Answer:
As consequence of the Taylor theorem with integral remainder we have that

If we ask that
has continuous
th derivative we can apply the mean value theorem for integrals. Then, there exists
between
and
such that

Hence,

Thus,

and the Taylor theorem with Lagrange remainder is
.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
When a polynomial f(x) is divided by (x - a) then remainder is f(a)
A
divided by (x + 4 ), then a = - 4
- 8(- 4)² + 16 = 256 - 128 + 16 = 144 ≠ 20
B
divided by (x - 2), then a = 2
3(2)³ + 7(2)² + 5(2) + 2
= 3(8) + 7(4) + 10 + 2
= 24 + 28 + 12 = = 64 ≠ 20
C
divided by (x + 5) , then a = - 5
(- 5)³ + 5(- 5)² - 4(- 5) + 6
= - 125 + 125 + 20 + 6 = 26 ≠ 20
D
divided by (x - 2), then a = 2
3
- 5(2)³ + 5(2) + 2
= 3(16) - 5(8) + 10 + 2
= 48 - 40 + 12 = 20 ← Remainder of 20
Answer:
0.1348 = 13.48% probability that 3 of them entered a profession closely related to their college major.
Step-by-step explanation:
For each graduate, there are only two possible outcomes. Either they entered a profession closely related to their college major, or they did not. The probability of a graduate entering a profession closely related to their college major is independent of other graduates. This, coupled with the fact that they are chosen with replacement, means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which
is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.
53% reported that they entered a profession closely related to their college major.
This means that 
9 of those survey subjects are randomly selected
This means that 
What is the probability that 3 of them entered a profession closely related to their college major?
This is P(X = 3).


0.1348 = 13.48% probability that 3 of them entered a profession closely related to their college major.
Answer:
Well you do what fraction says, 8 divided by 12 to get .6 repeating
Answer:
The probability of success is .12
The probability of failure is .88
According to the binomial theorem the probability of 3 success is
10! / (3! * 7!) * .12^3 * .88^7 = .085