Find an equation for the nth term of the sequence. -1, -4, -16, -64, … (7 points)  

(05.02 LC)  The Central Limit Theorem says that when sample size n is taken from any population with mean μ and standard deviation σ when n is large, which of the following statements are true? (4 points) The distribution of the sample mean is exactly Normal. The distribution of the sample mean is approximately Normal. The standard deviation is equal to that of the population. The distribution of the population is exactly Normal.

(05.02 LC)  The Central Limit Theorem says that when sample size n is taken from any population with mean μ and standard deviation σ when n is large, which of the following statements are false? (4 points) The distribution of the sample mean is exactly Normal. The distribution of the sample mean is approximately Normal. The standard deviation is equal to that of the population. The distribution of the population is exactly Normal.

(05.01 MC)  Suppose we select a simple random sample of size n = 125 from a large population with a proportion p of successes. Let p̂ be the proportion of successes in the sample. For which value of p is it appropriate to use the Normal approximation for the sampling distribution of p̂? (4 points)

Write the sum using summation notation, assuming the suggested pattern continues. 8 + 27 + 64 + 125 + … + n3 (7 points)

(05.01 MC) Mateo is roasting a chicken. He must make sure the chicken has a minimum internal temperature of 165 degrees so that it is safe to eat. Using a thermometer, he takes the temperature of the chicken in three random places. The minimum temperature in the sample is 172 degrees. Identify the population and the sample. (4 points)

(05.02 MC)  The amount of cream sauce on the fettuccine at Al Fred-O’s follows a Normal distribution, with a mean of 3.78 ounces and a standard deviation of 0.14 ounce. A random sample of 12 plates of fettuccine is selected every day and the sauce is measured. What is the probability that the mean weight will exceed 3.81 ounces? (4 points)

A beam is singly reinforced with the reinforcement in two rows. The bottom row contains 10 No. 7 bars at a depth of 16 in. The top row contains 8 No. 7 bars at a depth of 12.5 in. Determine the effective (centroidal) depth, d, of the steel.

The moment-curvature relationship is non-linear up to the cracking point and is referred to as the uncracked-elastic range.

A beam has dimensions of b = 18 in., h = 28 in., and d = 25.5 in. and is reinforced with 4 No. 7 bars. The concrete strength is 8,200 psi, and the yield strength of the reinforcement is 60,000 psi. If the depth to the neutral surface is c = 1.76581 in., determine the strain in the reinforcement.