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QuestionCalculate the sum: (155−151.49)2151.49+(131−134.51)2134.51+(179−161.03)2161.03+(125−142.97)2142.97+(103−124.48)2124.48+(132−110.52)2110.52\frac{(155-151.49)^{2}}{151.49} + \frac{(131-134.51)^{2}}{134.51} + \frac{(179-161.03)^{2}}{161.03} + \frac{(125-142.97)^{2}}{142.97} + \frac{(103-124.48)^{2}}{124.48} + \frac{(132-110.52)^{2}}{110.52}.

Studdy Solution

STEP 1

Assumptions1. We are given six fractions to add. . Each fraction is in the form of (a−b)/c(a-b)^/c where aa, bb, and cc are real numbers.

STEP 2

We will solve each fraction one by one and then add the results. Let's start with the first fraction.
(155−151.49)2151.49\frac{(155-151.49)^{2}}{151.49}

STEP 3

First, subtract151.49 from155.
(155−151.49)2151.49=(3.51)2151.49\frac{(155-151.49)^{2}}{151.49} = \frac{(3.51)^{2}}{151.49}

STEP 4

Next, square3.51.
(3.51)2151.49=12.3201151.49\frac{(3.51)^{2}}{151.49} = \frac{12.3201}{151.49}

STEP 5

Finally, divide12.3201 by151.49.
12.3201151.49=0.0813\frac{12.3201}{151.49} =0.0813

STEP 6

Now, let's move on to the second fraction.
(131−134.51)2134.51\frac{(131-134.51)^{2}}{134.51}

STEP 7

Subtract134.51 from131.
(131−134.51)2134.51=(−3.51)2134.51\frac{(131-134.51)^{2}}{134.51} = \frac{(-3.51)^{2}}{134.51}

STEP 8

Square -3.51.
(−3.51)2134.51=12.3201134.51\frac{(-3.51)^{2}}{134.51} = \frac{12.3201}{134.51}

STEP 9

Divide12.320 by134.51.
12.320134.51=.0915\frac{12.320}{134.51} =.0915

STEP 10

Next, we'll solve the third fraction.
(179−161.03)2161.03\frac{(179-161.03)^{2}}{161.03}

STEP 11

Subtract161.03 from179.
(179−161.03)161.03=(17.97)161.03\frac{(179-161.03)^{}}{161.03} = \frac{(17.97)^{}}{161.03}

STEP 12

Square17.97.
(17.97)2161.03=323.0409161.03\frac{(17.97)^{2}}{161.03} = \frac{323.0409}{161.03}

STEP 13

Divide323.0409 by161.03.
323.0409161.03=2.006\frac{323.0409}{161.03} =2.006

STEP 14

Now, let's solve the fourth fraction.
(125−142.97)2142.97\frac{(125-142.97)^{2}}{142.97}

STEP 15

Subtract142.97 from125.
(125−142.97)2142.97=(−17.97)2142.97\frac{(125-142.97)^{2}}{142.97} = \frac{(-17.97)^{2}}{142.97}

STEP 16

Square -.97.
(−.97)2142.97=323.0409142.97\frac{(-.97)^{2}}{142.97} = \frac{323.0409}{142.97}

STEP 17

Divide323.0409 by142.97.
323.0409142.97=2.2597\frac{323.0409}{142.97} =2.2597

STEP 18

Next, we'll solve the fifth fraction.
(103−124.48)2124.48\frac{(103-124.48)^{2}}{124.48}

STEP 19

Subtract124.48 from103.
(103−124.48)124.48=(−21.48)124.48\frac{(103-124.48)^{}}{124.48} = \frac{(-21.48)^{}}{124.48}

STEP 20

Square -.48.
(−.48)124.48=461.6704124.48\frac{(-.48)^{}}{124.48} = \frac{461.6704}{124.48}

STEP 21

Divide461.6704 by124.48.
461.6704124.48=3.7081\frac{461.6704}{124.48} =3.7081

STEP 22

Finally, we'll solve the sixth fraction.
(132−110.52)110.52\frac{(132-110.52)^{}}{110.52}

STEP 23

Subtract110.52 from132.
(132−110.52)110.52=(21.48)110.52\frac{(132-110.52)^{}}{110.52} = \frac{(21.48)^{}}{110.52}

STEP 24

Square21.48.
(21.48)110.52=461.6704110.52\frac{(21.48)^{}}{110.52} = \frac{461.6704}{110.52}

STEP 25

Divide461.6704 by110.52.
461.6704110.52=4.177\frac{461.6704}{110.52} =4.177

STEP 26

Now that we have all the results, we can add them together.
0.0813+0.0915+.0061+.259+3.7081+4.1776=12.32430.0813 +0.0915 +.0061 +.259 +3.7081 +4.1776 =12.3243The solution to the problem is12.3243.

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