Prime factorization for 40

2 · 2 · 2 · 5

Step-by-step explanation: To find the prime factorization of 40, first create a factor tree with two branches.

Since 40 ÷ 10 = 4, we know that 10 and 4 are factors of 40 so we write 4 and 10 at the bottom of our branches.

Since 10 ÷ 2 = 5, we know that 2 and 5 are factors of 10 so we write 2 and 5 at the bottom of our branches. Now, the number 2 is prime so we can't really come up with anything else to multiply together and 5 is prime because the only thing that will work is 1 · 5 so that's done. Now for 4, we can break down that into 2 · 2 and we already said that they are prime.

Now we multiply our prime factors together and we should get 40.

Image provided.

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.

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step-by-step explanation: