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Nataliya [291]
3 years ago
8

Jerry has a part-time job at a supermarket. The ordered pairs show the number of hours he worked for (input values) and the numb

er of dollars (output values) he earned over a five week period. (6,72) (8,96) (5.5, 66) (9,108) (7,84) Are the ordered pairs a relation?
Mathematics
1 answer:
Karo-lina-s [1.5K]3 years ago
8 0

Answer:

Yes

Step-by-step explanation:

The ordered pairs are (6,72) (8,96) (5.5, 66) (9,108) (7,84).

The number of hours worked is x and the money earned is  y.

Let us divide the values of y by x

\dfrac{72}{6}=12

\dfrac{96}{8}=12

\dfrac{66}{5.5}=12

\dfrac{108}{9}=12

\dfrac{84}{7}=12

The fuction which defines the above ordered pairs is y=12x

It can be seen that the amount of money earned is 12 times the number of hours worked.

So, per hour Jerry earns 12 dollars.

Hence, the ordered pairs are relation.

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See the graph attached.

The midpoint rule states that you can calculate the area under a curve by using the formula:
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In your case:
a = 0
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Therefore, you'll have:
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M_{4} = \frac{1}{4} [ f(\frac{1}{8}) +  f(\frac{3}{8}) +  f(\frac{5}{8}) + f(\frac{7}{8})]

Now, to evaluate your f(x), you need to look at the graph and notice that:
f(x) = x - x³

Therefore:
M_{4} = \frac{1}{4} [(\frac{1}{8} - (\frac{1}{8})^{3}) + (\frac{3}{8} - (\frac{3}{8})^{3}) + (\frac{5}{8} - (\frac{5}{8})^{3}) + (\frac{7}{8} - (\frac{7}{8})^{3})]

M_{4} = \frac{1}{4} [(\frac{1}{8} - \frac{1}{512}) + (\frac{3}{8} - \frac{27}{512}) + (\frac{5}{8} - \frac{125}{512}) + (\frac{7}{8} - \frac{343}{512})]

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Step-by-step explanation:

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