Answer:
x≤-3 2 ≤x<7
Step-by-step explanation:
(x^2+x-6) /(x-7) ≤0
Factor the numerator
(x+3)(x-2) / (x-7)≤0
Critical points are
X =-3 X =2 X=7
We need to check the values when
x≤3 -3 ≤ x≤2 2 ≤x<7 x>7
(x cannot be 7 because then the denominator is zero)
and see when it is less than 0
Substitute a value in and see if factor is positive or negative
x≤-3
(negative)(negative) / (negative) = negative
-3 ≤x≤2
(positive)(negative) / (negative) = positive this range does not work
2 ≤x<7
(positive)(positive) / (negative) = negative
x>7
(positive)(positive) / (positive)
Answer:
Mean: 40.17 years.
Standard deviation: 10.97 years.
Step-by-step explanation:
The frequency distribution is in the attached image.
We can calculate the mean adding the multiplication of midpoints of each class and frequency, and dividing by the sample size.
The midpoints of a class is calculated as the average of the bounds of the class.
Then, the mean can be written as:
The standard deviation can be calculated as:
![s=\sqrt{\dfrac{1}{N-1}\sum f_i(X_i-E(X))^2}\\\\\\s=\sqrt{\dfrac{1}{59}[3(15-40.17)^2+7(25-40.17)^2+18(35-40.17)^2+20(45-40.17)^2+12(55-40.17)^2]}](https://tex.z-dn.net/?f=s%3D%5Csqrt%7B%5Cdfrac%7B1%7D%7BN-1%7D%5Csum%20f_i%28X_i-E%28X%29%29%5E2%7D%5C%5C%5C%5C%5C%5Cs%3D%5Csqrt%7B%5Cdfrac%7B1%7D%7B59%7D%5B3%2815-40.17%29%5E2%2B7%2825-40.17%29%5E2%2B18%2835-40.17%29%5E2%2B20%2845-40.17%29%5E2%2B12%2855-40.17%29%5E2%5D%7D)
It should be 78.54.
Double check that.
Formula: V=πr2h/3
r2 is R squared
Answer: y= (x+2)² −
5
Step-by-step explanation:
The way I got this answer is by completing the square. The first step though, when looking at this equation, is to see if we can factor it. The way to check is to look at the coefficient for x² which is 1, and the constant, in this case -1. If we multiply those together, we get −. Now we look at the middle term, 4x. We need to find any numbers that multiply to equal − 1x² and add to 4x. There aren't any, which means it is not factorable.
Hope I helped
