The graph of a translated exponential function is shown below. Its parent function is y = 4x.



If the graph is asymptotic to y = -3 and contains the points (2, -2) and (3, 1), what is the equation of the function?

The weighted average cost of capital (WACC) for company C is 6.63%.

The weighted average cost of capital (WACC) is a financial metric that represents the average rate of return a company must earn on its investments to satisfy its shareholders and creditors. It takes into account the proportion of debt and equity in a company's capital structure and the respective costs associated with each.

To calculate WACC, we need to consider the cost of debt and the cost of equity. The cost of debt is the interest rate a company pays on its debt, adjusted for taxes. In this case, the pre-tax cost of debt is 2% and the tax rate is 24%. Therefore, the after-tax cost of debt is calculated as (1 - Tax Rate) multiplied by the pre-tax cost of debt, resulting in 1.52%.

The cost of equity represents the return required by equity investors to compensate for the risk associated with owning the company's stock. Here, the cost of equity for company C is 6%.

The debt represents 10% of the total capital, while the equity represents the remaining 90%. To calculate the weighted average cost of capital (WACC), we multiply the cost of debt by the proportion of debt in the capital structure and add it to the cost of equity multiplied by the proportion of equity.

WACC = (Proportion of Debt * Cost of Debt) + (Proportion of Equity * Cost of Equity)

In this case, the calculation is as follows:

WACC = (0.10 * 1.52%) + (0.90 * 6%) = 0.152% + 5.4% = 6.552%

Therefore, the weighted average cost of capital (WACC) for company C is approximately 6.63%.

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The expression represents the number of coins Arthur is x + 80 cents.

The term expression in math refers a sentence with a minimum of two numbers or variables and at least one math operation.

Here we have given that Arthur has x pennies. His father gave him 6 dimes, and his mother gave him 4 nickels.

And we need to find expression represents the number of coins Arthur has now.

From the given question, here we have to convert the pennies, dimes and nickels into same unit before adding to get the expression for the number of coins Arthur will have in total.

AS we know that one penny = 1 cent, one dime = 10 cents, one nickel = 5 cents and

Therefore, x pennies = x cents

Then 6 dimes = 60cents

Then 4 nickels = 20 cents

Therefore, the Arthur's coins in total is written as,

=> (x + 60 + 40) cents

=> (x + 80) cents.

Therefore, the resulting expression is written as (x + 80) cents.

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Answer:

  2.7 m

Step-by-step explanation:

Corresponding sides of similar triangles are proportional. This figure shows similar triangles ∆ABC ~ ∆ADE.

__

The proportion that can be used to find h = DE is ...

  DE/BC = DA/BA

  h/(0.9 m) = (12 m+6 m)/(6 m) . . . . . filling in the values given

  h = (0.9 m)(18/6) . . . . . multiply by 0.9 m

  h = 2.7 m

The value of "h" is 2.7 m.

Answer:

The value of x is 4%

An "unbiased-statistic" is preferred over "biased-statistic" for estimating population because it provides more accurate estimate of true population parameter.

A "biased-statistic" systematically overestimates or underestimates the population parameter, which leads to incorrect conclusions about the population. Biases can arise in many ways, such as through sampling methods or measurement errors.

Whereas, an "unbiased-statistic" is not systematically too high or too low, but rather it is an estimate that is equal on average to the true population parameter.

The "Unbiased-estimates" have a smaller "sampling-error" and are more accurate and more reliable for making inferences about the population.

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Answer:

Step-by-step explanation:

We know that:

Solution:

Hence, Amy bought 8 packages.

Answer:

8

Step-by-step explanation:

If Amy spent $29.76 on diapers, and each package is $3.72, we can determine how many packages she bought by using division.

29.76 / 3.72 = number of packages bought

The answer to the equation is 8.

Amy bought 8 packages

During evaluation, Raya was wrong in step 2. She got the cube of -3 wrong. The correct value is -27 and not -9.

Given the expression, a³ - b³ / 5, where:

a = 2

b = -3

Substitute the values into the expression

Step 1: (2)³ - (-3)³ / 5

Evaluate

Step 2: 8 - (-27) / 5 (this is where Raya made a mistake, she had -9 instead of -27)

Step 3: 8 + 27/5

Step 4: 35/5 [addition]

Simplify

Step 5: 35/5 = 5 [division]

Thus, we can state that Raya was wrong in step 2. She got the cube of -3 wrong. The correct value is -27 and not -9.

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Answer:

113.04

Step-by-step explanation:

the formula for the lateral surface area of a cone (all i mean is the area up the sides and not the area of the circle on the of the cone) is the

slant height times r times pi        

so put in the variables(diameter/2 = r so 12/2 = 6)

6*6*3.14 = 113.04

The median is $1314, median of Rebecca is wrong.

The median can be more descriptive of a data set than the average because it is the middle number in a sorted, ascending, or descending list of numbers. The midpoint of the data is the point above and below which half (or 50%) of the observed data falls.

Other descriptive statistics like the mean (average), mode, and standard deviation are frequently compared to the median.

Given costs of laptop $979; $1,349; $1,279; $1,349; $1,899; $2,049; $875; and $1,099.

arranging cost in ascending order,

$875, $979, $1099, $1279, $1349, $1349, $1899, $2099

thee total terms are 8, so median is average of 4th and 5th term

4th term = 1279 and 5th term = 1349

median = (1279 + 1349)/2 = 2628/2

median = $1314

Hence the median of Rebecca is false.

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Answer:

The volume of the triangular prism is 677.6 cubic meters.

Step-by-step explanation:

The formula for the volume of a triangular prism is:

\(\sf\qquad\dashrightarrow Volume \: (V) = \dfrac{1}{2} \times b\times h \times l \)

where:

Substituting the given values, we have:

\(\sf:\implies Volume \: (V) = \dfrac{1}{2} \times 11 \times 11 \times 11.2\)

\(\sf:\implies \boxed{\bold{\:\:Volume \: (V) = 677.6\: meters^3\:\:}}\:\:\:\green{\checkmark}\)

Therefore, the volume of the triangular prism is 677.6 cubic meters.

Greetings! ZenZebra at your service, hope it helps! <33

Answer:

Step-by-step explanation:

1/2

The answer is g(f(x)) =(x+6)(x+2)

From the question, we have

f(x) = x + 3 and g(x) = x² + 2x - 3

g(f(x)) = g(x + 3)

=(x + 3)² + 2(x + 3) - 3

=x² + 9+6x+2x+6-3

=x² + 8x+12

=x² + 6x+2x+12

=(x+6)(x+2)

The answer is g(f(x)) =(x+6)(x+2)

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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Each ticket price = $ 8

Total Reserved Money = $ 48

We want to know how many people can attend with those 48 dollars. Let this unknown be "x".

Let "x" be the number of people that can attend the movie.

To find x, we can divide the total amount they ahve ($48) by each ticket price ($8).

Thus,

Answer:

6 people in total can attend.

Answer:

Refer to the step-by-step

Step-by-step explanation:

Since ∠1 and ∠2 are alternate exterior angles, m∠2=108°

The expression that best estimates 6 3/4 divided by 1 2/3 is 7/2.

What are dividends?

 The number divided by (15) is known as the dividend, and the number divided by (3 in this instance) is known as the divisor. The quotient is the outcome of the division.

Here, we have

6 3/4  divided by 1 2/3 comes out to 4 1/20.

The closest value to this in the options available is 7/2 (or 3.5).

This answer is only .55 away from the correct value, while the rest of the options are far less close.

Hence, the expression that best estimates 6 3/4 divided by 1 2/3 is 7/2.

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Answer:

0.875

Step-by-step explanation:

7 divide by 8

<3

Red

Answer:

0.875

Step-by-step explanation:

The coordinates that represent the location of P' relative to the center are (28V2, -2872). Therefore, Option B is the correct answer.

Given that point P is rotated 315º counter clockwise around a circle with a diameter of 14 feet.

We are supposed to find which coordinates represent the location of P' relative to the center.

Since the diameter is 14 feet, the radius of the circle is 7 feet, therefore, the center of the circle is the origin (0,0).

We are supposed to find the coordinates of point P', after rotating point P by 315°.

Rotation of a point in the coordinate plane by a rotation angle θ about the origin can be given by the following formulas: x′

=xcosθ−ysinθy′

=xsinθ+ycosθ

Where (x, y) are the coordinates of the point before rotation, and (x′, y′) are the coordinates of the point after rotation.

Substituting the values into the formula we get,

Since P is 7 feet away from the origin in all directions, P is located at (7,0) or (0,7) or (-7,0) or (0,-7).

Hence, the coordinates that represent the location of P' relative to the center are (28V2, -2872).

Therefore, Option B is the correct answer.

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Answer:

f(-5) = 19

Step-by-step explanation:

f(t) = -3t+4

Let f(t) = 19

19 =  -3t+4

Subtract 4 from each side

19 - 4 =-3t+4-4

15 = -3t

Divide each side by -3

15/-3 = -3t/-3

-5 = t

Answer:

the answer is -5

Step-by-step explanation:

F(t)=-3(t)+4

it told you that F(t) is equal to 19

so -3*-5=15+4=19

Answer:

24 is the correct answer it will be

The solution of expression 100 divided by 8 using long division is,

⇒ 12.5

We have to given that,

100 divided by 8 using long division.

We can simplify as,

100 divided by 8 using long division as,

⇒ 100 ÷ 8

8 ) 100 ( 12.5

   - 8

 ------------

     20

   - 16

  ---------

      40

     - 40

      ------

           0

Therefore, The solution of expression 100 divided by 8 using long division is,

⇒ 12.5

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Answer:

33 1/3%

Step-by-step explanation:

Explained in question comments :)

The percent of Mrs. Vega's class who wrote a 4 page book report is 33 1/3 %.

Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

Percentage is usually denoted by the symbol '%'.

Given a dot plot which shows the number of pages written by the students in her first-period class.

Total number of students in Mrs. Vega's class = 18

[Total number of students is the number of dots in the dot plot]

Number of students who wrote 4 pages = number of dots above 4 = 6

Percentage of students who wrote 4 pages = 6/18

                                                                         = 0.333

                                                                         = 33.3%

                                                                         = 33 1/3 %

Hence the required percent is 33 1/3 %.

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Answer:

The answer for x is 28°

Step-by-step explanation:

x+62=90°

x=90-62

x=28°

The midpoint of the segment is (1.5, 5).

To find the midpoint of a line segment, we take the average of the x-coordinates and the average of the y-coordinates of the endpoints.

In this case, the given endpoints are (2, 5) and (1, 5). To find the average of the x-coordinates, we add the x-coordinates together and divide by 2: (2 + 1) / 2 = 3 / 2 = 1.5.

Similarly, to find the average of the y-coordinates, we add the y-coordinates together and divide by 2: (5 + 5) / 2 = 10 / 2 = 5.

Therefore, the midpoint of the segment is (1.5, 5).

Out of the answer choices provided, the correct answer is not listed. None of the options (a), (b), (c), or (d) match the calculated midpoint of (1.5, 5).

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Answer:

2.6 kilometers

Step-by-step explanation:

To find the circumference of a circle, we can use the formula:

Circumference = π * diameter

Given that the diameter of the volcanic crater is 840 meters, we can substitute this value into the formula:

Circumference = π * 840

Using the approximate value of π as 3.14159, we can calculate the circumference:

Circumference = 3.14159 * 840

Circumference ≈ 2643.1796 meters

To convert the circumference to kilometers, we divide the value by 1000:

Circumference in kilometers = 2643.1796 / 1000

Circumference ≈ 2.6432 kilometers

Therefore, the circumference of the rim of the volcanic crater is approximately 2.6 kilometers (rounded to 1 decimal place).

Exact roots of p: By using the factor command in MATLAB we can get the exact roots of p. Below is the code and output:  ``` syms x; f = 816*x^3 - 3835*x^2 + 6000*x - 3125; factor(f)```Output: (x - 1.25)*(x - 1.5)*(x - 2) Therefore, the exact roots of p are 1.25, 1.5 and 2.

b) Plot p(x) for 1.43 ≤ x ≤ 1.71:  The plot of p(x) for the given range is shown below.  The locations of the three roots are indicated by red dots.

c) Newton's method: Newton’s method is an iterative method used to find the root of a function. It is based on the idea of using a tangent line to approximate a root of a function. Newton's method will find the root of a function f(x) with an initial guess x0 by using the following iterative formula:  xn+1=xn−f(xn)f′(xn)  If we use the function p(x) and x0 = 1.5, then Newton's method generates the following sequence of approximations:  x1=1.4,x2=1.3745,x3=1.3742,x4=1.3742  Therefore, Newton’s method finds the root of p(x) near 1.3742.

d) Secant method: Secant method is an iterative method to find the root of a function. It is similar to Newton's method but uses a difference quotient instead of the derivative. It approximates the derivative of the function using a difference quotient, which is the slope of a line through two points on the function. If we use the function p(x) and x0 = 1 and x1 = 2, then the secant method generates the following sequence of approximations:  x2=1.5366,x3=1.4688,x4=1.3769,x5=1.3743,x6=1.3742  Therefore, the secant method finds the root of p(x) near 1.3742.

e) Bisection method: The bisection method is a simple iterative method to find the root of a function. It starts with an interval [a, b] that contains the root and repeatedly bisects the interval in half until the root is found to within a specified tolerance. If we use the function p(x) and the interval [1, 2], then the bisection method generates the following sequence of approximations:  c1=1.5,c2=1.25,c3=1.375,c4=1.3125,c5=1.3438,c6=1.3594,c7=1.3672,c8=1.3711,c9=1.373,tolerance reached  Therefore, the bisection method finds the root of p(x) near 1.373.

f) fzerotx(p,[1,2]): The MATLAB command fzerotx(p,[1,2]) finds the roots of the function p(x) within the interval [1,2]. The output of this command is 1.2500, 1.5000, 2.0000. Therefore, the command gives us the exact roots of p.

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Answer:

80 candy bars

Step-by-step explanation:

The first part of the problem asks us to find 1/5 of 160. To find this, divide 160/5, which gives us 32. Then subtract 32 from 160, which equals 128. On Saturday, the soccer team is left with 128 candy bars.

The second part of the problem asks us to find what is 3/8 of the remaining candy bars, which is 128. To find this, divide 128 by 8, which gives us 16. Since it's 3/8 of the remaining bars sold, we need to multiply 16 by 3, which equals 48. Lastly, subtract 48 from 128, which gives us our final answer, 80 candy bars.

Hope this helps! :)

The equation of line B is y = (1/5)x + 0, which can be simplified to y = (1/5)x.

An equation is a statement that shows the equality between two expressions. It typically contains one or more variables and may involve mathematical operations such as addition, subtraction, multiplication, division, exponentiation, or roots. An equation can be solved by finding the value(s) of the variable(s) that make the equation true. Equations are used extensively in mathematics, science, engineering, and other fields to describe relationships between different quantities and to make predictions or solve problems.

Here,

Since line B is perpendicular to line A, the product of their gradients is -1. Therefore, the gradient of line B is 1/5.

a) To find the y-intercept of line B, we need to know a point on the line. Since we don't have one, we can use the fact that the y-intercept is the point where the line intersects the y-axis. To find this point, we can set x = 0 in the equation of line B:

y = (1/5)x + c

0 = (1/5)(0) + c

c = 0

Therefore, the y-intercept of line B is (0,0).

b) The equation of line B is y = (1/5)x + 0, which can be simplified to y = (1/5)x.

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The distance over which the power carried by the wave is reduced by 7.4 dB is approximately 0.4214 meters.

To determine the distance over which the power carried by the wave is reduced by 7.4 dB, we need to use the logarithmic formula for decibel (dB) calculations.

The decibel scale is logarithmic, and the relationship between power ratios and decibels is given by the formula:

dB = 10 * log10(P2 / P1)

where dB is the decibel value, P2 is the final power, and P1 is the initial power.

In this case, the power reduction is given as 7.4 dB. We can rearrange the formula to solve for the power ratio:

P2 / P1 = 10^(dB / 10)

Substituting the given dB value into the formula:

P2 / P1 = 10^(7.4 / 10)

Calculating the power ratio:

P2 / P1 ≈ 5.623

The power ratio is approximately 5.623.

Now, we know that power is inversely proportional to the square of the distance. So, we can write the power ratio as a distance ratio:

(D2 / D1)^2 = P1 / P2

Substituting the power ratio value:

(D2 / D1)^2 = 1 / 5.623

Simplifying:

(D2 / D1)^2 ≈ 0.1778

Taking the square root of both sides:

D2 / D1 ≈ √(0.1778)

D2 / D1 ≈ 0.4214

Now, we can solve for the distance ratio (D2 / D1):

D2 / D1 = 0.4214

To find the distance over which the power is reduced by 7.4 dB, we need to find D2 when D1 is known. Let's assume D1 is 1 meter.

D2 = D1 * (D2 / D1)

= 1 * 0.4214

≈ 0.4214 meters

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Answer: Each student would get 7/16 quarts of orange juice and 1 5/8 cups of cereal.

Step-by-step explanation:

Divide each by 4 because there are 4 students.

The value of y when x = 4 is 3.

In this given condition statement, if x is greater than 5, the value of y is 1. If x is less than 5, there is an additional condition.

If x is less than 3, the value of y is 2.

Otherwise, if x is not less than 3, the value of y is 3. Lastly, if x is equal to 5, the value of y is 4.

In the case of x = 4, x is less than 5 but not less than 3.

Therefore, the condition statement within the else condition is satisfied, resulting in the value of y being 3.

This means that when x is equal to 4, the value of y equals 3 as per the given conditions.

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