) You want to rent an unfurnished one-bedroom apartment after you graduate from high school. The mean monthly rent for a random sample of 10 apartments advertised in the local newspaper is $940. The margin of error for a 95% confidence interval is $160. Find the 95% confidence interval for the mean monthly rent for unfurnished one-bedroom apartments available for rent in this community. Write your answer in this format: x to y

$780 to $1100

Step-by-step explanation:

A confidence interval has two bounds. A lower bound and an upper bound. They are dependent of the sample mean and of the margin of error M.

In this problem:

Sample mean: $940

Margin of error: $160

The lower end of the interval is the sample mean subtracted by M. So it is 940 - 160 = $780

The upper end of the interval is the sample mean added to M. So it is 940 + 160 = $1100

So the answer is

$780 to $1100

step-by-step explanation: where's the phrase?

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).