Math Answers

1. The average number of milligrams (mg) of cholesterol in a cup of a certain brand of ice cream is

660 mg, the standard deviation is 35 mg. Assume the variable is normally distributed. a. If a cup of

ice cream is selected, what is the probability that the cholesterol content will be more than 670 mg?

Prove: Use R - 3L for divisibility by 31.

Prove: Use R + 7L to determine if 23| N.

Prove: Methods for divisibility by 13.

1. Method 2. ( R + 4L) 

Prove: 12|N iff 4| N ^ 3 | N.

Prove:

The following methods are useful for divisibility by 11.

1. Get the difference of the sum of the digits in the odd places and the sum

of the digits in the even places. If the result is divisible by 11, then 11|N.

Prove that if 𝑎|𝑏 and 𝑏≠0, then |𝑎| ≤ |𝑏|.

Find the general solution.

1. 4y^(4) −4y′′′ −23y′′ +12y′ +36y = 0 

Determine the unique solution of the initial value problem. 

1. y′′ −2y′ +y=0,y(0)=7,y′(0)=4.

 Show that the functions 1, cos2 x, sin2 x are linearly dependent .