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Blizzard [7]
3 years ago
15

A manufacturer of matches randomly and independently puts 22 matches in each box of matches produced. The company knows that one

-tenth of 5 percent of the matches are flawed. What is the probability that a matchbox will have one or fewer matches with a flaw?
Mathematics
1 answer:
tangare [24]3 years ago
6 0

Answer:

The probability that a matchbox will have one or fewer matches with a flaw is 0.9946 approximately.    

Step-by-step explanation:

Consider the provided information.

A manufacturer of matches randomly and independently puts 22 matches in each box of matches produced. The company knows that one-tenth of 5 percent of the matches are flawed.

One-tenth of 5 percent can be written as 0.5%

Here we have the value of n=22 and the value of p=0.5%=0.005

We want the probability that a matchbox will have one or fewer matches with a flaw.

That means P(X\leq 1)=P(X=0)+P(X=1)

Thus the required probability is:

P(X\leq 1)=\binom{22}{0}0.005^0(1-0.005)^{22}+\binom{22}{1}0.005^1(1-0.005)^{21}\\P(X\leq 1)=(0.995)^{22}+\binom{22}{1}0.005^1(0.995)^{21}\\P(X\leq 1)\approx 0.8956+22\times 0.005\times (0.995)^{21}\\P(X\leq 1)=0.8956+0.099\\P(X\leq 1)=0.9946

Hence, the probability that a matchbox will have one or fewer matches with a flaw is 0.9946 approximately.

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Peggy is thinking of a number such that when twice the number is added to three times one more than the number she gets the same
mars1129 [50]

Answer:

-7

Step-by-step explanation:

Lets assume the number Peggy is thinking of be "x".

Now as given, when twice the number is added to three times one more than the number. We can write it as

∴ 2x+3(x+1)--- Equation 1

Again, it is given that Peggy gets the same result as when she multiplies four times one less than the number.

∴ 4(x-1)-- equation 2

Next, we can equate both the equation 1 and 2 as it is given that result is same.

2x+3(x+1)= 4(x-1)

Let´s distribute 3 into (x+1) and 4 into (x-1)

⇒ 2x+3x+3=4x-4

⇒ 5x+3=4x-4

Subtract both side by 4x and 3

∴ x=-7

∴ Peggy was thinking of -7

4 0
3 years ago
What’s the answer? Pls help soon
Vilka [71]
You get this or no??
6 0
3 years ago
Read 2 more answers
Q3. In a hydraulic lift, a 1400 N force is applied to a 0.5 m2 piston. Calculate the minimum surface area of the large piston to
blondinia [14]

Answer:

1.8m^2 approx

Step-by-step explanation:

Given data

P1= 1400N

A1=0.5m^2

P2=5000 N

A2=??

Let us apply the formula to calculate the Area A2

P1/A1= P2/A2

substitute

1400/0.5= 5000/A2

cross multiply

1400*A2= 5000*0.5

1400*A2= 2500

A2= 2500/1400

A2= 1.78

Hence the Area is 1.8m^2 approx

3 0
3 years ago
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insens350 [35]

Answer:

6 and hello there, how ya doing?

Step-by-step explanation:

Happy Birthday btw hopefully everything is working out for you and have a wonderful birthday.

7 0
2 years ago
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What's 221 rounded to the nearest 10
ycow [4]
It would be 220 rounded to the nearest ten because the number in the ones place does not equal or exceed 5. 

So 220 is your answer :)
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3 years ago
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