
In each of Problems 1 through 10, use elementary row and column operations to simplify the task of evaluating the determinant by cofactor expansions. If

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- 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…arrow_forward(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.arrow_forwardDungeons 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.arrow_forward
- 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?arrow_forwardQ4. Considering the following two normal distributions A and B, which statement (or statements) is correct? a) Mode of the distribution A is larger than that of distribution B. b) SD of the distribution B is larger than that of distribution A. c) Mean of the distribution A is smaller than that of distribution B. d) A data item with z-score of -1 falls between 20 to 30 in distribution A. e) A data item with z-score of +1 falls between 10 to 20 in distribution B. A 0 10 20 30 40 40 50 60 00 10 70 B 80 90 100arrow_forwardQ1. A traffic camera recorded number of red cars going through the intersection at 16th Ave N and Centre St. each day over 7 days was: 32 30 24 30 36 38 27 a) Calculate the mean, mode, range and median of the data set above. c) Calculate the standard deviation of this data set. Sarrow_forward
- Q2. Government of Canada is designing Registered Retirement Saving Plans (RRSP) for Canadians. According to statistics Canada, the life expectancy in Canada is 86 years with standard deviation of 4.8 years. a) Find the z-score of a person who is 90 years old? b) Find the age of a person whose z-score is -1.4? c) What percent of people age higher than 80? d) What percent of people age less than 83? e) What percent of people age between 85 and 88?arrow_forwardSafari File Edit View History Bookmarks Window Help Ο Ω OV O mA 0 mW ర Fri Apr 4 1 222 tv A F9 F10 DII 4 F6 F7 F8 7 29 8 00 W E R T Y U S D பட 9 O G H J K E F11 + 11 F12 O P } [arrow_forwardSo confused. Step by step instructions pleasearrow_forward
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