Christian worked for eight weeks over the summer as a landscaper. The pay he earned for each of the eight weeks is shown in the data table.
1. Determine the mean of the data.
2. Determine the difference of each weekly pay from the mean.
3. Calculate the square of each difference.
4. Add the squares of the differences.
5. Calculate the variance by dividing the sum of the squares by "n-1". Round to the nearest cent.
6. Determine the sample standard deviation. Round to the nearest cent.
Difference from the mean
(Difference from the mean)
Money Earned
X-
X-X
255
-7.5
56.25
300
37.5
1406.25
260
-2.5
6.25
200
-62.5
3906.25
250
- 12.5
156.25
235
-27.5
756.25
275
12.5
156.25
3906.25
325
Mean
262.5
62.5
Sum of (differences from mean)
(x-x)
Standard Deviation: 3(x-x)
Variance: 3(x-)
n-1
n-1

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.