Answers
Answer:i believe its 60 with x=30
Step-by-step explanation:
Step-by-step explanation:
M(<BAC)=95° , M(<ABC)=2x , M(<ACD)=145°
let M(<ACB)=y
Then M(<ACB)+M(<ACD)=180° , Because they are in a straight line and straight line can measure 180°.
so , y+145°=180°
y=180°_145°
y=35° , M(<ACB)=35°
The sum.of the interior angle of any triangle is 180° . so now we have 95° , 38° and 2x so the value of x be
95°+35°+2x =180°
130°+2x=180°
2x=180°_130°
2x=50° , divide both sides by 2 to find the value of x
x=25° , 2*25°=50° , M(<ABC)=50°
M(<BAC)=95°, M(<ABC)=50° , M(<ACB) =35°
95°+50°+35°=180°
Related Questions
Which of the following is a way you can get money out of your checking account?
Using your credit card to get cashback at a supermarket
Withdrawing cash using an ATM
Depositing a check at a bank branch
Having your paycheck deposited electronically
Answers
Answer:
All of the following are ways you can get money out of your checking account:
Using your credit card to get cashback at a supermarket: Many credit cards offer a cashback feature that allows you to get cash back when you make a purchase at a store or supermarket. This cashback amount is typically added to your credit card balance, but you can request that it be transferred to your checking account instead.
Withdrawing cash using an ATM: Automated teller machines (ATMs) allow you to withdraw cash from your checking account by inserting your debit card and entering your PIN. You can usually withdraw cash from your checking account at any ATM that is affiliated with your bank or credit union.
Depositing a check at a bank branch: If you have a check that you want to deposit into your checking account, you can do so by visiting a bank branch and presenting the check to a teller. The teller will verify the check and deposit the funds into your checking account.
Having your paycheck deposited electronically: Many employers now offer direct deposit as a way to pay their employees. With direct deposit, your paycheck is deposited electronically into your checking account, eliminating the need to visit a bank or ATM to withdraw cash.
Which of the following functions represent the graph g(x) above?
Answers
Answer:
The first one, G(x)=| x+4 |
Step-by-step explanation:
the accompanying data file shows the average monthly debt payments (debt in $) for residents of 26 metropolitan areas.
Answers
Let X and Y be IID Unif(0, 1). the distance between X and Y.Expected value: 0 and Standard deviation: [tex]$\sqrt{\frac{1}{3}}$[/tex]
Expected value:
E(X-Y)
= E(X) - E(Y) = 0 - 0 = 0
Standard deviation:
Var(X-Y) = Var(X) + Var(Y) = 1 + 1 = 2
SD(X-Y) = [tex]$\sqrt{2}$ \\[/tex] [tex]= $\sqrt{\frac{1}{3}}$[/tex]
The expected value of X-Y is the difference of the expected values of X and Y, which are both 0 since they are both IID Unif(0, 1). The variance of X-Y is the sum of the variances of X and Y, which are both 1. Since the standard deviation is the square root of the variance, the standard deviation of X-Y is the square root of 2
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Newton's Law of Gravitation states that two bodies with masses m1 and m2 attract each other with a force F, where r is the distance between the bodies and G is the gravitational constant. F = G(m_1m_2)/r^2 Use Newton's Law of Gravitation to compute the work W required to propel a 1100 kg satellite out of the earth's gravitational field. You may assume that the earth's mass is 5.98✕1024 kg and is concentrated at its center. Take the radius of the earth to be 6.37✕106 m and G = 6.67✕10-11 Nm2/kg2. (Round your answer to three significant digits.)
Answers
The two bodies are being drawn together by a force of 10812 N, according to Newton's Law of Gravitation.
Every particle in the universe is drawn to every other particle with a force that is directly proportional to the product of their masses and inversely proportional to their separation from one another, according to Newton's Law of Universal Gravitation.
Symbolically, Newton came to the following conclusion on the strength of the gravitational force:
F = G(m₁ × m₂) / r²
F is the gravitational force between two bodies, m1 and m2 are the bodies' masses, r is the distance between their centres, and G is the gravitational constant of the universe.
According to the query,
satellite's mass is m1 = 1100 kg.
mass of earth = 5.98 ×10²⁴ kg
Radius of the earth = 6.37 × 10⁶ m
G = 6.67 × 10⁻¹¹ Nm² / kg²
Force = G(m₁ × m₂) / r²
Substituting the values,
F = 6.67 × 10⁻¹¹( 1100 × 5.98 ×10²⁴) /( 6.37 × 10⁶)²
=> F = 6.67 × 1100 × 5.98 × 10¹³ / 40.58 × 10¹²
=> F = 43,875.26 × 10 / 40.58
=> F = 10812 N
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What information do you need to know to write the equation of a line?
the slope of the line in quadrant 2
the location of two ordered pairs that lie along the line
the slope of the line and the location of the origin
the location of 1 ordered pair the lies along the line
Answers
The location of two ordered pairs that lie along the line. Therefore, option B is the correct answer.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
To write the equation of a line we need two at least two ordered pairs that lie along the line
By using two ordered pairs, we can find slope of a line
The formula to find the slope of a line is (y2-y1)/(x2-x1)
Using the slope and one ordered pair we can find y-intercept
By substituting slope(m) and y-intercept(c) in y=mx+c, we get equation of line.
Therefore, option B is the correct answer.
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Select all the expressions that are equal to
2/3 to power of 2
4/9 , 4/3, 1/9 x 4 , 1/3 x 1/3, 2/3 x 2/3
Answers
Answer to the problem:
4/9, 1/3 x 1/3, 2/3 x 2/3
Reconsider the paint-drying situation of Example 8.2, in which drying time for a test specimen is normally distributed with σ = 9. The hypotheses H0: μ = 75 versus Ha: μ < 75 are to be tested using a random sample of n = 25 observations.
Answers
A random sample of n = 25 observations will be used to test the hypotheses H0: Î14 = 75 and Ha: Î14 75.the test statistic is lower than -1.96, we can reject the null hypothesis and conclude that the mean drying time is less than 75.
H0: μ = 75
Ha: μ < 75
Test Statistic: z = (x - μ) / (σ / √n)
critical Value: z crit = -1.96
Conclusion: Reject H0 if the test statistic is less than -1.96.
We can test the hypotheses H0: μ = 75 versus Ha: μ < 75 by using the test statistic z = (x - μ) / (σ / √n). The critical value for this test is z crit = -1.96. The decision rule for this test is to reject H0 if the test statistic is less than -1.96. This means that if the test statistic is lower than -1.96, we can reject the null hypothesis and conclude that the mean drying time is less than 75.
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which of the following statements are true regarding the probability density function f(x) and the cumulative density function f(x) of a continuous random variable? select all that apply. multiple answers: multiple answers are accepted for this question select one or more answers and submit. for keyboard navigation...show more a f(x)
Answers
The likelihood that a random cumulative variable will fall within a specific range of values rather than taking on a single value is specified by the Probability Density Function.
The probability density function (PDF), also known as the density of a continuous random variable, is a function whose value at any specific sample (or point) in the data point (the range of potential values for the random variable) can be understood as having given a relative likelihood that the value of something similar to the random variable would be closer to that sample.
There is no absolute probability that a random variable will take on any specific value because there are an unlimited number of alternative values to begin with. However, the PDF value at two samples can be used to estimate how much more likely it is for the random variable to have that particular value in any given draw.
The Cantor distribution, which although having no discrete component, does not assign positive probabilities to any specific locations, and discrete random variable probability distributions do not all have a density function.
A distribution has a density function if and only if the cumulative distribution function F(x) is fully continuous. In this case, F is typically always differentiable, and its derivative can be used to symbolize the probability density.
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What is the range of the function y = x + 3 when the domain is {-2, 0, 4}?
Answers
Answer:
The answer is the range of the function y = x + 3 when the domain is {-2, 0, 4}, which is the set {1, 3, 7}.
Step-by-step explanation:
The range of the function y = x + 3 is the set of all possible values of y for a given value of x in the domain of the function. In this case, the domain of the function is the set {-2, 0, 4}, so the range of the function is the set of all possible values of y for x equal to -2, 0, and 4.
To find the range, we need to substitute each of these values of x into the equation y = x + 3 and solve for y. When x = -2, we have y = -2 + 3 = 1. When x = 0, we have y = 0 + 3 = 3. And when x = 4, we have y = 4 + 3 = 7. Therefore, the range of the function y = x + 3 when the domain is {-2, 0, 4} is the set {1, 3, 7}.
with a coupon, you can get a pair of shoes that normally costs $84 for only $72. what percentage was the discount? round to the nearest tenth of a percent if necessary. type the answer in the box below.
Answers
The discount on the pair of the shoes after applying the coupon is 14.2%
The normal cost of the pair of shoes is $84
The discounted price of those pair of shoes is $72
The discount in price is = 84 - 72 = 12
Discount percentage = discount / cost price x 100
Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. It is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".
= 12/84 x 100
= 1/7 x 100
= 14.2%
Therefore, the discount on the pair of the shoes after applying the coupon is 14.2%
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7.) Bart is required to pass out 80 flyers for an upcoming event. He passes out an average of 10 flyers per minute. The situation can be represented using the function f(x)=80-10x where x represents time in minutes.
a.) Create a graph of the situation
Answers
After finding the point from the given function, we draw the graph. The graph of the given function is given below:
In the given question, Bart is required to pass out 80 flyers for an upcoming event. He passes out an average of 10 flyers per minute.
The situation can be represented using the function f(x)=80-10x
where x represents time in minutes.
We have to create a graph of the situation.
To create the graph we firstly find the value of f(x) for x=0,1,2,3,..............
The given function is f(x) = 80-10x
Now put x = 0
So f(0) = 80-10(0)
f(0) = 80-0
f(0) = 80
Now put x = 1
So f(1) = 80-10(1)
f(1) = 80-10
f(1) = 70
Now put x = 2
So f(2) = 80-10(2)
f(2) = 80-20
f(2) = 60
Now put x = 3
So f(3) = 80-10(3)
f(3) = 80-30
f(3) = 50
Now put x = 4
So f(4) = 80-10(4)
f(4) = 80-40
f(4) = 40
Now the table is
x 0 1 2 3 4
f(x) 80 70 60 50 40
Firstly we denote the point in the graph then we connect the all point to form a graph.
The graph of the given function is given below:
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A bag contains 100 marbles which are red, green, and blue. suppose a student randomly selects a marble without looking, record's the color,and then places the marble back in the bag the student has recorded 7 red marbles, 2 green marbles and 11 blue marbles. predict how many green marbles are in the bag
Answers
Answer: 10 marbles
Step-by-step explanation:
First, arrange all the numbers of marbles that the student picked in a ratio
red:green:blue
7:2:11
When adding all the coloured marbles that the student picked together, you get 20 marbles or "parts" as you would usually say in ratio.
Then, it would be helpful to rewrite the ratios as fractions, with 20 as the denominator:
[tex]\frac{7}{20}:\frac{2}{20}:\frac{11}{20}[/tex]
However, the bag contains 100 marbles so we should have 100 as the denominator instead of 20. 20 is a fifth of 100, so in this case, we would multiply everything (the numerator and the denominator) by 5:
[tex]\frac{7*5}{20*5} :\frac{2*5}{20*5} :\frac{11*5}{20*5}[/tex]
[tex]\frac{35}{100}:\frac{10}{100}:\frac{55}{100}[/tex]
Therefore, you could predict you would get 35 red marbles, 10 green marbles, and 55 blue marbles.
la suma de dos números es 45. dividiendo el mayor por el menor se obtiene 2 como cociente y 6 como resto. encontrar los dos números
Answers
Answer:
13 and 32
Step-by-step explanation:
x + y = 45
x = 2y + 6
2y + 6 + y = 45
3y = 45 - 6
3y = 39
y = 39/ 3
y = 13
x = 2 · 13 + 6
x = 26 + 6
x = 32
PLEASE HELP WILL MARK BRAINLIEST
Answers
Answer: C. [tex]y=2(x+4z)[/tex]
Step-by-step explanation:
[tex]m=\frac{0-8z}{-4z-0}=2\\\\\therefore y=2x+8z=2(x+4z)[/tex]
Substitute 3 for x in new equation. Do you get a ture statement explain
Answers
Traffic flow is defined as the rale at which traffic flow at particular cars pass through an intersection , measured in cars intersection is modeled by the function F defined per minute. The Fl) = 82 4sin for 0 < [ < 30, where F) is measured in cars per minute and IS measured in minutes_ To the nearest whole number; how many cars pass through the intersection Is the traffic flow increasing Or decreasing at over the 30-minute period? 7 ? Give Whal is the reason for your answer: average value Of the traffic now Whal = over the time interval 10 < Is the < 15 average rale of change of Indicate units of measure. measure . the traffic flow over the time interval 10 < <15 Indieate units
Answers
The average rate of change of the traffic flow over the time interval 10 < t < 15 is 0.1085 cars per minute. Since this value is positive, the traffic flow is increasing over this time interval.
The traffic flow at the intersection is modeled by the function F(t) = 82 - 4sin(t) for 0 < t < 30, where F(t) is measured in cars per minute and t is measured in minutes.
To find the total number of cars that pass through the intersection over the 30-minute period, we can integrate the function over the time interval from 0 to 30 minutes. The integral of the function is given by:
∫F(t)dt = ∫(82 - 4sin(t))dt
= 82t - 4cos(t) + C
Evaluating this integral at t = 0 and t = 30, we get:
82(0) - 4cos(0) + C = 0
82(30) - 4cos(30) + C = 2184
Solving for C, we get C = -246.
Substituting this value back into the integral equation, we get:
∫F(t)dt = 82t - 4cos(t) - 246
Plugging in t = 30, we get:
∫F(t)dt = 82(30) - 4cos(30) - 246 = 2184 - 246 = 1939
Therefore, the total number of cars that pass through the intersection over the 30-minute period is 1939 cars.
To determine whether the traffic flow is increasing or decreasing over the time interval 10 < t < 15, we can find the average rate of change of the traffic flow over this time interval. The average rate of change is given by:
(F(t2) - F(t1))/(t2 - t1)
Plugging in t1 = 10 and t2 = 15, we get:
(F(15) - F(10))/(15 - 10)
= (82 - 4sin(15) - (82 - 4sin(10)))/(5)
= (-4sin(15) + 4sin(10))/5
= (-4(√(6)/4) + 4(1/2))/5
= (-√(6) + 2)/5
= (-1.4575 + 2)/5
= 0.5425/5
= 0.1085
The units of measure for the average rate of change are cars per minute.
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q1 signaling when education is productive i 6 points grading comment: a single worker incurs a cost of obtaining education of amount ee given by: c(e)=3⋅e 2 The worker's wage is based on how much education he obtains. If he receives education less than a threshold amount e, then he receives a wage that is proportional to his level of education: w(e)=5⋅e And if he receives education greater than or equal to the threshold eˉ, then his wage is proportional to the threshold: w(e)=12⋅ e ˉ So the utility that he receives when he chooses a level of education e is a piecewise function: u(e)={ 5⋅e−3⋅e 2 12⋅ e ˉ −3⋅e 2 e< eˉ e⩾ eˉ Answer the following. Round all numeric answers to at least three decimal places. Suppose that
eˉ=0.5
Answers
The worker's marginal cost of education when e=0.5 is 6.00. the derivative of the cost function with respect to the amount of education obtained.
The worker's marginal cost of education is the rate of change in the cost of obtaining education with respect to the amount of education obtained. In this case, the worker's cost of obtaining education is given by the equation c(e)=3e². At e=0.5, we can calculate the marginal cost of education by taking the derivative of the cost function with respect to the amount of education obtained. This gives us the equation c'(e)=6. Thus, the worker's marginal cost of education when e=0.5 is 6.00.
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Cash 25 selects 6 numbers between 1 and 25.where repetition isn’t allowed but order doesn’t matter?
Answers
350•23•22
177100
if an exponentiated logistic regression coefficient, i.e. exp(b), is greater than one, when its associated x-variable increases, predicted odds will decrease, holding other x-variables constant.
Answers
For the exponential logistic regression coefficient Exp(b) is greater than one it represents the associated x-variable increases and the corresponds to predicted odds will decrease and holding other variables constant is false statement.
As given in the question,
Exponential logistic regression coefficient Exp(b) or given odds ratio, is the predicted change value in odds for a unit value increase in the predictor.The Exp represents the exponential value of b. When Exp(b) is less than 1, and increases values of the x- variable correspond to the decreasing odds of the occurring event's .Here exp(b) is greater than 1 which represents all the all other coefficients should lies between 0 and 1 or less than one.Therefore, the exponential logistic regression coefficient Exp(b) is greater than one it represents the associated x-variable increases is a false statement.
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Q is the average of A,B and C whrite a formula for calculating Q and then to solve A
Answers
The formula for calculating Q which is the bis
(A + B + C) / 3
To solve for A, the formula is
A = 3Q - (B + C)
What is average?In mathematics, the middle value which is determined by dividing the sum of all the values by the total number of values is the average value in a set of numbers.
If we want to calculate the average for a set of data, we add up all the values and divide this sum by the total number of values.
For the given problem the sum of the data is
= A + B + C
they are 3 hence we divide by 3
average, Q = (A + B + C) / 3
To solve for A we make A the subject
Q = (A + B + C) / 3
3Q = (A + B + C)
A = 3Q - (B + C)
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make x the subject of 5x-y=x+z
Answers
Answer: 4x=y+z
Step-by-step explanation:
To make x the subject, move all other variables besides x to the other side
5x-y=x+z
5x-y+y=x+z
5x=y+x+z
Move all numbers containing x to the left
5x-x=y+x-x+z
4x=y+z
Find the value of x and y .
x°=__
y°=___
Answers
In triangle PQR , the value of x and y is equal to 90° and 85° respectively.
As given in the question,
In the given triangle PQR,
Measure of ∠R = 5°
From the diagram,
PQ ≅ QR
⇒ ∠P ≅ ∠R
⇒m ∠P = m ∠R
⇒m ∠P = 5°
In ΔPQR,
∠P + ∠Q + ∠R = 180°
⇒ 5° + ∠Q + 5° = 180°
⇒ ∠Q = 170°
From the diagram,
y° = (1/2) ( ∠Q)
= 170°/2
= 85°
∠P + y° + x° = 180°
⇒ 5° + 85° + x° = 180°
⇒ x° = 180° - 90°
⇒ x° = 90°
Therefore, in triangle PQR the measure of x° and y° is equal to 90° and 85° respectively.
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Round 10.29 to the nearest tenth
Answers
Answer:
10.3
Step-by-step explanation:
10.29 rounded to the nearest tenth is 10.3.
Tyler hires a Lift driver to give him a ride to Wild
Rivers. It costs $4 to download the Lift app and then
$1.50 for every mile they have to drive you. Tyler's
trip to Wild Rivers cost $23.50. Write an equation
and solve to find the number of miles (m) the Lift
driver had to drive Tyler.
Answers
Answer:
23.50=1.50x+4, m=13
Step-by-step explanation:
The $4 is a constant, no matter how many times the app is used, the $4 amount will stay. The $1.50 is dependant on how many times the action is preformed so it has to be put with M. Overall, the cost is 23.50 which is why the entire equation is equal to $23.50.
Subtract 4 from the 23.50, then divide that result with 1.50
sage measured her rectangular house is 15.24m long and 9.1m wide. using her calculator she multiply the length by the width
Answers
Therefore, the area of rectangular house is 138.684 [tex]m^{2}[/tex].
Specify the area.The size of a region on a planar or curved surface can be expressed mathematically using the idea of area. The term "surface area" refers to the area of an open surface or the perimeter of a three-dimensional object, whereas the term "plane area" refers to the area of a shape or planar lamina.
Here,
Given :
the length of the rectangular house =15.24 m
the width of the rectangular house = 9.1 m
thus, we find the area of rectangular house
Using formula,
=> Area= length * width
=> Area = 15.24 * 9.1
=> Area = 138.684 [tex]m^{2}[/tex]
Therefore, the area of rectangular house is 138.684 [tex]m^{2}[/tex].
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[tex]f(x)= 5\sqrt{x^2}[/tex]
Answers
The values of f(x) for x = 1, 2, 3, 4, 5, ,,,, are 5, 10, 15, 20, 25, 30, , , ,
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
f(x) = 5 √x²
√x² = x
f(x) = 5x
For x = 1, 2, 3, 4, 5, ,,,,,,
f(1) = 5
f(2) = 10
f(3) = 15
f(4) = 20
f(5) = 25
Thus,
The final expression is f(x) = 5x.
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What is the value of s?
10
units
Answers
The value of s is 17.
What is the Pythagorean theorem?
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Here, we have
Given
AB = 5, BD = 15
We have to find AD.
By applying the Pythagorean Theorem, we get
AB² + BD² = AD²
5² +15² = AD²
AD² = 289
AD = 17
Hence, the value of s is 17.
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let l denote the linear system a x b; x 0, where a has dimensions mn and b has dimensions m1. prove that either l is non-empty or (mutually exclusively) 9y 2 rm y a 0; y b < 0.
Answers
the set of vectors b over Rm so that Ax=b has (at least) a solution, where the rank is the dimension of a column space. False: The rank-nullity theorem states that the null space is 0 if m=n.
What are the three categories of theorems?Principle of Linear Pairs Two angles are supplementary if they form a pair along a straight line. theorem addition Two angles are congruent if they are the same angle's supplements. The principle of congruent complements Two angles are congruent if they are the same angle's complements.
The Seventh Mathematical Theorem: What Is It?Theorem 7: To enquire about: the connection here between angle opposite the larger of two sides and also the degree opposite the smaller of two sides. both the side across from the smaller of the two aspects and the side across from the greater of the two angles.
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a car travels at an average speed of 48 miles per hour how many miles does it travel in 4 hours and 30 minutes
Answers
Answer:
4 hours= 192
30 min=24
192+24=216
Step-by-step explanation:
for findin 4 hours time multipky 4 with 48 as yk it travels 48 miles per hour and for findin the 30 mins u have to divide 48/2 bcuz it travelled 48 in one hour and 30 mins is its half so yah and then add both the answers
Dwight Donovan, the president of Munoz Enterprises, is considering two investment opportunities. Because of limited resources, he will be able to invest in only one of them. Project A is to purchase a machine that will enable factory automation; the machine is expected to have a useful life of four years and no salvage value. Project B supports a training program that will improve the skills of employees operating the current equipment. Initial cash expenditures for Project A are $106,000 and for Project B are $47,000. The annual expected cash inflows are $40,947 for Project A and $16,131 for Project B. Both investments are expected to provide cash flow benefits for the next four years. Munoz Enterprises’ desired rate of return is 6 percent. (PV of $1 and PVA of $1) (Use appropriate factor(s) from the tables provided.) Required Compute the net present value of each project. Which project should be adopted based on the net present value approach? Compute the approximate internal rate of return of each project. Which one should be adopted based on the internal rate of return approach?
Answers
The net present value of a project is the sum of the present values of all the expected cash inflows and outflows for the project, discounted at the desired rate of return. The net present value is used to evaluate the profitability of a project by taking into account the time value of money, which is the idea that a dollar received today is worth more than a dollar received in the future.
To calculate the net present value of Project A, we need to find the present value of each expected cash inflow and outflow, and then sum them together. The initial cash expenditure for Project A is $106,000, and the annual expected cash inflows are $40,947. Using the present value of $1 table, we can find the present value of each cash inflow and outflow by multiplying the amount by the present value factor corresponding to the desired rate of return (6 percent) and the number of years until the cash flow occurs:
Initial expenditure: $106,000 * 0.943 = $99,858
Annual inflows: $40,947 * 0.943 * 0.943 * 0.943 * 0.943 = $136,046
The net present value of Project A is the sum of the present values of all the cash inflows and outflows, which is $136,046 - $99,858 = $36,188.
To calculate the net present value of Project B, we can use the same approach. The initial cash expenditure for Project B is $47,000, and the annual expected cash inflows are $16,131. Using the present value of $1 table, we can find the present value of each cash inflow and outflow by multiplying the amount by the present value factor corresponding to the desired rate of return (6 percent) and the number of years until the cash flow occurs:
Initial expenditure: $47,000 * 0.943 = $44,441
Annual inflows: $16,131 * 0.943 * 0.943 * 0.943 * 0.943 = $52,210
The net present value of Project B is the sum of the present values of all the cash inflows and outflows, which is $52,210 - $44,441 = $7,769.
Based on the net present value approach, the best project to invest in is the one with the highest net present value. In this case, Project A has a higher net present value than Project B, so it would be the better choice.
The internal rate of return of a project is the discount rate that makes the net present value of the project equal to 0. In other words, it is the rate of return that an investor would expect to earn from the project if all the expected cash flows were realized.
To calculate the internal rate of return of Project A, we can use the present value of an annuity of $1 table. The initial cash expenditure for Project A is $106,000, and the annual expected cash inflows are $40,947. We can use the present value of an annuity of $1 table to find the present value of the cash inflows by multiplying the annual cash inflow by the present value factor corresponding to the desired rate of return (6 percent) and the number of years until the cash flow occurs:
Annual inflows: $40,947 * 4.597 = $187,340
We can then use the present value annuity formula to find the internal rate of return of Project A, which is the rate that makes the net present value of the project equal to 0:
0 = $106,000 + $187,340 / (1 + r)^4
Solving for r, we find that the internal rate of return of Project A is approximately 10.35 percent.
To calculate the internal rate of return of Project B, we can use the same approach. The initial cash expenditure for Project B is $47,000, and the annual expected cash inflows are $16,131. We can use the present value of an annuity of $1 table to find the present value of the cash inflows by multiplying the annual cash inflow by the present value factor corresponding to the desired rate of return (6 percent) and the number of years until the cash flow occurs:
Annual inflows: $16,131 * 4.597 = $73,711
We can then use the present value annuity formula to find the internal rate of return of Project B, which is the rate that makes the net present value of the project equal to 0:
0 = $47,000 + $73,711 / (1 + r)^4
Solving for r, we find that the internal rate of return of Project B is approximately 10.09 percent.
Based on the internal rate of return approach, the best project to invest in is the one with the highest internal rate of return. In this case, Project A has a higher internal rate of return than Project B, so it would be the better choice.
Overall, both the net present value approach and the internal rate of return approach suggest that Project A is the better investment option for Munoz Enterprises. Project A has a higher net present value and a higher internal rate of return than Project B, indicating that it is likely to be more profitable and provide a higher rate of return on the investment.