How many license plates can be made using 3 digits and 3 letters of repeated digits and letters are allowed? how many can be made if repeats are not allowed?

26 total letters, 10 total digits

with repeated letters/numbers:

26 * 26 *26 * 10* 10*10 = 17,576,000 ways

without repeats:

26 *25*24 *10 *9*8 = 11,232,000 ways

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.