Is the statement true or false? If false, give a counterexample. For all real numbers a, b and c, a(b + c) = ab + bc.

A. true
B. false; a(b + c) = ab − ac
C. false; if a = b = c = 1, then 1(1 + 1) ≠ 1(1) + 1(1)
D. false; if a = 1, b = 2, and c = 3, then 1(2 + 3) ≠ 1(2) + 2(3)

The graph below shows the amount of money left in the school’s desk fund, f, after d desks have been purchased. for each new desk that is purchased, by how much does the amount of money left in the school’s desk fund decrease?

Raj encoded a secret phrase using matrix multiplication. using a = 1, b = 2, c = 3, and so on, he multiplied the clear text code for each letter by the matrix to get a matrix that represents the encoded text. the matrix representing the encoded text is . what is the secret phrase? determine the location of spaces after you decode the text. yummy is the corn the tomato is red the corn is yummy red is the tomato

Max recorded the heights of 500 male humans. he found that the heights were normally distributed around a mean of 177 centimeters. which statements about max’s data must be true? a) the median of max’s data is 250 b) more than half of the data points max recorded were 177 centimeters. c) a data point chosen at random is as likely to be above the mean as it is to be below the mean. d) every height within three standard deviations of the mean is equally likely to be chosen if a data point is selected at random.