Math Answers

How many two-digit numbers can be formed from the digits 1, 2, 3 and 4 if

a. no digit is repeated in any number?

b . repetitions are allowed?

Two functions f : R → R and g : R → R are defined by f(x) = 5x3 + 1 and g(x) = 2x − 3 for all x ∈ R.

Determine the inverse of (f -1 ◦ g) and (g ◦ f )(2) and ( f ◦ g)(2).

Solve the inequalities. Give your answer in interval notation, and indicate the answer

geometrically on the real-number line.

a. t + 6 ≤ 2 + 3t

b. 3(2 – 3x) > 4(1 – 4x)

In the following problems, perform the operations and simplify as much as possible.

a. (x2 + 2x)/(3x2 – 18x + 24) ÷ (x2 – x – 6)/(x

2 – 4x + 4)

b. (x2 + 6x + 9)/x/(x + 3)

c. 1/(3x – 1) + x/(x2 – 9)

Let the function f : R → R and g : R → R be defined by f(x) 2x + 3 and g(x) = -3x + 5.

a. Show that f is one-to-one and onto.

b. Show that g is one-to-one and onto.

c. Determine the composition function g o f

d. Determine the inverse functions f -1 and g -1 .

e. Determine the inverse function (g o f) -1 of g o f and the composite f -1 o g -1 .

A ship is 20km west of another ship B. If a sails at 10km/hr. and at the same time B sails north 30km/hr. Find the rate of change of distance between them at the end of half hour.

Using the number 5, 10, 15, 20, 25, and 30 as the element of the population, construct the sampling distribution of the sample means with a sample size of 2. Find the population and sample mean, population and sample variance, and population and sample standard deviation.

According to NSC statistics,the life expectancy of Filipino women is 70.1 years. Suppose a random sample of 30 women in town B yields a mean of 72.5 years with a population variance of 4.76 years, would you say that the life expextancy of the women in town B is greater than the average?Formulate the null and alternative hypothesis and in symbol.

Seven hundred tickets will be sold and these will be raffled during the fiesta of Brgy. Masiete. One of these tickets will win ₱10,000 and the rest will win nothing. What will be the expected value and variance of your gain if you will buy one of the tickets?

A classroom teacher hypothesizes that using lecture method in teaching specific lesson is the same as teaching it using demonstration method in terms of students learning. This means that students who were taught using the lecture method would perform similary(say on test)than those were taught using demonstration method. Formulate the null and alternative hypothesis in sentence and in symbol.