Answer:
I believe the answer is $180
Step-by-step explanation:
130+10=140
55+25=80
150
105
160
130
170
155
180
180
80 volunteers take a meningitis test to help doctors see how accurate this test is at identifying whether someone has meningitis or not.
A positive result means the test has identified you as having meningitis.
Of the volunteers, only 8 people have meningitis.
The results show 2 people who have meningitis gets a negative result and 3 people who don't have meningitis get a positive result.
What was the accuracy of the test?
To calculate the accuracy of the test, we need to create a 2x2 contingency table:
Actual Positive (Meningitis)Actual Negative (No Meningitis)Test PositiveTrue Positive (TP) = 6False Positive (FP) = 3Test NegativeFalse Negative (FN) = 2True Negative (TN) = 69
From the information given, we know that there are 8 actual positive cases (people with meningitis) and 72 actual negative cases (people without meningitis). We also know that there were 3 false positive results (people who tested positive for meningitis but did not have it) and 2 false negative results (people who tested negative for meningitis but actually had it).
Using this information, we can calculate the accuracy of the test as:
Accuracy = (TP + TN) / (TP + TN + FP + FN)
Accuracy = (6 + 69) / (6 + 69 + 3 + 2)
Accuracy = 75 / 80
Accuracy = 0.9375 or 93.75%
Therefore, the accuracy of the meningitis test is 93.75%.
When would you use a pictograph?
more than one answer
A. if the data is numerical
B. to compare change over time
C. to save space for a large set of data
D. if the data is categorical
Answer:
The answer to your problem is, D. If the data is categorical
Step-by-step explanation:
What a pictograph is:
Remember that a pictographs are less useful for comparing change over time or for presenting large sets of numerical data, as they can become cluttered and difficult to read.
Here is a little example, if you want to show how the population of a city has changed over the years, a line graph or a bar graph would be a better choice than a pictograph
Thus the answer to your problem is, D. If the data is categorical
Reverse logistics involves: a. triage b. designing a supply management system from the customer's perspective c. understanding of e-procurement systems d. understanding of transportation options
Reverse logistics involves designing a customer-focused supply management system and understanding transportation options, but it does not necessarily require knowledge of e-procurement systems or triage.
Reverse logistics is the process of managing the flow of products, materials, and information from the end-user back to the point of origin. It involves activities such as returns, refurbishment, recycling, and disposal of products.
The options given are:
a. triage - This refers to the process of determining the priority of patients' treatments based on the severity of their condition. While triage is an important concept in healthcare, it is not directly related to reverse logistics.
b. designing a supply management system from the customer's perspective - This is a key aspect of reverse logistics. A successful reverse logistics system requires a customer-focused approach to ensure that products can be easily returned and that customers have a positive experience with the returns process.
c. understanding of e-procurement systems - While e-procurement systems can be helpful in managing the reverse logistics process, it is not a necessary component of reverse logistics. E-procurement systems are primarily used for purchasing and procurement activities.
d. understanding of transportation options - Transportation is a critical component of reverse logistics, as it is necessary to move returned products from the point of origin back to the manufacturer or retailer. Understanding transportation options and selecting the most cost-effective and efficient method of transportation is essential to managing the reverse logistics process.
In summary, reverse logistics involves designing a customer-focused supply management system and understanding transportation options, but it does not necessarily require knowledge of e-procurement systems or triage.
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The Cp statistic is more useful than the Cpk statistic since it can better account for non-centered distributions.TrueFalse
False.
The Cp and Cpk statistics are both used to assess the capability of a process to meet specifications, but they have different purposes.
The Cp statistic is a measure of how well the process spread (variation) fits within the specification limits. It assumes that the process mean is centered on the target value. It is calculated as the ratio of the specification width to the process spread (six times the process standard deviation).
The Cpk statistic, on the other hand, takes into account both the process spread and the deviation of the process mean from the target value. It is calculated as the minimum of two values: the difference between the process mean and the closest specification limit divided by three times the process standard deviation (assuming the process is centered within the specification limits), or the Cp value adjusted for the deviation of the process mean from the target value.
Both statistics have their uses and limitations depending on the situation. If the process mean is not centered on the target value, the Cpk statistic may be more useful than the Cp statistic since it takes into account both the spread and centering of the process.
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What was the mortality rate for those humans who were infected with the bird flu?
a 0.3
b 0.5
c 0.7
d 0.9
Julia had a bag filled with gumballs. There were 3 lemon-lime, 2 watermelon, and 1 grape gumballs. What is the correct sample space for the gumballs in her bag?
Sample space = lemon-lime, watermelon, grape
Sample space = lemon-lime, lemon-lime, lemon-lime, watermelon, watermelon, grape
Sample space = 1, 2, 3
Sample space = 1, 2, 3, 4, 5, 6
Answer:
The answer to your problem is, B. Sample space = lemon-lime, lemon-lime, lemon-lime, watermelon, watermelon, grape
Step-by-step explanation:
We are given that, Julia had a bag filled with gumballs. There were 3 lemon-lime, 4 watermelon, and 6 grape gumballs.
There are 3 lemon-lime: Elements in sample space are lemon-lime, lemon-lime, lemon-lime
There are also 4 watermelon: Elements in sample space are watermelon, watermelon, watermelon, watermelon
Lastly there are 6 grape: Elements in sample space are grape, grape, grape, grape, grape, grape
Which can lead to the problem of:
3 + 4 + 6 = 13. Same as option B
Thus the answer to your problem is, B. Sample space = lemon-lime, lemon-lime, lemon-lime, watermelon, watermelon, grape
what is the solution set for the inequality 5-3k>35
Answer:
k<-10
Step-by-step explanation:
-3k+5>35
-3k+5-5>35-5
simplifica la expresión
k<-10
can someone please help me with my math work i can’t seem to understand where to go on this maze.
Answer:5
explanation:
you are doing great finding the slopes:
Which statement best describes the expression fraction 1 over 2 x (14 − 6) x 6 + 4? (2 points)
Find half the product of 6 and 4, then subtract the difference between 14 and 6.
Find half the difference of 14 and 6, multiply by 6, then add 4.
Find the product of 14 and 6, add the product of 6 and 4, then divide by 2.
Find the product of 6 and 4, subtract the difference between 14 and 6, then multiply by fraction 1 over 2
The correct statement is "Find half the difference of 14 and 6, multiply by 6, then add 4".
What is the solution of the expression?The solution of the fraction expression is calculated as follows;
1/[2 x (14 - 6) x 6 + 4]
To solve the above expression, we will apply the rule of BODMAS as shown below;
The difference of 14 and 6 = 14 - 6 = 8
The next is to divide 8 by 2
= 8/2
= 4
The next step is to multily the result by 6
= 4 x 6
= 24
The final step is to add 4 to it;
= 24 + 4
= 28
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if a newspaper reports that a recent opinion poll shows candidate a with 52% of the vote and candidate b with 48% of the vote, with a margin of error of /- 4%, which of the following statements is true?
Based on the newspaper report, it can be concluded that Candidate A is leading with 52% of the vote while Candidate B has 48% of the vote. However, it is important to note that the margin of error is +/- 4%. This means that there is a chance that the actual percentage of votes for each candidate could be 4% higher or lower than what the poll suggests.
For example, Candidate A's actual percentage of votes could be anywhere between 56% (52% + 4%) and 48% (52% - 4%), while Candidate B's actual percentage of votes could be anywhere between 52% (48% + 4%) and 44% (48% - 4%).
It is also important to note that opinion polls are not always accurate predictors of election results. They are simply a snapshot of public opinion at a particular moment in time and can be influenced by various factors such as the wording of the questions, the sample size, and the demographic makeup of the respondents.
In summary, based on the newspaper report, Candidate A has a slight lead over Candidate B with 52% of the vote, but there is a margin of error of +/- 4% which means that the actual percentage of votes for each candidate could be different. It is important to keep in mind that opinion polls are not always accurate predictors of election results.
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suppose that the distribution for total amounts spent by students vacationing for a week in florida is normally distributed with a mean of 650 and a standard deviation of 120 . suppose you take a simple random sample (srs) of 20 students from this distribution. what is the probability that a srs of 20 students will spend an average of between 600 and 700 dollars? round to five decimal places.
The probability that a srs of 20 students will spend an average of between 600 and 700 dollars is 0.92081.
We need to find the probability that a simple random sample of 20 students will spend an average of between 600 and 700 dollars.
To solve this problem, we will use the central limit theorem, which states that the sampling distribution of the sample means will be approximately normally distributed with a mean of μ and a standard deviation of σ/√(n), where n is the sample size.
Thus, the mean of the sampling distribution is μ = 650 and the standard deviation is σ/sqrt(n) = 120/√(20) = 26.83.
We need to find the probability that the sample mean falls between 600 and 700 dollars. Let x be the sample mean. Then:
Z1 = (600 - μ) / (σ / √(n)) = (600 - 650) / (120 / √t(20)) = -1.77
Z2 = (700 - μ) / (σ / √(n)) = (700 - 650) / (120 / √(20)) = 1.77
Using a standard normal distribution table or calculator, we can find the area under the standard normal distribution curve between these two Z-scores as:
P(-1.77 < Z < 1.77) = 0.9208
Therefore, the probability that a simple random sample of 20 students will spend an average of between 600 and 700 dollars is 0.9208, or approximately 0.92081 when rounded to five decimal places.
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26 students were randomly selected from a large group of students taking a certain calculus test. The mean score for the students in the sample was 83. Assume that o-8.70. Construct a 99% confidence interval for the mean score, H, of all students taking the test.
The 99% confidence interval for the mean score, μ, of all students taking the test is approximately (78.603, 87.397)
To construct a 99% confidence interval for the mean score, μ, of all students taking the calculus test, we need to follow these steps:
Step 1: Identify the sample mean, sample standard deviation, and sample size.
Sample mean (X) = 83
Sample standard deviation (σ) = 8.70
Sample size (n) = 26
Step 2: Determine the appropriate z-score for a 99% confidence interval.
For a 99% confidence interval, the z-score (z) is 2.576.
Step 3: Calculate the standard error of the mean (SEM).
[tex]SEM= \frac{σ }{\sqrt{n} } = \frac{8.70}{\sqrt{26} } = 1.706[/tex]
Step 4: Compute the margin of error (ME).
ME = z * SEM = 2.576 * 1.706 = 4.397
Step 5: Construct the 99% confidence interval.
Lower limit = X - ME = 83 - 4.397 = 78.603
Upper limit = X + ME = 83 + 4.397 = 87.397
Your answer: The 99% confidence interval for the mean score, μ, of all students taking the test is approximately (78.603, 87.397).
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A cube of side 5 is built with black and white cubes of side 1, so that the cubes next to each other have different colors and the corner cubes are black, as shown in the figure. How many white cubes were used?
Answer: 62
Step-by-step explanation:
top row has 12
the next row has 1 more =13
and it alternates
12+13+12+13+12=62
26. If BD = 8x - 27 and EC-2x + 33, find BD
The length of BD is 53 units.
We are given here that BD is (8x - 27) units and EC is (2x + 33) units. BD and EC are the diagonals of a trapezoid. As we know that diagonals of a trapezoid are equal. Therefore, we will equate the given diagonals of a trapezoid.
BD = EC
Substituting the given values of BD and EC
8x - 27 = 2x + 33
combining the like terms
8x - 2x = 33 + 27
6x = 60
x = 60/6
x = 10
Now, as we have to find BD, we will substitute the value of x in the given equation for BD.
BD = 8x - 27
BD = 8(10) - 27
BD = 80 - 27
BD = 53
Therefore, BD is 53 units.
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The complete question is " If BD = 8x - 27 and EC-2x + 33, find BD with respect to the image shown."
solve for length of segment D a=4 cm b=12 cm c=6 cm 4 • ? = ? • D
The length of segment d is 8 when the value segment a is 4 cm, b is 12 cm , c is 6 cm
If two segments intersect inside or outside the circle then ab=cd
Given values of a is 4 cm, b is 12 cm , c is 6 cm and d is x
ab=cd
Plug in the values of a, b , c and d
4×12=6×d
48=6d
Divide both sides by 6
8=d
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When given the equation for a function, how can you determine where it is increasing and where it is decreasing?
When you are given an equation for a function, it is important to know whether the function is increasing or decreasing. A function is said to be increasing if the value of the function increases as the input increases. Conversely, a function is said to be decreasing if the value of the function decreases as the input increases.
To determine whether a function is increasing or decreasing, you need to look at the sign of its first derivative. The first derivative of a function is the rate of change of the function with respect to its input. If the first derivative is positive, the function is increasing, and if it is negative, the function is decreasing. If the first derivative is zero, the function may have a local maximum or a local minimum.
To explain this in more detail, let's take the example of the function f(x) = x^2. To find the first derivative of this function, we need to differentiate it with respect to x. This gives us f'(x) = 2x. We can see that f'(x) is positive for x > 0, which means that the function f(x) = x^2 is increasing for x > 0. Similarly, f'(x) is negative for x < 0, which means that the function f(x) = x^2 is decreasing for x < 0.
In summary, to determine where a function is increasing or decreasing, you need to look at the sign of its first derivative. If the first derivative is positive, the function is increasing, and if it is negative, the function is decreasing. If the first derivative is zero, the function may have a local maximum or a local minimum.
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The graph shows the location of point P and point R. Point R is on the y-axis and has the same y-coordinate as point P. Point Q is graphed at ( n , ¯ 2 ) . The distance from point P to point Q is equal to the distance from point P to point R. What is the distance from point P to point Q? What is the value of n? Explain how you determined the distance from point P to point Q, and the value of n. Enter your answers and your explanations in the space provided.The graph shows the location of point P and point R. Point R is on the y-axis and has the same y-coordinate as point P. Point Q is graphed at ( n , ¯ 2 ) . The distance from point P to point Q is equal to the distance from point P to point R. What is the distance from point P to point Q? What is the value of n? Explain how you determined the distance from point P to point Q, and the value of n. Enter your answers and your explanations in the space provided.
The value of n is 5.
Given that, the Coordinate of P = (n,3)
R is on y-axis & the y-coordinate of P & R are equal.
So coordinate of R = (3,0)
Coordinate of Q = (n,-2)
Using distance formula,
Distance between P & Q =
[tex]=\sqrt{(n-n)^2+(-3-(-2)^2} \\\\=\sqrt{(3+2)^2} \\\\= \sqrt{25} = 5[/tex]
Distance between P & R =
[tex]\sqrt{(n-0)^2+(3-3)^2}[/tex]
= n
According to the question it is given that distance between P & Q is equal to the distance between P & R. So, n = 5.
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What is the area of this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
Answer:
48.8 square inches
Step-by-step explanation:
To find the area of the triangle, we can use the formula:
Area = 1/2 * base * height
In this case, the base of the triangle is the longer side, which is 13 inches, and the height is the shorter side, which is 7.5 inches. However, we need to make sure that the angle provided is the angle between the base and the height, and not one of the other angles of the triangle.
Assuming that the angle provided is indeed the angle between the base and the height, we can proceed with the calculation:
Area = 1/2 * 13 inches * 7.5 inches
Area = 48.75 square inches
Rounded to the nearest tenth, the area of the triangle is 48.8 square inches.
.PLEASE HURRY
What are the zeros of the following function?
Answer:
The zeroes are x = -4 and x = 2.
Consider the following set of equations:
Equation R: −3y = −3x − 9
Equation S: y = x + 3
Which of the following best describes the solution to the given set of equations?
a
No solution
b
One solution
c
Infinite solutions
d
Two solutions
The solution to the given set of equations is Infinite solutions.
We have the equation
R: -3y = -3x -9
S: y = x + 3
Now, solving the equation R and S as
-3y = -3x - 9
3y = 3x + 9
_________
0 = 0 + 0
0 = 0
Also, -3/1 = 3/(-1) = 9/(-3)
-3/1 = -3/1 = -3/1
Thus, the equation have Infinite many solutions.
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a wire whose length is given as x inches is bent into a square. express the length of a side of the square in terms of x.
Therefore, the length of a side of the square is x/4 inches by the equation.
In this context, we have a wire that we need to bend into a square. A square has four equal sides, so if we let s be the length of one side of the square, then the total length of the wire must be 4s.
The equation 4s = x represents this relationship, where x is the total length of the wire.
To solve for s, we can isolate s on one side of the equation by dividing both sides by 4. This gives us:
4s / 4 = x / 4
Simplifying, we get:
s = x / 4
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A soccer dome shaped like a hemisphere has a volume of 450,000 m^3. What is the area of its field? Use 3. 14 for pi
As per the given values, the area of the hemisphere is 45065.41 m³
Volume = 450000 m³
Calculating the volume of the hemisphere -
Volume = 2/3 πr³
Substituting the values -
450,000 =2/3 x 3.14 x r³
Solving for r³
r³ = 450000 x 3/(2 x 3.14)
r³ = 214968.1
r = √214968.1
r = 59.9
Calculating the area of the hemisphere -
Area = 4πr²
Substituting the values -
Area = 4 x 3.14 x (59.9)²
= 12.56 x (59.9)²
= 45065.41
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3/10 en notación decimal
Answer: 0.3
Step-by-step explanation:
3/10 = 30/100 = 0.3
Answer:
0.3
Step-by-step explanation:
3. Let X and Y be independent random variables, with X having a Poisson (2) distribution andy having the distribution given by the probability mass function 0:20:56 values 2 probabilities 0.2 0.5 0.3 (a) Find Ely). (b) Let F be the cumulative distribution function of X + Y. Find FC). (c) Find P(X - Y). (d) A student calculates E[XY2= ELX]0[Y2 – (2)((0.2)0% + (0.5)1? + (0.3)24) – 3.4 Is this calculation correct? If so, explain why cach step is valid. If not, what mistake is the student making?
The expected value of Y is: 1.8
The student made a mistake by using the formula for the variance of XY instead of the expectation of XY^2.
(a) E(Y) = (0.2)(2) + (0.5)(1) + (0.3)(4) = 1.8
(b) Since X and Y are independent, the distribution of X + Y is the convolution of their respective distributions. That is, if Z = X + Y, then for any real number z,
F(z) = P(Z ≤ z) = P(X + Y ≤ z) = ∑P(X = i, Y ≤ z − i) for i = 0, 1, 2, ...
Now, since X has a Poisson distribution with parameter 2 and Y takes values 2, 3, and 4 with probabilities 0.2, 0.5, and 0.3 respectively, we have
P(X = i, Y = j) = P(X = i)P(Y = j) = e^(-2) (2^i/i!)p_j for i = 0, 1, 2, ... and j = 2, 3, 4
where p_2 = 0.2, p_3 = 0.5, and p_4 = 0.3. Then, for z ≥ 2,
F(z) = P(Z ≤ z) = ∑_{i=0}^{z-2} P(X=i, Y≤z-i) = ∑_{i=0}^{z-2} e^(-2) (2^i/i!) ∑_{j=2}^{min(z-i, 4)} p_j
(c) P(X > Y) = ∑_{i=0}^∞ ∑_{j=0}^{i-1} P(X=i, Y=j) = ∑_{i=0}^∞ ∑_{j=0}^{i-1} e^(-2) (2^i/i!) p_j
(d) The calculation is incorrect. It should be E[XY^2] = E[X]E[Y^2] = 2(0.2)(2^2) + 2(0.5)(3^2) + 2(0.3)(4^2) = 11.6. The student made a mistake by using the formula for the variance of XY instead of the expectation of XY^2.
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Helppp this is so hard!,
Answer:
303.375 or 303 3/8
Step-by-step explanation:
First, we can split the polygon into three smaller shapes: a triangle, a big rectangle, and a small rectangle. We will call them A, B, and C.
A:
Length: 28.25 - (3 + 13) = 28.25 - 16 = 12.25 (12 1/4)
Height: 10 + 9 = 19
Area: (12.25 * 19) / 2 = 232.75 / 2 = 116.375 ft
B:
Length: 3 + 13 = 16
Width: 10
Area: 16 * 10 = 160 ft
C:
Length: 3
Width: 9
Area: 3 * 9 = 27 ft
Now we have to add all three digits:
116.375 + 160 + 27 = 303.375 or 303 3/8
-------------------------------------------------------------------------------------------------------------
Hope this helps :)
Sure, I can help with that. The problem is asking for the area of a polygon composed of two rectangles and a right triangle.
The area of a rectangle is given by the formula length * width, and the area of a right triangle is given by the formula 1/2 * base * height.
Let’s calculate the areas:
For the first rectangle with dimensions 9ft by 13ft, the area is 9 * 13 = 117 square feet.
For the second rectangle with dimensions 10ft by 8ft, the area is 10 * 8 = 80 square feet.
For the right triangle with dimensions 28ft by 4ft, the area is 1/2 * 28 * 4 = 56 square feet.
Adding these areas together gives the total area of the polygon:
117 + 80 + 56 = 253 square feet
So, the area of the polygon is 253 square feet.
Question 3 (10 marks) Find an equation for the plane tangent to the surface z = x²y + xy^2 + In x+R at (1,0,R). Z=
The equation of the plane tangent to the surface z = x²y + xy² + ln x + R at (1, 0, R) is z = x + y + (R - 1).
To find the equation of the plane tangent to the surface z = x²y + xy^2 + ln x + R at the point (1, 0, R), we'll need to find the partial derivatives with respect to x and y, and then use the point-slope form of the tangent plane equation. Here are the steps:
1. Find the partial derivatives of the surface function with respect to x and y:
∂z/∂x = 2xy + y² + (1/x)
∂z/∂y = x² + 2xy
2. Evaluate the partial derivatives at the given point (1, 0, R):
∂z/∂x(1, 0) = 2(1)(0) + (0)² + (1/1) = 1
∂z/∂y(1, 0) = (1)² + 2(1)(0) = 1
3. Use the point-slope form of the tangent plane equation:
z - z₀ = a(x - x₀) + b(y - y₀)
4. Substitute the point (x₀, y₀, z₀) = (1, 0, R) and the partial derivative values a = ∂z/∂x = 1, b = ∂z/∂y = 1:
z - R = 1(x - 1) + 1(y - 0)
5. Simplify the equation:
z - R = x - 1 + y
6. Rearrange the equation to the standard form:
z = x + y + (R - 1)
The equation of the plane tangent to the surface z = x²y + xy² + ln x + R at (1, 0, R) is z = x + y + (R - 1).
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Help please and thank you!
Answer:
height = 9 in
Step-by-step explanation:
The formula for volume (V) of a rectangular prism is V = lwh, where l is the length, w is the width, and h is the height
In the question, we're given the volume and in the diagram, we're given the length (8.5 in.) and the width (2 in.). We can solve for l by plugging in our volume, length, and width into the formula and solving for x (the length):
[tex]153=(8.5)(2)x\\153=17x\\9=x[/tex]
Write the coordinates of the vertices after a reflection over the x-axis
The coordinates of the vertices after a reflection over the x-axis would be:
A' (0, 3)B' (0, 1)C' (6, 2)What happens reflection over x - axis ?Reflecting a figure over the x-axis causes the y-coordinates of its vertices to change signs, while their respective x-coordinates remain unchanged.
To apply this principle to the given triangle, we flip the y-coordinate of point A from -3 to 3, that of point B from -1 to 1 and also for point C changing from -2 to 2 respectively. The outcome is as follows: A (0, 3), B (0, 1) and C (6, 2). It's noted that the x-coordinate remains constant across all points of the newly transformed shape.
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a) Event and are such that P(X ) 0.6 and P(Y) 0.2 and
P[(X Y ) (X Y)] 0.45 . Find P(X Y ) . Hence, determine if and are
independent.
5 marks
b) Given that and are two events with the following probabilities :
7 1 5
( ) , ( ' ) ( )
8 12 16
P A P A B and P A B
Find
i. P(B)
3 marks
ii. P(A B')
3 marks
a)
The events X and Y are not independent.
b)
(1)The value of P(B) is 1/124.
(ii) The value of P(A ∩ B') is 9/16.
We have,
a)
We have:
P(X) = 0.6
P(Y) = 0.2
P[(X Y) ∪ (X Y')] = 0.45 (using the distributive property of set operations)
We want to find P(X ∩ Y), which we can do using the formula:
P(X ∩ Y) = P(X) + P(Y) - P(X ∪ Y)
To find P(X ∪ Y), we can use the formula:
P(X ∪ Y) = P(X) + P(Y) - P(X ∩ Y)
Using the values given, we have:
P(X ∪ Y) = 0.6 + 0.2 - P(X ∩ Y) (substituting in P(X) and P(Y))
P[(X Y) ∪ (X Y')] = 0.45 (given)
We can rewrite the left-hand side as:
P[(X Y) ∪ (X Y')] = P(X Y) + P(X Y') (using the distributive property of set operations)
Since X and Y are disjoint events, we have:
P(X Y') = P(X) - P(X ∩ Y) (using the formula for the probability of the complement of an event)
Substituting these values into the expression for P[(X Y) ∪ (X Y')], we get:
P(X Y) + (P(X) - P(X ∩ Y)) = 0.45
Simplifying, we get:
P(X Y) = 0.45 + P(X ∩ Y) - P(X)
Substituting in the values of P(X) and P(Y) given, we get:
P(X Y) = 0.45 + P(X ∩ Y) - 0.6
P(X Y) = -0.15 + P(X ∩ Y)
Since probabilities cannot be negative, we know that P(X Y) ≤ P(X ∩ Y). Therefore, we can conclude that X and Y are not independent.
b)
i. We have:
P(A) = 7/8
P(B) = 1/12
P(A ∩ B) = 5/16
We want to find P(B). We can use the formula:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Since A and B are disjoint events, we have:
P(A ∪ B) = P(A) + P(B)
Substituting in the values given, we get:
P(A) + P(B) = 7/8 + P(B) = 1 - P(B') = 11/12
Solving for P(B), we get:
P(B) = 11/12 - 7/8 = 1/24
ii.
We want to find P(A ∩ B'). We can use the formula:
P(A ∩ B') = P(A) - P(A ∩ B)
Substituting in the values given, we get:
P(A ∩ B') = 7/8 - 5/16 = 9/16
Thus,
a)
X and Y are not independent.
b)
(i) P(B) = 1/124
(ii) P(A ∩ B') = 9/16
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The diameter of a circle is 21 cm. Find its area to the nearest whole number.