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3 years ago

Find the binomial coefficient (4 2)

1 answer:

5 0

$\large\begin{array}{l} \mathsf{\dbinom{4}{2}=\dfrac{4!}{2!\cdot (4-2)!}}\\\\ \mathsf{\dbinom{4}{2}=\dfrac{4!}{2!\cdot 2!}}\\\\ \mathsf{\dbinom{4}{2}=\dfrac{4\cdot 3 \cdot \diagup\!\!\!\! 2!}{2!\cdot \diagup\!\!\!\! 2!}}\\\\ \mathsf{\dbinom{4}{2}=\dfrac{4\cdot 3}{2\cdot 1}}\\\\ \mathsf{\dbinom{4}{2}=\dfrac{12}{2}}\\\\ \boxed{\begin{array}{c}\mathsf{\dbinom{4}{2}=6}\end{array}}\quad\longleftarrow\quad\textsf{this is the answer.} \end{array}$

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Need help pls<br>thank you in advance

ira [324]

Answer:

<u />

$\textsf{Mean}\:\overline{X}=\sf \dfrac{\textsf{sum of all the data values}}{\textsf{total number of data values}}$

$\implies \sf Mean\:(Nilo)=\dfrac{5+6+14+15}{4}=\dfrac{40}{4}=10$

$\implies \sf Mean\:(Lisa)=\dfrac{8+9+11+12}{4}=\dfrac{40}{4}=10$

<h3><u>Standard Deviation</u></h3>

$\displaystyle \textsf{Standard Deviation }s=\sqrt{\dfrac{\sum X^2-\dfrac{(\sum X)^2}{n}}{n-1}}$

$\begin{aligned}\displaystyle \textsf{Standard Deviation (Nilo)} & =\sqrt{\dfrac{(5^2+6^2+14^2+15^2)-\dfrac{(5+6+14+15)^2}{4}}{4-1}}\\\\& = \sqrt{\dfrac{482-\dfrac{40^2}{4}}{3}}\\\\& = \sqrt{\dfrac{82}{3}}\\\\& = 5.23\end{aligned}$

$\begin{aligned}\displaystyle \textsf{Standard Deviation (Lisa)} & =\sqrt{\dfrac{(8^2+9^2+11^2+12^2)-\dfrac{(8+9+11+12)^2}{4}}{4-1}}\\\\& = \sqrt{\dfrac{410-\dfrac{40^2}{4}}{3}}\\\\& = \sqrt{\dfrac{10}{3}}\\\\& = 1.83\end{aligned}$

<h3><u>Summary</u></h3>

Nilo has a mean score of 10 and a standard deviation of 5.23.

Lisa has a mean score of 10 and a standard deviation of 1.83.

The <u>mean</u> scores are the <u>same</u>.

Nilo's standard deviation is higher than Lisa's. Therefore, Nilo's test scores are more <u>spread out</u> that Lisa's, which means Lisa's test scores are more <u>consistent</u>.

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1 year ago

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Answer:

Step-by-step explanation:

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3 years ago

Amy has 12 brown golf tees, 8 white golf tees, 10 red golf tees, 6 blue golf tees, and 12 green golf tees in her golf bag. If sh

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Answer:

The green tee because i.t is the second largest then the blue or brown even though it is greater then the brown

Step-by-step explanation:

<u>Use mental math and common sense.</u>

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3 years ago

Activity

mina [271]

Answer:

Factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12. A positive integer greater than 1, or an algebraic expression, that has only two factors (i.e., itself and 1) is termed prime; a positive integer or an algebraic expression that has more than two factors is termed composite. The prime factors of a number or an algebraic expression are those factors which are prime. By the fundamental theorem of arithmetic, except for the order in which the prime factors are written, every whole number larger than 1 can be uniquely expressed as the product of its prime factors; for example, 60 can be written as the product 2·2·3·5.

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2 years ago

Ashlyn needs to bring a dessert to her dinner party. If the bakery has eight pies to choose from, how many ways can Ashlyn choos

Snowcat [4.5K]

<u>Ashely have </u><u>56 ways</u><u> to choose from</u>

This question can be solved using a system in mathematics called Permutation and it's in a topic of mathematics called combinatorics.

<h3 /><h3>Permutation</h3>

This is the process of arranging a particular set of data in different ways.

Since Ashely is choosing 3 desserts out of 8 in no specific ways

$P=\frac{n!}{(n-r)!}$

Where n = total number of ways available

r = total numbers that would be selected.

Data given

n = 8
r = 3

Let's substitute these values into the equation.

$P=\frac{8!}{(8-3)!3!} \\P=\frac{8*7*6*5*4*3*2*1}{5*4*3*2*1*3*2*1}\\P=56$

From the calculation above, Ashley have 56 ways in which can choose 3 dessert from an 8 choice.

Learn more about permutation here;

brainly.com/question/11871015

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