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stich3 [128]
3 years ago
12

A dumpling machine automatically inserts mixed vegetables and meat filled wontons into a plastic package. Past experience reveal

ed that some packages were underweight and some were overweight, but most of them had satisfactory weight.
Weight % of Total
Underweight 2.5
Satisfactory 90.0
Overweight 7.5

Required:
What is the probability of selecting two packages that are satisfactory?

a. 0.900
b. 0.729
c. 0.810
d. 0.075
Mathematics
1 answer:
Tanya [424]3 years ago
6 0

Answer:

c. 0.810

Step-by-step explanation:

Given, total % of satisfactory packages = 90% = 0.90

Now, since selecting a satisfactory package is independent of any other trials (i.e. all the selection trials are independent to each other)

Hence, Probability of selecting two packages that re satisfactory

P(Selecting 2 satisfactory packages) = (0.90)^2

P(Selecting 2 satisfactory packages) = 0.90*0.90

P(Selecting 2 satisfactory packages) = 0.810

Note: We are selecting product since the chance of selecting in each trials are independent.

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Step-by-step explanation:

Step  1  :

Equation at  step  1  :

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Step  2  :

Trying to factor by splitting the middle term

2.1     Factoring  2x2+5x-12  

The first term is,  2x2  its coefficient is  2 .

The middle term is,  +5x  its coefficient is  5 .

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Step-1 : Multiply the coefficient of the first term by the constant   2 • -12 = -24  

Step-2 : Find two factors of  -24  whose sum equals the coefficient of the middle term, which is   5 .

-24    +    1    =    -23  

     -12    +    2    =    -10  

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     -6    +    4    =    -2  

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Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  8  

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             Add up the last 2 terms, pulling out common factors :

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Step-5 : Add up the four terms of step 4 :

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            Which is the desired factorization

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