Math Answers

A mathematics teacher in senior high school develop a problem-solving test to randomly selected 40 students. These students had an average score of 85 and standard deviation of 5. If this population had a mean score of 90 and standard deviation of 3, use 5% Level of Significance to test the hypothesis.

Teachers in a certain private school have a mean age of 38 years with a standard deviation of 6 years and a mean monthly salary of Php 4,000 with a standard deviation of Php 1,500. Which is more variable: the teachers' ages or their salaries?

If the rate is at 1.25% effective, how long will Php 5,000 become Php 5,500?

) On average 2.5 faulty reports are made to a company’s switchboard per day.

i. Name the random variable present in this problem and state its distribution.

Calculate the probability that

ii. FOUR faulty reports will be made on Monday

iii. Less than 3 faulty reports in a 5-day work week

b) The number of attempts at shooting goals made by a netballer in a tournament can be modelled by a binomial distribution with a probability of success equal to 0.35.

(i) In a sample of 12 attempts at shooting goals, calculate the probability that EXACTLY 4 were successful.

(ii) Given that the netballer made a total of 120 attempts at shooting goals in a tournament, calculate the expected number of successful shoots. 

The director of admissions at a large university says that 15% of high school juniors to whom she sends university literature eventually apply for admission. In a sample of 300 persons to whom materials were sent, 30 students applied for admission. In a two-tail test at the 0.05 level of significance, should we reject the director’s claim?

The director of admissions at a large university says that 15% of high school juniors to whom she sends university literature eventually apply for admission. In a sample of 300 persons to whom materials were sent, 30 students applied for admission. In a two-tail test at the 0.05 level of significance, should we reject the director’s claim?

Expand (2x² + y³)⁵using combinations.

Find the fourth term of the binomial expansion (x-2y²)⁵

Using the definition of absolute value, evaluate "\\begin{vmatrix}\n X-2\/3 =3\/4\n \n\\end{vmatrix}\\mid"

Verify that the two given functions are inverses of each other

f(x)=x3+1andg(x)=√3 x−1