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2 years ago

5

Four friend started a dog walking business in the first month they made $140 and split the money equally among themselves they e

ach decided to save 40% of their money and spend the rest on new clothes how much money did each friend spend on new clothes

1 answer:

kati45 [8]2 years ago

8 0

40 dollars they each spent 40 dollars from 70 dollars

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Find S18 for geometric series given a5=-6 and a2= -48

Ganezh [65]

an = a1r^(n-1)

a5 = a1 r^(5-1)

-6 =a1 r^4

a2 = a1 r^(2-1)

-48 = a1 r

divide

-6 =a1 r^4

---------------- yields 1/8 = r^3 take the cube root or each side

-48 = a1 r 1/2 = r

an = a1r^(n-1)

an = a1 (1/2)^ (n-1)

-48 = a1 (1/2) ^1

divide by 1/2

-96 = a1

an = -96 (1/2)^ (n-1)

the sum

Sn = a1[(r^n - 1/(r - 1)]

S18 = -96 [( (1/2) ^17 -1/ (1/2 -1)]

=-96 [ (1/2) ^ 17 -1 /-1/2]

= 192 * [-131071/131072]

approximately -192

3 0

3 years ago

Seventeen added to the product of six and a number equals 113

serg [7]

Answer:

16

Step-by-step explanation:

113-17= 96

96/6= 16

6 0

2 years ago

Read 2 more answers

In a G.P the difference between the 1st and 5th term is 150, and the difference between the

liubo4ka [24]

Answer:

Either $\displaystyle \frac{-1522}{\sqrt{41}}$ (approximately $-238$ ) or $\displaystyle \frac{1522}{\sqrt{41}}$ (approximately $238$ .)

Step-by-step explanation:

Let $a$ denote the first term of this geometric series, and let $r$ denote the common ratio of this geometric series.

The first five terms of this series would be:

$a$ ,
$a\cdot r$ ,
$a \cdot r^2$ ,
$a \cdot r^3$ ,
$a \cdot r^4$ .

First equation:

$a\, r^4 - a = 150$ .

Second equation:

$a\, r^3 - a\, r = 48$ .

Rewrite and simplify the first equation.

$\begin{aligned}& a\, r^4 - a \\ &= a\, \left(r^4 - 1\right)\\ &= a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right) \end{aligned}$ .

Therefore, the first equation becomes:

$a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right) = 150$ ..

Similarly, rewrite and simplify the second equation:

$\begin{aligned}&a\, r^3 - a\, r\\ &= a\, \left( r^3 - r\right) \\ &= a\, r\, \left(r^2 - 1\right) \end{aligned}$ .

Therefore, the second equation becomes:

$a\, r\, \left(r^2 - 1\right) = 48$ .

Take the quotient between these two equations:

$\begin{aligned}\frac{a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right)}{a\cdot r\, \left(r^2 - 1\right)} = \frac{150}{48}\end{aligned}$ .

Simplify and solve for $r$ :

$\displaystyle \frac{r^2+ 1}{r} = \frac{25}{8}$ .

$8\, r^2 - 25\, r + 8 = 0$ .

Either $\displaystyle r = \frac{25 - 3\, \sqrt{41}}{16}$ or $\displaystyle r = \frac{25 + 3\, \sqrt{41}}{16}$ .

Assume that $\displaystyle r = \frac{25 - 3\, \sqrt{41}}{16}$ . Substitute back to either of the two original equations to show that $\displaystyle a = -\frac{497\, \sqrt{41}}{41} - 75$ .

Calculate the sum of the first five terms:

$\begin{aligned} &a + a\cdot r + a\cdot r^2 + a\cdot r^3 + a \cdot r^4\\ &= -\frac{1522\sqrt{41}}{41} \approx -238\end{aligned}$ .

Similarly, assume that $\displaystyle r = \frac{25 + 3\, \sqrt{41}}{16}$ . Substitute back to either of the two original equations to show that $\displaystyle a = \frac{497\, \sqrt{41}}{41} - 75$ .

Calculate the sum of the first five terms:

$\begin{aligned} &a + a\cdot r + a\cdot r^2 + a\cdot r^3 + a \cdot r^4\\ &= \frac{1522\sqrt{41}}{41} \approx 238\end{aligned}$ .

4 0

2 years ago

At 1 P.M., the total snowfall is 5 centimeters. At 4 P.M., the total snowfall is 16 centimeters. What is the mean hourly snowfal

Yuri [45]

Answer:

Mr. Snowbully

Step-by-step explanation:

I think the mean hourly snowfall is named Mr. Snowbully

It's a funny name!

Well, the snow would grow at a rate of 4 cm every hour so...

4

5 0

2 years ago

The perimeter of a chalkboard is 16 feet. The area is 15 square feet. What are the dimensions of the board

Daniel [21]

Answer:

5 by 3

Explanation:

15 = 5 x 3

16 = 5 + 5 + 3 + 3

4 0

3 years ago