The distributor of a machine for cytogenics has developed a new model. The company estimates that when it is introduced into the market, it will be very successful with a probability 0.6, moderately successful with a probability 0.3, and not successful with probability 0.1. The estimated yearly profit associated with the model being very successful is $15 million and with it being moderately successful is $5 million; not successful would result in a loss of $500,000. Let X be the yearly profit of the new model. Determine the probability mass function of X

Agroup of students want to create a garden. they do not know the exact measurements but they propose using a variable to represent the length and width of the garden. the length of the garden is 10 feet longer than double the width. use a single variable to write algebraic expressions for both the length and width of the garden. write an algebraic expression for the area of the garden. use mathematical terms to describe this expression.

Francisco's credit card has an apr of 28.98%, calculated on the previous monthly balance. his credit card record for the last 7 months is shown in the table below francisco is trying to figure out what this all means. answer the following questions: what is the total amount that francisco has paid in interest over the 7 months? what is the total amount that francisco has made in payments over the 7 months? how much of francisco's payments have gone to paying down the principal on his account? what is francisco's new balance at the end of month 8? what will francisco be charged for interest for month 8?

12 3 4 5 6 7 8 9 10 time remaining 42: 01 ryan gathered data about the age of the different dogs in his neighborhood and the length of their tails. which best describes the strength of the correlation, and what is true about the causation between the variables?