On solving the provided question, we can say that this is from integral type of quadric surface [tex]SA = (\pi / 6) * 26 = > SA = (13 * \pi) / 3[/tex]
what is integral?In mathematics, integrals translate integers into functions that express concepts like displacement, area, and volume that result from the combination of little facts. Integral discovery is a process that is referred to as integration.
We concentrate on the x distance from the y-axis since the rotation is about the y-axis.
function for x, which is
x = + or - sqrt(y)
x = sqrt(y)
This is function is g(y) = sqrt(y)
g(y) about the y-axis on the closed interval [c, d], that is, y is an element of [c, d] is
Surface Area(SA) = 2 * pi * integral from c to d of ( g(y) * sqrt(1 +(g’(y))^2 ) *dy
The given interval is x=0 to x=sqrt(2), using the given function y = x^2 we obtain y = 0 to y = 2
g(y) = sqrt(y) and g’(y) = 1/(2 * sqrt(y))
SA = 2 * pi * integral from 0 to 2 of sqrt(y) * sqrt(1 +(1/(2*sqrt(y)))^2) * dy
SA = 2 * pi * integral from 0 to 2 of sqrt(y *(1 +(1/(4*y)) * dy
SA = 2 * pi * integral from 0 to 2 of sqrt(y +(1/4) * dy
Apply u substitution, let u = y +(1/4), then take derivative of u which gives us du = dy. As part of the substitution, we need to change the bounds to 1/4 and 9/4
SA 2 * pi * integral from 1/4 to 9/4 of u^(1/2) du
[tex]f u^(1/2) is 2u^(3/2) / 3[/tex]
[tex]SA = evaluate 2 * \pi * ( 2u^(3/2) / 3 ) from 9/4 to 1/4\\SA = [ 2 * \pi * ( 2 * (9/4)^(3/2) / 3) ] - [ 2 * \pi * ( 2 * (1/4)^(3/2) / 3) ]\\2 * \pi * 2 * (1/3)\\SA =((4 * \pi) / 3) * { [ (9/4)^(3/2) / 3) ] - [ (1/4)^(3/2) / 3) ] }\\ 4^(3/2) = sqrt(64) = 8\\SA = ((4 * \pi) / 3) * [ ( 9^(3/2) -1) / 8 ]\\SA = (\pi / 6) * ( 27 -1)\\SA = (\pi / 6) * 26\\SA = (13 * \pi) / 3\\[/tex]
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Is Fergie or Francesca correct?
Answer:
Francesca
Step-by-step explanation:
a $129 product is marked up 20%. how much is the markup?
Answer:
$25.80
Step-by-step explanation:
Since we need to mark up the price of something, we need to find what 20% of 129 is, then add it to 129. To find our 20%, we put 129 in a fraction like this and get:
[tex]\frac{129}{5} = 25.8[/tex]
So, the markup is $25.80.
Hope this helped!
What are the different ways on writing proof
Answer:
There are several ways to write a proof, depending on the level of rigor and formality required. Some common methods include:
1- Direct proof: A direct proof is a logical argument that begins with the premises and uses logical deduction to arrive at the conclusion.
2- Proof by contradiction: A proof by contradiction starts by assuming the opposite of what needs to be proven and then showing that this leads to a contradiction.
3- Proof by contrapositive: A proof by contrapositive is a proof that starts by assuming the negation of the desired conclusion and then showing that this leads to the negation of the premises.
4- Proof by induction: A proof by induction is a proof that starts by showing that a statement is true for the first few natural numbers, and then showing that if it is true for a particular natural number, it must also be true for the next natural number.
5- Proof by construction: A proof by construction is a proof that shows the existence of a mathematical object by giving an explicit construction of it.
6- Proof by exhaustion: A proof by exhaustion is a proof that considers all possible cases and shows that in each case the statement is true.
7- Proof by casework: A proof by casework is a proof that is split into several cases, each of which is considered separately.
8- Proof by diagram: A proof by diagram is a proof that uses a visual representation to show that a statement is true.
These are some of the common ways of writing proof, and there could be other ways as well. It is important to use the most appropriate method for the problem at hand, and to clearly explain and justify each step of the proof.
A landscaping company placed two orders with a nursery. The first order was for 7
bushes and 4 trees, and totaled $226. The second order was for 6 bushes and 2 trees,
and totaled $148. The bills do not list the per-item price. What were the costs of one
bush and one tree?
Naturally, the task did not require the values of the two variables.Each tree costs $47 and each bush is $23.
How much did one tree and one bush cost?Although I don't have subtotals for the bushes and trees, I could try to add the bushes and trees to get 19 bushes and 6 trees, but this wouldn't help me at all.
So I'll choose two variables ("b" for the quantity of bushes and "t" for the quantity of trees) and construct an equational structure:
13b + 4t = 487 is the first order.
second order: 6b plus 2t equals 232.
When I divide the second row by -2, I obtain:
13b + 4t = 487
-12b – 4t = –464
Therefore, b must equal 23.
Using back-solving, I discover that t = 47.
Naturally, the task did not require the values of the two variables.
The answer, when translated back into English, is:
Each tree costs $47 and each bush is $23.
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Look at the line graphed below.
Which equation can be used to graph all the points on the line?
�
=
2
�
y=2x
�
=
�
+
1
y=x+1
�
=
�
−
1
y=x−1
�
=
2
�
−
1
y=2x−1
Answer:
y = x + 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 2) and (x₂, y₂ ) = (8, 9) ← 2 points on the line
m = [tex]\frac{9-2}{8-1}[/tex] = [tex]\frac{7}{7}[/tex] = 1
the line crosses the y- axis at (0, 1 ) ⇒ c = 1
y = x + 1 ← equation of line
Ditribute to create an equivalent expreion with the fewet ymbol poible. 1/3(3j6)
To find the equivalent expression with the fewest symbols possible for 1/3(3j6),One third of three times the value of six, which is equal to one times the value of two.
1/3(3j6)
= 1/3(3*6)
= 1/3(18)
= 18/3
= 6
= 1j2
To find the equivalent expression with the fewest symbols possible for 1/3(3j6), we need to start by multiplying 3 and 6 together. This gives us the result of 18. Next, we divide 18 by 3, which gives us the result of 6. Finally, we express the result as 1j2, which is the equivalent of 1/3(3j6) with the fewest possible symbols. By following these steps, we can easily calculate the equivalent expression with the fewest symbols. In this case, it is 1j2. The process of calculating the equivalent expression with the fewest symbols is relatively straightforward, but it is important to remember to use the correct order of operations when performing calculations. To ensure accuracy, it is best to work step by step, multiplying 3 and 6 together first and then dividing 18 by 3 to get the final result of 1j2.
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imagine i flip 100 coins in a sequence, and you need to guess the sequence. you are allowed to ask one yes/no question. what do you ask to maximize the probability of guessing the sequence?
On solving the provided question, we can say that the probability of guessing the sequence 2^99 possible combinations.
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true.
As soon as you realize there are more heads than tails, you realize you require at least 50 of them, and you ask 100 people to select 50 locations for them to go.
Considering that you have 250 options for the remaining coins, there are a total of (100 pick 50) + 250 combinations that are feasible.
There are 299 potential options if you simply inquire as to whether the first coin will land on heads.
Asking whether there are more heads than tails is preferable because, according to Wolfram Alpha, 299 is larger than (100 pick 50) + 250.
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helppp i need to finish my study guide but I don't get thissss
The trigonometrical ratios of the triangle are:
sin∠X = x/z
cos∠X = y/z
tan∠X = x/y
sin∠Y = y/z
cos∠Y = x/z
tan∠Y = y/x
How to find sin∠X in the triangle?We will use trigonometrical ratios to solve this problem. Below are the definitions of the trigonometrical ratios:
sin = opposite/hypotenuse
cos = adjacent/hypotenuse
tan = opposite/adjacent or tan = sin/cos
The opposite is the side the angle of consideration is facing
The hypotenuse is the side the right angle is facing
The adjacent is the side left after determining the opposite and hypotenuse
Thus, we have the following trigonometric ratios in the triangle:
sin∠X = x/z
cos∠X = y/z
tan∠X = x/y
sin∠Y = y/z
cos∠Y = x/z
tan∠Y = y/x
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Joshua is driving to the store. the average distance din miles, he travels over minutes is given by the function (1) - 0.57. what is the
75 miles
7.5 minutes
7.5 miles
15 minutes
Driving to the supermarket is Joshua. He covers 7.5 miles since he goes an average of 0.56 miles per minute.
Why is mean called the average?By dividing the entire specific number by sum of all the values, the average can be obtained. A mean may indeed be calculated by adding all of the values in a sample of data. In other terms, a means is also known as the arithmetic mean. The average is referred to as having a mean.
The provided function is
d(t) = 0.5t
Simply substitute it to get the figure set t = 15
7.5 miles are equal to d (15) 0.5 (15).
To get the distance, use the range equations d = st, which says "distance equals force times time." Rate and speed are equivalent because they both indicate a specific length of distance per unit time, such like km/h or kilometers per hour. R = s = d/t is true if clip r and mobility s are equal.
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One rule of thumb for estimating crowds is that each person occupies 2.5 square feet.
use this rule to estimate the size of a crowd attending a local concert that is 110ft deep
and 50ft wide.
Which of the following graphs does NOT describe y as a function of x?
Answer:
the first one
Step-by-step explanation:
using the vertical line rule, we can see that a vertical line would intersect the first graph more than once at any point to the right of the vertex. this cannot be said for the other graphs
Show all work to identify the asymptotes and state the end behavior of the function f of x is equal to 4x divided by the quantity of x minus 16 end quantity.
Answer:
Step-by-step explanation:
The function f(x) = 4x/(x-16) has two vertical asymptotes at x = 16. This can be seen by taking the limit of the function as x approaches 16 from the left and right sides.
On the left side, as x approaches 16 from the left, the denominator, (x-16), will approach 0, while the numerator, 4x, will approach -∞. This results in a limit of -∞, indicating a vertical asymptote at x = 16.
On the right side, as x approaches 16 from the right, the denominator, (x-16), will approach 0, while the numerator, 4x, will approach +∞. This results in a limit of +∞, also indicating a vertical asymptote at x = 16.
The end behavior of the function is that as x approaches +∞, the function will approach +∞, and as x approaches -∞, the function will approach -∞.
a sequence of complex numbers , , , satisfies the rulesuppose that and . how many possible values are there for ?
Four complex numbers are present. fulfilling the following equations of a sequence of complex numbers is √3, - √3, √15 i, - √15 i .
what is sequence ?A sequence is an arrangement of numbers, or "terms." Terms like 2, 5, and 8 are examples. By taking advantage of a specific pattern some sequences use, they can be made to go on forever. To continue the sequence, add 3 and use the example of 2,5,8. In a succession of words, there exist formulas that show where to look. In mathematics, a sequence is a collection of items that are arranged in some manner (or events). Because it has parts, it is similar to a set (also called elements or terms). The length of the sequence is defined as the total, possibly unlimited number of ordered objects. arranging two or more elements in a sensible sequence. Chronological.
given
Complex conjugation refers to the real line's reflection of the complex plane. Z or z can be used to represent the complex conjugate of z. Similar real and imaginary parts exist in the complex conjugate, but with the opposite sign on the imaginary portion.
This means that z=a+ib follows from z=a+ib.
Four complex numbers are present. fulfilling the following equations of a sequence of complex numbers is √3, - √3, √15 i, - √15 i .
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The question is in the picture
The value of x from the triangle is x = 30
What is the law of sines?The relationship between a triangle's sides and angles is provided by the Law of Sines. Trigonometry's law of sines can be expressed as a/sinA = b/sinB = c/sinC, where a, b, and c are the lengths of the triangle's sides, and A, B, and C are the triangle's respective opposite angles.
Law of Sines :
a / sin A = b / sin B = c / sin C
Given data ,
Let the triangle be represented as ABC
Now , the length of the side b = x
The length of the side a = x + 2
The measure of sin A = 4/5
The measure of sin B = 3/4
So , to find the value of x , we use the law of sines
a / sin A = b / sin B
Substituting the values in the equation , we get
( x + 2 ) / ( 4/5 ) = x / ( 3/4 )
On simplifying the equation , we get
5 ( x + 2 ) / 4 = 4x / 3
Multiply by 3 on both sides of the equation , we get
15 ( x + 2 ) / 4 = 4x
Multiply by 4 on both sides of the equation , we get
15 ( x + 2 ) = 16x
15x + 30 = 16x
Subtracting 15x on both sides of the equation , we get
x = 30
Therefore , the value of x is 30
Hence , the value of x is 30
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What are the possible values of g such that fg2 = 32, f < 20, g < 20, and f and g are integers? –2, 2 –4, 4 –1, 1, –2, 2 –1, 1, –4, 4 –2, 2, –4, 4
The possible values for f and g are -2, 2, -4, 4, -1, 1.
What is inequality?
A solution for an inequality in x is a number such that when we substitute that number for x we have a true statement. So, 4 is a solution for example 1, while 8 is not. The solution set of an inequality is the set of all solutions.
If fg^2 = 32, then either fg = ±4, ±2, or ±1. If f < 20 and g < 20, then the possible values for f and g are:
f = 2, g = 4
f = 4, g = 2
f = 1, g = 4
f = 4, g = 1
f = 2, g = 2
f = 1, g = 1
Hence, the possible values for f and g are -2, 2, -4, 4, -1, 1.
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You start at(-4, 3). You move right 5 units and down 8 units. Where do you end?
nate has a grid made of shaded and unshaded 2 cm by 2 cm squares, as shown. he randomly places a circle with a diameter of 3 cm on the board so that the centre of the circle is at the meeting point of four squares. the probability that he places the disk so that it is touching an equal number of shaded and unshaded squares is ab. what is a b ?
The value of a and b is 1.
THE PROBABILITY OF A AND BThe probability that Nate places the disk so that it is touching an equal number of shaded and unshaded squares is ab, where a and b are integers.
To find the value of a and b, we need to determine the total number of ways Nate can place the disk (the denominator of the probability fraction) and the number of ways he can place the disk so that it touches an equal number of shaded and unshaded squares (the numerator of the probability fraction).
Since the center of the circle must be at the meeting point of four squares, the only possible places for the center are the points where four squares meet. Since the grid is made of 2 cm x 2 cm squares, there are 4 shaded squares and 4 unshaded squares. So, there are 4 centers that could be placed on a shaded square and 4 centers that could be placed on an unshaded square.
So the denominator of the probability fraction is 8.
Now, to calculate the numerator, we need to determine the number of ways Nate can place the disk so that it touches an equal number of shaded and unshaded squares.
As the center of the circle is at the meeting point of four squares, the center of the circle is placed at the intersection of 2 shaded and 2 unshaded squares.
So, the numerator of the probability fraction is 8.
Therefore, the probability that Nate places the disk so that it is touching an equal number of shaded and unshaded squares is 8 ÷ 8 =1.
So the value of a and b is 1.
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a vacant lot measures 50' x 102'. if the lot sold for $108,250, what was the price per square foot...?
The price per square foot of a vacant lot that measures 50' x 102' and sold for $108,250 is $21.23.
To find the price per square foot of the vacant lot, we need to divide the total price by the total area of the lot.
We can find the area of the lot by multiplying the length by the width:
Area = 50' x 102' = 5100 sq.ft
Then, we can divide the total price by the total area to find the price per square foot:
Price per sq.ft = Total Price / Total Area
Price per sq.ft = 108,250 / 5100
Price per sq.ft = 21.23
Therefore, the price per square foot of the vacant lot is $21.23.
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Can a 3rd degree polynomial have all real roots?
The 3rd-degree polynomial has at least one or three real roots.
Yes, a third degree polynomial can have all real roots. This is because a third degree polynomial has at least one real root, as it is the lowest degree polynomial that can have an imaginary root. The other two roots can be real or imaginary, depending on the coefficients of the polynomial. If the discriminant of the polynomial is greater than or equal to zero, the polynomial will have all real roots. In a cubic polynomial, only one or three real roots are present. Polynomials having odd degrees have at least one real root. A cubic equation's graph must at least once cross the x-axis, giving you at least one real root. Only a quadratic polynomial has two real roots. Quadratic polynomials are those having a degree of two. Polynomials can be represented on the graph, on that basis we can determine whether the roots are real or not.
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Find the value of Zα.
Z0.07=
We may calculate the corresponding value of z = 1.476 using a conventional normal right-tailed z-table.
What is the location of the Z value table?Find the value corresponding to one decimal place of the z-score by first looking at the left side column of the z-table (e.g. whole number and the first digit after the decimal point). It is 1.0 in this instance. We then look up the last number, which in our example is 0.09, from across table (on top).
Why does Z appear in the Z-table?The amount of standard deviations a scoring or value (x) is from the mean is the number of Z scores (Z value). Z-score quantifies data dispersion in other terms. Z-score, informally, indicates however many standard deviations a number (x) is below or above population mean (µ).
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The vertices of triangle FGH has vertices F(-3, 0), G(6, -1) and H (5, -3). Name the vertices of the image reflected across the line y = x.
a. F' (0, -3), G' (-1, 6), H' (-3,5)
b. F' (3, 0), G' (-6, -1), H' (-5, -3)
c. F' (-3, 0), G' (6, 1), H' (5, 3)
d. F' (0, 3), G' (-1, -6), H' (-3, -5)
Answer:
b. F' (3, 0), G' (-6, -1), H' (-5, -3)
Factor out the greatest common factor ?
PLEASE HELP ME SUBJECT MATH
Answer:
11) y = -x + 9
12) y = 4x - 16
13) y = x - 5
14) y = -2x + 4
15)y = 0.5x - 3
Step-by-step explanation:
In all these equations isolate y by moving the other terms to the left side and dividing by the coefficient of x to get the slope intercept form
11)
x + y = 9
y = -x + 9 by moving x to the right side
12)
4x - y = 16
-y = -4x + 16
Multiply by -1 to get y = 4x - 16
13)
2x - 2y = 10
-2y = -2x + 10
Divide by -2 to get y = x - 5
14)
4x + 2y = 8
2y = -4x + 8
Divide by 2 to get y = -2x + 4
15)
x - 2y = 6
-2y = -x + 6
Divide by -2 to get y = x/2 - 6 = 0.5x -3
the sum of bill and ted's age is 60. in two years, bill will be three times as old as ted. how old are bill and ted now?
That bill age is currently 46 years old, and the ted age is currently 14 years old, according the provided statement.
You ancient soul, how are you?Frequently, having an ancient soul only means you see things differently. There is nothing improper about that. In fact, most individuals would contend that having a distinct outlook on life may be advantageous to both you and those in your life. Depending on how you do it with your understanding, the wider world may be a possibility.
Equations:
B+2 = 3(t+2), B+t = 60, B-t = 4, and B+t = 60
Solve for "t" by subtracting: 4t = 56 t Equals 14 (Ted's current age).
Calculate "b" as follows: b + t = 60 b + 14 = 60 b Equals 46 (Bill's current age).
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A plastic container has 264 yellow marbles. The rest of the marbles are blue. The number of yellow marbles is 60% of the total number of marbles. How many total marbles are blue?
Answer: 176 BLUE marbles
Explanation:
First --> Total marbles ==> 264 / 0.60 = 440
Second --> Hence, the total number of BLUE marbles is 440 - 264 = 176
and there is 176 BLUE marbles
Answer:
660
Step-by-step explanation:
first, 264 yellow marbles.
the percentage of yellow is 60.
If total percentage is 100 then, blue is 100-(yellow percentage)
that is: 40 percent
the next sentence.
total marbles of blue is:
40x/100 = 264.0.4x = 264.divide both sides by 0.4
x = 264/0.4x= 660.
If sally had 5,000,000 toys box to send to kids each box had 8 toys. How many box are there in total?
Answer:
The total boxes would be 625,000
Step-by-step explanation:
5,000,000÷8=625,00
If you have 5,000,000 toys and each box holds 8 toys, you need to divide the number of toys that will fit into a box from the total number of toys
Write the equation of this line in slope-intercept form.
Answer:
Step-by-step explanation:
The line passes through points (2,1) and (0,-5)
Using this, we can find the slope, which is
change in y/change in x = -6/-2 = 3
Therefore the slop of this line is 3.
Next, the y-intercept of this line is -5.
So we can find the equation of this line in slope-intercept form which is:
y=3x-5
find the percentage error if 3,750 is used as an approximation to 3,754.
give the answer rounded to four decimal places.
a.1066 %
b. -0.1066 %
c.0011 %
d. 0.1067 %
The percentage error if 3,750 is used as an approximation to 3,754 as calculated is found out to be as , 0.1066%.
We calculate the percentage of error as ,
| Vobs – Vtrue |/ Vtrue× 100%
Therefore the percentage error in this case will be ,
= 3754 - 3750/3750
= 4/3750
=0.1066%
Therefore, the required POE is found out to be as , 0.1066%.
Percent error tells us about the magnitude of our errors while measuring anything , this concept is used in approximation. Lower percentage errors suggest that we are getting close to the original number. A 1% inaccuracy, for example, implies that we were extremely close to the approved number, whereas a 48% error indicates that we were rather far from the genuine value.
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Isabel is going to rent a truck for one day. there are two companies she can choose from, and they have the following prices. company a charges $90 and allows unlimited mileage. company b has an initial fee of $75 and charges an additional $0.60 for every mile driven. for what mileages will company a charge less than company b? use m for the number of miles driven, and solve your inequality for m .
Company A charges $90 for unlimited mileages, while company B charges $75 initial fee and #0.6 per mile driven. Company A will charge less than company B if the number of miles driven is greater than 25 miles or m > 25.
To solve the problem, we need to translate the word problem into equations.
Let C(A) and C(B) represent the cost charged by company A and B respectively. Let m = the number of mileages.
Company A charges $90 and allows unlimited mileage, it means the charge is a constant and it is not a function of mileage.
Hence,
C(A) = 90
Company B has an initial fee of $75 and charges an additional $0.60 for every mile driven. Hence,
C(B) = 75 + 0.6 m
The inequality that translate: for what mileages will company A charge less than company B is:
C(A) < C(B)
90 < 75 + 0.6 m
To solve the above inequality, subtract 75 from both sides:
90 - 75 < 75 + 0.6 m - 75
15 < 0.6 m
m > 15/0.6
m > 25
Hence, if the mileages > 25 miles, company A charges less than company B.
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a company that manufactures video cameras produces a basic model and a deluxe model. over the past year, 42% of the cameras sold have been of the basic model. of those buying the basic model, 44% purchase an extended warranty, whereas 49% of all deluxe purchasers do so. if you learn that a randomly selected purchaser has an extended warranty, how likely is it that he or she has a basic model? (round your answer to four decimal places.)
If a randomly selected purchaser has an extended warranty the probability that he or she has a basic model is 0.3940.
By employing the criteria that certain events have occurred, the Bayes Theorem allows us to determine the posterior probability.
Given that,
E: Purchaser has extended Warranty.
A: He chooses a basic model.
B: He chooses a deluxe model.
P(A) = 0.42
P(B) = 0.58
P(E/A) = 0.44
P(E/B) = 0.49
The probability that a randomly selected customer has an extended warranty is given by:
P(E)= P(E/A)*P(A)+P(E/B)*P(B) = 0.44*0.42 + 0.49*0.58= 0.469
If a randomly selected purchaser has an extended warranty the probability that he or she has a basic model is given by:
P(A/E)= P(E/A)*P(A)/P(E) = 0.44*0.42/0.469 = 0.3940
Thus, If a randomly selected purchaser has an extended warranty the probability that he or she has a basic model is 0.3940.
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