Katie is k years old. harry is 4 years older than katie. rachel is twice as old as harry. if you add together the ages of katie, harry, and rachel the total comes to 36 years. algebraically, determine the age of each person.

Arestaurant gives out a scratch-off card to every customer. the probability that a customer will win a prize from a scratch-off card is 25%. design and conduct a simulation using random numbers to find the experimental probability that a customer will need more than 3 cards in order to win a prize. justify the model for your simulation, and conduct at least 10 trials.

Use the expression below.–4b + 8c + 12 – 8b – 2c + 6part asimplify the expression. enter your answers in the boxes. b + c + part bfactor the simplified expression using the gcf. a. 2(–2b + c + 3) b. 3(–2b + c + 3) c. 4(–2b + c + 3) d. 6(–2b + c + 3)part cwhat is the value of the expression when b = 2 and c = –3? enter your answer in the box.

The manufacturer of a new product developed the following expression to predict the monthly profit, in thousands of dollars, from sales of the productwhen it is sold at a unit price of x dollars.-0.5x^2 + 22x - 224what is represented by the zero(s) of the expression? a. the profit when the unit price is equal to 0b. the unit price(s) when the profit is equal to 0c. the profit when the unit price is greatestd. the unit price(s) when profit is greatest