At a charity fund raiser, adult tickets were sold for $11 each and children’s tickets were sold for $5 each. Write an algebraic expression for the total amount of money raised from the sale of tickets. How much money was raised if the fund raiser sold 247 adult tickets and 390 children’s tickets? Let a= number of adult tickets and c= number of child tickets.

Answer:

Since the instruction in the question indicates that the % symbol should not be used, the weighted average cost of capital (WACC) for Easy Car Corp is therefore 12.07.

Step-by-step explanation:

This can be calculated using the following steps:

Step 1: Calculation of the current bond price

Semiannual coupon amount = Bond face value * Semiannual coupon rate = $1000 * (10% / 2) = $50

Semiannual coupon discount factor = ((1 - (1 / (1 + r))^n) / r) .......... (1)

Where;

r = Semiannual yield to maturity (YTM) = 8% / 2 = 0.08 / 2 = 0.04

n = number of semiannuals = 23 years * 2 = 46

Substituting the values into equation (1), we have:

Semiannual coupon discount factor = ((1-(1/(1 + 0.04))^46) / 0.04) = 20.8846535613106

Present value of coupon = (Semiannual coupon amount * Semiannual coupon discount factor) = $50 * 20.8846535613106 = $1,044.23

Present value of the face value of the bond = Face value / (1 + r)^n = $1,000 / (1 + 0.04)^46 = $164.61

Therefore, we have:

Current bond price = Present value coupon + Present value of the face value of the bond = $1,044.23 + $164.61 = $1,208.84

Step 2: Calculation of weights of each finance source

Market value of common shares outstanding = Number common shares outstanding * Current price per share = 2,000,000 * $13 = $26,000,000.

Market value of bond = Number of bonds * Current bond price = 30,000 * $1,208.84 = $36,265,200

Total financing market value = Market value of common shares outstanding + Market value of bond = $26,000,000 + $36,265,200 = $62,265,200

Weight of Market value of common shares outstanding = Market value of common shares outstanding / Total financing market value = $26,000,000 / $62,265,200 = 0.42

Weight of Market value of bond = Market value of bond / Total financing market value = $36,265,200 / $62,265,200 = 0.58

Step 3: Calculation of return on equity

Current year dividend = Last year dividend * (1 + Dividend growth rate) = $2 * (1 + 4.0%) = $2.08

Next year dividend = Current year dividend * (1 + Dividend growth rate) = $2.08 * (1 + 4.0%) = $2.1632

The return on equity can now be calculated using the following formula:

Current share price = Next year dividend / (Return on equity – Dividend growth rate) ………………….. (2)

Where;

Current share price = $13

Next year dividend = $2.1632

Return on equity = ?

Dividend growth rate = 4.0%, or 0.04

Substituting the values into equation (2) and solve for return on equity, we have:

13 = 2.1632 / (Return on equity - 0.04)

13 * (Return on equity - 0.04) = 2.1632

(13 * Return on equity) – (13 * 0.04) = 2.1632

(13 * Return on equity) – 0.52 = 2.1632

13 * Return on equity = 2.1632 + 0.52

Return on equity = 2.6832 / 13

Return on equity = 0.21

Step 4: Calculation of Weighted average cost of capital

Weighted average cost of capital = (WS * CE) + (WD * CD * (1 – T)) ………………… (4)

Where;

WS = Weight of Market value of common shares outstanding = 0.42

WD = Weight of debt = Weight of Market value of bond = 0.58

CE = Cost of equity = Return on equity = 0.21

CD = Cost of debt = YTM = 8%, or 0.08

T = Tax rate = 30%, or 0.30

Substituting the values into equation (3), we have:

Weighted average cost of capital = (0.42 * 0.21) + (0.58 * 0.08 * (1 - 0.30)) = 0.12068, or 12.068%

Rounding to two decimal places, we have:

Weighted average cost of capital = 12.07%

Since the instruction in the question indicates that the % symbol should not be used, the weighted average cost of capital (WACC) for Easy Car Corp is therefore 12.07.

Answer:

yes

Step-by-step explanation:

Answer:

5x − 4 = 3x + 8

5x - 4 + 4 = 3x + 8 + 4

5x = 3x + 12

5x - 3x = 3x + 12 - 3x

2x = 12

2x / 2 = 12 / 2

x = 6

Answer:

x=6

Step-by-step explanation:

Let's solve your equation step-by-step.

5x−4=3x+8

Step 1: Subtract 3x from both sides.

5x−4−3x=3x+8−3x

2x−4=8

Step 2: Add 4 to both sides.

2x−4+4=8+4

2x=12

Step 3: Divide both sides by 2.

2x/2=12/2

x=6

Answer:

x=6

Answer:

45 R53

Step-by-step explanation:

Hope This Helps

Answer:

616

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

25% of 60 = 15

Answer:

Hmm graph 3, i think.

Step-by-step explanation:

Answer: X =5/2, 15/2   x=2.5, 7.5

Step-by-step explanation:

4/9 and 1/11

product means multiplying

4 times 1

4*1=4

9 times 11

9*11=99

answer: 4/99

Answer:

4:5 is the ratio in it simplest form

Answer:

155

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

I took the quiz

Answer:

-3 < x ≤ 6

Step-by-step explanation:

Left side is exclusive, right side is inclusive, hence the < and ≤, respectively.

Answer:

I think it is 5.

Step-by-step explanation:

5/8 in decimal form is 0.625. 0.625 x 8 = 5. I hope this helps/ sorry if it didn't.

Answer:

Option A (5, 0)

Step-by-step explanation:

Step 1:  Determine what is a solution

To find a solution of two lines, it has to be in the area where both of the colors intersect.  As you can see the red line goes up and the blue line goes down, but there is a shaded region where there is just white, just blue, just red, and the red and blue.  The shaded region where both red and blue is, that is where the solutions are.  

(5, 0) -> This means that the x-value is 5 and the y-value is 0 meaning that it is in the area where there is both red and blue.

(1, -3) -> This means that the x-value is 1 and the y-value is -3 meaning that it is in the area where there is only red.

(3, 3) -> This means that the x-value is 3 and the y-value is 3 meaning that it is in the area where there is only blue.

(2, 1) -> This means that the x-value is 2 and the y-value is 1 meaning that it is in the area where there is only blue.

Answer:  Option A (5, 0)

I'll do the first problem to get you started.

Part (a)

We have a separable equation. Get the y term to the left side and then integrate to get

[tex]\frac{dy}{dt} = ky^{1+c}\\\\\frac{dy}{y^{1+c}} = kdt\\\\\displaystyle \int\frac{dy}{y^{1+c}} = \int kdt\\\\\displaystyle \int y^{-(1+c)}dy = \int kdt\\\\\displaystyle -\frac{1}{c}y^{-c} = kt+D\\\\\displaystyle -\frac{1}{c*y^{c}} = kt+D\\\\[/tex]

I'm using D as the integration constant rather than C since lowercase letter c was already taken.

Let's use initial condition that [tex]y(0) = y_0[/tex]. This means we'll plug in t = 0 and [tex]y = y_0[/tex]. After doing so, solve for D

[tex]\displaystyle -\frac{1}{c*y^{c}} = kt+D\\\\\displaystyle -\frac{1}{c*(y_0)^{c}} = k*0+D\\\\\displaystyle D = -\frac{1}{c*(y_0)^{c}}\\\\[/tex]

Let's plug that in and isolate y

[tex]\diplaystyle -\frac{1}{c}y^{-c} = kt+D\\\\\\\diplaystyle -\frac{1}{c}y^{-c} = kt-\frac{1}{c*(y_0)^{c}}\\\\\\\diplaystyle y^{-c} = -ckt+\frac{1}{(y_0)^{c}}\\\\\\\diplaystyle y^{-c} = \frac{1-c*(y_0)^{c}kt}{(y_0)^{c}}\\\\\\\diplaystyle \frac{1}{y^{c}} = \frac{1-c*(y_0)^{c}kt}{(y_0)^{c}}\\\\\\\diplaystyle y^{c} = \frac{(y_0)^{c}}{1-c*(y_0)^{c}kt}\\\\\\\diplaystyle y = \left(\frac{(y_0)^{c}}{1-c*(y_0)^{c}kt}\right)^{1/c}\\\\\\\diplaystyle y = \frac{y_0}{\left(1-c*(y_0)^{c}kt\right)^{1/c}}\\\\\\[/tex]

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

We end up with [tex]\displaystyle y(t) = \frac{y_0}{\left(1-c*(y_0)^{c}kt\right)^{1/c}}\\\\[/tex] as our final solution. There are likely other forms to express this equation.

========================================================

Part (b)

We want y(t) to approach positive infinity.

Based on the solution in part (a), this will happen when the denominator approaches 0 from the left.

So [tex]y(t) \to \infty[/tex] as [tex]1-c*(y_0)^{c}kt \to 0[/tex] in which we can effectively "solve" for t showing that [tex]t \to \frac{1}{c*(y_0)^{c}k}[/tex]

If we define [tex]T = \frac{1}{c*(y_0)^{c}k}[/tex] , then approaching T from the left side will have y(t) approach positive infinity.

This uppercase T value is doomsday. This the time value lowercase t approaches from the left when the population y(t) explodes to positive infinity.

Effectively t = T is the vertical asymptote.

========================================================

Part (c)

We're told that the initial condition is y(0) = 5 since at time 0, we have 5 rabbits. This means [tex]y_0 = 5[/tex]

Another fact we know is that y(3) = 35 because after three months, there are 35 rabbits.

Lastly, we know that c = 0.01 since the exponent of dy/dt = ky^(1.01) is 1.01; so we solve 1+c = 1.01 to get c = 0.01

We'll use y(3) = 35, c = 0.01 and [tex]y_0 = 5[/tex] to solve for k

Doing so leads to the following:

[tex]\displaystyle y(t) = \frac{y_0}{\left(1-c*(y_0)^{c}kt\right)^{1/c}}\\\\\\\displaystyle y(3) = \frac{5}{\left(1-0.01*(5)^{0.01}k*3\right)^{1/0.01}}\\\\\\\displaystyle 35 \approx \frac{5}{\left(1-0.0304867k\right)^{100}}\\\\\\\displaystyle 35\left(1-0.0304867k\right)^{100} \approx 5\\\\\\\displaystyle \left(1-0.0304867k\right)^{100} \approx \frac{1}{7}\\\\\\[/tex]

[tex]\displaystyle \left(1-0.0304867k\right)^{100} \approx 7^{-1}\\\\\\\displaystyle 1-0.0304867k \approx \left(7^{-1}\right)^{1/100}\\\\\\\displaystyle 1-0.0304867k \approx 7^{-0.01}\\\\\\\displaystyle k \approx \frac{7^{-0.01}-1}{-0.0304867}\\\\\\\displaystyle k \approx 0.63211155281122\\\\\\\displaystyle k \approx 0.632112\\\\\\[/tex]

We can now compute the doomsday time value

[tex]T = \frac{1}{c*(y_0)^c*k}\\\\\\T \approx \frac{1}{0.01*(5)^{0.01}*0.632112}\\\\\\T \approx \frac{1}{0.00642367758836}\\\\\\T \approx 155.674064621806\\\\\\T \approx 155.67\\\\\\[/tex]

The answer is approximately 155.67 months

Answer:

(10x−7)^2

Step-by-step explanation:

(10x+7)(10x-7)

i stead of making it a "100" since they are both the same  but positive and negative () and bring it to the power of 2

Answer:

A = 50 square units

Step-by-step explanation:

Right Triangles

A right triangle is identified because it has one internal angle of 90°.

The longest side is called hypotenuse and the other two sides are called legs. Being c the hypotenuse and a and b the legs, the Pythagora's theorem relates the with the equation:

[tex]c^2=a^2+b^2[/tex]

If the triangle is also isosceles, then both legs have the same measure or a=b:

[tex]c^2=a^2+a^2=2a^2[/tex]

Since we know the hypotenuse has a measure of 10\sqrt{2}:

[tex](10\sqrt{2})^2=2a^2[/tex]

Operating:

[tex]100*2=2a^2[/tex]

Dividing by 2:

[tex]a^2=100~~\Rightarrow a=\sqrt{100}[/tex]

a = 10 units

The area of the triangle is:

[tex]\displaystyle A=\frac{a.b}{2}[/tex]

[tex]\displaystyle A=\frac{10*10}{2}[/tex]

A = 50 square units

Answer:

Step-by-step explanation:

Reflection of points across y-axis doesn't change the distance between the points so AB = A'B' = 10 units

Let the coordinates be:

Reflection:

Lets compare distances:

and

As we see the results are same

Answer:

Reflection of points across y-axis doesn't change the distance between the points so AB = A'B' = 10 units

Step-by-step explanation:

Answer:

The minimum sample required = 1296.65

Step-by-step explanation:

Given that:

Variance [tex]\sigma^2 = 2.89[/tex]

Standard deviation [tex]\sigma = \sqrt{2.89}[/tex]

Standard deviation [tex]\sigma = 1.7[/tex]

Margin of error = 0.11

Confidence Interval = 98%

Level of significance =  1 - 0.98 = 0.02

The critical value = [tex]Z _{\alpha//2} = Z_{0.02/2} = Z_{0.01}[/tex]

= 2.33  

Thus, the minimum sample size is given by the formula:

[tex]n = \bigg ( \dfrac{Z_{\alpha/2} \times \sigma }{E} \bigg)^2[/tex]

[tex]n = \bigg (\dfrac{2.33 \times 1.7 }{0.11} \bigg)^2[/tex]

n = 1296.65

Answer:

yes they are congruent

Step-by-step explanation:

they both the same shape and size

Answer:

The slope of the graph at x=-1 is 2

Step-by-step explanation:

Instant rate of change

Given a real function f(x), the instant rate of change with respect to x is defined as the derivative of f which coincides with the instant value of the slope of the tangent line in the point (x,y).

We have the function:

[tex]\displaystyle f(x) = x^5+\frac{1}{x^3}+7[/tex]

Prepare the function to apply the power rule of the derivative:

[tex]\displaystyle f(x) = x^5+x^{-3}+7[/tex]

Recall the power rule:

[tex](x^n)' = nx^{n-1}[/tex]

Also, the derivative of a constant is zero.

Taking the derivative:

[tex]\displaystyle f'(x) = 5x^4-3x^{-4}[/tex]

Evaluating for x=-1:

[tex]\displaystyle f'(-1) = 5(-1)^4-3(-1)^{-4}[/tex]

[tex]\displaystyle f'(-1) = 5*1-3*1=2[/tex]

The slope of the graph at x=-1 is 2

Answer:

Both are proportional, because as the value of x change (increases or decreases), the value of y changes (increases or decreases).

The first equation (y = 25x) could represent that amount of teachers per students. If x = teachers (let's say there is 1 teacher), then y = students (1 teacher would teach a class of 25 students).

The second equation (y = 5x + 25) could represent the amount of money you could earn babysitting. The starting/base amount would be $25, and you would earn $5 more for every hour you babysat.

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

The number of necessary tutors when you divide 27 into 72, is 2.6; therefore the necessary number of tutors is 3 because you can’t have .6 of a tutor. Hope this helps!

Answer: D

Step-by-step explanation:

No, the addition symbol was dropped in the second expression is not correct.

An expression is combination of variables, numbers and operators.

No, Vance did not apply the associative property correctly.

The associative property states that the grouping of terms in an expression can be changed without affecting the value of the expression.

However, in this case, Vance changed the order of the terms, but did not actually group them in a different way.

Additionally, Vance dropped the subtraction symbol in the second expression, which is incorrect.

The correct equivalent expression using the associative property would be:

(4.5 m + 7/8) - 9 = 4.5 m + (7/8 - 9)

From there, we could simplify the expression further, if needed.

Hence, No, the addition symbol was dropped in the second expression.

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ3

Answer:

No, every student will have 3.2 minutes

Answer:

Each student has approximately 3 minutes and 12 seconds.

Step-by-step explanation:

You divide the total amount of minutes by the total amount of students. 48/15=3.2

After you get your answer, you convert to minutes. There are 3 minutes and the .2 converts to 12 seconds

Answer: x=-9

Step-by-step explanation:

18/x=-2

multiply x

18=-2x

divide by -2

-9=x

x=-9

Answer:

[tex]18 \div x = - 2 \\ \frac{18}{x} = - 2 \\ x = \frac{18}{ (- 2)} \\ \boxed{x = - 9}[/tex]

Answer:

x=8 and y=21

Step-by-step explanation:

12x-28=7x+12 (the 2 angles are equivalent)

12x-7x=12+28

5x=40

x=8

9y-77 + 12x-28 =180 (the sum of those 2 angles is a flat angle (180°))

9y-77+12*8-28=180

9y=180+28+77-96

9y=189

y=21

Answer:

c= -20

x= 38

Explanation:

Solve for x and c by simplifying both sides of the equation, then isolating the variable.  

hope this helps!

Answer:

Brittany needs another $3.7405.              

Step-by-step explanation:

Per pound Cost of turkey = $5.96 per pound

The amount Brittany buys the turkey = 2.55 pounds

Brittany's cost for turkey = 2.55 × $5.96 = $15.198

Per pound cost for cheese = $3.35 per pound

The amount Brittany buys the cheese = 3.7 pounds

Brittany's cost for cheese = 2.55 × $3.35 = $8.5425

So,

Brittany's total cost = Turkey cost + Cheese cost

                                = $15.198 + $8.5425

                                = $23.7405

As brittany gave the clerk 20 dollars.

So, the amount she further needs will be:

$23.7405 - $20 =  $3.7405

Therefore, Brittany needs another $3.7405.