Math Answers

Determine if the following are probability distributions (if no, state why).

a. x 3 6 9 12 15

p(x) 4/10 2/10 1/10 1/10 1/10

b. x 1 2 3 4 5

p(x) 3/15 1/15 1/15 4/15 6/15

c. x 20 30 40 50

p(x) 1.1 0.2 0.9 0.3

Question text

Madison usually receives 4 letters in the mail each week. Find the probability of receiving 8 letters for the next 2 weeks.

a population consists of the five measurements 2, 6, 8, 3 & 1. how many different samples of size n=2 can be drawn from the population? what is the mean & variance of the sampling distribution of the sample means

I would like to ask for help with discrete mathematics, especially two's complement

1. Using two’s complement representation throughout your calculation, find 31 – 19. 
2.     Using Euclidean algorithm, find the GCD of 123 and 411.  

1.  How many ways can you pick a president, vice-president, and secretary from a group of six boys and five girls if 

a) there are no restrictions?

b) there must be at least one boy chosen?

c) there must be only one girl chosen?

Side effects A drug manufacturer claims that less

than 10% of patients who take its new drug for treat-

ing Alzheimer’s disease will experience nausea. To

test this claim, researchers conduct an experiment.

They give the new drug to a random sample of 300

out of 5000 Alzheimer’s patients whose families have

given informed consent for the patients to participate

in the study. In all, 25 of the subjects experience

nausea. Use these data to perform a test of the drug

manufacturer’s claim at the a = 0.05 significance

level.

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