Find the value of f(9)
y = f(x)

The company would incur a loss of $14,800,000 if it spends an additional $200,000 on advertising to achieve sales of 35,000 units.

Sales generally refer to the total amount of goods or services that a business sells during a given period of time, typically measured in monetary terms. Sales can also refer to the process of selling products or services, including activities such as prospecting, lead generation, sales presentations, and closing deals.

To calculate the operating profit with sales of 35,000 units and an additional selling expense of $200,000, we need to first calculate the total revenue and the total cost, and then subtract the total cost from the total revenue.

From the table provided, we can see that the selling price per unit is $900 and the variable cost per unit is $600. Therefore, the contribution margin per unit is:

Contribution margin per unit = Selling price per unit - Variable cost per unit

= $900 - $600

= $300

Since the sales target is 35,000 units, the total contribution margin is:

Total contribution margin = Contribution margin per unit x Number of units sold

= $300 x 35,000

= $10,500,000

The total cost can be calculated as follows:

Total cost = Fixed cost + Variable cost

= $3,500,000 + ($600 x 35,000)

= $25,100,000

Adding the additional selling expense of $200,000, the new total cost becomes:

New total cost = $25,100,000 + $200,000

= $25,300,000

Therefore, the operating profit with sales of 35,000 units and an additional selling expense of $200,000 is:

Operating profit = Total revenue - Total cost

= ($900 x 35,000) - $25,300,000

= $10,500,000 - $25,300,000

= -$14,800,000

This indicates that the company would incur a loss of $14,800,000 if it spends an additional $200,000 on advertising to achieve sales of 35,000 units.

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Answer:

Binomial = 0.8724

Normal approximation = 0.873

Step-by-step explanation:

Given that :

Sample size (n) = 20

p = 0.6

q = 1 - p = 1 - 0.6 = 0.4

.using normal approximation :

Mean = np

Mean (m) = 20 * 0.6 = 12

Standard deviation (s) = √npq

s = √(20 * 0.6 * 0.4) = 2.1908902

Probability of 10 or more lines in use :

p(x ≥ 10)

Applying for correction:

p(x ≥ 10 - 0.5) = p(x ≥ 9.5)

Using the z formula :

Z = (x - m) / s

Z = (9.5 - 12) / 2.1908902

Z = - 1.141

p(Z > - 1.141) = 0.87307 (Z probability calculator)

p(Z > - 1.141) = 0.873

Using the binomial distribution :

P(x = x) = nCx * p^x * (1 - p)^(n-x)

p(x ≥ 10) = p(x = 10) + p(x = 11) +.... + p(x = 20)

Using calculator :

p(x ≥ 10) = 0.87247

= 0.873

Answer:

A

Step-by-step explanation:

you can see graph of f(x) changed one unit to the left, since it goes to the left, you should +1 in terms of x. so sqr x+1 is the solution. one way to think about that is you plus one for every x value, that means you get to a point previously for one unit. and turns out it looks like you moves to the left.

Hope that helps

Answer:

x¹¹ • x⁹

Step-by-step explanation:

so hope it help

have a nice day

Answer:

in order

y = -3x + 5

y = 1/2(x) + 2

y = -x - 3

y = 2/3(x) - 2

Step-by-step explanation:

slope-intercept form is y= mx + b

10. 6x + 2y = 10

2y = -6x + 10, subtract 6x from both sides

y= -3x + 5, divide both sides by 2

11. x + 2y = 4

2y = x + 4, subtract x from both sides

y = 1/2(x) + 2, divide both sides by 2

12. x + y = -3

y = -x - 3, subtract x from both sides

13. -2x + 3y = -6

3y = 2x - 6, add 2x to each side

y = 2/3(x) - 2, divide both sides by 3

Answer:

x = 0 , x = 3

Step-by-step explanation:

y = - 2x(x - 3)²

to find the x- intercepts, where the graph crosses the x- axis, let y = 0

- 2x(x - 3)² = 0 ← product of factors on left

equate each factor to zero and solve for x

- 2x = 0 ⇒ x = 0

(x - 3)² = 0

x - 3 = 0

x = 3 with multiplicity 2

the x- intercepts are x = 0 and x = 3

The interest is 16% compounded semi-annually, is Rs. 121,179.10.

To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.

Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)

So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:

Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.

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The volume generated by rotating the region bounded by the curves \($x = \sqrt{y}$\), \($x = 0$\), and \($y = 4$\) about the x-axis using the method of cylindrical shells is \($4\pi$\) cubic units.

The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.

To find the volume generated by rotating the region bounded by the curves \($x = \sqrt{y}$\), \($x = 0$\), and \($y = 4$\) about the x-axis using the method of cylindrical shells, we need to follow these steps:

Sketch the region and the axis of rotation. The region bounded by the curves \($x = \sqrt{y}$\), \($x = 0$\), and \($y = 4$\) is a quarter-circle with radius 2 centered at the origin. The axis of rotation is the x-axis.

Choose a vertical strip with width $\Delta x$ that runs parallel to the y-axis and intersects the region. The height of this strip is given by the equation $y = 4 - x^2$.

Imagine rotating this strip around the x-axis to form a cylindrical shell with thickness \($\Delta x$\), height \($4 - x^2$\), and radius \($x$\).

The volume of this cylindrical shell is given by the formula \($V = 2\pi x(4-x^2)\Delta x$\).

To find the total volume of the solid, we need to add up the volumes of all the cylindrical shells. This can be done by taking the limit as the width of the strips $\Delta x$ approaches zero and summing up the volumes of the resulting shells. This gives us the integral:

\($V = \int_{0}^{2} 2\pi x(4-x^2) dx$\)

We can simplify this integral by expanding the expression inside the parentheses, which gives us:

\($V = \int_{0}^{2} 8\pi x - 2\pi x^3 dx$\)

We can then integrate each term separately to get:

\($V = [4\pi x^2 - \frac{1}{2}\pi x^4]_{0}^{2}$\)

\($V = (4\pi \cdot 2^2 - \frac{1}{2}\pi \cdot 2^4) - (4\pi \cdot 0^2 - \frac{1}{2}\pi \cdot 0^4)$\)

\($V = 8\pi - 4\pi = 4\pi$\)

Therefore, the volume generated by rotating the region bounded by the curves \($x = \sqrt{y}$\), \($x = 0$\), and \($y = 4$\) about the x-axis using the method of cylindrical shells is \($4\pi$\) cubic units.

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a. In interval notation, Increasing intervals: (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm). Decreasing intervals: (8am, 9am) U (11am, 12pm). Constant intervals: (9am, 10am) U (10am, 11am)

b. The increase in cost between 12 noon and 3 pm is $2.

c. Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

Interval notation is used to represent continuous intervals of numbers or values, like ranges on a number line.

The graph shows that from 8-9am, and 11-12pm, the cost from Swift Ride decreases.

We can represent it as (8am, 9am) U (11am, 12pm).

It increases at these times (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm).

And stays constant at : (9am, 10am) U (10am, 11am)

We simply deduct the 12pm's cost from 3pm's cost.

So, we have

Cost increase = $3.5 - $1.5

Evaluate the difference

Cost increase = $2

Hence, the cost increase is $2

When you plot the points provided for Yellow cab, you'll notice that Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

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Based on the given assumptions and calculations, the net present value (NPV) of the investment in the new piece of equipment is -$27,045.76, indicating that the investment is not favorable.

To calculate the after-tax cash flows for each year and evaluate the investment decision, let's use the following information:

Assumptions:

Tax depreciation is straight-line over five years.

Pre-tax salvage value is $10,000 in Year 5 and $15,000 if the asset is scrapped in Year 4.

Tax on salvage value is 30% of the difference between salvage value and book value of the investment.

The cost of capital is 12%.

Given:

Initial investment cost = $50,000

Useful life of the equipment = 5 years

To calculate the depreciation expense each year, we divide the initial investment by the useful life:

Depreciation expense per year = Initial investment / Useful life

Depreciation expense per year = $50,000 / 5 = $10,000

Now, let's calculate the book value at the end of each year:

Year 1:

Book value = Initial investment - Depreciation expense per year

Book value \(= $50,000 - $10,000 = $40,000\)

Year 2:

Book value = Initial investment - (2 \(\times\) Depreciation expense per year)

Book value \(= $50,000 - (2 \times$10,000) = $30,000\)

Year 3:

Book value = Initial investment - (3 \(\times\) Depreciation expense per year)

Book value = $50,000 - (3 \(\times\) $10,000) = $20,000

Year 4:

Book value = Initial investment - (4 \(\times\) Depreciation expense per year)

Book value \(= $50,000 - (4 \times $10,000) = $10,000\)

Year 5:

Book value = Initial investment - (5 \(\times\) Depreciation expense per year)

Book value \(= $50,000 - (5 \times $10,000) = $0\)

Based on the assumptions, the salvage value is $10,000 in Year 5.

If the asset is scrapped in Year 4, the salvage value is $15,000.

To calculate the tax on salvage value, we need to find the difference between the salvage value and the book value and then multiply it by the tax rate:

Tax on salvage value = Tax rate \(\times\) (Salvage value - Book value)

For Year 5:

Tax on salvage value\(= 0.30 \times ($10,000 - $0) = $3,000\)

For Year 4 (if scrapped):

Tax on salvage value\(= 0.30 \times ($15,000 - $10,000) = $1,500\)

Now, let's calculate the after-tax cash flows for each year:

Year 1:

After-tax cash flow = Depreciation expense per year - Tax on salvage value

After-tax cash flow = $10,000 - $0 = $10,000

Year 2:

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $0 - $0 = $0

Year 3:

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $0 - $0 = $0

Year 4 (if scrapped):

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $15,000 - $1,500 = $13,500

Year 5:

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $10,000 - $3,000 = $7,000

Now, let's calculate the net present value (NPV) using the cost of capital of 12%.

We will discount each year's after-tax cash flow to its present value using the formula:

\(PV = CF / (1 + r)^t\)

Where:

PV = Present value

CF = Cash flow

r = Discount rate (cost of capital)

t = Time period (year)

NPV = PV Year 1 + PV Year 2 + PV Year 3 + PV Year 4 + PV Year 5 - Initial investment

Let's calculate the NPV:

PV Year 1 \(= $10,000 / (1 + 0.12)^1 = $8,928.57\)

PV Year 2 \(= $0 / (1 + 0.12)^2 = $0\)

PV Year 3 \(= $0 / (1 + 0.12)^3 = $0\)

PV Year 4 \(= $13,500 / (1 + 0.12)^4 = $9,551.28\)

PV Year 5 \(= $7,000 / (1 + 0.12)^5 = $4,474.39\)

NPV = $8,928.57 + $0 + $0 + $9,551.28 + $4,474.39 - $50,000

NPV = $22,954.24 - $50,000

NPV = -$27,045.76

The NPV is negative, which means that based on the given assumptions and cost of capital, the investment in the new piece of equipment would result in a net loss.

Therefore, the investment may not be favorable.

Please note that the calculations above are based on the given assumptions, and additional factors or considerations specific to the business should also be taken into account when making investment decisions.

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The complete question may be like :

Assumptions: Tax depreciation is straight-line over five years. Pre-tax salvage value is $10,000 in Year 5 and $15,000 if the asset is scrapped in Year 4. Tax on salvage value is 30% of the difference between salvage value and book value of the investment. The cost of capital is 12%.

You are evaluating an investment in a new piece of equipment for your business. The initial investment cost is $50,000. The equipment is expected to have a useful life of five years.

Using the given assumptions, calculate the after-tax cash flows for each year and evaluate the investment decision by calculating the net present value (NPV) using the cost of capital of 12%.

Answer:

Slope = -18

Step-by-step explanation:

To find the slope plug in the coordinate values into the equation for slope:

Slope = (y2 - y1 ) / (x2 - x1)

(34, 12)

(32, 48)

y2 = 48

y1 = 12

x2 = 32

x1 = 34

(y2 - y1 ) / (x2 - x1) =

(48 - 12) / (32 - 34) =

36 / -2 =

-18

Based on the information we can infer that the equation shown in the image is 1.23 - 0.35 = 0.88 (option B).

To identify the correct equation we must look at the graph and identify the information it provides. In this case we have two squares divided into 100 squares each. Additionally, the square on the left has 88 squares painted in red and 12 squares with an X inside. In the case of the square on the right, it has 23 squares colored in red with an X inside.

In total we have 123 squares painted in red, which in decimal number is equivalent to 1.23. On the other hand, the number of squares painted red and with an X inside is 35, this value would be 0.35.

On the other hand, the squares painted only in red are 88, so the equivalent in decimal numbers would be 0.88. Therefore, the correct way to express this relationship through an equation would be:

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By solving the linear equation it can be obtained that

The value of x is 2

What is a linear equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

The given linear equation is

0.3 = 0.5x - 0.7

0.5x = 0.3 + 0.7

0.5x = 1

x = \(\frac{1}{0.5}\)

x = 2

The solution of this linear equation is x = 2

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See explanation below

The coordinates of triangle RST: R(7,4), S(5,-3), and T(2,6)

A reflection across the y = x means (x, y) becomes (y, x)

Plotting the graph of the original image:

After the reflection aross the line y = x, the new coordiantes will be:

R'(4, 7), S(-3, 5) and (T(6, 2)

plotting the graph of the image:

Both the original and new image:

Answer:

62/9

Step-by-step explanation:

Answer:

The ratio of apple juice to pineapple juice to grape juice is 6 : 2 : 4.

Step-by-step explanation:

You can factor out all of the other answers due to the order of the Pineapple, Grape, and Apple juice in the answers. You need to ensure the #'s in the ratios align with that of the numbers for each of the juices.

Answer: it’s the last one (c)

Answer:

A

Step-by-step explanation:

Answer: Students 1 and 3

Step-by-step explanation:

student 1=

- (5r+3s-1)=

-5r+3s-1=

the same answer as student 3

Answer:

d = 5 is a solution to the equation 13 - d = 8

Step-by-step explanation:

We have to solve 13 - d = 8

Now,

13 - d = 8,

We add d on both sides,

13 - d + d = 8 + d

13 = 8 + d

we subtract 8 from both sides,

13 - 8 = 8 - 8 + d

5 = d

d = 5

Hence the answer is 5

The value of the inverse function f-¹ (3) is (e) 11

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

f(x) = x - 8

To calculate the inverse value at f-¹ (3)

We set the value to 3

using the above as a guide, we have the following:

x - 8 = 3

Evaluate the like terms

x = 11

Hence, the value of the inverse function is (e) 11

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Complete question

if f(x) = x - 8, what is the value of f-¹ (3)?

Answer:

1 16/25

Step-by-step explanation:

I just recently learned this kind of stuff!

Answer:

1 16/25

Step-by-step explanation:

164-100=64

Common factors of 64 and 100:

1, 2, 4

Greatest common factor: 4

64/4=16

100/4=25

16/25

1 16/25

Yes, the deviation is greater than it was in tossing them 40 times.

A standard deviation (or σ) is a measure of how widely distributed the data is in reference to the mean. A low standard deviation suggests that data is grouped around the mean, whereas a large standard deviation shows that data is more spread out.

Given:

n= 400 trials

Tossing 2 coins 400 times gives 800 trials

so, \(\sigma_1\)² = np(1- p)

        = 800 x 1/2 x 1/2

      \(\sigma_1\)  = √200

      \(\sigma_1\) = 10√2

Now, n=40

and,  \(\sigma_2\)² = np(1- p)

        = 80 x 1/2 x 1/2

      \(\sigma_2\)  = √20

      \(\sigma_2\) = 2√5

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Answer:

\(x = 5\)

Step-by-step explanation:

From the given:

$18 ——→ 1 home

$90 ——→ x home

Cross multiply the above and make x the subject of formula.

\(18x = 90\)

Now, divide both sides by 18 to find the value of x.

\( \frac{18x}{18} = \frac{90}{18} \)

Therefore:

Tim made $90 from cleaning 5 homes.

This question is solved using the conditional probability concept.

Using this concept, we find that:

First, the concept is presented.

Conditional Probability

We use the conditional probability formula to solve this question. It is

\(P(A|B) = \frac{P(A \cap B)}{P(B)}\)

In which

P(A|B) is the probability of event A happening, given that B happened.

\(P(A \cap B)\) is the probability of both A and B happening.

P(B) is the probability of B happening.

----------------------------------------------------

Question a:

For relation with the formula presented above, I will change events A and B.

Event A: Person is infected.

Event B: Positive test.

Probability of a positive test:

Thus:

\(P(B) = 0.85\frac{1}{300} + 0.05\frac{299}{300} = \frac{0.85\times1 + 0.05\times299}{300} = 0.0527\)

Probability of a positive test and the person is infected.

85% = 0.85 out of 1/300. Thus:

\(P(A \cap B) = \frac{0.85}{300} = 0.0028\)

Desired probability:

\(P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.0028}{0.0527} = 0.053\)

0.053*100% = 5.3%, thus:

P(AIB)= 5.3%

---------------------

Question b:

Event A: Does not have the virus

Event B: Test negative.

Probability of a negative test:

Thus:

\(P(B) = 0.15\frac{1}{300} + 0.95\frac{299}{300} = \frac{0.15\times1 + 0.95\times299}{300} = 0.9473\)

Probability of a negative test and the person is not infected.

0.95 out of 299/300

Thus:

\(P(A \cap B) = \frac{0.95\times299}{300} = 0.9468\)

Desired probability:

\(P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.9468}{0.9473} = 0.999\)

0.999*100% = 99.9%, so:

P(A'|B') = 99.9%

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The correct statement regarding the residual in this problem is given as follows:

2.66; The line of best fit underpredicts the temperature change.

For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:

Residual = Observed - Predicted.

For a rain amount of 0.4 inches, the predicted temperature change is given as follows:

y = -1.4 x 0.4 + 0.2

y = -0.36.

Then the residual is given as follows:

R = 2.3 - (-0.36)

R = 2.66 -> underpredicts the change.

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Answer:

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sofiapenaloza

05/31/2023

Mathematics

College

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The equation for the line of best fit for change in temperature, y, to amount of rain, r, is given by ŷ = − 1.4r + 0.2. On Monday, the observed amount of rain was 0.4 inches and the temperature change was 2.3 degrees. Find and interpret the residual.

2.66; The line of best fit overpredicts the temperature change.

2.66; The line of best fit underpredicts the temperature change.

1.94; The line of best fit underpredicts the temperature change.

−1.94; The line of best fit overpredicts the temperature change.

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joaobezerra

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31.3K answers

261.9M people helped

The correct statement regarding the residual in this problem is given as follows:

2.66; The line of best fit underpredicts the temperature change.

What are residuals?

For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:

Residual = Observed - Predicted.

For a rain amount of 0.4 inches, the predicted temperature change is given as follows:

y = -1.4 x 0.4 + 0.2

y = -0.36.

Then the residual is given as follows:

R = 2.3 - (-0.36)

R = 2.66 -> underpredicts the change.

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Step-by-step explanation:

The 95% confidence interval for the effectiveness of the blood-pressure drug is given as follows:

\(22.6 < \mu < 24.4\)

The mean, the standard deviation and the sample size for this problem, which are the three parameters, are given as follows:

\(\overline{x} = 23.5, \sigma = 12.2, n = 775\)

Looking at the z-table, the critical value for a 95% confidence interval is given as follows:

z = 1.96.

The lower bound of the interval is then given as follows:

\(23.5 - 1.96 \times \frac{12.2}{\sqrt{775}} = 22.6\)

The upper bound of the interval is then given as follows:

\(23.5 + 1.96 \times \frac{12.2}{\sqrt{775}} = 24.4\)

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Answer:  parisslasheaa_ on IG