Math Answers

Two pipes empty a vat in 1hr and 12 min. When one pipe is used to fill and one to empty the vat, it is filled in 3 hrs. How long would it take each pipe to empty the vat if only one pipe is open?

It is claimed that the average weight of babies at birth is 3.4 kg. The average weight of the random

sample of 30 newly born babies was determined. It was found out that the average weight was 3.1 kg.

Is there a reason to believe that the average weight of babies at birth is not 3.4 kg.? Assume that the

population standard deviation is 1.1 kg. Use the 0.05 level of significance

1) What are the null hypotheses and alternative hypotheses of the research scenario?

2) What is the level of significance?

3) What is the test statistic?

4) What is the critical value in the scenario?

5) What could be the conclusion?

The Head of the Math Department announced that the mean score of Grade 11 students in the first

midterm examination in Statistics and Probability was 89 and the standard deviation was 12. One

student believed that the mean score was less than this, randomly selected 34 students and computed

their mean score. She obtained a mean score of 85. At 0.01 of level of significance, test the student’s

belief.

1) What are the null hypotheses and alternative hypotheses of the research scenario?

2) What is the level of significance?

3) What is the test statistic?

4) What is the critical value in the scenario?

5) What could be the conclusion?

An experiment involves studying the composition of genders of a set of triplets.what is probability that there are 2 boys and a girl in the sets

How many different permutations can be made from the letters in the word "CHICHARITO"

If the probability that it may rain tomorrow is 2/5, what is the probability of that it may not rain

Consider the composition of a 3-child family in which the children were born at different times but a girl is as likely as a boy at each birth.what is the probability that the oldest child and the youngest are of the same gender

Determine where the global extrema of  f(x)=3x^2/3−2x

on the interval [−1,1] occur.

Find the global maximum and minimum values of the following function on the given interval. If there are multiple points in a single category list the points in increasing order in x value and enter N in any blank that you don't need to use.

f(x)=4e−x−4e−2x  [0,1]

Global maxima

x = ____ Y=___

x=_____ Y=____

x=____ Y=___

Global minima

x=____ Y=___

x=____ Y=___

x=___ Y=___

x=____ Y=___

12. To determine the weights of w1, w2 and w3 of three objects A1, A2 and A3, the following weighing

design was adopted. The objects were first weighed separately (A1 then A2 then A3) and then all

three (A1, A2 , A3) using ordinary two-parts balance. If the balancing weights in these four weighing

are denoted by x1, x2, x3 and x4 respectively with the expected values and variances given by

E(x1) = w1, E(x2) = w2, E(x3) = w3

E(x4) = w1 + w2 + w3

and

V ar(xi) = iσ2,

i = 1, 2, 3.

(a) By an appropriate method of estimating w1, w2, and w3, generate their normal equations and

present in a matrix form.

(b) Hence or otherwise, find the least square estimators of w1, w2, and w3 if V ar(xi) = iσ2,

i =

1, 2, 3.

(c) Given that x1 = 2.2, x2 = 1.7, x3 = 6.0, x4 = 9.5 and σ = 1.5, find the estimates for w1 and

w3.