Answer:
Step-by-step explanation:
This is a standard normal distribution which means it has a mean of 0 and a standard deviation of 1. To shade 1 and 2 standard deviations above the mean just color in the area under the curve between 1 and 2
The percent of data is equal to .9772-.8413= .1359= 13.59%
Answer:
Joe would receive $9.10 for One hour of mowing the lawn and $39.50 for Five hours of babysitting, which (if needed) adds up to $48.60
Step-by-step explanation:
It's as simple as multiplication. Since he only mowed the lawn for one hour, it would only be $9.10. Since he babysat for 5 hours, you'd simply multiply $7.90 by five, giving you the answer $39.50
![f(x)=x+sin(x)\\ a=0\\ b=\pi \\ x_i=a+idelta(x)\\ Upper sum for n=2:\\ \\ delta(x)=\frac{b-a}{n} =\frac{\pi-0}{2} =\frac{\pi}{2}](https://tex.z-dn.net/?f=%20f%28x%29%3Dx%2Bsin%28x%29%5C%5C%20a%3D0%5C%5C%20b%3D%5Cpi%20%5C%5C%20x_i%3Da%2Bidelta%28x%29%5C%5C%20Upper%20sum%20for%20n%3D2%3A%5C%5C%20%5C%5C%20delta%28x%29%3D%5Cfrac%7Bb-a%7D%7Bn%7D%20%3D%5Cfrac%7B%5Cpi-0%7D%7B2%7D%20%3D%5Cfrac%7B%5Cpi%7D%7B2%7D%20%20%20)
![x_0=0, x_1=\frac{\pi}{2} ,x_1=\pi \\](https://tex.z-dn.net/?f=%20x_0%3D0%2C%20x_1%3D%5Cfrac%7B%5Cpi%7D%7B2%7D%20%2Cx_1%3D%5Cpi%20%20%5C%5C%20%20)
Length of the subintervals: ![[0,\frac{\pi}{2}], [\frac{\pi}{2}, \pi}]](https://tex.z-dn.net/?f=%20%5B0%2C%5Cfrac%7B%5Cpi%7D%7B2%7D%5D%2C%20%5B%5Cfrac%7B%5Cpi%7D%7B2%7D%2C%20%5Cpi%7D%5D%20)
Using Upper Riemann sum,
∑Max{f(x_i) delta(x)
![=[max{(f(x_1))+max(f(x_2))]delta(x)\\ =(3+3)\frac{\pi}{2} \\=9.42](https://tex.z-dn.net/?f=%20%3D%5Bmax%7B%28f%28x_1%29%29%2Bmax%28f%28x_2%29%29%5Ddelta%28x%29%5C%5C%20%3D%283%2B3%29%5Cfrac%7B%5Cpi%7D%7B2%7D%20%5C%5C%3D9.42%20%20)
Lower sum for n=2:
The minimum value for the function on
is 2.
![\int\limits^0_\pi {x+\sin x} \, dx =\sum_{n=0}^{n=2} min {f(x_i)} delta (x)\\](https://tex.z-dn.net/?f=%20%5Cint%5Climits%5E0_%5Cpi%20%7Bx%2B%5Csin%20x%7D%20%5C%2C%20dx%20%20%3D%5Csum_%7Bn%3D0%7D%5E%7Bn%3D2%7D%20min%20%7Bf%28x_i%29%7D%20delta%20%28x%29%5C%5C%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20)
![= (2+2)\frac{\pi}{2}\\ =6.28](https://tex.z-dn.net/?f=%20%20%3D%20%282%2B2%29%5Cfrac%7B%5Cpi%7D%7B2%7D%5C%5C%20%3D6.28%20)