What is the profitability index of a project that has an initial cash outflow of $600, an inflow of $250 for the next 4 years and a cost of capital of 10 percent?
The profitability index of a project that has an initial cash outflow of $600, an inflow of $250 for the next 4 years, and a cost of capital of 10 percent is 1.036.
Calculations and ParametersProfitability index= Present cash flow/Initial overlay
If we represent this with their given values:
The estimated annuity factor is 2.486851991
250 * 2.486851991/600
= 1.036.
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A few years ago, Paul got this email from his friend -
Hey Paul,
So I am thrilled to say we are all good to pay you. I apologize for how drawn out it has been! So l need two things, your bank transfer info and your math help.
Below are all the relevant terms of the contract. I did the math, and from the 5000 investment I come to a total of 6155.27 owed. Can you check this math, and let me know? Once I have your
account/routing/bank name info I will send it immediately!
Sorry again, I want to let you know how much the loan meant, and how it helped us do what we needed to do, and I hope how long it has taken to pay it back hasn't changed how you feel about
me, or lending, or anything like that!
Glad to be able to settle this up and miss you!
Dylan
You need to verify that Paul's friend Dylan is correct, that he owed him exactly $6155.27.
TERMS:
October 6th, 2009-November 9th, 2012
From and including: Tuesday, October 6, 2009
To and including: Friday, November 9, 2012
It is 1131 days from the start date to the end date, end date included. Or 3 years, 1
month, 4 days including the end date
730 days are under 6% compounded daily
401 days are overdue and operate under 8% compounded daily
Initial investment was $5000.00
Principal Sum shall bear interest at a rate per annum of [6]%, compounded daily.
Create a model of this scenario, then label your model.
Show step by step how you can find the final amount.
Show any separate calculations (side work) you used to support your final answer.
Since the first 730 days were under 6% compounded daily and the last 401 days were under 8% compounded daily, the final future value of the loan in the sum of $6,155.27 agrees with Dylan's calculations of what he owed Paul.
How is the final future value determined?The final future value combines two separate calculations using an online finance calculator.
The first computation determines the future value based on a present value of $5,000 at 6% for 730 days.
The final computation determines the future value based on a present value of $5,637.43 at 8% for 401 days.
$5,000 for 730 days at 6% Compounded Daily:
N (# of periods) = 730 days
I/Y (Interest per year) = 6%
PV (Present Value) $5,000
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $5,637.43
Total Interest = $637.43
$5,637.43 for 401 days at 8% Compounded Daily:
N (# of periods) = 401 days
I/Y (Interest per year) = 8%
PV (Present Value) = $5,637.43
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $6,155.27
Total Interest = $517.84
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-5(2x - 3) = 15 what is this
Answer:
x = 0
Divide both sides by the numeric factor on the left side, then solve.
Answer:
x=0
Step-by-step explanation:
1. Solve
-5(2x-3)=15
-10x+15=15
-10x+15-15=15-15
-10x=0
-10x/-10=0/-10
x=0
2. Check
-5(2x0-3)=15
-5(0-3)=15
-5x-3=15
15=15
3. Answer
x=0
What is meant in statistics by "scores having a central tendency"?
In statistics, the "central tendency" refers to a single value which represents middle or center of a set of data. The 3 common measures of central tendency are named as mean, median, and mode.
When scores have a central tendency, it means that most of the scores in a set of data are clustered around a particular value.
For Example, if we have a data set of test scores, and most of the scores are around 70, then 70 would be the central tendency of the data set.
The central tendency is an important concept in statistics because it provides a way to summarize a large set of data with a single value.
It can help you understand the overall pattern of the data and make comparisons between different data sets.
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What is f(−2) when f(x)=2x−3?
Answer:
-7
Step-by-step explanation:
To find f(-2), plug in -2 as x
F(-2)=2(-2)-3
-4-3
-7
Help me with this Question Please.
Answer:
\(3 \times \frac{1}{3 } + \frac{1}{2} \times - 12( \frac{1}{3} ) = \frac{1}{3} \)
Solve for w
6/12= w/10
Simplify your answer as much as possible
Answer:
the answer is in the picture
write the following algebraically using x as unknown
"i think of a number , take away 1 and multiply the result by 3
Answer: 3(x-1)
Step-by-step explanation:
3 (x-1)
Q.57 help me please please pleaseeee
The value of the expression are as follows
30-218How to solve an expression?An algebraic expression consists of unknown variables, numbers and arithmetic operators. It does not contain any equality or inequality symbols.
Let's solve the expression by substituting the actual values of the variables.
a.
5x when x = 6
5x = 5(6) = 30
b.
3y when y = -7
3y = 3(-7) = -21
c.
10z when z = 0.8
10z = 10(0.8) = 8
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f the current population size is x individuals, what fraction of the resources are they using collectively?
The fraction of resources used collectively by X individuals can be represented as X/R, where R represents the total resources available. The fraction of resources not being used is represented as (R-X)/R. The per-capita growth rate can be represented as dX/dt = kX, where k is the proportionality constant. The differential equation for the population's size is dX/dt = kX.
A detailed explanation:
a) If the current population size is X individuals, then the fraction of resources they are using collectively can be calculated as X/R, where R represents the total resources available. This calculation gives us the proportion of resources used by X individuals relative to the total resources available.
b) To calculate the fraction of resources not being used, we subtract the fraction of resources used by X individuals from 1. So, the fraction of resources not being used is (R-X)/R.
c) The per-capita rate of change of X can be represented as dX/dt = kX, where k is the proportionality constant. This equation states that the rate of change of X (dX/dt) is proportional to X and the constant of proportionality is k.
d) To convert the equation into a differential equation for the population's size, we simply make X' stand alone on the left-hand side of the equation. So, the differential equation for the population's size becomes dX/dt = kX.
e) This differential equation states that the rate of change of X (dX/dt) is proportional to X and the constant of proportionality is k. This equation can be used to model the growth of a population over time and to understand the relationship between the population size and the rate of change of the population.
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Complete questin:
If the current population size is X individuals, what fraction of the resources are they using collectively? c) In the same situation, what fraction of the resources are not being used? d) The per-capita rate of change of X can be written as 7%. The key assumption mentioned above says that this quantity is pro- portional to the expression you wrote down in part (c). Call the proportionality constant 1', and write an equation for the per-capita growth rate. e) Convert this equation into a differential equation (change equa- tion) for the population's size. (Just make X' stand alone on the left-hand side of the equation.)
Raju’s father’s age is 5 years more than three times Raju’s age. Find Raju’s age,
if his father is 44 years old. ( 13 years)
please help
Answer:
Step-by-step explanation:
In order to find the answer, let's work backwards to find the original. We have to do the opposite to get to the Raju's age. We will start with his fathers age. (44) Then we will subtract five from it so that it will be divisible by three.
44 - 5 = 39
Then we just have to divide by 3.
44/3 = 13
His age is 13 years old.
if you decide to have four officers, a president, a vice president, a secretary and a treasurer, how many possible choices for officers are there?
giving you a total of 4 x 3 x 2 x 1 = 24 possible combinations.
If you decide to have four officers, a president, a vice president, a secretary, and a treasurer, there are 24 possible choices for officers. This is because you can choose any of the four positions for the president, then any of the remaining three positions for the vice president, any of the remaining two positions for the secretary, and the last position for the treasurer, giving you a total of 4 x 3 x 2 x 1 = 24 possible combinations.
A permutation is an act of arranging objects or numbers in order.
Combinations are the way of selecting objects or numbers from a group of objects or collections, in such a way that the order of the objects does not matter.
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Which of the following equations has a slope of -2 and passes through the point (3,-4)?
Answer:
B
Step-by-step explanation:
y=-2x+2
y=mx+b
m is slope so.here m is -2
y=-2+10.passes through the point (3,-4)
because -4=-2*3+2
-4=-6+2
-4=-4
Modern commercial airliners are fargely made of aluminum, a tight and strong metal. But the fact that aluminum is cheap enough that airplanes can be made out of it is a bit of historical luck. Before the discovery of the Hall-Heroult process in 1886, aluminum was as rare and expensive as gold: What would happen if airplanes had to be made of steel? The fuselage of the Boeing 777 , which can carry 305 passengers, is approximately a hollow aluminum eylinder without ends, 64.0 m long, 6.2 m wide, and 2.5 mm thick (see sketch at right). Suppose this fuselape was made of steel (densty 7.87 g/cm ^3
) instead of aluminum (density 2.70 g/cm ), and lets tay the average passenger has a mass of 79 kg. We'll also assume the engines can't lift any greater mass than they already do. Calculate the number of passengers that the Boeing 777 could carry if its fuselage was made of steel.
If the fuselage of the Boeing 777 were made of steel instead of aluminum, the number of passengers it could carry would decrease.
Given that the fuselage of the Boeing 777 is a hollow aluminum cylinder, we can calculate its volume using the dimensions provided: length = 64.0 m, width = 6.2 m, and thickness = 2.5 mm. Using the formula for the volume of a cylinder, V = πr^2h, where r is the radius and h is the height, we can determine the volume of the aluminum fuselage. Since the cylinder has no ends, the height is the same as the length of the fuselage. The radius can be calculated by dividing the width by 2. By substituting these values into the formula, we can find the volume of the aluminum fuselage. Once we have the volume, we can multiply it by the density of aluminum to find the mass of the aluminum fuselage. Dividing the mass by the average passenger mass of 79 kg will give us the approximate number of passengers the Boeing 777 could carry if its fuselage were made of steel. However, we need the specific maximum total mass or engine's lifting capacity to provide an exact answer.
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Caitlyn was drawing in Art class. She had 20 hearts and 15 flowers.
What is the ratio of flowers to hearts?
Answer:
15:20
Step-by-step explanation: Well we know that we have 20 hearts and 15 flowers. In the question, it mentions flowers first so we put the flowers first in the ratio. flowers:hearts or 15:20
15 : 20 hope it helped:)
Express cos G as a fraction in simplest terms.
Answer: cos G =
E
F
Submit Answer
www
attempt 1 out of 2
cos G is equal to 4/5 since cos G can only be expressed mathematically in terms of a fraction.
What is a triangle?In geometry, a closed triangle is a two-dimensional figure with three straight sides and three angles.
The magnitude of the angles and the breadth of the sides can be used to classify triangles.
The three sides of a triangle meet at three points called vertices.
Two triangle sides meet at an angle, and the angle that confronts one side of the triangle is referred to as the opposing angle.
The sum of the three angles in a triangle can never be greater than 180 degrees.
To determine cos G, we can apply the cosine rule:
(E2 + F2 - G2) / cos G (2EF)
Using the provided values as input results in:
cosG = (20²+25²-15²)/(2*20*25)
(400 + 625 - 225) / 1000 = 800 / 1000 \s= 4 / 5
Since we must use mathematics to describe cos G as a fraction in the most basic terms, cos G equals 4/5.
Therefore, cos G is equal to 4/5 since cos G can only be expressed mathematically in terms of a fraction.
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Complete question:
Express cos G as a fraction in simplest terms.
Factor the expression completely.
-48-56x
Answer:
Factor- −8(7x+6)
Simplified- −56x−48
Step-by-step explanation:
With the metal detector we find 70 Roman coins underground,30 are Etruscan,15 are Greek. What is the probability ,that I draw a Greek coin?
Answer:
30*100/70= 42.85% chances that you will draw a Etruscan coin and same way 42.85-100= 57%
Answer:
3/23
Step-by-step explanation:
Probability (Greek) :
Number of Greek coins / Total coins15 / 70 + 30 + 1515/1153/23Please help me with this question :)
Answer:
0.9968
Step-by-step explanation:
0.32% of women have red/green color blindness
that means probability of women having red/green color blindness is
0.32 / 100 = 0.0032
so probability of not having color blindness is 1 - 0.0032 = 0.9968
Find the area of triangle ABC Remember, the distance between two points is \(d=\sqrt(x_{2} -x_{1} )+(y_{2} -y_{1} )^{2}\) Round the answer to the nearest tenth.
A.
3.8 square units
B.
9.5 square units
C.
108.7 square units
D.
109.9 square units
Answer:
B. 9.5 square units
Step-by-step explanation:
right on edge 2022
.- Alicia tiene una finca de 1 km2 de superficie. Dedica 28 hm2 a cultivar trigo, 3.900 dam2 a plantar olivos y el resto lo ha plantado de girasoles.¿ Cuántos metros cuadrados ocupan los girasoles?
Answer:
330 000 m²
Step-by-step explanation:
1. Area of farm
\(A = \text{1 km}^{2} \times\left (\dfrac{\text{1000 m}}{\text{1 km}} \right )^{2}= \text{1 000 000 m}^{2}\)
2. Area for wheat
\(A = \text{28 hm}^{2} \times \left (\dfrac{\text{100 m}}{\text{1 hm}}\right)^{2} = \text{280 000 m}^{2}\)
3.Area for olive trees
\(A = {\text{3900 dam}^{2} \times \left (\dfrac{\text{10 m}}{\text{1 dam}}\right )^{2}}= \text{390 000 m}^{2}\)
4. Area for sunflowers
Total area = 1 000 000 m²
- Area for wheat = 280 000 m²
- Area for olive trees = 390 000
670 000
Area for sunflowers = 330 000 m²
Sunflowers occupy 330 000 m².
Given vectors a=(3, 2) and b=(-5, 6), find – 3a+2b.Write your answer in component form.-3a + 2b =
Vector a = (3, 2), then;
\(-3a=-3(3,2)\text{ = (-9,-6)}\)Also, vector b = (-5, 6), then;
\(2b=2(-5,6)=(-10,12)\)Then, -3a + 2b = (-9, -6) + (-10, 12)
\(\begin{gathered} -3a+2b=(-9+(-10),-6+12)_{} \\ -3a+2b=(-19,6) \end{gathered}\)The answer is (-19,6)
If a pharmacist combined 50-ml portions of thre syrups having specific graveties of 1.10, 1.25, and 1.32, what would be the specific gravity of the combined product?
The specific gravity of the combined product is 1.22
Specific gravity is the ratio of the density of a substance to the density of some substance (such as pure water) taken as a standard when both densities are obtained by weighing in air.
Given,
The total quantity of portion= 50 ml
Specific gravities of the three syrups = 1.10,1.25 and 1.32
Then,
The specific gravity of the combined product= \(\frac{1.10+1.25+1.32}{3}\)
= 1.22
Hence, the specific gravity of the combined product is 1.22.
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when graphing two variables, if the line slopes upward as you move from left to right then the variables exhibit a positive relationship. true or false
Yes, when graphing two variables and observing an upward slope as you move from left to right, it indicates a positive relationship between the variables.
Do upward-sloping lines indicate a positive relationship between variables?As one variable increases, the other variable also tends to increase. This positive correlation can be visually represented by a line that slopes upward in a graph. It implies that there is a direct and proportional relationship between the variables being studied.
But downward-sloping line indicate a negative relationship, where as one variable increases, the other variable tends to decrease. The slope of the line provides insights into the magnitude and direction of the relationship between the variables.
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Perform the indicated operations. Write the answer in standard form, a+bi.
-5-7i / 13+4i
Answer:
\(thank \: you\)
calculate the perimeter of a square with vertices on a circle of diameter 4 cm
Answer:
I dont like sqaures.
Step-by-step explanation: Their pointy.
Which number sentence is true?
Answer:
B
Step-by-step explanation:
Edge 2021.
considering the attached box-and-whisker plot, what percent of data lies within the inter-quartile range (iqr)?
In the inter-quartile graph , the data is contained in about 75% of the total (IQR).
A sort of graph used to show numerical data visually is the box-and-whisker plot. In this graph, the inter-quartile range (IQR) of the data is shown as a rectangular box, and the median is shown as a line extending from the box. The minimum and maximum values of the data are indicated by the whiskers extending from the box. It is clear from the box-and-whisker plot's information that roughly 75% of the data falls inside the inter-quartile range. The first quartile (Q1) is subtracted from the third quartile to determine the IQR (Q3). The median of the lower half of the data is the lower quartile (Q1), and the median of the higher half is the upper quartile (Q3). The dispersion of the middle half of the data is thus indicated by the IQR. When evaluating data, having this knowledge is crucial since it makes it easier to see any outliers or numbers outside the IQR.
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The complete question is
considering the attached box-and-whisker plot, what percent of data lies within the inter-quartile range (iqr) and find the data?
Which number can be used as a common denominator for the fractions 1/4 and 5/6? Check all that apply.
[] 2
[] 6
[] 12
[] 16
[] 24
Two sides of a triangle are 4m and 5m in length and the angle between them is angle. write the formula for the area of the triangle as a function of angle
The rate at which the area of the triangle is increasing when the angle between the sides of fixed lengths is π/3 is 0.3 m²/s.
What is the rate of change of an area?If the lengths a and b for two sides of the triangle, as well as the included angle θ, are known, the area of a triangle can be calculated using the sine formula.
\(\text { Area }=\frac{1}{2} a b \sin \theta\)
Now, according to the question;
The two sides of the triangle are given;
Let a = 4m and b = 5m.
Let θ = π/3. be the angle between the two sides;
Then,
Differentiate the area with respect to time (as rate of change of area)
\(\begin{aligned}\frac{\mathrm{d} A}{\mathrm{~d} t}=\frac{\mathrm{d}}{\mathrm{d} t} \frac{1}{2} a b \sin \theta &=\frac{1}{2} * 4 * 5 * \frac{\mathrm{d}(\sin \theta)}{\mathrm{d} \theta} \cdot \frac{\mathrm{d} \theta}{\mathrm{d} t} \\&=10 *(\cos \theta) * 0.06 \frac{\mathrm{m}^{2}}{\mathrm{~s}}=0.6 \cos (\pi / 3) \frac{\mathrm{m}^{2}}{\mathrm{~s}} \\&=0.6 * 0.5 \frac{\mathrm{m}^{2}}{\mathrm{~s}}=0.3 \frac{\mathrm{m}^{2}}{\mathrm{~s}}\end{aligned}\)
Therefore, the area of the triangle as a function of angle is 0.3 m²/s.
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The complete question is-
Two sides of a triangle are 4m and 5 m in length and the angle between them is increasing at a rate of 0.06 rad/sec. Find the rate at which the area of the triangle is increasing when the angle between the sides of fixed lengths is π/3.