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2 years ago

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4x25x27 associate property

1 answer:

Pavel [41]2 years ago

7 0

(4x25)x27
(100)x27
2700

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For the following amount at the given interest rate compounded continuously, find (a) the future value after 9 years, (b) the

Stella [2.4K]

Answer:

(a) The future value after 9 years is $7142.49.

(b) The effective rate is $r_E=4.759 \:{\%}$ .

(c) The time to reach $13,000 is 21.88 years.

Step-by-step explanation:

The definition of Continuous Compounding is

If a deposit of $P$ dollars is invested at a rate of interest $r$ compounded continuously for $t$ years, the compound amount is

$A=Pe^{rt}$

(a) From the information given

$P=4700$

$r=4.65\%=\frac{4.65}{100} =0.0465$

$t=9 \:years$

Applying the above formula we get that

$A=4700e^{0.0465\cdot 9}\\A=7142.49$

The future value after 9 years is $7142.49.

(b) The effective rate is given by

$r_E=e^r-1$

Therefore,

$r_E=e^{0.0465}-1=0.04759\\r_E=4.759 \:{\%}$

(c) To find the time to reach $13,000, we must solve the equation

$13000=4700e^{0.0465\cdot t}$

$4700e^{0.0465t}=13000\\\\\frac{4700e^{0.0465t}}{4700}=\frac{13000}{4700}\\\\e^{0.0465t}=\frac{130}{47}\\\\\ln \left(e^{0.0465t}\right)=\ln \left(\frac{130}{47}\right)\\\\0.0465t\ln \left(e\right)=\ln \left(\frac{130}{47}\right)\\\\0.0465t=\ln \left(\frac{130}{47}\right)\\\\t=\frac{\ln \left(\frac{130}{47}\right)}{0.0465}\approx21.88$

3 0

3 years ago

Write the equation of the line passing through the points (-4,-1) and (2,8)

klio [65]

<h3><u>Explanation</u><u>:</u></h3>

Calculate the slope with two given coordinate points by using rise over run.

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Let these points

$\begin{cases}(x_1, y_1) = ( - 4, - 1) \\ (x_2, y_2) = ( 2, 8) \end{cases}$

$m = \frac{8 - ( - 1)}{2 - ( - 4)} \\ m = \frac{8 + 1}{2 + 4} \Longrightarrow \frac{9}{6} \Longrightarrow \frac{3}{2} \\ m = \frac{3}{2}$

Slope-Intercept

$y = mx + b \\ m = slope \\ b = y - intercept$

Substitute the value of m in the equation.

$y = \frac{3}{2} x + b$

Substitute any coordinate points that are given or part of the graph in the equation.

$(x_, y) = ( - 4, - 1)$

$- 1 = \frac{3}{2} ( - 4) + b$

Solve the equation for b-term.

$- 1 = \frac{3}{ \cancel{2}} ( \cancel{ - 4}) + b\\ - 1 = 3( - 2) + b \\ - 1 = - 6 + b \\ - 1 + 6 = b \\ 5 = b$

Rewrite the equation by substituting the value of b in the equation.

$y = \frac{3}{2} x + 5$

<h3><u>Answer</u></h3>

$\large \boxed{y = \frac{3}{2} x + 5}$

<em>If</em><em> </em><em>you</em><em> </em><em>have</em><em> </em><em>any</em><em> </em><em>questions</em><em> </em><em>related</em><em> </em><em>to</em><em> </em><em>the</em><em> </em><em>answer</em><em>,</em><em> </em><em>feel</em><em> </em><em>free</em><em> </em><em>to</em><em> </em><em>ask</em><em> </em><em>via</em><em> </em><em>comment</em><em>.</em>

7 0

3 years ago

A box stall is a square or rectangular enclosure that can house one or more animals. Derek wants to construct a square box stall

stepladder [879]

Your answer is 550000!!!

Hope this helped!!!XD

Also can I get brainiest?XD

4 0

3 years ago

Write the number of measures (sides/angles/diagonals) needed to construct the following :

gladu [14]

Square <em>:</em><em>4</em><em> </em><em>sides</em><em>,</em><em>each</em><em> </em><em>side</em><em> </em><em>9</em><em>0</em><em> </em><em>degrees</em><em> </em><em>.</em><em>.</em>

<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em>:each angle is 90 degrees

: 4 diagonals

Rectangle: 4 sides..4 angles..2 diagonals..
Rhombus : <u>4</u><u> </u><u>sides</u><u>.</u><u>.</u><u>2</u><u> </u><u>angles</u><u>.</u><u>.</u><u>.</u><u>2</u><u> </u><u>diagonals</u><u>.</u><u>.</u>
Parallelogram : 4 sides..4 angles..2 diagonals..
Quadrilateral: 4 sides...4 angles...4 diagonals..

<em>If</em><em> </em><em>this</em><em> answer</em><em> helps</em><em><u> you</u></em><em><u> plz</u></em><em><u> mark</u></em><em><u> as</u></em><em><u> brainlist</u></em><em><u>.</u></em><em><u>.</u></em>

3 0

2 years ago

Please help and explain why you got it right please

gtnhenbr [62]

Answer:

y+7 = -3 ( x-4)

Step-by-step explanation:

First find two points on the graph to find the slope

( 1,2) and ( 3,-4)

The slope is given by

m = ( y2-y1)/(x2-x1)

m = ( -4-2)/(3-1)

= -6/2

=-3

We can use the point slope form

y - y1 = m(x-x1) where m is the slope and x1,y1 is a point on the line

We have two choices with a slope of -3

We can either use and x coordinate of -2 or 4

for -2, the y coordinate is not shown

for 4 , the y coordinate is -7

Using ( 4, -7) and m = -3

y--7 = -3( x- 4)

y+7 = -3 ( x-4)

4 0

2 years ago

Read 2 more answers