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liraira [26]
3 years ago
9

Suppose a shipment of 170 electronic components contains 3 defective components. to determine whether the shipment should be​ ac

cepted, a​ quality-control engineer randomly selects 3 of the components and tests them. if 1 or more of the components is​ defective, the shipment is rejected. what is the probability that the shipment is​ rejected?
Mathematics
1 answer:
lbvjy [14]3 years ago
7 0
If nCk represents the number of ways k parts can be chosen from a pool of n, the probability of interest is the complement of the probability of selecting all good parts.
  1 - (167C3)/(170C3) = 42,085/804,440 ≈ 0.0523

_____
nCk = n!/(k!(n-k)!)
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slavikrds [6]

In your solving toolbox (along with your pen, paper and calculator) you have these 3 equations:

1. The angles always add to 180°:

A + B + C = 180°

When you know two angles you can find the third.

 

2. Law of Sines (the Sine Rule):

Law of Sines

When there is an angle opposite a side, this equation comes to the rescue.

Note: angle A is opposite side a, B is opposite b, and C is opposite c.

 

3. Law of Cosines (the Cosine Rule):

Law of Cosines

This is the hardest to use (and remember) but it is sometimes needed  

to get you out of difficult situations.

It is an enhanced version of the Pythagoras Theorem that works  

on any triangle.

With those three equations you can solve any triangle (if it can be solved at all).

Six Different Types (More Detail)

There are SIX different types of puzzles you may need to solve. Get familiar with them:

1. AAA:

This means we are given all three angles of a triangle, but no sides.

AAA Triangle

AAA triangles are impossible to solve further since there are is nothing to show us size ... we know the shape but not how big it is.

We need to know at least one side to go further. See Solving "AAA" Triangles .

 

2. AAS

This mean we are given two angles of a triangle and one side, which is not the side adjacent to the two given angles.

AAS Triangle

Such a triangle can be solved by using Angles of a Triangle to find the other angle, and The Law of Sines to find each of the other two sides. See Solving "AAS" Triangles.

 

3. ASA

This means we are given two angles of a triangle and one side, which is the side adjacent to the two given angles.

ASA Triangle

In this case we find the third angle by using Angles of a Triangle, then use The Law of Sines to find each of the other two sides. See Solving "ASA" Triangles .

 

4. SAS

This means we are given two sides and the included angle.

SAS Triangle

For this type of triangle, we must use The Law of Cosines first to calculate the third side of the triangle; then we can use The Law of Sines to find one of the other two angles, and finally use Angles of a Triangle to find the last angle. See Solving "SAS" Triangles .

 

5. SSA

This means we are given two sides and one angle that is not the included angle.

SSA Triangle

In this case, use The Law of Sines first to find either one of the other two angles, then use Angles of a Triangle to find the third angle, then The Law of Sines again to find the final side. See Solving "SSA" Triangles .

 

6. SSS

This means we are given all three sides of a triangle, but no angles.

SSS Triangle

In this case, we have no choice. We must use The Law of Cosines first to find any one of the three angles, then we can use The Law of Sines (or use The Law of Cosines again) to find a second angle, and finally Angles of a Triangle to find the third angle.

7 0
3 years ago
Read 2 more answers
For every integer k from 1 to 10, inclusive the "k"th term of a certain sequence is given by (−1)(k+1)∗(12k). If T is the sum of
Katena32 [7]

Answer:

Option D. is the correct option.

Step-by-step explanation:

In this question expression that represents the kth term of a certain sequence is not written properly.

The expression is (-1)^{k+1}(\frac{1}{2^{k}}).

We have to find the sum of first 10 terms of the infinite sequence represented by the expression given as (-1)^{k+1}(\frac{1}{2^{k}}).

where k is from 1 to 10.

By the given expression sequence will be \frac{1}{2},\frac{(-1)}{4},\frac{1}{8}.......

In this sequence first term "a" = \frac{1}{2}

and common ratio in each successive term to the previous term is 'r' = \frac{\frac{(-1)}{4}}{\frac{1}{2} }

r = -\frac{1}{2}

Since the sequence is infinite and the formula to calculate the sum is represented by

S=\frac{a}{1-r} [Here r is less than 1]

S=\frac{\frac{1}{2} }{1+\frac{1}{2}}

S=\frac{\frac{1}{2}}{\frac{3}{2} }

S = \frac{1}{3}

Now we are sure that the sum of infinite terms is \frac{1}{3}.

Therefore, sum of 10 terms will not exceed \frac{1}{3}

Now sum of first two terms = \frac{1}{2}-\frac{1}{4}=\frac{1}{4}

Now we are sure that sum of first 10 terms lie between \frac{1}{4} and \frac{1}{3}

Since \frac{1}{2}>\frac{1}{3}

Therefore, Sum of first 10 terms will lie between \frac{1}{4} and \frac{1}{2}.

Option D will be the answer.

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3 years ago
When twice a certain number is added to 7,the result is less than 17.what is the number.​
EleoNora [17]

Answer: 2?

Step-by-step explanation:

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Graphing required <br><br><br> Help me ASAP
marta [7]
In the original graph, R (0,3), S(3,3), T(4, -1) and Q(0, 1)
Reflecting it across y=-1, which is a horizontal line going through the point T, all the x coordinates stay the same,
the new confidantes are : R'(0, -5), S'(3, -5), T'(4, -1), Q(0', -3) (Notice; T stays where it is now, because it is right now the line y=-1)
Locate these new points, you have your graph. 
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3 years ago
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Gelneren [198K]

Answer:

A) pop? If you meant most

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Step-by-step explanation:

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