Math Answers

Solve using basic differentiation rule

𝑠 = (𝑡^2 − 3)^4

Solve using basic differentiation rule

𝑔(𝑥) =3−2𝑥/3+2𝑥

Consider the real space R³

 The following vectors form a basis S of R^3:

u1 = (1, −1, 0), u2 = (1, 1, 0), u3 = (0, 1, 1)

Find the coordinate vector [v] of v = (5, 3, 4) relative to the basis S .

Let 

L(x,y

) be the statement “xl loves y,” where the universe of discourse for both x and y consist of all people in the world. Express each of these quantifications in English.  (a)    

Every body loves somebody.

 (b)   

There is somebody whom everybody loves.

 (c) There is somebody whom Lynn does not love. 

A mathematics teacher in senior high school developed a problem-solving test to randomly selected 40 grade 11 students. These students had an average score of 85 and a standard deviation of 5. If the population had a mean score of 90 and a standard deviation of 3, use 5% level of significance to test the hypothesis.

A ball is drawn from a box containing 6 red balls, 4 white balls and 5 black balls . What is the probability that it is not red ball?

Consider a population consisting of 2, 4, 6, 8 and 10. Suppose samples of size 3 are drawn from this population.

a. Describe the sampling distribution of the sample means

b. What are the mean and variance of the sampling distribution of the sample means? c. Construct a histogram for the sampling distribution.

An insurance company found that 45% of all insurance policies are terminated before their maturity

date. Assume that 10 polices are randomly selected from the company’s policy database. Assume a

Binomial experiment.

Required:

a) What is the probability that eight policies are terminated before maturity?

b) What is the probability that at least eight policies are terminated before maturity?

c) What is the probability that at most eight policies are not terminated before maturity?

Consider a population with values 1, 2, 3, 5, 7, 11

a. Find the population mean

b. Find the population variance

c. Find the population standard deviation.

d. Find all possible samples of size 4 which can be drawn with replacement from this

population

e. Find the mean of the sampling distribution.

f. Find the variance of the sampling distribution of means.

g. Find the standard deviation of the sampling distribution of means

Find the area, take the elements of the area perpendicular to the x-axis. x²-y+1=0; x-y+1=0.