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3 years ago

Simplify. Your answer should contain only positive exponents.

Mathematics

1 answer:

Shkiper50 [21]3 years ago

5 0

<h3>Option A is your answer .</h3>

<u>Solution </u><u>:</u><u>-</u>

$\sf \implies 2^{-4} . \big(2^{-3}\big)^4\\\\\sf \implies\dfrac{1}{2^4}.\left(\dfrac{1}{2^{3}}\right)^4\\\\\sf\implies \dfrac{1}{2^4}.\left(\dfrac{1^4}{(2^3)^4}\right)\\\\\sf\implies\dfrac{1}{2^4}.\left(\dfrac{1}{2^{12}}\right)\\\\\sf\implies \dfrac{1}{2^{16}}$

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A website manager has noticed that during the evening hours, about 3.23.2 people per minute check out from their shopping cart

aleksandrvk [35]

Answer:

1. c. Poisson

2. 0.9592 = 95.92% probability that in any one minute at least one purchase is made.

3. 0.0017 = 0.17% probability that no one makes a purchase in the next 2 minutes.

Step-by-step explanation:

We have only the mean, which means that the Poisson distribution is used to solve this question, and thus the answer to question 1 is given by option c.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

Mean of 3.2 minutes:

This means that $\mu = 3.2n$ , in which n is the number of minutes.

2. What is the probability that in any one minute at least one purchase is made?

$n = 1$ , so $\mu = 3.2$ .

This probability is:

$P(X \geq 1) = 1 - P(X = 0)$

In which

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-3.2}*3.2^{0}}{(0)!} = 0.0408$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0408 = 0.9592$

0.9592 = 95.92% probability that in any one minute at least one purchase is made.

3. What is the probability that no one makes a purchase in the next 2 minutes?

2 minutes, so $n = 2, \mu = 3.2(2) = 6.4$

This probability is P(X = 0). So

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-6.4}*6.4^{0}}{(0)!} = 0.0017$

0.0017 = 0.17% probability that no one makes a purchase in the next 2 minutes.

7 0

3 years ago

The cost of packing a box of chocolates is given by x2, where x is the number of chocolates (a box can never have fewer than 3 c

Levart [38]

<span>For a box with x chocolates, the cost of packaging is C(x) = x^2 and the
weight is W(x) = x + 2. Thus the cost per unit weight is C(x) / W(x) = x^2 / (x + 2)</span>

7 0

3 years ago

Read 2 more answers

This is geometry. If possible please explain steps while solving.

White raven [17]

Don’t click the link. -

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3 years ago

Select all options that are equivalent to pi (π).

Natalija [7]

Answer:

first and last options only