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3 years ago

6

6 cubes are glued together to form the solid shown in the diagram if the edges of each cube measure 1 and 1/2 in into length wha

t's the surface area of the solid

1 answer:

Andreas93 [3]3 years ago

8 0

Answer 58 1/2:

Step-by-step explanation:

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The health of employees is monitored by periodically weighing them in. A sample of 54 employees has a mean weight of 183.9 lb. A

jolli1 [7]

I’m sure The correct answer is c

3 0

3 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 <em>perpetuity</em> is an <em>amount of money needed to invest today</em> to have a perpetuity, or an annuity paid for life, considering an interest rate of <em>r</em>.

PMT is a finance term for <em>payment</em> and <em>r </em>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 <em>n</em> represents the number of periods for the investment.

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

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

Solving this equation for <em>PV</em> (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 <em>limit</em> for the previous equation when <em>n</em> tends to <em>infinity</em>, 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 <em>n</em> tends to <em>infinity</em>, 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 <em>r</em>, 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).

6 0

3 years ago

F(-4)f(x) = x^2 -3x + 9

olganol [36]

Here you go. Hope this helps! :)

4 0

3 years ago

Alex swims at an average speed of 45 m/min. How far does he<br> swim in 1 min 24 sec?<br> m

denpristay [2]

Answer:

63 m

Step-by-step explanation:

We know the rate in 45 m / min

We need to change the time to min

1 min 24 sec

We know that 1 min = 60 sec so 24 seconds is 24/60 ths of a minute

1 min 24/60 min

1 2/5 min

Changing to decimal form

1.4 minutes

Now we multiply by the rate to get the distance

d = r *t

d = 45 m/ min * 1.4 min

d= 63 m

3 0

4 years ago

Read 2 more answers

Suppose you want to have $400,000 for retirement in 35years. Your account earns 4% interest.

Sedaia [141]

$\begin{equation*} \$437.76 \end{equation*}$

1) This is a question for Annuity usage. Note that we'll need the following formula below:

$\begin{gathered} P=\frac{A(\frac{r}{n})}{\lbrack(1+\frac{r}{n})^{nt}-1\rbrack} \\ P=\frac{400000(\frac{0.04}{12})}{\lbrack(1+\frac{0.04}{12})^{12\cdot35}-1\rbrack} \\ P=\frac{400000\cdot\frac{0.04}{12}}{\left(1+\frac{0.04}{12}\right)^{35\cdot\:12}-1} \\ P=\frac{400000\cdot\frac{0.04}{12}}{1.0033^{420}-1} \\ P=437.76563...\approx\$437.76 \end{gathered}$

Note that P is the value you'll need to deposit each month so that in 35 years you'll have $400,000 for your retirement.

6 0

1 year ago