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3 years ago

What is the volume of the following triangular prism?

Mathematics

2 answers:

BlackZzzverrR [31]3 years ago

7 0

Answer: 3000cm3

To find the area you need to find the area of the triangle and multiply that by the height of the prism.

The area of the triangle is

.5*12*10 = 60

And the height is .5m = 50cm

So the area will be

60*50 = 3000

nataly862011 [7]3 years ago

6 0

Hello!

<h2>Answer:</h2>

$\boxed{ \bf The~volume~of~the~triangular~prism~is~3,000~cm^3}$

_____________________________________________________

<h2>Explanation:</h2>

We'll need the formula for the volume of a triangular prism to solve this. The formula is: b × h × l ÷ 2

This simply means that you have to multiply the base by the height and length, and divide all of that by 2.

Base = 10 cm

Height = 12 cm

Length = 50 cm

(I converted the 0.5 m to cm. It's 50 cm)

Substitute these values into the formula and solve:

v = 10 × 12 × 50 ÷ 2

v = 6,000 ÷ 2

v = 3,000 cm³

Have a fabulous day! :)

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Suppose that you take a sample of 250 adults. If the population proportion of adults who watch news videos is 0.58, what is the

aliina [53]

Answer:

0.36% probability that fewer than half in your sample will watch news videos

Step-by-step explanation:

To solve this question, i am going to use the binomial approximation to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

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

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 $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 250, p = 0.58$

$\mu = E(X) = 250*0.58 = 145$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{250*0.58*0.42} = 7.80$

If the population proportion of adults who watch news videos is 0.58, what is the probability that fewer than half in your sample will watch news videos

Half: 0.5*250 = 125

Less than half is 124 or less

So this is the pvalue of Z when X = 124

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

$Z = \frac{124 - 145}{7.8}$