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kramer
3 years ago
7

The value of Q is given by the relation Q = 17m. If Q and m are integers with Q greater than 150 and less than 160, then which o

f the following is the value of m?
Mathematics
1 answer:
zloy xaker [14]3 years ago
6 0

Answer: Value of m = 9

Step-by-step explanation:

Given that the relationship between Q and m is;

Q = 17m

Make m the subject of formula

M = Q/17

If Q is greater than 150 and less than 160, then, let assume that

Q = 151, then

M = 151/17

M = 8.88

If Q = 159

M = 159/17

M= 9.35

Since m ranges from 8.88 to 9.35, the value of m = 9

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Continuous compounding is the mathematical limit that compound interest can reach.

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A train travels 80 miles per hour. If its speed remains the same, how far will the train have gone in 90 minutes?
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Three times each day, a quality engineer samples a component from a recently manufactured batch and tests it. Each part is class
soldier1979 [14.2K]

Answer:

a. Outcomes of A = { (C,C,C) , (D,D,D), (S,S,S) }

b. Outcomes of B = { (C,D,S),(C,S,D),(D,C,S),(D,S,C),(S,C,D),(S,D,C) }

c. Outcomes of C = { (C,C,C),(C,C,D),(C,C,S),(C,D,C),(C,S,C),(D,C,C),(S,C,C) }

d. Outcomes of A⋂C = { (C,C,C) }

e. Outcomes of Sample space = { (C,C,C), (C,C,D), (C,C,S), (C,D,C), (C,D,D), (C,D,S), (C,S,C), (C,S,D), (C,S,S), (D,C,C), (D,C,D),(D,C,S), (D,D,C), (D,D,D), (D,D,S), (D,S,C), (D,S,D), (D,S,S),   (S,C,C), (S,C,D), (S,C,S), (S,D,C), (S,D,D), (S,D,S), (S,S,C), (S,S,D), (S,S,S) }

f. Outcomes of A U B = { (C,C,C) , (D,D,D), (S,S,S), (C,D,S),(C,S,D),(D,C,S),(D,S,C),(S,C,D),(S,D,C) }

g. Outcomes of A⋂C^{c} = { (D,D,D), (S,S,S) }

h. Outcomes of A^{c}⋂C = {(C,C,D),(C,C,S),(C,D,C),(C,S,C),(D,C,C),(S,C,C)}

i. Events A and C are not mutually exclusive

j. Events B and C are mutually exclusive

Step-by-step explanation:

Given - Three times each day, a quality engineer samples a component

             from a recently manufactured batch and tests it. Each part is

             classified as conforming (suitable for its intended use),  

             downgraded (unsuitable for the intended purpose but usable for  

             another purpose), or scrap (not usable). An experiment consists

             of recording the categories of the three parts tested in a particular

              day.

To find - a. Let A be the event that all the parts fall into the same

                  category. List the outcomes in A.

              b. Let B be the event that there is one part in each category.

                  List the outcomes in B.

              c. Let C be the event that at least two parts are conforming.

                  List the outcomes in C.

              d. List the outcomes in A⋂C

              e. List the 27 outcomes in the sample space.

               f. List the outcomes in A U B.

              g. List the outcomes in A⋂C^{c}

              h. List the outcomes in ⋂C.

              i. Are events A and C mutually exclusive? Explain.

              j. Are events B and C mutually exclusive? Explain.

Proof -

Let

Conforming part = C

Downgraded part = D

Scrap part = S

a.)

Given , Let A be the event that all the parts fall into the same category.

Outcomes of A = { (C,C,C) , (D,D,D), (S,S,S) }

b.)

Given, Let B be the event that there is one part in each category.

Outcomes of B = { (C,D,S),(C,S,D),(D,C,S),(D,S,C),(S,C,D),(S,D,C) }

c.)

Given,  Let C be the event that at least two parts are conforming.

Outcomes of C = { (C,C,C),(C,C,D),(C,C,S),(C,D,C),(C,S,C),(D,C,C),(S,C,C) }

d.)

Outcomes of A⋂C = { (C,C,C) }

e.)

Outcomes of Sample space = { (C,C,C), (C,C,D), (C,C,S), (C,D,C), (C,D,D), (C,D,S), (C,S,C), (C,S,D), (C,S,S), (D,C,C), (D,C,D),(D,C,S), (D,D,C), (D,D,D), (D,D,S), (D,S,C), (D,S,D), (D,S,S),   (S,C,C), (S,C,D), (S,C,S), (S,D,C), (S,D,D), (S,D,S), (S,S,C), (S,S,D), (S,S,S) }

f.)

Outcomes of A U B = { (C,C,C) , (D,D,D), (S,S,S), (C,D,S),(C,S,D),(D,C,S),(D,S,C),(S,C,D),(S,D,C) }

g.)

Outcomes of C^{c}  =  {  (C,D,D), (C,D,S), (C,S,D), (C,S,S), (D,C,D),(D,C,S), (D,D,C), (D,D,D), (D,D,S), (D,S,C), (D,S,D), (D,S,S), (S,C,D), (S,C,S), (S,D,C), (S,D,D), (S,D,S), (S,S,C), (S,S,D), (S,S,S) }

Outcomes of A⋂C^{c} = { (D,D,D), (S,S,S) }

h.)

Outcomes of A^{c} = {(C,C,D), (C,C,S), (C,D,C), (C,D,D), (C,D,S), (C,S,C), (C,S,D), (C,S,S), (D,C,C), (D,C,D),(D,C,S), (D,D,C),  (D,D,S), (D,S,C), (D,S,D), (D,S,S),   (S,C,C), (S,C,D), (S,C,S), (S,D,C), (S,D,D), (S,D,S), (S,S,C), (S,S,D), }

Outcomes of A^{c}⋂C = {(C,C,D),(C,C,S),(C,D,C),(C,S,C),(D,C,C),(S,C,C) }

i.)

As we two that Two events A and C are mutually exclusive iff A ∩ C = ∅

Now,

A ∩ C = { (C,C,C) }

⇒Events A and C are not mutually exclusive.

j.)

As we two that Two events B and C are mutually exclusive iff B ∩ C = ∅

Now,

B ∩ C = ∅

⇒Events B and C are mutually exclusive.

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tia_tia [17]

Answer:

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Step-by-step explanation:

x coordinates of a and b remain same but their y coordinates become -4

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