Your company must maintain about 8,000 pumps that keep breaking down. The engineers claim that adding an extra brace to the devices will significantly increase the time between repairs. It requires a couple hours and $50 in parts to install each brace.
1. State the null and alternative hypothesis in context and symbolically.
2. Explain in context what the consequence of a type one error in this test.
3. Explain in context what the consequence of a type two error in this test.

Ariana starts with 100 milligrams of a radioactive substance. the amount of the substance decreases by 20% each week for a number of weeks, w. the expression 100(1−0.2)w finds the amount of radioactive substance remaining after w weeks. which statement about this expression is true? a) it is the difference between the initial amount and the percent decrease. b) it is the difference between the initial amount and the decay factor after w weeks. c) it is the initial amount raised to the decay factor after w weeks. d) it is the product of the initial amount and the decay factor after w weeks.

Aaron invested a total of $4,100, some in an account earning 8% simple interest, and the rest in an account earning 5% simple interest. how much did he invest in each account if after one year he earned $211 in interest? select one: a. $200 at 8%, $3,900 at 5% b. $3,200 at 8%, $900 at 5% c. $900 at 8%, $3,200 at 5% d. $3,900 at 8%, $200 at 5%

Which statement accurately explains whether a reflection over the y axis and a 270° counterclockwise rotation would map figure acb onto itself?