Get total lengths by multiplying:
10 x 12.6 = 126
6 x 16.1 = 96.6
Add the total lengths together and divide by 16:
126 + 96.6 = 222.6
222.6 / 16 = 13.9125
Rounded to 2 decimal places = 13.91
answer: 13.91
Maya's math teacher said that each question answered correctly on a test would be worth 5 points. Answer the questions below regarding the relationship between the number of questions correct and the score on the test.
PLEASE HELP
Select the statements that are true.
O Correlation coefficients must be between 0 and 1.
Correlation coefficients must be between - 1 and 1
A correlation coefficient of r = 0.92 indicates a strong, positive correlation.
A correlation coefficient of r = 0.01 means there is no significant correlation.
A correlation coefficient of r = 0.17 indicates a strong, negative correlation.
Correlation coefficient is a numeric measure of the strength and the direction between two quantative variables.
Correlation measures the relationship between variables
The true statements are:
Correlation coefficients must be between - 1 and 1A correlation coefficient of r = 0.92 indicates a strong, positive correlation.Correlation coefficient is a numeric measure of the strength and the direction between two quantative variables.How to determine the true statements?For a correlation coefficient to be valid, the following, must be true:
The value of the correlation coefficient must be between -1 and 1Correlation greater than 0 are positive correlationCorrelation closer to 1 and -1 are strong correlationUsing the above highlights, the true statements are: (b) (c) and (e)
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4.72x 10 to the 10th power in standard form
Answer:
47,200,000,000
Step-by-step explanation:
[tex]4.72*10^{10}[/tex] is in scientific form (notation).
To change this to standard form, we must move the decimal over the amount in the exponent. In this case, that is 10.
Answer:
Step-by-step explanation:
A 5-year project will require an investment of $100 million. this comprises of plant andmachinery worth $80 million and a net working capital of $20 million. the entire outlay willbe incurred at the project’s commencement.financing for the project has been arranged as follows:80,000 new common shares are issued, the market price of which is $500 per share. theseshares will offer a dividend of $4 per share in year 1, which is expected to grow at a rate of 9%per year for an indefinite tenure.remaining funds are borrowed by issuing 5-year, 9% semi-annual bonds, each bond having aface value of $1,000. these bonds now have a market value of $1,150 each.at the end of 5 years, fixed assets will fetch a net salvage value of $30 million, whereas the networking capital will be liquidated at its book value.the project is expected to increase revenues of the firm by $120 million per year. expenses,other than depreciation, interest and tax, will amount to $80 million per year. the firm is subjectto a tax rate of 30%plant and machinery will be depreciated at the rate of 25% per year as per the written-downvalue method.you are required to:1. compute the cost of equity for this project (2 marks)2. compute the relevant cost of debt for this project. (2 marks)3. compute the wacc (4 marks)4. determine the initial cash flow for the project. (1 mark)5. determine the earnings before taxes for years 1 through 5 (2 marks)6. compute the ocf for years 1 through 5 (3 marks)
Answer:
1. The cost of equity can be derived from the share price, which is the present value of the expected dividend one year from now(using the present value of growing perpetuity) as shown below:
share price=D1/(r-g)
share price=$500
D1=expected dividend one year from now=$4
r=cost of equity=unknown
g=constant growth rate=9%
$500=$4/(r-9%)
$500*(r-9%)=$4
r-9%=$4/$500
r=($4/$500)+9%
r=9.8
the Cost of Equity for the project is 9.8%
2. Compute the relevant cost of debt for this project is 5.53%
Market Value= 1,150
Face Value= 1,000
Term= 5 years, 10 semi-annual periods
Coupon Rate= 9%, 4.5% semi-annual rate
Tax Rate= 30%
N=10(semiannual coupons in 5 years)
PMT=45(semiannual coupon=face value*coupon rate/2=$1000*9%/2=$45)
PV=-1150(current market price)
FV=1000(face value of the bond is $1,000)
CPT(press compute)
I/Y=2.762766%(semiannual yield)
annual yield=2.762766%*2
annual yield=5.53%
3. The weighted average cost of capital is the sum of equity and the after-tax cost of debt multiplied by their respective market value weights
WACC=(cost of equity*weight of equity)+(after-tax cost of debt*weight of debt)
cost of equity=9.80%
the market value of equity raised=shares issued*market price of the share
the market value of equity raised=80,000*$500
the market value of equity raised=$40 million
weight of equity=market value of equity/total amount raised
weight of equity=$40 million/$100 million
weight of equity=40.00%
weight of debt=1-weight of equity
weight of debt=1-40.00%
weight of debt=60.00%
after-tax cost of debt=bond yield*(1-tax rate)
the after-tax cost of debt=5.53%*(1-30% )
the after-tax cost of debt=3.87%
WACC=(9.80%*40.00%)+(3.87%*60.00%)
WACC= 6.2426% or 6.24%
Therefore the WACC is 6.2426% or 6.24% rounded off to 2decimal place
4. Determine the initial cash flow for the project =$100 million
The initial cash outlay is the sum of the plant and machinery and net working capital investment required to commence the project
Plant and machinery= $80 million
Networking capital = $20 million
Total Initial Cash Flow= $100 million
5. Determine the earnings before taxes for years 1 through 5
Year
1 2 3 4 5
Revenue
120,000,000 120,000,000 120,000,000 120,000,000 120,000,000
Expenses
(80,000,000) (80,000,000) (80,000,000) (80,000,000) (80,000,000)
Depreciation (20,000,000) (15,000,000) (11,250,000) (8,437,500) (6,328,125)
EBT
20,000,000 25,000,000 28,750,000 31,562,500 33,671,875
Step-by-step explanation:
5. Depreciation schedule:
Year 1 = 80 × 25% = 20
Year 2 = (80-20) × 25% = 15
Year 3 = (80-20-15) × 25% = 11.25
Year 4 = (80-20-15-11.25) × 25% = 8.4375
Year 5 = (80-20-15-11.25-8.4375) × 25% = 6.328125
EBT = revenue - Expenses - depreciation
Year 1 = 120 - 80 - 20 = 20 Million
Year 2 = 120-80- 15 = 25 Million
Year 3 = 120-80- 11.25 = 28.75 Million
Year 4 = 120-80- 8.4375 = 31.5625 Million
Year 5 = 120-80- 6.328125 = 33.671875Million
The cost of equity of the project through the use of Gordan's formula will be 9.87%.
How to compute the cost of equity?It should be noted that the price of stock is computed thus:
= Previous dividend + Growth / Cost of equity - Growth
Po = Do + g/Ke - g
500 = 4 + 9%/Ke - 9%
500 = 4 + (0.09 × 4) / Ke - 9%
500 = 4.36/Ke - 9%
500(Ke - 9%) = 4.36
500Ke = 4.36 + 45
500Ke = 49.36
Ke = 49.36/500
Ke = 9.87%
The cost of debt will be:
= Interest rate (1 - Tax rate)
= 9% × (1 - 30%)
= 9% × 0.7
= 6.30%
The amount of the cost of debt will be:
= $1000 × 6.30%
= $63.00
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GIVING BRAINLIEST+20 POINTS TO BEST ANSWER FOR THESE 2 QUESTIONS!
1.Which story represents the equation six sevenths times one fourth?
1. Victoria drinks six sevenths of a cup of milk. She drinks one fourth of a cup more of milk. How much milk did she drink in all?
2. Mike walked one fourth mile and then he took the bus for six sevenths mile to school. How many miles did he travel in total?
3.Victoria has six sevenths of a pizza. She ate one fourth of it for dinner. How much pizza did Victoria eat for dinner?
4.Mike has six sevenths of a pie. He gives one fourth to his brother. How much pie does he have left
Answer:
3.
Step-by-step explanation:
Hey there!
This scenario shows that Victoria ate 6/7 of a pizza and ate 1/4 of that pizza the same day for dinner showing that she at one fourth of the six-sevenths pieces
Answer:
It is the third one.
Step-by-step explanation:
Let's take a look at each story. We need to find out which story is [tex]\frac{6}{7}[/tex]×[tex]\frac{1}{4}[/tex].
1. Victoria drinks six-sevenths of a cup of milk. She drinks one-fourth of a cup more of milk. How much milk did she drink in all?
This story is adding the fractions together since it wants to know how much did she drink in ALL. So this is not it.
(Here are some keywords to tell you if you need to add, altogether, all, in all, together, total, total number, add, increase, increased by, more than.)
2. Mike walked one-fourth mile and then he took the bus for six-sevenths mile to school. How many miles did he travel in total?
Once again this story is adding. It uses the word total. So this is not it.
3.Victoria has six-sevenths of a pizza. She ate one-fourth of it for dinner. How much pizza did Victoria eat for dinner?
This is correct since it wants to know how much she ate for dinner. She ate [tex]\frac{1}{4}[/tex] of [tex]\frac{6}{7}[/tex] of the pizza.
4.Mike has six-sevenths of a pie. He gives one-fourth to his brother. How much pie does he have left
This story is subtracting. So it is not it. (Subtracting words, minus, greater than, take away, fewer than, less than, subtract, decreased by.)
The figure shows a blueprint of a dining room, kitchen, and living room. Each square has a side length of 1/4 inch. Hardwood floors cost $11 per square foot. What is the cost of hardwood flooring for the dining room?
The cost of the hardwood flooring for the dining room is $
.
Step-by-step explanation:
Each square has a side length of 1/4 inch but you have said each square=1/4
Once you have found the amount of 1/4 inches you multiply the two numbers together, only then do you multiply it to $11 for the square area.
Area:-
side²0.25²0.0625in²Cost:-
0.0625(11)0.6875$Solve for bbb.
-11b+7 = 40−11b+7=40
b=-3
Step-by-step explanation:The equation, -11b + 7 = 40, can be solved using the properties of equality.
Solving For b
First, subtract 7 from both sides
-11b = 33Then, divide both sides by -11
b = -3Checking the Answer
We can check our answer by plugging the answer back into the original equation.
First, rewrite the equation with the answer
-11(-3) + 7 = 40Next, multiply out the terms
33 + 7 = 40Then, add together like terms
40 = 40Because this is a true statement, the answer must be correct.
1534 divided by 26 what is the answer help me out.
Answer:
59
Step-by-step explanation:
1534/26=59
It's 59 because I used a calculator
Find the surface area of the composite figure.
The Surface area of the figure is 520 square centimeters
How to calculate the surface area of a figureThe figure is made up of rectangular prisms
The formula for calculating the surface area of rectangular prism is expressed as:
SA = 2(lw + wh + lh)
l is the lengthw is the widthh is the heightSurface area of the figure = 2(2(8) + 2(14) + 8(14)) + 2(6(8) + 6(4) + 8(4))
Surface area of the figure = 2(16+28+112) + 2(48 + 24+32)
Surface area of the figure = 312 + 208
Surface area of the figure = 520 square centimeters
Hence the Surface area of the figure is 520 square centimeters
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Please answer number 14. It would mean so much to me.
Answer:
100.1 ftStep-by-step explanation:
You have dimensions of the original and scaled figures.
The missing dimension can be found using proportions as below
52.8 in ⇒ 57.2 ft (width)92.4 in ⇒ x ft (height)52.8/57.2 = 92.4/xx = 92.4*57.2/52.8x = 100.1 ftWhat is the value of tan 0 in the circle below
Answer:
tan theta = root3/3
see image
Step-by-step explanation:
The tangent is y/x in the unit circle. Use Keep-Change-Flip to simplify. See image. You also cannot leave a radical (square root) on the bottom of a fraction, so we need to "fix" that also. Multiply to rationalize (the "fix") see image.
The sum of two consecutive odd numbers is 28. Find their product
We will see that the first odd number is 13 and the second odd number is 15, the product is:
P = 13*15 = 195
How to find the two consecutive odd numbers?
Let's say that the first number is x, the next odd number will be x + 2.
The sum of these two odd numbers must be 2, then we need to solve the linear equation:
x + (x + 2) = 28
We can solve that for x:
2x + 2 = 28
2x = 28 - 2 = 26
x = 26/2 = 13
Then the first number is x = 13 and the second number is x + 2 = 13 + 2 = 15.
The product of these two numbers is:
13*15 = 195
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Convert 3 kilometres into metres
Answer:
3000m
Step-by-step explanation:
First, note that km is the same as kilometers and m is the same as meters. Thus, when you are asking to convert 3 km to m, you are asking to convert 3 kilometers to meters.
A kilometer is larger than a meter. Simply put, km is larger than m. In fact, a kilometer is "10 to the power of 3" larger than a meter.
Since a kilometer is 10^3 larger than a meter, it means that the conversion factor for km to m is 10^3. Therefore, you can multiply 3 km by 10^3 to get 3 km converted to m.
Here is the answer with the math showing you how to convert 3 km to m by multiplying 3 by the conversion factor of 10^3.
3 x 10^3
= 3000
3 km
= 3000 m
Answer:
3000 m
Step-by-step explanation:
Unit conversion :
1000 m = 1 kmSolving :
Let the missing value be 'x' mThen, according to this ratio :x/3 = 1000/1x = 1000 * 3x = 3000 mWhat is the difference between the mean and median of the set {3,8,10,15}?
Answer:
the difference is 0
Step-by-step explanation:
[tex]\large \text Mean =\frac{3+8+10+15}{4} = 9[/tex]
[tex]\large \text{Median} =\frac{8+10}{2} =9[/tex]
the difference = 9 - 9 = 0
In the equation y=2(3)^x what does the 2 represent? What does the 3 represent?
Answer:
This is an exponential function equation.
Therefore,
The 2 represents: Original amount (Y-intercept)
The 3 represents: Growth factor or (1+r)
if the diameter of the clock face is 10.5 inches, what is the radius?
Answer:
The radius is 5.25
Step-by-step explanation:
The radius is always exactly 1/2 of the diameter!
Hope this helps! <3
There are 7 red counters in a bag.
The rest of the counters in the bag are blue,
There are more blue counters than red counters in the bag.
Two counters are to be taken at random from the bag.
The probability that there will be one counter of each colour is
7/15.
Work out the total number of counters in the bag before any counters are taken from the bag.
Let x be the number of counters in the bag.
Pr(red counter) is drawn first = 7/x
Pr(blue counter) is drawn first = (x-7)/x
Pr(counters will be same) = 8/15
solution:with replacement:
P^req= 7/7+x × x/7+x= 7/15
so, the total number of counters in the bag before any counters are taken from the bag are 7/15.
Solve the following inequality for s. Write your answer in simplest form.
-10 + 5(78 + 8) < - 4s +3 - 8
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: - 10 + 5(78 + 8) < - 4s + 3 - 8[/tex]
[tex]\qquad \sf \dashrightarrow \: - 10 + 5(86) < - 4s - 5[/tex]
[tex]\qquad \sf \dashrightarrow \: - 10 +430 < - 4s - 5[/tex]
[tex]\qquad \sf \dashrightarrow \: 420 + 5 < - 4s [/tex]
[tex]\qquad \sf \dashrightarrow \: 42 5 < - 4s [/tex]
[tex]\qquad \sf \dashrightarrow \: 42 5 \div 4 < - s [/tex]
[tex]\qquad \sf \dashrightarrow \: 106.25 < - s [/tex]
Inequalities change when it is multiplied by -ve number
[tex]\qquad \sf \dashrightarrow \: - 106.25 > s [/tex]
15 days ago, the share of the Valmont family business was worth $156. Over the next 5 days, the stock value increased by $3 per day. Then its value went down by $5 a day for 10 days.
What is the value of the stock today?
Using Order of Operation
please answer i need it today :'(
Answer:
compute the company's price-to-earnings (P/E) ratio.
Step-by-step explanation:
When companies issue additional shares, it increases the number of common stock being traded in the stock market. For existing investors,
Answer number 1 please. Thank you.
Find the values of x and y
Answer:
well, y=8 and x=50
Step-by-step explanation:
you actually have the angle 128 wrong, and it is suppose to be 32 degrees, which changes it up and all you have to do to find y because angle 32 and 4y are vertical, is divide 32/4=y which is 8, for x, it is vertical to 148 making those even, and it would be as simple as reversing the equation so, 148+2=150, and ddivided by 3 is 50 degrees
Answer:
x=50
y=8
Step-by-step explanation:
3x-2 and 148 are vertical angles and vertical angles are equal
3x-2 =148
Add 2 to each side
3x-2+2 =148+2
3x= 150
Divide by 3
3x/3 =150/2
x = 50
148 and the empty angle form a straight line so they add to 180
180-148 = 32
The empty angle is 32
4y and 32 are vertical angles so they are the same
4y = 32
4y/4 = 32/4
y = 8
I need help with this
Answer:
Class 1.
Step-by-step explanation:
Class 1 has the greater interquartile range.
Answer:
Class #2
Step-by-step explanation:
IQR of Class #1:
85 - 72 = 13
IQR of Class #2:
90 - 70 = 20
Class #2 has a greater IQR!
Hope this helps!
What is the meaning of ^
Answer:
Symbol. ^ or (English symbol name wedge) (mathematics, logic) The conjunction operator, forming a Boolean-valued function, typically with two arguments, returning true only if all of its arguments are true. (mathematics) wedge product
Answer;
It is the symbol used in computer language to denote the square or cube or other power of any number . for example; 2^2, it means the square of 2.
A gardener uses a triangular prism clay pot to plant flowers. The triangular base is 3 units along the base and 5 units high. The pot has a height of 16 units high. What is the volume of the pot.
the volume of the pot.
solution:bolume of a triangular prism= BH
area of a triangle= 1 / 2 × base × height
B = 1 / 2 × b × h
b = 3 units
h = 5 units
B = 1 / 2 × 3 × 5
B = 15 / 2
B = 7.5 units²
H = 26 units
B = 7.5 units²
V = 7.5 × 26
V= 195 unit³
so, the volume of the pot is 195 unit³.
(7-2)² - 5 / 5 I dont get the exponent part can someone help me with whole problem
(7-2)² - 5/5
Do the math in the parentheses first.
7 - 2 = 5
Now the equation should read
(5)² - 5/5 or just 5² - 5/5
Do the exponent(s).
5² = 25
25 - 5/5
Do the division.
5/5 = 1
25 - 1 = 24
Therefore, according to our equation, the answer is 24.
I hope this answered your question.
if p(x) = -2x²-3x+1, find p( -2)
help me please
[tex]\large{\mathcal{QUESTION:}}[/tex]
if p(x) = -2x²-3x+1, find p( -2)
[tex]\large{\mathcal{ANSWER:}}[/tex]
the answer is on the photo
The scale on a map is 1 cm for every 400 km. If Maine and Japan are 26cm apart on the map, what is the distance between Maine and Japan
Please Help Fast!!!
Solve the system of equations:
25−x=−4y
3x−2y=30
Answer:
{x,y} = {7,-9/2}
Step-by-step explanation:
System of Linear Equations entered :
[1] 25-x=-4y
[2] 3x-2y=30
Equations Simplified or Rearranged :
[1] -x + 4y = -25
[2] 3x - 2y = 30
Graphic Representation of the Equations :
4y - x = -25 -2y + 3x = 30
Solve by Substitution :
// Solve equation [1] for the variable x
[1] x = 4y + 25
// Plug this in for variable x in equation [2]
[2] 3•(4y+25) - 2y = 30
[2] 10y = -45
// Solve equation [2] for the variable y
[2] 10y = - 45
[2] y = - 9/2
// By now we know this much :
x = 4y+25
y = -9/2
// Use the y value to solve for x
x = 4(-9/2)+25 = 7
Solution :
{x,y} = {7,-9/2}
Answer:
x=7, y=-4.5 or (7, -4.5)
Step-by-step explanation:
Hi there!
We are given the following system of equations:
25-x=-4y
3x-2y=30
Before we do anything, let's move our x and y values to one side, while keeping the numbers on the other side
So for 25-x=-4y, start by adding 4y to both sides
25-x=-4y
+4y +4y
_____________
25 + 4y - x = 0
Now subtract 25 from both sides
4y - x = -25
Now the system is this:
4y-x=-25
3x-2y=30
We can solve this equation by substitution, where we solve one of the equations for one of the variables, and then use the expression that the variable is equal to, in order to find the value of the other variable. Then, once the value of that variable is found, use that value to find the value of the first variable.
Start with 4y-x=-25
Subtract 4y from both sides
-x=-4y-25
Now multiply both sides by -1
x=4y+25
Substitute 4y+25 as x in 3x-2y=30
3(4y+25)-2y=30
Multiply
12y+75-2y=30
Simplify
10y+75=30
Subtract 75 from both sides
10y=-45
Divide both sides by 10
y = -4.5
Now substitute -4.5 as y in x=4y+25
x=4(-4.5)+25
Subtract
x= -18 +25
x= 7
The answer is x=7, y=-4.5. As a point, it's (7, -4.5)
Hope this helps!
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Ashley needs new batteries for the flashlights at her house. Each flashlight takes 4
batteries. Write an equation to show how the number of batteries needed, b, depends on the number of flashlights, f.
Answer: b = 4f
Step-by-step explanation:
Since every flashlight needs 4 batteries, every flashlight added (f) will be 4 more batteries needed total (b). With this information in mind, we can write the equation:
b = 4f
Answer:
b = 4f
Step-by-step explanation:
4 batteries per flashlight
Please help I will give brainliest.
Answer:
See below
Step-by-step explanation:
x = silk yards
y = cotton yards
y = 4.25 - x sub this in to the second equation
16.90 x + 4 ( 4.25 - x ) = 36.35
x = 1.50 yards of silk
y = 4.25 - 1.50 = 2.75 yards of cotton