3. Carlos Quintero, Treasurer of X Corp is analyzing an investment on two projects, C and D. The data to
consider are shown below
Initial Investment
Annual Rate of
Return
Pessimistic
Most Likely
Optimistic
Amount
$135,000
39%
27%
25%
Project C
Probability
.30
.45
.25
Amount
$145,000
25%
15%
30%
Project D
Probability
.35
.40
.25
A. Determine the rates of return for each of the two projects. (6 points)
The rates of return for each of the two projects for X Corp are as follows:
Project C = 30.1%Project D = 19.75%.What is the rate of return?The rate of return refers to the percentage gain or loss over the initial cost of the investment.
For this purpose, the rate of return is expressed as the percentage of the expected returns (which is a product based on the probability of different scenarios) over the initial investment cost.
Project C Project D
Amount Probability Amount Probability
Initial Investment $135,000 $145,000
Annual Rate of Return
Pessimistic 39% .30 25% .35
Most Likely 27% .45 15% .40
Optimistic 25% .25 30% .25
Returns from Project C:Pessimistic $15,795 ($135,000 x 39% x 30%)
Most likely $16,402.50 ($135,000 x 27% x 45%)
Optimistic $8,437.50 ($135,000 x 25% x 25%)
Total expected returns = $40,635
Rate of return = 30.1% ($40,635/$135,000 x 100)
Returns from Project D:Pessimistic $9,062.50 ($145,000 x 25% x 35%)
Most Likely $8,700 ($145,000 x 15% x 40%)
Optimistic $10,875 ($145,000 x 30% x 25%)
Total expected returns = $28,637.50
Rate of return = 19.75% ($28,637.50/$145,000 x 100)
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A square room has a floor area of 49 square meters. The height of the room is 8 meters. What is the total area of all four walls?
The total area of all four walls is 224 square meters.
According to the question,
We have the following information:
A square room has a floor area of 49 square meters.
So, we have:
Area of square = 49 square meters
Side*side = 49
Side = [tex]\sqrt{49}[/tex] m
Side of the square = 7 m
Now, the side of the floor will be the width of the wall.
So, we have the width of the wall = 7 m.
The height of the room is 8 meters.
It means that the height of the wall is 8 m.
Area of 1 rectangular wall = length*width
Area of wall = 8*7
Area of 1 wall = 56 square meters
Now, the are of 4 walls will be (4*56) square meters or 224 square meters.
Hence, the total are of all four walls is 224 square meters.
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Martin and Isabelle go bowling. Each game costs $10, and they split that cost. Martin has his own bowling shoes, but Isabelle pays $3 to rent shoes.Which graph shows a proportional relationship? Explain why.
We have the following:
Martin's graph is good and correct, although it is not totally straight, but the relationship that it keeps is totally proportional.
On the other hand, Isabelle's graph, although it is totally straight, is wrong, because she must start from 3, which is the rental value of the shoes, and her graph starts at 0, therefore it is wrong, despite of which shows a proportional relationship.
Therefore the correct answer is Martin's graph.
Answer:
Step-by-step explanation:
What is the slope of this horizontal line from 10-13 minutes?
We are asked to determien the slope of the line between 10 and 13 minutes. Since this is a horizontal line, it's slope is 0.
debbie and tom's bill for dinner was $58. They left a tip of $8.70. what percent of the bill was the tip?
The value of the bill was $58. The tip was $8.7. Percentage is expressed in terms of 100. To determine the percentage of the bill that was the tip, we would find the ratio of the tip to the bill and multiply by 100. It becomes
8.7/58 * 100
= 15%
The tip was 15% of the bill
If TW =6, WV =2, and UV =25, find XV to the nearest hundredth.
TW = 6
WV = 2
UV = 25
XV = ?
XV/UV = WV/TV
XV/25 = 2 /(6 + 2)
XV = 2(25)/7
XV = 50/7
XV = 7.1428
Rounded to the nearest hundredth
XV = 7.14
Simplify (5x + 7) - (x + 2)
You have the following expression:
(5x + 7) - (x + 2)
in order to simplify the previous expression, eliminate parenthesis and take into account that if a parenthesis is preceeded by a minus sign, when you elminate th eparenthesis the sign inside change to the opposite, just as follow:
(5x + 7) - (x + 2) =
5x + 7 - x - 2 =
5x - x + 7 - 2 =
4x + 5
Hence, the simplified expression is 4x + 5
im having a hard time understanding this could you please help me
Given -
The odds against winning a prize in the raffle = 9:1
To Find -
Probability of winning prize =?
Step-by-Step Explanation -
Total possible outcome = 9 + 1 = 10
Favourable outcome = 9
So,
Probability = Total outcome / Favourable outcome
Probability = 9/10 = 0.9
Final Answer -
Probability of winning prize = 0.9
i need these answered , i am very confused The options for them are:constant rational square root exponential growth cube root linear absolute value cubic logarithmic quadratic
Based on the question and the options provided, we have that:
[tex]7)\text{ The name of the parent function for g(x) = 3}\sqrt[]{x}\text{ is a square root}[/tex][tex]8)\text{ The name of the parent function for f(x) =}2^{x^{}}+5\text{ is exponential growth}[/tex][tex]9)\text{ The name of the parent function for f(x)=}\frac{5}{4}\sqrt[3]{x}\text{ is cube root}[/tex][tex]10)\text{ The name of the parent function for h(x) =}8x\text{ is linear}[/tex][tex]11)\text{ An example of an absolute value equation is: y = }\lvert x+5\rvert-3[/tex]O GRAPHS AND FUNCTIONSWriting an equation for a function after a vertical and horizo
Given:
The point (0,0) lies on the graph f(x) and (4,-3) lies on the graph h(x).
To find:
We need to find the equation for the function h(x).
Explanation:
Consider the translation point which is translated horizontally a unit and vertically as b units.
[tex](x^{\prime},y^{\prime})\rightarrow(x+a,y+b)[/tex]The point (4,-3) can be written as follows.
[tex](4,-3)\rightarrow(0+4,0-3)[/tex]We get the function h(x) after f(x) translated horizontally 4 units right and vertically 3 units down.
The function can be written as follows.
[tex]h(x)=f(x-4)-3[/tex][tex]\text{Replace x=x-4 in f(x)=}\sqrt[]{x\text{ }}\text{ and substitute in the equation.}[/tex][tex]h(x)=\sqrt[]{x-4}-3[/tex]Final answer:
[tex]h(x)=\sqrt[]{x-4}-3[/tex]Solve 6 < x + 5 < 11
we have the following:
[tex]\begin{gathered} 6Please help me this is so confusing .which of the following, names a ray in the drawing?
From the given figure, let's select the rays given in the option.
A ray can be said to be a straight line which starts from a point and goes to infinity at the other end.
From the given figure, the rays are:
• NK
,• NJ
,• NL
,• NM
Therefore, from the list the, the ray is NK.
ANSWER:
NK
Grade 12 math can you please explain each step, what are you doing, why and the final result that contributes to the sketch.
ANSWER and EXPLANATION
We want to sketch the graph of the given function:
[tex]y=\frac{2x^2-7x+5}{2x-1}[/tex]First, we have to check for the asymptotes of the function.
To find the vertical asymptote, we have to equate the denominator to 0 and solve for x:
[tex]\begin{gathered} 2x-1=0 \\ 2x=1 \\ x=\frac{1}{2} \end{gathered}[/tex]That is the vertical asymptote.
To find the horizontal asymptote, we have to check the degrees of the numerator and denominator. Since the degree of the numerator is greater than the denominator's, there is no horizontal asymptote.
To find the slant asymptote, divide the numerator by the denominator and identify the quotient:
This implies that the slant asymptote is:
[tex]y=x-3[/tex]The asymptotes will provide the boundaries for the graph of the function as follows:
Now, we have to find some coordinate points that satisfy the function.
Let us solve for y for values of x = -2, -1, 0, 1, 2, 3:
[tex]\begin{gathered} \Rightarrow x=-2 \\ y=\frac{2(-2)^2-7(-2)+5}{2(-2)-1}=-5.4 \\ \Rightarrow x=-1 \\ y=\frac{2(-1)^2-7(-1)+5}{2(-1)-1}=-4.67 \\ \Rightarrow x=0 \\ y=\frac{2(0)^2-7(0)+5}{2(0)-1}=-5 \\ \Rightarrow x=1 \\ y=\frac{2(1)^2-7(1)+5}{2(1)-1}=0 \\ \Rightarrow x=2 \\ y=\frac{2(2)^2-7(2)+5}{2(2)-1}=-0.33 \\ \Rightarrow x=3 \\ y=\frac{2(3)^2-7(3)+5}{2(3)-1}=0.4 \end{gathered}[/tex]We also have to identify the x and y intercepts of the function.
For the x-intercept, solve for x when y = 0:
[tex]\begin{gathered} 0=\frac{2x^2-7x+5}{2x-1} \\ \Rightarrow2x^2-7x+5=0 \\ 2x^2-2x-5x+5=0 \\ 2x(x-1)-5(x-1)=0 \\ (2x-5)(x-1)=0 \\ x=\frac{5}{2};x=1 \end{gathered}[/tex]For the y-intercept, solve for y when x = 0:
[tex]\begin{gathered} y=\frac{2(0)^2-7(0)+5}{2(0)-1} \\ y=\frac{5}{-1} \\ y=-5 \end{gathered}[/tex]Let us draw the table of values:
Now, we can use the calculated points, the intercepts, and the asymptotes to sketch the graph of the function:
That is the sketch of the function.
1: 9 11. The cost for a group of people to go to the movies is given by the expression 9a + 5b, where a is the number of adults and b is the number of children. What are the variables of this expression? of of A. 9 and 5 B. a and b C. 9a and 5b D. + and x
the variables are
a and bwhere
a -----> is the number of adults
b-------> is the number of children.
answer is option B
Drew has a video game with five differentchallenges. He sets the timer to play his gamefor 10.75 minutes. He spends the same amountof time playing each challenge. How long doesDrew nlay the fifth challenge?
For each game, Drew spends 10.75 minutes, this means in total Drew spends
[tex]5\cdot10.75\text{ minutes}[/tex]this product gives
[tex]5\cdot10.75=53.75\text{ minutes}[/tex]then, in the fifth challenge Drew spends 53.75 minutes
in exponential growth functions the base of the exponent must be greater than 1.how would the function change if the base of the exponent were1? how would the function change if the base of the exponents were between 0 and 1
help meeeeeeeeee pleaseee !!!!!
The solution to the composite function is as follows;
(f + g)(x) = x² + 3x + 5(f - g)(x) = x² - 3x + 5(f. g)(x) = 3x³ + 15x(f / g)(x) = x² + 5 / 3xHow to solve composite function?The composition of a function is an operation where two functions say f and g generate a new function say h in such a way that h(x) = g(f(x)).
If we are given two functions, it is possible to create or generate a “new” function by composing one into the other.
Composite functions are when the output of one function is used as the input of another.
In other words, a composite function is generally a function that is written inside another function.
Therefore,
f(x) = x² + 5
g(x) = 3x
Hence, the composite function can be solved as follows:
(f + g)(x) = f(x) + g(x) = x² + 5 + 3x = x² + 3x + 5
(f - g)(x) = f(x) - g(x) = x² + 5 - 3x = x² - 3x + 5
(f. g)(x) = f(x) . g(x) = (x² + 5)(3x) = 3x³ + 15x
(f / g)(x) = f(x) / g(x) = x² + 5 / 3x
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The volume, V, of a cube with edge length s cm is given by the equation V=s3.Is the volume of a cube with edge length s=3 greater or less than the volume of a sphere with radius 3?If a sphere has the same volume as a cube with edge length 5, estimate the radius of the sphere?Compare the outputs of the two volume functions when the inputs are 2?
We have that the volume of sphere is
[tex]\begin{gathered} V_s=\frac{4}{3}\pi\cdot r^3 \\ \end{gathered}[/tex]and the volume of a cube is
[tex]V_c=s^3[/tex]so if s=r=3. The volume of the sphere is greater.
If they have the same volume, we get that
[tex]\begin{gathered} \frac{4}{3}\pi\cdot r^3=125\rightarrow \\ r^3=\frac{3}{4\cdot\pi}\cdot125\approx29.84\approx30 \\ r=\sqrt[3]{30}\approx3.10 \end{gathered}[/tex]when s=r=2 we have that
[tex]\begin{gathered} V_s=\frac{4}{3}\pi\cdot8=\frac{32}{3}\pi \\ V_c=8 \end{gathered}[/tex]so the volume of the sphere is greater
Find fractional notation of 87.5%
To find the fractional notation, we have to transform 87.5% into a fraction. To do that, we just have to divide the percentage by 100.
[tex]\frac{87.5}{100}[/tex]Then, we multiply each part by 10.
[tex]\frac{87.5\times10}{100\times10}=\frac{875}{1000}[/tex]At last, we simplify the fraction by 125 to get 7/8.
[tex]\begin{gathered} \frac{875}{125}=7 \\ \frac{1000}{125}=8 \end{gathered}[/tex]Hence, the given percent, in fractional notation, is 7/8.15 = a/3 - 2
what is a?
Answer: a is 51
Step-by-step explanation:
Hope this help.
Answer:
a==51
Step-by-step explanation:
15=a/3-2
a/3-2+2=15+2
a/3=17
a=17*3
a=51
Converting between scientific notation and standard form in a real-world situation
Answer:
[tex]\begin{gathered} a)9.54\times10^6\text{square miles} \\ b)0.0061\sec onds_{} \end{gathered}[/tex]Explanations:
a) The scientific notation is generally expressed as;
[tex]A\times10^n[/tex]A is any real numbers between 1 and 10
n is an integer
Given that the total surface area of North America is 9,540,000 square miles. This is expressed in scientific form as;
[tex]9,540,000=9.54\times10^6mi^2[/tex]From the scientific notation, A = 9.54 and n = 6
b) Given the scientific notation as shown:
[tex]6.1\times10^{-3}\text{seconds}[/tex]Writing in standard form means writing in the normal way we write numbers/decimals. Hence;
[tex]6.1\times10^{-3}=0.0061\text{seconds}[/tex]Cylinder A has radius r, height h, and a volume of 10 pi cubic units. Cylinder B hastwice the radius and twice the height.hATBWhat is the volume of cylinder B?I2r2h
Volume of a cylinder:
[tex]V=h*r^2*\pi[/tex]For cylinder A:
[tex]10\pi cm^3=h*r^2*\pi[/tex]For cylinder B:
[tex]V_B=2h*(2r)^2*\pi[/tex]Simplify the equation for volumen of cylinder B:
[tex]\begin{gathered} V_B=2h*4r^2*\pi \\ V_B=8*(h*r^2*\pi) \end{gathered}[/tex]in the equation for the volume of cylinder A you have the value of h*r^2*π:
[tex]\begin{gathered} V_B=8*(10\pi cm^3) \\ V_B=80\pi cm^3 \end{gathered}[/tex]Then, the volume of cylinder B is 80π cubic centimeters.What is the measure of the angle at the bottom of home plate?
We will ave the following:
*First: We will determine the sum of all internal angles of the polygon:
[tex](n-2)\cdot180\Rightarrow(5-2)\cdot180=3\cdot180[/tex][tex]=540[/tex]*Second: Now, that we know that the sum of all internal angles will be 540°, the following is true:
[tex]90+90+135+135+\alpha=540[/tex]Now, we solve for alpha [The angle]:
[tex]\Rightarrow\alpha=540-135-135-90-90\Rightarrow\alpha=90[/tex]So, the measure of the angle at the bottom is 90°.
A projectile is fired vertically upwards and can be modeled by the function h(t)= -16t to the second power+600t +225 during what time interval will the project I’ll be more than 4000 feet above the ground round your answer to the nearest hundredth
Given:
[tex]h(t)=-16t^2+600t+225[/tex]To find the time interval when the height is about more than 4000 feet:
Let us substitute,
[tex]\begin{gathered} h(t)\ge4000 \\ -16t^2+600t+225\ge4000 \\ -16t^2+600t+225-4000\ge0 \\ -16t^2+600t-3775\ge0 \end{gathered}[/tex]Using the quadratic formula,
Here, a= -16, b=600, and c= -3775
[tex]\begin{gathered} t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ =\frac{-600\pm\sqrt[]{600^2-4(-16)(-3775)}}{2(-16)} \\ =\frac{-600\pm\sqrt[]{360000^{}-241600}}{-32} \\ =\frac{-600\pm\sqrt[]{118400}}{-32} \\ =\frac{-600\pm40\sqrt[]{74}}{-32} \\ =\frac{-75\pm5\sqrt[]{74}}{-4} \\ t=\frac{-75+5\sqrt[]{74}}{-4},x=\frac{-75-5\sqrt[]{74}}{-4} \\ t=7.99709,t=29.5029 \end{gathered}[/tex]So, the interval is,
[tex]8.00\le\: t\le\: 29.50[/tex]2. Consider drawing a card at random from a standard deck of cards,Part A: Determine the probability that the card is a spade, given that it is black,Part B: Determine the probability that the card is red, given that it is a heart,Part C: Determine the probability that the card is an ace, given that it is black.Part D: Determine the probability that the card is a queen given that it is a face card,
Consider drawing a card at random from a standard deck of cards,
Part A: Determine the probability that the card is a spade, given that it is black,
Part B: Determine the probability that the card is red, given that it is a heart,
Part C: Determine the probability that the card is an ace, given that it is black.
Part D: Determine the probability that the card is a queen given that it is a face card,
we have 52 cards
A standard 52-card deck comprises 13 ranks in each of the four French suits: clubs (♣), diamonds (♦), hearts (♥) and spades (♠)
so
Part A: Determine the probability that the card is a spade, given that it is black,
If the card is black, that means the possible outcomes are 26 cards
so
P=13/26
P=0.5Part B: Determine the probability that the card is red, given that it is a heart,
if the card is a heart, that means, the possible outcomes are 13
so
P=13/13
P=1because all the cards that are heart are red
Part C: Determine the probability that the card is an ace, given that it is black.
if the card is black the possible outcomes are 26
therefore
P=2/26
P=1/13Part D: Determine the probability that the card is a queen given that it is a face card
Eduardo's school is selling tickets to a play. On the first day of ticket sales the school sold 4 adult tickets and 9 child tickets for a total of $108. The school took in $114 on the second day by selling 10 adult tickets and 3 child tickets. What is the price each of one adult ticket and one child ticket?
The price of one adult ticket is $9 and the price of child ticket is $8
First day of ticket sales the school sold 4 adult tickets and 9 child tickets for a total of $108
Consider the price of adult ticket as x and child ticket as y
Then the equation will be
4x+9y = 108
Similarly the school took in $114 on the second day by selling 10 adult tickets and 3 child tickets
10x+3y = 114
Here we have to use the elimination method
Multiply the first equation by 10 and second equation by 4
40x+90y = 1080
40x+12y = 456
Subtract the equation 2 from equation 1
90y-12y = 1080-456
78y = 624
y = 624/78
y = $8
Substitute the value of y in any equation
10x+3y =114
10x+3×8 =114
10x +24 =114
10x = 90
x = 90/10
x = $9
Hence, the price of one adult ticket is $9 and the price of child ticket is $8
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Solve fort 30 on t =(Type (Type an integer or a simplified fraction)
Multiply both sides by t:
[tex]\frac{12t}{10}=30[/tex]Multiply both sides by 10:
[tex]12t=300[/tex]Divide both sides by 12:
[tex]\begin{gathered} t=\frac{300}{12} \\ t=25 \end{gathered}[/tex]Please help me I don’t know how to do this
We have a point (4,-9) it moves to (9,-14)
(4+x = 9, -9+y= -14)
x = 9-4
x = 5
y = -14 +9
y = -5
We are moving to the right 5 and down 5
We want to move the point (-9,-8) exactly the same way
(-9+5, -8-5)
(-4, -13)
(-4, -13)
Instructions: Find the value of the trigonometric ratio. Makesure to simplify the fraction if needed.
sin C = 3/5
Explanation:Given:
CB = 32
AC = 40
AB = 24
To find:
sin C
To determine sinC, we will apply the sine ratio:
[tex]\begin{gathered} sin\text{ C = }\frac{opposite}{hypotenuse} \\ \\ oppoite\text{ =side opposite the angle = AB = 24} \\ hyp\text{ = 40} \end{gathered}[/tex][tex]\begin{gathered} sin\text{ C}=\text{ }\frac{24}{40} \\ \\ sin\text{ C}=\text{ }\frac{3}{5} \end{gathered}[/tex]Dylan’s boat can carry 40 people across a river. Last month, 2504 people road on Dylan’s boat. What is the least number of trips that Dylan could have made across that river.
The required least number of trips that Dylan would have made across the river is 62.
Given that,
Dylan’s boat can carry 40 people across a river. Last month, 2504 people rode on Dylan’s boat. What is the least number of trips that Dylan could have made across that river is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
Total people road = 2504
Maximum people can road at single trip = 40
Least number of trip = 2504 / 40
Least number of trip = 62
Thus, the required least number of trips that Dylan would have made across the river is 62.
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