Answer:
Mode
Step-by-step explanation:
Mean:
Before replacing = 464/8 = 58
After replacing 42 with 98 = 520/8 = 65
Mode:
Before replacing = 42
After replacing 42 with 98 = 98
Median:
25, 42 , 42 , 47, 55 , 59, 96,98
Before replacing = 47+55/2 = 51
25, 42 , 47, 55 , 59, 96,98 , 98
After replacing 42 with 98 = 55+59/2 = 114/2 = 57
Answer:
Total Tim's score = 0 points
Step-by-step explanation:
Given:
Total number of question missed = 12
Each correct question mark = 6 points
Find:
Total Tim's score
Computation:
Total Tim's score = Total correct question x Each correct question mark
Total Tim's score = 0 x 6 points
Total Tim's score = 0 points
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Split up the integration interval into 4 subintervals:
![\left[0,\dfrac\pi8\right],\left[\dfrac\pi8,\dfrac\pi4\right],\left[\dfrac\pi4,\dfrac{3\pi}8\right],\left[\dfrac{3\pi}8,\dfrac\pi2\right]](https://tex.z-dn.net/?f=%5Cleft%5B0%2C%5Cdfrac%5Cpi8%5Cright%5D%2C%5Cleft%5B%5Cdfrac%5Cpi8%2C%5Cdfrac%5Cpi4%5Cright%5D%2C%5Cleft%5B%5Cdfrac%5Cpi4%2C%5Cdfrac%7B3%5Cpi%7D8%5Cright%5D%2C%5Cleft%5B%5Cdfrac%7B3%5Cpi%7D8%2C%5Cdfrac%5Cpi2%5Cright%5D)
The left and right endpoints of the 
-th subinterval, respectively, are
for 
, and the respective midpoints are
We approximate the (signed) area under the curve over each subinterval by
so that
We approximate the area for each subinterval by
so that
We first interpolate the integrand over each subinterval by a quadratic polynomial 
, where
so that
It so happens that the integral of reduces nicely to the form you're probably more familiar with,
Then the integral is approximately
Compare these to the actual value of the integral, 3. I've included plots of the approximations below.
