How many ways are there to distribute 4 balls into 3 boxes so that each box contains at least one object if: (a) both the balls and boxes are distinguishable (b) the balls are indistinguishable and the boxes are distinguishable (c) the balls are distinguishable and the boxes are indistinguishable (d) both balls and boxes are indistinguishable
Answers
(a) There are 15 ways to distribute 4 distinguishable balls into 3 distinguishable boxes so that each box contains at least one object.
(b) There are 3 ways to distribute 4 indistinguishable balls into 3 distinguishable boxes so that each box contains at least one object.
(a) When both the balls and boxes are distinguishable, we can think of each distribution as a sequence of choices. For the first ball, we have 3 choices of which box to place it in. For the second ball, we have 3 choices as well, and so on. Therefore, the total number of ways to distribute the balls is 3 * 3 * 2 * 1 = 18. However, this count includes some cases where one or more boxes are empty. Since we want each box to contain at least one object, we need to subtract those cases. There are 3 ways to have one box empty (all balls in one box), and 3 ways to have two boxes empty (each ball in a separate box). So, the final count is 18 - 3 - 3 = 15.
(b) When the balls are indistinguishable and the boxes are distinguishable, the problem is equivalent to distributing identical objects into distinct boxes. In this case, we can use the stars and bars method. We can represent the balls as stars and the boxes as bars. We have 4 stars representing the 4 balls, and we need to place 2 bars to separate them into 3 boxes. There are 3 - 1 = 2 spaces between the stars where we can place the bars. Using the stars and bars formula, the number of ways to distribute the balls is (2 + 2)C2 = 3C2 = 3.
For cases (c) and (d), the question asks about indistinguishable balls or indistinguishable boxes. However, the question does not specify whether the boxes can be empty or not. Depending on the interpretation, the answer may vary. If we assume that empty boxes are allowed, the answers would be different compared to when each box must contain at least one object. To provide a comprehensive explanation, please clarify if empty boxes are allowed or not.
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Related Questions
A fair spinner has 8 equal section. Here is a probability scale
a) which letter shows the probability of spinning a 1
b) which letter shows the probability of spinning a 2
Answers
The letter that shows the probability of spinning a 1 is B
The letter that shows the probability of spinning a 2 is C
a) which letter shows the probability of spinning a 1From the question, we have the following parameters that can be used in our computation:
The spinner
Where, we have
P(1) = 2/8
This is represented with
B = 1/8
b) which letter shows the probability of spinning a 2Here, we have
P(2) = 4/8
Simplify
P(2) = 1/2
This is represented with
C = 1/2
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answer asap no wrong answers
Answers
Since A and B are opposite angles on parallel lines, we know that they sum up to 180:
\((8x + 74) + (2x + 56) = 180\)
\(10x + 130 = 180\)
\(10x = 50\)
\(x = 5\)
We can plug this into the equation for angle B to get the actual angle:
\(B = 2x + 56\)
\(B = 2(5) + 56\)
\(B = 10 + 56\)
\(B = 66\)
Which expression represents the number -2i(5- i) + (17- 8i) rewritten in a + bi
form?
O 15-18i
O 15-2i
O 19 - 18i
O 11 + 8i
Answers
Answer:
(a) 15 -18i
Step-by-step explanation:
You want the simplified form of the expression -2i(5- i) + (17- 8i).
Complex numbersFor many purposes, the value i in a complex number can be treated in the same way a variable would be treated. When simplifying an expression involving i, any instances of i² can be replaced with the real value -1.
-2i(5- i) + (17- 8i) = -10i +2i² +17 -8i
= -2 +17 +(-10 -8)i
= 15 -18i
__
Additional comment
Your scientific or graphing calculator can probably help you evaluate such expressions.
2. pvalue
3.critical value
4.test value
5.make a desision
Noise Levels in Hospitals In a hospital study, it was found that the standard deviation of the sound levels from 30 areas designated as "casualty doors" was 6.4 dBA and the standard deviation of 28 areas designated as operating theaters was 4.1 dBA. At a 0.10, can you substantiate the claim that there is a difference in the standard deviations? Use a, for the standard deviation of the sound levels from areas designated as "casualty doors." Part 1 of 5 (a) State the hypotheses and identify the claim. H_0: sigma_1^ = sigma_2^ _____
H_1: sigma_1^ ≠ sigma_2^ _____
This hypothesis test is a___test.
Answers
The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.
The hypotheses for the test are:
H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)
H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)
This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.
To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.
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Which of the following are prime factorizations of the number 100? Check all
that apply.
A. 5, 2, 2,5
B. 2, 5, 10
C. 5, 10, 2
D. 5, 2, 5, 2
Answers
Answer:
Step-by-step explanation:
A. 5, 2, 2, 5 is a prime factorization of 100 since 5 and 2 are prime factors of 100 and multiplying them gives 100.
B. 2, 5, 10 is not a prime factorization of 100 since 10 is not a prime factor of 100.
C. 5, 10, 2 is not a prime factorization of 100 since 10 is not a prime factor of 100.
D. 5, 2, 5, 2 is not a prime factorization of 100 since it can be simplified as 5x2x5x2 = 100, but it is not a unique prime factorization.
Therefore, the correct answer is A. 5, 2, 2, 5.
a transformation is applied to a figure to create a new figure on a coordinate grid. which transformation does not preserve congruence?
Answers
Dilation does not preserve congruence, as it changes the size of the figure while keeping the same overall shape.
A transformation that does not preserve congruence is a dilation. A dilation is a transformation that changes the size of a figure while keeping the same overall shape. The formula for dilation is:
D(x,y)=(kx,ky)
Where k is the scale factor. A scale factor of less than 1 will decrease the size, whereas a scale factor greater than 1 will increase the size.
For example, if we have a triangle ABC with vertices A(1,1), B(3,3) and C(4,1), after dilation with a scale factor of 0.5, the vertices of the new triangle A'B'C' will be A'(0.5,0.5), B'(1.5,1.5) and C'(2,0.5).
As can be seen from the example, dilation does not preserve congruence. The triangle A'B'C' is not congruent to triangle ABC, since the length of the sides and the angles have changed.
Dilation does not preserve congruence, as it changes the size of the figure while keeping the same overall shape.
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Kara, Harry, and Erin served a total of 86 orders Monday at the school cafeteria.
Henry served 10 fewer orders than Kira. Erin served 4 times as many orders as Kira.
How many orders did they each serve?
Answers
The required orders are Kara served 12.5 orders, Harry served 22.5 orders, and Erin served 50 orders.
What are conditional equation?An equation that holds true for one or more values of the variable but holds false for other values of the variable is known as a conditional equation. In Hannah's example, the equation holds true for the value of x equal to 10, but not for other values, such as 1. The equation is a conditional equation as a result.
According got question:Let we consider the number of orders Kara served as x.
Then, Harry served x + 10 orders and Erin served 4x orders.
The total number of orders they served is x + x + 10 + 4x = 86 orders.
So, 6x + 10 = 86
6x = 76
x = 12.5
Kara served 12.5 orders, Harry served 22.5 orders, and Erin served 50 orders.
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Answer:
Step-by-step explanation:
Let the orders served by Kira be k.
Orders served by Henry= 10 less than Kira
= k-10
Orders served by Erin= 4 times of Kira
= 4k
Total orders served= 86
Kira+Henry+Erin= 86
k+k-10+4k= 86
6k-10= 86
6k= 86+10
6k= 96
k= 96/6
k= 16
Kira= k= 16
Henry= k-10= 16-10= 6
Erin= 4k= 4x16= 64
∴ Kira served 16 orders, Henry served 6 orders & Erin served 64 orders
serena leans a 24-foot ladder against a 22.8-foot-tall building to climb on the roof.
Answers
Serena leans a 24-foot ladder against a 22.8-foot-tall building to climb on the roof is 71.8 degree.
Measurement of Angle:
The measurement of angles is done using basic geometric tools such as protractors and compasses. This tool helps to find precise measurements of angles. A protractor helps provide accurate measurements of angles, while compasses help construct angles. Angles are measured in three ways: degrees, radians, and revolutions.
According to the Question:
Suppose the measure of angle is θ, then we have
Sinθ = 22.8/24
⇒ Sinθ = 0.95
Therefore,
θ = Sin⁻¹ (0.95)
= 71.8 degree.
Therefore, Serena leans a 24-foot ladder against a 22.8-foot-tall building to climb on the roof is 71.8 degree.
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Can anyone help me pleaseeee!! I will mark yooo
Answers
HELP image is provided
Answers
Answer:
yes
Step-by-step explanation:
angles z and b both have 2 congruent lines
angle y and a have one congruent line
and lines CA and XY have a congruent tick mark
the 8000 that he invested in fund a returned a 6% profit.the amount that he invested in fund b returned a 2% profit how much did he invest in fund b if both funds together returned a 3 % profit
Answers
Let
\(\begin{gathered} x=\text{ the amount invested in fund b} \\ m=\text{ the profit from the fund a investment} \\ n=\text{ the profit from the fund b investment} \end{gathered}\)Therefore,
\(\frac{m}{8000}=\frac{6}{100}\)Hence,
\(m=\frac{6}{100}\times8000=6\times80=\text{ \$480}\)\(\begin{gathered} \text{ Also} \\ n=0.02x------(1) \\ \frac{m+n}{8000+x}=0.03 \\ \text{therefore} \\ \frac{n+480}{8000+x}=0.03 \end{gathered}\)Thus
\(n+480=0.03(8000+x)-----------------(2)\)Substituting equation(1) into equation(2), we have
\(\begin{gathered} 0.02x+480=0.03(8000+x) \\ 0.02x+480=240+0.03x \\ \text{ Thus} \\ 0.03x-0.02x=480-240 \\ 0.01x=240 \\ x=\frac{240}{0.01}=2400 \end{gathered}\)Hence, the amount he invested is $2400
assume that the life span in honolulu is approximately normally distributed, does this information indicate that the population mean life span for honolulu is less than 77 years? find the p-value to test the hypothesis
Answers
The p-value represents the probability of observing a sample mean as extreme as, or more extreme than, the one obtained, assuming the null hypothesis is true.
To determine whether the population mean life span for Honolulu is less than 77 years, we can conduct a hypothesis test using the given information. Let's set up the hypotheses:
Null Hypothesis (H0): The population mean life span for Honolulu is greater than or equal to 77 years.
Alternative Hypothesis (Ha): The population mean life span for Honolulu is less than 77 years.
To find the p-value, we would need additional information such as the sample mean and standard deviation. Without those values, we cannot directly calculate the p-value. However, we can describe the process of hypothesis testing.
To test the hypothesis, we would collect a sample of life spans in Honolulu, calculate the sample mean and standard deviation, and perform a one-sample t-test or z-test depending on the sample size and information available. This test would yield a test statistic and corresponding p-value.
A small p-value (less than the significance level, typically 0.05) would provide evidence to reject the null hypothesis in favor of the alternative hypothesis, suggesting that the population mean life span for Honolulu is indeed less than 77 years.
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a customer at cavallaro's fruit stand picks a sample of 3 oranges at random from a crate containing 40 oranges, of which 5 are rotten. what is the probability that the sample contains 1 or more rotten oranges?
Answers
The probability that the sample contains 1 or more rotten oranges be, 1/8.
Given, a customer at cavallaro's fruit stand picks a sample of 3 oranges at random from a crate containing 40 oranges, of which 5 are rotten.
we have to find the probability that the sample contains 1 or more rotten oranges,
first we will find the probability that the sample contains no rotten oranges,
P(E) = 35/40
P(E) = 7/8
Now, the probability that the sample contains 1 or more rotten oranges be,
1 - 7/8
P(E) = 1/8
Hence, the probability that the sample contains 1 or more rotten oranges be, 1/8.
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-2a
0b
-2
× -5b
4
× -b
Answers
Answer:
Step-by-step explanation:
Army DA administrative publications and forms by the Army Publishing Directorate APD. The latest technologies high quality electronic pubs and forms view ...
5/8 - 5/24
I am doing some homework my brain isnt working right now can someone help me out?
Answers
Answer:
5/12
Step-by-step explanation:
i just looked it up...
====================================================
Explanation:
Multiply top and bottom of 5/8 by 3 to get 15/24
This means 5/8-5/24 is the same as 15/24-5/24
The denominators are the same, so we can subtract the numerators to have them placed over the common denominator
15/24 - 5/24 = (15-5)/24 = 10/24
Then we reduce by dividing each part of the fraction by the GCF 2
10/2 = 5
24/2 = 12
Meaning that 10/24 = 5/12
Note how multiplying top and bottom of 5/12 by 2 leads to 10/24 again.
So overall,
5/8 - 5/24 = 5/12
brianna is driving on a long road trip. she created the graph below to represent the gallons of gas left in her tank. what does the x-intercept in the graph represent?
Answers
The x-axis represents the distance traveled (in miles).
Considering that the x-axis shows the distance travelled (in miles) and the y-axis represents the amount of gas left in the tank (in gallons), the x-intercept would represent the point at which Brianna's gas tank is empty, and she would need to refill her tank to continue traveling. In other words, the x-intercept is the distance Brianna can travel before running out of gas, assuming her car's fuel efficiency remains constant and she does not refill her tank.
Two key lines known as the x and y axes are the building blocks of a graph.
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Evaluate the expression when b=2
b·5
Answers
Answer:
\(Solution,\\When,b=2\\Now, b*5=2*5=10\)
Step-by-step explanation:
2/5 minute = ____ seconds
3/5 hour =_______ minutes
3/5 meter =_____centimeters
Answers
Answer:
24 second
36 minutes
60 centimeters
Answer:
A: 24 second
B: 36 minutes
C: 60 centimeters
ROUND TO THE NEAREST WHOLE NUMBER
16968.3
Answers
Answer:
16968
Step-by-step explanation:
Answer:
16,968
Hope this helps :)
if h(t)=1248-160t+16t
Answers
Answer: 816
Step-by-step explanation:
h(3) = 1248 - 160(3) + 16(3)
h(3)= 1248 - 480 + 48
h(3)= 816
Combine like terms to write an equivalent expression. Then complete the statements.
2f + 5 + f – 3
The constants, _________, are like terms.
_________ are also like terms.
Combine the constant terms by __________
Combine the variable terms by adding the _________
The equivalent expression is ________
Answers
Answer:
The constants, 5 and -3, are like terms
2f and f are also like terms. Combine the constant terms by adding them together.
Combine the variable terms by adding the
Equivalent expression is 3f+2
Step-by-step explanation:
Like terms are terms that are the same so in this case the variables are like terms. And the constants or just the numbers are the same.
(3f and f)
(5 and -3)
setenta y uno por tres dividido 43
Answers
Answer:
4.95
Step-by-step explanation:
espero que te ayude
WET TEDDY BEARS, GET YOUR WET TEDDY BEARS
(Liberty Mutual)
Answers
Step-by-step explanation:
Hell yes, I'll take 5 please
Answer:
Yes! Wet teddy bears are fire! I'll take 4, pls!
Step-by-step explanation:
sat math scores follow a normal distribution with a mean of 511 and a standard deviation of 110. suppose we choose a student at random. what is the probability that the student scores between 450 and 600?
Answers
The probability that a student scores between 450 and 600 on the SAT math section is approximately 0.4147 or 41.47%.
To find the probability that a student scores between 450 and 600 on the SAT math section, we need to use the properties of the normal distribution. We know that the mean is 511 and the standard deviation is 110.
First, we need to standardize the values of 450 and 600 using the formula:
z = (x - μ) / σ
where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.
For 450:
z = (450 - 511) / 110 = -0.55
For 600:
z = (600 - 511) / 110 = 0.81
Next, we need to find the area under the normal curve between these two standardized values. We can use a table or a calculator to find that the area between z = -0.55 and z = 0.81 is approximately 0.4147.
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Find the lower quartile (Q1).
55, 60, 65, 95, 90, 75, 75, 80, 85, 80, 85, 85
Answers
Answer:
Hi! The answer to your question is 65
Step-by-step explanation:
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☆Brainliest is greatly appreciated!☆
Hope this helps!!
- Brooklynn Deka
Chloe earns a 3.35 % raise in her annual salary. She correctly writes the expression s + 0.325s to represent her new annual salary, where s represents her current annual salary.
Write an equivalent expression to represent Chloe's new annual salary, s + 0.325s, using only one term.
Answers
An equivalent expression to represent Chloe's new annual salary, s + 0.325s, using only one term is 1.325s.
To represent Chloe's new annual salary using only one term, we need to simplify the expression s + 0.325s.
The expression s + 0.325s represents Chloe's current annual salary (s) plus 3.25% (0.325) of her current annual salary.
To combine the terms, we can factor out the common factor of s:
s + 0.325s = (1 + 0.325)s
Simplifying further, we find:
1 + 0.325 = 1.325
This means that Chloe's new annual salary is 1.325 times her current annual salary (s), reflecting the 3.35% raise she received.
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can someone try this
Answers
Answer:
no I can't but I hope someone can
Fill in the blank: 9(4x + 5) = 36x +
Answers
Answer:
45
Step-by-step explanation:
9(4x + 5)
9*4x + 9*5
36x + 45
Answer:
45Step-by-step explanation:
9*4x +9*5
= 36x + 45
Bye
:-)
What happens to the parent graph y= square root of X when the equation is changed to y=-2 square root of x-8 select all that apply.
Shift down 8 units, vertical stretch, reflect over the x-axis, shift up 8 units
Answers
Answer:
All except shift up.
Help plz find the value of m and n
Answers
Answer:
jdksbjsd
Step-by-step explanation:
ndjksbcsdbckdsbcsd sorry for points im sorry SORRY SORRY IM SO SORRY
IM RUDE AND UGLY SORRY