Math Answers

Two students are to be selected at random from a class with 10 girls and 12 boys. What is the probability that both will be girls, if selected

a) With replacement

b) Without replacement

A student has 6 different notebooks and decided to give 5 of them to a friend. How many ways does he have to give away these notebooks?

Differentiate the following without solving for y in terms of x.

1. x²/9 + y²/4 =1
2. x²/4 + y²=1
3. x²+ y²/9 =1

Differentiate the following without solving for y in terms of x.

1. x²+10x+y²+17=0
2. x²+y²-2x+4y=3
3. x² +y²+2y=45
4. x²-4x+y²+2y=15
5. x²-2x+y²+2y=23

Differentiate the following functions

1. y=(x²+5x+2)³
2. y=(2x²-x+3)⁵
3. y=(x²-2x+6)⁷
4. ∛4x-5
5. ∛6-7x

1. Draw the Hasse diagram representing the partial ordering {(a, b) |a divides b} on {1, 2, 3, 4, 6, 8, 12}.

The management of a restaurant has been studying whether or not new customers return

within a month. The collected data reveal that 60% of the new customers have returned.

If 90 new customers dine at the restaurant this month, what is the probability that at least

60 will return next month? Use Normal approximation to Binomial distribution.

The mean annual salary of all the frontlines (nurses, medical technologists,

radiologic technologists, phlebotomists) in the Philippines is Php 42,500.

Assume that this is normally distributed with standard deviation Php 5,600.

A random sample of 25 health workers is drawn from this population, find

the probability that the mean salary of the sample is:

Greater than php 41, 000?

The quantity produced daily at the ABC cement factory is approximately normally

distributed with mean 0.82 and standard deviation 0.14. The units are on millions of tons.

Find the probability that the total production will between 0.80 and 0.85 million tons.

A student majoring in marketing is trying to decide on the number of firms to which she

should apply. Given her work experience, grades, and extra curricular activities, she has

been told by a placement counselor that she can expect to receive a job offer from 80% of

the firms to which she applies. Wanting to save time, The student applies to only five firms.

Assuming the counselor’s estimate is correct, find the probability that the student receives

at least three offers.