Math Answers

A market researcher at a major company classified households by car ownership. The relative frequencies of households for each category of ownership are shown in Table 1.

Table 1. The relative frequencies of households

Number of cars House hold 0 1 2 3 4 5

Relative Frequency 0.1 0.3 0.4 0.12 0.06 0.02

Calculate the mean value and standard deviation of the random variable and interpret the result.

Prove that there are infinitely many primes

Let "p_1,p_2,\\dots,p_n" be distinct pisitive primes. Show that "(p_1p_2\\dots p_n)+1" is divisible by none of these primes.

Show that if a nd b are positive untegers, then ab=LCM(a,b)*GCD(a,b)

If there are integers a, b, s, and t such that, the sum at+bs=1, show that GCD(a,b)=1

Let "a" and "b" be two integers. If "a|b" and "b|a", them show that "a=\\pm b"

Find x if, 2^sin²x + 2^cos²x = 3

Compute the area of the plane region bounded by the curve x=y²-2 and the line y=-x using integration along the y-axis.

There is a spinner with 11 equal areas, numbered 1 through 11. If the spinner is spun one time, what is the probability that the result is a multiple of 2 or a multiple of 3?

Use the grid to illustrate: 2 5 of 3 4 . Show the strategy clearly by using different types of shading. (4)