Several common systems have a "two state" nature. Coins land with either Heads or Tails, electronic spins have magnetic moments m pointing either (Up) or (Down). The terms "microstate" and "macrostate" describe these systems, each containing a number of objects or steps: System One Particular MicrostateMacrostate (usually what we measure) Coins H TTHTHHH TH H T Total heads (NHNT) Spins U D D U D U U U D U U D Net Moment-μ (NU-ND) 3) What is the probability of finding exactly half of the 12 spins up and half of the spins down?
Answers
The probability of finding exactly half of the 12 spins up and half of the spins down is approximately 0.1934 or 19.34%.
Using the binomial distribution with n = 12 and p = 0.5, it is possible to determine the probability of discovering precisely half of the 12 spins up and half of the spins down.
The probability mass function of the binomial distribution is:
P(X = k) = (n choose a) * pᵃ* (1 - p)ⁿ⁻ᵃ
where (n choose a) = n! / (a!(n-a)!) is the binomial coefficient.
So, the probability of exactly 6 spins up and 6 spins down is:
P(X = 6) = (12 choose 6) * 0.5⁶ * 0.5⁶
= 924 * 0.5¹²
= 0.1934
As a result, the likelihood of finding precisely 12 spins up and 12 spins down is roughly 0.1934, or 19.34%.
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Related Questions
given 2 vectors a=3i+4j-4k and b=-2i-6j+2k, the value of |a+b| (magnitude of their sum) is Sqrt (7) Sqrt (10) Sqrt (8) Sqrt (9) Sqrt (11)
Answers
Thus, the magnitude of value of |a+b| is Sqrt (9), which simplifies to just 3.
To find the magnitude of the sum of two vectors, we need to add the two vectors together and then take the square root of the sum of their squares.
So, let's first add the two vectors together:
a+b = (3i+4j-4k) + (-2i-6j+2k)
= i - 2j - 2k
Now, we can find the magnitude of this vector by squaring each of its components, summing them, and then taking the square root:
|a+b| = sqrt((1^2) + (-2^2) + (-2^2))
= sqrt(1 + 4 + 4)
= sqrt(9)
= 3
Therefore, the value of |a+b| is Sqrt (9), which simplifies to just 3.
In summary, the magnitude of the sum of two vectors can be found by adding the vectors together, squaring each of their components, summing them, and then taking the square root.
For the given vectors a=3i+4j-4k and b=-2i-6j+2k, their sum is i - 2j - 2k, and the magnitude of this vector is 3.
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Help me please i dont get how to do it
Answers
The linear graph of y = 2x + 3 is shown below.
How to Draw the Graph of a Linear Equation?To graph the linear equation, plot each points from the table of values on a coordinate plane then connect the points to each other as a straight line.
Given the table, to fill it, substitute each value of x into y = 2x + 3:
For x = -2:
y = 2(-2) + 3
y = -4 + 3
y = -1
For x = -1:
y = 2(-1) + 3
y = -2 + 3
y = 1
For x = 0:
y = 2(0) + 3
y = 3
Thus, plot the points, (-2, -1), (-1, 1), (0, 3), (1, 5), and (2, 7) on a graph. The graph is shown below.
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a ball dropped from a height of 13 feet begins to bounce. each time it strikes the ground, it returns to 3/4 of its previous height. what is the total distance traveled by the ball if it bounces infintely many times
Answers
On solving the provided question, we got to know that 91/4 feet is the vertical distance that ball traveled.
What is equation?
An equation in algebra is a formula that proves two other formulas are equivalent. For instance, the equation 3x + 5 = 14 is produced when the two equations 3x + 5 and 14 are combined with an equal sign. Mathematical equations in algebra frequently have one or more variables.
If the balls land in a straight line:
dropped = 13 ft
rebounds 3/4 (13) ft = 39/4 ft
vertical travel = 13 + 39/4 = 91/4 ft
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212.65 x 10? = 21,265.0
A 102
B 109
C 103
Answers
Answer:
I'm confused what your asking because 212.65 x 10 does equal 21,265.0
The flow of water from a faucet can fill a
3-gallon container in 18 seconds. Give the ratio of gallons to seconds as a rate in gallons per second and as a reduced fraction.
Answers
Answer:
3/18 gallons/seconds, or 1/6 gallons/seconds
Step-by-step explanation:
We know that for every 3 gallons, the faucet fills that amount up in 18 seconds. Another way we can write that is "3 gallons for 18 seconds", or 3 gallons / 18 seconds.
Therefore, in terms of gallons to seconds, we can write this as 3 gallons/18 seconds.
One cool thing we can do with fractions is that if we multiply/divide the numerator by the same thing, the fraction is still the same amount, like if we divided by one. For example, if we multiply 1/10 by 10/10 = 1, we would get 10/100 = 1/10, changing the numbers but still keeping the fraction intact. We can apply this concept here to reduce the fraction.
Reducing the fraction means that we want to make the numerator and denominator as small as possible while still keeping them as integers. This means that, if possible, we should divide both the numerator and denominator by their greatest common factor (if it is greater than 1).
To find the greatest common factor, we can list factors and find the greatest one among them.
We have two numbers, 3 and 18.
The factors of 3 are 1 and 3 while the factors of 18 are 1, 2, 3, 6, 9, and 18. The greatest common number among these two is 3. Therefore, we can divide both these numbers by 3 to get
3/18 = 1/6 gallons/seconds as our answer
Write four equal fractions for each fraction. Multiply the numerator and the
denominator by the same number. Use the multipliers 2,3,4,5.
rin N/m
Answers
Answer:
1/5 = 2/10 = 3/15 = 4/20 = 5/25
2/3 = 4/6 = 6/9 = 8/12 = 10/15
Step-by-step explanation:
Multiply both numerator and denominator by same number.
example:
1 2 2
_ x _ = _
5 2 10
do this for each multiplier, so
1/5 × 2/2; 1/5 × 3/3; 1/5 × 4/4; 1/5 × 5/5;
and
2/3 × 2/2; 2/3 × 3/3; 2/3 × 4/4; 2/3 × 5/5;
A ticket for a statewide lottery costs $1. With probability 0.0000001, you win a million dollars ($1,000,000), and with probability 0.9999999 you win nothing. Let y denote the winnings from buying one ticket. Construct the probability distribution for y. Show that the mean of the distribution equals 0.10, corresponding to an expected return of 10 cents for the dollar paid.
Answers
The probability distribution for y is as follows:
y = 0 (with probability 0.9999999)
y = 1,000,000 (with probability 0.0000001)
In this scenario, there are two possible outcomes when buying a lottery ticket: winning $1,000,000 or winning nothing. The probability of winning $1,000,000 is 0.0000001, while the probability of winning nothing is 0.9999999.
To calculate the mean of the distribution, we multiply each outcome by its corresponding probability and sum them up.
Mean (μ) = (0)(0.9999999) + (1,000,000)(0.0000001)
= 0 + 0.1
= 0.1
The mean of the distribution is 0.1, which corresponds to an expected return of 10 cents for the dollar paid. This means that, on average, for every dollar spent on a lottery ticket, the expected return is 10 cents.
It is important to note that the expected return of 10 cents does not imply that an individual will always receive 10 cents back for every dollar spent. It is an average value based on the probabilities and outcomes of the lottery. Some individuals may win $1,000,000, while the majority will win nothing, resulting in an average return of 10 cents per dollar.
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please help me find the area of the kite
Answers
Answer:
A = 36 m²
Step-by-step explanation:
The area (A) of a kite is calculated as
A = \(\frac{1}{2}\) d₁ d₂ ( d₁, d₂ are the diagonals )
Here d₁ = 4 + 5 = 9 and d₂ = 4 + 4 = 8 , then
A = \(\frac{1}{2}\) × 9 × 8 = \(\frac{1}{2}\) × 72 = 36 m²
public class BinarySearch \{ public static void main(Stringll args) f int [1]yl ist ={1,2,3,7,10,12,20}; int result = binarysearch ( inylist, 20); if (result =−1 ) System, out, println("Not found:"); else System.out.println("The index of the input key is " + result+ ". "): y public static int binarysearch(int]l List, int key) \{ int low =0; int high = iist. length −1 while (high >= low) \& int mid =( low + high )/2; if (key < List [mid] high = mid −1; else if (key =1 ist [ mid ] ) return inid; else low = mid +1; return −1; // Not found \} l TASK 4: Binary Search in descending order We have learned and practiced the implementation of the binary search approach that works on an array in ascending order. Now let's think about how to modify the above code to make it work on an array in descending order. Name your new binary search method as "binarysearch2". Implement your own code in Eclipse, and ensure it runs without errors. Submit your source code file (.java file) and your console output screenshot. Hint: In the ascending order case, our logic is as follows: int mid =( low + high )/2 if ( key < list [mid] ) else if (key = ist [mid]) return mid; In the descending order case; what should our logic be like? (Swap two lines in the above code.)
Answers
The task involves modifying the given code to implement binary search on an array in descending order. The logic of the code needs to be adjusted accordingly.
The task requires modifying the existing code to perform binary search on an array sorted in descending order. In the original code, the logic for the ascending order was based on comparing the key with the middle element of the list. However, in the descending order case, we need to adjust the logic.
To implement binary search on a descending array, we need to swap the order of the conditions in the code. Instead of checking if the key is less than the middle element, we need to check if the key is greater than the middle element. Similarly, the condition for equality also needs to be adjusted.
The modified code for binary search in descending order would look like this:
public static int binarysearch2(int[] list, int key) {
int low = 0;
int high = list.length - 1;
while (high >= low) {
int mid = (low + high) / 2;
if (key > list[mid])
high = mid - 1;
else if (key < list[mid])
low = mid + 1;
else
return mid;
}
return -1; // Not found
}
By swapping the conditions, we ensure that the algorithm correctly searches for the key in a descending ordered array.
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show step by step explanation
Answers
Congruent triangles have corresponding sides that are also congruent. As a result, we can say that side PC and side BQ are equal.
Proving the sides of an isosceles triangle.We can use the principle of parallel lines to demonstrate that side PC is equal to side BQ in an isosceles triangle ABC, where AB = AC and line PQ is parallel to BC.
Take the triangle ABC, where AB = AC, for example.
We can infer that angle BPC is congruent to angle BQC since line PQ is parallel to BC. This is because the parallel lines BC and PQ, as well as the transversal line PQ, produce congruent alternate interior angles.
The base angles of an isosceles triangle are similar. Angles ABC and ACB are therefore similar.
When we examine triangles BPC and BQC, we see the following:
Angle BPC and angle BQC are parallel, as was already established.
Angle AB is similar to Angle ABC (Isosceles property of triangle)
Triangles BPC and BQC can be said to be congruent using the angle-side-angle (ASA) principle.
Congruent triangles have corresponding sides that are also congruent. As a result, we can say that side PC and side BQ are equal.
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. The land area of Charlotte, NC is approximately 3 x 102 square miles.
There are 6.4 x 102 square acres in a square mile. How many square
acres are in the city of Charlotte?
A 1.92 x 105 square acres
B. 2.13 x 104 square acres
C. 4.7 x 105 square acres
D. 9.4 x 104 square acres
Answers
Answer:
Option A
Step-by-step explanation:
Land area of Charlotte, NC = \(3\times 10^2\) square miles
Scale to be used,
1 square miles = \(6.4\times 10^2\) square acres
By this scale,
\(3\times 10^2\) square miles = \((6.4\times 10^2)\times(3.2\times 10^2)\) square acres
= \((6.4\times 3)\times 10^{2+2}\)
= \(19.2\times 10^4\) square acres
= \(1.92\times 10^5\) square acres
Therefore, Option A will be the correct option.
heights of statistics students were obtained by the author as part of an experiment conducted for class. the last digits of those heights are listed below. con-struct a frequency distribution with 10 classes. based on the distribution, do the heights appear to be reported or actually measured? what do you know about the accuracy of the results?
Answers
The heights of statistics students were obtained by the author as part of an experiment conducted for class.
Last Digits of Heights: 0, 8, 4, 6, 8, 0, 3, 1, 7, 5
Frequency Distribution:
Class Frequency
0-9 4
10-19 3
20-29 1
30-39 1
40-49 0
50-59 0
60-69 0
70-79 1
80-89 2
90-99 0
Based on the frequency distribution, the heights appear to be reported rather than actually measured. This suggests that the accuracy of the results may be questionable, as it is possible that the heights were rounded or estimated.
The heights of statistics students were obtained by the author as part of an experiment conducted for class. From the frequency distribution, it appears that the heights were reported rather than actually measured, suggesting that the accuracy of the results may be questionable.
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According to a 2009 Reader's Digest article, people throw away approximately 11% of what they buy at the grocery store. Assume this is the true proportion and you plan to randomly survey 220 grocery shoppers to investigate their behavior. What is the probability that the sample proportion is between 0.05 and 0.07
Answers
The probability that the sample proportion is between 0.05 and 0.07, would be 3 %.
How to find the probability ?First, find the standard deviation :
= √ ([0.11 * 0.89] / 220)
= 0.0217
Standardize our two boundaries (0.05 and 0.07) using the Z-score formula: Z = (x - μ) / σ.
Z1 = (0.05 - 0.11) / 0.0217 = -2.76
Z2 = (0.07 - 0.11) / 0.0217 = -1.84
We want the probability that the Z-score is between -2.76 and -1.84, i.e., P(-2.76 < Z < -1.84).
Using the z - table, we get:
P(Z < -2.76) = 0.0029,
P(Z < -1.84) = 0.0329.
The probability that the sample proportion is between 0.05 and 0.07 is:
= 0.0329 - 0.0029
= 3 %
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Please answer all 5 questions in order correctly.
You will be marked as Brainliest.
Answers
Answer:
whyd you delte my answer
Step-by-step explanation:
Order least to greatest: 1.5, 1.1, .9, 1, 1.7, 1.25
Answers
Answer:
1,1.1,1.25,1.5,1.7,9
Ellie has 14 of a pound of cheese. She wants to eat the same amount each day for 7 days. If she has the same amount each day, how much will she eat the first day?
Answers
Answer:
2 pounds.
Step-by-step explanation:
Ellie has 14 lbs of cheese. She wants to eat the same amount for 7 days, or a week.
We would have to divide the number of pounds by the number of days that she wants to eat the same amount.
=========================================
\(\frac{\text{pounds of cheese}}{\text{number of days}} =\frac{14\text{lb.}}{7\text{ days}} = \frac{{14\text{lb.}/7}}{7\text{days}/7} }= \boxed{\frac{2\text{lb.}}{\text{1 day}}}\)
=========================================
Since Ellie would have the same amount each day, she would eat 2 lbs not for just the first day, she would have 2 lbs per day for the whole week.
=========================================
Hope this helps!
2 4/5 x 3 1/8 = ? I really need the answer please
Answers
Answer:
= 35/4 or 8 3/4 or 8.75
Step-by-step explanation:
i hope this helps :)
Answer:
8.75 or 8 3/4
Step-by-step explanation:
How do you find the product of 3x^2y^5 and 4x^3y^7
Answers
Answer:
S
=
{
(
−
2
,
5
)
}
Step-by-step explanation:
Through: (1, 5) perpendicular to: y = - ½ x + 4
Answers
Answer:
y = 2x+5
Step-by-step explanation:
Instead of throwing next snowball, Max decides to kick it off the ground He can kick it at a speed of 24 feet per second.
How long will it take for
Max's kicked snowball to
hit the ground, and what
is its maximum height.
Answers
Answer:
To solve this problem, we can use the equations of motion for a vertically launched object. First, we need to find the initial velocity of the snowball when it is kicked off the ground. We know that its speed is 24 feet per second, but we also need to take into account the angle at which it is kicked. Let's assume that Max kicks the snowball at a 45-degree angle. Using trigonometry, we can find that the horizontal velocity of the snowball is also 24 feet per second, and the vertical velocity is 24 feet per second times the sine of 45 degrees, which is approximately 16.97 feet per second. Now we can use the following equation to find the time it takes for the snowball to hit the ground: h = vi*t + 0.5*a*t^2 where h is the maximum height, vi
if you were planning a meal for 24 people, how many dozens eggs would you need to buy if each person were to have 2 eggs each
Answers
Answer:
4
Step-by-step explanation:
If each person has 2 eggs, you'd need 48, and since a dozen is 12, 12*4=48.
Answer:
4 dozen eggs
Step-by-step explanation:
12 is a dozen and 12+12=24.
So you would need 4 dozen eggs to give each person 2 eggs.
28 divided my someing =4
Answers
Question :- 28 divided my something =4
Answer:- let something be x
\( \frac{28}{x} = 4 \\ \frac{28}{4} = x \\ 7 = x \: \: ans\)
Answer:
7
Step-by-step explanation:
28 divided by 7 would give you 4.
(It's easier to solve this problem if you count by 4's: 4, 18, 12, 16, 20, 24, 28)
hope this helped!
can somebody help me and explain how to do this
Answers
Answer:
=> 24m²
Step-by-step explanation:
Area of small rectangle = l×b
=> 2m× 3m
=> 6m²
Area of large rectangle = L×B
=> 9m × 2m
=> 18 m²
Area of figure = area of small rectangle + area of large rectangle
=> 18 m² + 6m ²
=> 24m²
(8) In how many ways can a five-man committee be chosen from among the 18 employees and one manager? What percentage of these is the manager not included?2(9) Suppose a California license plate has one number followed by three let ters, followed by three more numbers. How many unique license plates can California make? (10) The School of Natural Sciences has to select for a committee 5 TA's from a pool of 8, 2 lecturers from a pool of 6, and 3 professors from a pool off. In how many ways can SNS do this?
Answers
8.) The percentage of these committees that do not include the manager is 99.28%
9.) The total number of unique license plates that can be made is: 17,576,000
10.The total number of ways the committee can be selected is 8,400 ways.
8.)A five-man committee can be chosen from 18 employees and 1 manager in C(18,5) ways, where C(n,r) denotes the number of combinations of r objects selected from a set of n objects.
C(18,5) = 18!/(5!(18-5)!) = 18!/5!13! = (18x17x16x15x14)/(5x4x3x2x1) = 856,368
The manager is not included in the committee in C(18,5) - C(17,5) ways, where C(17,5) denotes the number of committees of 5 employees that can be formed from the 18 employees (excluding the manager).
C(17,5) = 17!/(5!(17-5)!) = 17!/5!12! = (17x16x15x14x13)/(5x4x3x2x1) = 6,188
Therefore, the number of ways the manager is not included in the committee is C(18,5) - C(17,5) = 856,368 - 6,188 = 850,180.
The percentage of these committees that do not include the manager is:
(850,180 / 856,368) x 100% = 99.28% (rounded to two decimal places)
9.) There are 10 possible choices for the first number on the license plate (0-9), and 26 choices for each of the three letters (A-Z). There are 10 choices for each of the last three numbers. Therefore, the total number of unique license plates that can be made is:
10 x 26 x 26 x 26 x 10 x 10 x 10 = 17,576,000
10.)The number of ways the committee can be selected is equal to the product of the number of ways each group of positions can be filled:
Number of ways to select 5 TA's from 8: C(8,5) = 56
Number of ways to select 2 lecturers from 6: C(6,2) = 15
Number of ways to select 3 professors from 5: C(5,3) = 10
Therefore, the total number of ways the committee can be selected is: 56 x 15 x 10 = 8,400 ways.
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2. C is at (-5.1) & D is at (7.6). Where is the midpoint on segment CD?
Answers
Answer:
1.25
Step-by-step explanation:
Find the average.
-5.1+7.6=2.5
2.5/2
1.25
Find the volume of the sphere.
Either enter an exact answer in terms of π or use 3.14 for π and round your final answer to the nearest hundredth.
Answers
Answer:
Volume of a sphere = 4πr³/3
r=10
V = 4πx10³/3
=4000π/3
V= 1333.33π (in terms of pi)
or
V= 4188.79(Nearest Hundredth).
what is the critical value for 96 confidence interval for a sample size of 15
Answers
The critical t-value is approximately 1.753.
To find the critical value for a 96% confidence interval with a sample size of 15, we need to determine the t-value from the t-distribution table. The t-distribution table is a statistical tool used to determine the probability of a t-value given the degrees of freedom (df) and the desired level of significance (α).
In this case, we have a sample size of 15, which means our degrees of freedom are 14 (n - 1). Looking at a t-distribution table for 14 degrees of freedom and a 96% confidence interval.
This means that if we were to construct a confidence interval from a sample size of 15, the margin of error would be calculated by multiplying the critical t-value of 1.753 by the standard deviation of the sample and dividing by the square root of the sample size. The resulting interval would contain the population mean with 96% confidence.
It's essential to note that the critical value will change as the sample size and confidence level change. Therefore, it's crucial to use the correct table to find the corresponding critical values for a given dataset's sample size and confidence level.
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if I got 15 credits in i need 24 to graduate how many more i need
Answers
Step-by-step explanation:
I would have 9 to graduate
Answer: 9 credits
Step-by-step explanation:
24 - 15 = 9
determine f(x) and f(x) for the following function. then give the horizontal asymptotes of f, if any. f(x)=4x/8x 6
Answers
The function f(x) is defined as f(x) = 4x/8x-6.
This can be simplified to f(x) = 1/2x-3. The horizontal asymptote for this function is y = 0, as its denominator approaches 0 as x approaches infinity or negative infinity.The function f(x) is defined as f(x) = 4x/8x-6. To find the vertical asymptote, we need to set the denominator to 0. We can solve this equation to find that the vertical asymptote of f(x) is x = 6. This means that as x approaches the value of 6, the function approaches infinity. Therefore, the horizontal asymptote of this function is y = 0 and the vertical asymptote is x = 6.
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The difference of the same side interior angles of two parrelels lines is 50 degrees find all angles
Answers
Answer:
Angle 1 = 115 degrees
Angle 2 = 65 degrees
Step-by-step explanation:
Angle 1: Same-side interior angle of Line 1
Angle 2: Same-side interior angle of Line 2
We know that the difference between the angles is 50 degrees. Since the angles are supplementary, we can write the equation:
Angle 1 + Angle 2 = 180
Now, we need to express the difference between the angles in terms of Angle 1 or Angle 2. We can choose either angle, so let's express it in terms of Angle 1:
Angle 1 - Angle 2 = 50
We can rewrite this equation as:
Angle 1 = 50 + Angle 2
Now substitute this expression for Angle 1 into the first equation:
(50 + Angle 2) + Angle 2 = 180
Combine like terms:
2Angle 2 + 50 = 180
Subtract 50 from both sides:
2Angle 2 = 130
Divide by 2:
Angle 2 = 65
Now substitute this value back into the equation for Angle 1:
Angle 1 = 50 + Angle 2
Angle 1 = 50 + 65
Angle 1 = 115
Therefore, the angles are as follows:
Angle 1 = 115 degrees
Angle 2 = 65 degrees