Answer:
a) 3x^2-6x-3
b) 6
Step-by-step explanation:
f(x)=2x^2−4x+3
g(x)=x^2−2x−6
a) (f+g)(x) = (2x^2−4x+3) + (x^2−2x−6)
collect like terms
(f+g)(x) = 2x^2+x^2-4x-2x+3-6
(f+g)(x) = 3x^2-6x-3
b) (f+g)(3). This implies that x=3
recall (f+g)(3) = 3x^2-6x-3
(f+g)(3) = 3(3)^2-6(3)-3 = 27-18-3
(f+g)(3) = 27-21 =6
Find the coordinate vector [Bold x ]Subscript Upper B of x relative to the given basis BequalsStartSet Bold b 1 comma Bold b 2 comma Bold b 3 EndSet
Answer:
The answer to this question can be defined as follows:
Step-by-step explanation:
In the question equation is missing so, the equation and its solution can be defined as follows:
[tex]B={b_1,b_2}\\\\b_1= \left[\begin{array}{c}5&5\end{array}\right] \ \ \ \ \b_2= \left[\begin{array}{c}2&-5\end{array}\right] \ \ \ \ \x= \left[\begin{array}{c}-7&-35\end{array}\right][/tex]
[tex]\left[\begin{array}{c}a&c\end{array}\right] =?[/tex]
[tex]\to \left[\begin{array}{c}-7&-35\end{array}\right]= a\left[\begin{array}{c}5&5\end{array}\right]+c \left[\begin{array}{c}2&-5\end{array}\right] \\[/tex]
[tex]\to \left[\begin{array}{c}-7&-35\end{array}\right]= \left[\begin{array}{c}5a+2c&5a-5c\end{array}\right]\\\\\to 5a+2c=-7....(1)\\\\\to 5a-5c=-35....(2)\\\\[/tex]
subtract equation 1 from equation 2:
[tex]\to 7c=28\\\\\to c=\frac{28}{7}\\\\\to c= 4\\\\[/tex]
put the value of c in equation 1
[tex]\to 5a+2(4)=-7\\\to 5a+8=-7\\\to 5a=-7-8\\\to 5a=-15\\\to a= -3[/tex]
coordinate value is [-3,4].
A line is definitely by the equation y = -x + 3 which shows the graph of this line ?
Answer:
A graph with a slope of -1, and a y-intercept (crosses the y-axis) at 3
PLEASE, NEED HELP WITH ALGEBRA ASAP!
Answer: The answer is (D) t = √2d/₅
Step-by-step explanation:
Since a = 2d/t²
Now making t the subject of the formula
at² = 2d
t² = 2d/a, to find t , take the square root of both sides
t = √2d/₅ since a = 5m⁻².
The answer is d
Do you play brawl stars the game? Real question: (x-8)^2
Answer:
your answer is x^2 - 16x + 64.
Answer:
x^2 - 16x + 64
Step-by-step explanation:
an auto dealer offers a compact car, a midsize, a sport utility vehicle, and a light truck, each either in standard, custom, or sport styling, a choice of manual or automatic transmission, and a selection from 7 colors. How many ways of buying a vehicle from this dealer are there?
Answer: 168
Step-by-step explanation:
First, let's count the types of selection:
We can select:
Type of car: a compact car, a midsize, a sport utility vehicle, and a light truck (4 options)
Pack: standard, custom, or sport styling, (3 options)
type of transmission: Manual or automatic (2 options)
Color: (7 options)
The total number of combinations is equal to the product of the number of options in each selection:
C = 4*3*2*7 = 168
HELP ASAP PLEASE :(!!!
given the following linear function sketch the graph of the function and find the domain and range. Upload your
document in the box below.
f(x) = -3x+7
Answer:
Step-by-step explanation:
You have the following function:
[tex]f(x)=-3x+7[/tex]
The y-intercept of the function is given by the independent coefficient, which is 7.
y-intercept = 7
To obtain the x-intercept you equal the function to zero and solve for x, as follow:
[tex]0=-3x+7\\\\3x=7\\\\x=\frac{7}{3}\approx2.33[/tex]
x-intercept = 2.33
Due to the coefficient of x is negative, the slope of the function is negative.
The function is a straight line, then, its domain all all real numbers and its range are all real numbers.
The graph of the function is attached in the image below.
A sample of 900 computer chips revealed that 75% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature claimed that above 72% do not fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.05 level to support the company's claim
Answer:
No the evidence is not sufficient
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 900[/tex]
The sample proportion is [tex]\r p = 0.75[/tex]
The population proportion is [tex]p = 0.72[/tex]
The Null hypothesis is
[tex]H_o : p = 0.72[/tex]
The Alternative hypothesis is
[tex]H_a : p > 0.72[/tex]
The level of significance is given as [tex]\alpha = 0.05[/tex]
The critical value for the level of significance is [tex]t_{\alpha } = 1.645[/tex]
Now the test statistic is mathematically evaluated as
[tex]t = \frac{\r p - p }{ \sqrt{\frac{p(1-p)}{\sqrt{n} } } }[/tex]
substituting values
[tex]t = \frac{ 0.75 - 0.72 }{ \sqrt{\frac{0.72 (1-0.72)}{\sqrt{900} } } }[/tex]
[tex]t = 0.366[/tex]
Since the critical value is greater than the test statistics then the Null hypothesis is rejected which there is no sufficient evidence to support the claim
linear regression model describing the relationship between the carat weight and price of very high quality diamonds is summarized below.
A diamond seller lists a very high quality diamond weighing 0.8 carats at a price of $10,999. Does this model over- or under-predict the price of this diamond? Select the option below that best summarizes the answer.
A. The model under-predicts the price of this diamond because the residual is positive.
B. The model over-predicts the price of this diamond because the residual is positive.
C. The model over-predicts the price of this diamond because the residual is negative.
D. We do not have enough information to answer this question.
E. The model under-predicts the price of this diamond because the residual is negative.
Answer:
A. The model under-predicts the price of this diamond because the residual is positive.
Step-by-step explanation:
The diamond seller has listed its 0.8 weighting diamonds at a price of $10,999. The price of the diamond is set as the market maker. The model is used to predict the price of the diamonds. This model has under predicted the value of diamonds and actual price of diamonds must be higher.
A salesperson earns 6% commission on $25,000. How much
commission was earned?
Answer:
1,500
Step-by-step explanation:
[tex]6*(\frac{25,000}{100} )=1,500[/tex]
Which equation is the inverse of y = 16x2 + 1? y = plus-or-minus StartRoot StartFraction x Over 16 EndFraction minus 1 EndRoot y = StartFraction plus-or-minus StartRoot x minus 1 EndRoot Over 16 EndFraction y = StartFraction plus-or-minus StartRoot x EndRoot Over 4 EndFraction minus one-fourth y = StartFraction plus-or-minus StartRoot x minus 1 EndRoot Over 4 EndFraction
Answer:
The inverse is ±sqrt((x-1))/ 4
Step-by-step explanation:
y = 16x^2 + 1
To find the inverse, exchange x and y
x = 16 y^2 +1
Then solve for y
Subtract 1
x-1 = 16 y^2
Divide by 16
(x-1)/16 = y^2
Take the square root of each side
±sqrt((x-1)/16) = sqrt(y^2)
±sqrt((x-1))/ sqrt(16) = y
±sqrt((x-1))/ 4 = y
The inverse is ±sqrt((x-1))/ 4
Answer:
D
Step-by-step explanation:
Solve the equation 2x^2-3x-6=0 give your answer correct to two decimal places
Answer:
x = - 1.14 or x = 2.64Step-by-step explanation:
2x² - 3x - 6 = 0
Using the quadratic formula
[tex]x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
a = 2 , b = - 3 , c = 6
Substituting the values into the above formula
We have
[tex]x = \frac{ - - 3± \sqrt{ { - 3}^{2} - 4(2)( - 6)} }{2(2)} [/tex]
[tex]x = \frac{3± \sqrt{9 +48 } }{4} [/tex]
[tex]x = \frac{3± \sqrt{57} }{4} [/tex]
[tex]x = \frac{3 - \sqrt{57} }{4} \: \: \: \: or \: \: \: \: \: x = \frac{3 + \sqrt{57} }{4} [/tex]
We have the final answer as
x = - 1.14 or x = 2.64Hope this helps you
Amy and Bob decide to paint one wall of a building. Working alone, Amy takes 12 hours to paint the entire wall while Bob takes 18 hours for the same. Amy painted the wall for 4 hours and then Bob took over and completed the wall. How long did it take for them to paint the entire wall
Answer:
16 hours
Step-by-step explanation:
From the above question, we are given the following information
For one wall, working alone,
Amy can paint for 12 hours
Which means, in
1 hour , Amy would have painted = 1/12 of the wall
Bob can paint for 18 hours
Which means ,
in 1 hour, Bob would have painted = 1/18 of the wall.
We are told Amy painted the wall for 4 hours and then Bob took over and completed the wall.
Step 1
Find the portion of the wall Amy painted before Bob took over.
Amy painted the wall for 4 hours before Bob took over.
If:
1 hour = 1/12 of the wall for Amy
4 hours =
Cross multiply
4 × 1/12 ÷ 1
= 4/12 = 1/3
Amy painted one third(1/3) of the wall
Step 2
Find the number of hours left that Bob used in painting the remaining part of the wall
Let the entire wall = 1
If Amy painted 1/3 of the wall
Bob took over and painted = 1 - 1/3
= 2/3 of the wall
If,
Bob painted 1/18 of the wall = 1 hour
2/3 of the wall = ?? = Y
Cross multiply
2/3 × 1 = 1/18 × Y
Y = 2/3 ÷ 1/18
Y = 2/3 × 18/1
Y = 36/3
Y = 12 hours.
This means, the number of hours Bob worked when he took over from Amy = 12 hours.
Step 3
The third and final step is to calculate how many hours it took them to paint the wall
Number of hours painted by Amy + Number of hours painted by Bob
= 4 hours + 12 hours
= 16 hours
Therefore, it took them 16 hours to paint the entire wall.
A rectangular parking lot has a perimeter of 384 meters. The length of the parking lot is 36 meters less than the width. Find the length and the width
Answer: 78
Step-by-step explanation:
The biology faculty at a college consists of 8 professors, 11 asscociate professors , 12 assistant professors and 4 instructors. If one faculty members is randomly selected , find probability of choosing a professor or instructor. Round to nearest thousandth
Answer:
0.343
Step-by-step explanation:
First, find the different ways one can chose a professor or instructor. In this case, there are 8 professors and 4 instructors. So there are a total of 12 ways you can choose a professor or instructor.
Second, you want to find the different ways you can choose any member of the faculty. In this example, since you are only choosing one person, then you just find the total number of people in the faculty, which is 8 + 11 + 12 + 4 = 35.
Third, all you do is divide the different ways you can get a professor or instructor by the total different ways you can choose. So it's 12/35, or 0.343.
Solve the system using multiplication for the linear combination method. 6x – 3y = 3 –2x + 6y = 14 What is the solution to the system
Answer:
work is shown and pictured
Answer:
2/3
Step-by-step explanation:
got right n edg 2021
Consider the y-intercepts of the functions. F(c)=1/5lx-15l, g(x) =(x-2)2, the y-coordinate of the greatest y-intercept is ______
Answer: 4
Step-by-step explanation:
Given functions:
[tex]f(x)=\dfrac{1}{5}|x-15|\\\\ g(x)=(x-2)^2[/tex]
We know that the y--intercept of a function is the value of the function at x=0.
so, put x=0 in both the functions.
The y-coordinate of the y-intercept of f(x) = [tex]f(0)=\dfrac{1}{5}|0-15|=\dfrac{15}{5}=3[/tex]
The y-coordinate of the y-intercept of g(x) = [tex]g(0)=(0-2)^2=2^2=4[/tex]
As 4 > 3, that means he y-coordinate of the greatest y-intercept is 4.
Tom compared 2/12 and 7/6 by first comparing each fraction to 1/2 and 1. In which step did Tom make his first mistake?
Answer:
2/12 is not 1/2 it is 1/6 and 7/6 is greater than 1
Step-by-step explanation:
His comparison to each fraction was incorrect, to simplify fractions you must do to the numerator what you do to the denominator. Find the common number between them and divide. In the case of 2/12 the number would be 2, divide each by that and you get 1/6, Toms comparisons are not proportionate
The automatic opening device of a military cargo parachute has been designed to open when the parachute is 135 m above the ground. Suppose opening altitude actually has a normal distribution with mean value 135 and standard deviation 35 m. Equipment damage will occur if the parachute opens at an altitude of less than 100 m. What is the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes? (Give your answer to four decimal places.)
Answer:
the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes is 0.4215
Step-by-step explanation:
Let consider Q to be the opening altitude.
The mean μ = 135 m
The standard deviation = 35 m
The probability that the equipment damage will occur if the parachute opens at an altitude of less than 100 m can be computed as follows:
[tex]P(Q<100) = P(\dfrac{X- 135}{\sigma} < \dfrac{100 - 135}{35}})[/tex]
[tex]P(Q<100) = P(z< \dfrac{-35}{35}})[/tex]
[tex]P(Q<100) = P(z<-1)[/tex]
[tex]P(Q<100) = 0.1587[/tex]
If we represent R to be the number of parachutes which have equipment damage to the payload out of 5 parachutes dropped.
The probability of success = 0.1587
the number of independent parachute n = 5
the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes can be computed as:
P(R ≥ 1) = 1 - P(R < 1)
P(R ≥ 1) = 1 - P(R = 0)
The probability mass function of the binomial expression is:
P(R ≥ 1) = [tex]1 - (^5_0)(0.1587)^0(1-0.1587)^{5-0}[/tex]
P(R ≥ 1) =[tex]1 - (\dfrac{5!}{(5-0)!})(0.1587)^0(1-0.1587)^{5-0}[/tex]
P(R ≥ 1) = 1 - 0.5785
P(R ≥ 1) = 0.4215
Hence, the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes is 0.4215
Condense each expression. 5 log5 x - 1/4 log5 (8 -x)
Step-by-step explanation:
5 log₅ x − ¼ log₅ (8−x)
log₅ x⁵ − log₅ (8−x)^¼
log₅ x⁵ − log₅ ∜(8−x)
log₅ (x⁵ / ∜(8−x))
The expression 5 log₅ x - 1/4 log₅ (8 - x) can be condensed to [tex]log_{5} \frac{x^5}{\sqrt[4]{8-x} }[/tex] , using the laws of logarithms and exponents.
What are logarithmic expressions?A logarithmic expression x = logₐb, implies that aˣ = b.
What are the properties used in solving logarithmic expressions?Some properties used to solve logarithmic expressions are:
Power law: logₐ xⁿ = n.logₐ xProduct law: logₓ a + logₓ b = logₓ abQuotient law: logₓ a - logₓ b = logₓ a/bHow to solve the given question?In the question, we are asked to condense the expression:
5 log₅ x - 1/4 log₅ (8 - x)
= [tex]log_{5}x^{5} - log_{5}(8 - x)^{1/4}[/tex], (using the power law: logₐ xⁿ = n.logₐ x)
= [tex]log_{5}x - log_{5}\sqrt[4]{8 - x}[/tex], (since, [tex]x^{1/a} = \sqrt[a]{x}[/tex])
= [tex]log_{5} \frac{x^5}{\sqrt[4]{8-x} }[/tex] , (using the quotient law: logₓ a - logₓ b = logₓ a/b).
∴ The expression 5 log₅ x - 1/4 log₅ (8 - x) can be condensed to [tex]log_{5} \frac{x^5}{\sqrt[4]{8-x} }[/tex] , using the laws of logarithms and exponents.
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6th grade math, help me please:)
Answer:
A. 3/5
Step-by-step explanation:
Simple math, 9/15. Divide both by 3.
3*3=9 and 3*5=15 so answer is 3/5!
Answer:
answer is A
Step-by-step explanation:
this is a probability question
divide the number of baskets made by the total number of attempts
9/15 = 3/5
When solving the equation, which is the best first step to begin to simplify the equation? Equation: -2 (x + 3) = -10 A: (-2)(-2)(x+3)= -10(-2) B: -1/2(-2)(x+3)= -10(-1/2) C: -2/2(x+3)= -10/2 D: -2/-10(x+3)= -10/-10
Answer:
Step-by-step explanation:
Given the shape of the equation -2(x+3) = -10. Since x is being multiplied by -2, the first step would be to divide by -2, which is equivalent to multiply by (-1/2) on both sides. Hence the answer is B
what is the 20th term of the arithmetic sequence a(n)=-5+(n-1)3
Answer:
52
Step-by-step explanation:
a(n)=-5+(n-1)3
a(20)=-5+(20-1)3
a(20)=52
The 20th term of the arithmetic sequence is 52.
What is Arithmetic sequence?An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.
For example,
In an arithmetic sequence, the difference between consecutive terms is always the same. For example, the sequence 3, 5, 7, 9 ... is arithmetic because the difference between consecutive terms is always two.
The nth term of an arithmetic sequence is given by an = a + (n – 1)d.
Given:
a(n)=-5+(n-1)3
First term,
a(1)= -5 + 0
a(1)= -5
second, a(2)= -5 + 1*3
a(2)= -2
Third, a(3)= -5+6
a(3)= 1
d= 3
So, the 20th term
a(20)= -5+ (20-1)3
a(20)= -5 + 57
a(20)= 52
Hence, the 20th term is 52.
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Which one doesn’t belong? Why? Explain.
Answer:
IT IS (M-4)(M+1)
Step-by-step explanation:
BECAUSE ALL THE OTHER QUESTION HAVE THE VARIABLE AS X
AND THIS ONE IS M
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
Triangle A B C is shown. Angle B C A is a right angle. The length of hypotenuse A B is 5, the length of B C is 3, and the length of A C is 4. What is the length of the side opposite Angle B? 3 units 4 units 5 units 6 units
Answer:
B. 4 unitsStep-by-step explanation:
Triangle ABC is a right angled triangle. A right angle triangle has three sides (The hypotenuse which is the longest side and the other two sides which are the adjacent and the opposite).
The side facing the angle of a right angled triangle is the opposite side depending on the angle in consideration.
According to the triangle, AB = hyp = 5, BC = 3 and AC = 4
Side AB is facing the right angle, side BC is opposite to the angle A while side AC is opposite to the angle B.
Based on the conclusion in the last paragraph, it can be concluded that the length of the side opposite Angle B is AC and since the measurement of AC is 4 units, then the length we are looking for is 4 units.
Answer:
B. 4 units
Step-by-step explanation:
Which sequence of transformations on preimage Triangle ABC will NOT produce the image A’B’C’
Answer:
b
Step-by-step explanation:
ANSWER NEEDED ASAP!According to the table below, what is the probability that the age of a student chosen at random will be 15 or younger?
A) 0.74
B) 0.59
C) 0.56
D) 0.54
The correct answer is C) 0.56
Explanation:
In general terms, the probability of two or more events can be calculated by adding the probability of each event. This rule applies when an event is considered as mutually exclusive. Age is considered as a mutually exclusive event because if a random individual is selected he/she will be only one age. In this context, if you need to know the probability that a student is 15 or younger it is necessary to add the probability that a student is 15, the probability that the student is 14, and the probability that the student is 13. The process is shown below:
P (A or B or C) = P(A) + P(B) + P(C)
P = P(13) + P(14) + P(15)
P= 0.001 + 0.25 + 0.30
P= 0.56
Answer:
0.59
Step-by-step explanation:
add the probabilities of 13, 14, and 15
0.01 + 0.28 + 0.3 = 0.59
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the trigonometric ratios with their values based on the triangle shown in the diagram.
Answer:
A-2, B-DNE*, C-3, D-DNE, E-4, F-1
---------------------
The first attachment shows the solutions to A and C.
The second attachment shows the solutions to E and F.
There are no real number solutions to systems B and D.
_____
In general, you can solve the linear equation for y, then substitute that into the quadratic. You can subtract the x-term on the left and complete the square to find the solutions.
A.
(3-x) +12 = x^2 +x
15 = x^2 + 2x
16 = x^2 +2x +1 = (x +1)^2 . . . . add the square of half the x-coefficient to complete the square; next take the square root
±4 -1 = x = {-5, 3) . . . . . identifies the second solution set for system A
__
B.
(x -1) -15 = x^2 +4x
-16 = x^2 +3x
-13.75 = x^2 +3x +2.25 = (x +1.5)^2
roots are complex: -1.5 ±i√13.75
__
C.
(1-2x) +5 = x^2 -3x
6 = x^2 -x
6.25 = x^2 -x + .25 = (x -.5)^2
±2.5 +.5 = x = {-2, 3} . . . . . identifies the third solution set for system C
__
remaining problems are done in a similar way.
_____
* DNE = does not exist. There is no matching solution set for the complex numbers that are the solutions to this.
---------------------
Hope this helps!
Brainliest would be great!
---------------------
With all care,
07x12!
Wren recorded an outside temperature of –2°F at 8 a.m. When she checked the temperature again, it was 4°F at 12:00 p.m. If x represents the time and y represents the temperature in degrees Fahrenheit, what is the slope of the line through these two data points? Answer choices 0.5 -0.5 1.5 -1.5
Answer:
[tex]\boxed{1.5}[/tex]
Step-by-step explanation:
First point is given (8, -2)
(x₁, y₁)
Second point is given (12, 4)
(x₂, y₂)
Apply the slope formula.
[tex]slope=\frac{rise}{run}[/tex]
[tex]slope=\frac{change \: in \: y}{change \: in \: x}[/tex]
[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]slope=\frac{4-(-2)}{12-8}[/tex]
[tex]slope=\frac{6}{4}=1.5[/tex]
A slope is also known as the gradient of a line. The slope of the line through these two data points is 1.5°F per hour.
What is Slope?A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
slope = (y₂-y₁)/(x₂-x₁)
Given that the temperature recorded at 8 am is –2°F, while the temperature recorded at 12 pm is 4°F. The number of hours between 8:00 am to 12 pm is 4 hours. Therefore, the slope of the line through these two data points is,
Slope, m = [4°F – (–2°F)] / 4 hours = 6°F / 4 hours = 1.5°F per hour
Hence, the slope of the line through these two data points is 1.5°F per hour.
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(1/6 + 3/7) + 2/7=
Answer:
37/42 or 0.88
Step-by-step explanation:
[tex]( \frac{1}{6} + \frac{3}{7} ) + \frac{2}{7} \\ ( \frac{1}{6} + \frac{3}{7} ) = \frac{25}{42} \\ [/tex]
[tex]\frac{25}{42} + \frac{2}{7} = \frac{37}{42} \\ \\ answer = \frac{37}{42} [/tex]
Factories A, B and C produce computers. Factory A produces 4 times as manycomputers as factory C, and factory B produces 7 times as many computers asfactory C. The probability that a computer produced by factory A is defective is0.04, the probability that a computer produced by factory B is defective is 0.02,and the probability that a computer produced by factory C is defective is 0.03. Acomputer is selected at random and found to be defective. What is the probabilityit came from factory A?
Answer:
The probability is [tex]P(A') = 0.485[/tex]
Step-by-step explanation:
Let assume that the number of computer produced by factory C is k = 1
So From the question we are told that
The number produced by factory A is 4k = 4
The number produced by factory B is 7k = 7
The probability of defective computers from A is [tex]P(A) = 0.04[/tex]
The probability of defective computers from B is [tex]P(B) = 0.02[/tex]
The probability of defective computers from C is [tex]P(C) = 0.03[/tex]
Now the probability of factory A producing a defective computer out of the 4 computers produced is
[tex]P(a) = 4 * P(A)[/tex]
substituting values
[tex]P(a) = 4 * 0.04[/tex]
[tex]P(a) = 0.16[/tex]
The probability of factory B producing a defective computer out of the 7 computers produced is
[tex]P(b) = 7 * P(B)[/tex]
substituting values
[tex]P(b) = 7 * 0.02[/tex]
[tex]P(b) = 0.14[/tex]
The probability of factory C producing a defective computer out of the 1 computer produced is
[tex]P(c) = 1 * P(C)[/tex]
substituting values
[tex]P(c) = 1 * 0.03[/tex]
[tex]P(b) = 0.03[/tex]
So the probability that the a computer produced from the three factory will be defective is
[tex]P(t) = P(a) + P(b) + P(c)[/tex]
substituting values
[tex]P(t) = 0.16 + 0.14 + 0.03[/tex]
[tex]P(t) = 0.33[/tex]
Now the probability that the defective computer is produced from factory A is
[tex]P(A') = \frac{P(a)}{P(t)}[/tex]
[tex]P(A') = \frac{ 0.16}{0.33}[/tex]
[tex]P(A') = 0.485[/tex]