Point A is at (3,-8) and point B is at (5,-2.5). What is the midpoint of line segment AB?

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⋂[tex]C^{c}[/tex] = { (D,D,D), (S,S,S) }

h. Outcomes of [tex]A^{c}[/tex]⋂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⋂[tex]C^{c}[/tex]

              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 [tex]C^{c}[/tex]  =  {  (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⋂[tex]C^{c}[/tex] = { (D,D,D), (S,S,S) }

h.)

Outcomes of [tex]A^{c}[/tex] = {(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 [tex]A^{c}[/tex]⋂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.

Answer:

75.4

Step-by-step explanation:

Diameter * pi = circumference.

Answer:

Step-by-step explanation:

y+4 = 3(x-2)

Answer:

24.5%

Step-by-step explanation:

Simple Interest = (principal×rate×time)÷100. *Brackets First*

Transpose the formula to make rate the subject: rate= (100×simple interest) ÷ (principal×time).

Plug in values: rate = (100×37975) ÷ (31000×5).

The result is 24.5%.

Answer:

I understand your pain

Step-by-step explanation: sadge

Answer:

x < -4

Step-by-step explanation:

First step is to subtract 9 from each side to isolate the variable, x.

x + 9 - 9 < 5 - 9

Solve

x < -4

hope this helps :)

p.s. i really need brainliest

Answer:

7w

Step-by-step explanation:

1w + 1w +5w = 7w, add all of the w's up

Answer:

[tex]H = 53.30[/tex]

Step-by-step explanation:

Given

[tex]Side\ 1 = 7x + 41[/tex]

[tex]Side\ 2 = 5x[/tex]

Required

Determine side x

The hypotenuse (H) is calculated using:

[tex]H^2 = Side\ 1^2 + Side\ 2^2[/tex]

[tex]H^2 = (7x + 41)^2 + (5x)^2[/tex]

Substitute 9 for x:

[tex]H^2 = (7*9 + 41)^2 + (5*9)^2[/tex]

[tex]H^2 = 10816 + 2025[/tex]

[tex]H^2 = 12841[/tex]

So:

[tex]H = \sqrt {2841[/tex]

[tex]H = 53.30[/tex]

Answer:

a

Step-by-step explanation:

Answer:

Answer h = 34 i hope it is helpful have a nice day

Answer:

h = 34

Step-by-step explanation:

64 = h + 30

64-30 = h

34 = h

h = 34

Answer:

16n + 8

Step-by-step explanation:

g(f(n)) = g(4n+2)

= 4(4n +2)

= 16n + 8

Answer:

62 degrees

Step-by-step explanation:

so that means it is

31*2= 62 degrees(arcs)

if my answer helps please mark as brainliest.

Answer:

119

Step-by-step explanation:

Angle ADC is 61 degrees and Angle ABD is 180. 180-61 so the answer will be 119.

Answer:

m= -4

Step-by-step explanation:

Answer:

-32

Step-by-step explanation:

4(+6)=−8

4+24=−8

4+24=−8

4+24−24=−8−24

Subtract the numbers

4m = -32

Answer:

1.) p = 88.66

2.) m = 17

Step-by-step explanation:

1.) p - 23.76 = 64.9

p - 23.76 + 23.76 = 64.9 + 23.76

p = 88.66

2.) m + 78 = 95

m + 78 - 78 = 95 - 78

m = 17

Hope this helps and stay safe, happy, and healthy, thank you :) !!

Answer:

50/87

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

Answer:

1 and 2, 3 and 4, 5 and 6, 7 and 8

Step-by-step explanation:

Supplementary angles are angles that add up to 180°. Since 180° would basically be a straight line, those angles are supplementary

Answer:

Parallel

Step-by-step explanation:

In a parallelogram there are two sets of parallel lines, and they are always opposite sides.

For example: a square has 4 sides, the ones along the top and bottom are parallel and the ones along the left and right are also parallel

Answer:

789

Step-by-step explanation:

Answer:

789

Step-by-step explanation:

8 goes into 63 7 times which is 56. 63 - 56 is 7. Bringing down the 1 makes it 71, 8 goes into 71 8 times, which is 64. 71 - 64 is 7. Lastly bringing down the 2 is 72. 8 goes into 72 9 times. So, you get the numbers 789.

Answer:

900 cans and bottles.

Hope that helps!

Step-by-step explanation:

360 / 4 = 90

90 x 100 = 900

Hope that helps!

Answer:

hi peps

Step-by-step explanation:

Solution :

Given the number of the edges are = 11

Therefore we take [tex]$\frac{1}{11}=0.091$[/tex]

And the number of the vials total is = 100

Thus we can multiply = [tex]$100 \times 0.091 = 9.1$[/tex]

From the table provided below, we can obtained :

1. Null hypothesis and alternate hypothesis :

The following null and alternate hypothesis needs to be tested :

[tex]$H_0:p_1=0.091, \ p_2 = 0.091, p_3=0.091, \p_4=0.091, \p_5=0.091, \p_6=0.091, \p_7=0.091,$[/tex] [tex]$p_8=0.091, \ p_9=0.091, \ p_{10}=0.091, \ p_{11}=0.091 $[/tex]

[tex]$H_a :$[/tex] some of the population differ from the values stated in the null hypothesis. It corresponds the Chi-square test that is for the Goodness of the Fit.

2. Rejection region :

It is given --

significance level, α = 0.05

number of degrees of freedom, df = 11 - 1

                                                         = 10

Then the rejection region of this test is :

[tex]$R=\{ x^2:x^2 >18.307\}$[/tex]

3. Test statistics

The Chi-Squared statistics is computed as :

[tex]$x^2=\sum_{i=1}^n \frac{(O_i-E_i)^2}{E_i}$[/tex]

    [tex]$=7.21+4.089+0.133+0.089+1.056+3.825+2.638+0.924+1.671+0.001+0.001$[/tex]

    = 21.638

4. Decision about null hypothesis

Since we see that :    [tex]$x^2=21.638>x^2_c = 18.307$[/tex], we can concluded that we can reject the null hypothesis.

5. Conclusion :

It is concluded that the null hypothesis [tex]$H_0$[/tex] is rejected. So there is enough evidence for us to claim that the population proportions differ from that stated in null hypothesis at α = 0.05 significance level.

Answer:

48 cm² is the correct answer.

Answer:

2.704

Step-by-step explanation:

when dividing by 10 with exponents, you place a decimal point starting from the ones, going left the amount of the exponent. hope that made sense!

Answer:

2.704

Step-by-step explanation:

equation:

2704 ÷ [tex]10^{3}[/tex]

steps:

⇒ 2704 ÷ (10 x 10 x 10)

⇒ 2704 ÷ 1000

⇒ 2.704

Answer:

0.9398 = 93.98% probability that the student is not of Asian origin.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Business student

Event B: Not of Asian origin.

Probability that the student is an undergraduate majoring in business.

15% of 13%(Of Asian origin).

35% of 100 - 13 = 87%(Not of Asian origin). So

[tex]P(A) = 0.15*0.13 + 0.35*0.87 = 0.324[/tex]

Business student and not of Asian origin:

35% of 87%. So

[tex]P(A \cap B) = 0.35*0.87 = 0.3045[/tex]

One undergraduate student majoring in Business is randomly selected from this university. Find the probability that the student is not of Asian origin.

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.3045}{0.324} = 0.9398[/tex]

0.9398 = 93.98% probability that the student is not of Asian origin.

My name is Ankush kumar I am A boy

Answer:

4:9

Step-by-step explanation:

There's 4 of men and 9 to children and 5 of women