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Aliun [14]
3 years ago
13

Divide p(x)=x^3-4x^2+x+6 by (x-3). Find the remainder and the quotient.

Mathematics
1 answer:
klemol [59]3 years ago
6 0

Answer:

Quotient is <u>x²</u><u> </u><u>-</u><u> </u><u>x</u><u> </u><u>-</u><u> </u><u>2</u>

<u>Remainder</u><u> </u><u>is</u><u> </u><u>0</u>

You might be interested in
What is the mean of this data set? {6, 11, 5, 2, 7} Enter your answer as a decimal in the box.
Elenna [48]

Answer:

The mean is 6.2.

Step-by-step explanation:

The "mean" is the same thing as the "average". Essentially, the question is asking for the average of the numbers.

So:

Add up all of the terms. [6 + 11 + 5 + 2 + 7] = 31

You find the average by dividing the sum of the terms (31) by the number of terms (5).

31/5 = 6.2

The mean is 6.2.

I hope this helped! :)

4 0
2 years ago
The half-life of the radioactive element unobtanium-43 is 10 seconds. If 48 grams of unobtanium-43 are initially present, how ma
natka813 [3]

Answer:

At time, 10 seconds, the mass remaining is 24 grams

At time, 20 seconds, the mass remaining is 12 grams

At time, 30 seconds, the mass remaining is 6 grams

At time, 40 seconds, the mass remaining is 3 grams

At time, 50 seconds, the mass remaining is 1.5 grams

Step-by-step explanation:

Given;

initial mass of the radioactive element  = 48 grams

half life, t = 10 seconds

time of decay (s)                          remaining mass of the  radioactive element

0 ------------------------------------------------- 48 grams

10------------------------------------------------- 24 grams

20 ------------------------------------------------- 12 grams

30 -------------------------------------------------- 6 grams

40 --------------------------------------------------- 3 grams

50 ----------------------------------------------------- 1.5 grams

60------------------------------------------------------0.75 grams

Thus;

At time, 10 seconds, the mass remaining is 24 grams

At time, 20 seconds, the mass remaining is 12 grams

At time, 30 seconds, the mass remaining is 6 grams

At time, 40 seconds, the mass remaining is 3 grams

At time, 50 seconds, the mass remaining is 1.5 grams

7 0
3 years ago
In a recent survey of 25 voters, 17 favor a new city regulation and 8 oppose it. What is the probability that in a random sample
Rasek [7]

Answer:

P(X=2)=(6C2)(0.68)^2 (1-0.68)^{6-2}=0.0727

Step-by-step explanation:

1) 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".

2) Solution to the problem

The probability in favor of the regulation based on the recent survey is:

p = \frac{17}{25}=0.68

Let X the random variable of interest "Number of favor respondents about the regulation", on this case we now that:

X \sim Binom(n=6, p=0.68)

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 we want to find this probability:

P(X=2)=(6C2)(0.68)^2 (1-0.68)^{6-2}=0.0727

If we use X= "Number of respondednts opposed to the regulation we got the same answer", but on this case p = 1-0.68=0.32, and we want this probability:

P(X=4)=(6C4)(0.32)^4 (1-0.32)^{6-4}=0.0727

6 0
3 years ago
David goes into a candy store with $5.00. He buys 9 peppermints for $0.15 each and some sour candies. Each sour candy costs $0.2
Agata [3.3K]

Answer:

5 ≥ 9*.15 + x*.25

He can buy up to 14 candies

Step-by-step explanation:

Total money ≥number of peppermints * cost per peppermint + number of sour candies * cost per sour candy

We know he has 5 dollars.  He bought 5 peppermints at $.15 cents each and x sour candies at $.25 each

Substituting in

5 ≥ 9*.15 + x*.25

5≥1.35 + .25x

Subtract 1.35 on each side

5-1.35 ≥ 1.35-1.35+.25x

3.65≥.25x

Divide by .25 on each side

3.65/.25 ≥ .25x/.25

14.6 ≥ x

He can buy up to 14 candies.  You can't buy part of a candy

6 0
3 years ago
307,407 rouned to the nereist thousandth
kobusy [5.1K]
Rounded to the thousands would be 307,000 and thousandths is 307.407
6 0
3 years ago
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