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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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What’s the answer to this?

babymother [125]

Answer:

○ $\displaystyle x > -3 \\ 5y ≥ -4x - 10$

Step-by-step explanation:

This system of inequalities has a shared portion at the origin, so we can easily jump to using the zero-interval test [test point (0, 0)] to verify the inequalities as false or true:

$\displaystyle 5[0] ≥ -4[0] - 10 → 0 ≥ -10$ ☑

$\displaystyle 0 > -3$ ☑

Plus, the top inequality has a dashed line ["<" or ">"], and the bottom inequality has a solid line, so this must have an equivalence line underneath each inequality symbol ["≤" or "≥"].

** Hold on though! Although it looks obvious about what the second inequality is, we need to double-check and make sure anyway, just to be on the safe side ☺:

$\displaystyle \frac{5y}{5} ≥ \frac{-4x - 10}{5} → y ≥ -\frac{4}{5}x - 2$

From the y-intercept of $\displaystyle [0, -2],$ we do $\displaystyle \frac{rise}{run}$ by either moving four blocks north over five blocks west or four blocks south over five blocks east [west and south are negatives]. This IS what our solid graph looks like, so we are correct!

So, from all what was explained, you have your answer.

I am joyous to assist you anytime.

8 0

3 years ago

Cara evaluated the expression below.

s2008m [1.1K]

Answer:

Cara multiplied only 4 and 7 together and did not multiply 4 and 13.

Step-by-step explanation:

Let us evaluate the given expression step by step,

$\frac{4(7-13)}{3} +(-4)^{2} -2(6-2)\\$

We can evaluate this expression in two ways; either by subtracting -13 from 7 and then multiply by 4 or by multiplying 4 to 7 and -13.

$\frac{28-52}{3} +16-2(4)$

$\frac{-24}{3} +16-8$

$-8+16-8=-16+16=0$

Now let us see where Cara made an error. We can see Cara just multiplied only 4 and 7 together and did not multiply 4 to 13.

Therefore, Cara made error in her first step.

5 0

3 years ago

Read 2 more answers

2/6 + 1/8 A) 11/24 B) 3/14 C) 5/24 D) 8/18

raketka [301]

So with these two fractions you're gonna have to find the LCD (lowest common denominator) before you start adding them. With 6 and 8, the LCD is 24.

So with the numerator and denominator of $\frac{2}{6}$ multiply them by 4. It'll look like this $\frac{2}{6} * \frac{4}{4} = \frac{8}{24}$

As for $\frac{1}{8}$ , do the same except multiply by 3. It'll look like this: $\frac{1}{8} * \frac{3}{3} = \frac{3}{24}$ .

Now add the new fractions together: $\frac{8}{24} + \frac{3}{24} = \frac{11}{24}$

A is the answer

4 0

3 years ago

If the volume of the pyramid is 64 ft³; and the height is 16 ft, what is the base area measured in square feet?

Law Incorporation [45]

The volume of a pyramid would be the base area times the height.
Given the height and volume we can find the base ares by dividing the volume by the height.

64 / 16 = 4

The base area is 4 square feet

8 0

3 years ago

Read 2 more answers

10m-3(2m-9)=9(m-1)+1

Studentka2010 [4]

Reorder the terms 10m+(-9*-3+2m*-3)=9(m+-1)+1
combine like terms 10m+-6m=4m 27+4m = 9(m+-1)+1
solve 27+4m=-8+9m
m=7

3 0

3 years ago