A grocery store recently changed their apple supplying vendor. The vendor told the store manager that the mean weight for each apple is bell-shaped with # mean of 7.5 ounces and a standard deviation of 1.33 ounce (a) One customer comes to this grocery store and randomly picks 25 apples. What is the mean and standard deviation of the distribution of the mean weight for 25 apples? (b) What is the probability that the mean weight of 25 apples exceeds 8.2 ounces? (c) Another customer randomly picks 10 apples. Will the probability of the mean weight that the 10 apples exceeds 8.2 ounces of this customer be higher than the last customer in part b? Explain it.

Answer:

[tex]y'\approx -0.41[/tex]

Step-by-step explanation:

Implicit Derivatives

When it's not possible to express one variable as an explicit function of the other, we use implicit derivatives and solve for y'.

Find y' in the equation given below:

xe^y - 4y = 3x - 14 + 2e^2

Taking derivatives with respect to x, recalling y'=dy/dx, and dx/dx=1:

(xe^y)' - (4y)' = (3x)' - (14 + 2e^2 )'

Using the product rule for the first derivative, and simple rules for the rest:

e^y + xe^yy' - 4y' = 3 - 0

Recall the derivative of a constant is zero.

Group terms with y' in the left side and the rest in the right side:

xe^yy' - 4y' = 3 - e^y

Factoring y':

y'(xe^y - 4) = 3 - e^y

Solving:

[tex]\displaystyle y'=\frac{3 - e^y}{xe^y - 4}[/tex]

Evaluating for x=2, y=2:

[tex]\displaystyle y'=\frac{3 - e^2}{2e^2 - 4}[/tex]

Calculating:

[tex]\mathbf{y'\approx -0.41}[/tex]

Answer:

<M = 50

Step-by-step explanation:

The sum of the angles of a triangle is 180

52+ 78+x = 180

Combine like terms

130 +x = 180

Subtract 130 from each side

130+x-130 =180-130

x = 50

Answer:

50°

Step-by-step explanation:

180 is the total of all the angles added together.

so if you subtract the 2 you already know from the total, you’ll have the size of the angle M.

180 - (52+78) = 180 - 130 = 50°

Answer:

4:5 is the ratio in it simplest form

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:

c= -20

x= 38

Explanation:

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

hope this helps!

4/9 and 1/11

product means multiplying

4 times 1

4*1=4

9 times 11

9*11=99

answer: 4/99

Answer:

a = 18

b = 6√3

Step-by-step explanation:

WE can see in the diagram that there are two right angled triangles formed.

One with 45° angle as other interior angle and other with 60° interior angle.

So we will take the triangles one by one to find the required values.

As a is used in both triangles, first we will find the value of a using the left triangle.

In the triangle,

Hypotenuse = h = 18√2

θ = 45°

Using trigonometric ratio:

[tex]sin\ 45 =\frac{Perpendicular}{Hypotenuse}\\\frac{1}{\sqrt{2}}= \frac{a}{18\sqrt{2}}\\a = \frac{1}{\sqrt{2}} * 18\sqrt{2}\\a = 18[/tex]

Now in the right side triangle

θ1 = 60°

Perpendicular = a = 18

Base = b = ?

So,

[tex]tan\ 60 = \frac{perpendicular}{base}\\\sqrt{3} = \frac{\sqrt{18}}{b}\\b = \frac{18}{\sqrt{3}}\\b = \frac{6*3}{\sqrt{3}}\\b = \frac{6*\sqrt{3}*\sqrt{3}}{\sqrt{3}}\\b = 6\sqrt{3}[/tex]

Hence,

a = 18

b = 6√3

Answer:

-2.1

Step-by-step explanation:

Answer:

-2.1

Step-by-step explanation:

Answer:

(£x - £T - £250) / 2

Step-by-step explanation:

Colin's total wages = £x

Tax = £T

Rent = £250

Total amount remaining = Total wages - tax - rent

= £x - £T - £250

he then shares what's left between himself and his wife. how much do they both get?

He and his wife = 2 people

Each person gets = Total amount remaining / number of people

= (£x - £T - £250) / 2

Or

= 1/2 (£x - £T - £250)

Answer:

he would be 22 ft smaller than the tree

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:

406%

Step-by-step explanation:

cuz google says so

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:

7/25

Step-by-step explanation:

From randomly guessing, it depends on how many you think you got right and how many you really don't know. You could get all 25 wrong, but more likely at random get 7 right.

Answer:

The minimum score you can get is 0.

Step-by-step explanation:

Answer:

You can order pizza in 56 ways.

Step-by-step explanation:

A pizza can be ordered in 56 ways

Step-by-step explanation:

From the information that the problem gives to us, we have that:

For each topping, there are four different choices for the size of the pizza.

For each size of pizza, there are two possible choices of crust.

There are seven toppings for us to choose.

So

4*2*7 = 56

A pizza can be ordered in 56 ways

Answer:

$3.50

Step-by-step explanation:

5.25/3 = 1.75

1.75 x 2 = 3.5

Answer:

A

Step-by-step explanation:

Becuase he wanted more then 3000

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:

25%

Step-by-step explanation:

25% of 60 = 15

Answer : Graph the line that contains the point (-2,6) and has a slope of -1/3

Answer:

[tex]y = - \frac{1}{3} x - \frac{20}{3} [/tex]

Step-by-step explanation:

Answer: (B) Addison can eliminate $45 from Food/Clothes and $41 from Entertainment.

Based on the information given, Addison should eliminate $45 from the money budget for Food/Clothes ($445.00) and $41 from Entertainment ($270.00).

Given the following data:

Mathematically, the monthly payment for a credit card can be calculated by using this formula:

[tex]M=P(\frac{r}{1-(1+r)^{-nt}} )[/tex]

Where:

In this scenario, Addison should eliminate $45 from the money budget for Food/Clothes ($445.00) and $41 from Entertainment ($270.00) because they are the least cuts to her current expenses and they would avail her an opportunity to pay off her balance in 24 months (2 years).

Read more on monthly payment here: https://brainly.com/question/2151013

Answer:

-3 < x ≤ 6

Step-by-step explanation:

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

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:

(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:

67.

Step-by-step explanation:

First we find the mean:

Mean is add up everything and divide by how much numbers there are.

The numbers are:

[tex]49, 65, 41, 38, 87, 55, 95, 106[/tex].

So we add them up which is 536.

Then we divide by how much numbers there are.

There are 8 numbers so 536/8 which is 67.

Hope this helps :D

Answer: X =5/2, 15/2   x=2.5, 7.5

Step-by-step explanation: