Answer:
B
Step-by-step explanation:
Answer: 2.76 g
Step-by-step explanation:
The formula to find the standard deviation:-
![\sigma=\sqrt{\dfrac{\sum(x_i-\overline{x})^2}{n}}](https://tex.z-dn.net/?f=%5Csigma%3D%5Csqrt%7B%5Cdfrac%7B%5Csum%28x_i-%5Coverline%7Bx%7D%29%5E2%7D%7Bn%7D%7D)
The given data values : 560 g, 562 g, 556 g, 558 g, 560 g, 556 g, 559 g, 561 g, 565 g, 563 g.
Then, ![\overline{x}=\dfrac{\sum_{i=1}^{10} x_i}{n}\\\\\Rightarrow\ \overline{x}=\dfrac{560+562+556+558+560+556+559+561+565+563}{10}\\\\\Rightarrow\ \overline{x}=\dfrac{5600}{10}=560](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%3D%5Cdfrac%7B%5Csum_%7Bi%3D1%7D%5E%7B10%7D%20x_i%7D%7Bn%7D%5C%5C%5C%5C%5CRightarrow%5C%20%5Coverline%7Bx%7D%3D%5Cdfrac%7B560%2B562%2B556%2B558%2B560%2B556%2B559%2B561%2B565%2B563%7D%7B10%7D%5C%5C%5C%5C%5CRightarrow%5C%20%5Coverline%7Bx%7D%3D%5Cdfrac%7B5600%7D%7B10%7D%3D560)
Now, ![\sum_{i=1}^{10}(x_i-\overline{x})^2=0^2+2^2+(-4)^2+(-2)^2+0^2+(-4)^2+(-1)^2+1^2+5^2+3^2\\\\\Rightarrow\ \sum_{i=1}^{10}(x_i-\overline{x})^2=76](https://tex.z-dn.net/?f=%5Csum_%7Bi%3D1%7D%5E%7B10%7D%28x_i-%5Coverline%7Bx%7D%29%5E2%3D0%5E2%2B2%5E2%2B%28-4%29%5E2%2B%28-2%29%5E2%2B0%5E2%2B%28-4%29%5E2%2B%28-1%29%5E2%2B1%5E2%2B5%5E2%2B3%5E2%5C%5C%5C%5C%5CRightarrow%5C%20%5Csum_%7Bi%3D1%7D%5E%7B10%7D%28x_i-%5Coverline%7Bx%7D%29%5E2%3D76)
Then, ![\sigma=\sqrt{\dfrac{76}{10}}=\sqrt{7.6}=2.76](https://tex.z-dn.net/?f=%5Csigma%3D%5Csqrt%7B%5Cdfrac%7B76%7D%7B10%7D%7D%3D%5Csqrt%7B7.6%7D%3D2.76)
Hence, the standard deviation of his measurements = 2.76 g
4g+3(-3+4g)=1-g
Distribute the 3(-3+4g)
4g-9+12g=1-g
Add 4g and 12g
16g-9=1-1g
Add 1g and 16g (variables always have an invisible 1 in front)
17g-9=1
Add 9 and 1
17g=10
Divide both sides by 17 and the answer is g=10/17
Answer:
Step-by-step explanation:
Givens
pi = 3.14
d = 3.8
r = d/2
r = 3.8/2 = 1.9
Formula
V = (4/3) * pi * r^3
Solution
V = (4/3) * 3.14 * 1.9^3
V = 4/3 * 3.14 * 6.859
V = 28.7163
Answer:
Step-by-step explanation:
y + 2 = -7(x + 7)
y + 2 = -7x - 49
y = -7x - 51
answer is b