we randomly put 80balls into 40 boxes (as explained in class). question: a) f.q. what is the probability that 1st and 2nd boxes are both empty b) f.q. what is the probability that the 1st and 2nd boxes both have 3 balls? c) what is the probability that 1st box has more balls than the 2nd box?
Answers
The probability of a) is (80 * 79 * 78 * ... * 2 * 1) / (40^80), b) is (C(80, 3) * C(77, 3)) / (40^80) and c) is (number of ways for case 1 + number of ways for case 2 + ... + number of ways for case n) / (40^80).
Let us know how we arrived at the answers:
a) To find the probability that both the first and second boxes are empty, we need to determine the number of ways this can happen and divide it by the total number of possible outcomes.
First, let's calculate the number of ways the first box can be empty. Out of 80 balls, there are 80 options to choose from for the first ball, and 79 options for the second ball, and so on. This gives us 80 * 79 * 78 * ... * 2 * 1 ways to arrange the balls in the first box. Similarly, the second box can be empty in the same number of ways.
Since each ball has 40 options for which box it goes into, there are 40^80 ways to distribute the balls into the boxes.
Therefore, the probability that both the first and second boxes are empty is (80 * 79 * 78 * ... * 2 * 1) / (40^80).
b) To find the probability that both the first and second boxes have 3 balls each, we need to determine the number of ways this can happen and divide it by the total number of possible outcomes.
The number of ways to choose 3 balls out of 80 is given by the combination formula: C(80, 3) = (80 * 79 * 78) / (3 * 2 * 1).
Once we have selected the 3 balls for the first box, we need to choose 3 balls out of the remaining 77 balls for the second box. Again, using the combination formula, we have C(77, 3) = (77 * 76 * 75) / (3 * 2 * 1).
Since each ball has 40 options for which box it goes into, there are 40^80 ways to distribute the balls into the boxes.
Therefore, the probability that both the first and second boxes have 3 balls each is (C(80, 3) * C(77, 3)) / (40^80).
c) To find the probability that the first box has more balls than the second box, we need to determine the number of ways this can happen and divide it by the total number of possible outcomes.
First, let's consider the cases where the first box has more balls than the second box. We can have 1 ball in the second box and any number of balls from 2 to 80 in the first box, 2 balls in the second box and any number of balls from 3 to 80 in the first box, and so on.
For each case, we need to calculate the number of ways to arrange the balls in the first and second boxes.
The total number of ways to distribute the balls into the boxes is 40^80.
Therefore, the probability that the first box has more balls than the second box is the sum of the probabilities of each case: (number of ways for case 1 + number of ways for case 2 + ... + number of ways for case n) / (40^80).
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Related Questions
Solve the equation. You may find using algebra tiles to be helpful. 2x + 9 = 15
Answers
Answer:
\(\boxed{\bf{x=3}}\)Step-by-step explanation:
Hello! The first step in solving our equation is subtracting 9 from both sides. Upon doing this, we obtain: \(\bf 2x=15-9\), which later simplifies to \(\bf 2x=6\).
Then, we need to divide both sides by 2, since both sides are multiplied by 2. Remember, we always use inverse operations to solve equations.
We arrive at \(\boxed{\bf{x=3}}\), which is our final answer.
I hope it helped! :)
If L = 3 inches, W = 2 inches, and H = 5 inches, what is the volume of the rectangular prism?
Answers
Answer:
3 x 2 x 5 = 30
Step-by-step explanation:
To calculate a rectanglars prism all you have to do is multiply the length, width and height together.
find the variables in the figure 4x-6 5y+11 3x+22
Answers
Answer:
x and y
Step-by-step explanation:
In algebraic expressions, letters represent variables. These letters are actually numbers in disguise. In this expression, the variables are x and y. We call these letters "variables" because the numbers they represent can vary—that is, we can substitute one or more numbers for the letters in the expression.
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The ratio of Samantha’s postcards to Erica’s postcards was 8 to 5. Erica counted their actual number of postcards and found that she had 60 fewer postcards than Samantha. How many postcards does Erica have?
Answers
Let's assume that the number of postcards Samantha has is represented by x.
Given that the ratio of Samantha's postcards to Erica's postcards is 8 to 5, we can set up the following proportion:
\(\(\frac{x}{\text{{Erica's postcards}}} = \frac{8}{5}\)\)
We are also given that Erica has 60 fewer postcards than Samantha, which can be represented as:
\(\(\text{{Erica's postcards}} = x - 60\)\)
Substituting this expression into the proportion, we have:
\(\(\frac{x}{x - 60} = \frac{8}{5}\)\)
To solve for x, we can cross-multiply:
\(\(5x = 8(x - 60)\)\)
Expanding the equation:
\(\(5x = 8x - 480\)\)
Bringing the terms involving x to one side:
\(\(8x - 5x = 480\)\)
\(\(3x = 480\)\)
Dividing both sides by 3:
\(\(x = \frac{480}{3}\)\)
\(\(x = 160\)\)
Therefore, Samantha has 160 postcards.
To find out how many postcards Erica has, we substitute the value of x into the expression we derived earlier:
\(\(\text{{Erica's postcards}} = 160 - 60 = 100\)\)
Hence, Erica has 100 postcards.
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What is the solution to this equation?
5x+15 + 2x = 24 +4x
A. x = 3
B. x=9/11
C. x = 13
D. x =39/11
Answers
Answer:
the answer is A x = 3
Step-by-step explanation:
5x + 15 +2x = 24 + 4x
or, 5x + 2x - 4x = 24 - 15
or, 3x = 9
or, x = 9/3
x = 3
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Convert 1.9647 to a percent.
Answers
Answer:
196.47%
Step-by-step explanation:
1 is 100
So the rest just add in
What is the mean for the data shown in the line plot? please help fast!
a. 10
b. 6
c. 4
d. 5
Answers
Answer:
D. 5
Step-by-step explanation:
read each number from the plot. remember each x represents one number so there are 11 numbers. you divide it then it gives you 5
Answer: The answer is 6
Hopefully, this is correct!
Suppose the function f(x) = - x ^ 2 + kx + 8 is translated up 17 units and left 3 units from the parent function g(x) = - x ^ 2 . What is a possible value of
Answers
Answer:
x
y x
y
0
−
2
2
0
0
−
2
2
0
Step-by-step explanation:
Show all the calculation if it is a numerical question.
Simplify this radical. 16a5b3−−−−−√
Group of answer choices
4a2b
4a2bab−−√
16a2b
16a2bab−−√
Answers
yOU guys can just put A. B. C. or D.
Answers
Answer:
c i think
Step-by-step explanation:
what 3d shape is this
Answers
Answer:
10: Rectangular Prism
11: Pyramid
12: Triangular prism
Step-by-step explanation:
Refer to the Journal of behavioural decision making (Jan. 2007) study of how guilty feelings impact decisions, Excersise 3.59 (p.142). Recall that 57 students were assigned to a guilty state through a reading/writing task. Immediately after the task, the students were presented with decision problem where the stated option has predominantly negative features. Of those 57 students ,45 choose the stated option. Suppose 10 of 57 guilty state students are selected at random. Define x as the number in the sample of 10 who chose the stated option.
A) Find p(x=5)
(B) Find p(x=8)
(C) What is the expected value (mean) of x?
Answers
A) The value of p(x=5) is 0.2017
B) The value of p(x=8) is 0.1167
C) The expected value (mean) of x7.89.
A) We are required to find P(x = 5).P(x = 5) is the probability that 5 out of the 10 students selected chose the stated option.
Using the binomial distribution formula, we have
P(x = 5) = nCx px q(n - x)
where n = 10, x = 5, p = 45/57 = 0.789, and q = 1 - p = 1 - 0.789 = 0.211
Thus, P(x = 5) = (10C5) (0.789)5 (0.211)5= 0.2017 (rounded to four decimal places)
B) We are required to find P(x = 8).P(x = 8) is the probability that 8 out of the 10 students selected chose the stated option.
Using the binomial distribution formula, we have
P(x = 8) = nCx px q(n - x)
where n = 10, x = 8, p = 45/57 = 0.789, and q = 1 - p = 1 - 0.789 = 0.211
Thus, P(x = 8) = (10C8) (0.789)8 (0.211)2= 0.1167 (rounded to four decimal places)
C) We are required to find the expected value (mean) of x.
Using the binomial distribution formula, we have
E(x) = np
where n = 10, and p = 45/57 = 0.789
Thus, E(x) = 10 × 0.789= 7.89 (rounded to two decimal places)
Therefore, the expected value (mean) of x is 7.89.
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Kim has no more than $500 to spend on home repairs. HandyMan Co is charging her $125 for supplies needed and $25 per hour. Write and solve an inequality to show how many hours of repair she can afford.
Answers
Divide the numbers.
$125 divded by $25 = 5
Answer: Kim can afford 5 hours lf repair time. (Brainlest?)
Have a good rest of your day/night!!
A 3-column table with 4 rows is shown. The first column has entries Florida, Hawaii, Montana, Oregon. The second column is labeled Population with entries 19,317,568, 1,392,313, 1,005,141, and 3,899,353. The third column is labeled Area (miles squared) with entries 53,927, 6,423, 145,552, and 95,997.
Which statements are true? Check all that apply.
The population density for Montana can be found using the ratio 1,005,141:145,552.
The population density for Oregon can be found using the ratio 95,997:3,899,353.
The population density for Hawaii is greater than the population density for Florida.
The state with the smallest population density is Oregon.
The state with the smallest population density is Montana.
Answers
Answer:
It's the first and last one
Step-by-step explanation:
I just did it
Answer:
A) The population density for Montana can be found using the ratio 1,005,141:145,552.
E)The state with the smallest population density is Montana.
Step-by-step explanation:
5.5cm+61mm
Please help me
Answers
61mm has to be converted to cm.
Simply divide by 10 [ 10mm = 1cm ]
61 mm = (61/10) = 6.1 cm
5.5 + 6.1 = 11.6cm
OR...
Convert 5.5cm to mm by multiplying by 10
5.5cm = (5.5×10) = 55mm
55+61 = 116mm
116mm = (116/10) = 11.6cm
The answer for this question is 11.6 cm or 116 mm.
You need to convert either millimeter to centimeter or vice versa
1 cm = 10 mm
converting 5.5 cm to mm :
5.5 X 10 = 55 mm
Now, add both the values of millimeter:
55 + 61 = 116 mm
If we need answer in centimeter
we can convert 116 mm into cm
116/10 = 11.6 cm
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The correct question is :
Add 5.5 cm to 61mm
Mikaela purchased a paddleboard originally priced at $799. If all merchandise was on sale for 40% off and the state tax rate is 7.25%, what is the total amount that Mikaela spent on the paddleboard?
$537.33
$514.16
$342.77
$377.53
Answers
The total amount that Mikaela spent on the paddleboard is $514.16
What is the total amount that Mikaela spent on the paddleboard?The given parameters are:
Original cost = $799
Discount = 40%
State tax = 7.25%
The total amount that Mikaela spent on the paddleboard is calculated as
Amount = Original cost * (1 - Discount) * (1 + State tax)
This gives
Amount = 799 * (1 - 40%) * (1 + 7.25%)
Evaluate
Amount = 514.16
Hence, the total amount that Mikaela spent on the paddleboard is $514.16
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Answer:
(B) $514.16
Step-by-step explanation:
Correct on my quiz.
Graph the function 3x-2y=-4
Answers
Answer:
3x=-4-2y=-2y x=-2y+3=1y
- Chong waits on tables at a restaurant. One day he served 4 different tables with bills without tips
as follows: $85.40, $125.00, S92.60, and $155.50. If he earned an average of 12% on tips for the
value of the meals, how much did he make on tips from the 4 tables?
Answers
Answer:
$55.02Step-by-step explanation:
Sum up the bills:
85.40 + 125.00 + 92.60 + 155.50 = 458.5Find 12% of the sum:
458.5*12/100 = 55.02Total bill:-
85.4+125+92.6+155.5=458.5$Total money he made
\(\\ \rm\Rrightarrow 12\%\:of 458.5\)
\(\\ \rm\Rrightarrow 0.12(458.5)\)
\(\\ \rm\Rrightarrow 55.02\$\)
how can I solve this linear equation x+y=7 3x+y=15
Answers
Answer:
(x, y) = (4, 3)
Step-by-step explanation:
The first step in solving any math problem is to read and understand what is given and what is asked.
GivenTwo linear equations are given, each in standard form. The coefficients of y are the same in the two equations, and both coefficients are 1 in the first equation.
x +y = 73x +y = 15FindYou are asked to "solve" this system of equations. That means you want an (x, y) ordered pair that will satisfy both equations. On a graph, these are the coordinates of the point where the lines cross.
SolutionThere are many ways to solve a system of linear equations. In this case, the y-coefficients being the same suggests that "elimination" or "linear combination" would be a good choice of solution method.
We note that the coefficients in the second equation are generally larger than those in the first equation. Subtracting the first equation from the second equation will generally leave positive coefficients, making the arithmetic less error-prone.
(3x +y) -(x +y) = (15) -(7) . . . . . . subtract the first equation from the second
2x = 8 . . . . . . simplify
x = 4 . . . . . . divide by 2
Using this value in the first equation, we can find y:
4 +y = 7
y = 3 . . . . . . subtract 4
The solution to this pair of equations is (x, y) = (4, 3).
__
Additional comment
A graphical solution is attached.
Either equation can be solved for y, and that expression substituted into the other. Solving the first equation for y gives ...
y = 7 -x
Substituting that into the second equation, we have ...
3x +(7 -x) = 15
2x = 8 . . . . . . . subtract 7
x = 4 . . . . . . divide by 2
y = 7-4 = 3
(x, y) = (4, 3) is the solution.
We have shown 3 methods of solving the given system of equations. There are other methods that can be used, too, including matrix methods and methods that make use of arrays of the coefficients.
Tamu ran 30 minutes and burned 170 calories. PART B: How many calories did Tamu burn per minute? Write your answer as a decimal. *
Answers
Answer:
Tamu burnt 5.66 calories per minute.
Step-by-step explanation:
Tamu ran for 30 minutes.
Calories burnt by Tamu = 170 calories
Unit rate = \(\frac{Calories\ burnt}{Time}\)
Unit rate = \(\frac{170}{30}\)
Unit rate = 5.66 calories per minute
Therefore,
Tamu burnt 5.66 calories per minute.
h added to the ratio of three and g
Answers
Answer: (3/g) + h
Step-by-step explanation:
Four drivers recorded the distance they drove each day for a week. Which driver's data set has a mode that is greater than the mean or median AND a median with the lowest value of the three measures?
a
Kadisha: 8, 17, 23, 16, 17, 18, 125
b
Cole: 14, 26, 34, 22, 47, 22, 45
c
Fabian: 7, 12, 11, 23, 13, 23, 30
d
Ling: 52, 36, 41, 31, 31, 37, 59
Answers
Driver's data set that has a mode that is greater than the mean or median is Fabian and a median with the lowest value of the three measures is Kadisha.
Data of Fabian: 7, 12, 11, 23, 13, 23, 30
Mean = sum of all observation / total no. of observation
Mean = (7+ 12+ 11+ 23+ 13+ 23+ 30) / 7
Mean = 17
Mode = most repeating observation
Mode = 23
For median we have to write observation in ascending order
7,11,12,13,23,23,30
Median = (N+1)/2
Where N = No. of observation
Median = (7+1)/2
Median = 4th observation
Median = 13
Here mode that is greater than the mean or median.
similarly for,
Kadisha: 8, 17, 23, 16, 17, 18, 125
Mean = 32
Median = 17
Mode = 17
Here median with the lowest value of the three measures.
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If we dcrease the radius of each cylinder by 2m , which one has the greater volume give your answer rounded to the nearest tenth use 3.14 for pi
Answers
Answer:
See Explanation
Step-by-step explanation:
Given
The question is incomplete, as the cylinders are not given.
Required
The cylinder with greater volume
To answer this question, I will assume the following dimensions.
Cylinder 1
\(r = 5\)
\(h = 10\)
Cylinder 2
\(r = 7\)
\(h = 5\)
Volume is calculated as:
\(V = \pi r^2h\)
When the radius is reduced by 2, the formula becomes
\(V = \pi (r - 2)^2h\)
For the first cylinder, we have:
\(V_1 = \pi (r - 2)^2h\)
\(V_1 = 3.14 * (5 - 2)^2 * 10\)
\(V_1 = 3.14 * 3^2 * 10\)
\(V_1 = 3.14 * 9 * 10\\\)
\(V_1 = 282.6\)
For the second cylinder, we have:
\(V_2 = \pi (r - 2)^2h\)
\(V_2 = 3.14 * (7 - 2)^2 * 5\)
\(V_2 = 3.14 * 5^2 * 5\)
\(V_2 = 3.14 * 25 * 5\)
\(V_2 = 392.5\)
Cylinder 2 has a greater volume because 392.5 > 282.6
Note: Irrespective of the dimension of the cylinders, the above step works fine.
at the movie theatre admission is $6.30 an adult admission is $9.60. on thursday twice as many adult tickets as child tickets were sold for a total sale of $535.50 how many child tickets were solf that day
Answers
Answer:
number of child tickets sold on saturday is 21
number of adult tickets sold on saturday is 42
Step-by-step explanation:
Let's assume
number of child tickets sold on saturday is x
number of adult tickets sold on saturday is y
On saturday, twice as many adult tickets as child tickets were sold
so, we get
child admission is $6.30 and adult admission is $9.60
a total sales of $535.50
we get
now, we can plug y=2x
now, we can solve for x
now, we can find y
so,
number of child tickets sold on saturday is 21
number of adult tickets sold on saturday is 42.........Answer
What is the second integral of
\( \frac{1}{x} \)
?
Answers
Answer:
\(\displaystyle \int {\int {\frac{1}{x}} \, dx} \, dx = xln|x| - x + C\)
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationLogarithmic Differentiation
Integration
IntegralsIndefinite IntegralsIntegration Constant CIntegration Rule [Reverse Power Rule]: \(\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C\)
Logarithmic Integration
Integration by Parts: \(\displaystyle \int {u} \, dv = uv - \int {v} \, du\)
[IBP] LIPET: Logs, inverses, Polynomials, Exponentials, TrigStep-by-step explanation:
Step 1: Define
Identify
\(\displaystyle \int {\int {\frac{1}{x}} \, dx} \, dx\)
Step 2: Integrate Pt. 1
[Inner Integral] Logarithmic Integration: \(\displaystyle \int {ln|x|} \, dx\)Step 3: Integrate Pt. 2
Identify variables for integration by parts using LIPET.
Set u: \(\displaystyle u = ln|x|\)[u] Differentiate: \(\displaystyle du = \frac{1}{x} \ dx\)Set dv: \(\displaystyle dv = dx\)[dv] Integrate: \(\displaystyle v = x\)Step 4: Integrate Pt. 3
[Integral] Integration by Parts: \(\displaystyle \int {ln|x|} \, dx = xln|x| - \int {(x \cdot \frac{1}{x})} \, dx\)[Right Integral] Simplify: \(\displaystyle \int {ln|x|} \, dx = xln|x| - \int {} \, dx\)[Right Integral] Reverse Power Rule: \(\displaystyle \int {ln|x|} \, dx = xln|x| - x + C\)Redefine: \(\displaystyle \int {\int {\frac{1}{x}} \, dx} \, dx = xln|x| - x + C\)Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: ________
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
x < –3
x > –3
x < 3
x > 3
Answers
Answer:
The process of solving the inequality will be: -2(5 - 4x) < 6x - 4 8x - 10 < 6x - 4 -6 < -2x x > 3 This is in accordance to the rule of solving inequalities which states that whenever we multiply or divide by a negative number while solving an inequality, we must reverse the inequality sign.Pls helppp
Make table if u can
Answers
Answer:
they are star's and they are in straight line and all of them have more than one star
Step-by-step explanation:
because the figurers have same star
In 1993, the moose population in a park was measured to be 4760. By 1999, the population was measured again to be 5960. If the population continues to change linearly:
Answers
The formula for moose population is P = 4760 + (number of years x 200).
The moose population in 2003 would be 6760.
What would be the moose population in 2003?When a population increases linearly, it means that it increases by the same amount each year.
Rate of linear increase: (population in 1999 - population in 1993) / difference in years
(5960 - 4760) / (1999 - 1993)
1200 / 6 = 200
Linear function : initial population + (rate of increase x number of years)
Population in 2003: 4760 + (200 x 10)
4760 + 2000 = 6760
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Decide
10w
roots the equation
322 - 24z +48
Answers
Answer:
-34z + 370
Step-by-step explanation:
322 - 24z + 48
(322 + 48) - 34z
370 - 34z
Best of Luck!
There are (32)4 ⋅ 30 bacteria in a petri dish. What is the total number of bacteria in the dish?
Answers
The total number of bacteria in the dish is 31457280
How to determine the total number?The expression is given as:
Total = (32)^4 * 30
Start by evaluating the exponent
Total = 1048576 * 30
Next, evaluate the product
Total = 31457280
Hence, the total number of bacteria in the dish is 31457280
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Answer:
A (3^8)
Step-by-step explanation:
I have this question on my test. I'm just assuming the person didn't put ^.
(3^2)^4 times 3^0