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3 years ago

Troy is writing a book of short stories. It is his

Mathematics

1 answer:

joja [24]3 years ago

3 0

Answer:

91 short stories

Step-by-step explanation:

You just add 1 + 2 + 3 + 4 + 5 + 6... all the way to 13, and then at the end of 16 months, Troy still only wrote 91 stories since he only wrote them up until 13 months, and then stopped afterwards.

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A scientist is studying the growth and development of an epidemic virus with a growth rate of 9% per month that has infected 3,1

4vir4ik [10]

Answer:

About 6,785 people will be infected about nine months.

Step-by-step explanation:

We can write an exponential function to represent the situation. The standard exponential function is given by:

$\displaystyle f(x) = a(r)^x$

Where a is the initial value, r is the rate, and x, in this case, is the time that has passed in months.

3,124 people have already been infected. Thus, our initial value a = 3124.

And an additional 9% will be infected per month. Therefore, our rate r will be 1 + 9% or 1.09.

Hence, our function is:

$\displaystyle f(x) = 3124(1.09)^x$

Then after nine months, the total amount of infected people will be f(9):

$\displaystyle f(9) = 3124(1.09)^{(9)}$

Use a calculator:

$\displaystyle f(9) \approx 6785$

About 6,785 people will be infected about nine months.

6 0

3 years ago

A circular garden has a circumference of

hoa [83]

It will take him 3 hours

8 0

3 years ago

Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backu

JulsSmile [24]

Answer:

a) There is a 10.24% probability that both generators fail during a power outage.

b) There is an 89.76% probability of having a working generator in the event of a power outage, which is not high enough for the hospital.

Step-by-step explanation:

For each emergency backup generator, there are only two possible outcomes. Either they work correctly, or they fail. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

Assume that emergency backup generators fail 32% of the times when they are needed. So they work correctly 100-32 = 68% of the time. So $p = 0.68$

There are two generators, so $n = 2$

a. Find the probability that both generators fail during a power outage

This is $P(X = 0)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{2,0}.(0.68)^{0}.(0.32)^{2} = 0.1024$

There is a 10.24% probability that both generators fail during a power outage.

b. Find the probability of having a working generator in the event of a power outage. Is that probability high enough for the hospital? Assume the hospital needs both generators to fail less than 1% of the time when needed.

Either there are no working generators, or there is at least one working generator. The sum of the probabilities of these events is decimal 1. So

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