Given that the probability of event A is Pr(A) = 1/3 and the probability of the union of event A and event B, namely AUB, is Pr(AUB) = 5/6. The probability of event B is Pr(B) = 2/3.
Suppose that event A and event B are disjoint.
The probability of event B is Pr(B) = 1/2.
To find the probability of event B.
For disjoint events A and B, we know that A ∩ B = Φ (empty set).
Thus, we can express the union of A and B as: AUB = A + B, where A and B are disjoint.
In general, the probability of the union of two events can be expressed as: P(AUB) = P(A) + P(B) - P(A ∩ B).
For disjoint events, the intersection of the events is always an empty set.
Thus, P(A ∩ B) = 0.
Using this information, we can write:
P(AUB) = P(A) + P(B) - P(A ∩ B)
= P(A) + P(B) - 0
= P(A) + P(B)
Given P(A) = 1/3 and P(AUB) = 5/6, we can solve for P(B) as follows:
5/6 = P(A) + P(B)
=> P(B) = 5/6 - P(A)
=> P(B) = 5/6 - 1/3
=> P(B) = 2/3
Thus, the probability of event B is Pr(B) = 2/3.
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3. This spinner is divided into eight equal-sized sections. Each section is labeled with a number
Jake spins the arrow on the spinner once.
Drag and drop the events into the correct order from least likely to most likely.
Answer:
Least Likely: Arrow lands on a section labeled with an odd number.
_____: Arrow lands on a section labeled with the number 1.
Most Likely: Arrow lands on a section labeled with a number less than 4.
Step-by-step explanation:
The spinner:
There are 8 sections, 4 labeled with the number 1, 2 labeled with the number 3, 1 labeled with the number 3, and 1 labeled with the number 4.
Probabilities of the spinner:
Probability of landing on 1: 4/8 - 50%Probability of landing on 2: 1/8 - 12.5%Probability of landing on 3: 2/8 - 25%Probability of landing on 4: 1/8 - 12.5%The options:
A - Arrow lands on a section labeled with an odd number.
B - Arrow lands on a section labeled with the number 1.
C - Arrow lands on a section labeled with a number less than 4.
The least likely possibility out of the options would be B because, while a 50% chance sounds like a lot, it is the least of the three options.The mid possibility out of the options would be A. The odd numbers labeled on the spinner make up 75% of the whole. (1s and 3s - 50% + 25%)The most likely possibility out of the options is C because it accounts for every section except for the single section labeled with the number 4. (100% - 12.5%, 87.5%)Complete the table below for the equation y=1+2x
Which of these describe a unique polygon
Answer: d
Step-by-step explanation:
Find the distance between (5, -1) and (1,-5).
4 units I assume. that it is a very basic answer tho and I am not sure if a specific formula or lesson was supposed to be applied to that andwer
20 POINTS‼️‼️Which of the following does NOT represent the number of months in a year?
A and b are in the attached photo.
C. y= 12x, where x represents the number of years and y represents the number of months
D. There are 96 months in 8 years.
‼️PLEASE DO YOUR BEST TO SHOW WORK FOR BRAINLIEST‼️
Answer:
B because when you multiply the first number by twelve the first two are correct but the second ones are not
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
12 times 6 = 72, not 60
A company has dump trucks that repeatedly go through three activities: loading, weighing, and travelling. Assume that there are eight trucks and that, at time 0, all eight are at the loaders. Weighing time per truck on the single scale is uniformly distributed between 1 and 9 minutes, and travel time per truck is exponentially distributed with mean 85 minutes. An unlimited queue is allowed before the loader(s) and before the scale. All truck can be travelling at the same time. Management desires to compare one fast loader against the two slower loaders currently being used. Each of the slow loaders can fill a truck in from 1 to 27 minutes, uniformly distributed. The new fast loader can fill a truck in from 1 to 19 minutes, uniformly distributed. The basis for comparison is mean system response time over a 40 hour time horizon, where a response time is defined as the duration of time from a truck arrival at the loader queue to that truck's departure from the scale. Perform statistically valid comparison of the two options simulated using common random numbers. a
To perform a statistically valid comparison of the two loader options, we can use simulation and common random numbers. We simulate the process over a 40-hour time horizon and compare the mean system response times for each loader option.
For the two slower loaders, we generate random numbers uniformly distributed between 1 and 27 minutes to represent the time taken to fill a truck. For the fast loader, we generate random numbers uniformly distributed between 1 and 19 minutes.
By simulating the process multiple times using the same set of random numbers (common random numbers), we can compare the mean system response times between the two loader options.
After running the simulation, we calculate the mean system response time for each loader option by averaging the response times of all trucks. We repeat the simulation multiple times (e.g., 100 or more) to obtain reliable estimates of the mean system response times.
Once we have the mean system response times for each loader option from multiple simulation runs, we can perform a statistical analysis to determine if there is a significant difference between the two options.
This analysis can be done using a suitable statistical test, such as a t-test or confidence interval analysis, depending on the distribution of the response time data and the assumptions made.
The statistical analysis will provide insights into whether the fast loader option significantly reduces the mean system response time compared to the slower loader options. A lower mean system response time would indicate better performance in terms of faster truck processing.
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You are a civil engineer designing a bridge. The walkway needs to be made of wooden planks. You are able to use either Sitka spruce planks (which weigh 3 pounds each), basswood planks (which weigh 4 pounds each), or a combination of both. The total weight of the planks must be between 600 and 900 pounds in order to meet safety code. If Sitka spruce planks cost $3.25 each and basswood planks cost $3.75 each, how many of each plank should you use to minimize cost while still meeting building code?
The optimal solution to minimize cost while meeting the building code is to use 0 Sitka spruce planks and 150 basswood planks.
How to Minimize Cost Using Function Equations?To minimize the cost while meeting the building code, let's assume we use x Sitka spruce planks and y basswood planks.
We want to minimize the cost, so our objective function is the cost of the planks. The cost is given by:
Cost = 3.25x + 3.75y
We also have the constraint that the total weight of the planks must be between 600 and 900 pounds:
3x + 4y ≥ 600
3x + 4y ≤ 900
To solve this optimization problem, we can use linear programming. We'll use the Simplex method to find the optimal solution.
Let's rewrite the constraints in standard form:
-3x - 4y ≤ -600
3x + 4y ≤ 900
Now we have the following system of equations:
-3x - 4y ≤ -600
3x + 4y ≤ 900
The feasible region is a quadrilateral with vertices at (0, 150), (0, 225), (300, 150), and (225, 0).
To minimize the cost, we need to find the corner point of the feasible region that lies on the cost line, which is given by 3.25x + 3.75y.
Let's evaluate the cost at each corner point:
Cost at (0, 150) = 3.25(0) + 3.75(150) = 562.50
Cost at (0, 225) = 3.25(0) + 3.75(225) = 843.75
Cost at (300, 150) = 3.25(300) + 3.75(150) = 1500.00
Cost at (225, 0) = 3.25(225) + 3.75(0) = 731.25
From the evaluations, we can see that the minimum cost is achieved at (0, 150), which means we should use 0 Sitka spruce planks and 150 basswood planks.
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I have an hour to do this please help
Answer:
6
Step-by-step explanation:
27/9 =3
now 18/3
=6
I need help on this question and answering it
Answer:
75 feet
Step-by-step explanation:
the shadow to the object would be a 4:5 ratio
since the shadow of the flagpole is 60 ft,
4x=60 so x would =15
then you multiply 15 by 5 and end up with 75
Answer: 75 feet
Step-by-step explanation: trust me
 PLSSS HELP IMMEDIATELY!!!!! i’ll give brainiest, i’m not giving brainiest if u leave a link tho. (pls check whole picture!!) answer choices: (4,6) (0,1) (0,0) (5,4)
Answer:
(0, 1)
Step-by-step explanation:
All other choices do not match the two possible vertices of the square.
A regular heptagon is shown below. What is the value of x?
Answer:
108+x=180
X=180-108
X=72
The value of the exterior angle (x) in a regular heptagon is approximately 51.43 degrees.
Given is a regular heptagon with one of the exterior angle be x we need to find the value of x
To find the value of the exterior angle of a regular heptagon, we can use the formula:
Exterior Angle = 360 degrees / Number of Sides
In this case, the heptagon has seven sides, so we can substitute the values into the formula:
Exterior Angle = 360 degrees / 7
Exterior Angle ≈ 51.43 degrees
Therefore, the value of the exterior angle (x) in a regular heptagon is approximately 51.43 degrees.
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Are the ratios 18:6 and 3:1 equivalent?
Answer: no
Step-by-step explanation: here are all the ratios equivalent to 18:6 18 : 636 : 1254 : 1872 : 2490 : 30108 : 36126 : 42144 : 48162 : 54180 : 60198 : 66216 : 72234 : 78252 : 84270 : 90288 : 96306 : 102324 : 108342 : 114360 : 120378 : 126396 : 132414 : 138432 : 144450 : 150468 : 156486 : 162504 : 168522 : 174540 : 180558 : 186576 : 192594 : 198612 : 204630 : 210648 : 216666 : 222684 : 228702 : 234720 : 240738 : 246756 : 252774 : 258792 : 264810 : 270828 : 276846 : 282864 : 288882 : 294900 : 300918 : 306936 : 312954 : 318972 : 324990 : 3301008 : 3361026 : 3421044 : 3481062 : 3541080 : 3601098 : 3661116 : 3721134 : 3781152 : 3841170 : 3901188 : 3961206 : 4021224 : 4081242 : 4141260 : 4201278 : 4261296 : 4321314 : 4381332 : 4441350 : 4501368 : 4561386 : 4621404 : 4681422 : 4741440 : 4801458 : 4861476 : 4921494 : 4981512 : 5041530 : 5101548 : 5161566 : 5221584 : 5281602 : 5341620 : 5401638 : 5461656 : 5521674 : 5581692 : 5641710 : 5701728 : 5761746 : 5821764 : 5881782 : 5941800 : 600
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Answer:
yes
Step-by-step explanation:
18:6
18/6=3
6/6=1
3:1 is a simpler version of 18:6
how to read a q q q q q q q q q q q q q q q q q
Your read from left to right. Read intensively if you want to practice the fundamentals and learn vocabulary. Intensive reading is focused more on individual details of what you’re reading.
hope this helped <3
Answer:
This is how to read a
Pronounce it with your mouth open as in "ah" then smile with an "ee" sound. Say "Ay" and that's how you say A or "Ah"
How to read Q? Just pronounce it as "Kyuu" or when reading it say "Ck" with a sharper sound.
Hope this helped!
What is the volume of a cone with a radius 3 cm and a height 6 cm?
Answer:
56.55
Step-by-step explanation:
HELPPP PLSSS Choose the most appropriate translation of the English sentence.
The radius of a balloon (which depends on the amount of air inside) is 3
inches.
Answer:
A radius(radius) = 3The radius of a balloon (which depends on the amount of air inside) is 3
inches
3 questions
4 is about what percent of 9?
About what percent of 7560 is 3000?
1.3 is about what percent of 27?
Please help me my teacher does not explain how to do this well..
Write 0.4% in simplest form
Answer:
if simplest form by you mean fraction then the answer is 2/5
hope this is the answer you are looking for
Step-by-step explanation:
Which expression is equivalent to 36 + 24?
Answer:
60
Step-by-step explanation:
On Saturday, a local hamburger shop sold a combined total of 261 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Saturday?
Answer:
134 hamburgers
Step-by-step explanation:
Let H = # of hamburgers
# of cheeseburgers = 2H
H + 2H = 402
3H = 402
H = 402/3
H = 134
2. (1 point each) Let f(x) = √x and g(x) = 1/x. In the space
provided, compute each of the following, if possible:
(a) f(36)
(b) (g+f)(4)
(c) (f · g)(0)
(a) f(36) is equal to 6.
(b) (g+f)(4) = g(4) + f(4) = 9/4
(c) we cannot compute (f · g)(0).
(a) To find f(36), we substitute x = 36 into the function f(x) = √x:
f(36) = √36 = 6
Therefore, f(36) is equal to 6.
(b) To find (g+f)(4), we need to evaluate g(4) and f(4), and then add the results:
g(4) = 1/4
f(4) = √4 = 2
(g+f)(4) = g(4) + f(4) = 1/4 + 2 = 1/4 + 8/4 = 9/4
Therefore, (g+f)(4) is equal to 9/4 or 2.25.
(c) To find (f · g)(0), we need to evaluate f(0) and g(0), and then multiply the results:
f(0) = √0 = 0
g(0) = 1/0
However, g(0) is undefined because division by zero is not defined in mathematics.
Therefore, we cannot compute (f · g)(0) in this case.
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Find the missing length.
= ✓ [?]
C =
с
6
Pythagorean Theorem: a2 + b2 = c2
Enter
Answer:
Pythagoras theorem= 6 squared +11 squared
= 36 + 121
= 157
Step-by-step explanation:
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help║...................
Find the area of the figure.
Answer:
353.93 ft²
Step-by-step explanation:
Step 1:
Find the area of the Trapezoid.
(a + b) ÷ 2 × height
20 + 17 = 37
37 ÷ 2 = 18.5
18.5 × 13 = 240.5 ft²
Step 2:
Find the Area of the Semicircle:
1/2 × πr²
1/2 × 3.14 = 1.57
1.57 × 8.5² = 113.43 ft²
Step 3:
Add the two areas together:
240.5 + 113.43 = 353.93 ft²
Explain what you think that term dilation means.
Answer:
the action or condition of becoming or being made wider, larger, or more open.
Step-by-step explanation:
Cody did not understand the concepts of the “special cases” when factoring. Explain the concept of the perfect square binomial. Use an example to help explain to her how it is a special case and how to factor it using the special case rules.
A binomial expression of the form (a + b)² or (a - b)² is called a perfect square binomial.
This expression can be factored using the special case rules by rewriting it in the form
(a + b)(a + b) or (a - b)(a - b), respectively.
A perfect square binomial is a quadratic trinomial in which the first term is a perfect square and the second term is twice the product of the square root of the first term and the square root of the last term.
In the context of special cases, the perfect square binomial is a binomial that is formed by squaring a binomial.
This is a special case because it has a unique factorization, as we will see later.
An example of a perfect square binomial is (x + 4)².
This is because the first term, x², is a perfect square, and the second term, 8x, is twice the product of the square root of x² and the square root of 4, which is 2.
Hence, (x + 4)² can be factored using the special case rules as:
(x + 4)(x + 4),
which simplifies to
(x + 4)².
A perfect square binomial is a quadratic trinomial in which the first term is a perfect square and the second term is twice the product of the square root of the first term and the square root of the last term.
It is a special case because it has a unique factorization, which is given by the formula:
(a + b)² = a² + 2ab + b²
or
(a - b)² = a² - 2ab + b².
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Which solution for z makes the equation true?? 10+10+z=40=10 (pls explain why. Thanks)
Answer:
z=30
Step-by-step explanation:
40-10=30
10+10+?=30
30-10-10=10
I'm sorry cuz I don't know how to explain it
Answer:
z = 10
Step-by-step explanation:
10 + 10 + z = 40 - 10
10 + 10 + z = 30
10 + 10 + 10 = 30
since 40 - 10 = 30, then Z has to equal 10 because 10 + 10 + z needs to be 30
What does 1/3 represent for the picture below?
Answer:
c the ratio of the measure of arc QR and the circle
Step-by-step explanation:
i just took the quiz
hope this helps (:
help ASAP! Ill mark brainliest!
Answer:
55 students
Step-by-step explanation:
Just write down the answer.
Answer:
Step-by-step explanation:
Football: 500(.38)= 190
Basketball: 500(.25)= 125
55 students (65 students)
write both an explicit equation and recursive equation for the sequence 64,8,1,0,0.125..
HURRY PLEASE!!
Answer:
a(n) = n/8
Step-by-step explanation:
64/8 = 8, 8/8 = 1, 1/8 = 0.125.…
Explicit Equation: a(n) = n/8
Recursive Equation: a(1) = 64; a(n) = n/8
i dont know if this is correct or not but here you go!
if the third term is 20 and 7th is 1.25, find the 11th term
Answer:
the 11th term is 0.0000488 or 4.88*10^-5.
Step-by-step explanation:
a3 = 20, a7 = 1.25
a7 = a3r^7-3
1.25 = 20r^4
r^4 = 0.0625
r = 4th root of 0.0625
r = 0.5
a3 = a1r^3-1
20 = a1(20)^2
400a1 = 20
a1 = 0.05
a11 = 0.05(0.5)^11-1 = 0.0000488 or 4.88*10^-5