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Evgesh-ka [11]
2 years ago
15

Suppose an initial investment of $100 will return $50/year for 3 years (assume the $50 is received each year at the end of the y

ear). Is this a profitable investment if the discount rate is 20%?
Mathematics
1 answer:
nydimaria [60]2 years ago
4 0

With a positive NPV, it shows that the investment is profitable.

It is a profitable investment with a positive NPV at a discount rate of 20%.

Data and Calculations

Initial investment = $100

Annual cash inflows = $50

Period of investment = 3 years

Discount rate = 20%

<h3>What is the present value?</h3>

Present value (PV) is the current value of a future sum of money or stream of cash flows given a specified rate of return.

Present Value (PV) annuity factor for 3 years at 20% = 2.106

Present value of annual cash inflows = $105.3 ($50 x 2.106)

Net Present Value (NPV) = $5.3 ($105.3 - $100)

Thus, with a positive NPV, it shows that the investment is profitable.

To learn more about the investment visit:

brainly.com/question/12957049

#SPJ1

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A semicircle has a diameter of 17.6 cm.
Ray Of Light [21]

Answer:

B. 45.23 cm

Step-by-step explanation:

perimeter of the figure

=\frac{1}{2}\pi d+d

=\frac{1}{2}\times 3.14\times 17.6 +17.6

=\frac{1}{2}\times 55.264 +17.6

=27.632 +17.6

=45.232

=45.23\: cm

7 0
3 years ago
The distribution of the number of occurrences of the letter t on the pages of a book is found to be a normal distribution with a
Leno4ka [110]
The distribution of the number of occurrences of the letter t on the pages of a book is found to be a normal distribution with a mean of 44 and a standard deviation of 18. If there are 500 pages in the book, which sentence most closely summarizes the data?

A. The letter t occurs less than 26 times on approximately 170 of these pages. 

B. The letter t occurs less than 26 times on approximately 15 of these pages. 

C. The letter t occurs more than 26 times on approximately 420 of these pages. 

D. The letter t occurs more than 26 times on approximately 80 of these pages.

.Answer: 
<span>mean = 44 </span>
<span>sd = 18 </span>
<span>that means that "26" is 1 s.d. down, or at the 16th %ile </span>


<span>so, there is a .16 chance that "t" will occur less than 26 times on any single page. </span>
<span>consequently, there is a .84 chance that it will occur more than 26 times on any single page. </span>

<span>Using that information, and knowing that 16% of 500 is 80, and 84% of 500 is 420, can you see where "C" is correct? </span>
4 0
3 years ago
Read 2 more answers
PLEASE PLEASE PLEASE HELP ME WITH ALGEBRA 1 PLEASE!?!?!?!?!!!?!?!?!?!?! I WILL GIVE LOTS OF POINTS AND BRAINLEST
Damm [24]

<span>1.1 What are the different ways you can solve a system of linear equations in two variables? 

</span><span>A linear equation can be written in many ways, so the way we can use to solve a system of linear equations depends on the form the system is written. There are several methods to do this, the more common are: Method of Equalization, Substitution Method, Elimination Method. 

<span>1.2. Method of Equalization

</span>a. Write the two equations in the style [variable = other terms] either variable x or y.<span>
</span>b. Equalize the two equations 
c. Solve for the other variable and then for the first variable.

</span>

<span> 1.3. Substitution Method

a. Write one of the equations (the one that looks the simplest equation) in the style [variable = other terms] either variable x or y.
b. Substitute that variable in the other equation and solve using the usual algebra methods.
c. Solve the other equation for the other variable.<span>

1.4. Elimination Method

Eliminate</span> means to remove, so this method works by removing variables until there is just one left. The process is:
<span>
</span>a. Multiply an equation by a constant "a" such that there is a term in one equation like [a*variable] and there is a term in the other equation like [-a*variable]
b. Add (or subtract) an equation on to another equation so the aim is to eliminate the term (a*variable)
c. Solving for one variable and the for the other.
</span>

2.1 Benefits of Method of Equalization<span>
</span>


It's useful for equations that are in the form [variable = other terms] (both equations). In this way, it is fast to solve the system of linear equation by using this method. The limitations come up as neither of the equations are written in that way, so it would be necessary to rewrite the two equations to achieve our goal


2.2. Benefits and limitations of Substitution Method


This method is useful for equations that at least one of them is in the form [variable = other terms]. So unlike the previous method, you only need one equation to be expressed in this way. Hence, it is fast to solve the system of linear equation by using this method. The limitations are the same that happens with the previous method, if neither of the equations is written in that way, we would need to rewrite one equation to achieve our goal.


2.3. Benefits and limitations of Elimination Method


It's useful for equations in which the term [a*variable] appears in one equation and the term [-a*variable] appears in the other one, so adding (or subtracting). 


3.1. What are the different types of solutions


When the number of equations is the same as the number of variables there is likely to be a solution. Not guaranteed, but likely.

One solution: It's also called a consistent system. It happens as each equation gives new information, also called Linear Independence.

An infinite number of solutions: It's also called a consistent system, but happens when the two equations are really the same, also called Linear Dependence.

No solutions: It happens when they are actually parallel lines. 


3.2. Graph of one solution system


See figure 1, so there must be two straight lines with different slopes.


3.3. Graph of infinite number of solutions system


See figure 2. So there must be two straight lines that are really the same.


3.4. Graph of no solution system


See figure 3. So there must be two straight lines that are parallel.


4. Explain how using systems of equations might help you find a better deal on renting a car?


Q. A rental car agency charges $30 per day plus 10 cents per mile to rent a certain car. Another agency charges $20 per day plus 15 cents per mile to rent the same car. If the car is rented for one day in how many miles will the charge from both agencies be equal?

A. Recall: 10 cents = 0.1$, 15 cents = 0.15$

If you rent a car from the first car agency your cost for the rental will be:

(1) 30D+0.1M

<span>If you rent a car from the second car agency the total amount of money to pay is:

(2) 20D+0.15M</span>

Given that the problem says you want to rent the car just for one day, then D = 1, therefore:

First agency: 30(1)+0.1M=&#10;\boxed{30+0.1M}

Second agency: 20(1)+0.15M=&#10;\boxed{20+0.15M}

<span>At some number of miles driven the two costs will be the same:

30+0.1M=20+0.15M

Solving for M:

10=0.05M
M=200mi

There is a representation of this problem in figure 4. Up until you drive 200 miles you would save money by going with the second company.</span>

<span>

5. Describe different situations in the real world that could be modeled and solved by a system of equations in two variables </span>

<span>
</span>

For example, if you want to choose between two phone plans. The plan with the first company costs a certain price per month with calls costing an additional charge in cents per minute. The second company offers another plan at a certain price per month with calls costing an additional charge in cents per minute. So depending on the minutes used you should one or another plan.


3 0
3 years ago
Find the horizontal asymptote of the graph
sleet_krkn [62]

y = -  \frac{1}{2}
5 0
3 years ago
Read 2 more answers
Is the function shown in the graph one-to-one?
Cloud [144]

Answer:

  yes

Step-by-step explanation:

The graph is of a function (one output for every input) that also passes the horizontal line test (one input for every output). Hence it is one-to-one.

For a <em>function</em>, the key for it being one-to-one is that it pass the horizontal line test.

3 0
3 years ago
Read 2 more answers
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