Eric is working on the problem:
Hank's Auto Wash recently acquired an automatic car-washing machine that is
expected to generate $45,000 in revenue per year, t years from now, for the next 6
years. If the income is reinvested in a business earning interest at the rate of 8% per
year, compounded continuously, find the Accumulated Total Value of this income
stream at the end of 6 years.
Which of the following is NOT a good method for solving the problem?

The actual distance from the starting point to the ending point is 39.96 miles.

For someone working with the map or scaled drawing, we can define the scale factor as the ratio between a distance on the drawing or map and the corresponding actual distance in the real world.

From the question,

1.5 inches on the map = 5 miles in actual distance

1 inch on the map =  x miles

Perform cross multiplication

1 inch on the map =  (5 x 1) / 1.5  = 3.33 miles/inch (scale factor)

The scale factor can then be expressed as ratio:

5/1.5 = 1:0.3

0r

5/1.5 = 10:3

So, the actual distance between the starting point and the ending point can be found by multiplying the length on the map by the scale factor:

Actual distance = Map distance x Scale factor

Actual distance = 12 inches x 3.33 miles/inch = 39.96 miles

Therefore, the actual distance from the starting point to the ending point is approximately 39.96 miles.

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The cost of the fondue pot after the 45% discount and 6% sales tax is calculated using the following equations:

In this example, the original price of the fondue pot is $92 and the discount is 45%, which would make the discount amount $41.40. The sales tax is 6%, which would be $2.48

Therefore, the final price of the fondue pot would be $43.88

The value and the slope of the curve at point (x, y) = (7, 2) are 2 and 1 / 7, respectively.

In this problem we find the case of a line tangent to a curve at point (x, y) = (7, 2) and that passes through the point (x, y) = (0, 1). The equation of the line is described by following formula:

y = m · x + b

Where:

And the slope of the line is found by secant line formula:

m = Δy / Δx

First, determine the slope of the secant line:

m = (2 - 1) / (7 - 0)

m = 1 / 7

f'(7) = 1 / 7

Second, find the value of the curve:

f(7) = 2

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a. Probability of landing on A = 2/6 = 1/3. b. Probability of landing on C, D, or E = 3/6 = 1/2. c. The probabilities are not equal, the spinner is not fair.

a. Since there are 6 equal-sized sections on the spinner and only 2 sections labeled A, the probability of the pointer landing on A is given by:

Probability of landing on A = Number of favorable outcomes / Total number of possible outcomes

Number of favorable outcomes = 2 (since there are 2 sections labeled A)

Total number of possible outcomes = 6 (since there are 6 equal-sized sections on the spinner)

Probability of landing on A = 2/6 = 1/3

b. To find the probability of the pointer landing on C, D, or E, we need to determine the number of favorable outcomes (sections labeled C, D, or E) and the total number of possible outcomes.

Number of favorable outcomes = 3 (since there are 3 sections labeled C, D, or E)

Total number of possible outcomes = 6 (since there are 6 equal-sized sections on the spinner)

Probability of landing on C, D, or E = Number of favorable outcomes / Total number of possible outcomes

Probability of landing on C, D, or E = 3/6 = 1/2

c. To determine if the spinner is fair, we need to check if the probabilities of landing on each letter are equal. From the previous calculations, we found that the probability of landing on A is 1/3 and the probability of landing on C, D, or E is 1/2.

Since the probabilities are not equal, the spinner is not fair.

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The scale factor is 1/3

The formula for calculating scale factor is expressed as;

SF = IL/PL

Such that the parameters are expressed as;

From the information given, we have that;

IL = 3cm

PL =9cm

Substitute the values, we have;

Scale factor = 3/9

Divide the values, we have;

Scale factor = 1/3

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The area of triangle A is 98 sq cm. Option B is correct.

Since triangle A is a scaled version of triangle B, the ratio of their areas is equal to the square of the ratio of their corresponding side lengths.

If the dimensions of triangle A are twice the dimensions of triangle B, then the ratio of their side lengths is 2:1.

The ratio of their areas, therefore, is (2:1)² = 4:1.

Given that the area of triangle B is 24.5 sq cm, we can find the area of triangle A by multiplying 24.5 by the ratio of their areas:

Area of triangle A = 24.5 × 4 = 98 sq cm

Therefore, the area of triangle A is 98 sq cm.

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The probability P(x < 4) will be 0.273. The correct option is A.

Probability is a branch of mathematics that deals with the measurement and analysis of uncertainty. In other words, probability is the measure of the likelihood or chance that a particular event will occur.

Since X is a continuous uniform distribution between 1 and 12, the probability density function (PDF) is given by:

f(x) = 1/11 for 1 ≤ x ≤ 12

= 0 otherwise

The probability P(X < 4) can be calculated as follows:

P(X < 4) = ∫[from 1 to 4] f(x) dx

= ∫[from 1 to 4] 1/11 dx

= [1/11 * x] (from 1 to 4)

= (4/11) - (1/11)

= 3/11

Rounding this to three decimal places, we get:

P(X < 4) ≈ 0.273

Therefore, the answer is 0.273.

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Pick the first option.

f(x) is dependent on x.

the 2nd option is wrong; the dependent variable is the output, the independent variable is the input.

3rd option is wrong, dependent determines the range.

4th is wrong, x is independent variable.

The number of solutions the system of equations have is (a) more than one solutions

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

3y-3x = -9

4y-4x=-12

Simplify the equations

So, we have

y - x = -3

y - x = -3

Subtract the equations

0 = 0

The above equation is true for all values of x and y

This means that the number of solutions in the equation is many i.e. more than one solutions

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The image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7 is the point L'(-28,0).

A dilation with a center of (0,0) and a scale factor of 7 means that every point in the plane will be multiplied by a factor of 7 from the origin.

To find the image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7, we can simply multiply the coordinates of L by the scale factor.

The coordinates of the image point L' will be:

L' = (-4 × 7, 0 × 7) = (-28, 0)

Therefore, the image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7 is the point L'(-28,0).

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The lower quartile of the given data set is 63.

To find the lower quartile (Q1), we need to determine the value that divides the data set into the lower 25% of the values.

First, we need to sort the data set in ascending order: 61, 61, 62, 64, 66, 69, 69, 70, 72, 73, 74, 78.

Next, we calculate the position of the lower quartile using the formula: (n+1)/4, where n is the number of data points. In this case, we have 12 data points, so (12+1)/4 = 13/4 = 3.25.

Since 3.25 is not a whole number, we can find the lower quartile by taking the average of the data points at positions 3 and 4.

The data point at position 3 is 62, and the data point at position 4 is 64.

Therefore, the lower quartile (Q1) is the average of 62 and 64:

(Q1) = (62 + 64)/2 = 126/2 = 63.

Hence, the lower quartile of the given data set is 63.

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The width of the confidence interval is 1.2786.

From the question we are told that

The sample size is n = 16    

The mean time is x = 2.8 minutes

The standard deviation is = 1.2 minutes

Generally, the degree of freedom is mathematically represented as  

df = n-1

df = 15

From the question we are told the confidence level is 95%, hence the level of significance is =

α = 100-95

α = 0.05

Generally, the margin of error is mathematically represented as =

[tex]E = t_{\alpha/2}, 15 \times \sigma/\sqrt{n}[/tex]

E = 2.131 × 1.6 / √16

E = 0.6393

Generally, the width the confidence 95% confidence interval  

W = 2E

W = 1.2786

Hence the width of the confidence interval is 1.2786.

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The equation of the functions represented on the graph are (b)

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

The graph

On the graph, we have the following intervals:

When the intervals are represented as inequalities, we have the following:

Interval 1: x ≤ 1

Interval 2: x > 1

This means that the intervals of the graphs are x ≤ 1 and x > 1

From the list of options, we have the graph to be option (b

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Doing a change of units, we can see that 2.11 yd³ is equivalent to 1.7513 m³

We know that the relation between one yard and one meter is:

1yd = 0.91m

Then the relation between one cubic yard and one cubic meter is:

(1yd)³ = (0.91m)³

1 yd³ = 0.83 m³

Now we can perform a change of units between the volume in yards and the volume in meters, we will get:

2.11 yd³ = 2.11*(0.83 m³) = 1.7513 m³

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Part A: The total value of the loan with semi-annual compounding is $36,351.74.

Part B: The total value of the loan with quarterly compounding is $36,645.80.

Part C: The difference between the total interest accrued on each loan is $294.06, with the loan that compounds quarterly accruing more interest due to the more frequent compounding periods, which results in a higher effective interest rate over the same time period.

Part A:

To find the total value of the loan with semi-annually compounded interest, we can use the formula for compound interest:

[tex]A = P(1 + r/n)^{ (nt) }[/tex]

Where:

A = the total amount paid

P = the principal amount borrowed

r = the annual interest rate (as a decimal)

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

t = the number of years

In this case, P = $20,000, r = 0.06 (6%), n = 2 (semi-annually compounded), and t = 10 years.

[tex]A = 20000(1 + 0.06/2)^{(2*10) } = $36,109.13[/tex]

Therefore, the total value of the loan with semi-annually compounded interest is $36,109.13.

Part B:

To find the total value of the loan with quarterly compounded interest, we use the same formula but with n = 4 (quarterly compounded):

[tex]A = 20000(1 + 0.06/4)^{(4*10)} = $36,533.71[/tex]

Therefore, the total value of the loan with quarterly compounded interest is $36,533.71.

Part C:

The difference between the total interest accrued on each loan is the difference between the total amount paid for each loan minus the principal borrowed:

For the semi-annually compounded loan:

Total interest = $36,109.13 - $20,000 = $16,109.13

For the quarterly compounded loan:

Total interest = $36,533.71 - $20,000 = $16,533.71

The difference in total interest accrued between the two loans is:

$16,533.71 - $16,109.13 = $424.58

The loan with quarterly compounded interest accrues more interest due to the higher compounding frequency.

The difference in total interest accrued between the two loans is relatively small, but over time it can add up.

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Answer:

16/40 = 40%

Step-by-step explanation:

I divided 16/40 and got 0.4,

To turn a decimal into a percentage, either multiply by 100 or move the decimal to the right 2 times.

The perimeter of the square that is given in the diagram above would be = 96cm

To calculate the perimeter of a square, the formula for the perimeter of a square should be used and this is given below.

That is ;

perimeter = 4a

where ;

a = side length = 24cm

Perimeter = 4× 24 = 96cm

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The shopkeeper should have sold the pen for Rs. 13.80 in order to earn a profit of 15%. Option C

To determine the selling price of the pen in order to earn a 15% profit, we can use the concept of a profit margin.

Let's start by finding the cost price of the pen. Since the shopkeeper wants to make a 10% profit when selling the pen for Rs. 13.20, we can set up the equation:

Cost price + 10% profit = Selling price

Let's assume the cost price of the pen is C. Then, we can write theequation as:

C + 0.1C = 13.20

Simplifying the equation, we have:

1.1C = 13.20

Dividing both sides by 1.1, we find:

C = 12

So, the cost price of the pen is Rs. 12.

Now, to determine the selling price that will yield a 15% profit, we can use the formula:

Selling price = Cost price + Profit

Profit is calculated as a percentage of the cost price. In this case, the profit percentage is 15%. Substituting the values, we have:

Selling price = 12 + 15% of 12

Selling price = 12 + (0.15 * 12)

Selling price = 12 + 1.8

Selling price = 13.8

Therefore, the shopkeeper should have sold the pen for Rs. 13.80 in order to earn a profit of 15%.

The correct answer is option c. Rs. 13.80. Option C

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Answer:

3/4

Step-by-step explanation:

(75 divided by 25 / 100 divided by 25) = 3/4

The graph is given below.

The vertex for the function is located at (8, 1280).

We have,

The given function is a quadratic function of form f(x) = ax² + bx + c, where a = -40, b = 640, and c = 0.

To find the vertex, we need to use the formula:

x = -b/2a

where a = -40 and b = 640.

So,

x = -b/2a = -640/(2(-40)) = 8

Now, we can find the y-coordinate of the vertex by plugging x = 8 into the function:

y = -40(8)^2 + 640(8) = 1280

Therefore,

The vertex for the function is located at (8, 1280).

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a) The number of families that were surveyed is given as follows: 17.

b) The percentage of families with exactly one children is given as follows: 29.4%.

A bar graph shows the output considering a given input.

In this problem, the input is the number of children, while the output is the number of families that have the given number of children.

Hence:

Hence, for item a, the total number of families is given as follows:

4 + 5 + 5 + 2 + 1 = 17.

Out of the 17 families, 5 have exactly one children, hence the percentage is given as follows:

5/17 x 100% = 29.4%.

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The statement "The roots of the blues were in New York City" is NOT true.

among the late 19th and early 20th centuries, the blues first appeared among African American communities in the southern United States, particularly Mississippi.

African American musical traditions such field hollers, work songs, and spirituals were among those that influenced the development of the blues. African Americans utilised it to express their joys and achievements as well as their struggles and tribulations.

Even though the blues eventually spread to other parts of the United States and the world, its roots are firmly planted in the rural South.

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The rotation's angle is -45 degrees.

Quadrilateral A'B'C'D' is the representation of quadrilateral ABCD rotated around (0,0).

Consider D and D's coordinates.

D(2,3) and D'(-2,-3)

Now, Join D and D' then

<DOD = 45

Here, the actual rotation is  -45 degree rotation can be visualized as a reflection across the y-axis followed by a 45 degree rotation in the clockwise direction.

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A statement that describes how the graph of his different from the graph of g include the following: D. The graph of h is the graph of g vertically shifted up 1 unit.

In Mathematics and Geometry, the translation of a graph to the left simply means subtracting a digit from the numerical value on the x-coordinate of the pre-image;

g(x) = f(x + N)

Conversely, the translation a geometric figure or graph upward simply means adding a digit to the numerical value on the positive y-coordinate (y-axis) of the pre-image; g(x) = f(x) + N.

Based on the information provided, we have:

(x, y)                               →                  (x, y + 1)

g(x) = x²

h(x) = g(x) + 1   → h(x) = x² + 1

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There is a problem with the input -16 in the function f(x) = √x

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

f(x) = √x

g(x) = (x - 2)²

h(x) = 2x - 7

k(x) = -x -1

Also, we understand that

He puts the functions in the machine in order

So, we have

f(x) = √x

The input is -16

So, we have

f(-16) = √-16

The square root of -16 is not a real number

Hence, there is a problem with the input

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The compound interest is solved and answer to part b) is not double the answer to part a) because the interest is compounded monthly, not annually.

Given data ,

To calculate how much was in Tristan's account at the end of one year, we can use the formula for compound interest:

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

where A is the amount at the end of the time period, P is the principal (the initial deposit), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.

In this case, P = $750, r = 0.0325, n = 12 (since the interest is compounded monthly), and t = 1. Plugging in these values, we get:

A = $750(1 + 0.0325/12)⁽¹²ˣ¹⁾ = $8,086.43

Therefore, there was $8,086.43 in Tristan's account at the end of one year.

b)

To calculate how much was in Tristan's account at the end of two years,

t = 2,

A = $750(1 + 0.0325/12)⁽¹²ˣ²⁾ = $16,575.29

Hence , there was $16,575.29 in Tristan's account at the end of two years

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Answer:

D. -3 + 2i and E. 3+2i are the zeroes for the equation.

Step-by-step explanation:

The side length x and y of the right triangle are  [tex]\frac{8\sqrt{3} }{3}[/tex] and  [tex]\frac{16\sqrt{3} }{3}[/tex] respectively.

The figure in the image is a right triangle.

Angle θ = 60°

Opposite to angle θ = 8

Adjacent to angle θ = x

Hypotenuse = y

To solve for side lengths x and y, we use the trigonometric ratio.

Note that:

sine = opposite / hypotenuse

cosine = adjacent / hypotenuse

tangent = opposite / adjacent

First, we determine the value of x.

tanθ = opposite / adjacent

tan( 60 ) = 8/x

x = 8/tan( 60 )

x = [tex]\frac{8\sqrt{3} }{3}[/tex]

Next, solve for y:

sinθ = opposite / hypotenuse

sin( 60 ) = 8/y

y = 8/sin( 60 )

y = [tex]\frac{16\sqrt{3} }{3}[/tex]

Therefore, the value of x is  [tex]\frac{8\sqrt{3} }{3}[/tex] and the value of y is  [tex]\frac{16\sqrt{3} }{3}[/tex].

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180.6 is not a reasonable value for the true mean weight of the residents of the town.

Given that the mean weight to be 189 pounds with a margin of error of 8 pounds.

So, the range of the mean weight is =

(189 + 8, 189 - 8)

(197, 181)

Therefore the range will lie between 197 and 181.

Hence 180.6 is not a reasonable value for the true mean weight of the residents of the town.

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