Answer:
[tex]5\sqrt{2} +\sqrt{10}[/tex]
Step-by-step explanation:
[tex]\sqrt{5} (\sqrt{10} +\sqrt{2} ) < --Given[/tex]
[tex]\sqrt{5} \sqrt{10} +\sqrt{5} \sqrt{2} < -- Distribute[/tex]
An equation is in its simpliest form when you eliminate as many square roots as possible. Here are some rules:
1.) You cannot combine numbers through addition or subtraction if they are under square roots. However, you can combine numbers through multiplication or division if they are under square roots.
2.) You cannot take the square root of a number if the answer is not a whole number (unless the problem says you can). However, you can solve the square root if the number can be simplfied into a "rootable?" number. In other words, the number under a square root can be divided into a number that can have its square root taken.
The first part...
[tex]\sqrt{5} \sqrt{10} = \sqrt{5} * \sqrt{10} < --Multiply[/tex]
[tex]\sqrt{5} * \sqrt{10} =\sqrt{50}[/tex]
[tex]\sqrt{50} = \sqrt{25} *\sqrt{2} < --Separate[/tex]
[tex]\sqrt{25} = 5 < --Solve[/tex]
[tex]\sqrt{50} = 5 *\sqrt{2} < -- Substitute[/tex]
[tex]5*\sqrt{2} =5\sqrt{2} < --Rewrite[/tex]
The second part...
[tex]\sqrt{5} \sqrt{2} =\sqrt{5} * \sqrt{2} < -- Multiply[/tex]
[tex]\sqrt{5} *\sqrt{2} = \sqrt{10}[/tex]
Combine both parts...
[tex]5\sqrt{2} +\sqrt{10}[/tex]
Tanya's father travels every week for business. He has traveled around the
world many times. Over the past 10 years, he has accumulated approximately
460,000 frequent flyer miles. How is that number expressed in scientific
notation?
A. 4.6 × 103
B. 4.6 × 10 4
C. 4.6 × 10 5
D. 46 × 10 5
The correct answer would be: 4.6 x 10^5
Andy made 7 baskets during a basketball game each basket was worth 2 or 3 points how many different numbers could represent the total points scored by jordan
Answer:
2+3+2+3+2+3+2=17 because each was worth 2 or 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)
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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A college student was offered two different summer jobs. Job A would last 20 weeks and pay $300
per week with weekly raises of $10. Job B would last 5 months and pay $1200 per month, with monthly
raises of 10% of the previous month's salary. How much more would the college student earn by
accepting Job A?
Answer:
600yan lang po thank you
Answer:
$574
Step-by-step explanation:
[tex]\begin{aligned}\text { week } 1=w_{1} &=300 \\w_{2} &=300+10=310 \\w_{3} &=310+10=320=300+2 \times(10)\end{aligned}[/tex]
It’s obvious here that we add 10 each time to get the next week’s payment so we Are dealing an arithmetic sequence where its first term is 300 and its
Common difference is 10
Then In the twentieth week the payment will be :
[tex]\begin{aligned}W_{20} &=w_{1}+(20-1) \times(10) \\&=300+19 \times(10) \\&=490\end{aligned}[/tex]
Now we apply the formula for the sum of Consecutives terms of an arithmetic sequence :
[tex]\begin{aligned}S_{1} &=20 \times\left(\frac{w_{1}+w_{20}}{2}\right) \\&=20 \times\left(\frac{300+490}{2}\right) \\&=7900\end{aligned}[/tex]
Now let move on to Job B:
[tex]\\\\\begin{aligned}\text { month1 }=& m_{1}=1200 \\m_{2} &=1200+1200 \times \frac{10}{100}=1200 \times(1,1)=1320 \\m_{3} &=m_{2} \times(1,1)=\left[m_{1} \times(1,1)\right] \times(1,1)=m_{1} \times(1,1)^{2} \\m_{4} &=m_{1} \times(1,1)^{3} \\m_{5} &=m_{1} \times(1,1)^{4}\end{aligned}[/tex]
It’s obvious here that we multiply by (1.1) each time to get the next month’s payment so we Are dealing a geometric sequence where its first term is 1200 and its Common ratio is 1.1
Now we apply the formula for the sum of Consecutives terms of an geometric sequence :
[tex]\begin{array}{l}S_{2}=m_{1} \times\left(\frac{1-1,1^{5}}{1-1,1}\right) \\\approx 7326\end{array}[/tex]
Finally we can say confidently say that he would earn more :
7900 - 7326 = $574.
can someone help me with this
Answer:
B. across the y-axis
Step-by-step explanation:
The line of reflection is the perpendicular bisector of the segment between the orginal point and its image. If you plot the two points, you see that the y-axis is that bisector.
The point was reflected across the y-axis.
__
Additional comments
Changing the sign of the x-coordinate means a point that was some distance on one side of the y-axis is now that same distance on the other side. That is, the y-axis is the line of reflection when the sign of x changes.
Similarly, the x-axis is the line of reflection when the sign of y changes.
(x, y) ⇒ (-x, y) . . . . reflection across the y-axis
(x, y) ⇒ (x, -y) . . . . reflection across the x-axis
__
Changing the signs of both coordinates (in either order) is effectively a reflection across the origin. There are other names for this reflection, too.
(x, y) ⇒ (-x, -y) . . . . reflection across both axes, across the orign, rotation 180°
Bilquis is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 29 meters from the building. The angle of elevation from her eyes to the roof ((point AA)) is 17∘
, and the angle of elevation from her eyes to the top of the antenna ((point BB)) is 31∘
. If her eyes are 1.51 meters from the ground, find the height of the antenna ((the distance from point AA to point BB)). Round your answer to the nearest meter if necessary.
Using relations in a right triangle, it is found that the height of the antenna is of 10 m.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.In this problem, the vertical height from her eyes to the top of the antenna is the side opposite to the angle of 17º, while the adjacent side is the horizontal distance of 29 m, hence:
[tex]\tan{17^\circ} = \frac{h}{29}[/tex]
[tex]h = 29\tan{17^\circ}[/tex]
[tex]h = 8.87[/tex]
Adding the eye height:
h = 8.87 + 1.51 = 10.38 m.
Rounding to the nearest meter, the height of the antenna is of 10 m.
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Answer:
9
Step-by-step explanation:
I just took the test.
Brainliest and 50 points
are the polygons similar?
A) no; there is not a consistent ratio
B) yes; the scale factor from ADKG to WMLZ is 3/4
C) yes; the scale factor from ADKG to WMLZ is 3/2
D) yes; the scale factor from ADKG to WMLZ is 2/3
Answer:
A) no; there is not a consistent ratio
Step-by-step explanation:
If the polygons are similar than the corresponding sides will have similar ratios.
The corresponding sides of the polygons are (AD and WM) and (DK and ML)
The ratio from AD to WM is 6/4 or 1.5 and the ratio to DK to ML is 8/6 or 1.33
The corresponding sides do not have a common ratio therefore the polygon is not similar
Find y.
B
C
Зу
A
8 D
м
2
4
15
10
Answer:
y=4
Step-by-step explanation:
The question is asking what is the value of y:
Since all lengths have a dash on them they are all equal :
So 3y = y+8
3y = y + 8
First we subtract y from both sides:
3y-y = y+8-y
2y = 8
Divide both sides by 2:
2y÷2 = 8÷2
y = 4
Find the area of a circle with a radius of 21 inches. Use 22/7
for pi.
Answer:
Area of circle=πr^2
Step-by-step explanation:
Area of circle=πr^2
=22/7*21^2
=22/7*441
=9702/7
=1386 sq.inch
a number is greater than 12
Answer:
anything above 12
Step-by-step explanation:
would be greater than 12. 13, 14, 16...etc
Answer:
n > 12
Step-by-step explanation:
Represent the number by n. Then "a number is greater than 12" expressed symbolically is n > 12.
C.P and R are supplementary angles. If the measure of ZR is
37º, what is the measure of ZP? Picture blow
Answer:
143
Step-by-step explanation:
supplementary angles add to 180
37+x=180
x=143
A family goes to a fundraiser for their local library. Each ticket is $12, and they give a single donation of $10
at the end of the evening. There are six members of the family, and they spend a total of $82. Which equatic
could represent this situation?
Answer:
x=12y + 10 or even just entirely solved... 82=12(6) +10
Step-by-step explanation:
Answer:
ImnotI'm not sure
this is the same im on
Step-by-step explanation:
Marco travels from his house to the beach. The total distance he travels
is 120 miles. In the first hour, Marco traveled 54 miles. What percent of
the distance did he travel the first hour?
Answer:
45%
Step-by-step explanation:
Since he drove 54 miles out of 120 in the first hour, the equation for this would be 54/120×100. This equals 45 and that is the percentage
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
60 sq m
Step-by-step explanation:
Area of the figure
= Area of top rectangle + Are of the bottom rectangle
= 5*3 + 5*(3+3+3)
= 15 + 5*9
= 15 + 45
= 60 sq m
Answer:
60 m²
Step-by-step explanation:
Area of the figure
= Top rectangle vertical + Bottom rectangle horizontal
= 3 x 5 + 5 x 9
= 15 + 45
= 60 m²
Factor completely 9x3 + 36x2 - x - 4.
(3x + 4)(3x – 4)(x + 1)
(3x + 1)(3x - 1)(x + 4)
(9x2 - 1)(x + 4)
-
(3x + 1)(3x – 1)(x – 4)
-
The correct answer is: (3x + 1)(3x - 1)(x + 4)
Each graph shows a relation. The first and second numbers of each ordered pair in the relation are members of the set of real numbers. In each case, find the domain and range and determine whether the relation is a function.
Answer:
Domain: -2≤ x≤ 0
Range: -2≤ x≤ 2
The relation is a Function
Step-by-step explanation:
The Domain is all the x values.
All the x values are either equal to or greater than -2, and less than or equal to =-0
The Range is all the y values.
Apply the same logic as the domain.
A function is where no x values are the same, and since in this graph we see no vertical line, indicating the same x value, it means it is a function
Factor the trinomial 6x^{2} + 5x - 25. Which of the following is a factor?
Answer:
its (3x-5)
Step-by-step explanation:
Answer:
C. (3x - 5)
Step-by-step explanation:
1. Find a solution pair that gives the sum of b (5):
-10 + 15 = 5
2. Break the expression into groups:
(6x² - 10x) + (15x - 25)
3. Factor out the common factor in each group:
2x(3x - 5) + 5(3x - 5)
4. Factor out the common pair (3x - 5) using the distributive property:
(3x - 5)(2x + 5)
hope this helps!
Aline passes through the points (3,18) and (8,23). Write a linear function rule in terms of x and y for
this line.
The linear function rule is y=
Answer:
y= x+15
Step-by-step explanation:
I am pretty sure this answer is right
M= slope
B= the Y-intercept
I used a graphing calculator to figure this out
The slope is 1/1 with equals 1
and the y intercept is at (0,15) whitch we just use 15
plug them in and you get
y= x+ 15
(Don't need the 1 is frount of x)
2 Demi teaches drum classes. The equation B = 50t gives the dollar amount she earns as a function of the time in hours she teaches. Demi also takes spin classes. The graph shows how much she has left on a gift card as a function of the time in hours Demi is in class. Does Demi earn more teaching 1 hour of drum class or spend more taking 1 hour of spin class? Show your work.
The answer should be Demi earns more teaching drum class regardless of how many hours she puts in.
What is the Slope intercept form?The equation of a straight line whose slope and y-intercept are given. Suppose a non-vertical line has a gradient or slope of m and y-intercept equal to c. Let (x, y) be any point on the line and a line intersect the y-axis at the point (0, c).
y = mx + c
Using the slope-intercept form (y = mx + b) to find the function of the graph,
B = -100/5t + 500
Or B = -20t + 500.
After 1 hr or t = 1 Demi earns B = 50(1) or $50 teaching
After 1 hr or t = 1 Demi spends B = -20(1)
-$20 on spin class.
If it’s asking just the rate of increase or decrease, the slope of 50t is greater than the slope of -20t.
Thus, The answer should be Demi earns more teaching drum class regardless of how many hours she puts in.
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Multiple choice easy question. Please answer.
Answer:
I belive it should be # 3 i might be wrong thow.
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Car one rotated 90 degrees counterclockwise would be to car 4
then, it rotated 180 degrees clockwise would be car 2.
the answer is Car 2
please help me solve this?
Answer:
there are none (sorry if I got it wrong)
Step-by-step explanation:
also, there is none because there other numbers are really close to the other number
outliers are a number that is really small in the pack of numbers and outliers can also be the number that is really big for example I have the numbers 3 24 28 32 43 and then 100. 3 and 100 are outliers because one number (3) is really small from the other numbers are bigger and one number (100) is really big from the other number but sometimes there are no outliers
Suppose that the volume of a right circular cylinder is 288 cubic meters and the area of its base is 16 square meters. What is the height of the cylinder?
A. 12 m
B. 16 m
C. 18 m
D. 14 m
Answer: 18
Step-by-step explanation:
288 / 16 = 18
Answer:
C) 18 m
Step-by-step explanation:
What’s is the right answer choice to the picture.
Q has coordinates
(2,-4)P is 6units left
P(2-6,-4)=(-4,-4)R is 7units up
R(2,-4+7)R(2,3)Option B
Answer:
B) P (-4, 4) and R (2, 3)
Step-by-step explanation:
Q = (2, -4)
If ΔPQR is a right triangle, then
Missing point 1 will be on the x = 2 lineMissing point 2 will be on the y = -4 lineIf PQ is 6 units, then
P = (2-6, -4) = (-4, -4) or
P = (2, -4+6) = (2, 2)
If QR is 7 units, then
R = (2-7, -4) = (-5, -4) or
R = (2, -4+7) = (2, 3)
Therefore, P (-4, 4) and R (2, 3)
Please help, I am struggling with this. Question is in image.
Answer:
-7 15/17. 49 sq. 7.7 187/24
Step-by-step explanation:
thats the order least to greatest 187/24= 7.79 and 49 sq = 7
How does your Web browser get a file from the Internet? Your computer sends a request
for the file to a Web server, and the Web server sends back a response. For one
particular Web server, the time X (in seconds) after the start of an hour at which a
randomly selected request is received has the uniform distribution shown in the figure. in
The probability that the request is received by this server within the first 5 minutes (300 seconds) after the hour is 0.0833 or 8.33%.
How does your Web browser get a file from the Internet?Your computer sends a request for the file to a Web server, and the Web server sends back a response.
For one particular Web server, the time X (in seconds) after the start of an hour at which a randomly selected request is received has the uniform distribution shown in the figure.
The probability of finding value less than the X is,
[tex]P(X < x)=\dfrac{x-a}{b-a}[/tex]
Here, a and b are two bonds of uniform distribution.
The probability distribution of X can be modeled by a uniform density curve on the interval from 0 to 3600 seconds, as shown in the given figure.
The probability that the request is received by this server within the first 5 minutes (300 seconds) after the hour has to be found out. Thus,
[tex]P(X < x)=\dfrac{300-0}{3600-0}\\P(X < x)=0.0833\\P(X < x)=8.33\%[/tex]
Thus, the probability that the request is received by this server within the first 5 minutes (300 seconds) after the hour is 0.0833 or 8.33%.
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The group thought there was enough food for all 5 group members to
complete the trip, with each person getting the required 5600 calories per
day. However, they discover that they are missing 28,800 calories.
Using the map, create a plan a for the rest of the trip that includes taking as
many group members as possible to the South Pole, while sending the rest of
the group members directly back to base camp. Remember that each person
must have 5600 calories of food per day until he or she gets back to base
camp.
Be sure to explain how you came up with your plan. Include all work
necessary to support your answer.
To create a work plan for the food intake of each person in the group, there needs to be the required 5600 calories and there needs to be a replacement for the caloric deficit.
What is a Work Plan?This refers to the formal roadmap that is created for a project for the purposes of streamlining it.
Based on the fact that a map was not provided, there is insufficient data to solve the problem, so a general overview will be given about a work plan.
Because the group is 28,800 calories short and needs to complete the trip with their five members, then they need to ration their supplies.
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A bag with 6 marbles has 1 yellow marble 2 blue marbles and 3 red marbles. A marble is chosen from the bag at random what is the probability that it is yellow ? write your answer as a fraction in simplest form
A fraction/probability is created by taking what we want and putting that over the total.
In this case, we want yellow out of the total number of marbles.
Yellow Marbles = 1
Total Marbles = 6 + 1 + 2 + 3 = 12
Probability/Fraction = 1 / 12
Hope this helps!
Jessica has $40 to spend at the book fair. She buys 2 notebooks for $3 8. each and wants to spend the rest of her money on books. How many books can Jessica buy if each book costs $8? How much money does Jessica have left over?
Answer:
She can buy 4 books
Step-by-step explanation:
If each notebook is $3, and she bought two, she'd be left with $32 because 40-6=32. Simply multiply 8 by 4 to get 32, which is the rest of her money. Hope this helps!
Compare million, billion, and trillion. What is the largest number among them? What is the smallest number among them?
If x is directly proportional to y, and x = 4.5 when y = 3, find
(i) an equation connecting x and y
(ii) the value of x when y = 6,
(iii) the value of y when x = 12.
Answer:
1. don't know what you want for the first one but..
2. x=9
3. y= 8
Step-by-step explanation:
x = 1.5y
ex y=2 x=2
