Write the first four terms of each arithmetic sequence. first term 7 and common difference 15

The circumference of a child swimming pool is 6π.

What is circumference?

The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter.

Here, we have

Given: A child swimming pool that has a radius of 3 feet.

We have to find the circumference.

The circumference is diameter x π

The diameter is twice the radius

c = 2πr

c = 2π(3)

= 6π

Hence, the circumference of a child swimming pool is 6π.

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Answer:

Jamie gets £9.60

Step-by-step explanation:

sum the parts of the ratio, 2 + 3 = 5 parts

divide the amount by 5 to find the value of one part of the ratio.

£24 ÷ 5 = £4.80 ← value of 1 part of the ratio , then

2 parts = 2 × £4.80 = £9.60 ← amount Jamie gets

We can set up a proportion using the given ratio:

Weight on Earth : Weight on Planet X = 5 : 12

Let's let x be the weight of the elephant on Planet X. We can substitute the given weight on Earth to solve for x:

3800 : x = 5 : 12

We can cross-multiply to get:

3800 * 12 = 5 * x

Simplifying the right side, we get:

45600 = x * 5

Dividing both sides by 5, we get:

x = 9120

Therefore, the weight of the elephant on Planet X is 9120 pounds.

Answer:

45%

Step-by-step explanation:

72/160 = 0.45

0.45 x 100 = 45%

The given formula 9x - 5y = -160 is not in the form of direct variation.

The given formula 9x - 5y = -160 relates the temperature in degrees Fahrenheit y to the temperature in degrees Celsius x.

To determine whether the relationship is a direct variation or not, we need to consider the definition of direct variation.

A relationship is said to be a direct variation if one variable is a constant multiple of the other variable, i.e., y = kx or x = ky, where k is a constant of proportionality.

However, the given formula is not in the form of direct variation. It is a linear equation in two variables, and there is no constant of proportionality present.

Hence, we can conclude that the given relationship is not a direct variation.

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The resale value of the car after 3 years is $9,984.

Since the resale value decreases by 20%. Thus, the resale value of the car will be 80% of its original value.

After the first year, the resale value of the car will be 80% of its original value:

Resale value after 1 year = 80/100 * $19,500 = $15,600

After the second year, the resale value of the car will be 80% of its value after the first year:

Resale value after 2 years = 80/100 * $15,600 = $12,480

After the third year, the resale value of the car will be 80% of its value after the second year:

Resale value after 3 years = 80/100 * $12,480 = $9,984

Therefore, the resale value of the car after 3 years will be $9,984.

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We can expect 4 of the next 20 pastries served to be bran muffins based on the given data.

What is meant by the term data?

Data refers to a collection of facts, statistics, measurements, or observations that are gathered and analyzed to gain insights or information about a particular topic or subject. Data can be both quantitative (numerical) and qualitative (descriptive) in nature, and it can be obtained from various sources, such as surveys, experiments, sensors, or records. The processing and interpretation of data can lead to new discoveries, trends, or predictions in various fields, including science, business, and technology.

According to the given information

The proportion of bran muffins out of the total pastries served can be calculated by dividing the number of bran muffins by the total number of pastries:

The proportion of bran muffins = 2 / (1 + 3 + 2 + 2 + 2) = 2 / 10 = 0.2

This means that 20% of the pastries served are bran muffins. To find out how many of the next 20 pastries served should be expected to be bran muffins, we can multiply 20% by 20:

The number of expected bran muffins = 0.2 * 20 = 4

Therefore, we can expect 4 of the next 20 pastries served to be bran muffins based on the given data.

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None of the answer choices would result in an x-value being associated with two different y-values, the correct answer is:

e. None of the above.

what is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.

To check whether the relation is functional, we need to make sure that each x-value is associated with only one y-value.

We can see that the pairs (6,7), (-2,9), (8,8), and (-4,9) all have different x-values, and therefore are associated with different y-values. This means that the relation is currently functional.

To determine which ordered pair could not be substituted so that the relation is functional, we need to find an x-value that is associated with two different y-values.

Let's look at each of the answer choices and see if they fit this criteria:

a. (9,9): This pair does not already appear in the relation, so it's possible that it could be added without affecting the functionality of the relation.

b. (2,9): This pair does not already appear in the relation, so it's possible that it could be added without affecting the functionality of the relation.

c. (7,8): This pair does not already appear in the relation, so it's possible that it could be added without affecting the functionality of the relation.

d. (8,3): This pair does not already appear in the relation, so it's possible that it could be added without affecting the functionality of the relation.

Since none of the answer choices would result in an x-value being associated with two different y-values, the correct answer is:

e. None of the above.

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Answer:

D. 177 ft²

Step-by-step explanation:

the area of a circle is

pi×r²

r is the radius which is half of the diameter, of course.

so, in our case

area = pi×(15/2)² = pi×7.5² = pi×56.25 =

= 176.7145868... ft² ≈ 177 ft²

Here we have an exponential growth were the increase is of 26%, and it can be written as.

[tex]y = a*(1 + 0.26)^t[/tex]

Here we want to rewrite the function

[tex]y = a*(2)^{t/3}[/tex]

In the given form for the general exponential, so let's do that.

We can expand the product to get:

[tex]y = a*(2)^{t/3}\\\\y = a*((2)^{1/3})^t\\\\y = a*(1.26)^t\\\\y = a*(1 + 0.26)^t[/tex]

To identify if it is a growth or a decay we need to see the sign of r (the thing we are adding to the 1) in this case is +0.26

When it is positive we have a growth, so here we have a growth.

And to get the percentage multiply that number by 100%, we will get:

0.25*100% = 26%

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The amount (coupon interest) that is earned off the $1,000 bond with 4.3% coupon every 6 months is $21.50.

The coupon interest represents the periodic payment received by a bondholder from the date of issuance until the date of maturity of a bond.

The coupon interest is computed by applying the coupon rate on the face value of the bond.

Face value of the bond = $1,000

Coupon interest rate = 4.3%

Maturity period = 30 years

Coupon (bond) interest for 6 months = $21.50 ($1,000 x 4.3% x 6/12)

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Answer:

[tex]192[/tex] [tex]cm^2[/tex]

Step-by-step explanation:

Recall that the formula for the area of a parallelogram is:

[tex]A=bh[/tex]

Where b is the length of the base, and h is the length of the height.

We are given that the base is 24 cm.

So, b=24.

We are also given that the height is 8 cm.

So, h=8.

Let's plug these values into the formula:

[tex]A=bh=\\A=(24)(8)=\\A=192[/tex]

Since area is a two-dimensional measure, we need to label our answer using units squared.

Thus, the area is [tex]192[/tex] [tex]cm^2[/tex]

Area of a parallelogram => [tex]A=bh[/tex]

Where, b=24 cm and h=8 cm

Plug in the known values and solve.

[tex]\Longrightarrow A=bh \Longrightarrow A=(24 \ cm)(8 \ cm) \Longrightarrow A= \boxed{192 \ cm^2}[/tex]

The correct set of inequalities that model the constraints on the composition of the student body are:

600 ≤ a ≤ 700, 500 ≤ b ≤ 600 and a + b ≤ 1200

What is inequalities?

In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).

The correct set of inequalities that model the constraints on the composition of the student body are:

600 ≤ a ≤ 700 (the number of underclassmen must fall between 600 and 700, inclusive)

500 ≤ b ≤ 600 (the number of upperclassmen must fall between 500 and 600, inclusive)

a + b ≤ 1200 (the total number of students cannot exceed 1200)

Note that the inequalities 600 < a < 700 and 500 < b < 600 are not correct, as they do not take into account the inclusive limits of the ranges for the number of underclassmen and upperclassmen. Also, the inequality a + b > 1200 is not correct, as it contradicts the previous inequality a + b ≤ 1200.

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Based on the intersecting chords, the calculated value of x on the circle is 11

The given shape in the question is a circle

As a general rule, a circle is a shape with all points on its boundary equidistant from a central point called the center

In this case, the center is point W

The sum of angles on the circumference is 360

So, we have

17x - 20 + 75 + 2 * 59 = 360

Evaluating the like terms, we have

17x = 187

Divide by 17

x = 11

Hence. the value of x is 11

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A simplification of the fractions (-5/8) ÷ (-3/4) is equal to: B. -20/24.

The step in which Johnetta made her error include the following: A. step 1.

In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

Based on the information provided above, the division can be calculated as follows;

Fraction = (-5/8) ÷ (-3/4)

Fraction = -5/8 × (-4/3)

Fraction = -20/24

For Johnetta, we have:

Fraction = 7/9 ÷ 3/8

Fraction = 7/9 × 8/3

Fraction = 56/27

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The statement cos(theta) = √3/2 is correct.

Angles are the angles formed by 2 bisecting lines or surfaces at or near their intersection.

The following information has been provided:

The angle (theta) = [tex]\frac{2\pi }{3}[/tex] measurement has been given to us.

We must determine which propositions are true by determining the measure of angle (theta) =  [tex]\frac{2\pi }{3}[/tex]

cos(theta) = [tex]\frac{\sqrt{3} }{2}[/tex]

= cos30

theta = 30

tan(theta)= [tex]-\sqrt{3} = tan(90 + 30)[/tex]

tan(theta) = tan120

theta = 120

sin(theta) = [tex]-\frac{1}{2}[/tex] = [tex]cos(90 + 30)[/tex]

sin(theta) = sin120

theta = 120

Therefore the correct statement is cos(theta) = √3/2

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Complete question:

The measure of angle(theta) Is 2pi/3, which statements are true?

cos(theta) = √3/2

The measure of the reference angle is 30°.

The measure of the reference angle is 45°.

The measure of the reference angle is 60°.

tan(theta) = -√3

sin(theta)=-1/2​

The income statement, and stockholders equity are given below.

We have to show the income statement

The income statement for Coyote Corporation for the year ended December 31, 2024, is as follows:

Coyote Corporation

Income Statement

For the Year Ended December 31, 2024

Service Revenue $55,000

Less: Expenses

Salaries Expense $27,000

Rent Expense $6,000

Utilities Expense $6,000

Interest Expense $5,000

Total Expenses $44,000

Net Income $11,000

The statement of stockholders' equity for Coyote Corporation for the year ended December 31, 2024, is as follows:

Coyote Corporation

Statement of Stockholders' Equity

For the Year Ended December 31, 2024

Retained Earnings, December 31, 2023 $35,000

Add: Net Income for 2024 $11,000

Less: Dividends $0

Retained Earnings, December 31, 2024 $46,000

Classified Balance Sheet:

Assets

Current Assets

Cash $27,000

Accounts Receivable $26,000

Prepaid Rent $6,000

Supplies $5,000

Total Current Assets $64,000

Property, Plant, and Equipment

Land $55,000

Total Property, Plant, and Equipment $55,000

Total Assets $119,000

Liabilities and Stockholders' Equity

Current Liabilities

Accounts Payable $90,000

Salaries Payable $375,000

Interest Payable $6,000

Total Current Liabilities $471,000

Long-term Liabilities

Notes Payable (due in two years) $55,000

Total Liabilities $526,000

Stockholders' Equity

Common Stock $35,000

Retained Earnings $46,000

Total Stockholders' Equity $81,000

Total Liabilities and Stockholders' Equity $119,000

Therefore, the classified balance sheet for Coyote Corporation as of December 31, 2024, is as follows:

Coyote Corporation

Classified Balance Sheet

As of December 31, 2024

Assets

Current Assets

Cash $27,000

Accounts Receivable $26,000

Prepaid Rent $6,000

Supplies $5,000

Total Current Assets $64,000

Property, Plant, and Equipment

Land $55,000

Total Property, Plant, and Equipment $55,000

Total Assets $119,000

Liabilities and Stockholders' Equity

Current Liabilities

Accounts Payable $90,000

Salaries Payable $375,000

Interest Payable $6,000

Total Current Liabilities $471,000

Long-term Liabilities

Notes Payable (due in two years) $55,000

Total Liabilities $526,000

Stockholders' Equity

Common Stock $35,000

Retained Earnings $46,000

Total Stockholders' Equity $81,000

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complete question:

Kindly check if the photo below of income statement is wrong and correct which one is wrong in a excel or anything that makes it clear to me.

The statement The product of 3 and the difference of a number and 8 as an expression is 3(x - 8)

From the question, we have the following parameters that can be used in our computation:

The product of 3 and the difference of a number and 8

Represent the number with x

So, we have

The product of 3 and the difference of x and 8

The difference of x and 8 means x - 8

So, we have

The product of 3 and x - 8

The product of 3 * (x - 8)

So, we have

3(x - 8)

Hence, the expression is 3(x - 8)

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according to the question the balance in the account earning compound interest after 6 years is $4,156.22.

Multiply the principal with the rate of interest, the time period, and various other factors to determine simple interest. Simple returns = money + interests + hours is the marketing formula. This approach makes calculating interest the simplest. The approach to calculating interest that is most usually employed is as a percentage over the principal sum. For instance, he will just pay his share of the interest at 100% when he borrows $100 with a friend and agrees to shell out it back with 5% interest. $100 has been reduced to $5 (0.05). Every time you borrow money, you must pay interest, which is applied to whatever loans you make. On the loan balance, interest is typically calculated using an annual percentage.

given,

To calculate the balance in the account earning compound interest after 6 years, we can use the formula for compound interest:

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

Where:

A = the sum of money at the end of the period of time

P stands for the principle (beginning sum).

the decimal representation of the annual interest rate (r).

n represents how many times the interest rate is compounded annually.

t is the duration (in years).

In this case, we have:

P = $3500 (the principal)

r = 2.16% = 0.0216 (the annual interest rate)

Since interest is compounded four times a year (quarterly), n is equal to four.

t = 6 (the time period is 6 years)

With these values entered into the equation, we obtain:

A = 3500(1 + 0.0216/4)^(4*6)

A = $4,156.22

Therefore, the balance in the account earning compound interest after 6 years is $4,156.22.

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The balance in the account earning compound interest after 6 years when the principal is $3500 at an annual interest rate of 2.16% compounded quarterly is approximately $4,029.53.

Compound interest is the term used to describe the interest that is calculated on both the initial investment and any accumulated interest. It is interest on top of interest, to put it another way.

We can use the formula for compound interest to find the balance in the account after 6 years:

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

where:

A = balance after 6 years

P = principal = $3500

r = annual interest rate = 2.16%

n = number of compounded times  per year = 4 (quarterly)

t = time in years = 6

Plugging in the values, we get:

A = 3500(1 + 0.0216/4)^(4×6)

A ≈ $4,029.53

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Step-by-step explanation:

Steve spends 20% of £200 = 0.2 * £200 = £40 on his football magazine subscription.

The remaining amount he spends on football stickers, sweets, and fizzy drinks in the ratio of 5:2:1, which means that for every 5 parts he spends on football stickers, he spends 2 parts on sweets and 1 part on fizzy drinks.

So, let's call the amount he spends on football stickers "5x". Then, the amount he spends on sweets is "2x" and the amount he spends on fizzy drinks is "x".

The total amount he spends on these items is:

5x + 2x + x = 8x

We know that he has £200 - £40 = £160 left after paying for his magazine subscription. So, we can set up an equation:

8x = £160

Solving for x, we get:

x = £20

Therefore, Steve spends:

5x = 5 * £20 = £100

on football stickers.

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Answer:

5 : 2 : 1 = 100 : 40 : 20

Step-by-step explanation:

10% = 20 (200÷10=20)

20% = 40 (double both sides)

take away £40 from £200 = £160

£160 is left over after buying the magazine subscription

______________________________

add the radio all together = 5:2:1 = 8

divide 8 by 160 = £20

That now means 1 = 20

5 : 2 : 1

we already found 1, now to find 2 and 5

you times 2

1 = 20

2 = 40

and then do the same for 5

1 = 20

5 = 100

To know this is right, 100 + 40 + 20 = 160 the original number for the money left over.

there are 133,784,560 ways to draw 7 cards from a standard deck of 52 cards.

How to solve the question?

The number of ways to draw 7 cards from a standard deck of 52 cards can be calculated using the combination formula, which is:

C(52, 7) = 52! / (7! * (52-7)!)

where "!" represents the factorial function.

To simplify this expression, we can use the property that n! / k! = n * (n-1) * (n-2) * ... * (n-k+1) for positive integers n and k such that k ≤ n.

Using this property, we can rewrite the above expression as:

C(52, 7) = (52 * 51 * 50 * 49 * 48 * 47 * 46) / (7 * 6 * 5 * 4 * 3 * 2 * 1)

Simplifying this expression, we get:

C(52, 7) = 133,784,560

Therefore, there are 133,784,560 ways to draw 7 cards from a standard deck of 52 cards.

To understand why this is the case, we can think of each draw as a separate event with no replacement. The first card can be drawn in 52 ways, the second card can be drawn in 51 ways (since one card has already been drawn), the third card can be drawn in 50 ways (since two cards have already been drawn), and so on. Therefore, the total number of ways to draw 7 cards is the product of the number of ways to draw each individual card, which is 52 * 51 * 50 * 49 * 48 * 47 * 46. However, since the order in which the cards are drawn does not matter, we need to divide by the number of ways to arrange 7 cards, which is 7 * 6 * 5 * 4 * 3 * 2 * 1 (i.e., 7 factorial). This gives us the final answer of 133,784,560.

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✓ - True If the clerk continues at the same rate, he will meet his goal of 16 transactions in 1 hour.

       ➜ This is true. The clerk is currently going at 6 transactions per 1/3 hours. 6 * 3 = 18, and 18 > 16.

✗ - False At his current rate, the clerk will complete 12 transactions in 1 hour.

       ➜  This is false. As stated above, he will complete 18.

✓ - True At his current rate, the clerk will complete 9 transactions every half hour.

       ➜ Let us set up a proportion to check. Then we will cross-multiply and solve.

[tex]\frac{20\;min}{6} =\frac{30\;min}{x}[/tex]

180 = 20x

x = 9

       ➜ Yes, he will complete 9 every half hour.

✗ - False If the clerk continues at this rate for a 6-hour shift, he will complete 96 transactions.

       ➜  We can utilize a proportion again. 6 hours is equal to 360 minutes. Then, we will cross-multiply and solve.

[tex]\frac{20\;min}{6} =\frac{360\;min}{x}[/tex]

20x = 2,120

x = 106

       ➜ He will complete 106 transactions, not 96. It depends on if they're asking for exactly 96 or at least 96.

Step-by-step explanation:

slope,   m = ( y1-y2) / (x1-x2)   = ( 6-8) / (12-28) =  -2 / -16 = 1/8

The Addition Property of Equality allows us to add EF to both sides of the equation without changing its truth, giving us AB + EF = CD + EF.

We have,

The Addition Property of Equality states that if we add the same quantity to both sides of an equation, the equation remains true.

In the given equation,

AB = CD, we can add the same quantity, EF, to both sides of the equation to obtain:

AB + EF = CD + EF

This is because if two quantities are equal, and we add the same amount to both of them, the result is still equal.

Therefore,

The Addition Property of Equality allows us to add EF to both sides of the equation without changing its truth, giving us AB + EF = CD + EF.

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Answer:f/g=29

Step-by-step explanation:

Answer: (f/g)=29

Hope this helps

Answer:

-36

Step-by-step explanation:

To solve this problem, we need to integrate f'(x) to find f(x), and then evaluate f(3) and f(-1) to compute the expression f(3) - f(-1).

Integrating f'(x)=-4x - 5 with respect to x, we get:

f(x) = -2x^2 - 5x + C

Where C is the constant of integration.

To find the value of C, we can use the initial condition f(0) = 1. Substituting x = 0 and f(x) = 1 into the equation above, we get:

1 = -2(0)^2 - 5(0) + C

1 = C

So, we have:

f(x) = -2x^2 - 5x + 1

Now, we can evaluate f(3) and f(-1) and compute f(3) - f(-1):

f(3) = -2(3)^2 - 5(3) + 1 = -32

f(-1) = -2(-1)^2 - 5(-1) + 1 = 4

f(3) - f(-1) = (-32) - 4 = -36

Therefore, f(3) - f(-1) = -36.

Answer:

  -36

Step-by-step explanation:

You want F(3) -F(1) given f'(x) = -4x -5.

The desired difference is the definite integral ...

  [tex]\displaystyle \int_{-1}^3{(-4x-5)}\,dx=\left[-2x^2-5x\right]_{-1}^3=-2(9-1)-5(3+1)\\\\=\boxed{-36}[/tex]

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The compositions are:

f * f(x) = x⁴ - 2x²

g * g(x) = 81/64x

To find the composition f * f, we start by substituting f(x) into f(x) wherever we see x:

f * f (x) = f(f(x)) = f(x² - 1) = (x² - 1)² - 1

Expanding the expression, we get:

f * f (x) = x⁴ - 2x² + 1 - 1 = x⁴ - 2x²

So, f * f(x) = x⁴ - 2x².

To find the composition g * g, we substitute g(x) into g(x) wherever we see x:

g * g (x) = g(g(x)) = g(9/8x) = 9/8(9/8x) = 81/64x

So, g * g(x) = 81/64x.

Therefore, the compositions are:

f * f(x) = x⁴ - 2x²

g * g(x) = 81/64x

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The text format of the question is:

Suppose that the functions f and g are defined as follows.

f(x) = x² - 1

g(x) = 9/8x, x ≠

Find the compositions f * f and g * g

Simplify your answers as much as possible.

(Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain)

On solving the provided question we can say that area of the polygon is 24 cm sq.

A four-sided polygon having four edges and four corners is referred to as a quadrilateral. The word is derived from the Latin words quadri and latus, both of which imply "side". An object with a rectangle's four sides, four vertices, and four corners is a two-dimensional shape. There are essentially two sorts of concave and convex surfaces. Convex quadrilaterals also include the subclasses of trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up the two-dimensional shape of a rectangle. There are many different shapes for quadrilaterals, such as parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

Area of this polygon is -

A = 1/2 * 6* 8

A = 24 cm sq.

Hence, area of the polygon is 24 cm sq.

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The amount Troy (D, in dollars) charges to mow a lawn is proportional to the time (H, in hours) it takes him to mow the lawn.

Hence, we can write [tex]\text{D = kH}[/tex] ......... (1), where k is a constant.

Now, given that Troy charges $30 to mow a lawn that took him 1.5 hours to mow.

So, from equation (1) we get  

[tex]{30 = 1.5\text{k}[/tex]

[tex]\rightarrow \text{k = 20}[/tex].

Therefore, equation (1) becomes

[tex]\boxed{\bold{D = 20H}}[/tex] (Answer)

The surface area of the composite solid is given as follows:

194 units squared.

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.

The prism in this problem is composed as follows:

Hence the surface area of the prism is given as follows:

S = 2(4 x 7 + 4 x 3 + 3 x 7) + 4 x 3 + 5² + 5 x 7

S = 194 units squared.

More can be learned about the surface area of a rectangular prism at https://brainly.com/question/1310421

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