Math Answers

A. Determine if 1781 is divisible by 3, 6, 7, 8, and 9. (5 items x 2 points)

B. Determine if each of the following numbers is a prime or composite.

6. 828

7. 1666

8. 1781

9. 1125

10. 107

C. Find the greatest common divisor of each of the following pairs of integers.

11. 60 and 100

12. 45 and 33

13. 34 and 58

14. 77 and 128

15. 98 and 273

D. Find the least common multiple of each of the following pairs of integers.

16. 72 and 108

17. 175 and 245

18. 150 and 70

19. 32 and 27

20. 540 and 504

Consider all samples of size 4 from this population: 3, 6, 10, 13, 15, 20

a. Make a sampling distribution of the sample means

b. Compute the mean of the sample means

c. Compute the variance and standard deviation of the sample means

Let f:[ 0,π/2] → [-1,1] be a function defined by f(x)= cos 2x . Verify that f satisfies the condition of the inverse function theorem. Hence, what can you conclude about the continuity of f^-1?

Prove that the sequence (fn(x)), where fn(x)= nx/(1+ nx^2) is not uniformly convergent in [-2,2]

You are working as a Junior Engineer for a small motor racing team. You have been given a proposed mathematical model to calculate the velocity of a car accelerating from rest in a straight line. The equation is: 𝑣(𝑡) = 𝐴 (1 − 𝑒 − 𝑡 𝑡𝑚𝑎𝑥𝑠𝑝𝑒𝑒𝑑)

Ascari A10 5.0 V8 - [2006] t=2.8 tm(400)= 10.36 tmaxspeed= 7.8

derive an equation a(t) for the instantaneous position of the car as a function of time? Identify the acceleration of the car at t = 0s and asymptote of this function as t → ∞?

2. Survey tests on leadership skills and self-concept were administered to student-leaders.

Both tests use a 10-point Likert Scale, with 10 indicating the highest scores for each test.

Scores for the student-leaders on the tests follow:

Student Code: A B C D E F G H I J

Self-concept : 9.5 9.2 6.3 4.1 5.4 8.3 7.8 6.8 5.6 7.1

Leadership Skill :9.2 8.8 7.3 3.4 6.0 7.8 8.8 7.0 6.5 8.3

a. Compute the correlation coefficient r.

b. Interpret the results in terms of (a) strength and (b) direction of correlation.

c. Find the regression line that will predict the leadership skill if the self-

concept score is known.

d. Predict the leadership skill of a student leader whose self-concept skill is

1.5.

A student conducted a regression analysis between the math grades of his classmates

and the number of times they were absent in the subject. He found that the regression

line y = 97.732 – 2.61x will predict grade (y) if the number of absences (x) is known.

a) What is the predicted grade of a student who has no absences?

b) What is the predicted grade of a student who has ten absences?

c) Sketch the graph of the line predictor.

At the beginning of the first day (day 1) after grape harvesting is completed, a grape grower has 8000 kg of grapes in storage. On day n, for n = 1, 2, . . . , the grape grower sells 250n/(n + 1) kg of the grapes at the local market at the price of $2.50 per kg. He leaves the rest of the grapes in storage where each day they dry out a little so that their weight decreases by 3%. Let wn be the weight (in kg) of the stored grapes at the beginning of day n for n ≥ 1 (before he takes any to the market).

(a) Find the value of wn for n = 2.

(b) Find a recursive definition for wn. (You may find it helpful to draw a timeline.)

(c) Let rn be the total revenue (in dollars) earned from the stored grapes from the beginning of day 1 up to the beginning of day n for n ≥ 1. Find a recursive formula for rn.

Suppose that the bank customers arrive randomly and independently on an average of 3.2

customers every 4 minutes. What is the probability that:

a. Exactly two customers arrive in every 4 minutes?

At a certain college, it is estimated that approximately 19% of the students ride bicycles to school. Would you consider this to be valid estimate if, in a random sample of 85 college students, 20 are found to ride bicycles to class