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Answer 1

Answer:

Which video in YT has most number of views

Answer 2
Answer:

Step-by-step explanation:


Related Questions

In isosceles △HAM, m∡A =32°, . What is m∠H?



32°32 degrees


58°58 degrees


74°74 degrees


148°

Answers

Answer:

32°

Step-by-step explanation:

in 32° is right answer

In isosceles triangle, △HAM, m∠H is 74 degree.

What is isosceles triangle?

A triangle in which any two sides are equal in length and angles opposite to equal side are also equal. And sum of all angles in a triangle is 180.

Given, m∠A = 32°

sum of all angles = 180°

In △HAM

∠H = ∠M

∠H+ ∠A+ ∠M = 180°

2∠H = 180 - 32

2∠H = 148

∠H = 74°

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Jessica purchases a kayak in Florida, where the state sales taxes are 6%. She paid $72 in sales tax. What was the retail price of the kayak?

Answers

Answer:

72 is 6% of 1200.

Step-by-step explanation:

Multiply 72 by 100.

72*100

Then divide the number by 6

(72*100)/6

You should get 1200.

Anne plans to increase the prices of all the items in her store but 5%. To the nearest cent how much will an artist saved if the artist buys a canvas and a frame that each measures 24 by 36 in before the price increase goes into effect. 24/36 canvas price 22.80 and the frame price is 89.98

Answers

9514 404 393

Answer:

  5.64

Step-by-step explanation:

The increase in price for the given items will be ...

  5% × (22.80 + 89.98) ≈ 5.64

The artist will save 5.64 by making a purchase before the price increase.

Find the perimeter of WXYZ. Round to the nearest tenth if necessary.

Answers

Answer:

C. 15.6

Step-by-step explanation:

Perimeter of WXYZ = WX + XY + YZ + ZW

Use the distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex] to calculate the length of each segment.

✔️Distance between W(-1, 1) and X(1, 2):

Let,

[tex] W(-1, 1) = (x_1, y_1) [/tex]

[tex] X(1, 2) = (x_2, y_2) [/tex]

Plug in the values

[tex] WX = \sqrt{(1 - (-1))^2 + (2 - 1)^2} [/tex]

[tex] WX = \sqrt{(2)^2 + (1)^2} [/tex]

[tex] WX = \sqrt{4 + 1} [/tex]

[tex] WX = \sqrt{5} [/tex]

[tex] WX = 2.24 [/tex]

✔️Distance between X(1, 2) and Y(2, -4)

Let,

[tex] X(1, 2) = (x_1, y_1) [/tex]

[tex] Y(2, -4) = (x_2, y_2) [/tex]

Plug in the values

[tex] XY = \sqrt{(2 - 1)^2 + (-4 - 2)^2} [/tex]

[tex] XY = \sqrt{(1)^2 + (-6)^2} [/tex]

[tex] XY = \sqrt{1 + 36} [/tex]

[tex] XY = \sqrt{37} [/tex]

[tex] XY = 6.08 [/tex]

✔️Distance between Y(2, -4) and Z(-2, -1)

Let,

[tex] Y(2, -4) = (x_1, y_1) [/tex]

[tex] Z(-2, -1) = (x_2, y_2) [/tex]

Plug in the values

[tex] YZ = \sqrt{(-2 - 2)^2 + (-1 -(-4))^2} [/tex]

[tex] YZ = \sqrt{(-4)^2 + (3)^2} [/tex]

[tex] YZ = \sqrt{16 + 9} [/tex]

[tex] YZ = \sqrt{25} [/tex]

[tex] YZ = 5 [/tex]

✔️Distance between Z(-2, -1) and W(-1, 1)

Let,

[tex] Z(-2, -1) = (x_1, y_1) [/tex]

[tex] W(-1, 1) = (x_2, y_2) [/tex]

Plug in the values

[tex] ZW = \sqrt{(-1 -(-2))^2 + (1 - (-1))^2} [/tex]

[tex] ZW = \sqrt{(1)^2 + (2)^2} [/tex]

[tex] ZW = \sqrt{1 + 4} [/tex]

[tex] ZW = \sqrt{5} [/tex]

[tex] ZW = 2.24 [/tex]

✅Perimeter = 2.24 + 6.08 + 5 + 2.24 = 15.56

≈ 15.6

Answer:CCCCCCCCCCCCCCCCC

Step-by-step explanation:

If Mr. David does a job in x hours and Mr. Ludwig in y hours. What part of the job they could do together if they worked for k hrs?

Answers

Answer:

(1/x + 1/y)k is the answer :)

Simplify.
Rewrite the expression in the form 6^n6
n
6, start superscript, n, end superscript.
\dfrac{6^{4}}{6}=
6
6
4

Answers

Answer:

6^3

6 to the third power

or 3x3x3

Step-by-step explanation:

The solution of the expression 6⁻⁴.6⁶ will be 6².

What is an expression?

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the expression is 6⁻⁴.6⁶. The expression will be solved as below:-

6⁻⁴.6⁶ = 6⁻⁴⁺⁶

Use the exponent property when the bases are the same then the powers will be added.

6⁻⁴.6⁶ = 6²

Therefore, the solution of the expression 6⁻⁴.6⁶ will be 6².

The complete question is to simplify the expression 6⁻⁴.6⁶.

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The lebgth of a rrctangle is 3 inches more than its width.The perimeter of the rectangle is 34 inches.

Answers

Step-by-step explanation:

there is the answer. good luck

Please help NO LINKS

Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by
y
=
x
2
,
y
=
0
, and
x
=
5
,
about the
y
-axis.

V
=

Answers

Answer:

[tex]\displaystyle V = \frac{625 \pi}{2}[/tex]

General Formulas and Concepts:

Algebra I

FunctionsFunction NotationGraphing

Calculus

Integrals

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:                                                       [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Shell Method:                                                                                                         [tex]\displaystyle V = 2\pi \int\limits^b_a {xf(x)} \, dx[/tex]

[Shell Method] 2πx is the circumference[Shell Method] 2πxf(x) is the surface area[Shell Method] 2πxf(x)dx is volume

Step-by-step explanation:

Step 1: Define

y = x²

y = 0

x = 5

Step 2: Identify

Find other information from graph.

See Attachment.

Bounds of Integration: [0, 5]

Step 3: Find Volume

Substitute in variables [Shell Method]:                                                         [tex]\displaystyle V = 2\pi \int\limits^5_0 {x(x^2)} \, dx[/tex][Integrand] Multiply:                                                                                       [tex]\displaystyle V = 2\pi \int\limits^5_0 {x^3} \, dx[/tex][Integral] Integrate [Integration Rule - Reverse Power Rule]:                     [tex]\displaystyle V = 2\pi \bigg( \frac{x^4}{4} \bigg) \bigg| \limits^5_0[/tex]Evaluate [Integration Rule - FTC 1]:                                                             [tex]\displaystyle V = 2\pi \bigg( \frac{625}{4} \bigg)[/tex]Multiply:                                                                                                         [tex]\displaystyle V = \frac{625 \pi}{2}[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Applications of Integration

Book: College Calculus 10e

find the sum and difference between the place value and face value of 5 in the number 3508 6941​

Answers

Answer:

Sum= 5000005

Difference= 4999995

Step-by-step explanation:

The place value of 5 in the number 35086941 is 5000000

The face value is 5

The sum between the face value and place value can be calculated as follows

°= 5000000+5

= 5000005

The difference can be calculated as follows

= 5000000-5

= 4999995

answer it correctly:)
can anyone help me?:) ​

Answers

Answer:

JAR WITH MARBLES.

There's

5 Blue Marbles

3 Red Marbles

2 Yellow Marbles

Pr = No of desired outcome/No of Possible Outcomes

No of Possible Outcomes = 10.

1. Pr(yellow) = 2/10 = 1/5.

2. Pr(Red) = 3/10

3. Pr(Blue) = 5/10 = 1/2

4. Pr(Yellow and Red) = 2/10 x 3/10 = 6/100 = 3/50.

5.Pr(Blue and Red)= 5/10 x 3/10 = 15/100 = 3/20.

6.Pr( Yellow and Blue) = 2/10 x 5/10 = 10/100 = 1/10.

THE CHIPS ARE PLACED IN A JAR AND MIXED.

No of Possible Outcomes = 8.

The Numbers are 1,2,3,4,5,6,7,8.

There's

4 Even Numbers

4 Odd Numbers

1. Pr(Even) = 4/8 = 1/2

2. Pr(Odd) = 4/8 = 1/2

3. Pr(Chip with Biggest No) = 1/8.

Reason. There can only be one Number which Is the biggest amongst all. So the Probability of picking it is 1.

4.Pr(Smallest Number) = 1/8 (Same concept).

5.Pr(Prime Number)

The prime Numbers above are 2,3,5,7

Pr(Prime) = 4/8 = 1/2.

Hope this helps!.

Identify the sampling method that was used. Cattle tag numbers at a livestock auction are selected using a random number generator. The cattle are then tested for mad cow disease.
a. Stratified
b. Systematic
c. Random
d. Cluster

Answers

Answer:

c. Random

Step-by-step explanation:

In Statistics, sampling can be defined as a process used to collect or select data (objects, observations, or individuals) from a larger statistical population using specific procedures.

There are various types of sampling used by researchers and these are;

1. Systematic sampling.

2. Convenience sampling.

3. Stratified sampling.

4. Cluster sampling.

5. Random sampling.

Random sampling can be defined as a type of sampling in which the researcher select a sample of the population in order to determine an outcome.

Thus, the type of sampling used is random sampling.

48. What is the volume of the cuboid below? 3cm 2cm 2cm

Answers

Answer:

Cuboid = width*height*length

Cuboid = 24 cm^2

PLEASE HELP!!! What is the equation of the line perpendicular to 2x – 3y = 13 that passes through the point (–6, 5)?

Answers

Answer:

2x + 3y -3=0

Step-by-step explanation:

The given equation of the line is ,

[tex]\implies 2x - 3y = 13 [/tex]

Now convert it into slope intercept form to get the slope , we get ,

[tex]\implies 3y = 2x - 13 \\\\\implies y =\dfrac{2}{3}x -\dfrac{13}{2}[/tex]

Therefore the slope is ,

[tex]\implies m = \dfrac{2}{3} [/tex]

We know that the product of slope of perpendicular lines is -1 . Therefore the slope of the perpendicular line will be ,

[tex]\implies m_{perpendicular}= -\dfrac{2}{3} [/tex]

Now one of the point is (-6,5) .On Using point slope form , we have ,

[tex]\implies y-y_1 = m( x - x_1) \\\\\implies y - 5 = -\dfrac{2}{3}( x + 6 ) \\\\\implies 3y - 15 = -2x -12

\\\\\implies 2x + 3y -15+12=0 \\\\\implies \underline{\underline{ 2x + 3y -3=0 }}[/tex]

Answer:

y = - [tex]\frac{3}{2}[/tex]x - 4

Step-by-step explanation:

2x – 3y = 13

3y = 2x + 13

y = [tex]\frac{2}{3}[/tex]x + [tex]\frac{13}{3}[/tex]

slope = 2/3

negative reciprocal = -3/2

y = -3/2x + b

(-6, 5)

5 = (-3/2)(-6) + b

5 = 9 + b

b = -4

y = -3/2x - 4

what is the graph of this function?​

Answers

Answer:

You MADE IT EASY

Step-by-step explanation:

[tex] {y - 5 \times 9}^{2} \: times \: sevem \\ n \: equals \sec(x + {}^{2} ) [/tex]

8th Grade Which expression is equivalent to 1/27​

Answers

Answer:

[tex]( \frac{1}{3})^{3} [/tex]

Step-by-step explanation:

There are many expressions that can be equivalent to 1/27.

For example, 2/54, 3/81 etc

But I think the expression you are looking for is

[tex] \frac{1}{27} = \frac{1 \times 1 \times 1}{3 \times 3 \times 3} = \frac{ {1}^{3} }{ {3}^{3} } = ( \frac{1}{3} )^{3} [/tex]

Hope this is helpful

in the number 36,802 if the 8 was replaced with a 2 would the value increase or decrease

Answers

Answer:

decrease

Step-by-step explanation:

In a test of a heat-seeking rocket, a first rocket is launched at 2000 fts and the heat-seeking rocket is launched along the same flight path 20 s later at a speed of 3000 fts. Find
the timest, and t, of flight of the rockets until the heat-seeking rocket destroys the first rocket
What are the times of the flight?

Answers

Answer:

Time of flight of first rocket = 60 seconds

Time of flight of second rocket = 40 seconds

Step-by-step explanation:

Let the time of flight of first rocket be t1.

Since the second rocket is launched 20 seconds later, then it means that;

t1 = t2 + 20

Where t2 is the time of flight of the second rocket.

When destruction has occurred, it means that both of the rockets would have covered the same distance.

We know that;

Distance = speed × time

Thus;

2000t1 = 3000t2

We know that t1 = t2 + 20

Thus;

2000(t2 + 20) = 3000t2

2000t2 + 40000 = 3000t2

3000t2 - 2000t2 = 40000

1000t2 = 40000

t2 = 40000/1000

t2 = 40 seconds

Thus;

t1 = 40 + 20

t1 = 60 seconds

A random sample of 20 individuals who graduated from college five years ago were asked to report the total amount of debt (in $) they had when they graduated from college and the total value of their current investments (in $) resulting in the data set below.

Debt Invested
16472 37226
19048 33930
4033 66292
22575 24887
12020 44976
4731 59924
4571 59901

Which statement best describes the relationship between these two variables?

a. As college debt decreases current investment decreases.
b. College debt is not associated with current investment.
c. As college debt increases current investment decreases.
d. As college debt increases current investment increases.

Answers

Answer:

The answer is "Option c".

Step-by-step explanation:

Please find the complete question and its solution in the attached file.

Assume one individual from the group is randomly selected. Find the probability of getting someone who tests negative​, given that he or she had the disease. the probability is approximately?

Answers

Answer:

[tex]P(Negative | Yes) = 0.0486[/tex]

Step-by-step explanation:

Given

[tex]\begin{array}{ccc}{} & {Yes} & {No} & {Positive} & {137} & {24} & {Negative} & {7} & {132} \ \end{array}[/tex]

Required

[tex]P(Negative | Yes)[/tex]

This is calculated as:

[tex]P(Negative | Yes) = \frac{n(Negative\ n\ Yes)}{n(Yes)}[/tex]

So, we have:

[tex]P(Negative | Yes) = \frac{7}{137+7}[/tex]

[tex]P(Negative | Yes) = \frac{7}{144}[/tex]

[tex]P(Negative | Yes) = 0.0486[/tex]

What is the scale factor from ALMN to AOPQ?
M
P
3
3
3
3
2
4
N
0
4
A. 4
(
B. 0
c
C. 3
D. 1

Answers

Answer:

D

Step-by-step explanation:

There 2 ways to interpret this problem.

From the info given:

These two triangles are congruent by SSS and congruent triangles have congruent or equal side lengths so the answer have to be 1.

If the triangles are similar, the side lengths form a proportion of that

[tex] \frac{3}{3} = \frac{3}{3} [/tex]

So the ratio or scale factor is 1.

The scale factor in the figure is 1.

What is a scale factor?

A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object.

Given that two triangles, LMN and OPQ, we need to find the scale factor,

We can see triangles are congruent, and we know that

Two triangles are congruent, by the SSS congruence criterion, if they are similar and the scale factor happens to be 1,

Hence, the scale factor in the figure is 1.

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Find the volume of the box. The box shows the length is 6 feet, the width is 5 feet, and the height is 3 feet. The volume of the box is blank cubic feet. The solution is

Answers

6*5*3 = 90 cubic feet

Answer:

[tex]90[/tex] [tex]ft^3[/tex]

Step-by-step explanation:

----------------------------------------

The formula to find the volume of a rectangular prism is   [tex]V=lwh[/tex]

Let's substitute the number for the length, width, and height now.

[tex]V=(6)(5)(3)[/tex]

[tex]V=(30)(3)[/tex]

[tex]V=90[/tex]

--------------------

Hope this is helpful.

(2x4−7x3−6x2+23x−12)÷(x−4)

Answers

Answer:

[tex]\frac{23x-37}{x-4}[/tex]

Step-by-step explanation:

use dimensional analysis $3,000 to convert US Cash allowance into Peruvian currency.​

Answers

Answer:

200000

Step-by-step explanation:

29563487

Ross Times, the student newspaper of Ross College, printed a "What do you think?" column feature asking: "Do you think that the college is doing enough to provide student parking?" Anyone could mail in a response or use the paper's Web site to respond. In all, 126 answers were received. This is an example of what type of sample? A convenience sample A simple random sample A multistage sample A voluntary response sample

Answers

Answer: A simple random sample

Step-by-step explanation:

Simple random sampling refers to the probability sampling whereby the researcher chooses selects a subset of participants from the population.

In this case, every member has an equal chance of being chosen. Since anyone could mail in a response or use the paper's Web site to respond, then it's a simple random sampling.

work out the value of 5x8 x 5-2/5x4

Answers

Answer:

=6

Step-by-step explanation:

(5×8)×(5-2)/(5×4)

Numerator =40×3

=120

Denominator = 5×4

=20

simplifying 120/20

=6

Answer:

6

follow the BDMAS rule

bracket ,division ,multiplication, addition and last subtraction

you won't get any maths problem wrong

one story with author and summary please​

Answers

Answer:

The story tells of a plain-looking little bird (the Ugly Duckling) born in a barnyard. His brothers and sisters as well as the other birds and animals on the farm tease him for being plain and ugly, so he runs off to live with a flock of wild ducks and geese until hunters shoot down the flock. Alone again, the Ugly Duckling finds a home with an old woman, but her cat and hen also tease him, so he doesn't stay there long.

In his wanderings, the Ugly Duckling comes across a flock of migrating swans, and he wishes to join them but can't because he's too young and can't fly well enough. When winter sets in, a farmer rescues the Ugly Duckling, but the farmer's children and other animals frighten him with their noise and teasing, so again, he flees. He spends a cold and lonely winter hiding in a cave until springtime, when the flock of swans comes to the lake near his hiding place.

When the Ugly Duckling approaches the swans, he's delighted to find that they accept him and treat him like one of them. When he looks at his reflection in the lake, he realizes, to his astonishment, that he's matured into a beautiful swan himself. When the swans fly off from the lake, he spreads his wings and joins them, finally having found a family who accepts him.

WILL GIVE BRAINLIEST!!! I WILL BE VERY GRATEFUL IF YOU HELP ME ASAP

Answers

Answer:

According to me its 90 degree

Step-by-step explanation:

According to estimates by the office of the Treasury Inspector General of IRS, approximately 0.0746 of the tax returns filed are fraudulent or will contain errors that are purposely made to cheat the IRS. In a random sample of 318 independent returns from this year, what is the probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS

Answers

Answer:

0.6026 = 60.26% probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS

Step-by-step explanation:

We use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

Approximately 0.0746 of the tax returns filed are fraudulent or will contain errors.

This means that [tex]p = 0.0746[/tex]

Random sample of 318 independent returns

This means that [tex]n = 318[/tex]

Mean and standard deviation:

[tex]\mu = E(X) = np = 318*0.0746 = 23.7228[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{318*0.0746*0.9254} = 4.6854[/tex]

What is the probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS?

Using continuity correction, this is [tex]P(X \geq 23 - 0.5) = P(X \geq 22.5)[/tex], which is 1 subtracted by the p-value of Z when X = 22.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{22.5 - 23.7228}{4.6854}[/tex]

[tex]Z = -0.26[/tex]

[tex]Z = -0.26[/tex] has a p-value of 0.3974.

1 - 0.3974 = 0.6026

0.6026 = 60.26% probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS

g Assuming the probability of a single sample testing positive is 0.15​, find the probability of a positive result for two samples combined into one mixture. Is the probability low enough so that further testing of the individual samples is rarely​ necessary?

Answers

Solution :

The objective is to obtain the [tex]\text{probability of a positive result}[/tex] for 2 samples combined into a [tex]\text{mixture}[/tex].

Given that the [tex]\text{probability of a single sample testing positive is 0.15}[/tex]

The probability of the positive test result is calculated as follows :

P ( positive mixture ) = P(1 or more samples positive)

                                  = 1 - P (none +ve)

                                  = 1 - P ((-ve) x (-ve))

                                  [tex]$= 1-P(-ve )^2$[/tex]

                                  [tex]$=1-[1-P(+ve)]^2$[/tex]

                                  [tex]$=1-(1-0.15)^2$[/tex]

                                  [tex]$=1-(0.85)^2$[/tex]

                                  = 1 - 0.7225

                                  = 0.2775

No, the probability is not low enough.

 

You get GPS units from two manufacturers, A and B. You get 43% of your units from A and 57% of your units from B. In the past, 2% of the units from A have been defective, and 1.5% of the units from B have been defective. Assuming this holds true, if a GPS unit is found to be defective what is the probability that it came from manufacturer A (think Bayes Theorem AND round to two decimal places)

Answers

Answer:

0.5015 = 50.15% probability that it came from manufacturer A.

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: Defective

Event B: From manufacturer A.

Probability a unit is defective:

2% of 43%(from manufacturer A)

1.5% of 57%(from manufacturer B). So

[tex]P(A) = 0.02*0.43 + 0.015*0.57 = 0.01715[/tex]

Probability a unit is defective and from manufacturer A:

2% of 43%. So

[tex]P(A \cap B) = 0.02*0.43 = 0.0086[/tex]

What is the probability that it came from manufacturer A?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0086}{0.01715} = 0.5015[/tex]

0.5015 = 50.15% probability that it came from manufacturer A.

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