Answer:
And we can find the following probability:
And the last probability can be founded using the normal standard distribution or excel.
Step-by-step explanation:
For this case we define the random variable X as the ages of vehicles. We know the following info for this variable:
represent the mean
represent the deviation in years
They select a sample size of n=40>30. And they want to find this probability:
Since the sample size is large enough we can use the central limit theorem and the distribution for the sample mean would be:
We can use the z score formula given by:
And if we find the z score for 4 we got:
And we can find the following probability:
And the last probability can be founded using the normal standard distribution or excel.
Answer:
Vertex
Step-by-step explanation:
Answer:
B) 2
Step-by-step explanation:
The first differences are increasing by 1 from term to term:
8-12 = -4
5-8 = -3
3-5 = -2
2-3 = -1 . . . . . if the next term is 2, as we believe it should be.
_____
<em>Comment on number sequences</em>
Any finite length sequence of n numbers can be modeled exactly by an n-1 degree polynomial. That is, a 4th-degree polynomial can be made to describe the sequence regardless of the next term you may choose.
If you choose the next term to be 2 as we suggest, then the sequence can be modeled by a 2nd-degree polynomial ...
(n² -11n +34)/2 . . . . for n = 1, 2, 3, ...
Answer:
Step-by-step explanation:
<u>Roots of a polynomial</u>
If we know the roots of a polynomial, say x1,x2,x3,...,xn, we can construct the polynomial using the formula
Where a is an arbitrary constant.
We know three of the roots of the degree-5 polynomial are:
We can complete the two remaining roots by knowing the complex roots in a polynomial with real coefficients, always come paired with their conjugates. This means that the fourth and fifth roots are:
Let's build up the polynomial, assuming a=1:
Since:
Operating the last two factors:
Operating, we have the required polynomial:
2X^2+22x+318=1270
2x^2+22x-952=0
x^2+11x-476=0
(x+28)(x-17)=0
x=17
