MATHEMATICS COLLEGE

What is the volume of a cone with the given dimensions. radius=4 cm; height= 10 cm

Answers

Answer 1

Answer: 167.552 the volume of a cone is piR^2h/3

Answer 2

Answer:

Answer:

$167.47 \: {cm}^(3)$

Step-by-step explanation:

$V_(cone) = (1)/( 3) \pi {r}^(2)h \n \n = (1)/( 3) \pi * {4}^(2) * 10 \n \n = (1)/( 3) * 3.14 * 16 * 10 \n \n = (1)/( 3) * \: 502.4 \n \n = 167.466667 \n \n = 167.47 \: {cm}^(3)$

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"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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190 muitiplied by 186

Answers

Answer:

35340

Step-by-step explanation:

please like my answer

Answer: 35340

Step-by-step explanation: just multiply

F(x) = 6x2 + 2 what is the domain

Answers

Answer:

All Real Numbers

Step-by-step explanation:

$f(x)=6x^2+2$

To find the domain of a quadratic function, we can make a table.

x y f(x)=6x^2+2

-1 8 6(-1)^2+2

0 2 6(0)^2+2

1 8 6(1)^2+2

You can keep going and identity that all the x values/ domains are real numbers.

Find the equation of a line through (1,1) whichisperpendicular to a line through (1,3) and (2,5).

Answers

Answer:

$y=(-1)/(2)x+(3)/(2)$

Step-by-step explanation:

Point on a line is (1,3) and (2,5).

$slope=(y_2-y_1)/(x_2-x_1) =(5-3)/(2-1) =2$

slope of given line is 2

slope of perpendicular lines are negative reciprocal of one another

slope of perpendicular line is -1/2

slope = -1/2 (1,1)

$y-y_1=m(x-x_1)$

$y-1=(-1)/(2)(x-1)$

$y-1=(-1)/(2)x+(1)/(2))$

add 1 on both sides

$y=(-1)/(2)x+(3)/(2)$

PLSS I NEED HELP ASAP BECAUSE ITS DUE SOONNick has to build a brick wall. Each row of the wall requires 62 bricks. There are 10 rows in the wall. How many bricks will Nick require to build the wall?
A.
102 × 6
B.
106
C.
610
D.
10 × 62

Answers

D. 10 x 62

If one row needs 62 bricks and there's 10 rows, you multiply them to get how many bricks nick needs

Which is bigger 0.159 or 1.590

Answers

Answer:

1.590

Step-by-step explanation:

Answer:

0.159

Step-by-step explanation:its obvious hope this helped tho

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The lifetime of a certain type of battery is normally distributed with mean value 11 hours and standard deviation 1 hour. There are four batteries in a package. What lifetime value is such that the total lifetime of all batteries in a package exceeds that value for only 5% of all packages?