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3 years ago

Ashley, Bob, Claire, and Daniel are among 13 students who entered a lottery to win a free vacation to Paris.

Mathematics

1 answer:

AlladinOne [14]3 years ago

7 0

Answer:

0.0014 = 0.14% probability that Ashley, Bob, Claire, and Daniel will be chosen.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the students are chosen is not important, so the combinations formula is used to solve this question.

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.

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

Desired outcomes:

4 students from a set of 4(Ashley, Bob, Claire, and Daniel). So

$D = C_{4,4} = \frac{4!}{4!(4-4)!} = 1$

Total outcomes:

4 students from a set of 13(number of students in the lottery). So

$T = C_{13,4} = \frac{13!}{4!(13-4)!} = 715$

Probability:

$p = \frac{D}{T} = \frac{1}{715} = 0.0014$

0.0014 = 0.14% probability that Ashley, Bob, Claire, and Daniel will be chosen.

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If m (x) = StartFraction x + 5 Over x minus 1 EndFraction and n(x) = x – 3, which function has the same domain as (m circle n) (

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Question:

If m (x) = StartFraction x + 5 Over x minus 1 EndFraction and n(x) = x – 3, which function has the same domain as (m circle n) (x)?

h (x) = StartFraction x + 5 Over 11 EndFraction

h (x) = StartFraction 11 Over x minus 1 EndFraction

h (x) = StartFraction 11 Over x minus 4 EndFraction

h (x) = StartFraction 11 Over x minus 3 EndFraction

Answer:

Option C: $h(x)=\frac{11}{x-4}$ has the same domain as $(m \circ n)(x)$

Explanation:

It is given that $m(x)=\frac{x+5}{x-1}$ and $n(x)=x-3$

Let us find the domain of $(m \circ n)(x)$

$\begin{aligned}(m \circ n)(x) &=m(n(x))\\&=m(x-3) \\ &=\frac{(x-3)+5}{(x-3)-1} \\ &=\frac{x+2}{x-4} \end{aligned}$

Now, let us equate the denominator equal to zero to determine the domain.

$x-4=0$

$x=4$

Thus, the function becomes undefined at the point $x=4$

Hence, the domain of $(m \circ n)(x)$ is $(-\infty, 4) \cup(4, \infty)$

Now, we shall find the function which has the same domain as $(m \circ n)(x)$

Option A: $h(x)=\frac{x+5}{11}$

The function h(x) has the domain of set of all real numbers $$-\infty$

Thus, the interval $(-\infty,\infty)$ is not the same domain as $(-\infty, 4) \cup(4, \infty)$

Hence, Option A is not the correct answer.

Option B: $h(x)=\frac{11}{x-1}$

Equating the denominator equal to zero, the function becomes undefined at the point $x=1$

Thus, the function h(x) has the domain of $(-\infty,-1) \cup(-1, \infty)$ is not the same domain as $(-\infty, 4) \cup(4, \infty)$

Hence, Option B is not the correct answer.

Option C: $h(x)=\frac{11}{x-4}$

Equating the denominator equal to zero, the function becomes undefined at the point $x=4$

Thus, the function h(x) has the domain of $(-\infty, 4) \cup(4, \infty)$ is the same domain as $(-\infty, 4) \cup(4, \infty)$

Hence, Option C is the correct answer.

Option D: $h(x)=\frac{11}{x-3}$

Equating the denominator equal to zero, the function becomes undefined at the point $x=3$

Thus, the function h(x) has the domain of $(-\infty,3) \cup(3, \infty)$ is not the same domain as $(-\infty, 4) \cup(4, \infty)$

Hence, Option D is not the correct answer.

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Solving for the polynomial function of least degree with integral coefficients whose zeros are -5, 3i

We have:
x = -5

Then x + 5 = 0

Therefore one of the factors of the polynomial function is (x + 5)

Also, we have:
x = 3i
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x = Sqrt(-9)
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Therefore one of the factors of the polynomial function is (x^2 + 9)

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