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3 years ago

What the answer question now

Mathematics

1 answer:

RUDIKE [14]3 years ago

6 0

Step-by-step explanation:

Here,

radius (r)= 2cm

height(h)=5cm

now,

according to the question we must find the surface area of cylinder so,

by formulae ,

a= 2.pi.r(r+h)

now, 

a= 2×3.14×2(2+5)

by simplifying it we get, 

The surface area of cylinder is 87.92 cm^2.

Hope it helps 

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Almost all employees working for financial companies in New York City receive large bonuses at the end of the year. A sample of

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Answer:

The 90% confidence interval for the average bonus that all employees working for financial companies in New York City received last year is between $43,819 and $50,181

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

T interval

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 62 - 1 = 61

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 61 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.9}{2} = 0.95$ . So we have T = 1.67

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 1.67\frac{15000}{\sqrt{62}} = 3181$

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 47000 - 3181 = $43,819

The upper end of the interval is the sample mean added to M. So it is 47000 + 3181 = $50,181

The 90% confidence interval for the average bonus that all employees working for financial companies in New York City received last year is between $43,819 and $50,181

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2 years ago

Home heating oil is sold by the gallon. Last winter, the Romano family used 370 gallons of oil at $2.56 per gallon. If the price

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Answer:

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Step-by-step explanation:

Last winter:

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Next year,

price increases 9% per gallon

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Which values of x and y will make this quadrilateral a parallelogram?

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Answer:

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Step-by-step explanation:

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3 years ago

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What is the coordinates of the center of an ellipse defined by the equation 16x^2 + 25y^2 + 160x - 200y + 400 = 0 ? Please give

pickupchik [31]

16x^2 + 25y^2 + 160x - 200y + 400 = 0     Rearrange and regroup.

(16x^2 + 160x) + (25y^2 - 200y ) = 0-400.     Group the xs together and the ys together.

16(X^2 + 10x) + 25(y^2-8y) = -400.     Factorising.

We are going to use completing the square method.

Coefficient of x in the first expression = 10.

Half of it = 1/2 * 10 = 5. (Note this value)

Square it = 5^2 = 25.     (Note this value)

Coefficient of y in the second expression = -8.

Half of it = 1/2 * -8 = -4. (Note this value)

Square it = (-4)^2 = 16. (Note this value)

We are going to carry out a manipulation of completing the square with the values

25 and 16. By adding and substracting it.

16(X^2 + 10x) + 25(y^2-8y) = -400

16(X^2 + 10x + 25 -25) + 25(y^2-8y + 16 -16) = -400

Note that +25 - 25 = 0.    +16 -16 = 0. So the equation is not altered.

16(X^2 + 10x + 25) -16(25) + 25(y^2-8y + 16) -25(16) = -400

16(X^2 + 10x + 25) + 25(y^2-8y + 16) = -400 +16(25) + 25(16)    Transferring the terms -16(25) and -25(16)

to other side of equation. And 16*25 = 400

16(X^2 + 10x + 25) + 25(y^2-8y + 16) = 25(16)

16(X^2 + 10x + 25) + 25(y^2-8y + 16) = 400

We now complete the square by using the value when coefficient was halved.

16(x-5)^2 + 25(y-4)^2 = 400

Divide both sides of the equation by 400

(16(x-5)^2)/400 + (25(y-4)^2)/400 = 400/400              Note also that, 16*25 = 400.

((x-5)^2)/25 + ((y-4)^2)/16 = 1

((x-5)^2)/(5^2) + ((y-4)^2)/(4^2) = 1

Comparing to the general format of an ellipse.

((x-h)^2)/(a^2) + ((y-k)^2)/(b^2) = 1

Coordinates of the center = (h,k).

Comparing   with above   (x-5) = (x - h) , h = 5.

Comparing   with above   (y-k) = (y - k) , k = 4.

Therefore center = (h,k) = (5,4).

Sorry the answer came a little late. Cheers.

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