Math Answers

1. Express the following statements using quantifiers.

A. All cats have fleas.

B. No one in this class knows how to speak Mandarin.

2.Form the negation of each statement without applying negation to the left of any quantifier.

3. Express each negation in simple English.

Part 2

1. Given A = {4, 8, 12, 16} and B = {6, 12, 18, 24}, determine the following:

a. A U B

b. A ∩ B

c. A - B

d. B - A

Consider a population consisting of 1, 2, and 3. Suppose samples of size 3 are drawn from this population with and without replacement.

1. Determine the number of sets of all possible samples.

2. List all the possible samples, and compute the mean of each sample.

3. Construct the sampling distribution of the sample means

6. A force of 20 lb stretches a spring from a natural length of 7 inches to a length of 12 inches. How much work was performed in stretching the spring to this length?

The mean serum-creatinine level measured in 10 patients 24 hours after they received a

newly proposed antibiotic was 1.2 mg/dL with standard deviation of 0.4mg/dL. If the serum level in the general population is 1.0mg, test the hypothesis that the serum level in this group is different from that of the general population. Use significant significant level of 0.05

5. Suppose that a water tank is shaped like a right circular cone with the tip at the bottom, and has height 10 meters and radius 2 meters at the top. If the tank is full, how much work is required to pump all the water out over the top?

4. A spring has a natural length of 18 inches and a force of 201 lbs is required to stretch and hold the spring to a length of 24 inches. What is the work required to stretch the spring from a length of 21 inches to a length of 26 inches?

3. A force of F(x)=x²-cos(3x) +2, x is in meters, acts on an object. What is the work required to move the object from x=3 to x=7?

3) Solve the area bounded by the curve y = 4x-x and the lines x = -2 and y = 4.