Math Answers

 If Universal Set U = {90, 91 , 92 , 93 , 94, 95 , 96 , 97 , 98, 99 , 100} (10)

 A = {90, 92, 94, 96, 98, 100}, 

 B= {91, 93, 95, 97, 99}, 

 C = {90, 94, 98}

 1.4.1 What is (A ∩ C)c 

 1.4.2 What is(B ∪ C)c

Three points with position vectors, b and c are said to be colinear. If the parallelogram with adjacent sides a - b and a - c has zero geometry area. Use this fact to check whether or not the following triples of points are collinear

(a) (2,2,3), (6,1,5) (2,4,3)

(b) (2,3,3), (3,7,5), (0,-5,-1)

(c) (1,3,2), (4,2,1), (1,0,2)

Problem 1: Use the tabular method to determine if the limits of the following functions exist:

a) lim𝑥→3 2/(𝑥−3)^2

b) lim𝑥→3 2/(𝑥−3)^3

Use the method of disks/rings to determine the volume of the solid obtained by rotating the region bounded by y=2x^2 and y=x^3 about the x-axis.

1. If a student randomly guesses at five multiple-choice questions, find the probability that the student gets exactly three correct. Each question has five possible choices.

a chip is placed at room temperature of 40°c after minutes its temperature changes from 80c to 60c the proportionallity constant in case is k=0.05 ln2 find temperture of chip after 40 minute.

Check whether 𝑇 ∶ ℝ2 → ℝ2

, defined by 𝑇 (𝑥, 𝑦) = (−𝑦, 𝑥) is a linear transformation.

Left-tailed test, variance unknown, 𝛼 = 0.01, n = 23

A population consists of the five numbers 2, 3, 6, 8, and 11.

Consider the samples of size 2 that can be drawn from this

population.

A. List all the possible samples and the corresponding mean.

B. Construct the sampling distribution of the sample mean.

Suppose that the racial/ethnic distribution in a large city is given by the table that follows.

Black Hispanic Other

20% 15% 65%

Suppose that a jury of twelve members is chosen from this city in such a way that each resident has an equal probability of being selected independently of every other resident.

Lets find probability that the jury contains:

a. three Black, two Hispanic, and seven other members.

b. four Black and eight other members.

c. at most one Black member.