1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Dmitry_Shevchenko [17]
3 years ago
5

If P(x) = P

ormula">x^{n} + P_{n-1}x^{n-1} + · · · + P_{0} is divided by (x - a), show that the remainder is P(a)
Mathematics
1 answer:
seropon [69]3 years ago
3 0

If P(x) = p_nx^n + p_{n-1}x^{n-1}+\ldots+p_0 is divided by (x-a), then P(x) = (x-a) \cdot Q(x) + R(x) for some polynomials Q,R. Moreover, \deg R < 1 (because \deg (x-a) = 1), so there exists  \alpha \in \mathbb{R} such that R(x) = \alpha for all x \in \mathbb{R}. But if we calculate P(a), it turns out that P(a) = (a-a)\cdot Q(a) + \alpha, so R(x) = \alpha = P(a). \blacksquare

You might be interested in
A tablet computer costs 189.69. it is marked up 30%. What is the final price of the tablet computer after its marked up.
saveliy_v [14]
The initial cost is 189.69. It is marked up 30%.

By simple calculations, 

Final cost of the tablet computer = Initial price + 30% of marked price

= 189.69 + (30/100 x 189.69)

This gives us the net value of 245.7. Hence the price of the computer after it's been marked up will be 245.7
6 0
3 years ago
Read 2 more answers
Graph represents the solution of 2y +6 &gt; 4
NemiM [27]

Answer:

y = -32

Step-by-step explanation:

brainliest?

7 0
3 years ago
PLEASE HELP ASAP IM STUCK HELP PLEASE
sasho [114]

Answer:

x>-2  and x<5

-2 <x<5

Step-by-step explanation:

We have open circles at -2 and 5 and are between the two numbers so we have and AND statement. It can be written either

x>-2  and x<5

or

-2 <x<5

6 0
3 years ago
If 90 percent of automobiles in Orange County have both headlights working, what is the probability that in a sample of eight au
Marta_Voda [28]

Answer:

P(X \geq 7) = P(X=7) +P(X=8)

And we can find the individual probabilities using the probability mass function

P(X=7)=(8C7)(0.9)^7 (1-0.9)^{8-7}=0.3826  

P(X=8)=(8C8)(0.9)^8 (1-0.9)^{8-8}=0.4305  

And replacing we got:

P(X \geq 7) = P(X=7) +P(X=8)=0.3826 +0.4305=0.8131

Step-by-step explanation:

Previous concepts  

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".  

Solution to the problem

Let X the random variable of interest "number of automobiles with both headligths working", on this case we now that:  

X \sim Binom(n=8, p=0.9)  

The probability mass function for the Binomial distribution is given as:  

P(X)=(nCx)(p)^x (1-p)^{n-x}  

Where (nCx) means combinatory and it's given by this formula:  

nCx=\frac{n!}{(n-x)! x!}  

And for this case we want to find this probability:

P(X \geq 7) = P(X=7) +P(X=8)

And we can find the individual probabilities using the probability mass function

P(X=7)=(8C7)(0.9)^7 (1-0.9)^{8-7}=0.3826  

P(X=8)=(8C8)(0.9)^8 (1-0.9)^{8-8}=0.4305  

And replacing we got:

P(X \geq 7) = P(X=7) +P(X=8)=0.3826 +0.4305=0.8131

7 0
3 years ago
Read 2 more answers
Find the GCF of 6x+4 and divide
ella [17]
The GCF is 2
Merry Christmas
4 0
3 years ago
Other questions:
  • A personal code for an online account must be 6 characters, either letters or numbers, which can repeat. How many codes are poss
    6·1 answer
  • 50 tens equals how many hundreds
    7·2 answers
  • Aaden is packing boxes into a carton that is 8 inches long 8 inches wide and 4 inches tall. the boxes are 2 inches long 1 inch w
    7·1 answer
  • X-21=6 what does x equal??
    5·2 answers
  • How do you solve x/9-1/3=-5/3
    13·1 answer
  • Kaya used these steps to solve the equation 7+2x=2(x−1)+4. Which choice describes the meaning of her result, 7=2?
    15·1 answer
  • The graph of | x | is the solid black graph below. Which function represents the dotted graph? (pls help)
    8·1 answer
  • Suppose that the mean time that visitors stay at a museum is 94.2 minutes with a standard deviation of 15.5 minutes. The standar
    6·1 answer
  • Find the value of x. Round the length to the nearest tenth of a unit. <br><br> Please help!
    10·1 answer
  • How to find z scores
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!