Math Answers

Which of the following is a linear equation in x; y and z?

1. −x−1 + e−

√

2y = 3z, where e = 2.71828 ....

2. 2π ln(e−1

z ) − 2y + z = ln(3) − x.

3.

p

y2 + 4y − 2z = 7x.

4. y + 4y − 2z = 7x−2.

QUESTION 2 2.1. Find the change of basis matrix P∁←ℬ for the bases

ℬ = {(9, 2), (4, −3)} and ∁= {(2, 1), (−3, 1)} of ℝ2 .

2.2.Verify [v]∁ = P∁←ℬ[v]ℬ for v = (−5, 3). 

QUESTION 1 Find the coordinate vector [p(x)]ℬ of p(x) = 5 − x + 3x 2 with respect to the basis ℬ = {u1, u2, u3 } of P2 where u1 = 1 − x + 3x 2 , u2 = 2 and u3 = 3 + x 2

Say True or False with proof

Q1. If 𝑓(𝑥) = 2|𝑥 − 1| and 𝑔(𝑥) = 3𝑥 − 10,

then 𝑓𝑜𝑔(1) = 12.

Q2. (√2, 1,1/2)∈ 𝑸 × 𝒁 × 𝑹.

Q3. The domain of the function f defined by 𝑓(𝑥)

=√{(3-x)/(x-2)} is R-{2}.

How many key comparisons are required during a search from the root node to find whether the key "8" is stored in the binary search tree constructed from the following sequence of insertion:

17,7,11,9,22,3,8,35,16,6

A weight A pound on one side of a beam balances a weight of 40 pounds placed 6 feet from the fulcrum on the other side. If the unknow weight is moved 3 feet nearer the fulcrum, it balances a weight of 20 pounds place 7 1/2 feet from the fulcrum. Find the unknow weight and its distance from the fulcrum in the first instance. (Neglect the weight of the beam.)

Given a die, it has 6 faces in which each face has either dot/s of 𝑥=1,2,3,4,5 𝑎𝑛𝑑 6. Given it as the population, consider sample of size 𝑛=3. Find the population mean, population variance, population standard deviation, the mean, variance and standard deviation of the sampling distribution of the sample mean and illustrate its probability histogram of the sampling distribution of the sample means

Given a die, it has 6 faces in which each face has either dot/s of 𝑥=1,2,3,4,5 𝑎𝑛𝑑 6. Given it as the population, consider sample of size 𝑛=3. Find the population mean, population variance, population standard deviation, the mean, variance and standard deviation of the sampling distribution of the sample mean and illustrate its probability histogram of the sampling distribution of the sample means

Identify the region/area under the normal curve corresponding to each of the following.

1.Between Z=0 and z=1.36

2.between z=0 and z=1.87

3.between z=1.36 and z= 2.5

4.between -1.36 and z= -1.87

5. Between z=-1.36 and z=2.5

6.between z=1.36 and z=-2.5

A sample of 250 workers aged 16 and older produced an average length of time with the current employer of 4.4 years with standard deviation of 3.8 years. Construct a 99.9% confidence interval for mean job tenure of all workers aged 16 or older​