Math Answers

a) i) Give an inductive formula for the sum of the first n odd numbers:

1 + 3 + 5 + ... + 2n -1

Show your induction process.

ii) Use the proof by mathematical induction to prove the correctness of your

inductive formula in i) above.

a) i) Give an inductive formula for the sum of the first n odd numbers:

1 + 3 + 5 + ... + 2n -1

Show your induction process.

ii) Use the proof by mathematical induction to prove the correctness of your

inductive formula in i) above.

A group of people were asked if they had run a red light in the last year. 302 responded “yes”, and 158 responded “no”

find the probability that if a person is chosen at random, they have run a red light in the past year.

suppose 100 refrigerator were manufactured during a day. ninety five operated perfectly and 5 had at least one defect. a sample of four is selected at random

A new sneaker claims that it can make male athletes jump higher. A sample of 41 male athletes were asked to jump once with their own sneakers on and once wearing the new sneakers. The average jump increased by 1.28 inches with the new sneakers with a standard deviation of 1.02 inches. What is the margin of error of the 95% confidence interval for the average jump increase?

There are hundreds of apples on the trees, so you randomly choose just 45 apples and get a mean weight of 89.05 grams with a standard deviation of 4.43 grams. Assuming that the weight of the apples is normally distributed, what is the standard error of the 90% confidence interval for the mean weight of the apples.

The corresponding medians of two similar triangles are 8 and 20. If the perimeter of the larger triangle is 45, what is the perimeter of the smaller triangle?

Find

lim tan x sec^2 x- x/x^3

x→0

a)

i) Give an inductive formula for the sum of the first n odd numbers:

1 + 3 + 5 + ... + 2n -1

Show your induction process.

ii) Use the proof by mathematical induction to prove the correctness of your

inductive formula in i) above.

A study was conducted to determine the average salary of a teacher. With this, 81 teachers were invited as samples. It was known that the mean salary of these sample teachers is Php 24,000.00 with a standard deviation of Php 1,000.00. Construct a 90% confidence interval estimate for the average salary of all teachers.