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4 years ago

Which statement is true?

Mathematics

1 answer:

natka813 [3]4 years ago

7 0

Every square is a rectangle because it is a quadrilateral with all four angles right angles.

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What's 22 + 4? ghdjdhsbsjs

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Answer:LOL 26

Step-by-step explanation: 22=4 IS LIKE EASY BUT IF YOU FORGOT THEN THATS FINE

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4 years ago

Time value of money calculations can be solved using a mathematical equation, a financial calculator, or a spreadsheet. Which of

MA_775_DIABLO [31]

To answer this question, we can assume some different possibilities for the answer, since it is incomplete (or with not clear options):

a. $\\ \frac{PMT}{r}$

b. $\\ PMT*\frac{(1+r)^{n}-1}{r}*(1 + r)$

c. $\\ PMT*\frac{(1+r)^{n} - 1}{r}$

Answer:

a. $\\ PV_{perpetuity}=\frac{PMT}{r}$

Step-by-step explanation:

The present value of a perpetuity is an amount of money needed to invest today to have a perpetuity, or an annuity paid for life, considering an interest rate of r.

PMT is a finance term for payment and r is the interest rate (roughly, an important quantity that defines how much it can be obtained for an investment).

In general, the present value can be mathematically defined as:

$\\ PV(r) = \frac{PMT_{0}}{(1+r)^{0}} + \frac{PMT_{1}}{(1+r)^{1}} + \frac{PMT_{2}}{(1+r)^{2}}+\dotsc+\frac{PMT_{n}}{(1+r)^{n}}$

Where n represents the number of periods for the investment.

On the other hand, an annuity, given a present value PV, is defined by:

$\\ PMT= A = PV*(1+r)^{n}*(\frac{r}{(1+r)^{n}-1})$

Solving this equation for PV (present value) to define the present value of an annuity, we have:

$\\ PV = \frac{(1+r)^{n}-1}{(r*(1+r)^{n})}*PMT$

But the question is asking for an annuity paid for life (theoretically, for infinite periods of time); then, if we calculate the limit for the previous equation when n tends to infinity, we find that:

$\\ lim_{n\to\infty} \frac{(1+r)^{n}-1}{(r*(1+r)^{n})}*PMT$

$\\ (lim_{n\to\infty} \frac{(1+r)^{n}}{r*(1+r)^{n}} - lim_{n\to\infty} \frac{1}{r*(1+r)^{n}})*PMT$

$\\ (lim_{n\to\infty} \frac{(1+r)^{n}}{(1+r)^{n}}*\frac{1}{r} - lim_{n\to\infty} \frac{1}{r*(1+r)^{n}})*PMT$

$\\ (lim_{n\to\infty} 1*\frac{1}{r} - lim_{n\to\infty} \frac{1}{r*(1+r)^{n}})*PMT$

The second term of the previous expression tends to 0 (zero) when n tends to infinity, then:

$\\ (lim_{n\to\infty} 1*\frac{1}{r})*PMT$

$\\ (1*\frac{1}{r})*PMT$

$\\ \frac{PMT}{r}$ or

$\\ PV_{perpetuity}=\frac{PMT}{r}$

This expression represents that, with an interest of r, if we make an investment of PMT today, then we will have an annuity of $\\ \frac{PMT}{r}$ for life, because in each period PMT would be the same again due to the interest rate (r).

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3 years ago

The following data give the weights (in pounds) lost by 15 members of a health club at the end of 2 months after joining the clu

frutty [35]

First arrange the data in an order
3, 3, 3, 7, 7, 10, 10, 12, 12, 13, 14, 17, 17, 18, 21

a.) Q1 = (N + 1)/4th item = (15 + 1)/4 = 4th item = 7
Q2 = 2(16)/4 = 16/2 = 8th item = 12
Q3 = 3(16)/4 = 3(4) = 12th item = 17
IQR = (Q3 - Q1)/2 = (17 - 7)/2 = 10/2 = 5

b.) 82nd percentile = 82(16)/100 = 13th item = 17

c.) 12 is the 8th item which is in the middle of the data set, so the percentile rank is 50%

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3 years ago

1. Which expression is equivalent to 4(x + 1) – 7(x + 3)?

Nadusha1986 [10]

Answer:

Ez -3x+25

Step-by-step explanation:

4x+4-7x+21=

-3x+25

Brainliest plzzzz

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3 years ago

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The average national utility price is $270.48. Over a 6-month period, what is the average utility price in Orlando? How does thi

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Answer:

Step-by-step explanation:

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3 years ago