Sarah is purchasing pencils to share. each package has 12 pencils. the equation n = 12p, where n is the total number of pencils and p is the number of packages, can be used to determine the total number of pencils sarah purchased. determine which variable is dependent and which is independent. then, make a table showing the number of pencils purchased for 3–7 packages.

Answer and Step-by-step explanation:

Each package has 12 pencils

total number of pencils Sarah purchased: n = 12p

n = total number of pencils

p = number of packages

n depends on p, because the total number of pencils dependos on how many packages she will buy, so:

independent variable: p

dependent variable: n

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║ p     ║ n = 12p            ║ n  ║

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║ 3     ║ n = 12*3           ║ 36     ║

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║ 4     ║ n = 12*4           ║ 48     ║

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║ 5     ║ n = 12*5           ║ 60     ║

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║ 6     ║ n = 12*6           ║ 72     ║

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║ 7     ║ n = 12*7           ║ 84     ║

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(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

seems like d

step-by-step explanation: