MATHEMATICS COLLEGE

A cylinder is 5 centimeters tall and has a radius of 2.1 centimeters. Find the volume to the nearest tenth. Use 3.14 for .61.2 cm
33.0 cm
65.9 cm
69.2 cm

Answers

Answer 1

Answer:

Answer:

Option D

Step-by-step explanation:

Volume of a cylinder is $V=\pi r^2h$

h - height

r - radius

We are given the radius of 2.1 centimeters and the height of 5 centimeters.

Using 3.14 for pi:

$V=3.14*2.1^2*5\n\nV =69.237$

69.237 ≈ 69.2

Option D should be the correct answer.

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One number is 3 more than 3 times another. The sum of the numbers is 19. Find the two numbers.The two numbers are
and

Answers

Answer:

number x

y = 3x +3

sum = x + y

19 = x + 3x + 3

19 = 4x + 3

19- 3 = 4x

16 = 4x

16/4 = x

x = 4

Hey can you please help me posted picture of question

Answers

The correct answer is option D.

The function has a repeated root. We can find this by factorization.

x² - 2x + 1
= x² - x - x + 1
= x (x - 1) - 1(x - 1)
= (x -1)(x - 1)

This can also be checked by finding the discriminant. The discriminant is zero which shows the function has a repeated root.

Monty can use the number line to find an equivalent fraction with a denominator greater than 6

Answers

Yes, Monty can use the number line to find an equivalent fraction with a denominator greater than 6.

For Example,

Consider $(5)/(7)$

The equivalent fraction of $(5)/(7)$ is $(25)/(35)$ .

So, yes you can represent $(5)/(7)$ on a number line by putting 6 lines between 0 and 1 and Can Represent $(25)/(35)$ by putting 34 lines between 0 and 1.

There is no effect of denominator to find equivalent fraction of any rational number, whether the denominator is greater than 6 or less than 6, but denominator should not be equal to Zero.

We can find equivalent fraction of any rational number , the denominator of that rational number should not be equal to Zero.

Is this math? What's the question ?

"Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for metal sheets of a particular type, its mean value and standard deviation are 75 GPa and 2.1 GPa, respectively. Suppose the distribution is normal. (Round your answers to four decimal places.)(a) Calculate P(74 ? X ? 76) when n = 25.(b)How likely is it that the sample mean diameter exceeds 76 when n = 49?"

Answers

Answer:

a) $P(74 <\bar X <76)=P(-2.38< Z< 2.38) = P(Z<2.38)-P(Z<-2.38)=0.9913-0.0087=0.9827$

b) $P(\bar X >76)=P(Z>3.33)=1-P(Z<3.33)=1-0.9996=0.0004$

So on this case is very unlikely that the sample mean would be higher exceeds 76 when n =49

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

2) Part a

Let X the random variable that represent the Young modulus of a population, and for this case we know the distribution for X is given by:

$X \sim N(75,2.1)$

Where $\mu=75$ and $\sigma=2.1$

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu=75, (\sigma)/(√(n))=(2.1)/(√(25)))$

And we want to find this probability:

$P(74 <\bar X <76)=P((74-75)/((2.1)/(√(25)))<Z<(76-75)/((2.1)/(√(25))))$

$P(-2.38< Z< 2.38) = P(Z<2.38)-P(Z<-2.38)=0.9913-0.0087=0.9827$

3) Part b

For this case the new distribution is given by:

$\bar X \sim N(\mu=75, (\sigma)/(√(n))=(2.1)/(√(49)))$

$P(\bar X >76)=P(Z>(76-75)/((2.1)/(√(49)))=3.33)$

$P(Z>3.33)=1-P(Z<3.33)=1-0.9996=0.0004$

So on this case is very unlikely that the sample mean would be higher exceeds 76 when n =49

Final answer:

In this problem, we calculated the probabilities for a normal distribution with mean 75 and standard deviation 2.1. For part (a), the probability was found to be 0.9179 that the modulus lies between 74 and 76 for a sample size of 25. In part (b), the likelihood was found to be 0.0004 that the sample mean diameter of 49 pieces exceeds 76.

Explanation:

Given the problem, we are dealing with a normal distribution with a mean of 75 GPA and a standard deviation of 2.1 GPA.

(a) We are asked to find the probability that the modulus is between 74 and 76 for a sample size of 25. First, we calculate the standard deviation of the sample mean as sigma/sqrt(n), which is 2.1/sqrt(25)=0.42. Then, we find the Z-scores for 74 and 76 as (X - mean)/standard deviation, yielding -2.3809 and 2.3809. We lookup these Z-scores in a Z-table, find their corresponding probabilities, and subtract to get 0.9179.

(b) Next, we want to find how likely the sample mean diameter exceeds 76 GPA for n = 49. We find the new standard deviation as 2.1/sqrt(49)=0.3. The Z-score for 76 is (76 - 75)/0.3 =3.3333. We subtract the corresponding probability (0.9996) in the Z-table from 1 to find it's incredibly likely at 0.0004 that the sample mean diameter exceeds 76.

Learn more about Normal Distribution here:

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The area of a rectangle is (x^4+4x^3+3x^2-4x-4) and the length of the rectangle is (x^3

Answers

Answer:

what

Step-by-step explanation:

what is the question

You read that a study is planned for which a test of hypothesis will be done at significance level α = 0.10. Statisticians have calculated that for a certain effect size, the power is 0.7. What are the probabilities of Type I and Type II errors for this test?