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1 year ago

The volume of the triangular prism is 12.5 m³. The length is 2.5 m and the base is 2 m. What is the width?

Mathematics

1 answer:

Fantom [35]1 year ago

6 0

Answer:

(4) 5 m

Step-by-step explanation:

You want the length of side x of a right triangular prism with base edge lengths of 2.5 m and 2 m, and a volume of 12.5 m³.

<h3>Volume</h3>

The volume of the prism is given by the formula ...

V = Bh

where B is the area of the base:

B = 1/2bh . . . . where b and h are the leg dimensions of the right triangle

Using these formulas together, we have ...

V = 1/2(2.5 m)(2 m)x

12.5 m³ = 2.5x m²

Dividing by 2.5 m², we find x to be ...

(12.5 m³)/(2.5 m²) = x = 5 m

The dimension labeled x has length 5 meters.

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Step-by-step explanation:

10 out of 10 is 1 but there is still another tenth that needs to be added so it is 1 and one tenth.

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Step-by-step explanation:

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(a) if the programmes can be perfomed in any order ?

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2 years ago

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Step-by-step explanation:

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2 years ago

A theory predicts that the mean age of stars within a particular type of star cluster is 3.3 billion years, with a standard devi

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Answer:

Null hypothesis: $\mu \leq 3.3$

Alternative hypothesis: $\mu > 3.3$

$z=\frac{3.4-3.3}{\frac{0.4}{\sqrt{50}}}=1.768$

Since is a one right tailed test the p value would be:

$p_v =P(z>1.768)=0.039$

Step-by-step explanation:

Data given and notation

$\bar X=3.4$ represent the sample mean

$\sigma=0.4$ represent the population deviation for the sample

$n=50$ sample size

$\mu_o =3.3$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses to be tested

We need to conduct a hypothesis in order to determine if the mean is higher than 3.3, the system of hypothesis would be:

Null hypothesis: $\mu \leq 3.3$

Alternative hypothesis: $\mu > 3.3$

Compute the test statistic

We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

We can replace in formula (1) the info given like this:

$z=\frac{3.4-3.3}{\frac{0.4}{\sqrt{50}}}=1.768$

P value

Since is a one right tailed test the p value would be:

$p_v =P(z>1.768)=0.039$

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3 years ago