17. On average, Nestor works 7.5 hours of overtime in 4 weeks, so works an average of 7.5/4 = 1.875 overtime hours per week.
On average, each week Nestor gets paid for 7.5×5 + 2×1.875 = 41.25 hours, so is paid*
... (41.25 h)×($7.42/h) = $306.075
Each week Rita gets paid for 8×5 + 1.5×3 = 44.5 hours, so is paid
... (44.5 h)×($7.64/h) = $339.98
Their combined earning for a week are $306.075 + 339.98 = $646.055, so over a period of 12 weeks, they are paid a total of
... (12 weeks)×($646.055/week) = $7,752.66
18. Assuming Robin is paid time and a half for overtime, she was paid for
... 40 + 1.5×6 = 49 . . . hours
Then her hourly pay was ($392/week)/(49 hours/week) = $8.00 per hour
___
* The half-cent that shows up in Nestor's average weekly pay does not actually show up in Nestor's paycheck. Here, it is an artifact of dividing his monthly hour total by 4 to get a weekly average. Nestor's total pay for any given week is whole number of cents.
Answer:
452.4
Step-by-step explanation:
area is given by πradius squared which gives answer as 452.389
Answer: A. ![\left[\begin{array}{ccc}29&13\\13&10\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D29%2613%5C%5C13%2610%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
The question is asking us to find the product of the matrices. The key difference is the second A has a little <em>T</em> in the exponent. This <em>T</em> means transpose. You multiply A by the transpose of A. To find the transpose, you turn the rows into columns.
![A^T=\left[\begin{array}{ccc}5&3\\2&-1\\\end{array}\right]](https://tex.z-dn.net/?f=A%5ET%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%263%5C%5C2%26-1%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Now that we have our transpose, we can multiply the matrices.
![\left[\begin{array}{ccc}5&2\\3&-1\\\end{array}\right] \left[\begin{array}{ccc}5&3\\2&-1\\\end{array}\right] =\left[\begin{array}{ccc}5*5+2*2&5*3+2(-1)\\3*5+2(-1)&3*3+(-1)(-1)\\\end{array}\right] =\left[\begin{array}{ccc}29&13\\13&10\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%262%5C%5C3%26-1%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%263%5C%5C2%26-1%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%2A5%2B2%2A2%265%2A3%2B2%28-1%29%5C%5C3%2A5%2B2%28-1%29%263%2A3%2B%28-1%29%28-1%29%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D29%2613%5C%5C13%2610%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Answer:
Please find attached, the required drawing of quadrilateral ABCD and the dilation of quadrilateral ABCD scaled down by a scale factor of 1/3
Step-by-step explanation:
The coordinates of the quadrilateral ABCD are;
A(0, 6), B(6, 6), C(9, 0), D(0, 0)
From the dilation by a scale factor of 1/3, using D as the center of dilation, we have from the attached drawing, the following coordinates of the quadrilateral EFGH as E(0, 2), F(2, 2), G(3, 0) H(0, 0) which is the quadrilateral ABCD scaled down by 1/3
