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2 years ago

Evaluate Combination (6,6)

Mathematics

1 answer:

andrew11 [14]2 years ago

8 0

Answer:

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

On this case n =6 and x =6 we got:

$6C6 = \frac{6!}{6! (6-6)!} = \frac{6!}{6! 0!}= \frac{6!}{6!}=1$

Step-by-step explanation:

The utility for the combination formula is in order to find the number of ways to order a set of elements

For this case we want to find the following expression:

$6C6$

And the general formula for combination is given by:

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

On this case n =6 and x =6 we got:

$6C6 = \frac{6!}{6! (6-6)!} = \frac{6!}{6! 0!}= \frac{6!}{6!}=1$

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Determine the values of the constants b and c so that the function given below is differentiable. f(x)={2xbx2+cxx≤1x>1

Lera25 [3.4K]

Assuming the function is

$f(x)=\begin{cases}2x&\text{for }x\le1\\bx^2+cx&\text{for }x>1\end{cases}$

For $f(x)$ to be differentiable, it necessarily has to be continuous. For this condition to be met, we need

$\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1^+}f(x)=f(1)$
$\iff\displaystyle\lim_{x\to1}2x=\lim_{x\to1}(bx^2+cx)$
$\iff2=b+c$

For the derivative to exist, the one-sided limits of the derivative must also exist and be equal. We have

$f'(x)=\begin{cases}2&\text{for }x1\end{cases}$

$\displaystyle\lim_{x\to1^-}2=\lim_{x\to1^+}(2bx+c)$
$\iff2=2b+c$

Now we solve for $b$ and $c$ :

$\begin{cases}b+c=2\\2b+c=2\end{cases}\implies b=0,c=2$

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3 years ago

Solve using elimination 5x+7y=9 <br> 2x-3y=-37

uranmaximum [27]

Answer:

x = -8

y = 7

Step-by-step explanation:

5x + 7y = 9

2x - 3y = -37

1.) First, multiply each side to match either y-values or x-values. (In this example, we'll use match x-values)

10x + 14y = 18 (multiplied by 2)

10x - 15y = -185 (multiplied by 5)

2.) Then, subtract the entirety of one equation to isolate the y-value.

10x + 14y = 18

-10x + 15y = 185

3.) Add and subtract values and divide to find y.

29y = 203

y = 7

4.) Plug-in y to solve for x into one equation, or repeat steps 1-3.

15x + 21y = 27

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29x = -232

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2 years ago

5. Two unbiased dice are rolled. Calculate the probability that the sum of the two dice is:

IceJOKER [234]

The sample space has 36 possible pairs from 1,1 1,2 1,3 up to 6,5 and 6,6

(a). Three pairs add to 4 1,3 2,2 and 3,1 so P(4) = 3/36 = 1/12

(b). 6 pairs add to 7 so P(7) = 6/36 = 1/6

(c) 15 pairs add to less than 7 so P(<7) = 15/36 = 5/12

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2 years ago

Which type of transformation maps trapezoid PQRS onto trapezoid P'Q'R'S'? reflection rotation translation dilation

Keith_Richards [23]

Answer:

Dilation.

Step-by-step explanation:

From the given picture , it can be seen that the size of trapezoid P'Q'R'S' is decreased from trapezoid PQRS .

Reflection , rotation and translation are rigid motions that produces congruent images and do not change the size of the shapes.

But dilation is not a rigid motion because it changes the size of the shape by using a scale factor.

Hence, the transformation maps trapezoid PQRS onto trapezoid P'Q'R'S' is "Dilation".

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2 years ago

Read 2 more answers

You pay a registration fee and a monthly fee to join a local fitness center. The table shows the total cost of joining the fitne

Alekssandra [29.7K]

Answer:

100 divided by 3=33.33 therefore 33.33 per month

Step-by-step explanation:

Equation:

33.33x9= 299.97

This is for 9 months

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