Math Answers

Differentiate the function 𝑓(𝑥) = (3𝑥 + 1) 4 (2𝑥 − 1) 5 and simplify your answer

Find 𝑑𝑦 𝑑𝑥 if 𝑦 = 𝑢 3 − 3𝑢 2 + 1 and 𝑢 = 𝑥 2 + 2 

The division-wide aptitude test in

Mathematics was conducted to students.

The mean of the test is 58 and the standard

deviation is 12. The scores also approximate

the normal distribution. What percent of the

scores is between 55 and 65?

A. 9.87%

B. 18.23%

C. 21.90%

D. 31.77%

If a sample of 10 cups of ice cream is selected, what is the probability that the mean of the sample will be larger than 670 mg? 

Question :

The “Titans” cricket team has a winning rate of 75%. The team is planning to play 10 matches in the next season.

a)    Let X be the number of matches that will be won by the team. What are the possible values of X?

b)    What is the probability that the team will win exactly 6 matches?

c)    What is the probability that the team will lose 2 or less matches?

d)    What is the mean number of matches that the team will win?

e)    What are the variance and the standard deviation of the number of matches that the team will win?

Doubt in (c) = What is the probability that the team will lose 2 or less matches?

(Here, do we have to use P(X less than equal to 2)?

A dice is tossed 120 times with the following

results.

Number turned up 1 2 3 4 5 6 Total

Frequency 30 25 18 10 22 15 120

Test the hypothesis that the dice is un biased.

Using weiestrass M-test, show that the following series converges uniformly.

∞

∑n^3X^n,X belongs to[-1/3,1/3]

n=1

A manufacturer estimates that when q units of a certain commodity are produced, the total cost will be

C(x) rand where

C(q) = q2

25 + 80 000 − 104q.

Answer the following questions:

(i) Use marginal analysis to determine the production level at which the cost will be a minimum.

(ii) Determine the minimum cost.

A restaurant owner is concerned about the amount of time customers must wait before being served over

weekends. He collects data on the waiting times, to the nearest minute, of 20 tables on Friday evening and

15 tables on Saturday evening.

The average waiting time on Friday evening is 24 minutes per table.

The total waiting time for the 15 tables on Saturday evening is seven hours and three

quarters of an hour.

The mean waiting time per table for Friday and Saturday evening, rounded to the nearest minute, is

The ages (in years) of 50 individuals on a mailing list, in ascending order are:

10 11 13 14 14 15 15 17 18 20

20 21 22 24 26 26 26 27 29 30

31 31 33 34 36 36 36 37 38 39

40 41 41 43 44 45 45 46 47 48

49 51 53 55 57 58 59 59 60 60

Consider the frequency table for the data:

A B C D

Interval Frequency Frequency Frequency Frequency

0,5 – 15,5 5 7 7 5

15,5 – 30,5 14 13 12 15

30,5 – 45,5 16 17 18 14

45,5 – 60,5 15 13 13 16

The column that represents the correct frequencies for the data is

[1] A

[2] B

[3] C

[4] D