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hram777 [196]
3 years ago
14

Factorise x^2+11x+18

Mathematics
2 answers:
VashaNatasha [74]3 years ago
7 0

Answer:

(x+9) (x+2)

Step-by-step explanation:

x^2+11x+18

x^2+9x+2x+18

x(x+9)+2(x+9)

(x+9) (x+2)

Semenov [28]3 years ago
4 0

Answer:

(x + 9)(x + 2 )

Step-by-step explanation:

Sum =11

Product = 18

Factors = 9 , 2

When you multiply (9*2 = 18) and when you add (9 +2 = 11).

x² + 11x + 18 = x² + 9x + 2x + (9*2)

                   =x(x + 9) + 2(x + 9)

                  = (x + 9)(x + 2 )

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Which of these ordered pairs is a solution to the inequality
bezimeni [28]

Answer:

(1, -1)

Step-by-step explanation:

If you replace y and x with (1 and -1) you have -1 - 2^1 < -3

And that equals -3 if solved. The sign says equal to or less than, so you answer is (1, -1)

7 0
3 years ago
5 POINTS !! ANSWER FASTTT
MariettaO [177]
N= 2

Substitute 2 in for n in expression

=(5 + n) ÷ (n - 1)
=(5 + 2) ÷ (2 - 1)
=7 ÷ 1
=7

If n= 2, the expression equals 7.

Hope this helps! :)
3 0
3 years ago
The Washington, DC, region has one of the fastest-growing foreclosure rates in the nation, as 15,613 homes went into foreclosure
Ilia_Sergeevich [38]

Answer:

a) 0.6226 = 62.26% probability that in a given year, fewer than 2 out of 100 houses in the Washington, DC area will go up for foreclosure.

b) 0.7837 = 78.37% probability that in a given year, fewer than 2 out of 100 houses in the nation will go up for foreclosure.

c) The proportion of foreclosures in the Nation is lower than in Washington, which means that with a sample size of 100, it is likely to have a small number(fewer than 2) of foreclosures than Washington DC.

Step-by-step explanation:

For each home, there are only two possible outcomes. Either it goes into foreclosure, or it does not. The probability of a home going into foreclosure is independent of other homes. This 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.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

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

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

a. What is the probability that in a given year, fewer than 2 out of 100 houses in the Washington, DC area will go up for foreclosure?

The foreclosure rate is 1.31% for the Washington, DC area, which means that p = 0.0131

We wanto to find, with n = 100:

P(X < 2) = P(X = 0) + P(X = 1)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{100,0}.(0.0131)^{0}.(0.9869)^{100} = 0.2675

P(X = 1) = C_{100,1}.(0.0131)^{1}.(0.9869)^{99} = 0.3551

P(X < 2) = P(X = 0) + P(X = 1) = 0.2675 + 0.3551 = 0.6226

0.6226 = 62.26% probability that in a given year, fewer than 2 out of 100 houses in the Washington, DC area will go up for foreclosure.

b. What is the probability that in a given year, fewer than 2 out of 100 houses in the nation will go up for foreclosure?

Foreclosure rate of 0.87% for the nation, which means that p = 0.0087. So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{100,0}.(0.0087)^{0}.(0.9913)^{100} = 0.4174

P(X = 1) = C_{100,1}.(0.0087)^{1}.(0.9913)^{99} = 0.3663

P(X < 2) = P(X = 0) + P(X = 1) = 0.4174 + 0.3663 = 0.7837

0.7837 = 78.37% probability that in a given year, fewer than 2 out of 100 houses in the nation will go up for foreclosure.

c. Comment on the above findings.

The proportion of foreclosures in the Nation is lower than in Washington, which means that with a sample size of 100, it is likely to have a small number(fewer than 2) of foreclosures than Washington DC.

7 0
3 years ago
I need help PLEASE! :(
Sedaia [141]

Answer:

B

Step-by-step explanation:

7 0
3 years ago
10. A random sample of 10 fibers is taken from a collection of 92 fibers that consists of 43 fibers of polymer A, 17 fibers of p
vazorg [7]

Answer:

0.1150 = 11.50% probability that the sample does not contain any fibers of polymer B

Step-by-step explanation:

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

In this question:

Fibers are chosen without replacement, which means that we use the hypergeometric distribution.

92 fibers means that N = 92

Sample of 10 means that n = 10

No polymeter B which means that x = 0

17 fibers of polymeter B which means that k = 17

a. What is the probability that the sample does not contain any fibers of polymer B

This is P(X = 0).

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

P(X = 0) = h(0,92,10,17) = \frac{C_{17,0}*C_{75,10}}{C_{92,10}} = 0.1150

0.1150 = 11.50% probability that the sample does not contain any fibers of polymer B

4 0
2 years ago
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