An entomologist hypothesizes that the mean life expectancy of a particular species of insect is 12.5 days. Researchers believing that the true mean is less than 12.5 days plan a hypothesis test at the 5% significance level on a random sample of 50 of these insects.

(a) If the alternative hypothesis is correct, for which values of μ will the power of the test be greatest?

Mr switzer needs to buy new 1-foot tiles to cover his bathroom floor. the floor is 12 feet long and 8 feet wide. each square foot of tile will cost $1.79. in dollars what will be the total cost of the tiles he needs to buy.

Use addition and subtraction to simplify the following polynomials. a. add polynomials: (3 – 4x + 8x^2) + (–6 + 2x – 5x^2) step 1: rewrite the polynomials without the parentheses. step 2: write the polynomial in descending order and use parentheses around like terms. step 3: add the like terms identified in step 2 to simplify the polynomial. b. subtract polynomials: (3x – 5 – 7x^2) – (–2 + 6x^2 – 5x) step 1: rewrite the polynomials without the parentheses. remember to multiply each term in the second parentheses by –1. show your work. step 2: write the polynomial in descending order and use parentheses around like terms. step 3: add the like terms identified in step 2 to simplify the polynomial.

Prove that 3: 8 is equivalent to 12: 32.a. use diagrams to support your answer.