Math Answers

Suppose that in t hours, a truck travels s(t) miles, where s(t)= 10t² . Find the average rate of change of distance with respect to time from t1 = 2 and t2 = 5.

1.1 Prove that the characteristic polynomial of a 2 × 2 matrix A can be expressed as

λ^2 − tr(A)λ + det(A), where tr(A) is the trace of A.

1. The number of accidents in a production facility has a Poisson distribution with a mean of 2.7 per month. For a given month, what is the probability that there will be more than three (3) accidents?

1. The blood groups of 200 people are distributed as follows: 40 have type A blood, 75 have type B blood, 60 have type O blood, and 25 have type AB blood. If a person from any of the group is selected at random, what is the probability that this person has an O blood type? How about the AB blood type?

The Following are the heights of four students in centimeters. Suppose samples of size 2 ae taken from this population of four students.

cardo-125 cm

alyana-120cm

joaquin-130 cm

flora-110 cm​

a. How many samples are possible? List them and compute the mean of each sample?

b. Construct the sampling distribution of the sample means

c. Construct the histogram of the sampling distribution of the sample means

You have a bag of marbles. 5 yellow, 5, green, 5

purple, 5 black, and 5 red. What is the

probability of pulling out a purple marble,

replacing it, then pulling out a black marble?

5

6

7

a division wide aptitude test in mathematics was conducted to 1,000 pupils the mean of the test is 58 and the standard deviation is 12. find the z-value that corresponds to a score x = 70. draw the normal curve distribution. what is your conclusion regarding the scores of the pupils

The volume of a cube is increasing at a rate of 1200 cm3/min at the

moment the lengths of the sides are 20 cm. How fast are the lengths of

the sides increasing at that moment?

[8]

1. Let f be the function defined by

f (x) = x2

-------------

(2x + 1)2

:

(a) Determine the vertical and horizontal asymptotes (show all limits). (4)

(b) Use the sign pattern for f ' (x) to determine

(i) the interval(s) over which f rises and where it falls; (4)

(ii) the local extrema. (2)

(c) Use the sign pattern for f " (x) to determine

(i) where the graph of f is concave up and where it is concave down. (4)

(ii) the inflection points (if any) (2)

3. A division wide aptitude test in Mathematics was conducted to 3 800 students. The mean of the test is 58 and the standard deviation is 14.

a. What is the score that divides the distribution into two such that 80% of the cases is below it.

b. What are the scores that bounds the middle 90% of the distribution.

c. How many scores are between 60 and 96?

d. How many students belong to the top 12% of the examinees?