Math Answers

The lengths (in minutes) of a random selection of popular children’s animated films are

listed below. Estimate the true mean length of all children’s animated films with 95%

confidence.

90 84 83 91 75 88 78 96 78 79 77

Given r1 = 3i − 4j + 3k, r2 = 5i + 3j − 6k, r3 = 2i + 7j + 3k and r4 = 4i + 3j + 5k.

Find the scalars a, b and c such that r4 = ar1 + br2 + cr3

2. Changes in airport procedures require considerable planning. Arrival rates of aircraft are important factors that must be taken into account. Suppose small aircraft arrive at a certain airport, according to a Poisson process, at the rate of 5 per hour. Thus, the Poisson parameter for arrivals over a period of hours is μ = 5t.

(a) What is the probability that exactly 4 small aircraft arrive during a 1-hour period?

(b) What is the probability that at least 4 arrive during a 1-hour period?

(c) If we define a working day as 12 hours, what is the probability that at least 75 small aircraft arrive during a working day?

Let the function f : R → R and g : R → R be defined by f(x) 2x + 3 and g(x) = -3x + 5.

a. Show that f is one-to-one and onto.

b. Show that g is one-to-one and onto.

c. Determine the composition function g o f

d. Determine the inverse functions f ^-1 and g ^-1 .

e. Determine the inverse function (g o f) ^-1 of g o f and the composite f ^-1 o g ^-1

Every continuous function is differentiable.

True or false with full explanation.

Solve the inequalities. Give your answer in interval notation, and indicate the answer geometrically on the real-number line.

a) t + 6 ≤ 2 + 3t

b) 3(2 – 3x) > 4(1 – 4x) 

Determine the digit 100 places to the right of the decimal point in the decimal representation 7/27. (Apply Polya’s Strategy)

Activity 1: Draw Me

Directions: Given the following information, construct the rejection region. Show the solution in a step-by-step procedure.

1. H0 : = 84

Ha : 84

m= 87, s= 10, n = 35, alpha= 0.05

2. H0 : = 45

Ha : < 45

m= 40, s = 12, n = 32, alpha= 0.01

The average zone of inhibition (in mm) for mouthwash L as tested by the medical technology students has been known to be 9mm. A random sample of 10 mouthwash L was tested and the test yielded an average zone of inhibition of 7.5mm with a variance of 25 mm. Is there enough reason to believe that the anti-bacterial property of the mouthwash has decreased? Test the hypothesis that the average zone of inhibition of the mouthwash is no less than 9mm using 0.05 level of significance.

A. State the hypotheses.

B. Determine the test statistic to use.

C. Determine the level of significance, critical value, and the decision rule.

D. Compute the value of the test statistic.

E. Make a decision.

F. Draw a conclusion.

If the average time spent studying is 10 hours and the standard deviation is 4 hours, what it the probability that a student will spend more than 13 hours studying?