Answer: $25.46
Step-by-step explanation:
Year 1 FCFE = 1.8 * (1 + 10%) = $1.98
Year 2 FCFE = 1.98 * 1.1 = $2.18
Year 3 FCFE = 2.178 * 1.1 = $2.40
Year 4 FCFE = 2.3958 * 1.05 = $2.52
Year 5 FCFE= 2.51559 * 1.05 = 2.64
Terminal Value = (2.64 * 1.03) / (12% - 3%)
= $30.21
Now discount all these cashflows to find the value:
= (1.98 / 1.12) + (2.18 / 1.12²) + (2.40 / 1.12³) + (2.52 / 1.12⁴) + (2.64 / 1.12⁵) + (30.21 / 1.12⁵)
= $25.46
At a high school with over 500 students, a counselor wants to estimate the mean number of hours per week that students at the school spend in community service activities. The counselor will survey 20 students in the Environmental Club at the school. The mean number of hours for the 20 students will be used to estimate the population mean. Which of the following conditions for inference have not been met?
1. The data are collected using a random sampling method.
2. The sample size is large enough to assume normality of the distribution of sample means.
3. The sample size is less than 10 percent of the population size.
Complete option:
The sample size is less than 10 percent of the population size. A. II onlyB. III onlyC. II and III onlyD. I, II, and III
Answer:
D.) I, II, and III
Step-by-step explanation:
The sample are not well randomly selected as the samples were only selected from a single source, the environmental club in the school.
Similarly only 20 samples were chosen, these 20 samples are not enough to assume normality as the minimum number of samples required to assume normality according to the Central limit theorem is 30 samples or more.
10% of the population size is :
Population size = 5000
0.10 * 5000 = 500 samples
Hence, sample size used is less than 10% of population size.
What is the Supplimentary angle of 21°?
Answer:
159 degrees
Step-by-step explanation:
Answer:
159°
Step-by-step explanation:
We can calculate supplementary angles by subtracting the given one angle from 180 degrees. To find the other angle, use the following formula: ∠x = 180° – ∠y or ∠y = 180° – ∠x where ∠x or ∠y is the given angle.
so 180° – ∠ 21= 159°
find the area of the shaded segment of the circle
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Answer:
(3/2π -(9/4)√3) m² ≈ 0.8 m²
Step-by-step explanation:
The area of the segment is the difference between the area of the sector and the area of the triangle.
sector area = 1/2r²α . . . . where r is the radius and α is the central angle in radians
triangle area = 1/2r²·sin(α) . . . . same variable definitions
Then the area of the segment is ...
segment area = sector area - triangle area
segment area = (1/2)r²(α -sin(α))
The central angle subtended by the segment is 360° -300° = 60° = π/3 radians
Then the segment area is ...
A = (1/2)(3 m)²(π/3 -√3/2) = (3/2π -(9/4)√3) m² ≈ 0.8 m²
Kazi ran 1.2km how many centimeters did she run
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Answer:
120,000 cm
Step-by-step explanation:
There are 100 cm in 1 m, and there are 1000 m in 1 km. So, there are 100,000 cm in 1 km.
1.2 km is 120,000 cm
Does anyone know what the answer is for the question???
A normal distribution has a mean of 14 and a standard deviation of 4. What percent of values are from 14 to 22?
Answer:
80% of the values will occurs above 68.24.
Step-by-step explain
thinking this is right but im sorry if its wrong
a person invested $330 in an account growing at a rate allowing the money to double every 8 years. Write a function showing the amount of money in the account after tt years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year, to the nearest hundredth of a percent.
Answer:
The percentage of growth is of 9.05%.
The amount of money in the account after t years is given by [tex]P(t) = 330(1.0905)^t[/tex]
Step-by-step explanation:
Amount of money after t years:
The amount of money in an account after t years is given by:
[tex]P(t) = P(0)(1+r)^t[/tex]
In which P(0) is the initial deposit and r is the growth rate, as a decimal.
Money doubles every 8 years.
This means that [tex]P(8) = 2P(0)[/tex]. So
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]2P(0) = P(0)(1+r)^8[/tex]
[tex](1+r)^8 = 2[/tex]
[tex]\sqrt[8]{(1+r)^8} = \sqrt[8]{2}[/tex]
[tex]1 + r = 2^{\frac{1}{8}}[/tex]
[tex]1 + r = 1.0905[/tex]
[tex]r = 1.0905 - 1[/tex]
[tex]r = 0.0905[/tex]
The percentage of growth is of 0.0905 = 9.05%.
Person invested $330
This means that [tex]P(0) = 330[/tex]
So
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]P(t) = 330(1+0.0905)^t[/tex]
[tex]P(t) = 330(1.0905)^t[/tex]
The amount of money in the account after t years is given by [tex]P(t) = 330(1.0905)^t[/tex]
A wooden box has the shape of a rectangular prism. The inside of the box is also a rectangular prism. What is the volume of the solid part of the box? Enter your answer below.
A coach recommends that Nathan get 64 minutes of exercise per day. Today Nathan lifts weights for 16 minutes. What percent of his recommended exercise has Nathan completed?
Answer:
25%
Step-by-step explanation:
16 x 100 ÷ 64.
you simply take the minutes that he exercised and thereafter divide it by the recommended exercise that was prescribed by his coach.
A cooler contains 12 bottles of apple juice and 18 bottles of orange juice. You reach into the cooler without looking and pull out one bottle of apple juice. Then you reach into cooler and pull out another bottle of juice. What is the probability of pulling apple juice and then pulling another apple juice?
Answer:
P = 0.232
Step-by-step explanation:
In the cooler, we have 12 bottles of apple juice and 18 bottles of orange juice.
This adds up to a total of 30 bottles.
Now we want to find the probability of pulling a bottle of apple juice after you pulled one bottle of apple juice.
The probability of pulling a bottle of apple juice at the beginning is equal to the quotient between the number of apple juice bottles in the cooler and the total number of bottles in the cooler,
This means that 12 out of 30 are apple juice, then the probability of getting first a bottle of apple juice is:
p = 12/30
Now, we want to find the probability of getting another, we will do the same calculation than above, but now the number of bottles of apple juice is 11 (because we took one) and the total number of bottles is 29.
In this case, the probability is:
q = 11/29
The joint probability (the probability of both events happening) is equal to the product of the individual probabilities.
Then the probability of pulling apple juice and then pulling another apple juice is:
P = p*q = (12/30)*(11/29) = 0.232
184 is what percent more than 148
A group of children were asked if they like eating cupcakes or brownies.
The table shows the probabilities of the results.
Like cupcakes Do not like cupcakes Total
Like brownies 0.15 0.15 0.3
Do not like brownies 0.35 0.35 0.7
Total 0.5 0.5 1
What is the probability that a child likes brownies given that he likes cupcakes?
.70
.43
.50
.30
Answer:
It’s 0.30
Step-by-step explanation:
I took the test bro
Help me please!!!!
10. The table shows the change in your hair length over a year.
January
February
August
September
December
Month
Change in hair
length (inches)
2
-1
3
4
3
a. What is the total change in your hair length at the end of the year?
b. Is your hair longer in January or December? Explain your reasoning.
c. When is your hair the longest? Explain your reasoning.
Answer:
3
December. total change in December is greater than change in January. 3 is greater than 2
August. the total change in hair growth is 4.
Step-by-step explanation:
total change in hair length = 2 - 1 + 3 - 4 + 3 = 3
My hair is longer in January .
total change in hair length in February = 2 -1 = 1
total change in hair length in August = 1 + 3 = 4
total change in hair length in September = 4 - 4 = 0
total change in hair length in December = 0 + 3 = 3
My hair is the longest in August because that is the month that has the highest change in hair length
what kind of angle does an acute triangle have
Answer:
An acute angle is an angle that measures less than 90 degrees. A triangle formed by all angles measuring less than 90˚ is also known as an acute triangle. For example, in an equilateral triangle, all three angles measure 60˚, making it an acute triangle.
hope this answer helps you.....
if c and d vary inversely, and d=5/3 and c=5. write a function that models inverse variation and find d when c=10
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Answer:
cd = 25/3d = 5/6Step-by-step explanation:
The inverse variation described can be either of ...
c = k/d
or
d = k/c
Either way, the equation can also be written as ...
cd = k
For the given values of c and d, the value of k is ...
(5)(5/3) = k = 25/3
So, the model can be written as ...
cd = 25/3
or
d = (25/3)/c
__
For c=10, the value of d is ...
d = (25/3)/10 = 25/30
d = 5/6
The sum of 4 consecutive integers is 354.
What is the second number in this sequence?
Answer:
87
Step-by-step explanation:
Step 1: X is the first number
Step 2: X + 1 is the second number
Step 3: X + 2 is the third number
Step 4: X +3 is the fourth number
Step 5: Take the sum of all of those:
4x+6=354
4x=348
x=87
The second number in the sequence is 88.
87,88,89,90 = 354
Answer: Second integer is 87
Step-by-step explanation:
Sum of four consecu. integers = 354
Let the integers be x, x+1, x+2 , x+3.
Sum = 354
x+x+1+x+2+x+3 = 354
4x+6 = 354
4x = 354 - 6
4x = 348
x = 348/4
x = 87
Therefore, first integer = x =87
Second integer = x+1 = 88
Third integer = x+2 = 89
Fourth integer = x+3 = 90
So, second integer is 88 .
i need an answer not a link that don't work!
Answer:
B
Step-by-step explanation:
[tex]if \: a = 3 + 2 \sqrt{2} .find \: a \times \frac{1}{a} [/tex]
Answer:
1
Step-by-step explanation:
Given that,
[tex]a=3+2\sqrt{2}[/tex]
We need to find the value of [tex]a\times \dfrac{1}{a}[/tex].
So,
[tex]=3+2\sqrt{2} \times \dfrac{1}{3+2\sqrt{2}}\\\\=\dfrac{3+2\sqrt{2}}{3+2\sqrt{2}}[/tex]
As numerator and dinominator is same. It means,
[tex]=\dfrac{3+2\sqrt{2}}{3+2\sqrt{2}}\\\\=1[/tex]
So, the value of the given expression is equal to 1.
A triangular garden has an area of 9 square yards. Which figure could represent the garden? 9 yd 9yd,
6 yd 6 yd , 6yd 3yd, 3yd 3yd
Answer:
3yds by 3yds
Step-by-step explanation:
3×3=9
Find the range of the function
x) = 10- x
a 15.)
b. (2-1) U[0,
C. (10]
d (2-1) U. 10)
Please select the best answer from the choices provided
ОА
B
ос
OD
Simplify and write answer in standard form.
Step-by-step explanation:
2x^3 - 10x^2 + 8x -3
hope this helps
The
Olympic time for men's 400-m hurdles
has been decreasing by about 0.09 seconds per
year since 1930, when the record was 52 seconds.
Predict what the time will be in 2010
Answer:
In 2010 the time will be 44.8 seconds.
Step-by-step explanation:
Given that the Olympic time for men's 400-m hurdles has been decreasing by about 0.09 seconds per year since 1930, when the record was 52 seconds, to predict what the time will be in 2010 the following calculation must be performed:
52 - ((2010 - 1930) x 0.09) = X
52 - (80 x 0.09) = X
52 - 7.2 = X
44.8 = X
Thus, in 2010 the time will be 44.8 seconds.
Suppose y varies directly with x. Write an equation relating x and y. y=-12 when x=20
Answer:
[tex]y = 8 - x[/tex]
when x=20 so y=-12
Please help is for now
the answer 16 im pretty sure
calculate by rounding off and compensating 823-273
a. find the area
b. find the perimeter
Answer:
Area= 4y^2 + 14y + 12
Perimeter = 10y + 16
Step-by-step explanation:
Area of a reactangle = length × width
= (4y+6) × (y+2)
= 4y^2 + 6y + 8y + 12
= 4y^2 + 14y + 12
Perimeter of a rectangle = 2 × (a +b)
= 2 × ( 4y + 6 + y+ 2)
= 2 × ( 5y + 8)
= 10y + 16
Which statement about the net is true?
Answer:
A
Step-by-step explanation:
The net can be folded to form a pyramid
What is the opposite of -45?
Answer:
45 or positive 45
Step-by-step explanation:
Answer: 45
Step-by-step explanation:
Q2) What are the rules for probability distributions ? I
Answer:
Probability Distributions
A listing of all the values the random variable can assume with their corresponding probabilities make a probability distribution.
A note about random variables. A random variable does not mean that the values can be anything (a random number). Random variables have a well defined set of outcomes and well defined probabilities for the occurrence of each outcome. The random refers to the fact that the outcomes happen by chance -- that is, you don't know which outcome will occur next.
What is the value of m in mn= 12?
A) m= 12-n
B) m = 14
C) m= 12n
D) m = 12 + n
Answer: There is no choice available for the answer.
Step-by-step explanation:
The question is asking for the value of m in terms of n, so we need to isolate m to one side.
Given
mn=12
Divide n on both sides
mn/n=12/n
m=12/n
Hope this helps!! :)
Please let me know if you have any questions