Math Answers

The salary distribution ('000) of 1000 employees at a certain company is as follows:

Salary (years) frequency

25-39 20

40-49 32

50-59 30

60-64 10

65-69 8

a, Construct the bar-chart of the data

b, Construct the histogram of the data.

The lateral surface area of a given right circular cylinder is twice its volume. If the height of the cylinder is twice its base diameter, determine the volume of the largest sphere you can put on the cylinder. Determine also the difference of the volume of the cylinder and sphere. 

A laboratory supervision in Type III hospital is investigating a number of reported on-the-job training accidents related to needle stick injuries over a period of one month. Based on the past records, she has the following records on the needle stick injuries that were recorded:

Needlestick injuries reported: 0, 1, 2, 3, 4, 5

Frequency: 8, 10, 2, 5, 3, 7

How many ways are there to select 15 countries in the United Nations to serve on a council if 4 are selected from a block of 35, 5 are selected from a block of 40, and the others are selected from the remaining 55 countries?

2. A roulette wheel is divided into 25 sectors of equal area numbered from 1 to 25. Find a formula for the probability distribution of X, the number that occurs when the wheel is spun

find the volume of the solid generated by revolving region bounded by the curves y = x, y = 2 - x, y = 0, about y = -1

3d^2y/dx^2+dy/dx-14y=0 ; y(0)=1 , y'(0)=-1

 Solve the following LPP:  

Minimize Z= 120x1+60x2 

Subject to:  

20x1+30x2>= 900  

40x1+30x2>=1200  

x1,x2>=0

show that y=c1e^x+c2e^2x is the general solution of y′′−3y′+2y=0 on any interval and find the particular solution for which y(0)=-1 and y'(0)=1

Mae purchased a home for ₱4,570,000 and obtained a 20-year loan with an annual interest rate of 8.5%, after paying a down payment of 25%. Find the the amount of interest paid on the loan over the 20 years.