The prior probabilities for events A1, A2, and A3 are P(A1) = 0.50, P(A2) = 0.20, and P(A3) = 0.30. The conditional probabilities of event B given A1, A2, and A3 are P(B | A1) = 0.50, P(B | A2) = 0.40, and P(B | A3) = 0.20. (Assume that A1, A2, and A3 are mutually exclusive events whose union is the entire sample space.)
Required:
Compute P(B â© A1), P(B â© A2), and P(B â© A3).
Answers
Answer:
P( B∩ A₁ ) = 0.25
P( B∩ A₂ ) = 0.08
P( B∩ A₃ ) = 0.06
Step-by-step explanation:
As we know that
P( B∩ A₁ ) = P( B| A₁) × P(A₁)
P( B∩ A₂ ) = P( B| A₂) × P(A₂)
P( B∩ A₃ ) = P( B| A₃) × P(A₃)
As we have
P(A₁) = 0.50, P(A₂) = 0.20, and P(A₃) = 0.30.
P(B | A₁) = 0.50, P(B | A₂) = 0.40, and P(B | A₃) = 0.20
⇒P( B∩ A₁ ) = P( B| A₁) × P(A₁)
= 0.50(0.50)
= 0.25
⇒P( B∩ A₁ ) = 0.25
Now,
⇒P( B∩ A₂ ) = P( B| A₂) × P(A₂)
= 0.40(0.20)
= 0.08
⇒P( B∩ A₂ ) = 0.08
Now,
⇒P( B∩ A₃ ) = P( B| A₃) × P(A₃)
= 0.20(0.30)
= 0.06
⇒P( B∩ A₃ ) = 0.06
∴ we get
P( B∩ A₁ ) = 0.25
P( B∩ A₂ ) = 0.08
P( B∩ A₃ ) = 0.06
Related Questions
Given the function h(x) = -22 + 4x + 11, determine the average rate of change of the function over the interval 0 < x < 6. Answer: Submit Answer attempt to
Answers
Answer:
Step-by-step explanation:
First of all, I'm going to assume that you accidentally left out an x-squared term on that -22. Going with that assumption, the average rate of change is the same thing as the slope between 2 points on that graph. It's parabolic, so there is no slope anywhere that is constant except for at a line that is tangent to a point. Our line is a secant line, not a tangent line. Since that is calculus and finds the instantaneous rate of change, I'm assuming that this is not calculus. The method is simple: plug 0 in for x in the function and you'll get a y value for that x; plug 6 in for x and you'll get a y value for that x. Then you plug both those coordinates into the slope formula to find the slope between the 2 points on the graph.
\(h(0)=-22(0)^2+4(0)+11\\h(0)=11--->(0,11)\\h(6)=-22(6)^2+4(6)+11\\h(6)=-757\)
That gives us the coordinate (6, -757). Plugging into the slope formula:
\(m=\frac{-757-11}{6-0}=\frac{-768}{6}=-128\)
I opened a grocery account at my bank with $100. Every week thereafter, I withdraw $45 from the account to pay for groceries. If x is the number of weeks I've had the account, then y is the amount in the account. Find an equation of a line in the form y = mx + b that describes my grocery account balance.
Answers
Answer:
y=-45x + 100
Step-by-step explanation:
The slope-intercept form is y=mx+b where m is the slope and b is the y-intercept or in other words the initial amount (when x is 0). Since you start off with 100 dollars the y-intercept is going to be 100 since after 0 weeks (when you opened the account) you put 100 dollars in... so you should have 100 dollars. The slope is going to be -45 since you are withdrawing 45 each week so the value is going to be decreasing by 45 every week. If you put that together you get y=-45x+100
A shoe manufacturer claims that among the general adult population in the United States that the length of the left foot is longer than the length of the right foot. To compare the average length of the left foot with that of the right foot, we will take a random sample of adults and measure the length of the left foot and then the length of the right foot. Based on our sample, does the data indicate that the length of the left foot is greater than the length of the right foot? Is the hypothesis one-tailed or two-tailed?
Answers
We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot.
How to test the data indicate that the length of the left foot is greater than the length of the right foot?A statistical test is required to determine whether the length of the left foot is greater than the length of the right foot. The null hypothesis states that there is no difference in average length between the left and right feet. The alternative hypothesis is that the left foot's average length is greater than the right foot's average length.
This hypothesis is one-tailed, as we are only interested in whether the left foot is longer than the right foot. We are not considering the possibility that the right foot could be longer than the left foot.
A t-test can be used to determine whether the difference in average length between the left and right feet is statistically significant. We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot if the p-value of the t-test is less than the chosen significance level (e.g., 0.05).
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how many ping pong balls do you need if you want to arrange them in the shape of an equilateral triangle with 23 rows
Answers
You would need a total of 276 ping pong balls
Step by step explanation:
To determine the number of ping pong balls needed to form an equilateral triangle with 23 rows, we can calculate the total number of balls in the triangle. In an equilateral triangle, each row has one more ball than the previous row. The formula for the sum of the first n natural numbers is given by:
Sum = (n * (n + 1)) / 2
In this case, we want to find the sum of the first 23 natural numbers. Substituting n = 23 into the formula, we get:
Sum = (23 * (23 + 1)) / 2 = 276
Therefore, you would need 276 ping pong balls to arrange them in the shape of an equilateral triangle with 23 rows.
anyone know???
x²-3x+2
Answers
Answer:
-x+2
Step-by-step explanation:
X has the power of two so two x minus three x is a minus and because two isnt a x u just leave it at two
solve the absolute value equation
2 = |x|-1
Answers
If you're looking for x, then:
2 = |x|-1
lxl-1 = 2
lxl-1+1=2+1
lxl=3
so x = -3, x=3
whats 1,000,000 times 1,00,000 =
Answers
Answer:
\(10000000000\)Step-by-step explanation:
\(1,000,000\times 1,00,000\)
\(=10000000000\)
Have a good day!
PLEASE HELP ME
The function f(x) = -2(4)^x+1 +140
represents the number of tokens a child has x hours after arriving at an arcade.
What is the practical domain and range of the function?
If necessary, round to the nearest hundredth.
The practical domain of the situation is ?
The practical range of the situation is ?
PLEASE SEE PHOTO FOR FUNCTION
Answers
The function f(x) = -2(4)ˣ⁺¹ +140 represents the number of tokens a child has x hours after arriving at an arcade. The practical domain and range of the function are x ≥ 0 and The practical range of the situation is [140, ∞).
The given function is f(x) = -2(4)ˣ⁺¹+ 140, which represents the number of tokens a child has x hours after arriving at an arcade.
To determine the practical domain and range of the function, we need to consider the constraints and limitations of the situation.
For the practical domain, we need to identify the valid values for x, which in this case represents the number of hours the child has been at the arcade. Since time cannot be negative in this context, the practical domain is x ≥ 0, meaning x is a non-negative number or zero.
Therefore, the practical domain of the situation is x ≥ 0.
For the practical range, we need to determine the possible values for the number of tokens the child can have. Looking at the given function, we can see that the term -2(4)ˣ⁺¹represents a decreasing exponential function as x increases. The constant term +140 is added to shift the graph upward.
Since the exponential term decreases as x increases, the function will have a maximum value at x = 0 and approach negative infinity as x approaches infinity. However, due to the presence of the +140 term, the actual range will be shifted upward by 140 units.
Therefore, the practical range of the situation will be all real numbers greater than or equal to 140. In interval notation, we can express it as [140, ∞).
To summarize:
- The practical domain of the situation is x ≥ 0.
- The practical range of the situation is [140, ∞).
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Tom bought a bicycle on hire purchase from a store. He made a down payment of $250.00 and paid $20.75 every month for a year . How much money did he pay in all?
Answers
Answer:
$499
Step-by-step explanation:
He payed at first a down payment = 250
and 20.75 a month for a year
and there is 12 months in a year which means he payed 20.75 12 times multiply these numbers 12x20.75
=$249
Plus the down payment
=249+250
=$499
determine the value of X?
Determine the Magnitude of FTD?
Answers
The value of x is 50 and FTD = 130°
How to find the value of x?Both of the angles in the diagram must have the same measure because are vertical, then:
3x - 20 = 2x + 30
3x - 2x = 30 + 20
x = 50
That is the value of x.
And we can see that FTD = 2x + 30 = 2*50 + 30 = 130
That is the measure.
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NEED HELP ASAP
please give me the answer asap.
Answers
Answer:
you again ask your family
Step-by-step explanation:
Answer:
im not a man or a woman i am...
Step-by-step explanation:
DINOSAURR RAWr
math hw for tonight
help solve this problem! Thank you!
ap cal bc
Answers
Answer:
3t^2i + 2tj is the correct answer.
Simplify
8!/(8-2)
A. 720
b. 0.018
C. 8
d. 56
e. 40320
f. 1.333
Answers
Answer:
D) 56
Step-by-step explanation:
\(\displaystyle \frac{8!}{(8-2)!}=\frac{8!}{6!}=\frac{8*7*6*5*4*3*2*1}{6*5*4*3*2*1}=8*7=56\)
The sides of a triangle are 21 ,29 , and 11 . Use the Pythagorean Theorem to determine if the triangle is right, acute, or obtuse. The triangle is because the square of the largest side the sum of the squares of the other two sides.
Answers
The triangle is obtuse because 11^2 + 21^2 does not equal 29^2.
The Pythagorean Theorem states that the sum of the squares of the two shorter sides of a triangle must equal the square of the longest side in order for the triangle to be a right triangle.
We can use this theorem to determine the type of triangle by calculating the square of the longest side (29^2), and then comparing it to the sum of the squares of the other two sides (11^2 + 21^2). Since 11^2 + 21^2 does not equal 29^2, the triangle is obtuse.
The Pythagorean Theorem states that the sum of the squares of the two shorter sides of a triangle must equal the square of the longest side in order for the triangle to be a right triangle.
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A cylinder open on both ends has a diameter of 10 decimeters(dm) and a height of 10 decimeters(dm). What is the
surface area of the cylinder?
314 dm ²
471 dm ²
628 dm ²
157dm2
Answers
the surface area of the cylinder is approximately 471 dm².
Now, For the surface area of the cylinder, we need to find the lateral area and the area of the two circular bases.
Since, The formula for the lateral area of a cylinder is
L = 2πrh,
where r is the radius of the cylinder and h is the height.
In this case, the diameter is 10 dm,
So the radius is 5 dm.
And the height is also 10 dm.
Therefore, the lateral area is:
L = 2πrh
L = 2π(5 dm)(10 dm)
L = 100π dm²
The formula for the area of a circle is
A = πr²,
where r is the radius.
In this case, the radius is 5 dm,
So the area of each base is:
A = πr²
A = π(5 dm)²
A = 25π dm²
To find the total surface area, we add the lateral area and the area of the two bases:
SA = 2(Area of Base) + Lateral Area
SA = 2(25π dm²) + 100π dm²
SA = 50π dm² + 100π dm²
SA = 150π dm²
Substitute pi as 3.14, we can calculate:
SA ≈ 150(3.14) dm²
SA ≈ 471 dm²
Therefore, the surface area of the cylinder is approximately 471 dm².
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Tickets for a raffle costs
9. There were 709 tickets sold. One ticket will be randomly selected as the winner, and that person wins
1300. For someone who buys a ticket, what is the Expected Value (the mean of the distribution)?
If the Expected Value is negative, be sure to include the "-" sign with the answer. Express the answer rounded to two decimal places.
Expected Value = $
Answers
The expected value of the raffle ticket is $-7.17.
What is the expected value?The expected value is the probability-weighted value.
It is computed by multiplying the sum of the values by the probability of winning.
In mathematics, the expected value describes the product of the probability of an event occurring and the value of the actual observed occurrence.
The cost per raffle ticket = $9
The number of tickets sold = 709
The winning value = $1,300
The probability of winning the raffle = 1/709
The expected value = $-7.17 [($1,300 x 1/709) - $9].
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Which statement is true about 68 and 112?
A. 68 is greater than 112 because the benchmark 0 is closer to 68 than it is to 112.
B. 68 is less than 112 because 68 is less than the benchmark 12, and 112 is greater than the benchmark 12.
C. 68 is less than 112 because benchmark 1 is closer to 68 than it is to 112.
D.68 is greater than 112 because 68 is greater than the benchmark 12, and 112 is less than the benchmark 12.
Answers
Answer:
D.68 is greater than 112 because 68 is greater than the benchmark 12, and 112 is less than the benchmark 12.
A rectangular prism is 4 units high 2 units wide and 6 units long What is the surface area in square units
Answers
Answer:
Step-by-step explanation:
surface area=2×l×b+2(l+b)×h=2(lb+lh+bh)
=2(6×2+6×4+2×4)
=2(12+24+8)
=2×44
=88 square units.
The surface area of a given rectangular prism is 88 square units.
Given that, a rectangular prism is 4 units high 2 units wide and 6 units long.
We need to find the surface area of a rectangular prism in square units.
What is the surface area of a rectangular prism?The total area of a rectangular prism's rectangular faces is referred to as the prism's surface area. There are two different kinds of it: lateral surface area and total surface area. In contrast to the lateral surface area, which only includes the lateral faces and excludes the base areas, the total surface area of a rectangular prism refers to the area of all six faces.
The surface area of rectangular prism formula =2×l×b+2(l+b)×h=2(lb+lh+bh)
Now, 2(6×2+6×4+2×4)
=2(12+24+8)
=2×44
=88 square units
Therefore, the surface area of a given rectangular prism is 88 square units.
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If f (x) = 2 x + 5 and three-halves are inverse functions of each other and StartFraction 41
Answers
The inverse of the function → f(x) = 2x + 5 is → f⁻¹(x) = (x/2) - (5/2).
What is the procedure to find inverse of function ?Inverse of a function can be calculated by following the steps mentioned below -
Step 1 - Replace {y} with {x} and vice - versa.Step 2 - Rewrite the equation by solving for {y}.Step 3 - Replace {y} with f⁻¹(x).According to the question, the equation given is as follows
y = f(x) = 2x + 5
y = 2x + 5
Replace 'y' with 'x', we get -
x = 2y + 5
Now, solve for y -
2y = x - 5
y = (x/2) - (5/2)
Replace 'y' with f⁻¹(x) -
f⁻¹(x) = (x/2) - (5/2)
Hence, the inverse of the function → f(x) = 2x + 5 is → f⁻¹(x) = (x/2) - (5/2).
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need help badly image above
Answers
Answer:
2m³ + 9m² - 19m - 11
Step-by-step explanation:
3f(m) - 2g(m)
= 3(3m² - 5m + 1) - 2(- m³ + 2m + 7) ← distribute parenthesis
= 9m² - 15m + 3 + 2m³ - 4m - 14 ← collect like terms
= 2m³ + 9m² - 19m - 11
Complete the table above. Also, find the number students that can be chaperoned by 9 teachers.
Answers
The number of students would be 45
How many terms are in the expression
3a + 2b + C + 100
Answers
Answer:
4
Step-by-step explanation:
3a, 2b, (1)c, and 100 are all their own terms. None of them having the same variable making them each their own. (including whole numbers without a variable, the absence of a variable still means its a term)
Find the value of x
Answers
Answer: The value of x is 49.
Step-by-step explanation:
To find the value of x, you will first need to cross multiply the fractional variables together.
5x - 80 = 3x + 18
Then, move the numerical term 80 to the right side of this equation and add it to 18.
5x - 80 = 3x + 98
Move 3x to the left side of the equation and subtract it this time to the variable 5x.
2x = 98
Finally, you divide both of the equation's sides by 2 and you will get 49.
x = 49
When you actually add x to this problem, you would get 33/55.
49 - 16/49 +6 = 33/55
You can then simplify 33/55 and get the same answer 3/5.
3/5
Therefore, the value of x for this variable equation with the fractions would be equal to x = 49. Hope this helps!
-From 5th Grader Honors Student
Math. Please Help Me Answer All The Questions Please
Find the equation of the line that passes though the following points
1. (0,0),(1,3)
2. (3-2),(-6,3)
3. (-2,3),(3,-4)
4. (4,3),(06)
5. (0,2),2,-2)
6. (2,3),(0,4)
7. (2,3),(-1,-3)
8. (0,0),(-6,-6)
9. (-1,1),(2,4)
10. (1,1),(0,5
Answers
o find the equation of a line that passes through two points, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).
1. The equation of the line that passes through (0,0) and (1,3) is y = 3x.
2. The equation of the line that passes through (3,-2) and (-6,3) is y = -x/2 - 1.
3. The equation of the line that passes through (-2,3) and (3,-4) is y = -7/5x - 6/5.
4. The equation of the line that passes through (4,3) and (0,6) is y = 3/2x + 3.
5. The equation of the line that passes through (0,2) and (2,-2) is y = -x.
6. The equation of the line that passes through (2,3) and (0,4) is y = 2x + 1.
7. The equation of the line that passes through (2,3) and (-1,-3) is y = -2x - 5.
8. The equation of the line that passes through (0,0) and (-6,-6) is y = -x.
9. The equation of the line that passes through (-1,1) and (2,4) is y = 3/2x + 1/2.
10. The equation of the line that passes through (1,1) and (0,5) is y = 5x - 5.
Find the slope of the line that passes through (-13, 64) and (69, 23).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answers
Answer:
-2
Step-by-step explanation:
Find the missing term 24:96=5:?
Answers
Answer:
24:96=5:x
Step-by-step explanation:
x=(96*5)/24=20
make it braintliest please
pls help this is not graded
Answers
Answer:
70 degrees
Step-by-step explanation:
Help me with this math question :)
Answers
\( \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star\)
To prove two lines parallel, we need to check if the two angles involving the lines acts as some angle pair with defininte property.
In the given figure,
Angle 3 is congruent to Angle 19( by Alternate Exterior angle pair )
Hence, the two lines are parallel.
\( \qquad \large \sf {Conclusion} : \)
Option C is correctassuming a frictionless maaless pulley determine the acceleration of the blocks once they are released from rest
Answers
Answer: Assuming a frictionless, massless pulley, the acceleration of the blocks once they are released from rest can be determined using the equation for acceleration:
a = F/m
where a is the acceleration, F is the force acting on the object, and m is the mass of the object.
In this case, the force acting on the blocks is the force of gravity, which is equal to the weight of the blocks. The weight of an object is equal to the mass of the object multiplied by the acceleration due to gravity, which is 9.8 m/s^2 on Earth. Therefore, the force acting on the blocks is equal to the mass of the blocks multiplied by 9.8 m/s^2.
The acceleration of the blocks will be equal to the force acting on them divided by the mass of the blocks. This means that the acceleration of the blocks will be equal to their weight divided by their mass.
Therefore, to determine the acceleration of the blocks once they are released from rest, you will need to know their mass and their weight. Once you have this information, you can use the equation a = F/m to calculate their acceleration.
need help with some practice questions since all are different types I'm asking alot sorry!
Answers
Answer:
Yes
Step-by-step explanation:
If they're perpendicular, that means that angle ECM = 90 degrees and angle ACE = 90 degrees. To figure out if this works, plug that into the two equations they give:
ECM = 3x + 15
becomes
90 = 3x + 15
75 = 3x
25 = x
ACE = 4x - 10
becomes
90 = 4x - 10
100 = 4x
25 = x
Since you get x = 25 for both, you know that they are perpendicular because they both measure 90 degrees