= 968 -3. 34x can be used to predict the amount of

monthly interest paid on a loan after x months. Suppose

the amount of monthly interest after 30 months was

$865. 93.

What is the residual for the amount of monthly interest

paid on a loan after 30 months?

O-202. 27

0 -1. 87

O 1. 87

O 202. 27

The** residual **for the amount of monthly interest paid on a loan after 30 months is $0.13.

To find the residual, we need to compare the **actual value** of monthly interest paid after 30 months with the predicted value based on the regression equation.

The **regression equation** is:

monthly interest = 968 - 3.34x

To find the predicted value for **30 months**, we substitute x = 30 into the equation:

monthly interest = 968 - 3.34(30) = 865.8

So the predicted value for monthly **interest** after 30 months is $865.8.

The residual is the **discrepancy** between the actual and expected values:

residual = actual value - predicted value

residual = $865.93 - $865.8 = $0.13

Therefore, the residual for the **amount** of monthly interest paid on a loan after 30 months is **$0.13.**

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Determine which function has the greatest rate of change as x approaches infinity. f(x) = 2x − 10 g(x) = 16x − 4 h(x) = 3x2 − 7x 8 there is not enough information to determine the answer.

The** rate of change** of a **function** as x approaches infinity is determined by the leading term in the function.

For f(x) = 2x - 10, the leading term is **2x.**

For g(x) = 16x - 4, the leading term is **16x.**

For h(x) = 3x^2 - 7x + 8, the leading term is **3x^2.**

Since the coefficient of the leading term in** h(x) is positive**, and it has a **higher degree **than the leading terms of f(x) and g(x), h(x) has the greatest rate of change as x approaches infinity.

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Which expression is equivalent to 1/4(8 - 6x + 12)?

The **expression** that is **equivalent** to 1/4(8 - 6x + 12) is 2 - 3x/2 + 6

**Algebraic expressions **are simply defined as those mathematical expressions that are composed of terms, variables, their coefficients, their factors and constants.

These mathematical expressions are also comprised of **arithmetic operations**.

These operations are listed thus;

BracketParenthesesAdditionSubtractionMultiplicationDivisionFrom the information given, we have that;

1/4(8 - 6x + 12)

expand the bracket, we have;

8 - 6x + 12/4

Divide in group, we have;

8/4 - 6x/4 + 12/4

Divide the values

2 - 3x/2 + 6

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Amy works 15 hours a week at walmart. she earns $8 an hour.

what statement about her weekly income is true?

a) her net income is more than $120.

b) her gross income is less than $120.

c) her net income is less than $120.

d) her gross income is more than $120.

The true statement about Amy's weekly income is that her** net income** is less than $120 (option c).

To find out the true statement about Amy's weekly income, we need to calculate her** gross income** first.

Step 1: Multiply the hours worked per week by the hourly wage.

Amy works 15 hours a week and earns $8 an hour, so:

15 hours * $8/hour = $120

Now we have her gross income, which is $120.

Comparing the gross income to the statements given:

a) Her net income is more than $120: False, as net income is usually less than gross income due to deductions **(taxes, **social security, etc.).

b) Her gross income is less than $120: False, as we calculated her gross income to be exactly $120.

c) Her net income is less than $120: True since net income is generally less than the gross income due to** deductions.**

d) Her gross income is more than $120: False, as her gross income is exactly $120.

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2. Reemplaza los valores correspondientes de "a", "b" y "c", y calcula: a = -2 b = 3 c = 4 a) a + b – c = b) a – b + c = c) a + 2. B – 2c = d) (7. B) : (b + c) = e) a ∙ c + 2. B – 2. C = f) c · (b – a) =

For each expression, the value is calculated by following the order of operations, i.e. first solving any **multiplication **or division, then addition or subtraction. The resulting values are: a + b - c = -3, a - b + c = -1, a + 2b - 2c = -5, (7b)/(b+c) = 3, ac + 2b - 2c = -10, and c(b-a) = 20.

To calculate a + b - c, we **substitute **a = -2, b = 3, and c = 4. So,

a + b - c = -2 + 3 - 4 = -3

To calculate a - b + c, we substitute a = -2, b = 3, and c = 4. So,

a - b + c = -2 - 3 + 4 = -1

To calculate a + 2b - 2c, we substitute a = -2, b = 3, and c = 4. So,

a + 2b - 2c = -2 + 2(3) - 2(4) = -5

To **calculate **(7b) / (b + c), we substitute b = 3 and c = 4. So,

(7b) / (b + c) = (7(3)) / (3 + 4) = 21 / 7 = 3

To calculate ac + 2b - 2c, we substitute a = -2, b = 3, and c = 4. So,

ac + 2b - 2c = (-2)(4) + 2(3) - 2(4) = -10

To calculate c(b - a), we substitute a = -2, b = 3, and c = 4. So,

c(b - a) = 4(3 - (-2)) = 4(5) = 20

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12. Julie is buying a house for $225,000. She obtains a mortgage in the amount of $156,000 at a

4. 5% fixed rate. The bank offers a 4. 25% interest rate if julie pays 2. 25 points. What is the cost

of points for this mortgage rounded to the nearest dollar?

$3,510

$5,063

$6,630

$7,020

The **cost of points **for this mortgage** **is **$3,510** rounded to the nearest dollar if Julie pays 2.25 points.

Cost of house = $225,000.

Mortgage amount = $156,000

Fixed-rate = 4.5%

Bank offer rate = 4.25%

Points to pay = 2.25 points

If we assume that one point is equal to 1%, then 2.25 points are equal to 2.25% of the** loan amount**.

The cost of points for the mortgage can be calculated by the **product** of the loan amount by 2.25%.

Cost of points = 0.0225 × $156,000

Cost of points = $3,510

Therefore, we can conclude that the cost of points for this mortgage is **$3,510 **rounded to the nearest dollar.

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Can someone please help me ASAP? It’s due tomorrow.

**Answer:**

There are 16 total outcomes for tossing 4 quarters

This is because each coin flip has 2 possibilities, so if you flip the coin 4 times it will equal

2x2x2x2.

you select a marble without looking and then put it back if you do this 90 times what is the best predictions that you will pick an orange or a pink marble?

If you select a marble without looking and then put it back if you do this 90 times, the **probability** of selecting an orange or a pink marble on any given trial is 1/2 or 0.5.

If you select a marble without looking and then put it back, the probability of selecting any particular marble on any given trial is the same for all marbles. Assuming there are only two possible **outcomes** - selecting an orange marble or a pink marble - the probability of selecting an orange or a pink marble on any given trial is 1/2 or 0.5.

Since the probability of selecting an orange or a pink marble on each trial is the same, the best **prediction** for the number of times you will select an orange or a pink marble out of 90 trials is an equal number of times for each color. Therefore, the best prediction for the number of times you will select an orange or a pink marble is 45 times each.

This is only a prediction based on probability, and the actual number of times you select an orange or a pink marble may differ from the prediction due to chance. However, over a large number of **trials**, the actual outcomes should approach the predicted probabilities.

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A student is painting a brick for his teacher to use as a doorstop in the classroom. He is only painting the front of the brick. The vertices of the face are (−6, 2), (−6, −7), (6, 2), and (6, −7). What is the area, in square inches, of the painted face of the brick? 144 in2 108 in2 72 in2 42 in2

The **area **of the **painted face **of the brick is given as follows:

108 in².

How to obtain the area of a rectangle?The area of a rectangle of** length l and width w** is given by the multiplication of dimensions, as follows:

A = lw.

The **dimensions **for this problem are given as follows:

Hence the **area **of the **painted face **of the brick is given as follows:

A = 12 x 9 = 108 in².

(the area of a rectangle is given by the multiplication of the dimensions, which we did here).

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Solve the differential equation. dy + 6ydx=9e -⁶x dx y=

The general** solution** to the given **differential equation:**

[tex]y = (9x + C)e^(-6x)[/tex]

To solve the given **differential equation**, dy + 6ydx = 9e^(-6x)dx, we can first rewrite it as a first-order linear differential equation:

[tex]dy/dx + 6y = 9e^(-6x)[/tex]

Now, we will find the** integrating factor**, which is e^(∫P(x)dx), where P(x) is the coefficient of y in the equation:

Integrating factor =[tex]e^(∫6dx) = e^(6x)[/tex]

Next, we multiply the entire differential equation by the integrating factor:

[tex]e^(6x)(dy/dx + 6y) = 9e^(-6x)e^(6x)[/tex]

This simplifies to:

[tex]e^(6x)(dy/dx) + 6e^(6x)y = 9[/tex]

Now, the left side of the equation is the **derivative** of the product of y and the integrating factor:

[tex]d/dx(y * e^(6x)) = 9[/tex]

To solve for y, integrate both sides with respect to x:

[tex]∫[d/dx(y * e^(6x))]dx = ∫9dx[/tex]

This results in:

[tex]y * e^(6x) = 9x + C[/tex]

Finally, we solve for y by dividing by e^(6x):

[tex]y = (9x + C)e^(-6x)[/tex]

And that is the general solution to the given differential equation.

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HELP DUE TOMORROW!!!!!!!!

**Answer:**

The third choice is the correct answer.

Consider the histogram shown in the figure.

Which best describes the histogram?

Skewed left

Skewed right

symmetric

Vertical

Thank you!!!

I'm sorry, i don't have access to the histogram you are referring to. Please provide more information or attach the image so I can help you better.

The monthly demand function for x units of a product sold by a monopoly is p = 5,300 - dollars, and its average cost is C = 3,010 + 2x dollars. Production is limited to 100 units. Find the revenue function!

To find the **revenue function**, we need to multiply the price (p) by the quantity sold (x). The price function given is p = 5,300 - dollars, so we can substitute this into our revenue function as follows:

Revenue = p * x

Revenue = (5,300 - dollars) * x

We also know that **production **is limited to 100 units, so we need to take that into account when determining the revenue function. If x is greater than 100, then the revenue will be limited to 100 units sold. If x is less than or equal to 100, then the revenue will be based on the actual quantity sold.

To incorporate this constraint into our revenue function, we can use a piecewise function:

Revenue = { (5,300 - dollars) * 100 if x > 100

(5,300 - dollars) * x if x <= 100 }

Simplifying the piecewise function, we get:

Revenue = { 530,000 - (dollars * 100) if x > 100

(5,300 - dollars) * x if x <= 100 }

Therefore, the revenue function for this monopoly is:

Revenue = { 530,000 - 100 * dollars if x > 100

(5,300 - dollars) * x if x <= 100 }

Hi! To find the revenue function, we first need to determine the total **revenue**, which is the product of the price per unit (p) and the number of units sold (x). Given the demand function p = 5,300 - x dollars and the average cost function C = 3,010 + 2x dollars, we can find the revenue function as follows:

Revenue function, R(x) = p * x

R(x) = (5,300 - x) * x

By simplifying the equation, we get:

R(x) = 5,300x - x^2

So, the revenue **function **for this monopoly is R(x) = 5,300x - x^2.

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The equation r = 3cos(6θ) represents a rose curve. How many petals does the graph contain

Check the picture below.

**Answer:**

C (12)

**Step-by-step explanation:**

square peg sydney smith wrote in ""on the conduct of the understanding"" that it is im-possible to fit a square peg in a round hole.

On the basic of square peg sydney smith written point the **probability** that it is im-possible to fit a square peg in a round hole is equals to the zero.

Probability is defined as the number of chances of occurrence of an **event**. It is the **ratio** of the number of favorable outcomes to the total outcomes in that **sample space**. Mathematical formula is written as, probability of an event, P(E) = (Number of favorable outcomes)/(Total possible outcomes). Now, we have specify that according to sydney smith written in on the conduct of the understanding about square peg that it is impossible to fit a square peg in a round hole. Let consider an event A of fit a **square peg** in a round hole. We have specify that it is impossible to fit a square peg in a round hole. So, the **favourable** possible **outcomes** for event A = 0. Therefore, the probability that to fit a square peg in a round hole, P(A) = 0

Hence, required probability value is zero.

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1 1/5, 1 2/5,1 2/5, 1 2/5, 1 3/5, 1 3/5 , 1 3/5, 1 4/5, 1 4/5, 2 What fraction of the packages weighed more than 1 2 /5 pounds?

2/5 of the packages **weighed **more than 1 2/5 pounds.

To find the **fraction **of packages that weighed more than 1 2/5 pounds, we need to count the number of packages that weighed more than 1 2/5 pounds and divide it by the total number of packages.

There are a total of 10 packages. Out of these, we can see that 4 packages weighed more than 1 2/5 pounds: 1 1/5, 1 3/5, 1 3/5, and 1 4/5.

Therefore, the fraction of packages that weighed more than 1 2/5 **pounds **is:

4/10

This can be simplified to:

2/5

Hence, only 2/5 of the package weighed more.

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A line is described by the equation y=3/5x+4/7 in slope intercept form identify the slope and y-intercept to the line

The slope of the line is 3/5 and the** y-intercept** is 4/7.

The equation of the line in** slope-intercept form** is y = mx + b, where m is the slope of the line and b is the y-intercept.

In this form, the slope of the line tells us how steeply the line is rising or falling, while the y-intercept tells us where the line crosses the y-axis.

In the given equation y = 3/5x + 4/7, we can see that the coefficient of x, 3/5, is the slope of the line. This means that for every 1 unit increase in x, the line will increase by 3/5 units in y.

A positive slope means that the line is rising from left to right, while a negative slope means that the line is falling.

We can also see that the constant term, 4/7, is the y-intercept of the line. This tells us that the line crosses the** y-axis** at the point (0, 4/7). In other words, when x is 0, y is equal to 4/7.

So, to** summarize**, the slope of the line y = 3/5x + 4/7 is 3/5, which means the line rises 3 units for every 5 units it moves to the right.

The y-intercept is 4/7, which tells us the line crosses the y-axis at the point (0, 4/7).

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Dante has a tent shaped like a triangular prism. The tent has an equilateral base that measures 5 feet on each side. The tent is 8 feet long and 4. 3 feet tall.

101. 5ft

120 ft.

141. 5 ft.

184 ft

What is the surface area of the tent

The **surface area** of Dante's tent is approximately 180 square feet.

To find the surface area of Dante's tent, we need to find the area of each of its **faces** and then add them up. Since the tent is in the shape of a triangular prism, it has three rectangular faces and two triangular faces.

First, let's find the area of each **rectangular face**. We know that the tent is 8 feet long and 4.3 feet tall. To find the width of each face, we need to use the **Pythagorean theorem** since the base of the tent is equilateral. So, we can use a triangle with sides of 5 feet (the base of the tent) and 4.3 feet (the height of the triangular face) to find the width of each rectangular face.

a^2 + b^2 = c^2

5^2 + 4.3^2 = c^2

25 + 18.49 = c^2

43.49 = c^2

c = √43.49

c ≈ 6.6 feet

Now that we know the **width** of each rectangular face, we can find the area of each face:

Area of rectangular face = length x width

Area of rectangular face = 8 x 6.6

Area of rectangular face ≈ 52.8 square feet

Next, let's find the area of each triangular face. Since the base of the tent is **equilateral**, each triangular face has a base of 5 feet and a height of 4.3 feet. The area of each triangular face is:

Area of triangular face = (base x height) / 2

Area of triangular face = (5 x 4.3) / 2

Area of triangular face ≈ 10.8 square feet

Now we can add up the areas of all **five faces** to find the total surface area of the tent:

Surface area of tent = 3 x area of rectangular face + 2 x area of triangular face

Surface area of tent = 3 x 52.8 + 2 x 10.8

Surface area of tent = 158.4 + 21.6

Surface area of tent ≈ 180 square feet

Therefore, the surface area of Dante's tent is **approximately** 180 square feet.

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can the side length make a triangle 5cm, 1cm and 5cm if not explain?

**Answer:**

so

**Step-by-step explanation:**

Let's call the length of each of the other two sides x. Since the triangle is isosceles, it has two sides of equal length. Therefore, the perimeter of the triangle can be expressed as 6 + x + x Simplifying this equation, we get 2x + 6 We know that the perimeter is 22 cm so we can set up an equation and solve for x. 22 = 2x + 6 Subtracting 6 from both sides, we get 16 = 2x Dividing both sides by 2, we get x=8

Researchers in scotland have been following the development of a sample of 11-year-old children since 1932. what type of study are they conducting

In this case, the **researchers** have been following the development of a sample of 11-year-old children since 1932, which is a very long period of time, making it a classic example of a **longitudinal study**

The type of **study** that the researchers in Scotland are conducting is a longitudinal study. Longitudinal studies involve following a group of individuals over an **extended** period of time, often years or even decades, in order to observe changes or continuity in their development, behaviors, or other characteristics.Longitudinal studies are considered to be one of the most powerful research designs for understanding how **individuals** change over time. By following a group of people over an extended period, researchers can gain insight into how different factors, such as social, environmental, and biological, interact to **shape** development.

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The box plot represents the miles Emilia ran after school for 21 days.

3

4

5

9

10

6 7

8

Miles Run

Part B

Can you use the box plot to find the IQR? Explain.

The **IQR** is approximately 1 unit.

Yes, you can use the box plot to find the IQR (**Interquartile Range**).

The IQR is the distance between the upper quartile (Q3) and the lower quartile (Q1) of the data. In a box plot, Q1 is the bottom of the box, and Q3 is the top of the box. The IQR is the height of the box.

Therefore, in the given box plot, you can find the IQR by measuring the height of the box and calculating the difference between Q3 and Q1.

The length of the whiskers and the **positions** of the outliers are not used in calculating the IQR.

So, looking at the box plot, we can see that the **height** of the box is approximately 4 units (the units are not specified in the question).

The bottom of the box (Q1) is at approximately 3 units, and the top of the box (Q3) is at approximately 7 units.

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Use the rules to find derivatives of the functions at the specified values.

f(x) = 4x^3 at x = 2

f(2) = _____

The value of the** function** f(x) at x = 2 is 48.

The question asks us to find the value of the function f(x) = 4[tex]x^3[/tex] at x = 2 and its derivative f'(x) at x = 2.

The value of the function f(x) at x = 2, we simply plug in x = 2 into the function and evaluate:

f(2) = 4[tex](2)^3[/tex] = 4(8) = 32

Therefore,

The value of the function f(x) at x = 2 is 32, which we can write as f(2) = 32.

To find the **derivative** of the function f(x) at x = 2, we first need to find the general formula for the derivative of f(x), which we can do using the power rule for derivatives.

The **power rule** states that

To find the derivative of f(x) at x = 2, we simply plug in x = 2 into the **formula** for f'(x) that we just found:

f'(2) = [tex]12(2)^2[/tex] = 48

Therefore,

The derivative of the function f(x) at x = 2 is 48, which we can write as f'(2) = 48To find the derivative of the function

f'(x) = 12[tex]x^2[/tex]

To find the value of f(2), we can simply plug in x = 2 into the original function:

f(2) = 4[tex](2)^3[/tex] = 32

To find the value of f'(2), we can plug in x = 2 into the derivative we just found:

f'(2) = 12[tex](2)^2[/tex] = 48

Therefore,

f(2) = 32 and f'(2) = 48.

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1. The cost of renting a car for a day is $0.50 per mile plus a $15 flat fee.

(a) Write an equation to represent this relationship. Let x be the number of miles driven and y be the total cost for the day.

(b) What does the graph of this equation form on a coordinate plane? Explain.

(c) What is the slope and the y-intercept of the graph of the relationship? Explain

**Answer:**

a) y=0.50x+15

b) The graph of this equation form on a coordinate plane is a line.

c) Slope =0.50 and y-intercept = 15

**Step-by-step explanation:**

Let x = Number of miles driven by car

Given: The cost of renting a car for a day is $0.50 per mile plus a $15 flat fee.

a) Total cost = 0.50x+15

If y =total cost of renting the car, then y=0.50x+15 (i)

b) Above equation is similar to y= mx+c (ii) [m = slope , xc=y-intercept] which a linear equation .

So the graph of this equation form on a coordinate plane is a line.

c) Comparing (i) and (ii)

m=0.50 , c=15

Hope this helps :)

State the number of complex zeros and the possible rational zeros for the function

show your work

The function f(x) = x² + 12x - 3 has two distinct real roots and no rational or **complex roots**. The possible rational roots are ±1 and ±3, but they are not actual roots of the equation.

To find the number of complex zeros and possible **rational zeros** of the function f(x) = x² + 12x - 3 = 0, we can use the same methods as in the previous question.

According to the rational root theorem, any rational root of the polynomial must be of the form p/q, where p is a **factor **of the constant term (-3) and q is a factor of the leading coefficient (1). The possible rational roots are therefore ±1, ±3.

To determine if there are any complex roots, we can use the quadratic formula. The solutions to the equation f(x) = 0 are given by

x = (-b ± √(b² - 4ac)) / 2a

Plugging in the coefficients of the polynomial, we get

x = (-12 ± √(12² - 4(1)(-3))) / 2(1)

x = (-12 ± √(156)) / 2

x = -6 ± 3√(13)

Since the discriminant (b² - 4ac) is positive, the square root is real, and the roots are two distinct **real numbers**. Therefore, there are no complex roots.

The possible rational roots we found earlier, ±1 and ±3, are not actual roots of the equation, since plugging them into the equation does not give us zero. Therefore, there are no rational roots either.

In conclusion, the equation f(x) = x² + 12x - 3 = 0 has two distinct real roots and no complex or rational roots.

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--The given question is incomplete, the complete question is given

" State the number of complex zeros and the possible rational zeros for the function f(x) = x² + 12x -3 = 0

show your work"--

Full Boat Manufacturing has projected sales of $115. 5 million next year. Costs are expected to be $67. 4 million and net investment is expected to be $12. 3 million. Each of these values is expected to grow at 9 percent the following year, with the growth rate declining by 1 percent per year until the growth rate reaches 5 percent, where it is expected to remain indefinitely. There are 4. 8 million shares of stock outstanding and investors require a return of 10 percent return on the company’s stock. The corporate tax rate is 21 percent

Based on the given information, the estimated **current stock price** for Full Boat Manufacturing is $13.11. This is calculated using the discounted cash flow model, taking into account the projected future cash flows, growth rates, and required rate of return.

To calculate the current stock price, we need to estimate the free cash flows and discount them at the required rate of return.

First, we calculate the free **cash flow **to the firm (FCFF) for next year as follows

FCFF = Sales - Costs - Net Investment*(1-t)

= $115 million - $67 million - $12 million*(1-0.21)

= $31.02 million

Next, we calculate the expected growth rate in FCFF using the formula:

g = (FCFF Year 2 / FCFF Year 1) - 1

where FCFF Year 2 = FCFF Year 1 * (1 + g)

Using the given information, we get

g = (FCFF Year 2 / FCFF Year 1) - 1

= (FCFF Year 1 * (1 + 0.14) * (1 - 0.02) / FCFF Year 1) - 1

= 0.12

We can now use the **Gordon growth model** to estimate the current stock price

Current stock price = FCFF Year 1 * (1 + g) / (r - g)

where r is the required rate of return.

Substituting the values, we get

Current stock price = $31.02 million * (1 + 0.12) / (0.13 - 0.12)

= $72.13 million

Finally, we divide the current stock price by the number of shares outstanding to get the estimate of the current stock price per share:

Current stock price per share = $72.13 million / 5.5 million

= $13.11 per share

Therefore, the estimate of the current stock price is $13.11 per share.

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--The given question is incomplete, the complete question is given

" Full Boat Manufacturing has projected sales of $115 million next year. Costs are expected to be $67 million and net investment is expected to be $12 million. Each of these values is expected to grow at 14 percent the following year, with the growth rate declining by 2 percent per year until the growth rate reaches 6 percent, where it is expected to remain indefinitely. There are 5.5million shares of stock outstanding and investors require a return of 13 percent on the company’s stock. The corporate tax rate is 21 percent.

What is your estimate of the current stock price?

1pt A clothing company needs to determine how much fabric to use for a sleeve on a shirt. It uses the following model arm as a way to test the fit. The sleeve needs to cover

the 20 centimeters from the shoulder to the elbow.

Upper Arm

What solid best represents the model for the sleeve? What is the minimum surface area of fabric needed for the sleeve?

The minimum surface area of **fabric** needed for the sleeve is approximately 628.32 cm².

Based on the given **model arm**, a right circular cylinder would best represent the model for the sleeve.

To calculate the minimum surface area of fabric needed for the sleeve, we need to find the lateral surface area of the right circular cylinder.

The lateral surface area of a right circular cylinder is given by the formula:

Lateral surface area = 2πrh

where r is the radius of the cylinder, h is the height of the cylinder.

In this case, the height of the cylinder needs to be 20 cm (to cover the distance from the shoulder to the elbow), and the radius can vary depending on the desired** fit.** Let's assume a radius of 5 cm for the purposes of this calculation.

Plugging in the values, we get:

Lateral surface area = 2π(5 cm)(20 cm)

= 628.32 cm²

Therefore, the minimum surface area of fabric needed for the **sleeve** is approximately 628.32 cm².

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Classify triangle ABD by its sides and then by its angles.

Select the correct terms from the drop-down menus.

Image shows a triangle ABD having three sides of unequal length and one angle larger than 90 degrees.

Triangle ABD is

and

.

.

Triangle ABD is **scalene **and **obtuse**.

The triangle has three sides of unequal length, hence it is classified as an **scalene **triangle.

(it would be equilateral if all had the same length, and isosceles if two sides have the same length).

The triangle has one angle larger than 90º, hence it is classified as an **obtuse **triangle.

(acute with no angles of 90º or greater, right with one angle of exactly 90º).

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Please show me explanations on these

**Answer:**

1)55,44

2)6,4

3)49,8

4)11,7

5)12,444

6)23,04

7)12,46

8)15,06

9)31,68

10)30,4

**Step-by-step explanation:**

Recheck them and make sure there are no mistakes

Complete parts a through c for the given function. 2 f(x) = xº(x-2) on [ -2,2] O A. The local minimum/minima is/are at x = and there is no local maximum. (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) B. The local maximum/maxima is/are at x = and the local minimum/minima is/are at x = (Use a comma to separate answers as needed. Type integer or simplified fractions.) C. The local maximum/maxima is/are at x = 1 and there is no local minimum. (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) O D. There is no local maximum and there is no local minimum. c. Identify the absolute maximum and minimum values of the function on the given interval (when they exist). Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The absolute maximum is at x= and there is no absolute minimum. (Use a comma to separate answers as needed. Type integers or simplified fractions.) B. The absolute maximum is at x = and the absolute minimum is at x= 11. (Use a comma to separate answers as needed. Type integer or decimals rounded to two decimal places as needed.) O C. The absolute minimum is at x= and there is no absolute maximum. (Use a comma to separate answers as needed. Type integers or simplified fractions.)

The **absolute maximum** occurs at x = -2 and the absolute minimum occurs at x = 0 and x = 2 and The absolute maximum is at x = -2 and the absolute minimum is at x = 0, 2.

a. The local minimum is at x=2 and there is no local maximum.

b. The** local maximum** is at x=1 and the local minimum is at x=-2 and x=2.

c. The absolute maximum is at x=0 and the absolute minimum is at x=2.

(Note: To find the absolute maximum and minimum, we need to evaluate the function at the critical points and endpoints of the interval. The critical points are x=0 and x=2, and the endpoints are x=-2 and x=2. The absolute maximum is the largest value among these, which is f(0)=0. The absolute minimum is the **smallest value** among these, which is f(2)=-4.)

Given the function f(x) = x²(x - 2) on the interval [-2, 2]:

A. To find the local minima and maxima, we need to take the first derivative and find its critical points.

f'(x) = 3x² - 4x

Solving for x, we get x = 0 and x = 4/3.

However, x = 4/3 is not within the **interval **[-2, 2], so the only critical point within the interval is x = 0.

There is a local minimum at x = 0, and no local maximum. Therefore, the answer is:

A. The local minimum is at x = 0 and there is no local maximum. (Type an integer or a simplified fraction.)

B. For the absolute maximum and minimum, we need to evaluate the function at the endpoints and the critical point within the interval.

f(-2) = (-2)²(-2 - 2) = 16

f(0) = (0)²(0 - 2) = 0

f(2) = (2)²(2 - 2) = 0

The absolute maximum occurs at x = -2 and the absolute minimum occurs at x = 0 and x = 2. The answer is:

B. The absolute maximum is at x = -2 and the absolute minimum is at x = 0, 2. (Use a comma to separate answers as needed. Type integers or simplified fractions.)

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Gareth pays $60 for 9m of climbing rope. How much will Sophie pay for 15m at the same store?

Sophie will pay** money** equivalent to **$100** for 15m at the same store.

The term "**money**" in mathematics refers to a form of payment, such as bills, coins, and demand deposits, that is used to purchase goods and services. **Money** is used to pay for the worth or price of an item or service.

A country's monetary system is referred to as its currency.

In the case of Gareth,

**Money** paid for 9 m of climbing [tex]=\$60[/tex]

**Money** paid per m of climbing [tex]=\$60\div9[/tex]

Thus, money paid by Sophie for 15 m of climbing [tex]= 15 \times (60\div9)[/tex]

[tex]\boxed{\bold{= \$100}}[/tex]

Hence Sophie will pay** money** equivalent to **$100** for 15m at the same store.

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**Answer:**

$100

**Step-by-step explanation:**

We know that for **9m of rope**, Gareth had to pay **$60**.

The question is asking us to find out how much Sophie will pay for 15m of rope. To do this, we have to find out how much is** paid per meter of rope**.

[tex]60/9\\=6\frac{2}{3}[/tex]

For the sake of not using fractions, let's keep it as an **improper fraction: 60/9**

So, we can write an equation for the price of 15m of rope:

(60/9)·15

=100

So, Sophie will pay **$100** for 15m of rope.

Hope this helps! :)

The volumes of two similar solids are 15 cubic cm and 45 cubic cm. What is the ratio of their surface areas ? (ANSWER BOTH)

1. The **ratio **of the surface areas of the two similar solids is 3. 2. The ratio of the volumes of the two similar solids is 3.

Surface area is a measure of the total area of the surface of a three-dimensional object. It is the sum of the areas of all the faces, sides, and bases of the object. Surface area is expressed in square units, such as square meters (m²) or square feet (ft²).

The formula for calculating the surface area of a particular object depends on its shape. Some common shapes and their formulas for surface area include:

Rectangular prism: Surface area = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.

Cube: Surface area = 6s², where s is the length of one side.

Sphere: Surface area = 4πr², where r is the radius.

Cylinder: Surface area = 2πr² + 2πrh, where r is the radius and h is the height.

Cone: Surface area = πr² + πrl, where r is the radius and l is the slant height.

1. To find the ratio of the surface areas of two similar solids, we need to use the fact that the ratio of the surface areas is equal to the square of the ratio of their corresponding side **lengths**. Since the solids are similar, their corresponding side lengths are in proportion.

Let's call the ratio of the corresponding side lengths "r". Then, we have:

Ratio of surface areas = r²

To find "r", we can use the fact that the ratio of the volumes of two similar solids is equal to the cube of the ratio of their corresponding side lengths. Therefore:

(Ratio of side lengths)³ = Ratio of volumes

Let's call the ratio of the corresponding side lengths "k". Then, we have:

k³ = 45/15 = 3

k = ∛3

Now, we can find the ratio of surface areas:

Ratio of surface areas = (corresponding side length ratio)²

Ratio of surface areas = (∛3)² = 3

Therefore, the ratio of the surface areas of the two similar solids is 3.

2. To find the ratio of the **volumes **of the two similar solids, we simply divide the larger volume by the smaller volume:

Ratio of volumes = 45/15 = 3

Therefore, the ratio of the volumes of the two similar solids is 3.

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