All the line segments of this 22-gon meet at right angles. The radius of the smallest circle that will completely surround the polygon is
Answers
Answer:
√61 ≈ 7.81
Step-by-step explanation:
It appears that the polygon can be enclosed by a rectangle that is 12 units wide and 10 units high. The enclosing circle is the one that will circumscribe that rectange. Its radius is half the length of the diagonal, so is ...
(1/2)√(12² +10²) = 1/2√244 = √61
The smallest circle that will surround the polygon will have a radius of √61 ≈ 7.81 units.
_____
The Pythagorean theorem is used to find the length of the diagonal. It tells you the square of the diagonal is the sum of the squares of the sides of the rectangle. Our radius is half the diagonal, so is half the square root of the sum of the squares of the side lengths.
Related Questions
if the diameter of the clock face is 10.5 inches, what is the radius?
Answers
Answer:
The radius is 5.25
Step-by-step explanation:
The radius is always exactly 1/2 of the diameter!
Hope this helps! <3
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)
Answers
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
Learn more about cost of equity on:
https://brainly.com/question/14041475
What is the meaning of ^
Answers
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.
In the equation y=2(3)^x what does the 2 represent? What does the 3 represent?
Answers
Answer:
This is an exponential function equation.
Therefore,
The 2 represents: Original amount (Y-intercept)
The 3 represents: Growth factor or (1+r)
Find the values of x and y
Answers
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
Please answer number 14. It would mean so much to me.
Answers
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 ftPLEEEEEAAAASEEE HELPPPPPP
simplify the polynomial
3a(6a^2-4ab^2)+8a^2b^2-2b^3
Answers
Answer:
Simplified: -4a²b²+18a³-2b³
3a(6a²-4ab²)+8a²b²-2b³
Multiply 3a by 6a² and-4ab²
18a³-12a²b²+8a²b²-2b³
combine like terms (-12a²b² and 8a²b²)
-4a²b²+18a³-2b³
Hope this helps
Step-by-step explanation:
Here we have to simplify the polynomial :
[tex] \\ \longrightarrow \sf \qquad3a(6a^2-4ab^2)+8a^2b^2-2b^3\\ \\[/tex]
Using Distributive property we get :
[tex]\longrightarrow \sf \qquad18a^3- {12}^{2} b^2+8a^2b^2-2b^3\\ \\[/tex]
Combining the like terms we get :
[tex]\longrightarrow \sf \qquad18a^3-4a^2b^2-2b^3\\ \\[/tex]
Therefore,
The Simplified expression is [tex] \sf 18^3-4a^2b^2-2b^3[/tex]Please Help Fast!!!
Solve the system of equations:
25−x=−4y
3x−2y=30
Answers
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!
See more on solving systems of equation here: https://brainly.com/question/24420448
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.
Answers
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)
Read more about correlation coefficients at:
https://brainly.com/question/18054482
Answer number 16 please thank you
Answers
14 g of copper was heated from 50°C to 85°C. How much energy was used to heat Cu? (Specific heat capacity of Cu is 0.385 J/g °C)
HELP PLEASE GIVING OUT BRIANLEST TO THE CORRECT ANSWER THANK YOUU
Answers
Q = mcΔt
Q = 14 x 0.385 x (85-50)
Q = 161.7 J
4.72x 10 to the 10th power in standard form
Answers
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:
I need the vocab word for problems 5-8
Answers
Answer:
5. Foci, 6. eccentricity, 7. Center, 8. HyperbolaStep-by-step explanation:
Below statements include the required information or property
5. An ellipse is "the set of all points in a plane such that the sum of the distances from two fixed points (foci) is constant".6. In an ellipse, the ratio c/a is called the eccentricity and is denoted by the letter e . Eccentricity measures the elongation of an ellipse. The closer e is to 0, the more an ellipse looks like a circle.7. A circle is a set of all points in a plane that are all an equal distance from a single point, the center.8. Hyperbolas have a center and two foci, but they do not form closed figures like ellipsesGIVING 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
Answers
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.)
Solve for bbb.
-11b+7 = 40−11b+7=40
Answers
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.
Answers
Answer:
59
Step-by-step explanation:
1534/26=59
It's 59 because I used a calculator
Answer number 1 please. Thank you.
Answers
The lifetime of a certain type of light bulb can be approximated by a normal distribution. The list
gives the number of days a bulb can last for 10 light bulbs selected at random. Find the mean and
standard deviation of the data set. Then sketch a normal curve to represent the distribution.
25, 24, 32, 16, 22, 34. 19. 27, 18, 29
Answers
The standard deviation of the dataset is the square root of the variance
The mean and the standard deviation of the dataset are 24.6 and 5.70, respectively
How to determine the mean?The dataset is given as;
25, 24, 32, 16, 22, 34. 19. 27, 18, 29
Calculate the mean using:
μ = Sum/Count
So, we have:
μ = (25+ 24+ 32+ 16+ 22+ 34+ 19+ 27+ 18+ 29)/10
Evaluate
μ = 24.6
How to determine the standard deviation?The standard deviation is then calculated using:
[tex]\sigma =\sqrt{ \frac{\sum(x - \mu)^2}{n}[/tex]
So, we have:
[tex]\sigma = \sqrt{\frac{(25 - 24.6)^2 + .................. + (27- 24.6)^2 + (18- 24.6)^2 + (29- 24.6)^2}{10}}[/tex]
Evaluate
[tex]\sigma = \sqrt{32.44}[/tex]
Evaluate the square root
[tex]\sigma = 5.70[/tex]
Hence, the mean and the standard deviation of the dataset are 24.6 and 5.70, respectively
Read more about variance at:
https://brainly.com/question/15858152
An investor buys 400 shares of stock in a fund when the net asset value is $19.62 and the offer price is $19.84. the investor sells these shares when the net asset value is $43.19 and the offer price is $43.56. determine the amount of profit the investor earns. a. $9,576 b. $9,488 c. $9,428 d. $9,340 please select the best answer from the choices provided a b c d
Answers
The amount of profit the investor earns is 9340 dollars. Then the correct option is D.
What is Algebra?Algebra is the study of mathematical symbols and the rule involves manipulating these mathematical symbols.
An investor buys 400 shares of stock in a fund when the net asset value is $19.62 and the offer price is $19.84.
The investor sells these shares when the net asset value is $43.19 and the offer price is $43.56.
Then total cost price of the shares will be
→ 19.84 × 400 = $7936
The total selling price of the shares will be
→ 43.19 × 400 = $17,276
Then the profit is the difference between the total cost price of shares and the total selling price of the shares.
→ 17276 - 7936 = $ 9340
More about the Algebra link is given below.
https://brainly.com/question/953809
Convert 3 kilometres into metres
Answers
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 m(7-2)² - 5 / 5 I dont get the exponent part can someone help me with whole problem
Answers
(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.
What is the value of tan 0 in the circle below
Answers
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.
if p(x) = -2x²-3x+1, find p( -2)
help me please
Answers
[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 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 $
.
Answers
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 $11 for the square area.
Area:-
side²0.25²0.0625in²Cost:-
0.0625(11)0.6875$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.
Answers
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.
Find the angle marked y in the figure below
Answers
Answer: 75 degrees
Step-by-step explanation:
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.
Answers
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
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
Answers
What is the difference between the mean and median of the set {3,8,10,15}?
Answers
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
Please help I will give brainliest.
Answers
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