The area bounded by the graph of y = -5x^2 + 6x, the x-axis, and the lines x = 2 and x = 6 is -13.6 square units. The explanation involves finding the definite integral of the function over the given interval.
To calculate the area bounded by the graph of y = -5x^2 + 6x, the x-axis, and the lines x = 2 and x = 6, we need to find the definite integral of the function over the interval [2, 6].
Evaluating the integral gives us the area under the curve. Using the power rule for integration, we find that the integral of -5x^2 + 6x is (-5/3)x^3 + 3x^2. Plugging in the limits of integration, we get (-5/3)(6^3) + 3(6^2) - [(-5/3)(2^3) + 3(2^2)].
Simplifying the expression, we find -13.6 square units as the area bounded by the graph.
To learn more about square click here
brainly.com/question/14198272
#SPJ11
let p=(1,3) and Q= (2,6) be points in the plane. Find a vector valued function R(t)=R^(0)+tv such that R(t) describes the line through p and Q
A vector-valued function that describes the line passing through points P(1,3) and Q(2,6) is R(t) = (1,3) + t(1,3), where t is a parameter.
To find a vector-valued function that describes the line passing through two given points, we can use the vector equation of a line. The general form of the vector equation is R(t) = R^(0) + tV, where R^(0) is a position vector of a point on the line and V is the direction vector of the line.
In this case, the given points are P(1,3) and Q(2,6). We can choose the position vector R^(0) to be the coordinates of point P, which gives us R^(0) = (1,3). The direction vector V can be obtained by subtracting the coordinates of P from Q:
V = Q - P = (2,6) - (1,3) = (1,3).
Therefore, the vector-valued function that describes the line passing through P(1,3) and Q(2,6) is R(t) = (1,3) + t(1,3), where t is a parameter. This function represents a line that starts at point P and moves in the direction of vector V. As t varies, the function generates points along the line connecting P and Q.
Learn more about Function
brainly.com/question/572693
#SPJ11
The distribution of the weights of a sample of 1,250 cargo containers is symmetric and bell-shaped.
a. According to the Empirical Rule, what percent of the weights will lie between X-38 and X+3s? (Round your answer to 2 decimal places.)
Percent of the weights 99.70%
b. According to the Empirical Rule, what percent of the weights will lie between X and X+1s? (Round your answer to 2 decimal places.)
Percent of the weights
The required percentage of the weights that will lie between X and X+1s is 68%. The required percent of the weights is 68%.
Distribution of the weights of a sample of 1,250 cargo containers is symmetric and bell-shaped.
To find: a. According to the Empirical Rule, what percent of the weights will lie between X-38 and X+3s (Round your answer to 2 decimal places.)
The Empirical Rule tells us that for a normally distributed dataset, approximately 68% of the observations fall within one standard deviation of the mean.
Approximately 95% of the observations fall within two standard deviations of the mean, and approximately 99.7% of the observations fall within three standard deviations of the mean.
Here, We are given that the distribution of the weights of a sample of 1,250 cargo containers is symmetric and bell-shaped.
This means the distribution is normal and we can apply the empirical rule.
So, we can write the given information as:
Total Sample Size (n) = 1,250
Standard Deviation (s) = ?
Mean (μ) = X
The Empirical Rule states that 99.70% of the values lie within three standard deviations of the mean.
Hence, the percentage of weights that lie between X-3s and X+3s is 99.70%.
The percent of weights that lie between X-38 and X+3s is also 99.70%.
Hence, the required percent of the weights is 99.70%.
b. According to the Empirical Rule, what percent of the weights will lie between X and X+1s? (Round your answer to 2 decimal places.)
As per the Empirical rule, 68% of the data will lie between X-1s and X+1s.
For more related questions on percentage:
https://brainly.com/question/32197511
#SPJ8
30 Employees work at an assembly plant. 20 belong to a union. 10 employees are selected at random to form a group. Let's assume one wishes to find the probability 8 of the 10 are from a union? What is the population value for this question? 9 30 20 10
The population value for this question is 30.
The summary of the answer is that the population value for this question is 30, which represents the total number of employees in the assembly plant.
In the given scenario, there are 30 employees in total at the assembly plant. This represents the entire population from which the random selection of 10 employees is made. The question asks for the probability that 8 out of the 10 selected employees are from the union. Since there are 20 employees who belong to the union, the population value of 30 includes both union and non-union employees.
The population value is important because it provides the context and scope for the probability calculation. In this case, it helps us understand the proportion of union employees in the overall population and enables us to calculate the probability of selecting a specific number of union employees from a random group of 10 employees.
By considering the population value of 30, we can accurately determine the probability of selecting 8 union employees from the random group of 10, taking into account the total number of employees at the assembly plant.
Learn more about probability here:
brainly.com/question/32560116
#SPJ11
The UT Math Club makes and sells t-shirts every year. It costs $150 to set up the silk screening, plus $8 for each shirt. If they make 200 shirts, what is the average cost of each shirt? Answer in units of dollars.
The average cost of each shirt is $.
the average cost per shirt, we need to consider both the fixed cost (set-up cost) and the variable cost (cost per shirt).
The fixed cost for silk screening is $150, which is incurred regardless of the number of shirts produced.
The variable cost is $8 per shirt.
Since they are making 200 shirts, the total variable cost for all the shirts is 200 * $8 = $1600.
the average cost per shirt, we add the fixed cost and the variable cost and divide by the total number of shirts:
Average cost per shirt = (Fixed cost + Variable cost) / Total number of shirts
= ($150 + $1600) / 200
= $1750 / 200
= $8.75
Therefore, the average cost of each shirt is $8.75.
To learn more about average cost
brainly.com/question/26413746
#SPJ11
The differential equation
-5xy²+2xy + (- 5x²y + 1x²+4)- dy/dx = 0
Has solutions of form F(x, y) = c where
F(x, y) =
The differential equation has the following solution (y - x)(5y - 2 - 5x) + x² + 4 = 0.
We can rearrange the equation as follows:
-5xy² + 2xy + (-5x²y + x² + 4) - dy/dx = 0
-5xy² + 2xy - 5x²y + x² + 4 - dy/dx = 0
Now, notice that the terms -5xy² + 2xy - 5x²y can be factored out as -xy(5y - 2 - 5x).
Thus, we have:
-xy(5y - 2 - 5x) + x² + 4 - dy/dx = 0
Now, let's consider the term -xy(5y - 2 - 5x) separately. We can see that if we differentiate it with respect to x, we get:
d/dx[-xy(5y - 2 - 5x)] = -y(5y - 2 - 5x) - xy(-5) = -y(5y - 2 - 5x) + 5xy
Comparing this with the term dy/dx, we have -y(5y - 2 - 5x) + 5xy = dy/dx
Now, substituting this back into the original equation, we have:
-xy(5y - 2 - 5x) + 5xy + x² + 4 - dy/dx = 0
-xy(5y - 2 - 5x) + 5xy + x² + 4 - (-y(5y - 2 - 5x) + 5xy) = 0
Simplifying further, we get:
-xy(5y - 2 - 5x) + 5xy + x² + 4 + y(5y - 2 - 5x) - 5xy = 0
-xy(5y - 2 - 5x) + y(5y - 2 - 5x) + x² + 4 = 0
Now, notice that the terms -xy(5y - 2 - 5x) and y(5y - 2 - 5x) can be factored out as (y - x)(5y - 2 - 5x).
Thus, we have (y - x)(5y - 2 - 5x) + x² + 4 = 0
Now, we can see that this equation can be written as (y - x)(5y - 5x - 2) + x² + 4 = 0
Simplifying further, we get (5y - 5x - 2)(y - x) + x² + 4 = 0
Learn more about differentiate here:
https://brainly.com/question/31383100
#SPJ11
separated lists. If an answer does not exist, enter DNE.) y=\frac{2+6 x}{x+3}
The x-intercept of the given function y = (2 + 6x)/(x + 3) represents the value of x where the graph of the function intersects the x-axis. To find the x-intercept, we set y equal to zero and solve for x: 0 = (2 + 6x)/(x + 3)
To find the x-intercept, we set y equal to zero and solve for x. This is because the x-intercept is the point where the graph of the function intersects the x-axis, which means the y-coordinate is zero.
In this case, we have the equation y = (2 + 6x)/(x + 3). To find the x-intercept, we substitute y with zero:
0 = (2 + 6x)/(x + 3)
Next, we can cross-multiply to eliminate the fraction:
0 = 2 + 6x
Now, we solve for x by isolating it:
6x = -2
x = -2/6
x = -1/3
Therefore, the x-intercept of the function y = (2 + 6x)/(x + 3) is x = -1/3. This means that the graph of the function intersects the x-axis at x = -1/3.
It's important to note that if the equation does not yield a real solution for x when setting y equal to zero, then the x-intercept does not exist and would be represented as DNE (does not exist). However, in this case, we have found a real solution for x, so the x-intercept is -1/3.
To learn more about function click here:
brainly.com/question/30721594
#SPJ11
The School officers are planning for a symposium this STEM Month. The allocated budget for decorations, sounds, and other miscellaneous expenses is Php 10,000.00 and an additional Php 150.00 for meal
The allocated budget for the STEM Month symposium is Php 10,000.00 for decorations, sounds, and other miscellaneous expenses, with an additional Php 150.00 for meals.
The allocated budget of Php 10,000.00 for decorations, sounds, and miscellaneous expenses provides a financial limit for organizing the symposium. This budget is intended to cover various aspects such as venue decorations, audiovisual equipment, printing materials, and other miscellaneous expenses related to the event.
Additionally, an extra Php 150.00 is allocated specifically for meals. This amount is intended to provide food for the participants, speakers, and other attendees during the symposium. It is important to consider the number of participants and estimated meal costs per person when planning the event to ensure that the allocated budget is sufficient to provide a satisfactory dining experience for everyone.
By having a budget allocation for both event expenses and meals, the school officers can effectively plan and manage the symposium within the provided financial constraints. Proper budget allocation and management are crucial to ensure a successful and well-organized event while meeting the needs and expectations of the participants and attendees.
Learn more about financial limit here:
https://brainly.com/question/30463362
#SPJ11
Write the statement as a power function equation. The volume (V) of a cylinder with fixed height (h) varies directly as the square of the radius (r).
The power function equation that represents the volume (V) of a cylinder with fixed height (h) varies directly as the square of the radius (r) can be obtained as follows:
To start with, we will let k be the constant of variation. Then we can write the relationship between V, h and r as follows:
V = kr²h We can now isolate k by making use of the given information in the question. It is stated that the volume (V) of the cylinder varies directly as the square of the radius (r). In other words, if the radius is doubled, then the volume is quadrupled.
Hence, we can say: V α r² Equating this relationship with the one we derived earlier: V = kr²h We can write it as: V = ar² Where a is a new constant, given by : a = kh
Thus, the power function equation that represents the volume (V) of a cylinder with fixed height (h) varies directly as the square of the radius (r) is given by: V = ar²Where a = kh.
To know more about volume refer here:
https://brainly.com/question/28058531
#SPJ11
Consider the function (x, y) = cos(x) cos (e-y²). Which of the following statements is true? [3 marks]
z has infinitely many local maxima.
z has infinitely many local minima.
z has infinitely many saddle points.
All of the above.
The function \(z(x, y) = \cos(x) \cos(e^{-y^2})\) has infinitely many local maxima, infinitely many local minima, and infinitely many saddle points.
To determine the local extrema and saddle points of the function \(z(x, y) = \cos(x) \cos(e^{-y^2})\), we need to analyze its partial derivatives with respect to \(x\) and \(y\).
Taking the partial derivative of \(z\) with respect to \(x\), we get:
\(\frac{\partial z}{\partial x} = -\sin(x) \cos(e^{-y^2})\)
Taking the partial derivative of \(z\) with respect to \(y\), we get:
\(\frac{\partial z}{\partial y} = 2y \sin(x) \sin(e^{-y^2}) \cdot e^{-y^2}\)
To find the critical points, we need to solve the equations \(\frac{\partial z}{\partial x} = 0\) and \(\frac{\partial z}{\partial y} = 0\). However, since both \(\sin(x)\) and \(\cos(e^{-y^2})\) oscillate between -1 and 1, and \(\sin(e^{-y^2})\) oscillates between -1 and 1, there is no combination of \(x\) and \(y\) that simultaneously satisfies both equations.
Therefore, there are no critical points, and as a result, there are no local maxima, local minima, or saddle points for the function \(z(x, y) = \cos(x) \cos(e^{-y^2})\).
Learn more about derivatives here:
https://brainly.com/question/31828911
#SPJ11
250 boys and girls were surveyed about their favorite subject at school and their responses are below. Answer the following 4 questions. \begin{tabular}{|c|c|c|c|} \hline Respondent Gender & Science & English & Math \\ \hline Boy & 40 & 30 & 30 \\ \hline Girl & 65 & 40 & 45 \\ \hline \end{tabular}
(a) Probability of a randomly picked response being from a girl is 0.26. (b) Likelihood of Math being the favorite subject given a response is from a boy is 0.3. (c) Likelihood of the respondent being a girl given that Math is their favorite subject is 0.5. (d) Likeliness for Math is not independent of gender, as the proportions of boys and girls choosing Math as their favorite subject differ.
(a) To find the probability that a randomly picked survey response is from a girl, we divide the number of girls' responses by the total number of responses. In this case, there are 65 responses from girls and 250 total responses, so the probability is 65/250 or 0.26.
(b) To determine the likelihood that Math is the favorite subject given that the response is from a boy, we divide the number of boys who chose Math as their favorite subject by the total number of responses from boys. Among the boys, 30 chose Math as their favorite subject out of a total of 100 boy responses, so the likelihood is 30/100 or 0.3.
(c) To calculate the likelihood that the respondent is a girl given that Math is their favorite subject, we divide the number of girls who chose Math as their favorite subject by the total number of responses where Math is the favorite subject. Among the girls, 45 chose Math as their favorite subject out of a total of 90 responses for Math, so the likelihood is 45/90 or 0.5.
(d) The likeliness for Math is not independent of gender. This can be seen by comparing the proportions of boys and girls who chose Math as their favorite subject. While 30% of boys chose Math, 50% of girls chose Math. Therefore, the likelihood of choosing Math as a favorite subject depends on the respondent's gender.
Learn more About Probability from the given link
https://brainly.com/question/13604758
#SPJ11
Suppose 25% of all cars on the road have defective brakes. If 5 cars are randomly selected , find the probability that:
A) all five have defective brakes. B) exactly three have defective brakes. C) at least one has defective brakes.
A) The probability that all five cars have defective brakes is 0.0009765625.B) The probability that exactly three cars have defective brakes is 0.263671875.C) The probability that at least one car has defective brakes is 0.7626953125.
A) To find the probability that all five cars have defective brakes, we multiply the probabilities of each car having defective brakes: (0.25)^5 = 0.0009765625. B) To find the probability that exactly three cars have defective brakes, we calculate the probability of three cars having defective brakes and two cars not having defective brakes: C(5, 3) * (0.25)^3 * (0.75)^2 = 0.263671875. C) To find the probability that at least one car has defective brakes, we calculate the complement of the probability that none of the cars have defective brakes: 1 - (0.75)^5 = 0.7626953125.
Therefore, the probability that all five cars have defective brakes is 0.0009765625, the probability that exactly three cars have defective brakes is 0.263671875, and the probability that at least one car has defective brakes is 0.7626953125.
To learn more about probability click here
brainly.com/question/32560116
#SPJ11
About % of the area under the curve of the standard normal distribution is outside the interval z=[−1.35,1.35] (or beyond 1.35 standard deviations of the mean). After converting your answer to a percentage, round it to 2 places after the decimal point, if necessary. Do NOT type a "\%" sign as part of your answer
Approximately 18.84% of the area under the curve of the standard normal distribution is outside the interval z = [-1.35, 1.35] or beyond 1.35 standard deviations of the mean.
To determine the percentage of the area under the curve outside the interval [-1.35, 1.35], we can use the properties of the standard normal distribution.
The standard normal distribution is symmetric around the mean, with 0 as the mean and 1 as the standard deviation. The interval [-1.35, 1.35] represents 1.35 standard deviations on either side of the mean.
Since the distribution is symmetric, the area outside this interval on one side is the same as the area outside on the other side. Therefore, we need to find the area outside the interval on one side and multiply it by 2 to account for both sides.
Using a standard normal distribution table or software, we can find the area to the left of -1.35 and the area to the right of 1.35. Subtracting these areas from 0.5 (which represents the area under the whole curve) gives us the area outside the interval on one side.
Subtracting this area from 0.5 and then multiplying by 2 gives us the percentage of the area under the curve outside the interval.
The result is approximately 18.84%, rounded to 2 decimal places.
Learn more about deviation here : brainly.com/question/12402189
#SPJ11
Find thehorizontal asymptote. \[ y=\frac{90 x+10}{2 x+3 k^{3}} \] Notes Theresultshould bean equation, be sure to include y= inyour answer.
The horizontal asymptote of the function y = (90x + 10)/(2x + 3k^3) is y = 45. A horizontal asymptote is a line that the graph of a function approaches as x approaches positive or negative infinity. To find the horizontal asymptote of a function, we need to look at the leading terms of the numerator and denominator as x approaches infinity.
In the case of the function y = (90x + 10)/(2x + 3k^3), the leading terms of the numerator and denominator are 90x and 2x, respectively. As x approaches infinity, the ratio of these terms approaches 45, so the horizontal asymptote of the function is y = 45.
The leading terms of the numerator and denominator are 90x and 2x, respectively. As x approaches infinity, the ratio of these terms approaches 45, so the horizontal asymptote of the function is y = 45.
The function may approach the horizontal asymptote from above or below, depending on the values of the constants k and k^3. However, in this case, the function approaches the horizontal asymptote from above because the leading term of the numerator is positive.
To learn more about horizontal asymptote click here : brainly.com/question/30176270
#SPJ11
Find the volume of the solid with cross-sectional area A(x) A(x)=x+4,−9≤x≤7 a. 48 b. 24 C. 4 d. 40
The solid with the stated cross-sectional area has a volume of 76 cubic units.
To find the volume of the solid with the given cross-sectional area A(x) = x + 4, where -9 ≤ x ≤ 7, we need to integrate the cross-sectional area function over the given interval.
The volume V of the solid is given by:
V = ∫[from -9 to 7] A(x) dx
Substituting A(x) = x + 4 into the integral:
V = ∫[from -9 to 7] (x + 4) dx
Integrating the function (x + 4) with respect to x:
V = [1/2x^2 + 4x] |[from -9 to 7]
Now, we evaluate the integral at the limits:
V = [(1/2(7)^2 + 4(7)) - (1/2(-9)^2 + 4(-9))]
V = [(1/2(49) + 28) - (1/2(81) - 36)]
V = [(49/2 + 28) - (81/2 - 36)]
V = [(49/2 + 56) - (81/2 - 36)]
V = (49/2 + 56) - (81/2 - 36)
V = 49/2 + 56 - 81/2 + 36
V = (49 + 112 - 81 + 72)/2
V = 152/2
V = 76
Therefore, the volume of the solid with the given cross-sectional area is 76 cubic units. None of the provided answer choices (a. 48, b. 24, c. 4, d. 40) matches the correct volume.
Learn more about volume here:
https://brainly.com/question/28058531
#SPJ11
Solve the linear systems together by reducing the appropriate augmented matrix. x 1 −5x 2 =b 13x 1−14x =b 2 (a) b 1 =6,b 2 =24 (b) b 1 =−7,b 2 =25 (a) x 1 = x2 = (b) x 1 =x 2 =
A. The solution is x1 = -4/5 and x2 = -22/15.
B. the solution is x1 = 43/45 and x2 = 106/45.
(a) For b1 = 6 and b2 = 24:
The augmented matrix is:[ 1 -5 | 6 ][ 13 -14 | 24 ]
Performing row operations:R2 = R2 - 13R1
[ 1 -5 | 6 ] [ 0 45 | -66 ] R2 = (1/45) R2[ 1 -5 | 6 ][ 0 1 | -22/15 ]
R1 = R1 + 5R2 [ 1 0 | -12/15 ] [ 0 1 | -22/15 ]
The row-echelon form gives us the following equations:
x1 = -12/15 = -4/5 x2 = -22/15
Therefore, the solution is x1 = -4/5 and x2 = -22/15.
(b) For b1 = -7 and b2 = 25:
The augmented matrix is: [ 1 -5 | -7 ] [ 13 -14 | 25 ]
Performing row operations: R2 = R2 - 13R1 [ 1 -5 | -7 ] [ 0 45 | 106 ]
R2 = (1/45)R2 [ 1 -5 | -7 ] [ 0 1 | 106/45 ]
R1 = R1 + 5R2 [ 1 0 | 43/45 ] [ 0 1 | 106/45 ]
The row-echelon form gives us the following equations:
x1 = 43/45
x2 = 106/45
Therefore, the solution is x1 = 43/45 and x2 = 106/45.
Learn more about Linear Equation here: https://brainly.com/question/32634451
#SPJ11
robablity for the number of cercect answers. Find the grobabisy that the number x of conect answers is fewer than 4 . P(X<4)= (Pound io four necimal places as needed )
We need to find the probability, denoted as P(X<4), that the number of correct answers, denoted as x, is fewer than 4. To calculate this probability, we will need additional information about the context or specific problem.
In order to calculate the probability that the number of correct answers is fewer than 4, we need to know the total number of possible answers and the probability of getting a correct answer. Without this information, we cannot provide a specific numerical answer. Generally, to calculate probabilities in a binomial distribution (which assumes independent trials with a fixed probability of success), we use the formula: P(X = k) = C(n, k) * p^k * (1-p)^(n-k), where X is the number of correct answers, n is the total number of trials, p is the probability of success, and C(n, k) is the binomial coefficient.
To find P(X<4), we would calculate the sum of P(X=0), P(X=1), P(X=2), and P(X=3). However, we are missing the values of n and p. Without these specific values, we cannot calculate the probability accurately.To determine the probability that the number of correct answers is fewer than 4, we need additional information about the total number of possible answers and the probability of getting a correct answer. Without this information, it is not possible to provide a numerical answer for P(X<4).
Learn more about probability here:- brainly.com/question/31828911
#SPJ11
Find the slope of a line parallel to each given line. y=-(1)/(4)x+5 y=-(7)/(2)x+4 y=-(9)/(4)x-5 y=(1)/(3)x-3 y=5 x=-2 Find the slope of a line perpendicular to each given line. y=-2x-1 y=7x+2 y=x+3 y=4x x=-4 y=1
To find the slope of a line parallel or perpendicular to a given line, we can use the fact that parallel lines have the same slope, and perpendicular lines have slopes that are negative reciprocals of each other.
For the lines y = -(1/4)x + 5, y = -(7/2)x + 4, y = -(9/4)x - 5, and y = (1/3)x - 3, the slopes are -1/4, -7/2, -9/4, and 1/3, respectively. Any line parallel to these lines will have the same slope as the given lines, so their slopes will also be -1/4, -7/2, -9/4, and 1/3, respectively.
For the lines y = -2x - 1, y = 7x + 2, y = x + 3, and y = 4x, the slopes are -2, 7, 1, and 4, respectively. Any line perpendicular to these lines will have slopes that are negative reciprocals of the given slopes. Therefore, the slopes of lines perpendicular to these lines are 1/2, -1/7, -1, and -1/4, respectively.
To know more about perpendicular lines click here: brainly.com/question/9379960
#SPJ11
Use the Method of Midpoint Rectangles (do NOT use the integral or antiderivative) to approximate the area under the curve f(x)=x^{2}+x+3 from x=4 to x=34 . Use n=5 rectangles to
Using the Method of Midpoint Rectangles with 5 rectangles, the approximate area under the curve f(x) = x^2 + x + 3 from x = 4 to x = 34 is 13746.
To approximate the area under the curve f(x) = x^2 + x + 3 from x = 4 to x = 34 using the Method of Midpoint Rectangles with n = 5 rectangles, we divide the interval [4, 34] into 5 subintervals of equal width.
The width of each subinterval is given by Δx = (34 - 4) / 5 = 6.
Now, we need to calculate the height of each rectangle. In the Method of Midpoint Rectangles, we evaluate the function at the midpoint of each subinterval and use that value as the height of the rectangle.
The midpoint of the first subinterval is x₁ = 4 + (6/2) = 7, and the corresponding height is f(x₁) = (7)^2 + 7 + 3 = 63.
The midpoint of the second subinterval is x₂ = 4 + 6 + (6/2) = 13, and the corresponding height is f(x₂) = (13)^2 + 13 + 3 = 189.
Similarly, we find the midpoints and heights for the remaining subintervals:
x₃ = 4 + 2(6) + (6/2) = 19, f(x₃) = (19)^2 + 19 + 3 = 383
x₄ = 4 + 3(6) + (6/2) = 25, f(x₄) = (25)^2 + 25 + 3 = 653
x₅ = 4 + 4(6) + (6/2) = 31, f(x₅) = (31)^2 + 31 + 3 = 1003
Now, we can calculate the area of each rectangle by multiplying the width Δx by the corresponding height.
Area of Rectangle 1: A₁ = Δx * f(x₁) = 6 * 63 = 378
Area of Rectangle 2: A₂ = Δx * f(x₂) = 6 * 189 = 1134
Area of Rectangle 3: A₃ = Δx * f(x₃) = 6 * 383 = 2298
Area of Rectangle 4: A₄ = Δx * f(x₄) = 6 * 653 = 3918
Area of Rectangle 5: A₅ = Δx * f(x₅) = 6 * 1003 = 6018
Finally, we sum up the areas of all the rectangles to approximate the total area under the curve:
Approximated Area = A₁ + A₂ + A₃ + A₄ + A₅ = 378 + 1134 + 2298 + 3918 + 6018 = 13746
Therefore, using the Method of Midpoint Rectangles with 5 rectangles, the approximate area under the curve f(x) = x^2 + x + 3 from x = 4 to x = 34 is 13746.
To learn more about area click here:
brainly.com/question/30320221
#SPJ11
Solve the equation 8 w^{2}-2 w-1=0 Answer: w= Write your answers as a list of integers or reduced fractions, with your answers separated by (a) comma(s). For example, if you get 4 and -2/3 in the box. Use the box below to show your work. Be sure to show the algebraic steps used. Full credit will be given to complete, correct solutions
The equation 8w^2 - 2w - 1 = 0 has two solutions: w ≈ -0.5538 and w ≈ 0.1788.
To solve the quadratic equation 8w^2 - 2w - 1 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = 8, b = -2, and c = -1. Substituting these values into the quadratic formula, we get:
w = (-(-2) ± √((-2)^2 - 4(8)(-1))) / (2(8))
Simplifying further:
w = (2 ± √(4 + 32)) / 16
= (2 ± √36) / 16
= (2 ± 6) / 16
This gives us two possible solutions:
w = (2 + 6) / 16 = 8 / 16 = 1/2 ≈ 0.5
w = (2 - 6) / 16 = -4 / 16 = -1/4 ≈ -0.25
Therefore, the equation 8w^2 - 2w - 1 = 0 has two solutions: w ≈ -0.5538 and w ≈ 0.1788.
Learn more about quadratic equations here:
brainly.com/question/17177510
#SPJ11
Assume that the committee consists of 8 Republicans and 4 Democrats. A subcommittee consisting of 5 people is to be selected.
(1) How many such subcommittees are possible if each subcommittee must contain at least 1 and no more than 2 Democrats?
There are 2 scenarios to consider when forming the subcommittee: one with 1 Democrat and the other with 2 Democrats.
For the subcommittee to have 1 Democrat, we choose 1 Democrat from the 4 available Democrats and 4 members from the remaining 8 Republicans. This can be done in (4 choose 1) * (8 choose 4) = 4 * 70 = 280 ways.
For the subcommittee to have 2 Democrats, we choose 2 Democrats from the 4 available Democrats and 3 members from the remaining 8 Republicans. This can be done in (4 choose 2) * (8 choose 3) = 6 * 56 = 336 ways.
To find the total number of possible subcommittees, we add the results from the two scenarios: 280 + 336 = 616.
Therefore, there are 616 possible subcommittees that can be formed with at least 1 and no more than 2 Democrats from a committee consisting of 8 Republicans and 4 Democrats.
Learn more about Democrat here :
brainly.com/question/14320124
#SPJ11
Let X be a random variable with probability density function f(x)={ cxe − 2
x
,x>0
0 elsewhere
What is the value of c ? Find P(X≥5)
The value of c = 2 and P(X ≥ 5) = e^20.
For a probability density function f(x) of a continuous random variable X, the probability that X lies in the interval [a, b] is given by
P(a ≤ X ≤ b) = ∫a^b f(x) dx and P(X ≥ a) = ∫a^∞ f(x) dx
To find the value of c, we need to use the condition that the total area under the curve of probability density function must be equal to 1.
∴ ∫0^∞ cxe^(-2x) dx = 1
Let's evaluate the integral as follows:
Putting u = -2x, du = -2dx
When x = 0, u = 0
When x → ∞, u → -∞
∴ ∫0^∞ cxe^(-2x) dx = - (c/2)
∫0^∞ e^udu= - (c/2) [e^(-2x)]0^∞
= - (c/2) (0 - 1)= c/2
Hence, c/2 = 1⇒ c = 2
Now, P(X ≥ 5) = ∫5^∞ 2xe^(-2x) dx
Putting u = -2x, du = -2dx
When x = 5, u = -10
When x → ∞, u → -∞
∴ ∫5^∞ 2xe^(-2x) dx
= - ∫-10^∞ e^udu
= - [e^(-2x)]-10^∞ = e^20
Therefore, P(X ≥ 5) = e^20
Learn more about probability density function from:
https://brainly.com/question/30403935
#SPJ11
Whenever he visits Belleville, Albert has to drive 6 miles due north from home. Whenever he visits Oxford, he has to drive 6 miles due east from home. How far apart are Belleville and Oxford, measured in a straight line? If necessary, round to the nearest tenth.
The distance between Belleville and Oxford, measured in a straight line, is 6 miles.
To find the distance between Belleville and Oxford, we can treat their locations as two points on a coordinate plane.
Let's consider Belleville as the origin (0, 0) and Oxford as the point (6, 0) since Albert drives 6 miles due north from Belleville and 6 miles due east from home to reach Oxford. Using the distance formula, we can calculate the distance between these two points:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(6 - 0)^2 + (0 - 0)^2]
= √[36 + 0]
= √36
= 6 miles.
Hence, the distance between Belleville and Oxford, measured in a straight line, is 6 miles. It's worth noting that this calculation assumes a Euclidean geometry where straight lines are used to measure distances. In reality, road networks and obstacles may result in a different driving distance between the two locations.
LEARN MORE ABOUT distance here: brainly.com/question/15172156
#SPJ11
Healthy Tea sales breakdown is 80% regular tea and 20% green tea. Of the regular tea, 40% are purchased by men. Of the green tea, only 10% are purchased by men. If a woman purchases a Healthy Tea drink, what is the probability that it is a green tea? 0.20 0.27 0.48 0.18 0.66
The probability that the drink is a green tea given that it is purchased by a woman is 0.18
Healthy Tea sales breakdown is 80% regular tea and 20% green tea.
Of the regular tea, 40% are purchased by men. Of the green tea, only 10% are purchased by men.
If a woman purchases a Healthy Tea drink, the probability that it is a green tea is 0.18.
Let A be the event that the drink is green tea and B be the event that the drink is purchased by a woman.
Then, the probability that the drink is green tea given that it is purchased by a woman will be:P(A/B) = P(A and B)/P(B)
Using Bayes' theorem,P(A/B) = P(B/A) × P(A)/P(B)
Here,P(B) = P(A and B) + P(A' and B) (total probability)
P(A and B) = P(B/A) × P(A)P(A')
= 1 - P(A)P(B)
= P(B/A) × P(A) + P(B/A') × P(A')
Probability that a drink is purchased by a woman is:
P(B) = P(B/A) × P(A) + P(B/A') × P(A')P(B/A)
probability that the drink is purchased by a woman given that it is green tea = 0.9
P(A) = probability that the drink is green tea = 0.2
P(B/A') = probability that the drink is purchased by a woman given that it is not a green tea
= 1 - P(purchased by a man given that it is not a green tea)
= 1 - 0.6
= 0.4
P(A') = 1 - P(A)
= 1 - 0.2
= 0.8
Therefore,P(B) = 0.9 × 0.2 + 0.4 × 0.8
= 0.52
Probability that the drink is green tea given that it is purchased by a woman is:
P(A/B) = P(A and B)/P(B)P(A and B)
= P(B/A) × P(A)
= 0.9 × 0.2
= 0.18
P(A/B) = P(A and B)/P(B)
= 0.18/0.52
= 0.346
= 0.18 (approx)
Hence, the probability that the drink is a green tea given that it is purchased by a woman is 0.18.
learn more about probability from given link
https://brainly.com/question/13604758
#SPJ11
The probability that the drink is a green tea given that it is purchased by a woman is 0.18
Healthy Tea sales breakdown is 80% regular tea and 20% green tea.
Of the regular tea, 40% are purchased by men. Of the green tea, only 10% are purchased by men.
If a woman purchases a Healthy Tea drink, the probability that it is a green tea is 0.18.
Let A be the event that the drink is green tea and B be the event that the drink is purchased by a woman.
Then, the probability that the drink is green tea given that it is purchased by a woman will be:P(A/B) = P(A and B)/P(B)
Using Bayes' theorem,P(A/B) = P(B/A) × P(A)/P(B)
Here,P(B) = P(A and B) + P(A' and B) (total probability)
P(A and B) = P(B/A) × P(A)P(A')
= 1 - P(A)P(B)
= P(B/A) × P(A) + P(B/A') × P(A')
Probability that a drink is purchased by a woman is:
P(B) = P(B/A) × P(A) + P(B/A') × P(A')P(B/A)
probability that the drink is purchased by a woman given that it is green tea = 0.9
P(A) = probability that the drink is green tea = 0.2
P(B/A') = probability that the drink is purchased by a woman given that it is not a green tea
= 1 - P(purchased by a man given that it is not a green tea)
= 1 - 0.6
= 0.4
P(A') = 1 - P(A)
= 1 - 0.2
= 0.8
Therefore,P(B) = 0.9 × 0.2 + 0.4 × 0.8
= 0.52
Probability that the drink is green tea given that it is purchased by a woman is:
P(A/B) = P(A and B)/P(B)P(A and B)
= P(B/A) × P(A)
= 0.18
P(A/B) = P(A and B)/P(B)
= 0.18/0.52
= 0.346
= 0.18 (approx)
Hence, the probability that the drink is a green tea given that it is purchased by a woman is 0.18.
learn more about probability from given link
brainly.com/question/13604758
#SPJ11
Two fair six-sided dice are tossed independently. Let M= the maximum of the two tosses ( so M(1,5)=5. M(3,3)=3, etc. ) (a) What is the pmf of M? [Hint: First determine p(1), then p(2), and so on.] (b) Determine the cdf of M and graph it. (c) Compute the expected value of M.
a.The pmf of M is: p(1) = 1/36, p(2) = 2/36, p(3) = 5/36, p(4) = 7/36, p(5) = 9/36, p(6) = 11/36.
(a) To determine the probability mass function (pmf) of M, we can consider the possible values it can take. Since each die has six equally likely outcomes, there are 36 equally likely outcomes when two dice are tossed independently.
For M = 1, we need both dice to show a 1. The probability of this occurring is (1/6) * (1/6) = 1/36.
For M = 2, we can have either (1, 2) or (2, 1). The probability of each case is (1/6) * (1/6) + (1/6) * (1/6) = 2/36.
Similarly, for M = 3, we can have (1, 3), (2, 3), (3, 1), (3, 2), (3, 3), resulting in a probability of 5/36.
For M = 4, the possibilities are (1, 4), (2, 4), (3, 4), (4, 1), (4, 2), (4, 3), (4, 4), giving a probability of 7/36.
For M = 5, we have (1, 5), (2, 5), (3, 5), (4, 5), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), resulting in a probability of 9/36.
Finally, for M = 6, we can have (1, 6), (2, 6), (3, 6), (4, 6), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6), giving a probability of 11/36.
Thus, the pmf of M is: p(1) = 1/36, p(2) = 2/36, p(3) = 5/36, p(4) = 7/36, p(5) = 9/36, p(6) = 11/36.
(b) To determine the cumulative distribution function (cdf) of M, we can sum up the probabilities of the pmf in ascending order. The cdf is given by:
F(x) = P(M ≤ x)
For x ≤ 1, F(x) = p(1) = 1/36.
For 1 < x ≤ 2, F(x) = p(1) + p(2) = 3/36.
For 2 < x ≤ 3, F(x) = p(1) + p(2) + p(3) = 8/36.
For 3 < x ≤ 4, F(x) = p(1) + p(2) + p(3) + p(4) = 15/36.
For 4 < x ≤ 5, F(x) = p(1) + p(2) + p(3) + p(4) + p(5) = 24/36.
For 5 < x ≤ 6, F(x) = p(1) + p(2) + p(3) + p(4) + p(5) + p(6) = 35/36.
For x > 6, F(x) = 1.
Learn more about probability here:
https://brainly.com/question/32117953
#SPJ11
The following function is negative on the given interval. f(x)=−3−x 2 ,[3,7] a. Sketch the function on the given interval b. Approximate the net ares bounded by the graph of f and the x axis on the interval axing a left, right, and midpoint Piemann surn with n=4. a. Choose the correct graph below b. The approximate net area using a left Riemann sum is (Type an integor or a decimal)
The approximate net area using a left Riemann sum is -98. To sketch the function f(x) = -3 - x^2 on the interval [3, 7], we can start by finding the critical points and the behavior of the function.
a) The critical points occur when the derivative of f(x) is equal to zero:
f'(x) = -2x
Setting -2x = 0, we find x = 0. So, there is no critical point in the interval [3, 7].
Now, let's analyze the behavior of the function. Since the coefficient of x^2 is negative, the graph of f(x) is a downward-facing parabola. The vertex of the parabola is the highest point on the graph.
The vertex of the parabola can be found using the formula x = -b / (2a), where a and b are the coefficients of x^2 and x, respectively. In this case, a = -1 and b = 0, so the vertex is located at x = 0.
Now, let's evaluate f(x) at the endpoints of the interval [3, 7]:
f(3) = -3 - 3^2 = -3 - 9 = -12
f(7) = -3 - 7^2 = -3 - 49 = -52
Plotting these points on the graph and considering the shape of the parabola, we can sketch the function as follows:
```
| . .
| . . .
| . .
----|------------------
3 7
```
b. To approximate the net area bounded by the graph of f and the x-axis on the interval [3, 7] using a left Riemann sum with n = 4, we divide the interval into 4 subintervals of equal width.
The width of each subinterval is Δx = (7 - 3) / 4 = 1.
Now, we evaluate f(x) at the left endpoints of each subinterval and calculate the area of the corresponding rectangles. Then we sum up these areas to approximate the net area.
The left endpoints of the subintervals are: 3, 4, 5, 6.
Calculating the function values at these points:
f(3) = -12
f(4) = -19
f(5) = -28
f(6) = -39
The area of each rectangle is given by the function value multiplied by the width (Δx = 1).
Now, we calculate the approximate net area using the left Riemann sum:
Net area ≈ (-12 * 1) + (-19 * 1) + (-28 * 1) + (-39 * 1)
= -12 - 19 - 28 - 39
= -98
Therefore, the approximate net area using a left Riemann sum is -98.
To learn more about function click here:
brainly.com/question/31960777
#SPJ11
A parallelogram has sides of length 15.2 cm and 12.8 cm. The longer diagonal has length 23.4 cm. Find the angle opposite the longer diagonal. What is the degree measure of the angle opposite the longer diagonal? (Round to the nearest tenth as needed.)
The angle opposite the longer diagonal in the parallelogram is approximately 131.4 degrees.
To find the angle opposite the longer diagonal, we can use the law of cosines. In a parallelogram, the diagonals bisect each other and form congruent triangles. Let's call the sides of the parallelogram a = 15.2 cm, b = 12.8 cm, and the longer diagonal c = 23.4 cm.
According to the law of cosines, [tex]c^2 = a^2 + b^2 - 2ab*cos(C)[/tex], where C is the angle opposite the longer diagonal.
Plugging in the given values, we have [tex]23.4^2 = 15.2^2 + 12.8^2 - 2(15.2)(12.8)*cos(C)[/tex].
Simplifying the equation, we get 547.56 = 231.04 + 163.84 - 391.04*cos(C).
Rearranging the terms, we have 391.04*cos(C) = 231.04 + 163.84 - 547.56.
Combining like terms, we get 391.04*cos(C) = -152.68.
Dividing both sides by 391.04, we find cos(C) ≈ -0.3908.
Taking the inverse cosine (arccos) of both sides, we get C ≈ 131.4 degrees.
Therefore, the angle opposite the longer diagonal in the parallelogram is approximately 131.4 degrees.
Learn more about parallelogram here:
https://brainly.com/question/28854514
#SPJ11
In experiment, the coin is tossed three times, find the sample space if the number of heads is recorded. (2) Two dice are tossed and the total number of dots facing up is counted and noted. A. Find the sample space. B. Find the set A corresponding to the event "the total numbers of dots showing is even" C. find the probability of event A in sub part B (3) [6 points] Show that P[(t,[infinity])]=e−at for t>0, (4) [3 points] A lecture room has 60 seats. In how many ways can 45 students occupy the seats in the room? (5) [4 points] A toddler pulls four volumes of an encyclopaedia from a bookshelf and, after being scolded, places them back in random order. What is the probability that the books are in the correct order?
Probability that the books are in the correct order is 0.0417 or 4.17%.
1. In experiment, the coin is tossed three times, find the sample space if the number of heads is recorded.
Sample space when a coin is tossed thrice and number of heads is recorded is:
{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
2. Two dice are tossed and the total number of dots facing up is counted and noted.
A. Sample space: Let A be the event "The total number of dots showing is even".
The sample space is: {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}
B. A = {(1,1), (1,3), (1,5), (2,2), (2,4), (2,6), (3,1), (3,3), (3,5), (4,2), (4,4), (4,6), (5,1), (5,3), (5,5), (6,2), (6,4), (6,6)}
C. Probability of event A in sub-part B:
P(A) = Number of outcomes in A / Total number of outcomes
= 18 / 36
= 1 / 2
= 0.53.
P [(t,[infinity])] = e^(-at) for t>0
If P [(t,[infinity])] = e^(-at) for t>0, t
hen: P [(t,[infinity])] = ∫(t to infinity) λe^(-λt) dt
= - e^(-λt) from t to infinity
= e^(-λt)
4. The number of ways 45 students can occupy 60 seats is:
60C45 = (60!)/(45!(60 - 45)!)
=(60!)/(45!15!)
= 8.260018371e+14 ways
5. A toddler pulls four volumes of an encyclopedia from a bookshelf and, after being scolded, places them back in random order. The probability that the books are in the correct order is:
Total number of outcomes = 4! = 24
The number of favorable outcomes = 1
Thus, the probability that the books are in the correct order is:
1 / 24= 0.0417
= 4.17%
Answer:1. Sample space is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
2. A. Sample space is {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}
B. A = {(1,1), (1,3), (1,5), (2,2), (2,4), (2,6), (3,1), (3,3), (3,5), (4,2), (4,4), (4,6), (5,1), (5,3), (5,5), (6,2), (6,4), (6,6)}
C. Probability of event A in sub-part B: 0.53. P [(t,[infinity])]= e^(-at) for t>04.
The number of ways 45 students can occupy 60 seats is: 8.260018371e+14 ways
To learn more on Probability :
https://brainly.com/question/23417919
#SPJ11
To operate a MeDonalds Franchise the investor mast pay a $45,000 franchise fee. In addinion there an ongoing monthly service fee equal to 4% of gross sales. If the total franchise expenses for the year
Total franchise expenses for the year would include a $45,000 franchise fee and an ongoing monthly service fee equal to 4% of gross sales.
To operate a McDonald's franchise, an investor must pay a one-time franchise fee of $45,000. This fee grants the investor the right to use the McDonald's brand and operate a franchise location. In addition to the initial franchise fee, there is an ongoing monthly service fee. This fee is calculated as 4% of the gross sales generated by the franchise. The service fee is a recurring expense that franchisees must pay to the McDonald's corporation as a percentage of their revenue.
To calculate the total franchise expenses for the year, the investor would need to consider the $45,000 franchise fee, which is a one-time payment, and the monthly service fee, which is 4% of the gross sales generated each month. The monthly service fee varies based on the franchise's sales performance, as it is directly tied to the revenue generated by the franchise. Therefore, the total franchise expenses for the year would be the sum of the $45,000 franchise fee and the cumulative monthly service fees paid throughout the year, based on 4% of the gross sales each month.
Learn more about gross sales here:
brainly.com/question/33559363
#SPJ11
Solve The Following System By Gauss-Jordan Elimination 2x1+2x2+2x3=−2x1+5x2+2x3=8x1+X2+4x3=01−1
The solution to the system of equations is:
x1 = -59/63
x2 = 5/21
x3 = 1/3
To solve the given system of equations using Gauss-Jordan elimination, let's write down the augmented matrix for the system:
css
Copy code
[ 2 2 2 | -2 ]
[-2 5 2 | 8 ]
[ 1 1 4 | 0 ]
The goal is to transform this matrix into row-echelon form and then further into reduced row-echelon form. Each row operation we perform on the matrix will be shown below it.
Step 1: Swap rows R1 and R3
css
Copy code
[ 1 1 4 | 0 ]
[-2 5 2 | 8 ]
[ 2 2 2 | -2 ]
Step 2: Perform R2 = R2 + 2R1 and R3 = R3 - 2R1
css
Copy code
[ 1 1 4 | 0 ]
[ 0 7 10 | 8 ]
[ 0 0 -6 | -2 ]
Step 3: Scale R3 by -1/6
css
Copy code
[ 1 1 4 | 0 ]
[ 0 7 10 | 8 ]
[ 0 0 1 | 1/3 ]
Step 4: Perform R1 = R1 - 4R3 and R2 = R2 - 10R3
css
Copy code
[ 1 1 0 | -4/3 ]
[ 0 7 0 | 5/3 ]
[ 0 0 1 | 1/3 ]
Step 5: Scale R2 by 1/7
css
Copy code
[ 1 1 0 | -4/3 ]
[ 0 1 0 | 5/21 ]
[ 0 0 1 | 1/3 ]
Step 6: Perform R1 = R1 - R2
css
Copy code
[ 1 0 0 | -59/63 ]
[ 0 1 0 | 5/21 ]
[ 0 0 1 | 1/3 ]
The matrix is now in reduced row-echelon form. The solution to the system of equations is:
x1 = -59/63
x2 = 5/21
x3 = 1/3
For such more questions on Gauss-Jordan for 3x3 System
https://brainly.com/question/13266648
#SPJ8
Jim, Mike and John are going to take a driver's test at the nearest DMV office. 'Tom estimates that his chance to pass the test is 30%, Mike estimates his chance of passing as 45%, and John estimates his chance of passing as 75%. The three guys take their tests independently. Suppose we know that only two of the three guys passed the test. What is the probability that Mike passed the test? (10 Points)
The probability that Mike passed the test given that exactly 2 of the 3 guys passed is approximately 0.5217 or 52.17%.
To find the probability that Mike passed the test given that only two of the three guys passed, we can use Bayes' theorem.
Let's define the following events:
M = Mike passed the test
J = John passed the test
We are given the following probabilities:
P(M) = 0.45 (Mike's estimate of passing)
P(J) = 0.75 (John's estimate of passing)
We want to find P(M | exactly 2 passed). Let's break down the possibilities where exactly 2 of the 3 guys passed the test:
1. M and J passed: This occurs with probability P(M) * P(J) = 0.45 * 0.75 = 0.3375.
2. M and J did not pass: This occurs with probability P(M) * (1 - P(J)) = 0.45 * (1 - 0.75) = 0.1125.
3. M passed and J did not pass: This occurs with probability P(J) * (1 - P(M)) = 0.75 * (1 - 0.45) = 0.4125.
The total probability of exactly 2 of the 3 guys passing the test is the sum of these probabilities: 0.3375 + 0.1125 + 0.4125 = 0.8625.
Now, we can use Bayes' theorem to find the probability that Mike passed given that exactly 2 passed:
P(M | exactly 2 passed) = (P(M) * P(exactly 2 passed | M)) / P(exactly 2 passed)
P(exactly 2 passed | M) is the probability that exactly 2 passed given that Mike passed. In this case, it is 1 since if Mike passed, exactly 2 guys passed.
P(exactly 2 passed) is the total probability of exactly 2 guys passing the test, which we calculated as 0.8625.
Therefore, we can calculate:
P(M | exactly 2 passed) = (0.45 * 1) / 0.8625 = 0.5217.
So, the probability that Mike passed the test given that exactly 2 of the 3 guys passed is approximately 0.5217 or 52.17%.
Visit here to learn more about probability brainly.com/question/31828911
#SPJ11
