rationalize the denominator:

Answer:

a. The probability that the finished product selected is defective is 2.45%.

b. The probability that product chosen randomly was defective and made by machine B3 is 20.41%.

Step-by-step explanation:

Let A represents the defective product.

We also have the following from the question:

P(B1) = Probability or percentage of the made by machine B1 = 30%, or 0.30

P(B2) = Probability or percentage of the made by machine B2 = 45%, or 0,45

P(B3) = Probability or percentage of the made by machine B3 = 25%, or 0.25

P(A/B1) = Probability or percentage of product B1 that is defective = 2%, or 0.02

P(A/B2) = Probability or percentage of product B2 that is defective = 3%, or 0.03

P(A/B3) = Probability or percentage of product B3 that is defective = 2%, or 0.02

We can therefore proceed as follows:

A. Suppose that a finished product is randomly selected. What is the probability that it is defective?

To determine this, the rules of elimination is applied and we have:

P(A) = (P(B1) * P(A/B1)) + (P(B2) * P(A/B2)) + (P(B3) * P(A/B3)) ………… (1)

Where;

P(A) = Probability that the selected product is defective = ?

Substitutes the values defined above into equation (1), we have:

P(A) = (0.30 * 0.02) + (0.45 * 0.03) + (0.25 * 0.02)

P(A) = 0.006 + 0.0135 + 0.005

P(A) = 0.0245, or 2.45%

Therefore, the probability that the finished product selected is defective is 2.45%.

B. If a product were chosen randomly and found to be defective, what is the probability that it was made by machine B3.

To calculate this, the Bayes’ rule is employed as follows:

P(B3/A) = (P(B3) * P(A/B3)) / [(P(B1) * P(A/B1)) + (P(B2) * P(A/B2)) + (P(B3) * P(A/B3))] = (P(B3) * P(A/B3)) / P(A)  ………….... (2)

Where;

P(B3/A) = The probability that product chosen randomly was defective and made by machine B3 = ?

Also, from the values already defined and obtained in part A, we have:

P(B3) = 0.25

P(A/B3) = 0.002

P(A) = 0.0245

Substituting the values into equation (2), we have:

P(B3/A) = (0.25 * 0.02) / 0.0245

P(B3/A) = 0.005 / 0.0245

P(B3/A) = 0.2041, or 20.41%

Therefore, the probability that product chosen randomly was defective and made by machine B3 is 20.41%.

Answer:

I think it's 118°73°49° not really sure

sorry

Answer:

The prime factorization of 5 is 5 x 1

Step-by-step explanation:

5 is a prime number but the only factors that make up 5 are 5 and 1

Hope this helps!

Answer:

The required probability = 0.7143

Step-by-step explanation:

From the information given:

From a group of eight candidates

The no. of candidates that enrolled in internships = 5

The no. of candidates that enrolled in teaching = 3

Also, supposed all the eight candidates are equally qualified;

Then, Let assume that:

Y to represent the number of internship trainee candidates hired.

N to represent no. of candidates in a group = 8

r to represent those who enrolled in paid internship = 5

Now, N - r = 3 (for those who enrolled in traditional teaching program)

Suppose; n represent the positions for local teaching which is given as 3;

Then; selecting 3 from 8 whereby some enrolled in internships and some in traditional teaching programs;

Then,  let assume Y is a random variable that follows a hypergeometric distribution; we have:

[tex]p(Y = y) = \left \{ {{\dfrac{ \bigg (^r_y \bigg)\bigg (^{N-r}_{n-y} \bigg) }{ \bigg ( ^N_n \bigg) } } _\atop { ^{0, otherwise} } } \right.[/tex]

[tex]p(Y = y) = \left \{ {{\dfrac{ \bigg (^5_y \bigg)\bigg (^{3}_{3-y} \bigg) }{ \bigg ( ^8_3 \bigg) } } } } \right, y= 0,1,2,3[/tex]

Thus, the probability that two or more internship trained candidates are hired can be computed as:

p(Y ≥ 2) = p(Y=2) + p(Y =3)

[tex]p(Y \geq 2) = \dfrac{ \bigg ( ^5_2\bigg) \bigg ( ^3_1 \bigg)}{\bigg (^8_3 \bigg)} + \dfrac{\bigg (^5_3 \bigg) \bigg (^3_0 \bigg)}{\bigg ( ^8_3\bigg)}[/tex]

[tex]p(Y \geq 2) = \dfrac{40}{56}[/tex]

[tex]\mathbf{p(Y \geq 2) = 0.7143}[/tex]

Answer:

0.57142

Step-by-step explanation:

A normal random variable with mean and standard deviation both equal to 10 degrees Celsius. What is the probability that the temperature at a randomly chosen time will be less than or equal to 59 degrees Fahrenheit?

We are told that the Mean and Standard deviation = 10°C

We convert to Fahrenheit

(10°C × 9/5) + 32 = 50°F

Hence, we solve using z score formula

z = (x-μ)/σ, where

x is the raw score = 59 °F

μ is the population mean = 50 °F

σ is the population standard deviation = 50 °F

z = 59 - 50/50

z = 0.18

Probability value from Z-Table:

P(x ≤59) = 0.57142

The probability that the temperature at a randomly chosen time will be less than or equal to 59 degrees Fahrenheit

is 0.57142

Step-by-step explanation:

Given parameters:

Perimeter of triangle  = 69cm;

Unknown:

Length of each side  = ?

Solution:

   Side a is 5cm shorter than side b;

         b  = a + 5  ----- i

   Side c is 5 more than twice side b;

          c = 2b + 5

The three sides of triangle are a, b and c;

  Perimeter is the sum of sides of a body;

      a + b + c  = 69

From i;

        a  = b - 5

        b

       c  = 2b + 5

so;

          b - 5 + b + 2b + 5  = 69

           4b = 69

            b  = 17.25cm

a  = b -5  = 17.25 - 5 = 12.25cm

c = 2(17.25) + 5  = 39.5cm

Answer:

translate the road down 4 units

Hope this helps

Answer: m<10 less than 10 is the answer so it would be m<10

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

definitely  not d

Answer:

A

Step-by-step explanation:

Answer:

19/21=0.9

I hope this is good enough:

Answer:

Supplementary angles,

x = 50

Step-by-step explanation:

These angles are supplementary, meaning that they add up to form a 180-degree angle or a straight line.

Knowing this, now form and solve the equation,

76 + 2x + 4 = 180

Combine like terms,

76 + 2x + 4 = 180

80 + 2x = 180

Inverse operations,

80 + 2x = 180

-80           -80

2x = 100

/2    /2

x = 50

Answer : 12z - 32

Explaination:

Uhhh yeah math?

Answer:

Caleb will run 237 ft

Step-by-step explanation:

Answer:

Caleb will run 220 ft.

Step-by-step explanation:

70 * pi = 220 ft

Answer:

14.49272

Step-by-step explanation:

16.852 × 0.86 = 14.49272

Answer:

b 56

Step-by-step explanation:

for the anaconda  5.23 + 1.27 m  where m is the number of months,  and the total length is in meters

The anaconda starts at 5.23 meters and grows 1.27 meters each month for m months

for the python 4.76 + 2.04m   where m is the number of months, l is the length of the python in meters

The python starts at 4.76 meters and grows 2.04 meters each month for m months

5.23 + 1.27 m  = 4.76 + 2.04m   m is the number of months  Each side is

Answer:

(20,0)

Step-by-step explanation:

Trust me :)

Answer:

(20,0)

Step-by-step explanation: trust the guy ^

Answer:The solution to a system of linear equations is the point at which the lines representing the linear equations intersect. Two lines in the x y xy xy -plane can intersect once, never intersect, or completely overlap.

A system of linear equations is usually a set of two linear equations with two variables. x + y = 5 x+y=5 x+y=5x, plus, y, equals, 5 and 2 x − y = 1 2x-y=1 2x−y=12, x, minus, y, equals, 1 are both linear equations with two variables. When considered together, they form a system of linear equations.

a numerical or constant quantity placed before and multiplying the variable in an algebraic expression.

a constant term is a term in an algebraic expression that has a value that is constant or cannot change, because it does not contain any modifiable variables. For example, in the quadratic polynomial the 3 is a constant term.

Step-by-step explanation:

Answer:a

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

-3+4+2+1=4

Answer:

15

Step-by-step explanation:

B) Side length of B to side length of C is 4:5.

Perimeter of C is 280, so let's put that into the side length of C's place:

4:280

But the 4 also would have to change so let's figure out how much we multiplied 5 by to get 280:

280 / 5 = 56

So let's do 4 x 56 = 224

Our new ratio is 224:280

Therefore the perimeter of mirror B is 224cm.

C) Side length of A to side length of B is 3:4.

We know the perimeter of B from the previous part (224) so let's put that in the 4s place:

3:224

But we also have to change 3, so let's figure out how much we multiplied 4 by to get 224:

224 / 4 = 56

Therefore to determine A's perimeter we do 3 x 56 = 168.

Mirror A's perimeter is 168cm.

D) The side length of mirror A is the perimeter divided by 4 (as they are squares).

168 / 4 = 42. Side length of mirror A is 42cm.

E) Area of a square is side length squared, so the area of mirror A is 42².

42² = 1,764cm².

Answer:

c 12 red marbles and 9(origninally i had 12 rad marbles and 8 blue i ment 9) blue marbles XD

Step-by-step explanation:can i get brainliest

Answer:

there are 12

Step-by-step explanation:

24/2 = 12 that means that there are 12 cycles per stand

Answer: 12 cycles

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

Answer:

X=38(8m)#7=274*€7£

Step-by-step explanation:

There you go my answer is pretty much the explanation

not sure what grade this is but if this is collage than that would be the answer

Answer:

the answer is 9

Step-by-step explanation:

3/8 = 9

1/4=6

9+6=15

24-15=9

so 9 is your answer

DONT FORGET TO MARK BRAINLIEST

Answer:

The correct option is f.

Step-by-step explanation:

The (1 - α)% confidence interval for the population proportion is:

[tex]CI=\hat p\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

It is provided that an experimenter flips a coin 100 times and gets 58 heads.

That is the sample proportion of heads is, [tex]\hat p=0.58[/tex].

The critical value of z for 90% confidence level is, z = 1.645.

*Use a z-table.

Compute the 90% confidence interval for the probability of flipping a head with this coin as follows:

[tex]CI=\hat p\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

     [tex]=0.58\pm 1.645\cdot\sqrt{\frac{0.58\times(1-0.58)}{100}}\\\\=0.58\pm 0.0812\\\\=(0.4988, 0.6612)\\\\\approx (0.499, 0.661)[/tex]

Thus, the 90% confidence interval for the probability of flipping a head with this coin is (0.499, 0.661).

The correct option is f.