Answer:
286 possible outcomes.
Step-by-step explanation:
We have been given total 13 identical marbles
We need to select 10 out of 13
We will use combination:
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
here,n=13 and r=10 on substituting the values in the formula we get:
[tex]^13C_{10}=\frac{13!}{10!(13-10)!}[/tex]
[tex]^13C_{10}=\frac{13\cdot 12\cdot 11\cdot10!}{10!\cdot 3!}[/tex]
[tex]\Rightarrow ^13C_{10}=\frac{13\cdot12\cdot11}{3\cdot2\cdot1}[/tex]
[tex]\Rightarrow 286[/tex]
So, there are 286 possible outcomes.
Possible number of outcome that she can select [tex]10[/tex] marbles from [tex]13[/tex] identical marbles are [tex]\boxed{286}[/tex].
Further explanation:
The formula of combination can be expressed as,
[tex]\boxed{^n{C_r} = \frac{{n!}}{{r!\left( {n - r} \right)!}}}[/tex]
Given:
A bag contains [tex]13[/tex] identical marbles.
Calculation:
Suzy randomly picks [tex]10[/tex] marbles from a bag of [tex]13[/tex] identical marble.
The number of possible outcomes that she can select [tex]10[/tex] marbles can be obtained as,
[tex]{\text{Possible}}\,{\text{outcomes}} = {\,^{13}}{C_{10}}[/tex]
Substitute [tex]13[/tex] for [tex]n[/tex] and [tex]10[/tex] for [tex]r[/tex] in equation [tex]{^n{C_r} = \frac{{n!}}{{r!\left( {n - r} \right)!}}}[/tex] to obtain the possible outcomes that she can select [tex]10[/tex] marbles from [tex]13[/tex] identical marbles.
[tex]\begin{aligned}{\text{Possible}}\,{\text{outcomes}}&= {\,^{13}}{C_{10}} \\ &= \frac{{13!}}{{10!\left( {13 - 10} \right)!}} \\ &= \frac{{13!}}{{10!\left( {3!} \right)}} \\ &= \frac{{13 \times 12 \times 11 \times 10!}}{{10!\, \times 3 \times 2 \times 1}} \\ &= 286\\\end{aligned}[/tex]
Hence, possible number of outcome that she can select [tex]10[/tex] marbles from [tex]13[/tex] identical marbles are [tex]\boxed{286}[/tex].
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Combination
Keywords: Suzy, picks, marbles, 13 identical marbles, 10 marbles, possible, outcomes, select, combination, randomly picks, a bag contains 13 marbles.
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What is the transverse axis of a hyperbola?"The transverse axis is a line segment that passes through the center of the hyperbola and has vertices as its endpoints."
Given, the vertices of the hyperbola are at (-9, 0) and (9, 0).
Therefore, the length of the transverse axis is
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Therefore, the length of the transverse axis is 18 units.
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Step-by-step explanation:
Find the lowest common denominator of the following fractions. 5/n-2 and n+2/n^2-4
Final answer:
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Explanation:
The question asks to find the lowest common denominator (LCD) of two fractions: 5/(n-2) and (n+2)/[tex]n^2 - 4,[/tex]. To do this, we need to factor each denominator, if possible, and then determine the LCD. The second denominator can be factored into (n+2)(n-2) since it is a difference of squares. For the LCD, we need each factor present at least as many times as it occurs in any one of the denominators. The first fraction is already missing the (n+2) factor, so we multiply the numerator and the denominator of this fraction by (n+2) to have an equivalent fraction with the common denominator.
The common denominator then is (n+2)(n-2), equivalent to[tex]n^2 - 4,[/tex] So the LCD of the two fractions is[tex]n^2 - 4.[/tex] We can use this denominator to combine fractions or compare them. No further steps are necessary because the second fraction already has the LCD. Therefore, the LCD for both fractions is [tex]n^2 - 4.[/tex]
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Step-by-step explanation:
Interquartile Range:
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PLEASE DO THE WORK AND SHOW ME!!!!!
Please answer, and I'll ask this and I'll do the question again, and I'll do the same points.
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