Elijah put 2x+3
2
x
+
3
dollars in the bank the first week. The following week he doubled the first week’s savings and put that amount in the bank. The next week, he doubled what was in the bank and put that amount in the bank. He now has $477 in the bank. How much money did he put in the bank the first week?
Elijah put $53 in the Bank in the first week .
In the question ,
it is given that Elijah put (2x+3) in the first week .
In the second week Elijah put double the first week savings
that means second week deposit = 2*(2x+3) = 4x+6
in the third week he doubled the amount that was in the bank ,
which means third week deposit = 2*(first week + second week deposit)
= 2*(2x+3+4x+6)
Also given that total amount in the bank = $477
total amount = first week + second week + third week deposit
substituting the values we get
477 = (2x+3) + (4x+6) + 2*(2x+3+4x+6)
477 = 2x+3+4x+6+4x+6+8x+12
477 = 18x + 27
18x = 477-27
18x = 450
x = 450/18
x = 25
the amount deposited in the first week = 2x+3
= 2(25)+3
= 50+3 = $53
Therefore , Elijah put $53 in the Bank in the first week .
The given question is incomplete , the complete question is
Elijah put 2x+3 dollars in the bank the first week. The following week he doubled the first week’s savings and put that amount in the bank. The next week, he doubled what was in the bank and put that amount in the bank. He now has $477 in the bank. How much money did he put in the bank the first week?
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can someone please answer this step by step asap? im confused and dont know how to solve this
3 equations that can be used to solve the given scenario are:
10x + 15x + 20x = 500045x = 500010x + 15x + 20x = 300What exactly are equations?In mathematical equations, the equals sign is used to show that two expressions are equal.An equation is a mathematical statement that uses the word "equal to" in between two expressions of the same value.As an illustration, 3x + 5 equals 15.There are many different types of equations, including linear, quadratic, cubic, and others.The three primary types of linear equations are slope-intercept, standard, and point-slope equations.So, equations that can be used to solve the following scenario are:
Let, the number of students in each group is 'x'.Then,
10x + 15x + 20x = 500045x = 500010x + 15x + 20x = 300Therefore, 3 equations can be used to solve the given scenario are:
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Write the equation of the line that is perpendicular to the x-axis and contains point (0,
4).
The line of the equation which passes through the point (0, 4) and is parallel to the x-axis is 2y = 8.
What are equations?A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 = 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. A mathematical equation is a formula that uses the equals sign to express the equality of two expressions.So, the equation is as:
A line formed needs to be parallel to the x-axis which means x = 0.Should pass through points (0, 4)Then, the equation can be:
2y = 8(Refer to the graph attached below)
If you solve will become:
2y = 8y = 4Therefore, the line of the equation which passes through the point (0, 4) and is parallel to the x-axis is 2y = 8.
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A rental car company charges $37.50 per day to rent a car and $0.05 for every mile
driven. Alyssa wants to rent a car, knowing that:
. She plans to drive 100 miles.
. She has at most $200 to spend.
Write and solve on
Hello!
Knowing that Alyssa wants to rent a car where the company charges $37.50 per day to rent a car and $0.05 for each mile driven we have to find out how many days she is planning on renting a car for.
Step-by-step explanation:
Using the information we have we can see that it will be an additional $5 based on how many miles she is planning on driving.
If the base cost to rent a car is $37.50 you will have to add an additional $5 for the number of miles she plans to drive making the total $42.50.
Since she has at most $200 to spend on a car rental she can rent a car for a total of 5 days at a total cost of $192.50
[tex]37.50[/tex] × [tex]4=150[/tex] + [tex]42.50[/tex] = [tex]192.50[/tex]
Hope this helps!
The inequality will be 37.5x + (0.05 ×100) ≤ 200, and Alyssa can afford 5.2 days to rent while staying within her budget
How to write and solve an inequality to determine the number of days?Given that the rental car company charges $37.50 per day to rent a car and $0.05 for every mile driven
She plans to drive 100 miles and has at most $200 to spend.
Let x is the number of days, Alyssa can afford to rent while staying within her budget
The inequality can be written as;
37.5x + (0.05 ×100) ≤ 200
Now solve for x:
37.5x + (0.05 ×100) ≤ 200
37.5x + 5 ≤ 200
37.5x ≤ 200 - 5
37.5x ≤ 195
x ≤ 195/37.5
x ≤ 5.2
Therefore, she can afford 5.2 days to rent while staying within her budget.
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If cos∠E = sin∠F and m∠E = 26°, what is m∠F?
Step 1
Given;
[tex]\begin{gathered} cosE=sinF \\ measure\text{ of angle E=26}^o \end{gathered}[/tex]Required; To find the measure of angle F
Step 2
[tex]\begin{gathered} cos26=sinF \\ \sin\left(90^{\circ\:}-26^{\circ\:}\right)=cos26 \end{gathered}[/tex][tex]\begin{gathered} \sin\lparen F)=\sin\left(90^{\circ\:}-26^{\circ\:}\right) \\ sin(F)=sin(64) \end{gathered}[/tex]Answer;
[tex]m\angle F=64[/tex]A number was tripled, then decreased by 10, then doubled, and then increased by 2. The result was 5 times the original number.
If the original number was x, the equation will be
x=
Answer:
x = 18
The number is 18.
Step-by-step explanation:
Convert the words into an equation.
let x;
( 3x - 10 )( 2 ) + 2 = 5x;
6x - 20 + 2 = 5x;
6x - 18 = 5x;
Subtract both sides by 5x.
6x - 5x - 18 = 5x - 5x;
x - 18 = 0;
Add 18 to both sides.
x - 18 + 18 = 18;
x = 18;
Rewrite in simplest terms: -4f-6(6f-10)
The given expression: -4f-6(6f-10) in simplified form
is: -40f + 60.
What is an algebraic expression and how is it simplified?
The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it. Simplifying the algebraic expressions is to carry out operations on the expressions and then clear it out.
Given, the expression for simplification is: y = -4f-6(6f-10)
Working on the expression above, we have:
y = -4f-6(6f-10) = -4f -36f + 60 = -40f + 60
Therefore the given expression: -4f-6(6f-10) in simplified form
is: -40f + 60.
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31. a statistics class has 26 students. the instructor would like to select a random sample of 3 students to work together on a group project. a. how many different samples are possible? b. if 13 of the 26 students in class are freshmen, what is the probability that all 3 of the selected students are freshmen?
a. 2600 ways different samples are possible.
b. 0.11 is the probability that all 3 of the selected students are freshmen.
total student = 26
3 students are randomly selected on group project
a. the possible different sample are
[tex]26 C_{3}[/tex] = [tex]\frac{26}{3 (26-3)}[/tex]
= [tex]\frac{26}{3 (23)}[/tex]
= 2600 ways.
b. 13 students are freshmen
Pr ( 3 selected students is freshman)
[tex]\frac{13C_{3} }{26C_{3} }[/tex] = [tex]\frac{286}{2600}[/tex] = 0.11
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
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determine the equation of line from the graph
Answer:
y = -x
Step-by-step explanation:
Answer: Y=-X
Step-by-step explanation:
albert brought a blanket for 32.75, a pillow for 12.75,and a glove for 16.25. he paid 50 and the rest he borrowed from his friend. if albert for 5.25 in change from the cashier, how much did he borrow from his friend to pay for all of the items.
Albert borrowed $17 from his friend.
Given,
Albert brought some items:
Cost of blanket = $32.75
Cost of pillow = $12.75
Cost of glove = $16.25
Amount paid by Albert = 50
Amount borrowed by Albert from his friend = x
Cashier gave back the change = $5.25
We have to find the amount borrowed by Albert from his friend:
This is simply arithmetic operations:
Total cost in shop = 32.75 + 12.75 + 16.25 = $61.75
Total amount given to the cashier = 61.75 + 5.25 = 67
Amount borrowed by Albert from his friend = Total amount given to the cashier - Amount paid by Albert
x = 67 - 50
x = 17
That is,
Albert borrowed $17 from his friend.
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PLEASE FOLLOW THE DIRECTIONS IN THE PICTURES. PLEASE HURRY. Thank you very much
Answer:
E
Step-by-step explanation:
[tex]\sqrt{144} = 12\\ \frac{234}{3}= 78\\[/tex]
12, 68.12, 78
PLEASE HELP SOON!!!! Pre-calc, Trig, Calculus studentsss
Answer:
Step-by-step explanation:
A company makes concrete bricks shaped like rectangular prisms. Each brick is 11 inches long, 8 inches wide, and 5 inches tall. If they used 11,000in3 of concrete, how many bricks did they make?
Answer:
25 bricks
Step-by-step explanation:
Calculate the volume of one brick:
Volume = (11')(8")(5") = 440 in^3
Divide the volume of a one brick into the volume of concrete that will be used:
(11000 in^3 concrete)/(440 in^3 concrete/brick) = 25 bricks
O EQUATIONS AND INEQUALITIESSolving a word problem with two unknowns using a linear...
Given:
Total number of hamburgers and cheeseburgers sold = 439
There were 61 fewer cheeseburgers than hamburgers sold.
Let's determine the number of hamburgers sold.
Let C represent the number of cheeseburgers
Let H represent the number of hamburgers sold.
We have the system of equations:
• H + C = 439
,• C = H - 61
Now, let's solve the equations simultaneously using the substitution method.
Substitute (H - 61) for C in the first equation.
We have:
H + (H - 61) = 439
H + H - 61 = 439
2H - 61 = 439
Add 61 to both sides:
2H - 61 + 61 = 439 + 61
2H = 500
Divide both sides by 2:
[tex]\begin{gathered} \frac{2H}{2}=\frac{500}{2} \\ \\ H=250 \end{gathered}[/tex]Therefore, they sold 250 hamburgers on Friday.
ANSWER:
250 hamburgers
What is the maximum volume of a rectangular prism (or box) if the prism has a square base and a total surface area of 100 cm^2?
A) First, let x = the side length of the base and h = the height of the prism. Write and solve the equation for h.
B) Write a function for the volume of the box, V, in terms of x.
Answer: A. 100/x^2 = h, B. v(x) = x^2*h
Step-by-step explanation:
A. Volume = b * h
100 cm^2 = x^2 * h
100/x^2 = h
B. v(x) = x^2*h
2 1/3 - 4/7
what is the answer to this question
The solution for the algebraic expression 2 1/3 - 4/7 is 37/21
Given,
The algebraic expression ; 2 1/3 - 4/7
We have to solve this expression;
First lets solve the mixed fraction 2 1/3
2 1/3 = (2 x 3) + 1 / 3 = 6 + 1 / 3 = 7/3
Mixed fraction;
A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.
Now,
7/3 - 4/7 = (7 x 7) / (3 x 7) - (4 x 3) / (7 x 3) = 49/21 - 12/21
That is,
49/21 - 12/21 = (49 - 12) / 21 = 37/21
That is,
The solution for the algebraic expression 2 1/3 - 4/7 is 37/21
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A line has a slope of – 1 and includes the points (9,2) and (8,p). What is the value of p?
Answer:
p = 3
Step-by-step explanation:
y = mx + b They gave us the slope of -1. We need to find the y intercept. We will use the x of 9 and the y of 2 to find b. We will plug these numbers in to find b.
y = mx + b
2 = -1(9) + b
2 = -9 + b Add 9 to both sides
11 = b
y = -x +11
Now, plug in 8 for x
y = -1(8) + 11
y = -8 + 11
y = 3
In this case p is 3.
Math
Classify each algebraic expression below as polynomial or non-polynomial
In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.
How are polynomials and non-polynomials categorized?
There are two ways to categorize polynomials: by degree and by number of terms. According to degree, polynomials can be classified as zero, linear, quadratic, or cubic. Monomials, binomials, trinomials, etc. are the different types of polynomials based on the quantity of terms.
A polynomial is, in general, an expression containing more than one term and non-negative integral exponents of a variable. A polynomial expression might look like this: ax + by + ca, x3 + 2x + 3, etc.
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I just need the answer
At x=0
[tex]\begin{gathered} f(x)=14 \\ c=14 \end{gathered}[/tex]at x=1
[tex]\begin{gathered} f(x)=10.5 \\ a+b=10.5-14 \\ a+b=-3.5 \end{gathered}[/tex]at x=2
[tex]\begin{gathered} f(x)=8 \\ 4a+2b=8-14 \\ 4a+2b=-6 \end{gathered}[/tex]a=1/2
So correct option is (c).
What’s 4/6 - 1/3 simplified
Answer:
1/3
Step-by-step explanation:
(4/6) - (1/3)
The denominators need to be the same, so let's convert the second term to (2/6), which is the same as (1/3)
(1/3)*(2/2) = (2/6)
Now we can wite:
(4/6) - (2/6)
This is equal to 2/6 or 1/3
Hello!
The equation [tex]\frac{4}{6} - \frac{1}{3}[/tex] simplified is [tex]\frac{1}{3}[/tex].
Step-by-step explanation:
Begin by giving both equations common denominators in this case we will use 18.
For the first set of fractions we multiply 4 by 3 to get 12 and for the second set of fractions we multiply 1 by 6 to get 6.
Our new set of fractions will look like this [tex]\frac{12}{18}[/tex][tex]- \frac{6}{18}[/tex]
Now we can subtract the numerators since our denominators match.
[tex]12-6=6[/tex] so the new answer will be [tex]\frac{6}{18}[/tex]
It's time to simplify both sets of fractions before we can completely solve the equation. (divide by 2, then 3)
[tex]\frac{6}{18}[/tex] ÷ [tex]2=\frac{3}{9}[/tex] ÷ [tex]3=\frac{1}{3}[/tex]
Since 3 is larger than 1 we are done reducing, time to solve for the final answer.
[tex]\frac{4}{6} -\frac{1}{3} =\frac{1}{3}[/tex]
Hope this helps!
ships a and b leave port together. for the next two hours, ship a travels at 20 mph in a direction 30o west of north while the ship b travels 20o east of north at 25 mph. a) what is the distance between the two ships two hours after they depart? b) what is the speed of ship a as seen by ship b?
Two hours after depart, the distance between two ships is 39.2 miles and the relative speed of ship A seen by ship B is 19.6 mph heading to 18.4⁰ South of East.
The situation can be depicted on the attached picture.
Let North - South be the y-axis and East - West ne the x-axis.
The velocities vector can be represented as:
Ship A, 20 mph 30⁰ west of north:
vA = - 20 . cos( 60⁰) i + 20 . sin( 60⁰) j
vA = -10 i + 10√3 j
Ship B, 25 mph 20⁰ east of north:
vB = 25 . cos( 70⁰) i + 25 . sin( 70⁰) j
vB = 8.55 i + 23.5 j
b) The speed of ship A relative to ship B is:
vAB = vA - vB
= ( -10 i + 10√3 j) - (8.55 i + 23.5 j)
= -18.55 i - 6.18 j
or vAB = sqrt (18.55² + 6.18²) = 19.6 mph with the angle tan⁻¹ (6.18/18.55) = 18.4⁰ South of East.
a) The distance between 2 ships after 2 hours:
d = vAB . 2 hours
d = 19.6 . 2 = 39.2 miles
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three ratios that are equivelent to 11 : 1
Answer: 22:2, 33:3 and, 44:4
Step-by-step explanation:
Answer:
Step-by-step explanation:
22 : 2
33 : 3
44 : 4
the hypotenuse of a right triangle is growing at a constant rate of a centimeters per second and one leg is decreasing at a constant rate of b centimeters per second. how fast is the acute angle between the hypotenuse and the other leg changing at the instant when both legs are 1 cm?
The acute angle between the hypotenuse and the other leg changing at the instant when both legs are 1 cm is dθ/dt = -b - a/[tex]\sqrt{2}[/tex] fast.
Differentiation is a process to find the instantaneous rate of change in function based on one of its variables.
The hypotenuse of a right triangle is growing at a constant rate of a centimeters per second
[tex]\frac{dH}{dt} = a[/tex]
One leg is decreasing at a constant rate of b centimeters per second
[tex]\frac{dy}{dt} = -b[/tex]
From the right triangle
sin θ = [tex]\frac{y}{H}[/tex] (y is the perpendicular and H is the hypotenuse)
Differentiate both sides with respect to t
cos θ*dθ/dt = (H*dy/dt - y*dH/dt) / H²
cos θ*dθ/dt = [H(−b)−y(a)] / H²........................(1)
If the both legs are 1 cm.
∴ H= [tex]\sqrt{ 2[/tex],cosθ=sinθ=1/[tex]\sqrt{2}[/tex]
Thus , Equation (1)
cos θ*dθ/dt = [H(−b)−y(a)] / H²
1/√2*dθ/dt = [√2 (−b)−(a)] / 2
dθ/dt = √2 [(√2 (−b)−(a)) / 2]
Therefore, we can conclude that the acute angle between the hypotenuse and the other leg changing at the instant when both legs are 1 cm is dθ/dt = -b - a/[tex]\sqrt{2}[/tex] fast.
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Please helpppppp!!!!!!!!!!!!!!!!!!!!!!!!3|x_5|-|4y|/|x+y|when x=8 & y=4
Answer:
29/49
Step-by-step explanation:
x:y = 3:4
let x = 3x , y = 5k
3x+4y/8x+5y
= 3(3k)+4(5k)/8(3k)+5(5k)
= 9k+20k/24k+25k
=29/49
Please help me i dont the answer
[tex] \huge\underline\mathcal{Answer \: -} [/tex]
We know that ,
exterior angle equals sum of two interior opposite angles.
therefore ,
[tex]\bold{x + x + 14 = 136\degree} \\ \\ \longrightarrow \: 2x + 14 = 136\degree \\ \\ \longrightarrow \: 2x = 136\degree - 14 \\ \\ \longrightarrow \: 2x = 122\degree \\ \\ \longrightarrow \: x = \cancel\frac{122}{2} \\ \\ \longrightarrow\boxed{ \: x = 61\degree}[/tex]
hence , the first option is correct.
hope helpful ! ;-;
Answer:
First find the last angle of the triangle.
180 - 136 = 44° (sum of angles on a straight line=180)
Form an equation with the unknown angles with the knowledge that sum of angles in a triangle add up to 180°.
x + (x + 14) + 44 = 180
Simplify and solve for x.
2x + 58 = 180
2x = 122
x = 61
Determine whether each order pair is a solution of the equation
Answer:
Given equation is, x+3y=6
To determine whether each order pair is a solution of the equation
(3,1)
we have that, when x=3 we get y=1
Let us check this in the equation.
Put x=3, we get
[tex]3+3y=6[/tex][tex]\begin{gathered} 3y=6-3 \\ 3y=3 \end{gathered}[/tex][tex]y=1[/tex]Hence (3,1) is the solution of the equation.
(6,0)
Put x=6, we get,
[tex]6+3y=6[/tex][tex]y=0[/tex]
Hence (6,0) is the solution of the equation.
(-2,2/3)
Put x=-2, we get,
[tex]-2+3y=6[/tex][tex]3y=6+2[/tex][tex]y=\frac{8}{3}[/tex]Hence (-2,2/3) is not the solution of the equation.
Question 2
help pls its hard i forgt how to do it
Answer: 52
Step-by-step explanation:
a^2+b^2=c^2
x is the hypotenuse (c). You can find the hypotenuse by finding the opposite of the right angle
48^2+20^2=2304+400=2704
√2704=52
x=52
A blueprint for a rectangular warehouse has a length of 18 inches and a width of 10 inches. It uses a scale of 1 inch for every 20 feet. 1. What is the actual area of the warehouse in square feet? 2. How do you know?
Answer:
The actual area of the warehouse would be:
[tex]72000~\text{feet}^{2}[/tex]
Step-by-step explanation:
Step 1: Convert all the blueprint lengths into real lengths:
Each inch in the blueprint represents 20 feet in the real world.
So, the real-life length (18 inches in blueprint) would be:
[tex]1~\text{inch}= 20~\text{feet}\\\\\text{Multiply by 18 on both sides}:\\1\times18~\text{inch}= 20\times18~\text{feet}\\18~\text{inch}= 360~\text{feet}\\[/tex]
Similarly, the real-life width would be:
[tex]1~\text{inch}= 20~\text{feet}\\\\\text{Multiply by 18 on both sides}:\\1\times10~\text{inch}= 20\times10~\text{feet}\\10~\text{inch}= 200~\text{feet}\\[/tex]
Step 2: Calculate the area
The area of the warehouse would be given by:
[tex]\text{Area}=\text{Length}\times \text{Width}[/tex]
The length is 360 feet, and the width is 200 feet, so the total area would be:
[tex]\text{Area}=\text{Length}\times \text{Width}\\\\\text{Substitute the values for the length and width}\\\text{Area}= 360\times 200\\\text{Area}=72000[/tex]
The radius of the base of a cylinder is 10 centimeters, and its height is 20 centimeters. A cone is used to fill the cylinder with water. The radius of the cone's base is 5 centimeters, and its height is 10 centimeters
The number of times one needs to use completely filled cone to completely fill the cylinder with water is...
The number of times one needs to use completely filled cone to completely fill the cylinder with water is 24
What is volume of cone and cylinder?The volume of cylinder is equal to the product of the area of the circular base and the height of the cylinder.
Given that radius of the base of a cylinder is 10 centimeters, and its height is 20 centimeters.
The radius of the cone's base is 5 centimeters, and its height is 10 centimeters.
The volume of cylinder is πr²h
For a volume of cone it is 1⁄3πr²h.
So volume of cylinder = 22/7×(10)2×20=3.142×100×20
=6284
volume of cone it is 1⁄3πr²h=1/3×3.142×(5)^2×10=261.16
Number of times one needs to use the completely filled cone to completely fill the cylinder with water =
= Volume of cylinder/Volume of cone
6284 / 261.16 = 24
Hence the number of times one needs to use completely filled cone to completely fill the cylinder with water is 24
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the probability of observing a window given there is no window at its location is 0.2, and the probability of observing a window given there is a window is 0.9. after incorporating the observation of a window, what are the robot's new probabilities for being in
Updated Probabilities are: P(L1/W) = 0.341 & P(L1/w) = 0.949
Let W be the event that the robot's camera observes a window
It is given that the Probability of observing a window there is no window at its location is given 0.2
P(W/ L1) = 0.2 ( L1 which does not have a window)
Also, probability of observing a window is 0.9
P(W/ L2) = 0.9 ( L2 has window)
Now we have to find updated probabilities for the robot being in L1 i.e:- P(L1/W) & P(L1/w)
w means the camera does not observe a window.
By Bayes Rule,
P(L1/W) = P(L1)P(W/L1)/P(L1)P(W/L1)+P(L2)P(W/L2)
= (0.7x 0.2)/ (0.7x0.2) + (0.3x0.9)
= (0.14)/ 0.14+0.27
≈0.341 (rounded to 3. decimal places)
Thus the probability of being in L1 if the camera observes a window is nearly 0.341.
P(L1/w) = P(L1)P(w/L1)/P(L1)P(w/L1)+P(L2)P(w/L2)
As P(W/L1) = 0.2;
P(w/L1) = 1 - P(w/L1) = 1-0.2 = 0.8
Also P(W/L2) = 0.1;
P(w/L2) = 1 - P(w/L2) = 1-0.9 = 0.1
P(L1/w) = (0.7 X 0.8)/ (0.7X0.8) + (0.3X0.1)
=(0.56)/ (0.56+0.03) = (0.56/ 0.59)
≈ 0.949 (rounded to 3 decimal places).
Thus the probability of being in L1 if observe not the window is nearly 0.949.
Updated Probabilities are: P(L1/W) = 0.341 & P(L1/w) = 0.949
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