Math Answers

A professor grades students on 5 quizzes, a project, and a final examination. Each quiz counts as 10% of the quiz grade. The project counts as 20% of the course grade. The final examination counts as 30% of the course grade. Tom has quiz scores of 80, 82, 88, 93 and 90. His project score is 96 and his final examination score is 95. Use the weighted mean formula to find Tom's average for the course *

The derivative of a differentiable function ff(xx) is given as

ff′

(xx) = xx + 3

(xx − 2)2 .

a. Find intervals of increase and decrease for ff(xx).

b. Determine values of xx for which relative maxima and minima occurs on the graph of

ff(xx).

c. Find ff′′(xx) and determine intervals of concavity for the graph of ff(xx).

d. For what values of xx do inflection points occur on the graph of ff(xx).

The raw data has been organised in the frequency table below.

games frequency

6 2

7 5

8 n

9 4

10 4

11 2

12 2

13 2

(a) Write down the value of n.

(b) Calculate the mean number of games played per set.

(c) What percentage of the sets had more than 10 games?

(d) What is the modal number of games?

Q1. Find the density function of Y = e^x if X is normally distributed with mean μ and standard

deviation σ.

Q2. Find the density function of Y = βX^(1/α) where α > 0, β > 0 if X is exponentially distributed

with mean μ = 1.

A random sample of 40 bys showed a mean weight of 120 lbs with a standard deviation of 12 lbs. The standard weight of their average age is about 130 lbs. Test the hypothesis that the selected boys are significantly lighter that the standard weight at 0.01 level of significance.

A. Solve the following problems:

1. On the assumption that variables are continuous, compute for the median of the following data:

a. 1, 4, 5, 9, 11

b. 4, 8, 16, 27, 52

c. 7, 26, 31, 36, 46, 65

2. Calculate the range for the following sets of measurements:

a. 3, 6, 7, 10, 2

b. 11, 27, 32, 45, 54

3. Calculate the variance and standard deviation of the following: 13, 18, 21, 19, 16, 15.

Define Semigroup and Monoid. Show that the set of positive Integer is a monoid for the operation

defined by aOb = max{ a,b}

If binomial distribution X~Bin(50,0.4) coincides with normal distribution X*~N(μ,σ²) , then find the value of μ, σ and

P[X ≤ 5] , P[X ≤ 15] , P[5 ≤ X ≤ 15] , P[5 < X < 15].

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

The drawing below shows a square with side a. A straight line intersects the square and encloses

an area A. The heights x and y on the left and right side (in a distance d from the square) of

the intersecting line can be varied. Assuming that x  y and x; y  a, nd an expression for

the enclosed area A(x; y) with respect to x and y.