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2 years ago

If L = 3 inches, W = 2 inches, and H = 5 inches, what is the volume of the rectangular prism?

Mathematics

2 answers:

Gennadij [26K]2 years ago

8 0

30 will be your correct answer.

gulaghasi [49]2 years ago

3 0

Answer:

3 x 2 x 5 = 30

Step-by-step explanation:
To calculate a rectanglars prism all you have to do is multiply the length, width and height together.

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Are A = {j, k, m} and B = {k, m, n} disjoint sets?

Fiesta28 [93]

Answer:

No.

Step-by-step explanation:

Both sets contain the elements k and m.

4 0

3 years ago

Find the ordered pairs for the x- and y-intercepts of the equation 5x − 6y = 30 and select the appropriate option below.

Amiraneli [1.4K]

5x - 6y = 30
6y = 5x - 30
Y = 5/6x - 5
y intercept = -5
Therefore (0, -5)

0 = 5/6x - 5
5/6x = 5
x = 6
x intercept = 6
therefore (6,0)

answer : first one
x intercept =

7 0

3 years ago

Read 2 more answers

Help help help! Im stuck please help!

ioda

Answer:

1) 8/15

Step-by-step explanation:

When dividing by a number, multiply by its reciprocal.

2/5 ÷ 3/4

2/5 × 4/3

8/15

8 0

3 years ago

Leakage from underground gasoline tanks at service stations can damage the environment. It is estimated that 25% of these tanks

Gnesinka [82]

Answer:

a) 3.75

b) 23.61% probability that fewer than 3 tanks will be found to be leaking

c) 0% the probability that at least 600 of these tanks are leaking

Step-by-step explanation:

For each tank there are only two possible outcomes. EIther they leak, or they do not. The probability of a tank leaking is independent of other tanks. So we use the binomial probability distribution to solve this question.

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.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

To solve question c), i am going to approximate the binomial distribution to the normal.

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

It is estimated that 25% of these tanks leak.

This means that $p = 0.25$

15 tanks chosen at random

This means that $n = 15$

a.What is the expected number of leaking tanks in such samples of 15?

$E(X) = np = 15*0.25 = 3.75$

b.What is the probability that fewer than 3 tanks will be found to be leaking?

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)$

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

$P(X = 0) = C_{15,0}.(0.25)^{0}.(0.75)^{15} = 0.0134$

$P(X = 1) = C_{15,1}.(0.25)^{1}.(0.75)^{14} = 0.0668$

$P(X = 2) = C_{15,2}.(0.25)^{2}.(0.75)^{13} = 0.1559$

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0134 + 0.0668 + 0.1559 = 0.2361$

23.61% probability that fewer than 3 tanks will be found to be leaking

c.Now you do a larger study, examining a random sample of 2000 tanks nationally. What is the probability that at least 600 of these tanks are leaking?

Now we have n = 2000. So

$\mu = E(X) = np = 2000*0.25 = 500$