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3 years ago

A prism with a base area of 5 ft² and a height of 10 ft is dilated by a factor of 6/5 . What is the volume of the dilated prism?

Mathematics

2 answers:

ludmilkaskok [199]3 years ago

7 0

The formula to find the volume of a prism is V=Bh (Volume = Base x height). Let's plug in the dimensions you were given:

V=Bh
V=(5)(10)
V=50 {tex] ft^{2} [/tex]

To find the new volume of the dilated prism, cube the dilated factor, then multiply by the volume you just found (old volume):

New Volume = ( $x^{3}$ )(Old Volume)
V = ( $\frac{6}{5}$ )³·50
V = ( $\frac{432}{5}$
V = 86.4

HACTEHA [7]3 years ago

6 0

Answer:

86.4 ft³

Proof:

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Farrah is making a dragon costume for her little brother. It would have triangular spikes down the head and back each head spike

lilavasa [31]

The question is not written properly! Complete question along with answer and explanation is provided below.

Question:

Farrah is making a dragon costume for her little brother. It would have triangular spikes down the head and back.

Each head spike has a base of 2 cm and a height of 6 cm.

Each back spike will be 10 cm high with a base of 6 cm.

if the costume has 6 spikes on the back and on the head 10 more spikes than the back then how many square centimeters of fabric will farrah need for all the dragon spikes?

Given Information:

Base of head spike = b₁ = 2 cm

Height of head spike = h₁ = 6 cm

Base of back spike = b₂ = 6 cm

Height of back spike = h₂ = 10 cm

Number of head spikes = n₁ = 10 + 6 = 16

Number of back spikes = n₂ = 6

Required Information:

How much fabric is needed = ?

Answer:

Farrah would need 276 cm² of fabric for all the dragon spikes.

Step-by-step explanation:

We are given that dragon costume have triangular spikes down the head and back.

The area of triangular shape is given by

Area = ½×b×h

Where b is the base and h is the height

The area of the head spike is

A₁ = ½×b₁×h₁

A₁ = ½×2×6

A₁ = ½×12

A₁ = 6 cm²

But we know that the number of head spikes is 16 so the total area of the head spikes is

A₁ = 16×6

A₁ = 96 cm²

The area of the back spike is

A₂ = ½×b₂×h₂

A₂ = ½×6×10

A₂ = ½×60

A₂ = 30 cm²

But we know that the number of back spikes is 6 so the total area of the back spikes is

A₂ = 6×30

A₂ = 180 cm²

The total area required is the sum of the area of head spikes and back spikes,

Total area = A₁ + A₂

Total area = 96 + 180

Total area = 276 cm²

Therefore, Farrah would need 276 cm² of fabric for all the dragon spikes.

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3 years ago

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Answer:

The probability is 0.789

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\sigma = 16, n = 400, s = \frac{16}{\sqrt{400}} = 0.8$

Find the probability that the mean age of the individuals sampled is within one year of the mean age for all individuals in the city.

Using $\mu = 30$ , this is the pvalue of Z when X = 31 subtracted by the pvalue of Z when X = 29. So

X = 31

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

By the Central Limit Theorem

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

$Z = \frac{31 - 30}{0.8}$

$Z = 1.25$

$Z = 1.25$ has a pvalue of 0.8944

X = 29

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

$Z = \frac{29 - 30}{0.8}$

$Z = -1.25$

$Z = -1.25$ has a pvalue of 0.1056

0.8944 - 0.1056 = 0.7888

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The probability is 0.789

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Answer:

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