Math Answers

Let 𝐴 and 𝐵 be sets such that 𝐴 ∪ 𝐵 ⊆ 𝐵 and 𝐵 ⊆ 𝐴 . Draw the corresponding Venn

diagram

Question

For sets H and K, we define the intersection H n K by H n K = {xI

X E H and X € K%. Show that if H ≤ G and K < G, then H n K < G.

(Remember: ≤ denotes "is a subgroup of," not "is a subset of.")

The lifetimes of light bulbs produced by a particular manufacturer have a mean of 1,200 hours and a standard deviation of 400 hours. The population distribution is normal. Suppose that you purchase nine bulbs, which can be regarded as a random sample from the manufacturer’s output

a. What is the mean of the sample mean life? (2 marks)

b. What is the variance of the sample mean? (2 marks)

c. What is the standard error of the sample mean? (2 marks)

d. What is the probability that, on average, those nine light bulbs have lives of fewer than 1,050 hours? (4 marks)

verify stoke’s theorem when f = x ^ 2 i + y ^2 j + z ^ 2k ,s is the upper hemisphere

z =√( a ^2 − x ^2 − y ^2)

Determine whether 𝐹 is conservative vector field. If so, find a potential

function for it is

f(x,y,z)=x^yi+5xy^2j

Evaluate using Green’s Theorem ∮ 3𝑥𝑦𝑑𝑥 + 2𝑥𝑦𝑑𝑦, where 𝐶 is the rectangle bounded by

𝑥 = −2, 𝑥 = 4, 𝑦 = 1 and 𝑦 = 2.

4. The mean hemoglobin level in the blood for a certain large group of individuals is 21.0 grams per milliliter (g/ml). The standard deviation is 2 g/ml. If a sample of 25 individuals is selected, find the probability that the mean will be greater than 21.3 g/ml. Assume that the variable is normally distributed.

 Television advertisers value the well-known Radio and TV awards scheme RTP as a measure of a TV/Radio show’s popularity among viewers. The RTP rating of a certain TV program is an estimate of the proportion of viewers, expressed as a percentage, who watch the program on a given day. In one survey, the RTP ratings team found that 101 out of 165 sampled families watched “The KSM Show” on the night of its premiere (the first time it is shown on television). In a separate survey several years later, the RTP ratings team found that 97 out of 180 sampled families watched “Music Music on TV3” on its premiere. (a) Estimate the true proportion p1 of all TV-viewing families who watched the premiere of “The KSM Show” and obtain a 95% confidence interval for p1. (b) Briefly explain what this 95% confidence interval means. (c) If the RTP team wanted to guarantee that all proportions are estimated to within ±0.05 with 95% confidence, how large should their samples be?

The class gained a mean of μ = 24 and a standard deviation of a = 8.48 and X= 6

a. What percentage of scores are lower than your score? Show Steps 1 to 4 completely.