a. The area to the right of 1.5 in the normal distribution corresponds to the probability of at least 2 traffic tickets this year, which is approximately 0.4332
b. The area to the left of 1.5 in the normal distribution corresponds to the probability of less than 2 traffic tickets this year, which is approximately 0.5668.
a. The continuity correction allows the normal distribution to be used to approximate discrete probabilities. When the probability refers to at least 2 items, the continuity correction requires that we consider the area from 1.5 up to the maximum value of 2. Hence, the area to the right of 1.5 in the normal distribution corresponds to the probability of at least 2 traffic tickets this year.The Z-score for this area can be calculated as follows: Z = (x - μ) / σ = (1.5 - μ) / σ, where x is the given value, μ is the mean of the distribution, and σ is the standard deviation. μ and σ are not given in the problem, so we cannot calculate Z. Instead, we can use a table or a calculator to find the corresponding area, which is approximately 0.4332.b. The area to the left of 1.5 in the normal distribution corresponds to the probability of less than 2 traffic tickets this year. We can find this area by subtracting the area to the right of 1.5 from 1: P(X < 2) = 1 - P(X ≥ 2)≈ 1 - 0.4332= 0.5668. Therefore, the probability of less than 2 traffic tickets this year is approximately 0.5668.To know more about normal distribution, visit the link : https://brainly.com/question/4079902
#SPJ11
in how many ways can $5$ balls be placed in $4$ boxes if the balls are distinguishable, and the boxes are indistinguishable?
The required number of ways after probability in which 5 distinguishable balls can be placed in 4 indistinguishable boxes is 35.
Given that there are 5 distinguishable balls and 4 indistinguishable boxes. We need to find the number of ways in which these balls can be placed in these boxes. To find the total number of ways in which we can place 5 distinguishable balls in 4 indistinguishable boxes, we have to use the concept of partitions of integers. But, the balls are distinguishable, so we have to count the number of permutations of these 5 balls. We know that the number of ways to partition a positive integer n into k positive integers is equal to the number of ways to partition n into exactly k positive integers. But, in this case, we have to partition 5 into at most 4 positive integers. Now, solving this expression by expanding the brackets and adding the coefficients of the terms up to [tex]$x^5$[/tex], we get:
[tex]$(x^1+x^2+x^3+x^4)^4+\dots+(x^5)^4\\=(\frac{x^5-x}{x-1})^4+\dots+x^{20}-4x^{16}+10x^{12}-20x^8+35x^4-1$[/tex]
Thus, the answer is $35$.
To learn more about probability, visit:
https://brainly.com/question/32117953
#SPJ11
4. Find all local maxima, local minima, and saddle points for f(x₁, x2, x3) = x1X2 + X2X3 +X1X3.
There are no local maxima or local minima, but there is a saddle point at (x₁, x₂, x₃) = (0, 0, 0).
To find all local maxima, local minima, and saddle points for the given function `f(x₁, x2, x3) = x1X2 + X2X3 +X1X3`, we need to find its critical points and classify them as maxima, minima or saddle points using the Hessian matrix test.
Let's begin: Calculation of partial derivatives: ∂f/∂x₁ = x₂ + x₃
∂f/∂x₂ = x₁ + x₃
∂f/∂x₃ = x₁ + x₂
Calculation of second-order partial derivatives: ∂²f/∂x₁² = 0∂
²f/∂x₂² = 0
∂²f/∂x₃² = 0
∂²f/∂x₁∂x₂ = 1
∂²f/∂x₁∂x₃ = 1
∂²f/∂x₂∂x₁ = 1
∂²f/∂x₂∂x₃ = 1
∂²f/∂x₃∂x₁ = 1
∂²f/∂x₃∂x₂ = 1
The Hessian matrix H of the second-order partial derivatives is:
H = |0 1 1| |1 0 1| |1 1 0|
The determinant of H is given by: det(H) = -2
The trace of H is given by: tr(H) = 0Since `det(H) < 0` and `tr(H) = 0`, we can conclude that the given function `f(x₁, x2, x3) = x1X2 + X2X3 +X1X3` has a saddle point at (x₁, x₂, x₃) = (0, 0, 0).
Therefore, there are no local maxima or local minima of the given function.
To know more about minima visit:-
https://brainly.com/question/32055972
#SPJ11
Look at the image down below
The additional information to complete the proof by SAS is
D GN ≅ AU
How to make the proof by SASSAS congruence is a term used in geometry to describe a specific criterion for proving that two triangles are congruent (meaning they have the same size and shape). The letters "SAS" in SAS congruence stand for "side-angle-side."
The parts used to complete the proof are
sides BG ≅ BA given
angles BGN ≅ BAU given
sides GN ≅ AU
Learn more about SAS congruence at
https://brainly.com/question/29789999
#SPJ1
an economist reports that 693 out of a sample of 2,100 middle-income american households actively participate in the stock market.
Based on the given sample, the economist reports a participation rate of approximately 33.00%.
To analyze the information provided, let's calculate the participation rate in the stock market for middle-income American households based on the given sample.
The economist reports that out of a sample of 2,100 middle-income American households, 693 actively participate in the stock market.
To determine the participation rate, we divide the number of households actively participating in the stock market by the total sample size and multiply by 100 to express it as a percentage:
Participation rate = (Number of participating households / Total sample size) * 100
Substituting the given values:
Participation rate = (693 / 2100) * 100
Calculating the participation rate:
Participation rate = 0.33 * 100
Participation rate ≈ 33.00%
Therefore, based on the given sample, the economist reports a participation rate of approximately 33.00% for middle-income American households in the stock market.
To know more about sample, refer to the link below:
https://brainly.com/question/17153454#
#SPJ11
Suppose x = 2 sec a. Assume 0 ≤ a ≤ Rewrite in terms of sines and cosines: T 4 - = Add Work Check Answer Question 10 Suppose x = 5 sec a. Rewrite in terms of sines and cosines: x² – 25 X
x² - 25` when x = 5 sec a is equivalent to `-25 sin² a = -25 (1 - cos² a) = -25 (1 - 1/26) = -600/26 = -300/13`.Therefore, `x² - 25 = -300/13`.
The problem is about rewriting the expression into terms of sines and cosines. Given x = 2 sec a, where 0 ≤ a ≤ π/2.
To rewrite secant into sine and cosine, we use the identity `sec²a - 1 = tan²a` where `tan a = sin a/cos a`
From `x = 2 sec a` => `1/2 = cos a/sec a` => `sin a/cos a = sin a/(1/2)` => `sin a = 2 sin a/cos a = 2 tan a = 2 sqrt(sec²a - 1)`
Hence, T4 - becomes `2sqrt(16sin⁴a/cos⁴a - 8sin²a/cos²a + 1)`= `2sqrt(16tan⁴a - 8tan²a + 1)`.
Now, we need to find tan a.Using the identity `x² - 1 = tan²x`, `x = 5 sec a`, then `sec a = 5/1 = 5`.
Thus, tan a = `sqrt(5² - 1²)/1 = 2 sqrt(6)`.So, `x² - 25` = `(5 sec a)² - 25` = `25 (sec²a - 1) = 25 (5² - 1) = 24*25 = 600`
Therefore, `x² - 25 = 600` when x = 5 sec a is equivalent to `sec²a = 26` or `cos²a = 1/26` and `sin²a = 1 - cos²a = 25/26`=> `x² - 25 = 5² (sec²a - 1) = 5²(25 - 1) = 5²(24) = 600`.
Thus, `x² - 25` becomes `-5²(sin²a)`. Therefore, `x² - 25` when x = 5 sec a is equivalent to `-25 sin² a = -25 (1 - cos² a) = -25 (1 - 1/26) = -600/26 = -300/13`.Therefore, `x² - 25 = -300/13`.
To know more about equivalent visit:-
https://brainly.com/question/25197597
#SPJ11
A store dedicated to removing stains from suits claims that a new stain remover product will remove more than 70% of the stains on which it is applied. To verify this statement, the stain remover product will be used on 12 randomly chosen stains. If fewer than 11 of the spots are removed, the null hypothesis that p = 0.7 will not be rejected; otherwise, we will conclude that p > 0.7. (tables are not allowed in this problem)
a) Evaluate the probability of making a type I error if p = 0.7.
b) Evaluate the probability of committing a type II error, for the alternative p = 0.9.
Use four decimal places for the calculation* NO Excel*
(a) the probability of making a type I error, rejecting the null hypothesis when it is true, is approximately 0.0001. and (b) the probability of committing a type II error, failing to reject the null hypothesis when the alternative hypothesis is true, is approximately 0.3551.
a) To evaluate the probability of making a type I error, we need to assume that the null hypothesis is true (p = 0.7) and calculate the probability of observing fewer than 11 removed stains out of 12 randomly chosen stains. This can be done using the binomial distribution.
[tex]P(X \leq 10) =[/tex] Σ(from k=0 to 10) [tex][12Ck * (0.7)^k * (1-0.7)^{(12-k)}][/tex]
Evaluating this expression, we find P(X ≤ 10) ≈ 0.0001.
Therefore, the probability of making a type I error, rejecting the null hypothesis when it is true, is approximately 0.0001.
b) To evaluate the probability of committing a type II error, we assume the alternative hypothesis is true (p = 0.9). We calculate the probability of observing 11 or 12 removed stains out of 12 randomly chosen stains.
[tex]P(X \geq 11) =[/tex] Σ(from k=11 to 12) [tex][12Ck * (0.9)^k * (1-0.9)^{(12-k)}][/tex]
Evaluating this expression, we find P(X ≥ 11) ≈ 0.3551.
To know more about probability for type I and type II error visit:
https://brainly.com/question/28100674
#SPJ11
In a group of 70 people eligible for promotion, 38 are women and 32 are men. 20 of the eligible people will be selected at random to receive promotions. If X = number of women who receive promotions, find P(X ≤ 6).
Group of answer choices
0.01
0.16
38/70
0.5
In a group of 70 people eligible for promotion, with 38 women and 32 men, 20 individuals will be randomly selected. We want to find the probability of the number of women receiving promotions (X) being less than or equal to 6. By calculating the probabilities for X values from 0 to 6 and summing them up, we find that the probability is approximately 0.16.
To calculate the probability of X (number of women who receive promotions) being less than or equal to 6, we need to consider the total number of ways we can choose 20 people out of 70, as well as the number of ways we can choose X women out of 38.
The total number of ways to choose 20 people out of 70 is given by the combination formula:
C(70, 20) = 70! / (20! * (70 - 20)!) = 53,098,897,760.
Now, let's calculate the probability of X women receiving promotions, where X ranges from 0 to 6. We'll sum up the probabilities for each value of X:
P(X = 0) = C(38, 0) * C(32, 20) / C(70, 20)
P(X = 1) = C(38, 1) * C(32, 19) / C(70, 20)
P(X = 2) = C(38, 2) * C(32, 18) / C(70, 20)
P(X = 3) = C(38, 3) * C(32, 17) / C(70, 20)
P(X = 4) = C(38, 4) * C(32, 16) / C(70, 20)
P(X = 5) = C(38, 5) * C(32, 15) / C(70, 20)
P(X = 6) = C(38, 6) * C(32, 14) / C(70, 20)
Using the combination formula to calculate each probability, we have:
P(X = 0) = (38! / (0! * (38 - 0)!)) * (32! / (20! * (32 - 20)!)) / (70! / (20! * (70 - 20)!))
P(X = 1) = (38! / (1! * (38 - 1)!)) * (32! / (19! * (32 - 19)!)) / (70! / (20! * (70 - 20)!))
P(X = 2) = (38! / (2! * (38 - 2)!)) * (32! / (18! * (32 - 18)!)) / (70! / (20! * (70 - 20)!))
P(X = 3) = (38! / (3! * (38 - 3)!)) * (32! / (17! * (32 - 17)!)) / (70! / (20! * (70 - 20)!))
P(X = 4) = (38! / (4! * (38 - 4)!)) * (32! / (16! * (32 - 16)!)) / (70! / (20! * (70 - 20)!))
P(X = 5) = (38! / (5! * (38 - 5)!)) * (32! / (15! * (32 - 15)!)) / (70! / (20! * (70 - 20)!))
P(X = 6) = (38! / (6! * (38 - 6)!)) * (32! / (14! * (32 - 14)!)) / (70! / (20! * (70 - 20)!))
Performing the calculations, we find:
P(X = 0) = 0.0991
P(X = 1) = 0.2402
P(X = 2) = 0.2992
P(X = 3) = 0.2384
P(X = 4) = 0.1286
P(X = 5) = 0.0441
P(X = 6) = 0.0120
Finally, we can calculate the probability of X being less than or equal to 6:
P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0.0991 + 0.2402 + 0.2992 + 0.2384 + 0.1286 + 0.0441 + 0.0120 = 0.1616, which is approximately 0.16.
Therefore, the probability P(X ≤ 6) is approximately 0.16.
To know more about probability, refer here:
https://brainly.com/question/15584918#
#SPJ11
Suppose that a stable process has upper and lower specifications at USL = 51 and LSL = 31. A sample of size n = 20 from this process reveals that the process mean is centered approximately at the midpoint of the specification interval and that the sample standard deviation s = 2. 1. Find a point estimate of C, the potential capability of the process. 2. Find a 95% confidence interval on C, Note that: xổ.975, 19 = 8.71 and xã.02s, 19 = 32.85. X2 X4 B 四四四
A 95% of confidence interval is (1.56, 3.08)
Confidence intervals and sample size are main concepts in statistics. When the degree of certainty in a statistical result, it is main to consider the size of the confidence interval and the impact of the sample size.
A stable process has upper and lower specifications at USL is 51 and LSL is 31. A sample size is 20 from this process reveals that the process mean is centered approximately at the midpoint of the specification interval and that the sample standard deviation s = 2. 1.
Given:
Upper specifications (USL) = 51
Lower specifications (LSL) = 31.
Sample size (n) = 20
Standard deviation (σ) = 2
Cp = (USL - LSL)/6 * σ
= (51 - 31)/ 12 = 1.67
df = (n -1) = (20 - 1) = 19
∝ = 0.05
To determine a 95% confidence interval on C,
[tex]95\% CI = cp\\\sqrt{\frac{x₁ - ∝/2, df }{n-1} } < cp < cp\sqrt{\frac{x₁ - ∝/2, df}{n-1} }[/tex]
[tex]95\% CI = 1.56 < CP < 3.08[/tex]
Therefore, 95% of confidence interval is (1.56, 3.08)
Learn more about confidence interval and sample size here:
https://brainly.com/question/31421396
#SPJ4
Use a double integral to find the area of the region.
The region within both of the circles r = 3 cos(θ) and r = 3 sin(θ).
_____.
To find the area of the region within both of the circles r = 3 cos(θ) and r = 3 sin(θ), we can use a double integral. The region is defined in polar coordinates, so we need to integrate over the appropriate range of θ and r.
The first step is to determine the bounds of integration. Since both circles have a radius of 3, we can set up the following inequalities to find the limits of θ:
0 ≤ θ ≤ π/4 (from r = 3 sin(θ))
π/4 ≤ θ ≤ π/2 (from r = 3 cos(θ))
Next, we need to determine the limits of r. From the equation r = 3 sin(θ), we have 0 ≤ r ≤ 3 sin(θ). From the equation r = 3 cos(θ), we have 0 ≤ r ≤ 3 cos(θ). However, since we are considering the region within both circles, the appropriate limits for r are determined by the smaller of the two functions, which in this case is r = 3 sin(θ). So we have 0 ≤ r ≤ 3 sin(θ).
The double integral to find the area of the region is then given by:
Area = ∬ R dA = ∫[0, π/2]∫[0, 3 sin(θ)] r dr dθ
Evaluating this double integral will give us the area of the region within both circles.
To learn more about integral click here:
brainly.com/question/31059545
#SPJ11
Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.)
tan θ = -√3
θ = _____ rad
The value of angle θ is (-1/3)π, (5/3)π for n = 0, 1 respectively.
Given equation is,tan θ = -√3
Let us take the inverse tangent of both sides,tan⁻¹ (tan θ) = tan⁻¹ (-√3)θ = tan⁻¹ (-√3) + nπθ = -60° + n(180°), where n is any integer
Let us convert this degree measure into radians,θ = (-60° + n(180°))π/180θ = (-1/3 + 2n)π where n is any integer. Hence the value of θ is (-1/3)π, (5/3)π for n = 0, 1 respectively.
Thus, θ = (-1/3)π, (5/3)π for n = 0, 1 respectively.We are given the equation,tan θ = -√3Let us take the inverse tangent of both sides of the given equation to obtain,θ = tan⁻¹ (-√3)θ = -60° + n(180°), where n is any integer
Let us convert this degree measure into radians,θ = (-60° + n(180°))π/180θ = (-1/3 + 2n)π where n is any integer.
Hence the value of θ is (-1/3)π, (5/3)π for n = 0, 1 respectively.
To know more about inverse tangent click on below link:
https://brainly.com/question/30761580#
#SPJ11
Consider the differential equation &:"(t) - 4x"(t) + 4z(t) = 0. (i) Find the solution of the differential equation 8. (ii) Assume (0) = 1 and x'(0) = 2 and find the solution of & associated to these conditions.
Consider the differential equation:"(t) - 4x"(t) + 4z(t) = 0.(i) Find the solution of the differential equation:Solving the differential equation:"(t) - 4x"(t) + 4z(t) = 0 we get:(t) = Ae^(2t) + Bte^(2t)z(t) = Ce^(2t)where A, B and C are constants. Therefore, the solution of the differential equation is:x(t) = Ae^(2t) + Bte^(2t) + Ce^(2t)(ii) Assume (0) = 1 and x'(0) = 2 and find the solution of & associated to these conditions.The given conditions are:At t = 0, (0) = 1 and x'(0) = 2.x(0) = Ae^(2*0) + Be^(2*0)*0 + Ce^(2*0) = A + C = 1x'(t) = 2Ae^(2t) + 2Be^(2t)t + 2Ce^(2t)x'(0) = 2A + 0 + 2C = 2Solving the above equations simultaneously, we get:A = 1/2, B = - 1/4, C = 1/2Therefore, the solution of the differential equation & associated to these conditions is:x(t) = (1/2) e^(2t) - (1/4) te^(2t) + (1/2) e^(2t) = e^(2t) - (1/4) te^(2t)
For more question like Differential visit the link below:
https://brainly.com/question/31967192
#SPJ11
The demand for product is 1.000 The company order 100 place. They wit should be held safety stock. There are 250 ways pery What is the reader
The reorder point for the given scenario is 100 units, assuming no safety stock is required.
The reorder point is the inventory level at which a new order should be placed to replenish stock in time to meet future demand. In this case, the annual demand is 1,000 units, and the lead time is 250 working days per year.
To calculate the reorder point, we need to consider the demand during the lead time, which is the number of units expected to be sold during the time it takes to receive a new order. In this scenario, since the order quantity is 100 units, the demand during the lead time is also 100 units.
Therefore, the reorder point is equal to the demand during the lead time, which is 100 units. This means that when the inventory level reaches 100 units, a new order should be placed to ensure sufficient stock availability.
To learn more about units click here
brainly.com/question/29256657
#SPJ11
Complete Question
What is the reorder point for a product with an annual demand of 1,000 units, an order quantity of 100 units, a lead time of 250 working days per year, and a desired service level?
to get cards from a shuffled deck. express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
The probability of drawing a card from a shuffled deck is therefore 4/52, which simplifies to 1/13. This probability value falls between 0 and 1 inclusive, indicating that it is a valid probability
To express the indicated degree of likelihood as a probability value between 0 and 1 inclusive when getting cards from a shuffled deck, we need to consider the concept of probability and the total number of possible outcomes.
Probability is a measure of the likelihood of an event occurring. It is defined as the number of favorable outcomes divided by the total number of possible outcomes.
In the context of getting cards from a shuffled deck, the total number of possible outcomes is the number of ways to arrange the cards in the deck. There are 52 cards in a standard deck, so the total number of possible outcomes is 52!.
To express the likelihood of a specific event, such as drawing a particular card, we need to determine the number of favorable outcomes. The number of favorable outcomes depends on the specific event we are considering.
For example, let's say we want to find the probability of drawing an Ace from a shuffled deck. There are 4 Aces in a deck, so the number of favorable outcomes is 4.
The probability of drawing an Ace from a shuffled deck is therefore 4/52, which simplifies to 1/13. This probability value falls between 0 and 1 inclusive, indicating that it is a valid probability.
Similarly, we can determine the probabilities for other events, such as drawing a specific suit, drawing a face card, or drawing multiple cards in a specific order, by counting the favorable outcomes and dividing by the total number of possible outcomes.
By considering the specific event and the total number of possible outcomes, we can express the indicated degree of likelihood as a probability value between 0 and 1 inclusive for various card-related scenarios.
Know more about probability here:
https://brainly.com/question/30034780
#SPJ11
The probability of drawing any single card from a shuffled deck is 1 out of 52. Since probabilities fall between 0 and 1 inclusive, it is accurate to express the probability as 1/52.
Explanation:This question is a probability question related to mathematics. Taking a card from a deck, each has an equal likelihood of being selected. This is because a standard deck of cards contains 52 cards, broken down into 4 suits (hearts, diamonds, clubs, and spades) each containing 13 cards (1 through 10, Jack, Queen, and King). As such, the probability of picking any single card is 1 out of 52, or 1/52. Therefore, the degree of likelihood (probability) falls within the value of 0 and 1 inclusive.
Learn more about Probability here:https://brainly.com/question/22962752
#SPJ12
A university learned that 1% of its students drop out of the introductory statistics course.
Suppose 7 students enrolled in that course this quarter.
a.What is the probability that two or less will unsubscribe?
b.What is the probability that exactly two will unsubscribe?
c.What is the expected number of students withdrawn?
a) Probability that two or less will unsubscribe is 0.99. B) probability that exactly two will unsubscribe is 0.0087 C)The expected number of students withdrawn is 0.07.
The probability of two or fewer students unsubscribing can be calculated using the binomial probability formula, where:P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)P(X) = [tex]nC_{x} xp^xq^(n-x)[/tex] Here, the probability of a student dropping out is p = 0.01 and the probability of staying is q = 1 - p = 0.99.
Therefore, [tex]nC_{X}[/tex] can be calculated as:(7C[tex]_{0}[/tex]) = ([tex]7C_{1}[/tex] = 7([tex]7C_{2}[/tex]) = 21 y substituting these values into the formula, we get: P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)= ([tex](7C_{2} )*(0.01)^2*(0.99)^5[/tex]= 0.932As a result, the probability that two or less students will unsubscribe is 0.932.
b) The probability of exactly two students unsubscribing can be calculated using the binomial probability formula. Using the formula:P(X = 2) = [tex](7C_{2} )*(0.01)^2*(0.99)^5[/tex]= 0.0087
Therefore, the probability that exactly two students will unsubscribe is 0.0087.c)The expected number of students who will unsubscribe is a statistical estimate of the average number of students who will unsubscribe.
The formula for calculating the expected number of students withdrawn can be expressed as follows: E(X) = np, where n is the number of students who enrolled in the course, and p is the probability that a student will drop out. Using the formula:E(X) = 7*0.01 = 0.07 Therefore, the expected number of students withdrawn is 0.07.
Know more about Probability here:
https://brainly.com/question/31828911
#SPJ11
Suppose a test is given to 20 randomly selected college freshmen in Ohio. The sample average score on the test is 12 points and the sample standard deviation is 4 points. Suppose the same test is given to 16 randomly selected college freshmen in Iowa. The sample average score on the test is 8 points and the sample standard deviation is 3 points.
We want to test whether there is a significant difference in scores of college freshmen in Ohio versus Iowa. What is the point estimate for the difference in population means, where difference is defined as (Ohio minus Iowa)?
Group of answer choices
3.43
not enough information
0
4
Please show work
The point estimate for the difference in population means, where the difference is defined as (Ohio minus Iowa), can be calculated by subtracting the sample mean of the Iowa group from the sample mean of the Ohio group.
In this case, the point estimate is 12 - 8 = 4. To obtain the point estimate, we simply subtract the sample mean of one group from the sample mean of the other group. In this case, the sample mean of the Ohio group is 12 points, and the sample mean of the Iowa group is 8 points. Therefore, the point estimate for the difference in population means is 12 - 8 = 4. This means that, on average, the college freshmen in Ohio scored 4 points higher on the test compared to the college freshmen in Iowa.
To know more about standard deviation click here: brainly.com/question/29115611
#SPJ11
If
cos(x) =17/26 find sin(2x)=
(show step by step please)
17 If cos(x) (in Quadrant-1), find 26 sin(2x) = (Please enter answer accurate to 4 decimal places.)
Using the given value of cos(x) and the Pythagorean identity, we find sin(x). Then, applying the double-angle identity, sin(2x) is approximately 0.6728.
sin(2x) = 0.6728. Given that cos(x) = 17/26, we can find sin(x) using the Pythagorean identity: sin^2(x) + cos^2(x) = 1.
sin^2(x) + (17/26)^2 = 1
sin^2(x) + 289/676 = 1
sin^2(x) = 1 - 289/676
sin^2(x) = 387/676
Taking the square root of both sides, we get:
sin(x) = sqrt(387/676)
Now, to find sin(2x), we can use the double-angle identity: sin(2x) = 2sin(x)cos(x).
sin(2x) = 2 * sqrt(387/676) * (17/26)
sin(2x) = 0.6728
Therefore, sin(2x) is approximately 0.6728.
Learn more about trigonometric identities here: brainly.com/question/24377281
#SPJ11
f(t) = 4t2; t = 3, t = 3 +
h
(a) Determine the net change between the given values of the
variable.
(b) Determine the average rate of change between the given values
of the variable.
The net change between the given values of the variable is[tex]24h + 4h^2[/tex], and the average rate of change between the given values of the variable is 24 + 4h.
To determine the net change and average rate of change for the function [tex]F(t) = 4t^2[/tex] between the given values of the variable t = 3 and t = 3 + h, we can follow these steps:
(a) Net Change:
The net change represents the difference in the function's values between the two given points.
F(t = 3 + h) - F(t = 3)
= [tex]4(3 + h)^2 - 4(3)^2[/tex]
= [tex]4(9 + 6h + h^2) - 36[/tex]
= [tex]36 + 24h + 4h^2 - 36[/tex]
= [tex]24h + 4h^2[/tex]
Therefore, the net change between t = 3 and t = 3 + h is [tex]24h + 4h^2.[/tex]
(b) Average Rate of Change:
The average rate of change represents the slope of the secant line passing through the two given points.
Average Rate of Change = (F(t = 3 + h) - F(t = 3))/(3 + h - 3)
= [tex](24h + 4h^2)/(h)[/tex]
= 24 + 4h
Therefore, the average rate of change between t = 3 and t = 3 + h is 24 + 4h
For more such questions on variable
https://brainly.com/question/27894163
#SPJ8
You are comparing two different cellular calling plans. Company A will charge you a flat fee of $25 per month and then 5 cents per minute for all calls. Company B doesn't charge any flat fee, but their per-minute charge is 10 cents per minute.
a. Determine the domain and range of the function for Company A and Company B.
b. For what total numbers of minutes per month is it cheaper to use Company A?
c. Is there a number of total minutes that would cost the same at either company?
The domain for both Company A and B would be any positive number of minutes because any number of minutes used would fall under the plans given is 500 minutes.
The range of Company A and B would be any number greater than or equal to $0.00 because as the number of minutes used increases, so does the cost.
To find the point where Company A is cheaper, you can use the following inequality:
$0.05x + $25 < $0.10x
$25 < $0.05x
500 < x
It is cheaper to use Company A if the total number of minutes per month is less than 500 minutes.
Yes, the total number of minutes that would cost the same at either company can be found by setting the two inequalities equal to each other:
$0.05x + $25 = $0.10x
$25 = $0.05x
500 = x
At 500 minutes, both companies would charge the same amount.
To learn more about domain, visit:
https://brainly.com/question/21853810
#SPJ11
If xx is a binomial random variable, compute P(x)P(x) for each of the following cases:
(a) P(x≤6),n=9,p=0.8
P(x)=
(b) P(x>8),n=9,p=0.3
P(x)=
(c) P(x<1),n=9,p=0.1
P(x)=
(d) P(x≥2),n=4,p=0.8
P(x)=
P(x < 1
a) P(x ≤ 6), n = 9, p = 0.8
Using the binomial cumulative distribution function, we can compute P(x ≤ 6) as follows:
P(x ≤ 6) = Σ P(x = i) for i = 0 to 6
= Σ (9 choose i) * (0.8)^i * (0.2)^(9-i) for i = 0 to 6
= 0.000015 + 0.000459 + 0.005902 + 0.042467 + 0.181904 + 0.393668 + 0.328126
= 1.352541 * 10^-5 + 0.000458818 + 0.005902008 + 0.042467328 + 0.181904316 + 0.393668288 + 0.328126005
= 0.952446763
Therefore, P(x ≤ 6) = 0.952.
(b) P(x > 8), n = 9, p = 0.3
Using the binomial cumulative distribution function, we can compute P(x > 8) as follows:
P(x > 8) = 1 - P(x ≤ 8)
= 1 - Σ P(x = i) for i = 0 to 8
= 1 - (0.43046721 + 0.25412184 + 0.07886593 + 0.016515105 + 0.002316831 + 0.000218700 + 1.0776 * 10^-5 + 2.43 * 10^-7 + 2.43 * 10^-9)
= 0.000011
Therefore, P(x > 8) = 1.1 * 10^-5.
(c) P(x < 1), n = 9, p = 0.1
Using the binomial cumulative distribution function, we can compute P(x < 1) as follows:
P(x < 1) = Σ P(x = i) for i = 0 to 0
= (9 choose 0) * (0.1)^0 * (0.9)^9
= 0.387420489 * 10^-9
= 3.874 * 10^-10
To learn more about
Binomial variable
brainly.com/question/17139967
#SPJ11
A newspaper article stated that students at a particular university spend an average of £95 on beer. A student investigator who believed this average was too high polled a random sample of 50 students and found that x = £92.25 and s = £10. Use these results to test at the 5% significance level the statement made by the newspaper. 152 Business Statistics
Based on the sample data, at the 5% significance level, we reject the newspaper's statement and conclude that the average amount spent on beer by students is lower than £95.
To test the statement made by the newspaper, we can perform a hypothesis test using the sample data. The null hypothesis is that the average amount spent on beer by students is £95, and the alternative hypothesis is that the average is lower than £95.
Given a sample of 50 students, with a sample mean (x) of £92.25 and a sample standard deviation (s) of £10, we can calculate the test statistic and compare it to the critical value.
The test statistic (t) is calculated using the formula:
t = (x - μ) / (s / √n)
Substituting the given values, we get:
t = (92.25 - 95) / (10 / √50) = -1.86
Next, we determine the critical value corresponding to a 5% significance level. Since we have a one-tailed test with the alternative hypothesis indicating a lower average, the critical value is obtained from the t-distribution table for 49 degrees of freedom.
Comparing the test statistic to the critical value, we find that -1.86 is less than the critical value. Therefore, we reject the null hypothesis and conclude that there is evidence to support the claim that students at the university spend less than £95 on beer.
To know more about significance level click here
brainly.com/question/4599596
#SPJ11
urgent help please
Consider the following SQA model, where the defect removal activities and effectiveness rates are list in the following table:
No. Quality assurance activity Defect removal effectiveness rate
1-SRR Specification Requirement Review 70%
2-DIR Design Inspection and Review 50%
3-CIUT Code Inspection and Unit Test 50%
4-IST Integration and System Test 40%
5-OPD Operation Phase Detection 100%
The software development process consists of four activities: Requirement specification, Design, Implementation, and Deployment. The representative average relative defect-removal costs are illustrated in the following table:
No. Requirement Design Implementation Deployment
1-SRR 1 2-DIR 6 1 3-CIUT 12 5 1 4-IST 20 10 10 1
5-OPD 35 25 20 10
Assume that there are 20, 40, 30, and 20 defects originated in Requirement specification, Design, Implementation, and Deployment, respectively. Find the total costs according to above SQA model. Show your calculation process.
The total costs according to the given SQA model can be calculated by multiplying the number of defects in each phase with their respective defect-removal costs and then summing them up.
What is the process for calculating the total costs according to the SQA model?To calculate the total costs, we need to multiply the number of defects in each phase by their corresponding defect-removal costs and then add them together. Let's break down the calculation process step by step:
Step 1: Calculate the total cost for each phase by multiplying the number of defects by their respective defect-removal costs:
- Requirement specification (SRR): 20 defects * 1 cost = 20
- Design (DIR): 40 defects * 6 costs = 240
- Implementation (CIUT): 30 defects * 12 costs = 360
- Deployment (IST): 20 defects * 20 costs = 400
Step 2: Calculate the total cost for each phase by summing up the costs from all previous phases:
- Requirement specification (SRR): 20 + 0 = 20
- Design (DIR): 240 + 20 = 260
- Implementation (CIUT): 360 + 260 = 620
- Deployment (IST): 400 + 620 = 1020
Step 3: Calculate the total cost for the entire software development process by summing up the costs from all phases:
Total Costs = 20 + 260 + 620 + 1020 = 1920
Therefore, the total costs according to the given SQA model is 1920.
Learn more about SQA models
brainly.com/question/23544299
#SPJ11
The marketing manager of a department store has determined that revenue, in dollars, is related to the number of units of television advertising and the number of units of newspaper advertising, y, by the function R(x,y) = 850(138x - 2y^2 + 3xy - 4x^2). Each unit of television advertising costs $600, and each unit of newspaper advertising costs $200. If the amount spent on advertising is 55600, find the maximum revenue
Therefore, the maximum revenue is approximately $10,065,464.17.
The given function for the revenue as a function of the number of units of television advertising, x, and the number of units of newspaper advertising, y is R(x,y) = 850(138x - 2y² + 3xy - 4x²).
It is also given that the cost of each unit of television advertising is $600 and the cost of each unit of newspaper advertising is $200.
Let x be the number of units of television advertising and y be the number of units of newspaper advertising.
Then, the cost equation is: C(x,y) = 600x + 200y Since the total amount spent on advertising is $55,600, the equation can be written as: 600x + 200y = 55600 Divide the equation by 200 to obtain: 3x + y = 278.
This equation can be rewritten as y = 278 - 3x. Substituting y = 278 - 3x into the given revenue equation, we get:
R(x) = 850(138x - 2(278 - 3x)² + 3x(278 - 3x) - 4x²)R(x) = 850(138x - 2(77284 - 1674x + 9x²) + 834x - 3x² - 4x²)R(x) = 850(138x - 154568 + 3348x - 12x² - 4x²)R(x) = 850(-16x² + 3486x - 154568)R(x) = -13600x² + 2954100x - 131387600
This is a quadratic function with a = -13600, b = 2954100, and c = -131387600. The x-value of the maximum revenue can be found using the formula: x = -b / 2a Substituting the given values, we get: x = -2954100 / 2(-13600)x = 108.85 (rounded to two decimal places) The maximum revenue is obtained when x = 108.85.
Substituting this value in the revenue equation, we get: R(108.85) = -13600(108.85)² + 2954100(108.85) - 131387600R(108.85) ≈ $10,065,464.17 Therefore, the maximum revenue is approximately $10,065,464.17.
To know more about revenue visit:
https://brainly.com/question/32455692
#SPJ11
given a(x) = x2 1, b(x) = x3 x2 1. compute a(x)b(x) mod p(x) in gf(24) using the irreducible polynomial p(x) = x4 x 1. (15 points)
The remainder x + 1 represents the end result of c(x) modulo p(x). Therefore, [tex]a(x) * b(x) mod p(x)[/tex] = x + 1 in [tex]GF[/tex]([tex]2^4[/tex]).
To compute the made-from polynomials [tex]a(x)[/tex] and [tex]b(x)[/tex] modulo the irreducible polynomial [tex]p(x)[/tex], we need to perform polynomial multiplication and reduction using the given irreducible polynomial.
Let's start with the given polynomials and the irreducible polynomial:
[tex]a(x) = x^2 + 1[/tex]
[tex]b(x) = x^3 + x^2 + 1[/tex]
[tex]p(x) = x^4 + x + 1[/tex]
First, we'll multiply [tex]a(x) and b(x)[/tex] to get the end result [tex]c(x) = a(x) * b(x):[/tex]
[tex]c(x) = (x^2 + 1) * (x^3 + x^2 + 1) = x^5 + x^4 + x^3 + x^4 + x^3 + x^2 + x^2 + 1 = x^5 + 2x^4 + 2x^3 + 2x^2 + 1[/tex]
Next, we want to perform discount modulo p(x) = [tex]x^4 + x + 1[/tex] to get the final end result [tex]c(x) mod p(x)[/tex]. To perform this reduction, we will, again and again, divide the polynomial c(x) through p(x) until the diploma of c(x) is much less than the diploma of p(x).
Dividing [tex]c(x)[/tex] by using [tex]p(x):[/tex]
[tex]x^4 + x + 1^5 + 2x^4 + 2x^3 + 2x^2 + 1[/tex]
[tex]- (x^5 + x^2 + x) (Multiply `x` by `p(x)`and subtract)[/tex]
[tex]x^2 + 2x^3 + 2x^2 + 1[/tex]
[tex]- (x^2 + x) (Multiply `x` through `p(x)` and subtract)[/tex]
[tex]2x^3 + x^2 + 1[/tex]
[tex]- (2x^3 + 2x) (Multiply `2x` through `p(x)` and subtract)[/tex]
[tex]x^2 + 2x + 1[/tex]
[tex]- (x^2 + x) (Multiply `x` by `p(x)` and subtract)[/tex]
x + 1
The remainder x + 1 represents the result of[tex]c(x)[/tex]modulo[tex]p(x)[/tex]. Therefore, [tex]a(x) * b(x) mod p(x) = x + 1 GF(2^4).[/tex]
Note that during this [tex]GF(2^4)[/tex], the coefficients are limited to binary values (0 or 1).
To know more about polynomials,
https://brainly.com/question/24662212
#SPJ4
Run the following code, (1) x = runif (200,min= -50,max=50) y = runif (200,min= -50,max=50) 2 = 2*x + 3*y + 5 + rnorm (200, mean=0, sd=15) Suppose you use the regression model that 2 = ax + b
data.x <- runif(200, min = -50, max = 50). To use the regression model with the given data, we need to fit a linear regression equation to estimate the values of a and b.
This can be done using the lm() function in R.
Here is the modified code to fit the linear regression model:
```R
x <- runif(200, min = -50, max = 50)
y <- runif(200, min = -50, max = 50)
z <- 2*x + 3*y + 5 + rnorm(200, mean = 0, sd = 15)
# Fit the linear regression model
model <- lm(z ~ x + y)
# Extract the estimated coefficients
a <- coef(model)["x"]
b <- coef(model)["y"]
# Print the estimated coefficients
print(a)
print(b)
```
In this code, we generate random values for x and y using the runif() function, and z is computed based on the given equation.
Then, we fit the linear regression model using the lm() function with the formula `z ~ x + y`. The estimated coefficients a and b are extracted from the model using the coef() function, and their values are printed.
y <- runif(200, min = -50, max = 50)
z <- 2*x + 3*y + 5 + rnorm(200, mean = 0, sd = 15)
# Fit the linear regression model
model <- lm(z ~ x + y)
# Extract the estimated coefficients
a <- coef(model)["x"]
b <- coef(model)["y"]
# Print the estimated coefficients
print(a)
print(b)
When you run this code, you will get the estimated values of a and b based on the regression analysis of the generated data.x <- runif(200, min = -50, max = 50)
learn more about equation here: brainly.com/question/29657983
#SPJ11
The monthly cost (in dollars) of water use is a linear function of the amount of water used (in hundreds of cubic feet, HCF). The cost for using 12 HCF of water is $32.87, and the cost for using 25 HCF is $55.62. What is the cost for using 20 HCF of water?
The cost for using 20 HCF of water is approximately $49.87.To find the cost for using 20 HCF of water,
we can use the given information to determine the equation of the linear function relating the cost to the amount of water used.
Let's denote the amount of water used as x (in HCF) and the corresponding cost as y (in dollars). We are given two data points: (12, 32.87) and (25, 55.62).
Using the two-point form of the equation of a line, we can write:
(y - y1) = m(x - x1),
where (x1, y1) is one of the given points and m is the slope of the line.
Using the point (12, 32.87), we have:
(y - 32.87) = m(x - 12).
We can rearrange this equation to solve for m:
y = mx - 12m + 32.87.
Now, using the point (25, 55.62), we can substitute the values into the equation to solve for m:
55.62 = m(25) - 12m + 32.87.
Simplifying the equation, we get:
22.75 = 13m.
Dividing both sides by 13, we find:
m = 1.75.
Now that we have the slope, we can substitute it back into the equation:
y = 1.75x - 12(1.75) + 32.87.
Simplifying further, we have:
y = 1.75x - 21 + 32.87.
Combining like terms, we get:
y = 1.75x + 11.87.
Now we can find the cost for using 20 HCF of water by substituting x = 20 into the equation:
y = 1.75(20) + 11.87.
Calculating, we find:
y ≈ $49.87.
Therefore, the cost for using 20 HCF of water is approximately $49.87.
Learn more about slope here: brainly.com/question/3605446
#SPJ11
L^-1 {y(s)} = L^-1 { 4 e^-2πs/s(s^2+4) + e^4πs/(s^2+4) + s/s^2+4 – 1/s62+4}
Y (t) = L^-1 {4 e^-2π2s/s(s^2+4)} + L^-1 {e_4πs/s^2+4} + L^-1 {s/S^2+4} + l-1 {-1/S^2+4}
Could you please do second shifting property (explain it in detail) and Solve the initial value problem by the laplace transform
To solve the initial value problem using the Laplace transform, we use the second shifting property, which states that the Laplace transform of f(t-a)u(t-a) is given by e^(-as)F(s), where F(s) is the Laplace transform of f(t). We apply this property to each term in the given expression and then take the inverse Laplace transform to find the solution to the initial value problem.
Using the second shifting property, we apply it to each term in the given expression:
L^-1 {4 e^-2π2s/s(s^2+4)} = 4 e^(2π2(t-2)) u(t-2) * L^-1 {1/s(s^2+4)}
L^-1 {e^-4πs/s^2+4} = e^(4π(t-0)) u(t-0) * L^-1 {1/(s^2+4)}
L^-1 {s/S^2+4} = e^(0(t-0)) u(t-0) * L^-1 {1/(s^2+4)}
L^-1 {-1/S^2+4} = e^(0(t-0)) u(t-0) * L^-1 {-1/(s^2+4)}
By applying the inverse Laplace transform to each term, we obtain the solution to the initial value problem:
y(t) = 4 e^(2π(t-2)) u(t-2) * sin(2(t-2))
+ e^(4π(t-0)) u(t-0) * sin(2(t-0))
+ u(t-0) * sin(2(t-0))
- u(t-0) * sin(2(t-0))
The second shifting property allows us to shift the original function in the time domain and adjust the Laplace transform accordingly. By applying this property and taking the inverse Laplace transform, we can find the solution to the initial value problem.
Learn more about second shifting property here: brainly.com/question/32593448
#SPJ11
Use the Convolution theorm to find the inverse L trans form of aplace 1 H(s)=1/ (5²+a²)²
The convolution theorem can be used to determine the inverse Laplace transform of a function. When a function is given in the frequency domain, the convolution theorem is used to convert it into the time domain. The inverse Laplace transform is then applied to the function in order to find the time-domain solution.
Use the convolution theorem to find the inverse L-transform of a place 1 H(s) = 1 / (5² + a²)²
To begin, we need to use the convolution theorem to find the inverse Laplace transform of the function given in the question. The convolution theorem states that if
L{f(t)}=F(s) and L{g(t)}=G(s), then [tex]L{f(t)*g(t)}=F(s)G(s)[/tex].
The function H(s) can be written as H(s) = 1 / (25 + a²)².
The inverse Laplace transform of this function can be found by using the convolution theorem and the Laplace transform of a Gaussian function.
[tex]=L{e^{-st}}[/tex]
[tex]=\frac{1}{s+1}[/tex] So,
[tex]H(s) = \frac{1}{(25 + a^2)^2}[/tex]
[tex]= \frac{1}{25^2(1 + (\frac{a}{5})^2)^2}[/tex]
This can be expressed as
[tex]H(s) =\frac{1}{25^2}L{e^{-5t}\cos(at)}*L{e^{-5t}\cos(at)}[/tex]
Applying the convolution theorem, we can find the inverse Laplace transform of H(s) as:
[tex]L{e^{-5t}\cos(at)}*L{e^{-5t}\cos(at)}[/tex]
[tex]= \frac{1}{2}(\delta(t - \frac{\pi}{2a}) + \delta(t + \frac{\pi}{2a}))[/tex]
Hence, the inverse Laplace transform of
H(s) is given by: [tex]L^{-1}(H(s)) = \frac{1}{50a^2}e^{-5t}\sin(at)[/tex].
To know more about convolution theorem visit:
https://brainly.com/question/31423480
#SPJ11
3. Find the length of (3 sint, 2t, 3 cost), t ∈ [0,2π)
the length of the vector is sqrt(9 + 4t^2) if (3 sint, 2t, 3 cost), t ∈ [0,2π)
Given, the vector is (3 sin(t), 2t, 3 cos(t)).To find: The length of the vector.
The length of a vector is the square root of the sum of the square of its components. Thus,
the length of vector (3 sin(t), 2t, 3 cos(t)) is given by
|[tex](3 sin(t), 2t, 3 cos(t)) |= sqrt((3 sin(t))^2 + (2t)^2 + (3 cos(t))^2)| (3 sin(t), 2t, 3 cos(t)[/tex]) |
= [tex]sqrt(9 sin^2(t) + 4t^2 + 9 cos^2(t))| (3 sin(t), 2t, 3 cos(t)) |[/tex]
= [tex]sqrt(9 sin^2(t) + 9 cos^2(t) + 4t^2)| (3 sin(t), 2t, 3 cos(t)) |[/tex]
=[tex]sqrt(9(sin^2(t) + cos^2(t)) + 4t^2)| (3 sin(t), 2t, 3 cos(t))[/tex] |
= [tex]sqrt(9 + 4t^2)[/tex]
Therefore, the length of the vector is sqrt(9 + 4t^2))[tex]sqrt(9 + 4t^2)[/tex].
To know more about vector Visit:
https://brainly.com/question/29740341
#SPJ11
Find the derivative of the function f(x) = 3x +4/ 5x + 5 a. T = ____ b. T' = Preview c. B= Preview d. B' = Preview e. f'(x) = Preview
f'(x) = 7 / (25(x + 1)^2)Hence, the derivative of the function
f(x) = (3x +4) / (5x + 5) is f'(x) = 7 / (25(x + 1)^2)
Given function is f(x) = (3x +4) / (5x + 5)
To find the derivative of the given function f(x), we can use the formula of the derivative of the function. For the given function:
f(x) = (3x +4) / (5x + 5)
Applying the derivative of the function on f(x), we get:
f'(x) = [(3x +4) * (d/dx)(5x + 5) - (5x + 5) * (d/dx)(3x +4)] / [(5x + 5)^2]
Now, calculating d/dx(3x +4) and d/dx(5x + 5), we get:
d/dx(3x + 4) = 3d/dx(x) + d/dx(4)
= 3d/dx(x) + 0
= 3d/dx(5x + 5)
= 5 * d/dx(x) + d/dx(5)
= 5 * d/dx(x) + 0 = 5
So,
f'(x) = [(3x +4) * 5 - (5x + 5) * 3] / [(5x + 5)^2]
Simplifying the above expression, we get:
f'(x) = 7 / [(5x + 5)^2]Therefore, f'(x) = 7 / (25(x + 1)^2)
Hence, the derivative of the function
f(x) = (3x +4) / (5x + 5) is f'(x) = 7 / (25(x + 1)^2)
To know more about derivative visit :
brainly.com/question/25324584
#SPJ11
AR= 360 - 249 - AR is given : Comment the relationship betreen (AR) (MR) where q units produced cu and number of al MR is double AR 5) MR is the same at AR c) The slope of MR slope at MR ir double that of AR d) The slope of AR is double that of MR
Given that AR=360−249−AR.The relationship between AR and MR in the different scenarios are as follows:
When q units are produced, cu and number of al MR is double ARIn this case, let the value of AR be x. Then, the value of MR is double that of x or 2x.MR = 2x
Therefore, the relationship between AR and MR is that AR = MR/2The value of MR is the same at AR
When the value of MR is equal to AR, we can say that the relationship between them is 1:1.
Therefore, we can say that AR = MRThe slope of MR slope at MR is double that of AR
Assume that the slope of AR is y.
Then, the slope of MR is double that of y or 2y.Therefore, the relationship between AR and MR is AR = (1/2)MR
The slope of AR is double that of MR Assuming the slope of MR is z. Then, the slope of AR is double that of z or 2z.
Therefore, the relationship between AR and MR is MR = (1/2)AR
In summary, the relationship between AR and MR in the different scenarios are as follows:
AR = MR/2 (when q units are produced, cu and number of al MR is double AR)AR = MR
(when the value of MR is the same at AR)AR = (1/2)MR (when the slope of MR slope at MR is double that of AR)MR = (1/2)AR (when the slope of AR is double that of MR)
To know more about AR and MR vsit:
https://brainly.com/question/32560187
#SPJ11
