Math Answers

Kagiso wants to buy a new gaming computer for R40 000.He decides to save by depositing an amount of R400 quarterly into an amount earning 16% intrest per year, compounded quarterly. Thr approximate number of quarter's it will take kagiso to have R40 000 available is?

The value of a delivery van depreciates at the rate of 15% per year. Show that

annual depreciation follows a geometric progression, and use this progression

to determine the value of the van after three years, if it is purchased for $4500?

Inayah is making a board game that is 16 inches by 24 inches. She wants to use square tiles. What is the largest tile she can use? Briefly explain the technique you used to solve this question.

An electronic company in Laguna manufactures resistors that have a mean resistance of 120 ohms and a standard deviation of 13 ohms. Find the probability that a random sample of 40 resistors will have an average resistance greater than 114 ohms.

Two samples consisting of 21 and 9 observations have variances given by s 1 2 =16 and s 2 2

=8 respectively. Test the hypothesis that the first population variance is greater than the

second at a (a) 0.05, (b) 0.01 level of significance.

Maximise 1170x1 + 1110x2

Subject to: 9x1 + 5x2 ≥ 500

7x1 + 9x2 ≥ 300

5x1 + 3x2 ≤ 1500

7x1 + 9x2 ≤ 1900 2x1 + 4x2 ≤ 1000 x1, x2 ≥ 0

-Find graphically the feasible region and the optimal solution.

Test whether the series ∞Σn=0 1/(n^5+x^3) converges uniformly or not

Show that the function f defined on [0,1] by f(x)= (-1)^(n-1) for 1/(n+1) < x/n ≤ 1/n where (n=1,2,3...) is integrable on [0,1]

10. Determine the probability density function for the cumulative distribution function

shown below.

F {0, x < −2

0.25x + 0.5, −2 ≤ x < 1

0.5x + 0.25, 1 ≤ x < 1.5

1 x > 1.5

Determine also the following probabilities.

(a) P(X > −1)

(b)P(X < 1.3)

(c) P(−1.5 ≤ X ≤ 1.8)

(d)P(X < 1.5)

From the probability mass function f(x) =2x+1/25

for x = 0,1,2,3,4, find the

cumulative distribution function of the random variable X. Using F(x), determine

the following probabilities.

(a) P(X ≤ 1)

(b)P(2 ≤ X < 4)

(c) P(X < 3)