Answer:
A) g is increasing, and the graph of g is concave up.
Step-by-step explanation:
g'(x) = ∫₀ˣ e^(-t³) dt
Since e^(-t³) is always positive, ∫₀ˣ e^(-t³) dt is positive when x > 0. So the function is increasing.
Find g"(x) by taking the derivative using second fundamental theorem of calculus:
g"(x) = e^(-x³)
g"(x) is always positive, so the function is always concave up.
Answer:
a) 25 is 3 standard deviation from the mean
b) Is far away from the mean, only 0,3 % away from the right tail
c) 25 is pretty close to the mean (just a little farther from 1 standard deviation)
Step-by-step explanation:
We have a Normal Distribution with mean 16 in.
Case a) we also have a standard deviation of 3 inches
3* 3 = 9
16 (the mean) plus 3*σ equal 25 in. the evaluated value, then the value is 3 standard deviation from the mean
Case b) 25 is in the range of 99,7 % of all value, we can say that value is far away from the mean, considering that is only 0,3 % away from the right tail
Case c) If the standard deviation is 7 then
mean + 1*σ = 16 + 7 =23
25> 23
25 is pretty close to the mean only something more than 1 standard deviation
Answer: coeficient is 20 and the constant which is 13
Step-by-step explanation:
Answer:
D: (5 * 3)^3
D: 125 x 27
Step-by-step explanation:
<span>Simplifying
3x + 10 = 5x + 22
Reorder the terms:
10 + 3x = 5x + 22
Reorder the terms:
10 + 3x = 22 + 5x
Solving
10 + 3x = 22 + 5x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-5x' to each side of the equation.
10 + 3x + -5x = 22 + 5x + -5x
Combine like terms: 3x + -5x = -2x
10 + -2x = 22 + 5x + -5x
Combine like terms: 5x + -5x = 0
10 + -2x = 22 + 0
10 + -2x = 22
Add '-10' to each side of the equation.
10 + -10 + -2x = 22 + -10
Combine like terms: 10 + -10 = 0
0 + -2x = 22 + -10
-2x = 22 + -10
Combine like terms: 22 + -10 = 12
-2x = 12
Divide each side by '-2'.
x = -6
Simplifying
x = -6</span>
