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3 years ago

A cylinder has a surface area of 339cm. The radius is two times greater than the height. what is the radius of the cylinder.

1 answer:

8 0

The answer is 6 cm.

The surface area of the cylinder is:
SA = 2πr² + 2πrh

SA = 339
r = 2h
⇒ h = r/2
r = ?
π = 3.14

339 = 2πr² + 2πr*r/2
339 = 2πr² + πr*r
339 = 3πr²
πr² = 339/3
πr² = 113
r² = 113/π
r² = 113/3.14
r² ≈ 36
r = √36
r = 6

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Starting at the point (-3,2) go left 9 and down 8. What ordered pair gives the location of this new point

tigry1 [53]

The new a=plot would be:

(-3-9,2-8)=

5 0

1 year ago

What are the first five terms of the sequence generated by the formula below?

Novay_Z [31]

Answer:

The correct option is:

2, 4, 12, 48, 240

Step-by-step explanation:

We have to determine the first 5 terms of the sequence by using following formula:

$a_n=2n!$

To Calculate the first 5 terms.

Put n = 1

a₁ = 2 (1)!

a₁ = 2(1)

a₁ = 2

Put n = 2

a₂ = 2 (2)!

a₂ = 2 (2·1) = 2(2)

a₂ = 4

Put n = 3

a₃ = 2(3)!

a₃ = 2(3·2·1)

a₃ = 2(6)

a₃ = 12

Put n = 4

a₄ = 2(4)!

a₄ = 2(4·3·2·1)

a₄ = 2(24)

a₄ = 48

Put n =5

a₅ = 2(5)!

a₅ = 2(5·4·3·2·1)

a₅ = 2(120)

a₅ = 240

8 0

3 years ago

Someone please help!

Vlad1618 [11]

Multiply the top equation by 6 and the bottom equation by 7. You will cancel x first by doing this and solve for y. You should get y=-1.
Substitute in y for either original equation.
You should get x=1.
Solution is (1,-1).

7 0

3 years ago

The realtor and her clients do not know the average home sale price for all of Guelph (500 was actually just a guess). However,

strojnjashka [21]

Answer:

a) The 99% confidence interval would be given by (346.708;453.292)

b) The 99% confidence interval would be given by (338.445;461.555)

Step-by-step explanation:

1) 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".

$\bar X=400$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=80$ represent the population standard deviation

n=15 represent the sample size

2) Part a

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

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that $z_{\alpha/2}=2.58$

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

$400-2.58\frac{80}{\sqrt{15}}=346.708$

$400+2.58\frac{80}{\sqrt{15}}=453.292$

So on this case the 99% confidence interval would be given by (346.708;453.292)

3) Part b

For this case we don't know the population deviation so we need to use the t distribution instead the normal standard distribution.

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

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

We need to find the degrees of freedom first df=n-1=15-1=14

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,14)".And we see that $t_{\alpha/2}=2.98$