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dangina [55]
3 years ago
6

A right cylinder has a height of 20 1/2ft and a diameter of 1 1/5 times it's height what is the volume of the cylinder? Use 3.14

for pi
Mathematics
1 answer:
anygoal [31]3 years ago
4 0
Volume (V) of a cylinder is the area of circular base (pi×r^2) times it's length/height (h):
V =  \pi {r}^{2} (h) \:  \: \pi = 3.14
h = 20.5 ft
diameter (d) = 1 1/5 × h, 1 1/5 = 6/5 = 1.20
d = 1.20 × 20.5 = 24.6 ft
radius (r) = 1/2 d = 24.6/2 = 12.3 ft
V =  \pi {r}^{2} (h)  \\ V = 3.14 ({12.3}^{2}) (20.5)  \\ V = 3.14 (151.29) (20.5) \\ V = 475.05 (20.5) = 9738.54  \: {ft}^{3}

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For a school fundraiser Jeff sold large boxes of candy for three dollars each and small boxes of candy for two dollars each if y
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Answer:

C

Step-by-step explanation:

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3 years ago
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A study was conducted to measure the effectiveness of hypnotism in reducing pain. The measurements are centimeters on a pain sca
saul85 [17]

Answer:

The 95% confidence interval for the difference would be given by (-1.776;0.376)

We are 95% confidence that the true mean difference is between -1.776 \leq \mu_d \leq 0.376. Since the confidence interval contains the value 0, we don't have enough evidence to conclude that hypnotism appear to be effective in reducing pain.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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".

Let put some notation  

x=test value before , y = test value after

x: 6.4 2.6 7.7 10.5 11.7 5.8 4.3 2.8

y: 6.7 2.4 7.4 8.1 8.6 6.4 3.9 2.7

The differences defined as d_i = y_i -x_i and we got:

d: 0.3, -0.2, -0.3, -2.4, -3.1, 0.6, -0.4, -0.1

We can calculate the mean and the deviation for the sample with the following formulas:

\bar d=\frac{\sum_{i=1}^n d_i}{n}

s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1}

\bar d=-0.7 represent the sample mean for the difference

\mu_d population mean (variable of interest)

s_d=1.32 represent the sample standard deviation

n=8 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

\bar d \pm t_{\alpha/2} *\frac{s_d}{\sqrt{n}}  (1)

In order to calculate the critical value t we need to find first the degrees of freedom, given by:

df=n-1=8-1=7

Since the Confidence is 0.95 or 95%, the value of alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,8)".And we see that t_(\alpha/2)=2.306

Now we have everything in order to replace into formula (1):

-0.7-2.306\frac{1.32}{\sqrt{8}}=-1.776    

-0.7+2.306\frac{1.32}{\sqrt{8}}=0.376    

So on this case the 95% confidence interval for the difference would be given by (-1.776;0.376)

We are 95% confidence that the true mean difference is between -1.776 \leq \mu_d \leq 0.376. Since the confidence interval contains the value 0, we don't have enough evidence to conclude that hypnotism appear to be effective in reducing pain.

6 0
3 years ago
Which are the solution of x2=-5x+8
yawa3891 [41]

rewrite the equation set = to 0.

x^2 + 5x - 8 = 0

The quadratic will not factor so you have to use the quadratic formula.

x = (-b + - sqrt(b^2 - 4ac))/2a

x = (5 + - sqrt(25 - 4* 1* -8))/2

x = (5 + - sqrt 57)/2


The x2is not the same as 2x. It is x^2. X tot he second power which makes the problem a quadratic equation. You cannot combine the terms x^2 and -5x because they so not have the same power.

4 0
3 years ago
What is the distributive property of 15+45
Taya2010 [7]
The distributive property is 15+45 = (10 + 40) + (5+5) = 50 + 10 = 60 Hope this helps you.
5 0
3 years ago
What is the average rate of change for 5/6 and 15/14
andreev551 [17]

Answer:

Average rate of change is <u>0.80.</u>

Step-by-step explanation:

Given:

The two points given are (5, 6) and (15, 14).

Average rate of change is the ratio of the overall change in 'y' and overall change in 'x'. If the overall change in 'y' is positive with 'x', then average rate of change is also positive and vice-versa.

The average rate of change for two points (x_1,y_1)\ and\ (x_2,y_2) is given as:

R=\frac{y_2-y_1}{x_2-x_1}

Plug in x_1=5,x_2=15,y_1=6,y_2=14 and solve for 'R'. This gives,

R= \frac{14-6}{15-5}\\\\R=\frac{8}{10}\\\\R=0.80

Therefore, the average rate of change for the points (5, 6) and (15, 14) is 0.80.

5 0
3 years ago
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