If n people are seated in a random manner in a row containing 2n seats, what is the probability that no two people will occupy adjacent seats? 10. a box contains 24 light bulbs, o
Answers
To find the probability that no two people will occupy adjacent seats, consider that n people are seated in a random manner in a row containing 2n seats. Using counting rule for combinations the total number of ways to select n seats of 2n seats is N=(2n/n).
Now consider an event M that all two people occupy adjacent seats. This can be done by occupying all odd seats so that the even seats are left empty. This arrangement leaves the last 2nth seat empty. Even if one occupies that seat the condition of the event will not break. So, we have (n + 1) seats available for the n people to seat so that no two people occupy adjacent seats. N(M) = (n+1). Thus, the probability that no two people will occupy adjacent seats in a row of 2n seats can be computed as shown :
The probability that no two people will occupy adjacent seats is [(2n-1)!!]/[(2n)!].
Explanation:To find the probability that no two people will occupy adjacent seats, we need to count the total number of possible arrangements where no two people are seated next to each other, and divide it by the total number of possible arrangements.
Let's consider a scenario where we have 2 people and 4 seats. In this case, the possible arrangements where no two people are seated next to each other are:
_ A _ A _A _ A __ A _ ASo, there are 3 possible arrangements where no two people are seated next to each other out of the total 6 possible arrangements.
Generalizing this, for n people seated in a row containing 2n seats, there are (2n-1)!! possible arrangements where no two people are seated next to each other. The double exclamation mark denotes the double factorial.
Hence, the probability is [(2n-1)!!]/[(2n)!].
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Related Questions
Question 14 a certain drug is made from only two ingredients: compound a and compound
b. there are 3 milliliters of compound a used for every 4 milliliters of compound
b. if a chemist wants to make 497 milliliters of the drug, how many milliliters of compound b are needed?
Answers
A : B = 3 : 4
A = 3 k
B = 4 k
3 k + 4 k = 7 k
7 k = 497 ml
k = 497 ml : 7 = 71 ml
B = 4 * 71 ml
B = 284 ml.
Answer: 284 ml of compound B are needed.
how can you use a number to explain what an integer and rational number are??
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The terms even and odd only apply to integers; 2.5 is neither even nor odd. Zero, on the other hand, is even since it is 2 times some integer: it's 2 times 0. To check whether a number is odd, see whether it's one more than some even number: 7 is odd since it's one more than 6, which is even.
Another way to say this is that zero is even since it can be written in the form 2*n, where n is an integer. Odd numbers can be written in the form 2*n + 1. Again, this lets us talk about whether negative numbers are even and odd: -9 is odd since it's one more than -10,which is even.
What is 16% of 43 minutes
Answers
Answer:
16% of 43 minutes are 6.8 minutes.
Step-by-step explanation:
To know the percentage of a quantity first you should divide the percentage by a hundred, then you should multiply the quantities, as follows.
1. Calculate the percentage:
[tex]\frac{16}{100}=0.16[/tex]
2. Multiply the percentage by the quantity:
[tex]0.16*43=6.88[/tex]
Therefore 16% of 43 minutes are 6.8 minutes.
The number of State Parks in California is 36 more than one third the number of State Parks in Florida. There are 85 State Parks in California. Which of the following equations would you use to find the number of State Parks in Florida? Note: f represents the number of state parks in Florida. 3(f − 36) = 85 1 over 3f + 36 = 85 Quantity f minus 36 all over 3 equals 85 Quantity f plus 36 all over 3 equals 85 Question 3(Mu
Answers
c = 85
1/3f + 36 = 85 <===
Can somebody PLEASE help me on this question, I really need an answer. What are the reasons for a,b,c, and, d?
Answers
Reason A: Distributive Property
Reason B: Additive Property of Equality
Reason C: Combine like terms
Reason D: Additive Identity Property
----------------------------------------------------------
Further Explanation:
Reason A: The distributive property is the idea where we multiply a number by a block of values inside a parenthesis. In this case we have 3 outside the parenthesis multiplied by the x inside and the -4 inside as well. So 3 times x = 3x and 3 times -4 = -12 indicating that 3*(x-4) = 3*x+3*(-4) = 3x-12. Be sure to multiply the outer 3 by EVERY term inside the parenthesis. Often it is easy to forget a term inside.
Reason B: We are adding 12 to both sides. The goal is to have the -12 go away. Notice in the next line -12+12 = 0 which is effectively canceled out. Adding the same value to both sides is the Additive Property of Equality. It must be done to both sides to balance things out. The general rule is that if a = b, then a+c = b+c. We have added c to both sides.
Reason C: We just do arithmetic here. On the left side -12+12 turns into 0. On the right side 33+12 turns into 45. This is considered "combine like terms" as all of these terms have something in common: they don't have variables attached to them. Which is why they are common or like terms
Reason D: The additive identity property says that adding 0 to anything leads to the same thing as before. For example, adding zero to 5 gets us 5+0 = 5. Nothing has changed, which is what we expect. That's why 3x+0 turns into 3x. At this point, the -12 a few steps prior has been canceled out. In general, the additive identity property is x+0 = x or 0+x = x
John and 3 friends are going out for pizza for lunch. They split one pizza and 4 large drinks. The pizza cost $13.00. After using a $6.00 gift certificate, they spend a total of $13.20. Write an equation to model this situation, and find the cost of one large drink. a. 3d + $13.00 – $6.00 = $13.20; $2.07 b. 4d + $13.00 – $6.00 = $13.20; $1.55 c. 4d – $13.00 + $6.00 = $13.20; $6.73 d. 4d + $13.00 – $6.00 = $13.20; $1.60
Answers
4d +13.00 -6.00 = 13.20
4d = 7.00 = 13.20
4d = 6.20
d - 6.20/4 =1.55
answer is B
TDC, Inc's . net profits were $-2000 each month last year . What was TDC's net profits for the year ?
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The TDC's net profits for the year were -$24,000 if TDC, Inc's. net profits were $-2000 each month last year option (A) is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
TDC, Inc.'s net profits were $-2000 each month last year.
Let x be the net profit for the year
As we know there are 12 months in 1 year.
So the net profit:
x = $-2000×12
x = -$24,000
Thus, the TDC's net profits for the year were -$24,000 if TDC, Inc. net profits were $-2000 each month last year option (A) is correct.
Learn more about the linear equation here:
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Five more than three times a number q is written as
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Answer:
Step-by-step explanation:
5+(3q) I think
What is 7 feet converted to miles?
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Answer:
Step-by-step explanation:
Use the factor-label method you learned in chemistry (also known as dimensional analysis), keeping in mind 2 things:
the label you want needs to be on the top of the equivalent ratio, and
that there are 5280 feet in 1 mile. Having said that:
[tex]7feet*\frac{1mile}{5280 feet}=[/tex]
The math tells us to divide 7 by 5280. That means that
7 feet = .0013257576 miles, to however many decimal places you need. That 7575 is repeating, btw.
the greatest wind speed ever recorded on earth's surface is 231 miles per hour. what is the speed in kilometers per hour
Answers
To convert 231 miles per hour to kilometers per hour, multiply by the conversion factor of 1.60934, resulting in approximately 371.76 km/h.
The greatest wind speed ever recorded on Earth's surface is 231 miles per hour (mph). To convert this speed into kilometers per hour (km/h), we use the conversion factor that 1 mile is approximately 1.60934 kilometers. Therefore, the speed in kilometers per hour is given by multiplying the speed in miles per hour by this conversion factor.
Here is the calculation:
231 mph x 1.60934 = 371.75774 km/h.
Approximately, the wind speed would be 371.76 km/h after converting from miles per hour.
HELP PLEASE!!
Graph the system of linear equations.
-1/2y=1/2x+5 and y=2x+2
The solution to the system is ( _ , _ )
Answers
the correct answer is -4, -6
The quotient of a number and 4, minus 1, equals 5/4. find the number
Answers
(x/4) - 3 = 5/4
x/4 - 12/4 = 5/4
x - 12 = 5
x = 17
Final answer:
The equation (x / 4) - 1 = 5/4 is solved by isolating x and simplifying, which reveals that the number sought is 9.
Explanation:
To solve the equation where the quotient of a number and 4, minus 1, equals 5/4, we can set up the following algebraic expression:
Let x = the number we want to find.
Now, we translate the problem into an equation:
(x / 4) - 1 = 5/4
To find the value of x, follow these steps:
Add 1 to both sides of the equation to get the fraction by itself:
(x / 4) - 1 + 1 = 5/4 + 1
Simplify both sides:
(x / 4) = 5/4 + 4/4
Add the fractions on the right side:
(x / 4) = 9/4
Multiply both sides of the equation by 4 to solve for x:
4 * (x / 4) = 4 * (9/4)
Simplify both sides:
x = 9
Therefore, the number we are looking for is 9.
Solve the inequality
5x < 16 + x.
A.) x < 1/4
B.) x > 1/4
C.) x < 4
D.) x > 4
Answers
x>4
Correct answer is D
if a = 0.6(the 6 repeating) and b= 0.75, then a·b= (blank) and a/b=(blank)
Answers
0.6666 (repeating) / 0.75 = 0.8888888 (repeating)
What is the measure of ∠ABC?
Enter your answer in the box.
Answers
The measure of the angle ∠ABC will be 95 degrees.
What is a quadrilateral?A quadrilateral is a shape made up of four sides having the sum of the angles 360 degrees. The given shape is like a parallelogram in which two sides are equal and at the same angles.
Given that angle A in the quadrilateral is 85 degrees. The value of the angle B will be calculated as:-
∠A + ∠B +∠C + ∠D = 360
85 + ∠B + 85 + ∠B = 360 ∠B = ∠D
170 + 2∠B = 360
2∠B = 360 - 170
2∠B = 190
∠B = 190 / 2
∠B = 95
Therefore, the measure of the angle ∠ABC will be 95 degrees.
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If h(x)= 5 for the function h(x)= 2x+1, what is the value of x?
Answers
In the diagram, JG = 5 cm and GE = 10 cm. Based on this information, can G be a centroid of triangle HJK? Point G cannot be a centroid because JG does not equal GE. Point G cannot be a centroid because JG is shorter than GE. Point G can be a centroid because GE and JG are in the ratio 2:1. Point G can be a centroid because JG + GE = JE.
Answers
in short terms it's b lol
Miranda wants to buy as many collectible dolls as possible, for $2.50 each. If she has $45.00 to spend, how many dolls can she buy?
Which equation BEST represents this situation?
A) 45x = 2.5
B) 2.5x = 45
C) x + 2.5 = 45
D) x + 45 = 2.5
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Hope I helped
Brainliest if happy :D
Evaluate the numerical expression. 4.2 − 3.5 ÷ 0.7 + 2.4 A) −3.2 B) 1.6 C) 11.6 D) 3.4
Answers
= 4.2 − 5 + 2.4
= -1.6
answer
- 1.6
4.2 -3.5/0.7+2.4
order of operations, do division first
-3.5/0.7 = -5
now you have:
4.2-5 +2.4
now just add/subtract from left to right
4.2-5 = -0.8 + 2.4 = 1.6
Answer is B
Why are black people always watched so closely at a liquor store?
Answers
A lot of people assume that because of the forced situations blacks have been in the past, that they're all bad people. Which is not always true. Although black people can still steal(like any other capable human being), so can white people. And hispanics, and middle easterns. But based on the history of America, specifically, black people have been the most common to shoplift or vandalize. But that was in the past, anyone today can easily steal a bottle of beer or a pack of gum from any store just like everyone else. I think the issue is that most priveledged people haven't let go of the past. Or at least what the media filtered as the past.
Hope this helps. :)
What number can you add to √7 to get a rational number?
−7√
7√
7
0
Answers
So if a=0 the answer is -√7, option answer 1.
Two radical expressions with the same degree and the same _____ are called like terms.
Answers
Answer:
Two radical expressions with the same degree and the same radicand are called like terms.
Step-by-step explanation:
All the terms that have same power and vari ables are called like terms.
For example: 3x²y and 5x²y are like terms, 2x³ and 7x³ are like terms, etc.
The number under the root is known as radicand.
Two radical expressions are like terms if
1. They have same degree.
2. They have same radicand.
Therefore the two radical expressions with the same degree and the same radicand are called like terms.
Two radical expressions are called like terms if they have the same degree and the same:
E. radicand
Two radical expressions are called like terms if they have the same degree and the same radicand. The radicand is the number or expression inside the radical symbol. For example, in the radical expression [tex]\(\sqrt{5}\)[/tex], the radicand is 5. For two radical expressions to be like terms, they must not only have the same index (degree) of the radical but also the same radicand.
Consider the expressions [tex]\(\sqrt{3}\) and \(2\sqrt{3}\)[/tex]. These are like terms because they both have the same degree (square root, which is an index of 2) and the same radicand (3). Similarly, [tex]\(\sqrt[3]{7}\) and \(4\sqrt[3]{7}\)[/tex] are like terms because both are cube roots with a radicand of 7.
However, [tex]\(\sqrt{2}\) and \(\sqrt{3}\)[/tex] are not like terms because their radicands differ. Likewise, [tex]\(\sqrt[4]{5}\) and \(\sqrt{5}\)[/tex] are not like terms because their degrees (indices) differ. Therefore, for radical expressions to be like terms, matching radicands and degrees are essential.
The correct question is:
Two radical expressions are called like terms if they have the same degree and the same
A. denominator
B. radical
C. term
D. number
E. radicand
find the center and radius for the circle, given the equation: x2+16x+y2-6y=-24
Answers
[tex]x^2+16x+y^2-6y=-24\\\\ x^2+2*8*x+64+y^2-2*3*y+9-64-9=-24\\\\ (x+8)^2+(y-3)^2=49\\\\ [/tex]
Center=(-8,3), radius=7
Y= f(x) 16x find f(x) when x= 1/2
Answers
The value of f(x) when x = 1/2 is 8.
Explanation:To find the value of f(x) when x = 1/2, we need to substitute x = 1/2 into the equation y = f(x) = 16x.
Substituting x = 1/2, we get y = f(1/2) = 16(1/2) = 8.
Therefore, f(1/2) = 8.
Write the ratio of dogs to cats in simplest form. 12 dogs, 16 cats
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WILL MARK BRAINLIEST ANSWER
2x^2+20x=-38
show work
Answers
2x^2 + 20x + 38 = 0
Divide both sides by 2.
x^2 + 10x + 19 = 0
The quadratic formula works very well here.
Let a = 1, b = 10 and c = 19
x = [-b +- sqrt{b^2 - 4ac}]/(2a)
Plug those values into the formula to find two answers for x.
One is negative and the other positive.
Good luck.
2x ^2 + 20x + 38 = 0
Use the quadratic formula to find the solutions.
−b±√b^2 − 4 (ac)/2a
Substitute a = 2, b = 20, and c = 38 into the quadratic formula and solve for x.
−20±√20 ^2 − 4⋅(2⋅38)/2⋅2
Simplify. x = −5±√6
The result can be shown in both exact and approximate form.
x = −5±√6
x ≈ −2.55051025, −7.44948974
Expand the logarithm. log₅ 5x⁻⁵
PLS HELP!
Answers
log₅5x⁻⁵=log₅5+log₅x⁻⁵=1-5log₅x.
Solve by completing the square
X^2+12x-13=0
Answers
(x+6)^2=49.
To solve the quadratic equation x^2 + 12x - 13 = 0 by completing the square, follow these steps. The solutions to the equation are x = 1 or x = -13.
Explanation:To solve the quadratic equation x^2 + 12x - 13 = 0 by completing the square, follow these steps:
Move the constant term to the other side of the equation:x^2 + 12x = 13Take half of the coefficient of the x-term and square it:(12/2)^2 = 36Add this value to both sides of the equation:x^2 + 12x + 36 = 13 + 36Factor the left side of the equation, which should be a perfect square:(x + 6)^2 = 49Take the square root of both sides and solve for x:x + 6 = ±√49x + 6 = ±7x = -6 ± 7Therefore, the solutions to the equation are x = 1 or x = -13.Find the special product (5s-3)^(2)
A. 10s2 - 9
B. 25s2 -30s - 9
C. 25s2 - 9
D. 25s - 9 30x + 9
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=> (5s - 3)^2 = (5s)^2 - 2(5s)(3) + (3)^2 = 25s^2 - 30s +9
The list of options is mistyped, so you must use the right list of choices and find which is 25s^2 - 30s + 9.
Answer: 25s^2 - 30s + 9
In the diagram below, ∠Q is bisected.
Find the perimeter of ΔPQS.
Answers
QP/QR = SP/SR
To be able to calculate the perimeter we need to know SP, which can be extracted from the formula QP/QR = SP/SR
QP/QR = SP/SR → 36/15 =SP/11 ; SP = (11x36)/15 = 26.4
And the perimeter is : 36+15+ (11+26.4) = 77.4 units