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3 years ago

Find the value of each of these quantities. C(5,3) C(8,8) C(12,6)

1 answer:

7 0

$C^n_k= \frac{n!}{(n-k)!c!} 
\\
\\C^5_3= \frac{5!}{(5-3)!3!} = \frac{5!}{2!3!} = \frac{5\times4\times3}{3\times2\times1} =10
\\
\\C^8_8= \frac{8!}{(8-8)!8!} = \frac{8!}{0!8!} = \frac{8!}{1\times8!}=1
\\
\\C^{12}_6= \frac{12!}{(12-6)!6!} = \frac{12!}{6!6!} = \frac{12\times11\times10\times9\times8\times7}{6\times5\times4\times3\times2\times1} =\frac{11\times3\times4\times7}{1} =924$

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Write an expression that simplify to -10

Ugo [173]

Answer:

-20/2 simplifies to -10.

8 0

3 years ago

Will mark brainliest! Thanks ! and like if you can please explain it cuz I want to understand it to :)

garik1379 [7]

Answer: F.) 7 triangles

Step-by-step explanation:

Congruent means completely equal in side lengths and angles. Think of this weird figure like 4 triangles that are see through and are covering a diamond underneath

Of those 4 "see through triangles", there are 3 equal to ΔABC

Now on the diamond underneath, there is another 4. Its hard to actually explain what I mean, but take two triangles from that dimaond. Theyre gonna be congruent to ΔABC.

That's 4 + 3 = 7 total triangles

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3 years ago

A segment has an endpoint at (1,−2). The midpoint is at (−4,−2). What are the coordinates of the other endpoint?

vodka [1.7K]

Answer:

The other midpoint is located at coordinates (-9,-2) (Second option)

Step-by-step explanation:

<u>Midpoints</u>

If P(a,b) and Q(c,d) are points in $\mathbb{R} ^2$ , the midpoint between them is the point exactly in the center of the line that joins P and Q. Its coordinates are given by

$\displaystyle x_m=\frac{a+c}{2}$

$\displaystyle y_m=\frac{b+d}{2}$

We are given one endpoint at P(1,-2) and the midpoint at M(-4,-2). The other endpoint must be at an equal distance from the midpoint as it is from P. We can see both given points have the same value of y=-2. This simplifies the calculations because we only need to deal with the x-coordinate.

The x-distance from P to M is 1-(-4)=5 units. This means the other endpoint must be 5 units to the left of M:

x (other endpoint)= - 4 - 5 = - 9

So the other midpoint is located at (-9,-2) (Second option)

5 0

3 years ago

A trucking firm has a large inventory of spare parts that have been in storage for a long time. It knowsthat some proportion of

Debora [2.8K]

Answer:

$0.1546\leq \widehat{p}\leq 0.3513$

Step-by-step explanation:

The firm tests 75 parts, and finds that 0.25 of them are notusable

n = 75

x = 0.25 \times 75 = 18.75≈19

$\widehat{p}=\frac{x}{n}$

$\widehat{p}=\frac{19}{75}$

$\widehat{p}=0.253$

Confidence level = 95%

So, Z_\alpha at 95% = 1.96

Formula of confidence interval of one sample proportion:

$=\widehat{p}-Z_\alpha \sqrt{\frac{\widehat{p}(1-\widehat{p}}{n}}\leq \widehat{p}\leq \widehat{p}+Z_\alpha \sqrt{\frac{\widehat{p}(1-\widehat{p}}{n}}$

$=0.253-(1.96)\sqrt{\frac{0.253(1-0.253)}{75}}\leq \widehat{p}\leq0.253+(1.96)\sqrt{\frac{0.253(1-0.253}{75}}$

Confidence interval $=0.1546\leq \widehat{p}\leq 0.3513$

7 0

3 years ago

Is 690,269 divisible by 9? Yes or No?

jonny [76]

Answer:

False.

Step-by-step explanation:

It is false because when dividing an odd number by an odd number, it usually isn't divisible. In this case, 690,26<u>9</u>. Is an odd number, because the last number, 9, is odd, which makes the whole thing odd. So, odd divided by odd never turns out well. (By the way the answer is 76,696.5555556).

8 0

2 years ago