A piece of cardboard measuring 8 inches by 9 inches is formed into an open-top box by cutting squares with side length x from each corner and folding up the sides. Find a formula for the volume of the box in terms of x

V(x) =

Find the value for x that will maximize the volume of the box

x =

Eis the midpoint of line segment ac and bd also line segment ed is congruent to ec prove that line segment ae is congruent to line segment be

How many real-number solutions does the equation have? -4x^2 + 10x + 6 = 0 a. no solutions b. two solutions c. infinitely many solutions d. one solution

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