Answer:
(A) -3 ≤ x ≤ 1
Step-by-step explanation:
The given function is presented as follows;
h(x) = x² - 1
From the given function, the coefficient of the quadratic term is positive, and therefore, the function is U shaped and has a minimum value, with the slope on the interval to the left of <em>h</em> having a negative rate of change;
The minimum value of h(x) is found as follows;
At the minimum of h(x), h'(x) = d(h(x)/dx = d(x² - 1)/dx = 2·x = 0
∴ x = 0/2 = 0 at the minimum
Therefore, the function is symmetrical about the point where x = 0
The average rate of change over an interval is given by the change in 'y' and x-values over the end-point in the interval, which is the slope of a straight line drawn between the points
The average rate of change will be negative where the y-value of the left boundary of the interval is higher than the y-value of the right boundary of the interval, such that the line formed by joining the endpoints of the interval slope downwards from left to right
The distance from the x-value of left boundary of the interval that would have a negative slope from x = 0 will be more than the distance of the x-value of the right boundary of the interval
Therefore, the interval over which <em>h</em> has a negative rate of change is -3 ≤ x ≤ 1
Answer:
(b)
Step-by-step explanation:
Let E: Event of getting a 3 in the spinner.
So, the number of favorable outcomes = 11
Total number of outcomes = Number of times the outcomes is {1,2,3,4,5,6}
= {13 +10 +11+16+11} = { 61}
So, the total number of outcomes = 61
So, here
Answer: C. 11/15
Step-by-step explanation:
Given : The fraction of stores inventory is children's clothing=
The fraction of stores inventory is women's clothing=
Since both events are independent.
Therefore, the fraction of the total inventory is children's or women's clothing = (Fraction of stores inventory is children's clothing ) + (Fraction of stores inventory is women's clothing )
∴ The fraction of the total inventory is children's or women's clothing
Hence, the correct answer is C. 11/15 .