in a hand of bridge the conditional probability that east has 3 spades given that north and south have a combined total of 8 spades
Answers
Therefore, the conditional probability that East has 3 spades given that North and South have a combined total of 8 spades is approximately 0.107.
To calculate the conditional probability that East has 3 spades given that North and South have a combined total of 8 spades, we need to use Bayes' Theorem.
Let A be the event that East has 3 spades and B be the event that North and South have a combined total of 8 spades. Then, we need to find P(A|B), which is the probability that East has 3 spades given that North and South have a combined total of 8 spades.
Bayes' Theorem states that:
P(A|B) = P(B|A) * P(A) / P(B)
where P(B|A) is the probability of North and South having a combined total of 8 spades given that East has 3 spades, P(A) is the probability of East having 3 spades, and P(B) is the probability of North and South having a combined total of 8 spades.
We don't have information to calculate these probabilities directly, so we need to use some assumptions. One common assumption is that each player has an equal chance of having any particular suit, and the distribution of suits is independent across players.
Under this assumption, the probability of East having 3 spades is the probability of drawing 3 spades from the remaining 10 spades, which is
P(A) = (10 choose 3) / (52 choose 13) ≈ 0.098
The probability of North and South having a combined total of 8 spades is the sum of the probabilities of the following cases:
North has 5 spades and South has 3 spades
North has 4 spades and South has 4 spades
North has 3 spades and South has 5 spades
Under our assumption, the probability of each of these cases is:
P(North has k spades) * P(South has 8-k spades) = (13 choose k) * (39 choose 8-k) / (52 choose 13)
Therefore,
P(B) = [ (13 choose 5) * (39 choose 3) + (13 choose 4) * (39 choose 4) + (13 choose 3) * (39 choose 5) ] / (52 choose 13) ≈ 0.211
Finally, we need to calculate P(B|A), which is the probability of North and South having a combined total of 8 spades given that East has 3 spades. Under our assumption, this probability can be calculated as:
P(B|A) = P(North and South have 5 spades in total) = (3 choose 2) * (10 choose 1) / (13 choose 2) ≈ 0.231
Putting it all together, we get:
P(A|B) ≈ P(B|A) * P(A) / P(B) ≈ 0.231 * 0.098 / 0.211 ≈ 0.107
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Related Questions
The drug warfarin, an anticoagulant, is metabolized by the body and leaves at a rate proportional to amount still in the body. Use this fact in both parts (a) and (b) below.
(a) If a patient, who has no Warfarin in his system, is given a pill containing 2.5 mg of Warfarin, write a differential equation for the quantity Q(t) (in mg) of warfarin in the body t hours later. Be sure to include an initial condition.
(b) A second patient, who has no Warfarin in her system, is given Warfarin intravenously at a rate of 0.5 mg/hour. Write a differential equation for the quantity Q(t) (in mg) of warfarin in the body of this patient t hours later. Be sure to include an initial condition.
*This is the problem, there is no more information provided.
These are my answers, just want to make sure they are right:
(a) Q' = -2.5Q Q(0) = 0
(b) Q' = 0.5Q - 2.5Q Q(0) = 0
Answers
The differential equation concerning the given question is Q' = -2.5Q Q(0) = 0 . Therefore the required correct answer for the question is Option A.
a) The differential equation expressing the quantity Q(t) of warfarin in the body, at t hours later when a patient who is suffering from Warfarin is given a pill containing 2.5 mg of Warfarin then,
dQ/dt = -kQ
here Q(0) = 2.5
b) The differential equation the expressing the quantity Q(t) of warfarin in the body, at t hours later when a patient who is not suffering from Warfarin is given a pill containing 0.5 mg/hr then,
dQ/dt = -kQ + r
where Q(0) = 0
Here
k = rate constant
r = rate of administration
The differential equation concerning the given question is Q' = -2.5Q Q(0) = 0 . Therefore the required correct answer for the question is Option A.
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The rate at which Warfarin leaves the body should be proportional to the amount still in the body, not a constant rate of 2.5. So the correct differential equation for part (b) is:
Q' = 0.5 - kQ, where Q(0) = 0
Where k is the proportionality constant for the rate of elimination.
Explanation
(a) Let's denote the rate of elimination as k, where k > 0. Since the elimination rate is proportional to the amount of warfarin, we can write the differential equation as:
Q'(t) = -kQ(t)
Given that the initial condition is a 2.5 mg pill, the initial condition should be:
Q(0) = 2.5
So the differential equation for part (a) is:
Q'(t) = -kQ(t), Q(0) = 2.5
(b) In this case, the patient receives warfarin intravenously at a rate of 0.5 mg/hour. Thus, we should add the rate of administration to our equation:
Q'(t) = 0.5 - kQ(t)
The initial condition is still that the patient has no warfarin in her system:
Q(0) = 0
So the differential equation for part (b) is:
Q'(t) = 0.5 - kQ(t), Q(0) = 0
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Quality is important when making cleaning products. The quality control department wants to test throughout each production day, select every 100th product produces. What type of sample is this an example of
Answers
This is an example of systematic sampling, where every nth item is selected for testing throughout the production day.
In this case, every 100th product produced is selected for quality control testing. Systematic sampling is a statistical technique used in survey methodology that involves choosing components from an ordered sampling frame. An equiprobability approach is the most typical type of systematic sampling.
This method treats the list's evolution in a cyclical manner, returning to the top after it has been completed. The sampling process begins by randomly choosing one element from the list, after which every subsequent element in the frame is chosen, where k is the sampling interval (sometimes referred to as the skip).
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Order Least to Greatest
l-4l l12l l-0.99l l0.2
Answers
Given the following LP model, which is the correct standard form? Max(Z)=2X1+X2 Restrictions / Constrains 11×1+3×2≥33
8×1+5×2≤40
7×1+10×2≤70
7×1+10×2≤70 X1,X2≥0 Use this problem's information to answer questions 19 to 21. a. Max(Z)=3×1+2X2
11×1+3×2−51≤33
8×1+5×2+52≥40
7×1+10×2+53≥70
b. Max(Z)=3×1+2×2 11×1+3×2+51=33 8×1+5×2−52=40 7×1+10×2−53=70
c. Max(Z)=3×1+2×2 11×1+3×2−51=33 8×1+5×2+52=40 7×1+10×2+53=70
d. Max(Z)=3×1+2×2 11X1+3×2+$1=33 8×1+5×2+52=40 7×1+10×2+53=70
Answers
The correct standard form for the given LP model is option C: Max(Z) = 3x1 + 2x2, subject to the constraints 11x1 + 3x2 - 5 <= 33, 8x1 + 5x2 + 5 >= 40, and 7x1 + 10x2 + 5 >= 70, with x1, x2 >= 0. This option aligns with the original objective function and constraints of the LP model.
To convert the LP model into standard form, we need to rewrite the constraints with the variables on the left-hand side and constants on the right-hand side, with inequality signs (<= or >=) consistent throughout. Additionally, we introduce slack or surplus variables to transform any non-standard constraints.
In option C, the constraints are correctly transformed as 11x1 + 3x2 - 5 = 33, 8x1 + 5x2 + 5 >= 40, and 7x1 + 10x2 + 5 >= 70. These constraints are consistent with the original model. The objective function remains the same, Max(Z) = 3x1 + 2x2.
Option A has incorrect signs in the transformed constraints, and option B introduces surplus variables (+5) instead of slack variables (-5), resulting in an incorrect standard form. Option D includes a non-standard term with a dollar sign, which is inconsistent with linear programming conventions.
Therefore, option C is the correct standard form, adhering to the original LP model's objective function and constraints.
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solve the initial-value problem.3y'' 7y' 4y = 0y(0) = 5y'(0) = −6
Answers
The general solution of the initial-value problem is y(x) = e^(-x/3)(c₁cos(2x) + c₂sin(2x)), where c₁ and c₂ are constants determined by the initial conditions.
To solve the initial-value problem, we first find the characteristic equation associated with the differential equation 3y'' + 7y' + 4y = 0. The characteristic equation is obtained by assuming a solution of the form y(x) = e^(rx), where r is an unknown constant. Substituting this into the differential equation, we get the characteristic equation:
3r^2 + 7r + 4 = 0.
We solve this quadratic equation to find the roots, which are r₁ = -1 and r₂ = -4/3. Since the roots are distinct, the general solution of the homogeneous equation is y(x) = c₁e^(-x) + c₂e^(-4x/3), where c₁ and c₂ are arbitrary constants.
To determine the particular solution that satisfies the initial conditions y(0) = 5 and y'(0) = -6, we substitute these values into the general solution:
y(0) = c₁e^(0) + c₂e^(0) = c₁ + c₂ = 5,
y'(0) = -c₁e^(0) - (4/3)c₂e^(0) = -c₁ - (4/3)c₂ = -6.
Solving this system of equations, we find c₁ = 1 and c₂ = 4. Therefore, the particular solution is y(x) = e^(-x)(cos(2x) + 4sin(2x)).
In summary, the solution to the initial-value problem 3y'' + 7y' + 4y = 0, y(0) = 5, y'(0) = -6 is y(x) = e^(-x/3)(c₁cos(2x) + c₂sin(2x)), where c₁ = 1 and c₂ = 4.
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pls help me on this question.
Answers
Answer:
36
Step-by-step explanation:
3 times 2 would equal 6. Squaring the number would be 6 times 6, equaling 36.
Answer:
36
Step-by-step explanation: Using PEMDAS we do 3x2 first which gives us 6 and then to the power of 2 which gives us 6 times it self. also 6x6 giving us 36
HELP 30 POINTS please in a hurry
Is the relation shown below a function? Use the graph below to justify your response.
(0, 0), (2, 0), (2, 2), and (3, 4)
Answers
To be a function every input value (x) can only have one output value (y)
On the graph there are 2 out put values for x = 2 so it is not a function.
The answer would be C.
Which expression has a total value of 30
4+1x12-6
(4+1x12-6)
(4+1)x(12-6)
(4+1)x12-6
Answers
Among these expressions, (4+1)x(12-6) has a total value of 30.
To determine which expression has a total value of 30, let's evaluate each expression one by one:
4+1x12-6
Following the order of operations (PEMDAS/BODMAS), we first do the multiplication:
4 + (1x12) - 6 = 4 + 12 - 6
Now, we do the addition and subtraction from left to right:
16 - 6 = 10
(4+1x12-6)
This expression has the same operations as the first one, so its total value is also 10.
(4+1)x(12-6)
First, we evaluate the expressions within the parentheses:
(5)x(6)
Now, we do the multiplication:
5 x 6 = 30
(4+1)x12-6
First, we evaluate the expression within the parentheses:
(5)x12 - 6
Now, we do the multiplication:
60 - 6
Finally, we do the subtraction:
54
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the square on the right is a scaled copy of the square on the left identify the scale factor
Answers
39/2 = 19.5
19.5/13 = 1.5
Find the future value of an annuity due of $100 each quarter for 8 1 years at 11%, compounded quarterly. (Round your answer to the nearest cent.) $ 5510.02 X
Answers
The future value of an annuity due of $100 each quarter for 8 years at 11%, compounded quarterly, is $5,510.02.
To calculate the future value of an annuity due, we need to use the formula:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future value of the annuity
P = Payment amount
r = Interest rate per period
n = Number of periods
In this case, the payment amount is $100, the interest rate is 11% per year (or 2.75% per quarter, since it is compounded quarterly), and the number of periods is 8 years (or 32 quarters).
Plugging in these values into the formula, we get:
FV = 100 * [(1 + 0.0275)^32 - 1] / 0.0275 ≈ $5,510.02
Therefore, the future value of the annuity due is approximately $5,510.02.
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sean has a total of 60 books on his book shelf of these, 25 are mystery books, 20 are fantasy books, 10 are biography books, and 5 are science books.
Answers
Answer:
Step-by-step explanation:
total type of books are 4 types
the probability of one book is 60
so the probability of type of a book is 4/60=1/15
1 Select the correct answer. Kalid simplified a polynomial expression as shown. (6x3 + 8x2 − 7x) − (2x2 + 3)(x − 8) step 1 (6x3 + 8x2 − 7x) − (2x3 − 16x2 + 3x − 24) step 2 6x3 + 8x2 − 7x − 2x3 − 16x2 + 3x − 24 step 3
Answers
Answer:
So, the step1 is correct.
Step-by-step explanation:
The expression is
\((6 x^3 + 8 x^2 - 7 x)-(2x^2 + 3)(x- 8)\\\\(6 x^3 + 8 x^2 - 7 x) - (2x^3 - 16 x^2 + 3 x - 24)\\\\6 x^3 + 8 x^2 - 7 x - 2 x^3 - 16 x^2 + 3 x - 24\\\\4 x^3 - 8 x^2 - 4 x - 24\)
So, the step 1 is correct.
I need help with these four problems please
Solve for x: 1:5x = 30
Solve for x: 2/3x = - 12
Solve for x: 2/3x - 1 = 5
Solve for x: 4(x - 2) - 3 = 9
Answers
Answer:
x = 20
x = -18
x = 7/15
x = 5
What is the answer to y=-6x-3, -8x-3y=-1.
Answers
Answer:
x=−y/6− 1/2
x= 1−3y/8
hope it helps
In order to fairly set flat rates for auto mechanics, a shop foreman needs to estimate the average time it takes to replace a fuel pump in a car. How large a sample must he select if he wants to be 90% confident that the average time is within 20 minutes of the sample average? Assume the standard deviation of all times is 40 minutes.
Answers
Answer:
ME = 1.96(45)/sqrt(n) 25 = 1.96(45)/sqrt(n) n = (1.96(45)/25)^2 = 6
Step-by-step explanation:
yw
A chess player ran a simulation twice to estimate the proportion of wins to expect using a new game strategy. Each time, the simulation ran a trial of 1,000 games. The first simulation returned 212 wins, and the second simulation returned 235 wins. Construct and interpret 95% confidence intervals for the outcomes of each simulation.
Answers
We are are 95% confident that the true proportion of wins using the new strategy will be between 0.1812 and 0.242895 in first simulation and between 0.1948 and 0.2732 in second simulation.
A chess player ran a simulation twice to estimate the proportion of wins to expect using a new game strategy. Each time, the simulation ran a trial of 1,000 games. The first simulation returned 212 wins, and the second simulation returned 235 wins. Construct and interpret 95% confidence intervals for the outcomes of each simulation.
A 95% confidence interval gives us a range of values that we are 95% confident contains the true proportion of wins that the new game strategy will produce in the long run. To construct the confidence interval for each simulation, we can use the following formula:
CI = p ± 1.96 * sqrt(p * (1 - p) / n)
where p is the sample proportion of wins, n is the number of trials, and 1.96 is the z-score corresponding to a 95% confidence level.
For the first simulation, p = 212 / 1000 = 0.212 and n = 1000, so the confidence interval is:
CI = 0.212 ± 1.96 * sqrt(0.212 * (1 - 0.212) / 1000)
CI = (0.1812, 0.2428)
This means that we are 95% confident that the true proportion of wins using the new strategy will be between 0.1812 and 0.2428.
For the second simulation, p = 235 / 1000 = 0.235 and n = 1000, so the confidence interval is:
CI = 0.235 ± 1.96 * sqrt(0.235 * (1 - 0.235) / 1000)
CI = (0.1948, 0.2732)
This means that we are 95% confident that the true proportion of wins using the new strategy will be between 0.1948 and 0.2732.
In general, larger sample sizes lead to narrower confidence intervals. In this case, both confidence intervals overlap, indicating that the two simulations are consistent with each other. This gives us additional confidence in the estimated proportion of wins using the new strategy.
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Answer:
the confidence interval for the first simulation is (0.187, 0.237), and the confidence interval from the second simulation is (0.209, 0.261). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.187 and 0.237. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.209 and 0.261.
Step-by-step explanation:
got it right on the test :)
The integers r, s and t all have the same remainder when divided by 5. What is the value of t?
(1) r + s = t
(2) 20 <= t <= 24
Answers
Let's analyze the given information and the statements provided.
We are told that the integers r, s, and t all have the same remainder when divided by 5. This means that these integers can be written in the form:
r = 5n + k
s = 5m + k
t = 5p + k
where n, m, and p are integers representing quotients and k is the common remainder.
Statement (1) r + s = t:
If r + s = t, we can substitute the expressions for r and s:
(5n + k) + (5m + k) = 5p + k
Combining like terms:
10n + 10m = 5p
Dividing both sides by 5:
2n + 2m = p
From this equation, we can see that p must be an even number. However, we cannot determine the exact value of t based on this equation alone. Statement (1) is not sufficient to answer the question.
Statement (2) 20 ≤ t ≤ 24:
This statement provides a range for the possible values of t. Since t has the same remainder when divided by 5 as r and s, it must be congruent to k modulo 5. From the given range, the only number that satisfies this condition is t = 20.
However, we need to consider the combined information from both statements to reach a conclusion.
By considering both statements, we find that the only value that satisfies both conditions is t = 20.
the value of t is 20.
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find the dimensions of the green space if it's length must be 40 ft less then twice its width with a total area of 33,600 ft^2
I found the equation but I don't know how to find the final width and length
Answers
Answer:
length = 240 units
Width = 140 units
Step-by-step explanation:
Width = w
Length = 2w - 40 ft
Area = 33,600 square feet
length * width = 33600
(2w - 40) *w = 33600
2w² - 40w = 33600
2w² - 40w - 33600 = 0
Divide the equation by 2
w² - 20w - 16800 = 0
Sum = -20
Product = -16800
Factors = -140 , 120
w² -140w + 120w - 140 * 120 = 0
w(w - 140) + 120(w - 140) = 0
(w - 140)(w + 120) = 0
w +120 = 0 is ignored because width won't be in negative.
w - 140 = 0
w = 140 units
length = 2*140 - 40
= 280 - 40
= 240 units
would it be appropriate to use the normal approximation for the number of winning plays? why or why not?
Answers
Whether or not normal approximation can be used for number of winning plays depends on sample size, probability of winning, and the distribution of the data. Careful consideration should be given to these factors before using th normal approximation.
The normal approximation can be used when the sample size is large enough and the distribution is approximately normal. In the case of winning plays, it depends on the number of total plays and the probability of winning.
If the number of total plays is large enough, such as in the case of a national lottery with millions of tickets sold, then the normal approximation can be used to estimate the number of winning plays. The probability of winning is usually very low, so the distribution can be approximated as a normal distribution.
However, if the number of total plays is small, such as in the case of a small local raffle, the normal approximation may not be appropriate. In this case, the distribution may not be normal and the sample size may not be large enough to justify the use of the normal approximation.
Additionally, if the probability of winning is very high or very low, the normal approximation may not be appropriate. For example, if the probability of winning is close to 0 or 1, the distribution may be skewed and the normal approximation may not accurately reflect the true distribution.
In conclusion, whether or not the normal approximation can be used for the number of winning plays depends on the sample size, probability of winning, and the distribution of the data. Careful consideration should be given to these factors before using the normal approximation.
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A rectangular swimming pool is 19 meters long, 13
1
2
meters wide, and 3
1
2
meters deep. What is its volume?
Answers
Answer:
897 3/4 m^3
Step-by-step explanation:
V = l*w*h
V = 19 * 13 1/2 * 3 1/2
Change the mixed number to improper fractions
V = 19 * 27/2 * 7/2
V =3591/4
Now change the improper fraction back to a mixed number
V = 897 3/4 m^3
Find (f•g)(x) when f(x)=sqrt x+3/x and g(x)=sqrt x+3/2x
Answers
The expression for (f•g)(x) is √x² + 6x + 9/ 2x²
What is a function?A function is an expression or rule showing the relationship between a dependent and independent variable.
From the information given we have that;
f(x) = \(\sqrt{\frac{x + 3}{x} }\)g(x) = \(\sqrt{\frac{x + 3}{2x} }\)(f•g)(x) means to multiply both functions;
\(\sqrt{\frac{x + 3}{x} } *\sqrt{\frac{x + 3}{2x} }\)
Multiply through
\(\sqrt{\frac{x^2 + 3x + 3x + 9}{2x^2} }\)
Add like terms
\(\sqrt{\frac{x^2 + 6x + 9}{2x^2} }\)
Thus, the expression for (f•g)(x) is √x² + 6x + 9/ 2x²
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1. Evaluate algebraic expression for the given value of "y". 6y -5 for y =7
Answers
-5
———
37
Is a triangle with side lengths of 9 feet, 12 feet, and 16 feet a
right triangle?
Answers
Answer:
No
Step-by-step explanation:
Suppose that you want to model the height of a ider on a Feris wheel as a function of time, in minutes. If the rider is
at the bottom of the Ferris wheel at t = 0 minutes, which of the following would be easiest to use?
A) the cosine function unreflected
B) the sine function unreflected
C) the cosine function reflected about its midline
D) the sine function reflected about its midline
Answers
Using trigonometric functions, it is found that the correct option regarding the appropriate function is:
B) the sine function unreflected
What are the trigonometric functions?The most famous are the sine and cosine, which give information about the angles.
In this problem, the rider is at the bottom of the Ferris wheel at t = 0, hence f(0) = 0, which is true for the sine function, which means that option B is correct.
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Answer:
Answer is C, the cosine function reflected about its midline
Step-by-step explanation:
Find the measure of angle B.
Answers
Answer:
C) 70 degrees
Step-by-step explanation
It cant be A bc its bigger than 110.
Its definitly not 20
and its not 110 bc it would be the same size.
3. A train travels 20 km at a uniform speed of 60 km/h and the next 20 km at a uniform speed of 80km/h. Calculate its average speed.
Answers
Answer:
Given,
Distance traveled = 20 km
Speed = 60 km/h
So, timetaken=DistanceSpeed=2060=13h
For the next journey
Distance traveled = 20 km
Speed = 80 km/h
So, timetaken=DistanceSpeed=2080=14h
Now,
Total distance traveled = 20 + 20 = 40 km
Total time taken = 13+14=712
We know,
Averagespeed=TotaldistancetraveledTotaltimetaken=40712=68.5 km/h
Hence the average speed of the train is 68.5 km/h
x+5y\(\leq\)-15
Answers
Answer:
y<= -1/5x-3
Step-by-step explanation:
x+5y<=-15
5y<=-x-15
y<=-1/5x-3
Abandoned mines frequently fill with water. Before an abandoned mine can be reopened, the water must be pumped out. The size of pump required depends on the depth of the mine. If pumping out a mine that is D feet deep requires a pump that pumps a minimum of + 4D – 250 gallons per minute, pumping out a mine that is 150 feet deep would require a pump that pumps a minimum of how many gallons per minute?
362
500
800
1,250
1,750
Answers
Answer:
350
Step-by-step explanation:
using the formula given
4D -250 substitute 150 for D
4(150)-250 = 350.
it's not shown? but it's the answer. unless there are pieces missing to the question.
help please asap!!! working too please not just the answers!!
Answers
Answer:
Area = 4600m
explanation: I worked it out in the image attached if that helps let me know if you need a more in depth explanation step by step
Answer:
244280
Step-by-step explanation:
you divide it into three rectangles so you have three diffenet products of 6480+57800+180000 to get 244280
what is the sum of the exterior angels of a 28 sided polygon ?
Answers
Answer: All polygons follow a rule that the sum of their exterior angles will equal 360 degrees.