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3 years ago

Simplify the expression. Write the answer using scientific notation. (4 × 108)2 16 × 1016 1.6 × 1016 8 × 1017 1.6 × 1017

Mathematics

1 answer:

sammy [17]3 years ago

6 0

Answer:

$\large\boxed{\bigg(4\times10^8\bigg)^2=1.6\times10^{17}}$

Step-by-step explanation:

$\text{The sicientific notation:}\ a\times10^k,\ \text{where}\ 1\leq a10\\\\=1.6\times10\times10^{16}\qquad\text{use}\ a^n\times a^m=a^{n+m}\\\\=1.6\times10^{17}$

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Answer:

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(b) The probability that a salesperson helps 3 customers until she finds the first person to make a purchase is 0.058.

Step-by-step explanation:

Let the random variable X be defined as the number of customers the salesperson assists before a customer makes a purchase.

The probability that a customer makes a purchase is, p = 0.52.

The random variable X follows a Geometric distribution since it describes the distribution of the number of trials before the first success.

The probability mass function of X is:

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(a)

Compute the expected number of should a salesperson expect until she finds a customer that makes a purchase as follows:

$E(X)=\frac{1-p}{p}$

$=\frac{1-0.52}{0.52}\\=0.9231$

This, the expected number of should a salesperson expect until she finds a customer that makes a purchase is 0.9231.

(b)

Compute the probability that a salesperson helps 3 customers until she finds the first person to make a purchase as follows:

$P(X=3)=(1-0.52)^{3}\times0.52\\=0.110592\times 0.52\\=0.05750784\\\approx 0.058$

Thus, the probability that a salesperson helps 3 customers until she finds the first person to make a purchase is 0.058.

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