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IceJOKER [234]
3 years ago
6

Micah has 294 songs stored in his phone which is 70% of the songs that Jorge has stored in his phone. How many

Mathematics
1 answer:
Liula [17]3 years ago
7 0
X - the numer of songs stored on Jorge's phone

70\%x=294 \\
\frac{70}{100}x=294 \\
\frac{7}{10}x=294 \\
x=294 \times \frac{10}{7} \\
x=42 \times 10 \\
x=420

420 songs are stored on Jorge's phone.
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Simplify the following expression.
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An expression is defined as a set of numbers, variables, and mathematical operations. The given exponential function when simplified will result in 4^(1/8). The correct option is A.

<h3>What is an Expression?</h3>

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given exponential expression can be simplified as shown below.

(4^{\frac14})^{\frac12}

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Read 2 more answers
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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