Math Answers

1. Find the general solution of the differential equation using the method

of variation of parameters y′′ + 4y = 4sec(2x)

It is required to inclose a rectangular field by a fence and then to divide it into two lots by a fence parallel to one of the sides. If the area of the field is given, find the ratio of the sides so that the total length of fence shall be a minimum.

1. Use double integration to find the volume of the solid bounded from above by the paraboloid z = 9x2 + y2, below by the plane z = 0, laterally by y=x^2 and y=x.

The weights (in kg) of Grade 11 ICT follow a normal distribution and has a mean of 52 and standard deviation of 6. How many students have weights greater than 55?

A small-time bingo card costs P100.00 for 5 games. The prize for the first three games is P5,000.00, the fourth is P10,000.00 and the last prize is P20,000.00. If 1,000 bingo cards are going to be sold and you could only win once, what is the expected value of a ticket? With explanation.

The average height of students in a freshman class of a certain school has been 168.67 cm with a population standard deviation of 8.67 cm. Is there a reason to believe that there has been a change in the average height if a random sample of 49 students in the present freshman class has an average height of 155.04 cm? Use a 0.1 level of significance.

What are the given? Write only the number. :

population mean:Blank 1 cm

population standard deviation:Blank 2 cm

sample size:Blank 3

sample mean:Blank 4 cm

level of significance:Blank 5

What are the critical values? Write the positive critical value first then the negative.

z:Blank 6 andBlank 7

What is the value of the calculated z? Round your answer to the nearest hundredths.

z:Blank 8

null hypothesis a nutrionist claims that the average amount of vitamin b in a bread is more than 5grams

Determine whether each of these functions from Z to Z is one-to-one.

a. f(n) = n2

+ 1

b. f(n) = n

In a random sample of 300 patients, 21 experienced nausea. A drug manufacturer claims that fewer than 10% of patients who take its new drug for treating Alzheimer’s disease will experience nausea. Test this claim at the 0.05 significance level. What is the appropriate null hypothesis for this situation

The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400. a. What is the probability of getting more than 12,000 hits?