Math Answers

A Pumpkin gets launched into the air from a cliff above a pond. The following equation represents the height of the pumpkin from the pond, h(t)=−16t2+56t+32where t is time in seconds.  What is the maximum height the pumpkin reaches?

Suppose a population consists of the number 97,89,98,93,95,97,97,90,60,94 construct a sampling distribution of all possible samples of size 3 from the population.

The Mathematics Club of the Ohio Science High School has six members. How many ways can this club select a president and secretary assuming that all members are eligible but no one can hold both positions?

Determine whether the polynomial x²+2y²+4xy+2yz+6xz is a quadratic form and if so write it in the form X^T AX, where A is a symmetric matrix.

Can ∫ (x^6 +8)^2 dx be integrated with u = x^6+8? Explain

(D^4 − 18D^3 + 119D^2 − 342D + 360)y = 0

1/x+ye^xy+2x)dx +(1/y+xe^xy+2y)dy=0

Express the null hypothesis and alternative hypothesis in notation form of the scenario “It is

believed that the mean yearly salary of professors in the Philippines is Php480,000.00. A

random sample of 65 professors revealed a mean salary of Php500,000.00 Can it be

concluded that the mean salary is greater than Php480,000.00?

A sample size n = 22 is a simple random sample selected from a normally distributed

population. Find the t such that the shaded area to the left of t is 0.05.

Present complete solutions for each item. Illustrate the normal curve if possible.

2. The scores of individual students on a national test have a normal distribution with mean of

18.6 and a standard deviation of 5.9. At Federico Ramos Rural High School, 76 students

took the test. If the scores at this school have the same distribution as national scores, solve

for the following:

a. determine the mean and standard deviation of the sampling distribution of the sample

mean.

b. find the probability that the sample mean falls between 17 and 20 (P(17 < x̅< 20).

c. the number of sample means that is above 19.3 kilograms.