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Mumz [18]
2 years ago
12

The amounts below show the change (measured in feet) in water level over four months. What is the average monthly change in wate

r level?
3/4, -9/4, -11/4, 5/4
Mathematics
1 answer:
Harlamova29_29 [7]2 years ago
5 0

Answer:

The average change in water level is: -3/4

Step-by-step explanation:

The average is calculated by adding up all the values and then dividing the sum by total number of values.

Given values are:

3/4, -9/4, -11/4, 5/4

The sum of values will be:

=\frac{3}{4}+(-\frac{9}{4})+(-\frac{11}{4})+\frac{5}{4}\\=\frac{3}{4}-\frac{9}{4}-\frac{11}{4}+\frac{5}{4}\\=\frac{3-9-11+5}{4}\\=\frac{-12}{4}\\=-3

Total number of values is 4

So,

Average = \frac{Sum}{Values}\\= \frac{-3}{4}

Hence,

The average change in water level is: -3/4

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Suppose that the probability that any particle emitted by a radioactive material will penetrate a certain shield is 0.01. If 10
AnnyKZ [126]

Answer:

a)P=0.42

b) n\geq 297

Step-by-step explanation:

We have a binomial distribution, since the result of each experiment admits only two categories (success and failure) and the value of both possibilities is constant in all experiments. The probability of getting k successes in n trials is given by:

P=\begin{pmatrix}n\\ k\end{pmatrix} p^k(1-p)^{n-k}=\frac{n!}{k!(n!-k!)}p^k(1-p)^{n-k}

a) we have k=2, n=10 and p=0.01:

P=\frac{10!}{2!(10!-2!)}0.01^2(1-0.01)^{10-2}\\P=\frac{10!}{2!*8!}0.01^2(0.99)^{8}\\P=45*0.01^2(0.99)^8=0.42

b) We have, 1-(1-p)^n=P, Here P is the probability that at least one particle will penetrate the shield, this probabity has to be equal or greater than 0.95. Therefore, this will be equal to subtract from the total probability, the probability that the particles do not penetrate raised to the total number of particles.

1-0.99^n\geq 0.95\\0.99^n\leq 1-0.95\\0.99^n\leq 0.05\\n\geq 297

4 0
2 years ago
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2 years ago
Does a rectangle have four congruent sides?
ololo11 [35]

Answer:

NO.

Step-by-step explanation:

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A rectangle has 2 pairs of parallel sides. One pair is longer than the other pair. Therefore, to be congruent, all sides have to be equal, which is a square, not a rectangle. So the answer is NO.

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3 years ago
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Simplify both sides if needed. The left-hand side needs simplification.

4(x - 6) \leq -2x + 6
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All is left to do is add and subtract to get the x variable all alone.

4x - 24  \leq -2x + 6
6x - 24  \leq  6    <-- Add 2x to both sides
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x           \leq 5    <-- Divide both sides by 6

In order to be in the solution set, x has to be less than or equal to 5.

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