10.

The length of the zip wire, with a 10-degree angle to the horizontal and a distance of 25 meters between the posts, is approximately 25.35 meters.

To calculate the length of the zip wire, we can use trigonometry. Let's consider the triangle formed by the zip wire, where the horizontal distance between the two posts is 25 meters and the angle between the zip wire and the horizontal is 10 degrees.

Using trigonometric functions, we can determine the length of the zip wire. In this case, we'll use the sine function because we have the opposite side (the vertical distance) and we want to find the hypotenuse (the length of the zip wire).

The formula for sine is:

sin(angle) = opposite / hypotenuse

Rearranging the formula, we have:

hypotenuse = opposite / sin(angle)

In this case, the opposite side is the vertical distance, which is h.

So, the formula becomes:

hypotenuse = h / sin(angle)

To find h, we can use the formula for the length of the zip wire:

h = 25 * tan(angle)

Substituting this into the previous formula, we get:

hypotenuse = (25 * tan(angle)) / sin(angle)

Calculating the value, we have:

hypotenuse = (25 * tan(10°)) / sin(10°)

Using a calculator, we find:

tan(10°) ≈ 0.1763

sin(10°) ≈ 0.1736

Substituting these values, we can calculate the length of the zip wire:

hypotenuse ≈ (25 * 0.1763) / 0.1736 ≈ 25.35 meters

Therefore, the length of the zip wire is approximately 25.35 meters.

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Answer:

LCM=18 and GCF = 3

Step-by-step explanation:

Multiples of 9: 9, 18, 27

Multiples of 6: 6, 12, 18

LCM = 18

Factors of 9: 1, 3, 9

Factors of 6: 1, 2, 3, 6

GCF = 3

Answer:

10^-5

Step-by-step explanation:

it is correct on plato

The sound intensity on the busy street is\(\(10^{-5}\) watts/meter^2\)

hus, option (a) is correct.

To find the sound intensity (I) on the busy street, rearrange the given formula:

\(\[ ? = 10 \log\left(\frac{I}{I_0}\right) \]\)

Given:

Sound level on the busy street ( ? ) = 70 dB

\(I_0 = 10^{-12} watts/meter^2\)

Let's plug in the given values and solve for I:

\(\[ 70 = 10 \log\left(\frac{I}{10^{-12}}\right) \]\)

To isolate the logarithm, divide both sides by 10:

\(\[ 7 = \log\left(\frac{I}{10^{-12}}\right) \]\)

Now, rewrite the equation in exponential form:

\(\[ 10^7 = \frac{I}{10^{-12}} \]\)

\(\[ 10^7 = I \cdot 10^{12} \]\)

Now, solve for I:

\(\[ I = \frac{10^7}{10^{12}} \]\)

Since dividing by a power with the same base is equivalent to subtracting the exponents:

\(\[ I = 10^{7-12} \]\)

\(\[ I = 10^{-5} \]\)

Therefore, the sound intensity is \(\(10^{-5}\) watts/meter^2\)

Thus, option (a) is correct.

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Answer:

C

Step-by-step explanation: