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kozerog [31]
3 years ago
11

A quality inspector at a valve manufacturer randomly selects one valve from each batch of fifty valves to inspect for noncomplia

nce. The first batch of fifty valves has five non-compliant ones. The second batch of fifty valves has four non-compliant valves. Find the probability that the inspector selects a non-compliant valve both times. A) 1/100 B) 1/125 C) 1/9 D) 9/50
Mathematics
2 answers:
trasher [3.6K]3 years ago
8 0
The actual answer is 1/125......................................
Tanzania [10]3 years ago
6 0

Answer:

The correct answer is B  \frac{1}{125}.

Step-by-step explanation:

Step 1

The fist step is to determine the probability of selecting a non-compliant valve from the first batch. Since there are 5 non-compliant valves in the batch out of 50 , we determine that the probability of finding a non-compliant valve is P(A)=\frac{5}{50}.

Step 2

The second step is to determine the probability of selecting a non-compliant valve from the second batch. Since there are 4 non-compliant valves in the batch out of 50 , we determine that the probability of finding a non-compliant valve is P(B)=\frac{4}{50}.

Step 3

The last step is to determine the probability of getting non-compliant valves both times. Since the two events are independent of each other, we find the probability by multiplying the probability  of both events. The calculation is carried out as shown below,

P(A)\times P(B)=\frac{5}{50} \times\frac{4}{50} =\frac{20}{2500} =\frac{1}{125}.

The probability of 2 non-compliant valves is \frac{1}{125}.


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algol [13]

Answer:

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Step-by-step explanation:

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5 0
3 years ago
The probability that Caroline wins a raffle is given by the expression
RSB [31]

Answer:  \frac{n-m}{n}

This is the same as writing (n-m)/n

Don't forget about the parenthesis if you go with the second option.

==================================================

Explanation:

The probability that she wins is m/n, where m,n are placeholders for positive whole numbers.

For instance, m = 2 and n = 5 leads to m/n = 2/5. This would mean that out of n = 5 chances, she wins m = 2 times.

The probability of her not winning is 1 - (m/n). We subtract the probability of winning from 1 to get the probability of losing.

We could leave the answer like this, but your teacher says that the answer must be "in the form of a combined single fraction".

Doing a bit of algebra would have these steps

1 - \frac{m}{n}\\\\\frac{n}{n} - \frac{m}{n}\\\\\frac{n-m}{n}\\\\

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8 0
3 years ago
In triangle abc, the perimeter is 36, and ab=ac. line ad is perpendicular to bc at the point d, and triangle abd's perimeter is
Musya8 [376]
Let x=ab=ac, and y=bc, and z=ad.

Since the perimeter of the triangle abc is 36, you have:

Perimeter of abc = 36
ab + ac + bc = 36
x + x + y = 36
(eq. 1) 2x + y = 36

The triangle is isosceles (it has two sides with equal length: ab and ac). The line perpendicular to the third side (bc) from the opposite vertex (a), divides that third side into two equal halves: the point d is the middle point of bc. This is a property of isosceles triangles, which is easily shown by similarity.

Hence, we have that bd = dc = bc/2 = y/2 (remember we called bc = y).

The perimeter of the triangle abd is 30:

Permiter of abd = 30
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x + y/2 + z =30
(eq. 2) 2x + y + 2z = 60

So, we have two equations on x, y and z:

(eq.1) 2x + y = 36
(eq.2) 2x + y + 2z = 60

Substitute 2x + y by 36 from (eq.1) in (eq.2):

(eq.2') 36 + 2z = 60

And solve for z:

36 + 2z = 60 => 2z = 60 - 36 => 2z = 24 => z = 12

The measure of ad is 12.

If you prefer a less algebraic reasoning:

- The perimeter of abd is half the perimeter of abc plus the length of ad (since you have "cut" the triangle abc in two halves to obtain the triangle abd).

- Then, ad is the difference between the perimeter of abd and half the perimeter of abc:

ad = 30 - (36/2) = 30 - 18 = 12
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