Chapter 1.1, Problem 30ES

(28 points) Define T: [0,1] × [−,0] → R3 by T(y, 0) = (cos 0, y, sin 0). Let S be the half-cylinder surface traced out by T. (a) (4 points) Calculate the normal field for S determined by T.

Question 21 of 28 (1 point) | Question Attempt: 5 of Unlimited Dorothy ✔ ✓ 12 ✓ 13 ✓ 14 ✓ 15 ✓ 16 ✓ 17 ✓ 18 ✓ 19 ✓ 20 = 21 22 > How many apps? According to a website, the mean number of apps on a smartphone in the United States is 82. Assume the number of apps is normally distributed with mean 82 and standard deviation 30. Part 1 of 2 (a) What proportion of phones have more than 47 apps? Round the answer to four decimal places. The proportion of phones that have more than 47 apps is 0.8783 Part: 1/2 Try again kip Part ی E Recheck == == @ W D 80 F3 151 E R C レ Q FA 975 % T B F5 10 の 000 园 Save For Later Submit Assignment © 2025 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | Accessibility Y V& U H J N * 8 M I K O V F10 P = F11 F12 . d

(14 points) Let S = {(x, y, z) | z = e−(x²+y²), x² + y² ≤ 1}. The surface is the graph of ze(+2) sitting over the unit disk. = (a) (4 points) What is the boundary OS? Explain briefly. (b) (4 points) Let F(x, y, z) = (e³+2 - 2y, xe³±² + y, e²+y). Calculate the curl V × F.

(6 points) Let S be the surface z = 1 − x² - y², x² + y² ≤1. The boundary OS of S is the unit circle x² + y² = 1. Let F(x, y, z) = (x², y², z²). Use the Stokes' Theorem to calculate the line integral Hint: First calculate V x F. Jos F F.ds.

Q5. Manager of car dealership is trying to see how number of sale associates can affect number of final sales in his dealership. He collects the following information: Number of cars Number of working sale associates per day sold in one day 2 2 3 5 3 3 4 1 3 1 2 4 5 Calculate the correlation coefficient for this data set using the equation given on slide#77? Comment on the association of the two variables. ΣΥ) - Σ) × Σ(Υ) (X) E(Y) N 2 (Σ(x²) - 2x²) × (Σ(12) - ²) N N

You are provided with data that includes all 50 states of the United States. Your task is to draw a sample of: 20 States using Random Sampling (2 points: 1 for random number generation; 1 for random sample) 10 States using Systematic Sampling (4 points: 1 for random numbers generation; 1 for generating random sample different from the previous answer; 1 for correct K value calculation table; 1 for correct sample drawn by using systematic sampling) (For systematic sampling, do not use the original data directly. Instead, first randomize the data, and then use the randomized dataset to draw your sample. Furthermore, do not use the random list previously generated, instead, generate a new random sample for this part. For more details, please see the snapshot provided at the end.) You are provided with data that includes all 50 states of the United States. Your task is to draw a sample of: o 20 States using Random Sampling (2 points: 1 for random number generation; 1 for random sample) o…

(28 points) Define T: [0,1] × [−,0] → R3 by T(y, 0) = (cos 0, y, sin 0). Let S be the half-cylinder surface traced out by T. (a) (4 points) Calculate the normal field for S determined by T.

Dungeons and Dragons: Part A A 20-sided die is often used in tabletop role-playing games like Dungeons and Dragons.  During the game players may face something called a "skill check" where they must roll a 20-sided die and get a result equal to or above a given value.  For example, a player may be required to roll a 15 or above in order to succeed and pass the skill check.  Rolling a 14 or lower would be a failure.  If the player rolls the die 10 times in a row, what is the expected number of rolls that would pass the skill check by rolling as a 15 or higher? For the previous calculations, what is the standard deviation for the number of times the die would be rolled 15 or above During a game of Dungeons and Dragons, the previously-mentioned player rolls the 20-sided die 30 times in total.  What is the probablity that they successfully roll a 15 or higher exactly 7 times during that game? Express your final answer as a percentage to 2 decimal places.

Q3. The distribution for the working lifetime of light bulbs, manufactured in a company, is found to be normally distributed with a mean of 1450 hours and a standard deviation of 60 hours. a) In this distribution, find the life time of a lightbulb whose z-score is -1.8? b) Which percentage of lightbulbs have life time less than 1400 hours? c) Which percentage of lightbulbs have life time greater than 1500 hours? d) Which percentage of lightbulbs have life time between 1420 to 1500 hours?