Evaluate the expression 4x² – 13y for x = 3 and y = 2.

Trader Bubba Industries should recommend buying the solar truck as it has a higher NPV than the electric-powered truck.

a) After-tax cost of the loans

The cost of the loan is given as $50 million borrowed at 3%. The tax rate is 40%.

Formula to calculate the after-tax cost of debt: After-tax cost of debt = cost of debt * (1 - tax rate)

After-tax cost of the loan = 3% * (1 - 0.4) = 1.8%

b) After-tax cost of the bonds

The cost of the bonds is given as $200 million, paying 4% coupon with semi-annual payments, and maturity of 10 years. Trader Bubba sold its $1,000 par-value bonds for $1020 and had to incur $20 flotation cost per bond. The tax rate is 40%.

Formula to calculate the after-tax cost of debt: After-tax cost of debt = cost of debt * (1 - tax rate) * (1 - flotation cost) / (1 - tax rate)

After-tax cost of bonds = 4% * (1 - 0.4) * (1 - 0.02) / (1 - 0.4) = 2.424%

c) After-tax cost of the preferred stocks

The cost of preferred stocks is given as $100 million, paying $15 dividends per share. Trader Bubba sold its preferred shares for $220 and had to incur $20 per share flotation cost. The tax rate is 40%.

Formula to calculate the after-tax cost of preferred stocks: After-tax cost of preferred stocks = cost of preferred stocks * (1 - flotation cost / market price) / (1 - tax rate)

After-tax cost of preferred stocks = $15 * (1 - 20 / 220) / (1 - 0.4) = 9.75%

d) After-tax cost of the common stocks

The beta of common stocks is given as 2, the risk-free rate is 2%, and the market rate is 6%. The tax rate is 40%.

Formula to calculate the after-tax cost of common stocks: After-tax cost of common stocks = risk-free rate + beta * (market rate - risk-free rate) * (1 - tax rate)

After-tax cost of common stocks = 2% + 2 * (6% - 2%) * (1 - 0.4) = 5.2%

e) Weighted average cost of capital (WACC)

WACC = w1r1 + w2r2 + w3r3 + w4r4

Where w = weight,

r = cost of capital.

W1 = $50 million / $400 million = 0.125 or 12.5% (weight of loans)

W2 = $200 million / $400 million = 0.5 or 50% (weight of bonds)

W3 = $100 million / $400 million = 0.25 or 25% (weight of preferred stocks)

W4 = $50 million / $400 million = 0.125 or 12.5% (weight of common stocks)

WACC = 0.125 * 1.8% + 0.5 * 2.424% + 0.25 * 9.75% + 0.125 * 5.2% = 3.874%

f) Net Present Value (NPV) and Internal Rate of Return (IRR) for both types of trucks

Formula to calculate NPV: NPV = -Initial Investment + ∑(Net Cash Flows / (1 + r)t)

Where Initial Investment is the cost of the truck,

Net Cash Flows are the cash flows of each year,

r is the discount rate, and

t is the year.

For the solar truck,Initial investment = $30,000

Net Cash Flows per year = $8,000

Discount rate = WACC

NPV = -$30,000 + $8,000 / (1 + 3.874%) + $8,000 / (1 + 3.874%)2 + ... + $8,000 / (1 + 3.874%)8 = $28,845.80IRR = 12.23%

For the electric-powered truck,Initial investment = $20,000

Net Cash Flows per year = $5,000

Discount rate = WACC

NPV = -$20,000 + $5,000 / (1 + 3.874%) + $5,000 / (1 + 3.874%)2 + ... + $5,000 / (1 + 3.874%)8 = $17,716.80IRR = 13.15%

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Answer:

The area of the room is 432 square feet

Step-by-step explanation:

Let us use the ratio method to solve the question

∵ The scale drawing of the room is 1 inch: 3 feet

→ That means each 1 inch in the drawing represents 3 feet in real

∵ The drawing is 8 inches long by 6 inches wide

∴ The drawing length of the room = 8 inches

∴ The drawing width of the room = 6 inches

→ By using the ratio method

→  inches  :  feet

→  1            :  3

→  8           :  L

→  6           :  W

→ By using the cross multiplication

∵ 1 × L = 8 × 3

∴ L = 24

∴ The actual length of the room is 24 feet

∵ 1 × W = 6 × 3

∴ W = 18

∴ The actual width of the room is 18 feet

Use the formula of the area of the rectangle to find the area of the room

∵ Area of rectangle = length × width

∴ Area of the room = 24 × 18

∴ Area of the room = 432 feet²

∴ The area of the room is 432 square feet

Answer:

Step-by-step explanation:

i think 1

Given:

∆y and dy.

∆x and dx.

Required:

To explain the difference between ∆y and dy, is there difference between ∆x and dx.

Explanation:

∆y and dy are same, dy/dx is the differentiation of y with respect to x or dx/dy is the differentiation of x with respect to y.

Whereas del y is the partial differential of x where we differentiate only one at a time keeping the other variables constant and we partially differentiate all to find who differential.

In the same way ∆x and dx are same, dx/dy is the differentiation of x with respect to y or dy/dx is the differentiation of y with respect to x.

Whereas del x is the partial differential of y where we differentiate only one at a time keeping the other variables constant and we partially differentiate all to find who differential.

Final Answer:

∆y and dy are same, dy/dx is the differentiation of y with respect to x or dx/dy is the differentiation of x with respect to y.

Whereas del y is the partial differential of x where we differentiate only one at a time keeping the other variables constant and we partially differentiate all to find who differential.

In the same way ∆x and dx are same, dx/dy is the differentiation of x with respect to y or dy/dx is the differentiation of y with respect to x.

Whereas del x is the partial differential of y where we differentiate only one at a time keeping the other variables constant and we partially differentiate all to find who differential.

Answer:

Step-by-step explanation:

To convert square meters to square centimeters, we need to multiply by the conversion factor (100 cm / 1 m)^2.

So,

3.9 m² = 3.9 × (100 cm / 1 m)²

3.9 m² = 3.9 × 10,000 cm²

3.9 m² = 39,000 cm²

Therefore, 3.9 square meters is equal to 39,000 square centimeters.

Answer:

D.

Step-by-step explanation:

The answer is D. because the vicinity of the playing field can be associated with the bleachers.

Answer:

Length of fencing: 4, 6, 7, 9, 10

Cost: 36, 54, 63, 81, 90

Step-by-step explanation: I hope this gave you your answer!!

thus, a = -39 is the solution to the equation -a = 4b-7 when (a, -8) is a solution

An equation is a fine statement that asserts the equivalency of two expressions. It generally consists of two sides, with an equal sign between them. Equations are used to describe connections between variables, and to break problems in colorful fields, including mathematics, wisdom, engineering, and economics.

Given by the question.

the equation given is -a = 4b - 7.

We are also told that (a, -8) is a solution to this equation. This means that if we substitute a for x and -8 for y, the equation will be true.

Substituting the given values, we get:

a = 4b - 7 (Given equation)

a = 4(-8) - 7 (Substituting b = -8, since (a, -8) is a solution)

a = -32 - 7 (Simplifying)

a = -39 (Final answer)

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Answer:

0.5 X 3 equals 1.5. So it would take One and a half buckets of paint to paint the walls

Answer:

64,81,100

Step-by-step explanation:

Answer: 64,81 and 100

Step-by-step explanation: 8^2=64, 9^2=81 and 10^2=100

The grocer makes a total of 31 packs of 6 baking potatoes, with the remaining amount of 9 potatoes left over.

To solve this problem, the first step is to subtract the number of individual potatoes (75) from the total number of baking potatoes (189). This leaves us with 114 baking potatoes. Next, we must divide the remaining amount potatoes (114) by the number of potatoes in a pack (6). The answer to this is 19, with a remainder of 4. The grocer can make 19 packs of 6 potatoes and has 4 potatoes left over. Finally, we must add the number of packs made (19) to the number of individual potatoes (75) to get the total number of packs (19+75=94). This means that the grocer makes a total of 31 packs of 6 baking potatoes, with the remaining 9 potatoes left over.

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The complete question: A grocer ha 189 baking potatoe. The grocer put 75 baking potatoes out individually and bags the rest of the potatoes into pack of 6. How many pack of 6 does the grocer make?

Answer:

5

Step-by-step explanation:

1/5 of 5 is one so I am going to say 5.

Can you plz mark as brainliest.

Answer:

When you graph the equation, you get a straight line that passes through the origin, which means the relationship is proportional. The constant of proportionality is the y-value when x = 1, which is 15.

Step-by-step explanation:

Hope this helps!!!!

Answer:

a- 15 b- 1292^cm this is the answer

o1qqqqqqqqqqqazzzxxxxxxxxxxxxxxxxxxxxxxxxxx

Step-by-step explanation:

Probably a cylinder would work best

volume of a cylinder = pi r^2 h

The answer to the equation (-2-3)2 + (-1). (10-30) = 45.

Bracket, of, division, multiplication, addition, and subtraction is referred to as BODMAS. When describing how a mathematical statement behaves in a specific sequence, the BODMAS is utilised. The BODMAS is also known as PEDMAS, which stands for Parentheses, Exponents, Division, Multiplication, Addition, and Subtraction.

According to the BODMAS rule, brackets must be solved first before powers or roots (i.e., division, multiplication, addition, and lastly subtraction), and then the remaining operations. The solution is only accepted as accurate when the BODMAS rule or the PEDMAS rule are applied to an expression.

Using the rule of BODMAS solve the parentheses first:

= (-5)² - 1 (- 20)

= 25 + 20

= 45

Hence, the value of the expression (-2-3)² +(-1). (10-30) = 45.

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Answer:

5230

Step-by-step explanation:

The amount of money in Carson's account after 14 years would be $5231.6

"Compound interest is the interest which is calculated from the original principal plus accumulated interest."

\(A=P(1+\frac{r}{n} )^{nt}\)

where,

A : Final amount

P : Initial amount (principal)

R : interest rate in percentage

r : interest rate (R/100)

n: number of  times the interest is compounded

t :  the overall tenure

For given question,

P = $3900, R = 2.1%, n = 12 (as compounded monthly), t = 14

for R = 2.1%,

\(r=\frac{2.1}{100} \\r=0.021\)

Now, we need to find the value of A.

Using the formula of compound interest,

⇒ \(A=3900 \times (1+\frac{0.021}{12} )^{12\times 14}\)

⇒ \(A=3900\times (1+0.00175)^{168}\)

⇒ \(A=3900\times(1.00175)^{168}\)

⇒ \(A=3900\times 1.3414\)

⇒ \(A=5231.61\)

⇒ \(A\approx \$ 5231.6\)

Hence, there would be $5231.6 in the account after 14 years.

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The directional derivative of the function g(u, v) = u²e^(-v) at the point (3, 0) in the direction of the vector v = 3i + 4j is -6. This is found by taking the dot product between the gradient of g and the unit vector in the direction of v.

The directional derivative of g(u, v) in the direction of vector v can be calculated using the dot product between the gradient of g and the unit vector in the direction of v. The gradient of g is given by:

∇g = (∂g/∂u)i + (∂g/∂v)j

Taking the partial derivatives of g(u, v) with respect to u and v, we have:

∂g/∂u = 2ue^(-v)

∂g/∂v = -u²e^(-v)

Evaluating these partial derivatives at the point (3, 0), we get:

∂g/∂u = 2(3)e^(0) = 6

∂g/∂v = -(3)²e^(0) = -9

Next, we need to find the unit vector in the direction of v. To do this, we normalize the vector v = 3i + 4j by dividing it by its magnitude:

|v| = √(3² + 4²) = 5

The unit vector in the direction of v is given by:

v_unit = (1/5)(3i + 4j)

Finally, we can calculate the directional derivative D_vg(3, 0) by taking the dot product between the gradient of g and the unit vector in the direction of v:

D_vg(3, 0) = ∇g(3, 0) · v_unit = (6i - 9j) · (1/5)(3i + 4j) = (6/5) - (36/5) = -30/5 = -6

Hence, the directional derivative of the function g(u, v) at the point (3, 0) in the direction of the vector v = 3i + 4j is -6.

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We are asked to find the left and right hand limits of the given function.

1. Left-hand limit:

The numerator is negative when we substitute -1, so the absolute value will be evaluated as a negative expression.

Now, factor the numerator

So, the left-hand limit is equal to 7

2. Right-hand limit:

The numerator is positive when we substitute +1, so the absolute value will be evaluated as a positive expression.

Now, factor the numerator and the denominator.

So, the right-hand limit is equal to -7

Hello!

Let's solve:

      \(\text{Copy down the equation}\\14+7.2n=11+7.5n\\\\\\\text{Move all the variables to one sides and constants to the other}\\14-11=7.5n-7.2n\\7.5n-7.2n = 14-11\\0.3n = 3\\\\\\\text{Divide both sides by 0.3}\\\dfrac{0.3n}{0.3} =\dfrac{3}{0.3} \\\\n = 10\)

Answer: 10

Hope that helps!

The correct answer is that the p-value must be a number between zero and one.

The p-value is a crucial statistical tool in hypothesis testing. It is defined as the probability of obtaining the observed outcome, or any outcome more extreme than it, given the null hypothesis is true.

The p-value measures the strength of the evidence against the null hypothesis. In general, the smaller the p-value, the stronger the evidence against the null hypothesis. Therefore, the p-value must be a number between zero and one.

When a p-value is close to zero, it indicates that the probability of observing the observed outcome under the null hypothesis is very low.

In contrast, when a p-value is close to one, it indicates that the observed outcome is very likely to have occurred by chance under the null hypothesis. In hypothesis testing, a p-value less than or equal to the significance level (usually 0.05) is considered significant.

If the p-value is significant, the null hypothesis is rejected, and the alternative hypothesis is supported. If the p-value is not significant, the null hypothesis is not rejected, and no conclusion can be drawn about the alternative hypothesis.

The p-value cannot be negative or outside the range of 0 to 1. Therefore, the correct answer is that the p-value must be a number between zero and one.

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Answer:  5.  The initial value corresponds to the y value when x = 0.

Step-by-step explanation: You are given the graph, so you do not need to plot anything. Finding rise over run does nothing to help you find the initial value.

The "initial value" on a graph of a linear function is also known as the "y-intercept." It is the y-value corresponding to x = 0.

Steps given by

He also added lettuce, tomatoes, and cheese. Kenneth also made sure to put plenty of condiments like mayonnaise and mustard on each sandwich.

Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.


Kenneth's family was excited to get to the beach. When they arrived, they set up their umbrellas and beach chairs and found a spot to settle down. After they were all settled, Kenneth passed out the sandwiches he had made. Everyone was satisfied with the delicious sandwiches Kenneth had created.

Kenneth's family enjoyed their day at the beach. They swam in the ocean, built sandcastles, and played volleyball. They even laid out and got a nice tan. As the day got hotter, Kenneth's family got hungrier. Fortunately, they still had the sandwiches Kenneth had made. Everyone was thankful for the delicious sandwiches that Kenneth had prepared for them.

After a fun day at the beach, Kenneth's family packed up their things and headed home. Kenneth was happy that he could provide for his family and make their day even better. He was grateful for the opportunity to make the sandwiches for his family and make their day at the beach even more enjoyable.

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The expressions for the lengths of the segments obtained using vectors notation are;

a. i. \(\overrightarrow{LA}\) = q - (1/2)·p  ii. \(\overrightarrow{AN}\) = (2/7)·(p - q)

b. The expressions for \(\overrightarrow{MN}\), \(\overrightarrow{LA}\), and \(\overrightarrow{AN}\) indicates;

\(\overrightarrow{MN}\) = (1/84)·(46·q - 11·p)

A vector is a quantity that has magnitude and direction and are expressed using a letter aving an arrow in the form, \(\vec{v}\)

a. i. \(\overrightarrow{LA}\) = \(\overrightarrow{BA}\) - \(\overrightarrow{LB}\) =  \(\overrightarrow{BA}\) - (1/2) × \(\overrightarrow{CB}\)

\(\overrightarrow{BA}\) - (1/2) × \(\overrightarrow{CB}\) = q - (1/2)·p

\(\overrightarrow{LA}\) = q - (1/2)·p

ii. \(\overrightarrow{AC}\) = \(\overrightarrow{BC}\) - \(\overrightarrow{BA}\)

\(\overrightarrow{AN}\) = (2/7) × \(\overrightarrow{AC}\)

\(\overrightarrow{AN}\) = (2/7) × \(\overrightarrow{BC}\) - \(\overrightarrow{BA}\)

\(\overrightarrow{AN}\) = (2/7) × (p - q)

b. \(\overrightarrow{MN}\) = \(\overrightarrow{MA}\) + \(\overrightarrow{AN}\)

\(\overrightarrow{MA}\) = (5/6) × \(\overrightarrow{LA}\)

\(\overrightarrow{LA}\) = q - (1/2)·p

\(\overrightarrow{AN}\) = (2/7) × (p - q)

Therefore;

\(\overrightarrow{MN}\) = (5/6) × ( q - (1/2)·p) + (2/7) × (p - q)

\(\overrightarrow{MN}\) = (1/84) × ( 70·q - 35·p + 24·p - 24·q) = (1/84)(46·q - 11·p)

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Answer:

94884959969449i9959595959595

Step-by-step explanation:

Answer:

(6f - 6.1)

Step-by-step explanation:

Since you are multiplying DIFFERENT signs, the signs change. SO the "-" turns into a "+" and the "+" turns into a "-".

Answer:

Step-by-step explanation: hope this helps :)

DOMAIN: (-INFINITY,0)

RANGE:(-INIFINITY,INFINITY)

All the conditions of Rolle's Theorem are satisfied. So, there exists a point c between -1 and 2 such that f'(c) = 0. \(f(x) = x^2 - x - 2\) has an x-intercept at x = 2 and x = -1.

Rolle's Theorem is a fundamental theorem in calculus named after the French mathematician Michel Rolle. It states that if a real-valued function f is continuous on a closed interval [a, b], differentiable on the open interval (a, b), and f(a) = f(b), then there exists at least one point c in the open interval (a, b) where the derivative of f is zero, i.e., f'(c) = 0.

To use Rolle's Theorem, we need to show that:

f(x) is continuous on the closed interval [a, b], where a and b are the x-coordinates of the two x-intercepts of f(x).

f(x) is differentiable on the open interval (a, b).

f(a) = f(b) = 0.

First, we need to find the x-intercepts of f(x):

\(f(x) = x^2 - x - 2\\\\0 = x^2 - x - 2\)

0 = (x - 2)(x + 1)

x = 2 or x = -1

So the x-intercepts of f(x) are x = 2 and x = -1.

Now, we need to check the conditions of Rolle's Theorem.

Since the x-intercepts are at x = 2 and x = -1, we need to show that f(x) is continuous on the closed interval [-1, 2].

f(x) is a polynomial and is continuous for all real numbers. Therefore, it is continuous on the closed interval [-1, 2].

We also need to show that f(x) is differentiable on the open interval (-1, 2).

f'(x) = 2x - 1

f'(x) is a polynomial and is defined for all real numbers. Therefore, it is differentiable on the open interval (-1, 2).

Finally, we need to show that f(-1) = f(2) = 0.

\(f(-1) = (-1)^2 - (-1) - 2 = 0\\\\f(2) = (2)^2 - (2) - 2 = 0\)

Therefore, all the conditions of Rolle's Theorem are satisfied. So, there exists a point c between -1 and 2 such that f'(c) = 0.

f'(x) = 2x - 1

0 = 2c - 1

2c = 1

c = 1/2

So, \(f(x) = x^2 - x - 2\) has an x-intercept at x = 2 and x = -1, and it crosses the x-axis at some point between x = -1 and x = 2, specifically at x = 1/2.

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