Solve the problem. Integrate f(x y) In(x2 + v2 x2 + y2 over the region 1 < x2 + y2 s 100. Seleccione una: O A. TI(In 10)2 O B.21(In 10) O C. T In 10 O D. 2rt In 10
Answers
We can use polar coordinates to perform this integration:
x = r*cos(θ)
y = r*sin(θ)
x^2 + y^2 = r^2
First, we integrate with respect to r:
∫[r^2 * ln(r^2) / 2 - r^2 / 4] from 1 to 10
Now, we evaluate the integral:
[(10^2 * ln(10^2) / 2 - 10^2 / 4) - (1^2 * ln(1^2) / 2 - 1^2 / 4)] = 50 * ln(100) - 25
Now, we integrate with respect to θ:
∫(50 * ln(100) - 25) dθ from 0 to 2π
Since this is a constant, the integral becomes:
(50 * ln(100) - 25) * (2π - 0) = 100π * ln(10) - 50π
Thus, the final answer is: 100π * ln(10) - 50π.
To solve this problem, we need to integrate f(x,y) = In(x2 + v2 / x2 + y2) over the given region, which is the set of all points (x,y) such that 1 < x2 + y2 < 100.
We can rewrite the integrand as In[(x2 + v2) / (x2 + y2)] = In(x2 + v2) - In(x2 + y2).
Using polar coordinates, we have x2 + y2 = r2 and the region is described by 1 < r < 10. Thus, the integral becomes:
∫∫(1 < r < 10) [In(x2 + v2) - In(x2 + y2)] r dr dθ
Integrating with respect to θ gives a factor of 2π, so we have:
2π ∫(1 < r < 10) [In(x2 + v2) - In(x2 + y2)] r dr
= 2π [∫(1 < r < 10) In(x2 + v2) r dr - ∫(1 < r < 10) In(x2 + y2) r dr]
To evaluate these integrals, we can use the substitution u = x2 + v2 (for the first integral) and u = x2 + y2 (for the second integral). Then, we have:
∫(1 < r < 10) In(x2 + v2) r dr = ∫(1 < u < 100+v2) In(u) du / 2v
∫(1 < r < 10) In(x2 + y2) r dr = ∫(1 < u < 100) In(u) du / 2
Plugging these into our expression for the integral and simplifying, we get:
2π [(In(100+v2) - In(2v)) / 2v - In(10) / 2]
= π In[(100+v2) / (40v2)]
Therefore, the answer is D. 2rt In 10.
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Related Questions
Write a quadratic function / whose only zero is -11.
Check
=
Answers
The quadratic value equation with zeroes at -11 is f(x) = a(x + 11)²
Given data ,
A quadratic function that has -11 as its only zero can be written in the form:
f(x) = a(x - r)²
where "a" is a non-zero constant and "r" is the zero of the function, in this case, -11.
On simplifying the equation , we get
f(x) = a(x - (-11))²
f(x) = a(x + 11)²
Hence , any quadratic function of the form f(x) = a(x + 11)^2, where "a" is a non-zero constant, will have -11 as its only zero
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9. Derrick Zoolander is working in the mines for $8.00 per hour, but he get overtime for every hour over 40 hours.
The overtime is time and a half, so he gets paid $12.00 per hour for overtime. Fill in the table and graph the
values. Then create a piecewise function that tracks the hours he works(x-values) to the money makes(y-values).
X(hours) Y(money)
Answers
What is the area of the orange box?
Answers
Answer:
\(2x^2+x\)
Step-by-step explanation:
The orange box shown is a rectangle; the area formula for rectangles is \(l*w\). Where \(l\) is the length and \(w\) is the width. So, multiply the binomial to solve. Do this by multiplying \(x\) by both 2x and 1. This equals \(2x^2\) and \(x\). Add the terms together for the final answer, \(2x^2+x\).
Which line is the graph of y = 1/2 x + 2?
line a
line c
line d
line b
Answers
Answer:
the answer is line A
Step-by-step explanation:
:3 why do i have to write at least 20 characters :/
but Hope its correct
Answer:
Line A
Step-by-step explanation:
By graphing the equation y = 1/2x + 2 you will see that the line intersects at 2. Hence + 2, while all of the other given lines do not intersect at 2.
To further prove the answer, you could also see that line A intersects at -4 when you graph the equation y = 1/2x + 2 you can also see that the line intersects at -4 on the x axis and 2 on the y axis.
Your answer is the first option or "line A."
Hope this helps.
ratio x : y is 3: 1
Which of the following statements is correct?
A x 3/4 of y
B y is 1/3 of x
C x is 1/3 of y
D y is 1/4 of x
Answers
Answer:
D
Step-by-step explanation:
1+3=4
1 out of 4 =1/4
remember x is bigger than y
Three softball players discussed their batting averages after a game.
Probability
Player 1 three sevenths
Player 2 four eighths
Player 3 four sixths
By comparing the probabilities and interpreting the likelihood, which statement is true?
Player 1 is more likely to hit the ball than Player 2 because P(Player 1) > P(Player 2).
Player 2 is more likely to hit the ball than Player 3 because P(Player 2) > P(Player 3).
Player 1 is more likely to hit the ball than Player 3 because P(Player 1) > P(Player 3).
Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2).
Answers
Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2).
What is Probability ?
Probability is a measure of the likelihood or chance that a particular event or outcome will occur. It is usually expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
Based on the given probabilities, we can compare the likelihood of each player hitting the ball:
Player 1 has a probability of hitting the ball of three sevenths, which can be written as P(Player 1) = 3÷7.
Player 2 has a probability of hitting the ball of four eighths, which can be written as P(Player 2) = 4÷8, which simplifies to 1÷2.
Player 3 has a probability of hitting the ball of four sixths, which can be written as P(Player 3) = 4÷6, which simplifies to 2÷3.
Comparing the probabilities, we can see that Player 3 has the highest probability of hitting the ball (2÷3), followed by Player 1 (3÷7), and then Player 2 (1÷2). Therefore, the correct statement is:
Therefore, Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2).
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−1 4/5−(−2 7/8)
4 3/4−(−1 1/12)
−1 4/5−(−2 7/8)
3 1/3-5
−1/3−(−1/2
Answers
Answer:
1) 43/40
2) 35/6
3) 43/40
4) -5/3
5) 1/6
Step-by-step explanation:
1) -1 4/5 = -(1*5 +4)/ 5= -9/5
or 1= 5/5 so -1 4/5= -( 5/5+ 4/5)=-9/5
-2 7/8= -(2*8+7)/8=-23/8
=> -9/5 - ( -23/8)= -9/5 + 23/8 = (( -9*8)+(23*5))/40= (-72+ 115)/40
= 43/40
2) 4 3/4= (4*4+3)/4= 19/4
-1 1/12= -(1*12+1)/12= -13/12
=> 19/4 - (-13/12)= 19/4 + 13/12 = ((19*3)+13)/12= (57+13)/12= 35/6
3) same like 1)
4) 3 1/3 = (3*3+1)/3= 10/3
=> 10/3 -5= (10- 3*5)/3= (10-15)/3= -5/3
5) -1/3 + 1/2= ((-1*2)+(1*3))/6 = (-2+3)/6= 1/6
Which expression represents a positive number? A. 1/5 divided by -4/7 B.-1/5 divided by 4/7 C. -1/5 divided by -4/7 D. 1/5 divided by 4/-7
Answers
Answer:
c
Step-by-step explanation:
remember,
a positive number multiplied or divided by a negative number = negative
a negative number multiplied or divided by a positive number = negative
a positive number multiplied or divided by a positive number = positve
a negative number multiplied or divided by a negative number = positive
so, if you have two numbers of the same sign being multiplied or divided, the answer will always be positive. if you have two numbers of different signs, the answer will always be negative.
within the answer choices, c is the only option where both numbers are negative, which means that if those two negative numbers are divided, you will get a positive answer.
Answer:
C and d!
Step-by-step explanation:
hope that helps!
Solve for x.
5(22−x)=40
Answers
Answer:
x = 14
Step-by-step explanation:
5(22 - x) = 40
Distribute the 5 into the parenthesis.
110 - 5x = 40
Subtract 110 from both sides.
-5x = -70
Divide both sides by -5.
x = 14.
Proof:
5(22 - x) = 40
Substitute variable.
5(22 - 14) = 40
Subtract inside parenthesis.
5(8) = 40
Multiply 5 and 8.
40 = 40.
What is the equation of the line that passes through the points( (-6,-5) and(-5, 5)?
Answers
Answer:
y=10x+55
Step-by-step explanation:
First, you need to find the slope.
y2-y1/x2-x1
-5-5/-6+5=-10/-1=10
Now, we substitute one of the points for the values in y=mx+b
y=10x+b
5=10(-5)+b
5=-50+b
55=b
The full equation is y=10x+55
When graphing an inequality, what is drawn to show that the number named
in the inequality is included in the solution?
Answers
Answer:
The line would be a solid line.
Step-by-step explanation:
To draw inequality graphs, solid lines represent \(\geq or \leq\) and dotted lines show > or <. Hope this helps.
! HELPPP ITS RLLY DUD IN 1 HOURRR HELP MEE PLEASESESS !!! A S A PPP!!!!!!
Answers
Answer:
combining 2x and 4x to make 6x
Step-by-step explanation:
Is 9.3 a rational number
Answers
Answer:
yes because you could write that as a fraction 9 3/10
-3c = 36
what does C =
Answers
Answer:
c= -12
Step-by-step explanation:
36 divided by -3 is -12
Evaluate the series 4 + 8 + 16 to S6.
Answers
WASTE Suppose the waste generated by nonrecycled paper and cardboard products in tons y after x days can be approximated by the function y=1000(2)0.3x.
a. Identify key features.
y-intercept: , 1 of 8.
domain: , 2 of 8.
range: , 3 of 8.
b. Identify the relevant domain and range.
Because time , 4 of 8. , the relevant domain is , 5 of 8. .
Because the amount of recycled paper and cardboard , 6 of 8. , and the amount when x=0
is , 7 of 8.tons, the relevant range is , 8 of 8. .
Answers
a. The key features of the exponential function y = 1000(2)^(0.3x) is given as follows:
y-intercept: y = 100.Domain: all real values.Range: y ≥ 1000.b. The relevant domain and range are given as follows:
Domain: x ≥ 0.Range: y ≥ 1000.What are the features of the exponential function?The exponential function for this problem is modeled as follows:
y = 1000(2)^(0.3x).
The features are given as follows:
Initial value, when x = 0, of y = 1000, representing the y-intercept.Rate of change of 2 for each period of 0.3 units.The domain of the function is the set that composes all input values of the function, and as the exponential function does not have any restrictions such as a fraction or an even root, it is composed by all real values.
However, the relevant domain is x ≥ 0, as the number of days does not assume negative values.
The range is the set containing all output values of the exponential function. As the initial value of the exponential function is of 1000 and the function is increasing, the range is y ≥ 1000.
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Triangle R T S is sitting on a horizontal line. Line S R extends through point Q to form exterior angle T R Q. Angle R T S is (25 x) degrees. Angle T S R is (57 + x) degrees. Exterior angle T R Q is (45 x) degrees.
Answers
Answer:
x = 3
Question: Find the value of x.
Step-by-step explanation:
Given:
- Triangle R T S is sitting on a horizontal line
- Line S R extends through point Q to form exterior angle T R Q
- m∠RTS is (25 x)°, m∠TSR is (57 + x)° , m∠TRQ is (45 x)°
Lets find the value of x
∠TRQ is an exterior angle of Δ RTS at the vertex R
The opposite interior angles to vertex R are ∠RTS and ∠TSR
∴ m∠TRQ = m∠RTS + m∠TSR
m∠TRQ = (45 x)°
m∠RTS = (25 x)°
m∠TSR = (57 + x)°
Substitute these measures in the equation above
45 x = 25 x + 57 + x
45 x = 26 x + 57
19 x = 57
x = 3
A population of values has a normal distribution with u = 211. 3 and 0 = 60. 3. You intend to draw a random sample of size n = 66. Please show your answers as numbers accurate to 4 decimal places. Find the probability that a single randomly selected value is less than 212. 8. P(X < 212. 8) = Find the probability that a sample of size n = 66 is randomly selected with a mean less than 212. 8. Plū < 212. 8)
Answers
The probability for the given sample of size n and randomly selected with a mean less than 212.8 is equal to 0.5871.
For the normal distribution,
u = 211. 3 and 0 = 60. 3
Sample size 'n' = 66
The probability that a single randomly selected value is less than 212.8 can be found by calculating the z-score corresponding to this value.
Using a standard normal distribution table or calculator to find the area under the standard normal distribution curve to the left of the z-score.
z = (212.8 - 211.3) / (60.3 / √(66))
≈ 0.2021
Using a standard normal distribution table or calculator,
find that the area to the left of a z-score of 0.2021 is approximately 0.5871.
The probability that a single randomly selected value is less than 212.8 is approximately 0.5871.
To find the probability that a sample of size n = 66 is randomly selected with a mean less than 212.8,
Use the central limit theorem,
which states that distribution of sample means from a population with any distribution approaches a normal distribution as sample size increases.
Mean of the sample means is equal to the population mean.
And standard deviation of sample means is equal to the population standard deviation divided by the square root of the sample size.
Thus, the sample mean can be standardized using the formula,
z = (X - μ) / (σ / √(n))
where X is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Substituting the given values, we have,
z = (212.8 - 211.3) / (60.3 / √(66))
≈ 0.2021
Using a standard normal distribution table or calculator,
find that the area to the left of a z-score of 0.5871 .
Therefore, the probability that a sample of size n = 66 is randomly selected with a mean less than 212.8 is approximately 0.5871.
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An ancient warship once covered 168 sea miles in 24 hours. Explain why at some point during this feat the ship's speed exceeded 6.6 knots (sea miles per hour). Use the Mean Value Theorem.
Suppose y = f(x) is continuous on a closed interval [a, b] and differentiable on the interval's interior (a, b). Then there is at least one point c in (a, b) at which the following is true.
f(b) - f(a) b-a
-=f'(c)
If f(t) is the function that represents the distance traveled after t hours, what is the closed interval for this application? Assume that the ship started at time t=0.
(Type your answer in interval notation.)
Answers
The closed interval for this application is [0, 24].
In this scenario, let's consider the function f(t) to represent the distance traveled by the ancient warship after t hours. We are given that the ship covered 168 sea miles in 24 hours, so we have f(24) - f(0) = 168.
We want to show that at some point during this feat, the ship's speed exceeded 6.6 knots (sea miles per hour), which means we need to prove that there exists a point c in the interval (0, 24) where the instantaneous rate of change of distance, f'(c), exceeds 6.6.
Using the Mean Value Theorem, we have:
f'(c) = (f(24) - f(0)) / (24 - 0)
Since f(24) - f(0) = 168, we can simplify the equation:
f'(c) = 168 / 24
= 7
Therefore, according to the Mean Value Theorem, there exists a point c in the interval (0, 24) where the instantaneous rate of change of distance, or the ship's speed, f'(c), equals 7 knots. Since 7 knots is greater than 6.6 knots, we can conclude that at some point during the 24-hour feat, the ship's speed exceeded 6.6 knots. Therefore, the closed interval for this application is [0, 24].
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Write down the factors of 28 Then,write down the prme factors of 28
Answers
the factors of 28 are : 1, 2, 4, 7, 14, and 28.
the prime factors of 28 are : 2, 2, and 7.
Gus has a fish tank that holds 4710 inches^3 cubed of water. He is using a cylinder shaped bucket with a radius of 5 inches and a height of 20 inches to fill the tank.
Answers
The number of times Gus needs to fill the bucket will be 3.
What is an expression?Expression in maths is defined as the collection of the 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.
Number of times = volume of tank /volume of cylinder
The volume of the cylinder = πr²h
3.14 x 5² x 20 = 1570
4710 / 1570 = 3 times
Therefore, the number of times Gus needs to fill the bucket will be 3
The complete question is given below:-
How many times will Gus need to fill the bucket to completely fill the fish tank if he doesn’t spill a drop? Use 3.14 for pi
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Answer: 3
Step-by-step explanation:
1. This problem calls for the formula for the volume of a cylinder which is
V=π\(r^{2}\)h
2. First let's find the volume of one bucket. The bucket has a radius of 5 inches and a height of 20 inches.
V= 3.14 x \(5^{2}\) x 20
= 3.14 x 25 x 20
= 1570
3. To find out how many buckets it will take to fill the tank, we can divide the total volume of the fish tank by the volume of each full bucket.
\(\frac{4710}{1570}=3\)
4. Gus will need to fill the bucket 3 times in order to completely fill the fish tank.
A group went on a hiking trip through the Grand Canyon. The first stop on the trail is 12 miles. At this point the hike is 60% finished. How many miles is the whole hike
Answers
To find the total distance of the hike, we can set up a proportion:
\(\[\frac{{\text{{Distance to first stop}}}}{{\text{{Total distance of the hike}}}} = \frac{{60}}{{100}}\]\)
Let's represent the total distance of the hike as "x" miles. The distance to the first stop is given as 12 miles:
\(\[\frac{{12}}{{x}} = \frac{{60}}{{100}}\]\)
To solve for "x," we can cross-multiply and solve for "x":
\(\[12 \times 100 = 60 \times x\]\)
\(\[1200 = 60x\]\)
Dividing both sides of the equation by 60, we get:
\(\[x = \frac{{1200}}{{60}} = 20\]\)
Therefore, the whole hike is 20 miles.
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College Algebra Applied Problem Four A medical professional is helping an individual balance their diet. The individual has asked for some certain foods to remain in their diet. They will always get 600 calories from carbohydrates. The individual says that they can be flexible about how many calories they consume in fats and proteins. The goal of the diet is to keep the individual at 1,800 calories per day ( 600 of which come from carbohydrates). Part One Write an equation that models the amount of calories from fats " f ' and protein "p" that the individual can consume in order to reach 1,800 calories. Part Two The diet being prescribed to the individual calls for calories from protein to be three times the calories from fat. Write an equation based on this information that relates calories from protein "p" to calories from fat " f ". Part Three Use your equations from parts "b" and "c" to solve this system of equations and determine the amount of calories that the individual should consume from fats and proteins. Part Four If the individual no longer required 600 calories from carbohydrates, and instead said that they would be flexible about how many carbohydrates they would consume, how many variables would there be for this problem on calories?
Answers
The system equation that models the amount of calories from fats (f) and proteins (p) that the individual can consume to reach 1,800 calories is: f + p = 1,200. The equation that relates calories from protein (p) to calories from fat (f) based on the prescribed diet is: p = 3f. Solving the system of equations, we find that the individual should consume 300 calories from fats and 900 calories from proteins.
To find the equation that models the amount of calories from fats and proteins that the individual can consume in order to reach 1,800 calories, we consider that 600 calories will come from carbohydrates. Since the total goal is 1,800 calories, the remaining calories from fats and proteins should add up to 1,800 - 600 = 1,200 calories. Therefore, the equation is f + p = 1,200.
Based on the prescribed diet, the individual is required to consume calories from protein that are three times the calories from fat. This relationship can be expressed as p = 3f, where p represents the calories from protein and f represents the calories from fat.
To solve the system of equations, we substitute the value of p from the second equation into the first equation: f + 3f = 1,200. Combining like terms, we get 4f = 1,200, and dividing both sides by 4 yields f = 300. Substituting this value back into the second equation, we find p = 3(300) = 900.
Therefore, the individual should consume 300 calories from fats and 900 calories from proteins to meet the diet requirements and achieve a total of 1,800 calories.
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Find QR
a. -8
b. 12
c. 6
d. 9
Answers
three less than a number what is the value of the expression if the number is equal to -1?
Answers
Answer:
n-3
(-1)-3=-4
hope this helps
have a good day :)
Step-by-step explanation:
Line a: y=2x+4
Line b: y=2x-3
Slope of line a is _______ and slope of line b is __________. Therefore, the two lines are __________.
Answers
Answer:
Step-by-step explanation:
2x4 = 8
2x3=6
the image of p(m,5-n) when reflected on line y=0 is p'(2m-3,2n-8) find the values of m and n
Answers
The value of m and n that shows that point p(m,5-n) when reflected on line y=0 is m = 3, n = 3.
What is a transformation?Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.
The rule for the reflection over the line y = 0 (x axis) is (x, y) ⇒ (x, -y)
If the point p(m,5-n) is reflected on line y=0, this would give (m, -(5 - n)) = p'(2m-3,2n-8). Hence:
2m - 3 = m
m = 3
Also:
-(5 - n) = 2n - 8
-5 + n = 2n - 8
n = 3
The value of m and n that shows that point p(m,5-n) when reflected on line y=0 is m = 3, n = 3.
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Find the value of the smaller angle. (Hint find the value of x first)
Answers
The sum of both angles must be 180°, therefore:
(2x+24) + (4x+36) = 180°
6x + 60 = 180°
6x = 120°
x = 120/6 = 20°
Then, the smaller angle is 2*20 + 24 = 64
Suppose you deposit $10,000 into an account earning 3.5% interest compounded quarterly. After n quarters the balance in the account is given by the formula:
10000 (1+0.035/4)^n
a) Each quarter can be viewed as a term of a sequence. List the first 5 terms.
b) Identify the type of sequence this is. Explain.
c) Find the balance in the account after 30 quarters.
2) An object with negligible air resistance is dropped from the top of the Willis Tower in Chicago at a height of 1451 feet. During the first second of fall, the object falls 16 feet; during the second second, it falls 48 feet; during the third second, it falls 80 feet; during the fourth second, it falls 112 feet. Assuming this pattern continues, how many feet does the object fall in the first 7 seconds after it is dropped?
Answers
The first five terms of the sequence representing the balance in the account after each quarter are calculated. The type of sequence is an exponential growth sequence.
a) To find the first five terms of the sequence, we can substitute the values of n from 1 to 5 into the formula. Using the given formula, the first five terms are calculated as follows:
Term 1: $10,000 * \((1 + 0.035/4)^1\) = $10,088.75
Term 2: $10,000 * \((1 + 0.035/4)^2\) = $10,179.64
Term 3: $10,000 *\((1 + 0.035/4)^3\) = $10,271.67
Term 4: $10,000 *\((1 + 0.035/4)^4\) = $10,364.86
Term 5: $10,000 * \((1 + 0.035/4)^5\) = $10,459.24
b) The sequence represents exponential growth because each term is calculated by multiplying the previous term by a fixed rate of growth, which is 1 + 0.035/4. This rate remains constant throughout the sequence, resulting in exponential growth.
c) To find the balance in the account after 30 quarters, we substitute n = 30 into the formula:
Balance after 30 quarters: $10,000 *\((1 + 0.035/4)^30\) = $13,852.15.
2) The pattern in the object's fall indicates that it falls a certain number of feet during each second. In the first second, it falls 16 feet; in the second second, it falls 48 feet; in the third second, it falls 80 feet, and so on. This pattern shows that the object falls an additional 32 feet during each subsequent second. To find the total distance the object falls in the first 7 seconds, we add up the distances for each second:
Total distance = 16 + 48 + 80 + 112 + 144 + 176 + 208 = 784 feet.
Therefore, the object falls 784 feet in the first 7 seconds after it is dropped.
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In Exercise 6, suppose that there is a probability of .01 that a digit is incorrectly sent over a communication channel (i.e., that a digit sent as a 1 is received as a 0, or a digit sent as a 0 is received as a 1). Consider a message that consists of exactly 60% 1s. a. What is the proportion of 1s received at the end of the channel
Answers
Answer:
The proportion of 1s received at the end of the channel is of 0.598.
Step-by-step explanation:
In this question:
60% of the bits sent are 1, 100 - 60 = 40% of the bits sent are 0.
For each bit receive, 0.01 probability of an error, so 0.99 probability it is correct.
a. What is the proportion of 1s received at the end of the channel?
99% of 60%(sent 1s, received 1).
1% of 40%(sent 0s, received 1). So
\(p = 0.99*0.6 + 0.01*0.4 = 0.598\)
The proportion of 1s received at the end of the channel is of 0.598.