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lesya [120]
3 years ago
8

A firm maintains 22 cars for business purposes. From past experience, it is known that approximately 10% will require major engi

ne service during a one-year period. What is the probability that at most 1 car will require major engine repair next year?
Mathematics
1 answer:
seropon [69]3 years ago
3 0

Answer:

The probability that at most 1 car will require major engine repair next year is P=0.3392.

Step-by-step explanation:

This can be modeled as a binomial random variable, with n=22 and p=0.1.

The probability that exavtly k cars will require major engine repair next year is:

P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}

Then, the probability that at most 1 car will require major engine repair next year is:

P(x\leq1)=P(x=0)+P(x=1)\\\\\\P(x=0) = \dbinom{22}{0} p^{0}(1-p)^{22}=1*1*0.0985=0.0985\\\\\\P(x=1) = \dbinom{22}{1} p^{1}(1-p)^{21}=22*0.1*0.1094=0.2407\\\\\\P(x\leq1)=0.0985+0.2407\\\\P(x\leq1)=0.3392

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A chemist has three different acid solutions. The first acid solution contains 25 % acid, the second contains 45 % and the third
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ALGEBRA WORD PROBLEM

Dorian S. asked • 06/28/17

THREE LINEAR EQUATIONS WITH THREE VARIABLES

A chemist has three different acid solutions. The first acid solution contains 15% acid, the second contains 25%,

and the third contains 70%. He wants to use all three solutions to obtain a mixture of 40 liters containing 45%

acid, using 2 times as much of the 70% solution as the 25% solution. How many liters of each solution should be used?

How to set up as three linear equations to find the answer?

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1 Expert Answer

By:

Best

Arthur D. answered • 06/28/17

TUTOR 4.9 (67)

Forty Year Educator: Classroom, Summer School, Substitute, Tutor

ABOUT THIS TUTOR ›

set up 2 equations

the first equation...

15%*x+25%*y+70%*2y=45%*40

0.15x+0.25y+1.4y=0.45*40

0.15x+1.65y=18

multiply all terms by 100

15x+165y=1800

divide all terms by 15

x+11y=120

the second equation...

x+y+2y=40

x+3y=40

x=40-3y

substitute into the first equation x+11y=120

40-3y+11y=120

40+8y=120

8y=120-40

8y=80

y=80/8

y=10 liters

x+3*10=40

x+30=40

x=40-30

x=10 liters

10 liters of 15%, 10 liters of 25%, and 20 liters of 70%

check:

10*15%=1.5

10*25%=2.5

20*70%=14

1.5+2.5+14=18

18/40=9/20=45/100=45%

45%*40=18

hope it helps

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