Imagine that you invest $95,000 in an account that pays 2.5% annual interest
compounded quarterly. What will your balance be at the end of 20 years?

The volume of the right circular cylinder with a radius of 6 m and a height of 9 m is 1018 m².

The volume of a substance is the total space occupied by a three-dimensional object.

The volume of a right circular cylinder with a radius of r units and a height of h units is given by the formula V = πr²h square units.

We are asked to find the volume of the right circular cylinder with a radius of 6 m and a height of 9 m.

Substituting these values in the formula, we get Volume,

V = π(6)²(9) m² = 324π m² = 1017.876 m² ≈ 1018 m².

Therefore, the volume of the right circular cylinder with a radius of 6 m and a height of 9 m is 1018 m².

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Step-by-step explanation:

Hello!

For this you multiply the numbers that intersect at that box

Box A 2x and 4 intersect

2x * 4 = 8x

Box B 3 and 4 intersect

3 * 4 = 12

Box C 2x and x intersect

2x * x = \(2x^{2}\)

Box D 3 and x intersect

3 * x = 3x

To solve this we put all these together

\(2x^{2} +3x+8x+12\)

Combine like terms

\(2x^{2} +11x+12\)

Hope this helps!

\( \qquad \qquad\huge \underline{\boxed{\sf Answer}}\)

Let's solve ~

\(\qquad \sf \dashrightarrow \: \dfrac{2x - 1}{5} = \dfrac{x - 2}{2} \)

\(\qquad \sf \dashrightarrow \: 2(2x - 1) = 5(x - 2)\)

\(\qquad \sf \dashrightarrow \: 4x - 2 = 5x - 10\)

\(\qquad \sf \dashrightarrow \: 5x - 4x = -2 + 10\)

\(\qquad \sf \dashrightarrow \: x = 8\)

Value of x is 8

From the steps shown in the solution below; the solution to the problem is x = -1.

An equation is any mathematical statement that contains the equality sign.

The first step here is to obtain the LCM of 2 and 5 which is 10. The next step is to multiply each term with the LCM of 2 and 5 which is 10. So;

10( 2x - 1)/5 = 10 (x - 2)/5

4x - 2 = 2x - 4

4x - 2x = -4 + 2

2x = -2

x = -1

The solution to the problem is x = -1.

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Step-by-step explanation:

By the Right Triangle Altitude Theorem, the two triangles formed by the altitude of a right triangle are similar to the original triangle and to each other.

In this case, triangle ABC is the original right triangle and CE is the altitude. Therefore, the similarity statement that is true is:

△ABC ∼ △AEC

This is because triangles ABC and AEC are both right triangles that share the angle at C, and the altitude CE creates two pairs of congruent angles (the right angles and the angle at A and E) and a pair of proportional sides (CE and AE are corresponding altitudes).

So, we can write the similarity statement as:

△ABC ~ △AEC

Answer:

The probabilities of each suspect being guilty are

   \(P(S)  =  0.243\)

    \(P(W)  =  0.027\)

\(P(T) = 0.001\)

Step-by-step explanation:

Generally from the question we are told that

The number of suspects is N = 3

The number of witnesses that reported seeing a short man is k = 2

The number of witnesses that reported seeing a woman is u = 1

The probability of a witness being correct is p = 0.90

The probability of a witness not being correct is q 0.10

Generally the number of  witnesses that reported seeing a tall  man is h =  0

Generally the probability the short man being guilty is mathematically represented as

\(P(S) = ^N C_k * p^k * q^{N - k }\)

Here C stands for combination

\(P(S) = ^3 C_2 * (0.90)^2 * (0.10)^{3 - 2 }\)

         \(P(S)  =  0.243\)

Generally the probability the woman being guilty is mathematically represented as

         \(P(W)  =  ^N C_u  *  p^u  *  q^{N - u }\)

=>       \(P(W)  =  ^3 C_1  *  p^1  *  q^{3 - 1 }\)

=>       \(P(W)  =  0.027\)

Generally the probability the  tall man being guilty is mathematically represented as

          \(P(T)  =  ^N C_h  *  p^h  *  q^{N - h }\)

=>       \(P(T)  =  ^3 C_0  *  p^0  *  q^{3 - 0 }\)

=>       \(P(T)  = 0.001\)

The correct answer that is an example of a permutation is; D: The number of ways 7 books can be selected from 50.

Formula for permutation is;

nPr = n!/(n - r)!

Now, permutation is defined as the arrangement of objects in a definite order. Thus, looking at the given options, the only one that depicts permutation is Option D.

Thus, the correct answer is the number of ways 7 books can be selected from 50.

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a) The probability that exactly one of them will be a girl = 0.3407

b) The probability that at least one of them will like the football = 0.7672

a) If we select three students then the probability that exactly one of them will be a girl

From the attached two way table we can observe that the total number of girls = 22

the total number of boys = 18

and the total number of students = 40

The possible outcomes for selecting 3 students from 40 would be,

⁴⁰C₃

Using combination formula,

⁴⁰C₃ = 40! / (3! × (40 - 3)!)

      = 9880

If there is exactly one girl then other two must be boys in the set of 3 selected students.

So, the required probability would be,

P = (²²C₁ × ¹⁸C₂) / ⁴⁰C₃

P = (22 × 153)/9880

P = 0.3407

b) The number of students like the football = 15

and the number of students who don't like the football are 40 - 15 = 25

The probability that at least one of them will like the football would be,

P = (¹⁵C₃ × ²⁵C₀ + ¹⁵C₂ × ²⁵C₁ + ¹⁵C₁ × ²⁵C₂) / ⁴⁰C₃

P = ((455 × 1) + (105 × 25) + (15 × 300)) / 9880

P = 0.7672

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Answer:

1 - \(\frac{2\sqrt{2} }{3}\)

Step-by-step explanation:

\(\frac{\sqrt{3}-\sqrt{6} }{\sqrt{3}+\sqrt{6} }\)

rationalise the denominator by multiplying the numerator and denominator by the conjugate of the denominator.

the conjugate of \(\sqrt{3}\) + \(\sqrt{6}\) is \(\sqrt{3}\) - \(\sqrt{6}\)

= \(\frac{(\sqrt{3}-\sqrt{6})(\sqrt{3}-\sqrt{6}) }{(\sqrt{3}+\sqrt{6})(\sqrt{3}-\sqrt{6}) }\) ← expand numerator/ denominator using FOIL

= \(\frac{3-\sqrt{18}-\sqrt{18}+6 }{3-\sqrt{18}+\sqrt{18}+6 }\)

= \(\frac{9-2\sqrt{18} }{3+6}\)

= \(\frac{9-2(3\sqrt{2}) }{9}\)

= \(\frac{9-6\sqrt{2} }{9}\)

= \(\frac{9}{9}\) - \(\frac{6\sqrt{2} }{9}\)

= 1 - \(\frac{2\sqrt{2} }{3}\)

a.The Industry Average Salary is $55,680. b.The Firm A's Average Salary is $51,718.40 .c. Firm B's average salary is approximately 112.27% of Firm A's average salary.

a. To determine the industry average salary, we can use the information that the industry average salary is 96% of Firm B's average salary. Firm B's average salary is $58,000. Therefore, we can calculate the industry average salary as follows:

Industry Average Salary = 96% of Firm B's Average Salary

= 0.96 * $58,000

= $55,680

b. Firm A's average salary is stated as 93% of the industry average salary. To calculate Firm A's average salary, we can multiply the industry average salary by 93%:

Firm A's Average Salary = 93% of Industry Average Salary

= 0.93 * $55,680

= $51,718.40

c. To express Firm B's average salary as a percentage of Firm A's average salary, we can divide Firm B's average salary by Firm A's average salary and multiply by 100:

Percentage = (Firm B's Average Salary / Firm A's Average Salary) * 100

= ($58,000 / $51,718.40) * 100

≈ 112.27%

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Step-by-step explanation:

Let first find the x and y xomponets.

X componets is 8 and the y componets is -7 so

\(r = \sqrt{ {x}^{2} + {y}^{2} } \)

\(r = \sqrt{ 64 + 49} \)

\(r = \sqrt{113} \)

\( \csc(x) = \frac{r}{y} \)

So

\( \csc(x) = - \frac{ \sqrt{113} }{ 7} \)

Answer:

The shape of a distribution is described by its number of peaks and by its possession of symmetry, its tendency to skew, or its uniformity. (Distributions that are skewed have more points plotted on one side of the graph than on the other.) PEAKS: Graphs often display peaks, or local maximums.

Answer: It is Skewed

Step-by-step explanation: More positive space than negative. So it is positively skewed.

Answer:

1a8?

Step-by-step explanation:

thi is how

The incorrect statement for the given condition is;

⇒ |a| > b

What is Number line?

Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.

Given that;

A number line shows 'a' to the left of 0 and 'b' to the right of 0. Point a is closer to 0 than point b.

Now,

Since, Point a is closer to 0 than point b.

And,  Number 'a' to the left of 0 and 'b' to the right of 0.

Hence,

Let the number 'a' = - 1

Then, The number 'b' = 2

So, We get;

|a| = |-1| = 1

And, |b| = 2

Clearly, |a| < b

Thus, The incorrect statement for the given condition is;

⇒ |a| > b

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Answer:

Using weighted average, the cost of goods sold for the sale of 23 units on July 31 is $2,504.70, and the inventory balance at July 31 is $ 1,306.90.

Step-by-step explanation:

Since Intercontinental, Inc., uses a perpetual inventory system, and on July 1, purchased 10 units for $ 910 or $ 91 per unit; on July 3, purchased 15 units for $ 1,590 or $ 106 per unit; on July 14, it sold 20 units; on July 17, purchased 20 units for $ 2,300 or $ 115 per unit; on July 28, purchased 10 units for $ 1,190 or $ 119 per unit; and on July 31, sold 23 units, to determine the average costs and the inventory balance as of July 31, the following calculations must be performed:

(910 +1590 + 2300 + 1190) / (10 + 15 + 20 + 10) = X

5990/55 = X

108.90 = X

108.90 x 23 = 2504.7

(55 x 108.9) - (43 x 108.9) = X

5990 - 4683.10 = X

1306.90 = X

Using weighted average, the cost of goods sold for the sale of 23 units on July 31 is $ 2504.70, and the inventory balance at July 31 is $ 1,306.90.

No, there are x values which map to more than 1 y-value.

Given that Matthew examines the relation as shown in the below.

{(4, -11), (3,1), (0,1), (2,6), (3, -1)}

We need to check whether the relation is a function or not,

So, we know that,

A relation can map inputs to multiple outputs. It is a function when it maps each input to exactly one output. The set of all functions is a subset of the set of all relations.

If any x values are repeated, and the corresponding y values are different, then we have a relation and not a function.

Here we can see that the y values are repeated, so it is not a function.

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Answer:

(f o h)(-5)=-33

Step-by-step explanation:

Let f(x) = 4x - 1, h(x) = - X-3.

(f o h)=4(-x-3)-1

(f o h)=-4x-12-1

(f o h)=-4x-13

(f o h)(-5)=-4(-(-5))-13

(f o h)(-5)=-20-13

(f o h)(-5)=-33

Answer:

The mean percentage of hourly employees being laid off at these stores is 52.

The median percentage of hourly employees being laid off at these stores is 55.

Step-by-step explanation:

Mean:

Sum of all values divided by the number of values.

So

\(M = \frac{55+56+44+43+44+56+60+62+57+45+36+38+50+69+65}{15} = 52\)

The mean percentage of hourly employees being laid off at these stores is 52.

Median:

Value that separate the lower 50% from the upper 50% in the sorted set.

The sorted set is

36 38 43 44 44 45 50 55

The set has cardinality 15, which is an odd number, so the median is the element at the position (15+1)/2 = 8 of the sorted set, which is 55.

The median percentage of hourly employees being laid off at these stores is 55.

Answer:

y = 5/4 x - 23/4

Step-by-step explanation:

4x + 5y = 31

5y = - 4x +31

y = -4/5 x + 31/5

⊥ slope = 5/4

-7 = 5/4 (-1) + B

-28 = -5 + 4b

-23 = 4B

b = -23/4

a) Using the four basic mathematical operations, the number of balloons that each person hang up is 9.

b) An equation representing the situation is x = (125 - 80)/5.

The four basic mathematical operations include addition, subtraction, division, and multiplication.

The mathematical operations provide solutions to mathematical problems using operands.

An equation is a mathematical statement showing that two or more mathematical expressions are equal or equivalent.

The total number of balloons that Andre has = 125

The number of balloons remaining after hanging some for the school party = 80

The difference (number of balloons used) = 45 (125 - 80)

The number of friends who hang the balloons = 5

The number of balloons hung by each friend of Andre = 9 (45/5)

Thus, we can conclude that each of the 4 friend and Andre hung 9 balloons, with 80 remaining.

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Altitude (AB) = 9cm

Base (BC) = 12cm

Hypotenuse (AC) = ?

\( \fbox \text{According To Pythagoras Theorem = }\)

\( \text{(Hypotenuse)² = (Altitude)² + (Base)²}\)

Inserting The Values

\( \text{(Hypotenuse)²} =( {9})^{2} + (12) {}^{2} \\ \\ \implies \text{(AC)} {}^{2} = 81 + 144 \\ \\ \implies \text{(AC}) {}^{2} = 225 \\ \\ \implies \text{AC} = \sqrt{225} \\ \\ \implies \text{AC} = 15\)

\( \therefore \text{Hypotenuse \: (AC)} = 15 \text{cm}\)

Option B= 15cm is the correct answer

During the morning rush hour, there are 6,400 junior and high school students, 3,400 adults, and 5,800 senior citizens riding the subway.

Let's assume the number of junior and high school students riding the subway during the morning rush hour is J, the number of adults is A, and the number of senior citizens is S.

From the given information, we can set up a system of equations based on the number of riders and the revenue generated.

Equation 1: J + A + S = 15,600 (total number of riders)

Equation 2: 1.04J + 2.20A + 1.04S = 32,464 (revenue equation with original ticket prices)

Equation 3: 1.24J + 2.60A + 1.04S = 38,264 (revenue equation with new ticket prices)

We can start by subtracting Equation 2 from Equation 3 to eliminate the J and S terms:

0.2J + 0.4A = 3,800

Next, we can multiply Equation 1 by 0.2 and subtract it from the above equation to eliminate the J term:

0.4A - 0.2J - 0.2A = 3,800 - 3,120

0.2A = 680

A = 680 / 0.2 = 3,400

Now, we can substitute the value of A back into Equation 1 to find the values of J and S:

J + 3,400 + S = 15,600

J + S = 15,600 - 3,400

J + S = 12,200

We have two equations with two variables (J + S = 12,200 and 1.04J + 1.04S = 12,264). By solving these equations simultaneously, we find J = 6,400 and S = 5,800.

Therefore, during the morning rush hour, there are 6,400 junior and high school students, 3,400 adults, and 5,800 senior citizens riding the subway.

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To find the number of subway riders in each category, we set up a system of equations based on the total number of passengers and the total revenue. Solving this system will give us the number of junior and high school students, adults, and senior citizens. The number of riders doesn't change with the increase of ticket prices.

To solve this problem, we set up a system of equations based on the information given in the question.

Let's denote the number of junior and high school students as J, adults as A, and senior citizens as S. We know that there's total of 15,600 passengers, so:

J + A + S = 15,600

We also know that the total revenue was $32,464. Given the ticket prices for each group, we can write:

$1.04J + $2.20A + $1.04S = $32,464

Solving this system of equations (possibly with the help of a calculator or computer software), we can find the number of riders in each category.

The number of riders for each category would only change if the number of riders changes, not the price of the tickets, so when the prices increase, the number of riders remains the same.

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9514 1404 393

Answer:

Step-by-step explanation:

Consider the function and its inverse shown in the second attachment. The function is ...

  f = {(a, 3), (b, 1), (c, 2)}

The inverse function is ...

  f^-1 = {(3, a), (1, b), (2, c)}

You will notice that the "x" and "y" of each pair are swapped between the function and its inverse. That is the point of an inverse function. It gives you the input that caused the function to create the output. For example, the pair (3, a) in the above inverse function tells you that the output 3 was the result of an input of 'a' to the original function.

__

On a graph, the swapping of input and output is essentially equivalent to relabeling the axes. If we keep the same x- and y-axis labels, it is equivalent to reflecting the function graph across the line y=x. That reflection is represented by the transformation (x, y) ⇒ (y, x).

__

The point of the exercise here is for you to identify some ordered pairs of one of the functions and realize that the inverse function reverses their order. You are to see that the graph of the function and its inverse are reflections of each other across the diagonal line y=x.

Answer:

8.80$

Step-by-step explanation:

Total 20.20. 6.06 x 2=12.12. 20.20-12.12=8.80$

Mathew paid 8.80$

Clarence paid 12.12$

Daniel paid 6.06$

Answer:

It would be 649

Step-by-step explanation:

118 ÷ 2= 59

59 x 11= 649

Answer:

649m

Step-by-step explanation:

\(\frac{118m}{2s} =\frac{59m}{s}\)

so that 59m/s we multiply by 11s

\(\frac{59m}{s} (11s)=649m\)

Answer:

\( {x}^{2} + {8}^{2} = {y}^{2} ...(1) \\ {x}^{2} + {23}^{2} = {z}^{2} ...(2) \\ {y}^{2} + {z}^{2} = {(23 + 8)}^{2} \\ {y}^{2} + {z}^{2} = {(31)}^{2} ...(3) \)

You should be able to solve this simultaneously...to find x,y and z.

The length of the other leg for triangle BCD will be 13.86cm.

From the triangle BCD is a right triangle. The length of the hypotenuse is 19 centimeters and the length of one of the legs is 13 centimeters.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side. The Pythagoras theorem formula is given as

H² = P² + B²

Let the unknown sides be x. Then we have,

19² = 13² + x²

361 = 169 + x²

x² = 361 – 169

x² = 192

 x = 13.856 ≈ 13.86 cm

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The triangle BCD is a right triangle. The length of the hypotenuse is 19 centimeters. The length of one of the legs is 13 centimeters.

What is the length of the other leg?

a) The value of the mean is μ = 22.5

   The value of the standard deviation is σ = 3.5

b) The Value of 15 girls or fewer is significantly low.

   The value of 30 girls or more is significantly high.

c) The result 36 is significantly high because 36 is greater than 30 girls. A         result of 36 girls is not necessarily definitive proof of the method's effectiveness.

The standard deviation is a measure of the amount of variability or dispersion in a set of data values. It is a statistical measure that tells you how much, on average, the values in a dataset deviate from the mean or average value.

a) Since the probability of having a girl for each couple is 0.5, the number of girls each couple will have can be modeled as a binomial distribution with parameters n=1 and p=0.5.

Let X be the random variable denoting the number of girls in 45 couples. Then, X follows a binomial distribution with parameters n=45 and p=0.5.

The mean of a binomial distribution is given by μ = np, so in this case, the mean number of girls in a group of 45 couples is:

μ = np = 45 x 0.5 = 22.5

Therefore, we expect to see around 22-23 girls in a group of 45 couples.

The standard deviation of a binomial distribution is given by σ = √(np(1-p)), so in this case, the standard deviation of the number of girls in a group of 45 couples is:

σ = √(np(1-p)) = √(45 x 0.5 x 0.5) = 3.535

Therefore, we can expect the number of girls in a group of 45 couples to have a standard deviation of around 3.5.

b) In this case, we can assume that the number of girls in a group of 45 couples follows a normal distribution due to the Central Limit Theorem.

Using the standard deviation we found in the previous answer (σ = 3.535), we can calculate the values that separate the results that are significantly high and significantly low.

Significantly high:

Mean + 2σ = 22.5 + 2(3.535) = 29.57

Significantly low:

Mean - 2σ = 22.5 - 2(3.535) = 15.43

c) To determine if the result of 36 girls is significantly high, we need to compare it to the values we calculated in the previous answer.

Mean + 2σ = 22.5 + 2(3.535) = 29.57

Since 36 is greater than 29.57, we can conclude that the result of 36 girls is significantly high.

This suggests that the method of gender selection may be having an effect on the probability of having a girl. However, we cannot conclusively say this without conducting further analysis or testing.

It is also important to note that the result of 36 girls is not necessarily definitive proof of the method's effectiveness.

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The answer to your problem is: X=17

Answer:

17

Step-by-step explanation:

x + 10 + 9x=14x-58

x + 9x + 10 =14x-58

10x + 10 =14x-58

By grouping like terms by moving 14x to the left and 10 to the right of the equation; we have:

10x - 14x =-58-10

-4x=-68

x=-68/-4=17{ dividing both sides by -4}

Answer:

a) 0.23x+0.21y=75

b) (For the Graph see the attached picture).

A possible solution for the inequality \(0.23x+0.21y\leq75\) would be any point inside the shaded region of the graph. For example (150,175) This is 150 minutes to the United Kingdom and 175 minutes to France.

\(0.23x+0.21y\leq75\)

\(0.23(150)+0.21(175)\leq75\)

\(34.5+36.75\leq75\)

\(71.25\leq 75\)

this inequality is true, so the number of minutes used for the United Kingdom and to France is valid.

Step-by-step explanation:

a)

In order to solve this problem, we must first set our variables:

x= Minutes to the United Kingdom.

y= Minutes to France

The greatest amount of money you can spend is $75 and each minute will cost $0.23 when calling to the United Kingdom and $0.21 when calling to France. So we can use this information to build our equation:

0.23x+0.21y=75.

b) So first, we need to convert our equation into an inequality where the total amount of money spent must be less than $75, so our inequality is:

[tex}0.23x+0.21y\leq75\)

so now we can proceed and graph. This is graphed exactly as you would graph a regular linear equation. You need to find two points on the graph that will satisfy the equation. Plot them and then connect them with a straight line. For example:

First, let's solve the equation for y:

0.23x+0.21y=75

we start by moving the 0.23x to the other side of the equation so we get:

0.21y=-0.23x+75

and next we divide both sides of the equation into 0.21 so we get:

\(y=\frac{-0.23x+75}{0.21}\)

which yields:

y= -1.095x+357.14

next we need to pic an x-value so we can find the first ordered pair. Let's say I pick x=0. So we get:

y= -1.095x+357.14

y= -1.095(0)+357.14

y=357.14

so our first point is (0, 357.14)

And we can follow the same procedure for the second point. Let's say I pick x=1. In that case our second point is (1, 354.04). We can now plot them. Once the graph is drawn, we need to shade it, for which we will pick an ordered pair to the left and an ordered pair to the right of the line. For the left region let's pick the point (0,0) and for the right of the graph, let's pick the point (150,357).

So let's test the inequality for these two points:

First, let's use the point (0,0)

\(0.23x+0.21y\leq75\)

\(0.23(0)+0.21(0)\leq75\)

\(0\leq75\)

This proves that the left side of the graph is the side to be shaded. We can still use the other point and see what we qet:

(150, 357) and let's use it on our inequality:

\(0.23x+0.21y\leq75\)

\(0.23(150)+0.21(357)\leq75\)

\(109.47\leq75\)

Is a false statement, so only the region on the left will contain the possible number of minutes to do the phone calls to the UK and France.

A possible solution for the inequality \(0.23x+0.21y\leq75\) would be any point inside the shaded region of the graph. For example (150,175) This is 150 minutes to the United Kingdom and 175 minutes to France.

\(0.23x+0.21y\leq75\)

\(0.23(150)+0.21(175)\leq75\)

\(34.5+36.75\leq75\)

\(71.25\leq 75\)

This is a true statement so the possible solution is correct.

Answer:

Step-by-step explanation:

First, we need to convert the dimensions of the room from feet to yards, since the price is given per square yard.

24 feet = 8 yards (since 1 yard = 3 feet)

So the dimensions of the room are 8 yards x 1 yard.

The area of the room is 8 x 1 = 8 square yards.

The cost of the carpeting per square yard is $9.97.

So, the estimated cost of the carpeting would be:

8 x $9.97 = $79.76

Rounding this to the nearest cent gives an estimated cost of $79.76.