A farmer bought a scratch ticket and found out later that he won $1,800,000. After 30% was deducted for income taxes he invested the rest; some at 4.75% and some at 6.25%. If the annual interest earned from his investments is $72,135, find the amount he invested at each rate. Define variables to represent the unknowns and setup the necessary equations to answer the question.

Arefrigeration system at your company uses temperature sensors fixed to read celsius (°c) values, but the system operators in your control room understand only the fahrenheit scale. you have been asked to make a fahrenheit (°f) label for the high temperature alarm, which is set to ring whenever the system temperature rises above –10°c. what fahrenheit value should you write on the label

Christine wong has asked dave and mike to her move into a new apartment on sunday morning. she has asked them both, in case one of them does not show up. from past experience, christine knows that there is a 40% chance that dave will not show up and a 30% chance that mik a. what is the probability that both dave and mike will show up? (round your answer to 2 decimal places.) b. what is the probability that at least one of them will show up? c. what is the probability that neither dave nor mike will show up? (round your answer to 2 decimal places.)e will not show up. dave and mike do not know each other and their decisions can be assumed to be independent.

Cate purchases $1600 worth of stock and her broker estimates it will increase in value by 4.2% each year. after about how many years will the value of cate's stock be about $2000