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romanna [79]
2 years ago
11

You are competing in a race. The table shows the times from last year's race. You want your time to be last year's median time w

ith an absolute deviation of at most 4
minutes. Complete the inequality to represent the time (in minutes) you hope to achieve.
Race times (minutes)
26 35 27 32
33 42 48 28
36 40 38 32
Mathematics
1 answer:
blondinia [14]2 years ago
8 0

Answer:

30≤t≤38

Step-by-step explanation:

Arrange the given data in ascending order and determine the median

26, 27,28,32,32,33,35,36,38,40,42,48

Median is (33+35)/2 =68/2 = 34

Absolute deviation is at most 4, this means:  median ± 4

Median high value = 34+4 = 38

Median low value= 34-4=30

Inequality to represent time, t will be

30≤t≤38

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Peter Johnson, the CFO of Homer Industries, Inc is trying to determine the Weighted Cost of Capital (WACC) based on two differen
Rzqust [24]

Answer:

Scenario 1 has WACC of 7.93%

Scenario 2 has WACC of 10.33%

Step-by-step explanation:

WACC=Ke*E/V+Kp*P/V+Kd(after tax)*D/V

Ke is the cost of equity =13%

Kp is the cost of preferred stock=10%

Kd(after tax) is the cost of debt of 8% adjusted for tax as below:

Kd(after tax )=Kd(before tax)*(1-t)

t is the tax rate of 30% or 0.3

Kd(after tax)=8%*(1-0.3)=5.60%

E is equity value,which is $1.8 million under scenario 1 and $3.8 under scenario 2

P is the value of preferred stock which is $1.2 million and $2.2 million respectively

D is the value of debt which is $5 million and $2 million

V=total value of capital structure=$8 million in both cases.

Scenario 1 WACC

WACC=13%*1.8/8+10%*1.2/8+5.6%*5/8=7.93%

Scenario 2 WACC

WACC=13%*3.8/8+10%*2.2/8+5.6%*2/8=10.33%

7 0
2 years ago
If f Superscript negative 1 Baseline (x) = negative one-fifth x, what is f Superscript negative 1 Baseline (x) = one-fifth x?
Artyom0805 [142]

Answer:

  a different inverse function

Step-by-step explanation:

If f^{-1}(x)=-\frac{1}{5}x then f^{-1}(x)=\frac{1}{5}x is a different inverse function.

__

The second (inverse) function is the first reflected over the y-axis.

5 0
2 years ago
Read 2 more answers
A mirror is made of two congruent parallelograms as shown in the diagram. The parallelograms have a combined area of 9 1/3 squar
Vika [28.1K]
Given:
2 parallelograms with an area of 9 1/3 yd²
height of each parallelogram is 1 1/3 yd

Area of parallelogram = base * height

We need to divide the combined area into two to get each parallelogram's base.

9 1/3 = ((9*3)+1)/3 = 28/3

28/3 ÷ 2 = 28/3 * 1/2 = 28/6 yd² or 4 4/6 yd² ⇒ 4 2/3 yd²

Area of each parallelogram is 4 2/3 yd²

4 2/3 yd² = base * 1 1/3 yd

14/3 yd² ÷ 4/3 yd = base

14/3 yd² x 3/4 yd = base
14*3 / 3*4 = base
42 / 12 = base
3 6/12 yd = base
or 3 1/2 yd = base

a) the base of each parallelogram is 3 1/2 yards
b) we can assume that the two parallelograms form a rectangle.
area of a rectangle is length times width.

length is 3 1/2 yds * 2 = 7 yds
width is 3 1/2 yds

Area of rectangle = 7 yds * 3 1/2 yds
Area = 7 yd * 7/2 yd
Area = 7*7 / 2 yd²
Area = 49 / 2 yd²
Area = 24 1/2 yd²


8 0
2 years ago
Read 2 more answers
Given E = I × R and P = E × I, select the formula that will solve for E when only R and P are known.
stiv31 [10]

E = \left\{(a,b) \mid a \in I \text{ and } b \in R \right\}, P = \left\{(a,b) \mid a \in E \text{ and } b \in R \right\} but we cannot solve for the set E because we are missing information.

3 0
2 years ago
Read 2 more answers
A food distributor is being sued for racial discrimination because 12% of newly hired candidates are not white when 53% of all a
Musya8 [376]

Answer:

Check Explanation

Step-by-step explanation:

A) The null hypothesis would be that the proportion of newly hired candidates that are not white is not significantly different from the proportion of the applicants that are not white & there is no significant evidence that the company's hiring practices are discriminatory.

Mathematically,

H₀: μ₀ = 0.53

And the alternative hypothesis would be that there is a significant difference between the proportion of newly hired candidates that are not white is not significantly different from the proportion of the applicants that are not white. More specifically, that the proportion of newly hired candidates that are not white is significantly less than the proportion of applicants that are not white & there is significant evidence that the company's hiring practices are indeed discriminatory.

Mathematically,

Hₐ: μ₀ < 0.53

B) The two errors that can come up in this hypothesis testing include -

Type I error: We reject the null hypothesis because we obtain that the proportion of newly hired candidates that are not white is significantly less than the proportion of applicants that are not white and conclude that there is indeed significant evidence that the company's hiring practices are discriminatory when in reality, there is no significant difference and hence, no discrimination.

Type II error: We accept the null hypothesis (fail to reject the null hypothesis) because we obtained that there is no significant difference between the proportion of newly hired candidates that are not white & th proportion of applicants that are not white and conclude that there is no discrimination in the company's hiring practices when in reality, there is significant difference in the stated proportions above and significant evidence that there is indeed significant evidence that the company's hiring practices are discriminatory.

C) The power of the test increases as the significance level reduces. This is because t-statistic increases as significance level reduces.

D) The standard error of the mean used in computing the t-score is given as

σₓ = (σ/√n)

It is evident that as the value of n increases, the standard error reduces and this widens the effect of the test, hence, the power of the test increases.

Hope this Helps!!!

7 0
2 years ago
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