Formulate but do not solve the problem.
mr. and mrs. garcia have a total of $125,000 to be invested in stocks, bonds, and a money market account. the stocks have a rate of return of 12%/year, while the bonds and the money market account pay 7%/year and 3%/year, respectively. the garcias have stipulated that the amount invested in the money market account should be equal to the sum of 15% of the amount invested in stocks and 20% of the amount invested in bonds. how should the garcias allocate their resources if they require an annual income of $11,000 from their investments? (let x, y, and z denote the amount, in dollars, in stocks, bonds, and money markets, respectively.)
=125,000
=11,000
= z

In a test for esp (extrasensory perception), the experimenter looks at cards that are hidden from the subject. each card contains either a star, a circle, a wave, a cross or a square.(five shapes) as the experimenter looks at each of 20 cards in turn, the subject names the shape on the card. when the esp study described above discovers a subject whose performance appears to be better than guessing, the study continues at greater length. the experimenter looks at many cards bearing one of five shapes (star, square, circle, wave, and cross) in an order determined by random numbers. the subject cannot see the experimenter as he looks at each card in turn, in order to avoid any possible nonverbal clues. the answers of a subject who does not have esp should be independent observations, each with probability 1/5 of success. we record 1000 attempts. which of the following assumptions must be met in order to solve this problem? it's reasonable to assume normality 0.8(1000), 0.2(1000)%30 approximately normal 0.8(1000), 0.2(1000)% 10 approximately normal srs it is reasonable to assume the total number of cards is over 10,000 it is reasonable to assume the total number of cards is over 1000