What is the area of the figure? ______

How much paper will be needed to cover the cylinder shown?

Advocard [28]

A=2πrh+2πr2=2·π·6·25+2·π·6^2 so the answer is D

5 0

3 years ago

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which of the following expresses the coordinates of the foci of the conic section shown below? (x-2)^2/4+(y+5)^2/9

elena55 [62]

Step-by-step explanation:

$\frac{(x - 2) {}^{2} }{4} + \frac{(y + 5) {}^{2} }{9} = 1$

This is the equation of the ellipse. Since the denominator is greater for the y values, we have a vertical ellipse. Remember a>b, so a

The formula for the foci of the vertical ellipse is

(h,k+c) and (h,k-c).

where c is

Our center (h,k) is (2, -5)

${c}^{2} = {a}^{2} - {b}^{2}$

Here a^2 is 9, b^2 is 4.

${c}^{2} = 9 - 4$

${c}^{2} = 5$

$c = \sqrt{5}$

So our foci is

$(2, - 5 + \sqrt{5} )$

and

$(2, - 5 - \sqrt{5} )$

6 0

2 years ago

A laptop producing company also produces laptop batteries, and claims that the batteries

gregori [183]

Answer:

There is enough evidence to support the claim that the batteries power the laptops for significantly less than 4 hours. (P-value = 0).

The null and alternative hypothesis are:

$H_0: \mu=4\\\\H_a:\mu< 4$

Step-by-step explanation:

The question is incomplete: To test this claim a sample or population standard deviation is needed.

We will estimate that the sample standard deviation is 2 hours, and use a t-test to test that claim.

NOTE (after solving): The difference between the sample mean and the mean of the null hypothesis is big enough to reject the null hypothesis, even when we have a sample standard deviation of 3.5 hours, which can be considered bigger than the maximum standard deviation for the sample.

This is a hypothesis test for the population mean.

The claim is that the batteries power the laptops for significantly less than 4 hours.

Then, the null and alternative hypothesis are:

$H_0: \mu=4\\\\H_a:\mu< 4$

The significance level is 0.05.

The sample has a size n=500.

The sample mean is M=3.5.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=2.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{2}{\sqrt{500}}=0.0894$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{3.5-4}{0.0894}=\dfrac{-0.5}{0.0894}=-5.5902$

The degrees of freedom for this sample size are:

$df=n-1=500-1=499$

This test is a left-tailed test, with 499 degrees of freedom and t=-5.5902, so the P-value for this test is calculated as (using a t-table):

$P-value=P(t$

As the P-value (0) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the batteries power the laptops for significantly less than 4 hours.

5 0

3 years ago

Find the area of the rectangle with a length of (x^2-2) and a width of (2x^2-x+2)

Katyanochek1 [597]

Area=legnth times width

so multiply them together use distributive property
a(b+c)=ab+ac so
in this problem
(a+b)(c+d+e)=(a+b)(c)+(a+b)(d)+(a+b)(e)

so
x^2-2 times (2x^2-x+2)=(x^2)(2x^2-x+2)-(2)(2x^2-x+2)=(2x^4-x^3+2x^2)-(4x^2-2x+4)
add like terms
2x^4-x^3+(2x^2-4x^2)-2x+4
2x^4-x^3-2x^2-2x+4

5 0

3 years ago

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If a snail crawls 12 centimeters per hour, how long will it take for the snail to travel 1 meter

Pavlova-9 [17]

Answer: 8 1/3 hours or 500 minutes

Step-by-step explanation:

Keep in mind that there are 100 centimeters in a meter.

The snail moves at a pace of 12 cm/h, and needs to go 100 cm. You can just divide 100/12 to get 8 1/3, which is how many hours (groups of 12 cm) it takes for the snail to travel 100 cm (1 meter).

If necessary, you can also multiply 8 1/3 by 60 to get the number of minutes the snail takes. 8 times 60 is 480, and 1/3 of an hour is 20, so add 480+20 to get 500 minutes.

5 0

3 years ago

What is the area of the figure? _______ ft2