Two machines, y and z, work at constant rates producing identical items. machine y produces 3 items in the same time machine z produces 2 items. if machine y takes 9 minutes to produce a batch of items, how many minutes does it take for machine z to produce the same number of items?

a. 6
b. 9
c. 9 1/2
d. 12
e. 13 1/2

E. 13 1/2

Step-by-step explanation:

As two machine Y and Z at constant rate is in 3/2 .So if a machine Y is working 3/2 then the rate of other machine Z is 2/3 time take. Y take 9 minutes.So, 9 = (2/3) the time

so T = 9 * 3 / 2

T = 13.5

So option E is true.  

you need more information to answer this question

step-by-step explanation:

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

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