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Bas_tet [7]
3 years ago
5

In a set of 25 aluminum castings, four castings are defective (D), and the remaining twenty-one are good (G). A quality control

inspector randomly selects three of the twenty-five castings without replacement to test. The sample space for selecting the group to test contains ____________ elementary events.
Mathematics
1 answer:
lianna [129]3 years ago
6 0

Answer:

The sample space for selecting the group to test contains <u>2,300</u> elementary events.

Step-by-step explanation:

There are a total of <em>N</em> = 25 aluminum castings.

Of these 25 aluminum castings, <em>n</em>₁ = 4 castings are defective (D) and <em>n</em>₂ = 21 are good (G).

It is provided that a quality control inspector randomly selects three of the twenty-five castings without replacement to test.

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

{n\choose k}=\frac{n!}{k!(n-k)!}

Compute the number of samples that are possible as follows:

{25\choose 3}=\frac{25!}{3!\times (25-3)!}

      =\frac{25\times 24\times 23\times 22!}{3!\times 22!}\\\\=\frac{25\times 24\times 23}{3\times 2\times 1}\\\\=2300

The sample space for selecting the group to test contains <u>2,300</u> elementary events.

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Will give brainliest and add more points to your acc if good awnser Please help ASAP
joja [24]
Hailey's mixing two different coffee blends.  Represent them by x and y (in pounds).  Then x + y = 5 lb, and x = 5 - y.How much puree Sum. beans are we talking about here?
0.20x +0.80y = 0.60(5 lb)  Mult all 3 terms by 100 to get rid of factions:
20x + 80 y = 300.  Substitute 5-y for x:
20(5-y) + 80y = 300 => 100-20y + 80y = 300 => 60y = 200,  so                                                                                  y = 20/6 or 10/3 lb                                              den x = 5-10/3, or    x =5/3 lb
Use 5/3 lb of the first blend and 10/3 lb of the second blend to come up with 5 lb of a 60% blend.
7 0
2 years ago
Increase 400litres by 20%
Sati [7]

Answer:

480 Litres

Step-by-step explanation:

Percentage increase = 20% × 400

New value =

400 + Percentage increase =

400 + (20% × 400) =

400 + 20% × 400 =

(1 + 20%) × 400 =

(100% + 20%) × 400 =

120% × 400 =

120 ÷ 100 × 400 =

120 × 400 ÷ 100 =

48,000 ÷ 100 =

480

3 0
2 years ago
Simplify this equation <br> Thanks a lot!!!
den301095 [7]

Answer:

-1

Step-by-step explanation:

We need to simplify the given expression . The given expression is ,

\rm\implies ( 2 \sqrt6 +5)^{2n-1} ( 2\sqrt6 - 5)^{2n-1}

Here we can see that the power of the both exponent is same that is (2n+1) . Recall the property of exponents ,

\bf\implies a^m \times b^m = (ab)^m

Using this property , we have ,

\rm\implies ( 2 \sqrt6 +5)^{2n-1} ( 2\sqrt6 - 5)^{2n-1}

This can be written as ,

\rm\implies\{( 2 \sqrt6 +5) ( 2\sqrt6 - 5)\}^{2n-1}

Simplifying using ( a+b)(a-b) = a² - b² ,

\rm\implies\{( 2 \sqrt6)^2 -5^2 \}^{2n-1}\\\\\rm\implies ( 24 - 25)^{2n-1}

Subtracting the numbers inside the brackets ,

\rm\implies (-1)^{2n - 1 }

Now we know that every odd number is in the form of 2n -1 , where n is any integer. Therefore , the <u>power is odd</u> .

Since the base is (-1) , for even power it is 1 and for odd power it is -1 . Therefore the final answer is ,

\rm\implies\boxed{\quad \red{ -1 }\quad }

<u>Hence </u><u>the</u><u> </u><u>required</u><u> answer</u><u> is</u><u> </u><u>(</u><u>-</u><u>1</u><u>)</u><u> </u><u>.</u>

4 0
3 years ago
HELP ME PLZ. I have no clue how to do this.
Varvara68 [4.7K]

Answer:

32

Step-by-step explanation:

3x+1=8x-24

25=5x

x=5

3 times 5 plus 1 is 16 and so the length is 32

comment section:

XM=MY because MN is segment bisector

XM=3x+1=3*5+1=16=MY and since XM+MY=XY 16+16=32

3 0
2 years ago
What is 30+11x-12-6x
Sladkaya [172]
11x-6x=5x
30-12=18
5x+18
8 0
3 years ago
Read 2 more answers
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