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3 years ago

What is the domain of the function f(x) = x+1 / x2-6x+8

1 answer:

7 0

For this case we have that by definition, the domain of a function, is given for all the values for which the function is defined.

We have:

$f (x) = \frac {x + 1} {x ^ 2-6x + 8}$

The given function is not defined when the denominator is equal to zero. That is to say:

$x ^ 2-6x + 8 = 0$

To find the roots we factor, we look for two numbers that when multiplied give as a result "8" and when added as a result "-6". These numbers are:

$-4-2 = -6\\-4 * -2 = 8$

Thus, the factored polynomial is:

$(x-4) (x-2) = 0$

That is to say:

$x_ {1} = 4\\x_ {2} = 2$

Makes the denominator of the function 0.

Then the domain is given by:

All real numbers, except 2 and 4.

Answer:

x |x≠2,4

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The sum of the measures of two angles is 107.3º. One angle has a measure of 51º. What is the measure of the second angle?

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56.3°

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If the total is 107.3° just subtract 51° to get 56.3°

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3 years ago

What is the answer too (17-6 divided by 2 )+ 4 multiplied by 3

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2 years ago

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Answer:

option C is the correct ans..

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A function f from A to B is a relation from A to B which assosciates each element of A to a unique element of B..

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3 years ago

A survey on British Social Attitudes asked respondents if they had ever boycotted goods for ethical reasons (Statesman, January

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Answer:

a) 27.89% probability that two have ever boycotted goods for ethical reasons

b) 41.81% probability that at least two respondents have boycotted goods for ethical reasons

c) 41.16% probability that between 3 and 6 have boycotted goods for ethical reasons

d) The expected number is 2.3 and the standard deviation is 1.33.

Step-by-step explanation:

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.

23% of the respondents have boycotted goods for ethical reasons.

This means that $p = 0.23$

a) In a sample of six British citizens, what is the probability that two have ever boycotted goods for ethical reasons?

This is P(X = 2) when n = 6. So

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

$P(X = 2) = C_{6,2}.(0.23)^{2}.(0.77)^{4} = 0.2789$

27.89% probability that two have ever boycotted goods for ethical reasons

b) In a sample of six British citizens, what is the probability that at least two respondents have boycotted goods for ethical reasons?

Either less than two have, or at least two. The sum of the probabilities of these events is decimal 1. So

$P(X < 2) + P(X \geq 2) = 1$

$P(X \geq 2) = 1 - P(X < 2)$

In which

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

$P(X = 0) = C_{6,0}.(0.23)^{0}.(0.77)^{6} = 0.2084$

$P(X = 1) = C_{6,1}.(0.23)^{1}.(0.77)^{5} = 0.3735$

$P(X < 2) = P(X = 0) + P(X = 1) = 0.2084 + 0.3735 = 0.5819$

$P(X \geq 2) = 1 - P(X < 2) = 1 - 0.5819 = 0.4181$

41.81% probability that at least two respondents have boycotted goods for ethical reasons

c) In a sample of ten British citizens, what is the probability that between 3 and 6 have boycotted goods for ethical reasons?

Now n = 10.

$P(3 \leq X \leq 6) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)$

$P(X = 3) = C_{10,3}.(0.23)^{3}.(0.77)^{7} = 0.2343$

$P(X = 4) = C_{10,4}.(0.23)^{4}.(0.77)^{6} = 0.1225$

$P(X = 5) = C_{10,5}.(0.23)^{5}.(0.77)^{5} = 0.0439$

$P(X = 6) = C_{10,6}.(0.23)^{6}.(0.77)^{4} = 0.0109$

$P(3 \leq X \leq 6) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0.2343 + 0.1225 + 0.0439 + 0.0109 = 0.4116$

41.16% probability that between 3 and 6 have boycotted goods for ethical reasons

d) In a sample of ten British citizens, what is the expected number of people that have boycotted goods for ethical reasons? Also find the standard deviation.

$E(X) = np = 10*0.23 = 2.3$

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{10*0.23*0.77} = 1.33$

The expected number is 2.3 and the standard deviation is 1.33.

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3 years ago

How does the volume of a cone change if the height is doubled ?

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If you keep the radius the same and double the height, you find that by experimentation with this a few times, doubles your volume as well. That means that instead of 1/3 pi r^2 h, we will have 2/3 pi r^2 h. Your answer B.

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3 years ago

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