geno3141

I believe that you also need to know the standard deviation of the population (at least the standard deviation of the sample) in order to do the calculation:

Formula:  E  =  z_{α/2 · σ / √n}

where:  z represents the z-score when α = .90, σ represents the standard deviation, and n represents the number in the sample.

31 x 0.48  =  14.88 (rounded to 15 pounds)

This can be approximated:  0.48 pounds is about 1/2 pound

1/2 of 31 students is 15.5 pounds; 15 would be enough, but buying 16 would allow for spilling. 

|x| splits at 0: 

   for x ≥ 0: |x| = x

   for x < 0: |x| = -x

So:

   for x ≥ 0: |x| + x² - 5x + 8 becomes x + x² - 5x + 8 --->   x² - 4x + 8

   for x  0: |x| + x² - 5x + 8 becomes -x + x² - 5x + 8 --->   x² - 6x + 8

Both of these are (partial) parabolas.

The vertex of y = x² - 4x + 8  occurs at (2,4) so the minimum value is 4.

The maximum value of x² - 4x + 8 on [0,4] occurs at x = 4 --->  y = 8.

The maximum value of x² - 6x + 8 on [-1,0] occurs at x = -1  --->   y = 15.

Thus, the maximum value is 15.

log₂y  =  (1/3)log₂27

Since a multiplier goes into the log expression as an exponent:

log₂y  =  log₂27^1/3

An exponent of 1/3 represents a cube root, so 27^1/3 = 3  (the cube root fo 27 is 3).

log₂y  =  log₂3

So:  y = 3.

Since there are  6  different letters, you have  6  choices for the first letter.

Now, since there are  5  letters remaining, you have  5  choices for the second letter.

Then, you have  4  choices for the third letter;  3  choices for the fourth letter;  2  choices for the fifth leetter; and only  1  choice for the sixth, and last letter.

Multiplying these choices together:  6 x 5 x 4 x 3 x 2 x 1  =  6!  =  720 choices.

You can arrange them into a 1 x 15 rectangle or a 3 x 5 rectangle, so there are 2 unique answers.

-2 + -6

Here, you are adding two negative numbers (this is like losing 2 and then losing another 6, so you have a total loss of 8, which is written as -8).

If you are adding two negative numbers, add the two numbers (ignoring the negative signs) and then put a negative sign in from of your answer.

Since 2 + 6 = 8, -2 + -6 = -8.

acosh(200/a)  =  30

--->   200/a  =  cosh(30)

--->   200  =  a · cosh(30)

--->   a  =  200 / cosh(30)

--->   a  =  3.74 x 10^-11  (approximately)

-√(128)  =  -√(64) · √(2)  =  -8 · √2  =  -8√2