Math Answers

Let 𝐴 and 𝐵 be two events. Suppose that the probability that neither event occurs is 3

8. What is the probability that at least one of the events occurs?

Let 𝐶 and 𝐷 be two events. Suppose 𝑃(𝐶) = 0.5, 𝑃(𝐶 ∩ 𝐷) = 0.2 and 𝑃((𝐶 ∪ 𝐷)′) = 0.4. What

is 𝑃(𝐷)?

1. Find the quadrant in which P(t) lies if sec t > 0 and csc t < 0.

2. Find the values of the 6 trigonometric functions of -7π/3.

3. Find the value of tan 7π/3 .

4. If sin t=√3/2 and cos t<0, find csc t.

5. Find the six trigonometric functions of an angle whose terminal side passes

through (-4,-3).

6. Find the remaining functions given that sin ϴ=513, sec t<0.

7. Find ϴ, if cot 2ϴ= √3, ϴ∈[0°,360°].

8. A ladder leans against the side of a building with its foot ten feet from the building. How far from the ground is the top of the ladder and how long is the ladder if it makes an angle of 60° with the ground?

9. At a certain moment Ship MV Alpha is 7.5 km. west of Ship MV Omega. Ship MV Omega is sailing S 30° 20’ E at the rate of 25 km./hr., while Ship MV Alpha is sailing directly north at rate of 20 km./hr. Find the distance between the two ships and the bearing with Ship MV Omega from Ship MV Alpha after 40 minutes.

Boxes of chocolates are produced with a mean weight of 510 g. Quality control checks show that 1 % of boxes are rejected because their weight is less than 485 g.

a Find the standard deviation of the weight of a box of chocolates.

b Hence find the proportion of boxes that weigh more than 525 g.

Find the area under the normal curve Between 𝑧 = −2.46 and 𝑧 = 1.55

How long does it take for 900 to accumulate to 1000 under an interest rate of 4% per annum?

A vendor claims that the variance for measurement of tiles that his factory produce were 13 square feet. A sample of nine tiles was measured in square feet and the results of the tiles produced were recorded as below:

204.5 206.3 202.4 207.8 203.1 206.2 203.8 206.6 205.8

(Assuming the sample comes from a normal population)

i) Calculate the point estimate of the population mean. (2 marks)

ii) Compute the variance and standard deviation. (3 marks)

iii) Determine the estimate of 95% confidence interval for the population mean of the tiles. (5 marks)

Prove that an ideal M neq R in a commutative ring R with identity is maximal if and only if for every r in R-M, there exists x in R such that 1_R - rx in M.

a population consistent of two numbers (3,7) consider all possible samples of size n=3 which can be drawn with replacement from the population

a person may earn 100,000.00 by investing in the stocks of an international company with a probability of 0.40 or lose 35,000,00 over the same period with a probability of 0.60. Let X denote the net gain of a perspn who will invest in the company construct the probability distribution of X, and the compute for the expected value of a person who will invest in the same company. ​

The following data give the numbers of orders received for a sample of 30 items at the Time-saver Mail Order Company.

34 44 31 52 41 47 38 35 32 39

28 24 46 41 49 53 57 33 27 37

30 27 45 38 34 46 36 30 47 50

Using 6 classes of equal width, construct a grouped frequency distribution of the above data. Let 22 be the

lower limit of the initial class.

Question 2 (5 Marks)

Calculate the median.

Question 3 (6 Marks)

Calculate the mid-70% range.

Question 4 (11 Marks)

Calculate the coefficient of variation and interpret the value obtained.