Math Answers

The average height of a random sample of 400 people from San Pablo City is 1.75m. It is known that the heights of the population are random variables that follow a normal distribution with a variance of 0.16. Determine the interval of 99% confidence for the average heights of the population. 

use the method of cylinders to determine the volume of the solid by rotating the region bounded by y=-x^2-10x+6 and y=2x+26 about the

a. line x=2 b. line x=-1 c. line x=-14

use the method of disks to determine the volume of the solid by rotating the region bounded by y=10-2x,y=x+1 and y=7 about the

a. line x=8 b. line x=1 c. line x=-4

false statement by finding a counterexample

1. x/x=1
2. x+3)/3=x+1
3. √(x^2+16)=x+4

The prevalence of a certain type of cancer among men aged 55−𝟔𝟎 is 1 in 100. A blood test will be positive 95% of the time if the cancer is present but it is also positive 4% of the time if the cancer is not present. 2.1. In a routine checkup, 56-year-old men receive a positive blood test. What is the probability that he has the type of cancer? 2.2. What is the probability that a randomly selected 56-year-old men tests negative?

1. a) Determine whether the following proposition is logically equivalent or not using the truth table.

((p⟶q)v(q⟶p))⇔p⟷q

b) Construct a truth table to determine whether the following compound statement is a tautology, a contradiction or a contingency.

~(p∧r)⟶~(q∨r)

c) Use the laws of logic to establish the following logical expression.

~(p∨q) v (~p∧q)⟺~p

Solve the following spherical triangle using Law of Sine and Cosine

A= 137°28´, C=135°44´, c= 160° Find : a

Find the orthogonal trajectories of the following curves (where a is a parameter). r = a(1 + sin θ)

In a given normal distribution, the population mean is 80 and the population standard deviation is 2.5. Find the corresponding standard z – score of the following values.

The population of each classroom for face-to-face classes consists of the numbers 10, 11, 15, and 9. List all the sample size of 3 from this population and compute the mean of each sample.