42,600 - 25,800 = 16800. That is the increase in 15 years.

You then calculate the increase as a percentage of the original population; 25,800.

16,800 / 25,800 * 100 = 65.11%

8 0

2 years ago

Determine determine whether the following geometric series converges or diverges. if the series converges find its sum.

Lilit [14]

For starters,

$\dfrac{3^k}{4^{k+2}}=\dfrac{3^k}{4^24^k}=\dfrac1{16}\left(\dfrac34\right)^k$

Consider the $n$ th partial sum, denoted by $S_n$ :

$S_n=\dfrac1{16}\left(\dfrac34\right)+\dfrac1{16}\left(\dfrac34\right)^2+\dfrac1{16}\left(\dfrac34\right)^3+\cdots+\dfrac1{16}\left(\dfrac34\right)^n$

Multiply both sides by $\frac34$ :

$\dfrac34S_n=\dfrac1{16}\left(\dfrac34\right)^2+\dfrac1{16}\left(\dfrac34\right)^3+\dfrac1{16}\left(\dfrac34\right)^4+\cdots+\dfrac1{16}\left(\dfrac34\right)^{n+1}$

Subtract $S_n$ from this:

$\dfrac34S_n-S_n=\dfrac1{16}\left(\dfrac34\right)^{n+1}-\dfrac1{16}\left(\dfrac34\right)$

Solve for $S_n$ :

$-\dfrac14S_n=\dfrac3{64}\left(\left(\dfrac34\right)^n-1\right)$

$S_n=\dfrac3{16}\left(1-\left(\dfrac34\right)^n\right)$

Now as $n\to\infty$ , the exponential term will converge to 0, since $r^n\to0$ if $0$ . This leaves us with

$\displaystyle\lim_{n\to\infty}S_n=\lim_{n\to\infty}\sum_{k=1}^n\frac{3^k}{4^{k+2}}=\sum_{k=1}^\infty\frac{3^k}{4^{k+2}}=\frac3{16}$

8 0

3 years ago

Read 2 more answers

A box contains four 75 W lightbulbs, three 60 W lightbulbs, and three burned-out lightbulbs. Two bulbs are selected at random fr

Law Incorporation [45]

Answer:

a. 0.689

b. 0.8

c. 0.427

Step-by-step explanation:

The given scenario indicates hyper-geometric experiment because because successive trials are dependent and probability of success changes on each trial.

The probability mass function for hyper-geometric distribution is

P(X=x)=kCx(N-k)C(n-x)/NCn

where N=4+3+3=10

n=2

k=4

P(X>0)=1-P(X=0)

The probability mass function for hyper-geometric distribution is

P(X=x)=kCx(N-k)C(n-x)/NCn

P(X=0)=4C0(6C2)/10C2=15/45=0.311

P(X>0)=1-P(X=0)=1-0.311=0.689

P(X>0)=0.689

The mean of hyper-geometric distribution is

μx=nk/N

μx=2*4/10=8/10=0.8

The variance of hyper-geometric distribution is

σx²=nk(N-k).(N-n)/N²(N-1)

σx²=2*4(10-4).(10-2)/10²*9

σx²=8*6*8/900=384/900=0.427

6 0

2 years ago

The original price of a sweater is $36. The sale price is 85% of the original price. What is the sale price of the sweater

wlad13 [49]

36 85

X 100

3600 = 85x

3600 divided by 85 =42.3529...

6 0

3 years ago