The point of the needle of a sewing machine moves in SHM along the x -axis with a frequency of 2.5 Hz. At t = 0 its position and velocity components are +1.1 cm and -15 cm/s, respectively. Find the acceleration component of the needle at t = 0.

A machine that fills quart orange juice cartons is set to fill them with 32.1 oz. If the actual contents of the cartons vary normally, with a standard deviation of 0.1 oz, what percentage of the cartons contain less than a quart (32 oz)?

Suppose you were to read that a new study based on 100 men had found that there was no difference in heart attack rates for men who exercised regularly and men who did not. Do you think the study found exactly the same rate of heart attacks for the two groups of men? In the context of the material, what would you suspect was the reason for that reported finding?

When a body of unknown mass is attached to an ideal spring with force constant $120 \mathrm{~N} / \mathrm{m}$, it is found to vibrate with a frequency of $6.00 \mathrm{~Hz}$. Find
($c$) the mass of the body.

Find the eigenvalues and eigenvectors of the matrix in the following problem

$$\left( \begin{array}{ccc} 2 & -3 & 4 \\ -3 & 2 & 0 \\ 4 & 0 & 2\end{array}\right)$$

When a body of unknown mass is attached to an ideal spring with force constant $120 \mathrm{~N} / \mathrm{m}$, it is found to vibrate with a frequency of $6.00 \mathrm{~Hz}$. Find
(b) the angular frequency;

The sum of the ages of two brothers is 22 and the product of their ages is 120. How old are the brothers?

Give an integral equal to each area. $A_{1}$

Write the given argument in words and determine whether each argument is valid. Let p: 4 gigabytes is better than no memory at all, q: We will buy more memory, r: We will buy a new computer.

$$\begin{array}{l} p\rightarrow r \\ r\rightarrow q \\ p \\ \hline \therefore q \end{array}$$

As a man walks barefoot along the beach, he steps on a sharp shell. His foot automatically jerks upward, even before he feels pain. What process is this an example of? How does it help protect the man?

Decide whether the statement is true or false. Give an explanation for your answer. If f(x) is a positive periodic function, then $\int _ { 0 } ^ { \infty } f ( x ) d x$ diverges.

Write the statement as an inequality. "6y is no more than 8."

Multiply. Write the product in simplest form. 4/9 x 3.

Amelia bought roast beef for $6.85 per pound. Find the total cost if Amelia bought 4 pounds of roast beef. Justify your answer by using the Distributive Property.