MATHEMATICS COLLEGE

An artist creates a cone shaped sculpture for an art exhibit. If the sculpture is 8 feet tall and has a base with a circumference of 21.352 feet, what is the volume of the sculpture? Use 3.14 for Pi

Answers

Answer 1

Answer:

Answer:

Volume, $V=96.79\ \text{feet}^3$

Step-by-step explanation:

An artist creates a cone shaped sculpture for an art exhibit.

Height of sculpture is 8 feets

The circumference of base of the cone is 21.352 feet.

The base of a con is circular shaped. So,

$2\pi r= 21.352$

r is radius of cone

$r= (21.352)/(2* 3.14) \n\nr=3.4\ ft$

The volume of cone shaped sculpture is given by :

$V=(1)/(3)\pi r^2 h\n\nV=(1)/(3)* 3.14* (3.4)^2 * 8\n\nV=96.79\ \text{feet}^3$

So, the volume of the sculpture is $96.79\ \text{feet}^3$ .

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Solve the equation by completing the square. X^2+10x+24=0

If f(x) = 7 sin x + 10 cos x,

Answers

Answer:

7+1x=8, 8+10 =x18 is your answer

Suppose you read online that children first count to 10 successfully when they are 32 months old, on average. You perform a hypothesis test evaluating whether the average age at which gifted children first count to 10 is different than the general average of 32 months. What is the p-value of the hypothesis test? Choose the closest answer.

Answers

Answer:

$p_v =2*P(t_((35))<-1.822)=0.0885$

Step-by-step explanation:

Assuming this info from R

hist(gifted$count)

## Min. 1st Qu. Median Mean 3rd Qu. Max.

## 21.00 28.00 31.00 30.69 34.25 39.00

## Sd

## [1] 4.314887

Data given and notation

$\bar X=30.69$ represent the mean

$s=4.3149$ represent the sample standard deviation

$n=36$ sample size

$\mu_o =32$ 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.

We need to conduct a hypothesis in order to check if the mean is different than 32, the system of hypothesis would be:

Null hypothesis: $\mu = 32$

Alternative hypothesis: $\mu \neq 32$

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=(\bar X-\mu_o)/((s)/(√(n)))$ (1)

t-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".

Calculate the statistic

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

$t=(30.69-32)/((4.3149)/(√(36)))=-1.822$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=36-1=35$

Since is a two sided test the p value would be:

$p_v =2*P(t_((35))<-1.822)=0.0885$

Through the points (1/2 , 3/4) and (-1/3 , 5/4).Question 2
Find, if possible, the slope of the line through the points (2 , 5) and (-4 , 5)

Answers

Answer:

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(5-5)/(-4-2)

m=0/-6

m=0

Please help me for a TEST review tomorrow!!

Answers

Answer:

Hope you understand my writing!

I am a 3-digit number. If you switch my first and last digits, I decrease by 297. Also, mymiddle digit is 6 less than my first digit, which is 2 less than 2 times my last digit. What
number am I?

Answers

Answer:

Step-by-step explanation:

Let the 3-digit number is abc = 100a + 10b + c.

We have:

100a + 10b + c - 100c - 10b - a = 297
b = a - 6
a = 2c - 2

Simplify the first equation:

99a - 99c = 297
a - c = 3
a = c + 3

Solve for c by substitution:

2c - 2 = c + 3
2c - c = 3 + 2
c = 5

Find a:

a = 3 + 5 = 8

Find b:

b = 8 - 2 = 6

The number is:

Blue ribbon taxis offers shuttle service to the nearest airport. You loop up online reviews for blue ribbon taxis and find that there are 17 reviews, six of which report that the taxi never showed up. Is this a biased sampling method for obtaining customer opinion on the taxi service?
If so, what is the likely direction of bias?
explain your reasoning carefully.

Answers

Answer:

In order for a sample to be considered biased, some members of the total population must have either a larger or lower chance of being included in the sample. In this case, your sample contained 17 reviews. It is biased because it was completely voluntary and customers who have a bad experience with a product or service generally tend to express more their dissatisfaction than satisfied customers show their satisfaction.

In marketing, there is a saying that unsatisfied clients talk bad about our product or service 4 times more than satisfied clients. I'm not sure if this saying is exact or not, but all marketing research point in the same direction.

This means that clients that did not get a good service or got no service at all, are more likely to post a review about the company than clients who got a good service. This is what makes the sample biased.

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