Math Answers

A canteen owner claims that the average meal cost of his usual clients is

Php180. In order to test his own claim, he took a random sample of 30

receipts and computed the mean cost of Php210 with a standard deviation of

Php25. Test the hypothesis at 0.01 level of significance. Show all steps

A company that supplies ready-mix concrete receives, on average, six orders per day.

(a) What is the probability that, on a given day:

(i) only one order will be received?

(ii) no more than three orders will be received?

(iii) at least three orders will be received?

(b) What is the probability that, on a given half-day, only one order will be received?

(c) What is the mean and standard deviation of orders received per day?

3 A recent survey by a local municipality established that daily water usage by its households is normally distributed with a mean of 220 liters and a standard deviation of 45 liters.

(i) What percentage of households is likely to use more than 300 liters of water per day?

(ii) What is the probability of finding a household that uses less than 100 liters of water per day?

(iii) What percentage of households is likely to use between 300 to 350 liters of water per day?

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"