Answer:
z = 8
Step-by-step explanation:
Solve for z:
(z + 4)/3 - 6 = (2 (5 - z))/3
Put each term in (z + 4)/3 - 6 over the common denominator 3: (z + 4)/3 - 6 = (z + 4)/3 - 18/3:
(z + 4)/3 - 18/3 = (2 (5 - z))/3
(z + 4)/3 - 18/3 = ((z + 4) - 18)/3:
(z - 18 + 4)/3 = (2 (5 - z))/3
Add like terms. 4 - 18 = -14:
(z - 14)/3 = (2 (5 - z))/3
Multiply both sides by 3:
(3 (z - 14))/3 = (3×2 (5 - z))/3
(3 (z - 14))/3 = 3/3×(z - 14) = z - 14:
z - 14 = (3×2 (5 - z))/3
(3×2 (5 - z))/3 = 3/3×2 (5 - z) = 2 (5 - z):
z - 14 = 2 (5 - z)
Expand out terms of the right hand side:
z - 14 = 10 - 2 z
Add 2 z to both sides:
2 z + z - 14 = (2 z - 2 z) + 10
2 z - 2 z = 0:
2 z + z - 14 = 10
z + 2 z = 3 z:
3 z - 14 = 10
Add 14 to both sides:
3 z + (14 - 14) = 14 + 10
14 - 14 = 0:
3 z = 10 + 14
10 + 14 = 24:
3 z = 24
Divide both sides of 3 z = 24 by 3:
(3 z)/3 = 24/3
3/3 = 1:
z = 24/3
The gcd of 24 and 3 is 3, so 24/3 = (3×8)/(3×1) = 3/3×8 = 8:
Answer: z = 8
The outlier in the given data set and the reason we know it is an outlier are;
<u><em>The outlier is 9.8</em></u>
<em><u>It is an outlier because it is the distance that is less than 10.</u></em>
- Outliers in mathematics are simply values that lie outside of the other values in a set of data. This means they are far larger than the given set of values or far smaller than the given set of values.
- Now, in this question, we see that the distances given in meters are;
10.1 m, 10.1 m, 10.2 m, 10.2 m, 10.3 m, 10.1 m, 10.2 m, 9.8 m
- From these set of data values, we can see that all but 1 of the values are more than 10. This number that is less than 10 is the odd one out of these set of data values and therefore it is the outlier.
Read more at; brainly.com/question/3631910
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I think it is $139.30. But I'm not 100% sure
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