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ch4aika [34]
3 years ago
13

La

Mathematics
1 answer:
Marysya12 [62]3 years ago
5 0

Answer:

Step-by-step explanation:

The formula you need for this is

A(t)=P(1+\frac{r}{n})^{nt where

A(t) is the amount after a certain number of years has gone by,

P is the initial deposit,

r is the interest rate in decimal form,

n is the number of compoundings done per year, and

t is the amount of time in years.

For us,

A(t) = 11900

P is 250

r is .048

n is 12 (there are 12 months in a year)

t is our unknown. Filling in:

11900=250(1+\frac{.048}{12})^{(12)(t) which simplifies a bit to

11900=250(1_.004)^{(12t) . Now we'll divide both sides by 250:

47.6=(1.004)^{12t and then take the natural log of both sides to bring that t down out front:

ln(47.6)=ln(1.004)^{12t and then

ln(47.6) = 12t ln(1.004). Now divide both sides by ln(1.004) to isolate the 12t:

967.6383216 = 12t and divide both sides by `12 to get

t = 80.6 months which is 6.7 years

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(a) The probability that a randomly selected U.S. adult uses social media is 0.35.

(b) The probability that a randomly selected U.S. adult is aged 18–29 is 0.22.

(c) The probability that a randomly selected U.S. adult is 18–29 and a user of social media is 0.198.

Step-by-step explanation:

Denote the events as follows:

<em>X</em> = an US adult who does not uses social media.

<em>Y</em> = an US adult between the ages 18 and 29.

<em>Z</em> = an US adult between the ages 30 and above.

The information provided is:

P (X) = 0.35

P (Z) = 0.78

P (Y ∪ X') = 0.672

(a)

Compute the probability that a randomly selected U.S. adult uses social media as follows:

P (US adult uses social media (<em>X'</em><em>)</em>) = 1 - P (US adult so not use social media)

                                                   =1-P(X)\\=1-0.35\\=0.65

Thus, the probability that a randomly selected U.S. adult uses social media is 0.35.

(b)

Compute the probability that a randomly selected U.S. adult is aged 18–29 as follows:

P (Adults between 18 - 29 (<em>Y</em>)) = 1 - P (Adults 30 or above)

                                            =1-P(Z)\\=1-0.78\\=0.22

Thus, the probability that a randomly selected U.S. adult is aged 18–29 is 0.22.

(c)

Compute the probability that a randomly selected U.S. adult is 18–29 and a user of social media as follows:

P (Y ∩ X') = P (Y) + P (X') - P (Y ∪ X')

                =0.22+0.65-0.672\\=0.198

Thus, the probability that a randomly selected U.S. adult is 18–29 and a user of social media is 0.198.

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3 years ago
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