The probability that no two adjacent people will stand is 47/256. This is a problem that represents a combination.
What is combination?A combination is a grouping of items where order does not matter. The formula of combination is
[tex]_{n}C_{r} = \frac{n!} {r! (n-r)!}[/tex]
Where
C = number of combinationsn = number of total itemsr = number of choosing itemsGiven the case eight people sit around a circular table, flip coins, and those who flip heads will stand while those who flip tails will remain seated.
What is the probability that no two adjacent people will stand?
First, we count the total standing arrangements. They will be 2⁸ = 256 arrangements. n(S) = 256.
The number of arrangements according to the number of people standing.
Case 1: 0 people standing = 1 arrangement.
Case 2: 1 people standing = [tex]_{8}C_{1}[/tex] = [tex]\frac{8!} {1! 7!}[/tex] = 8 arrangements.
Case3: 2 people standing = [tex]_{8}C_{2}[/tex] = [tex]\frac{8!} {2! 6!}[/tex] = [tex]\frac{7 \times 8} {2}[/tex] = 28 arrangements, but no two people are next to each other. There are 8 arrangements that two people in this case are standing next to each other. So, it will be 28 - 8 = 20 arrangements.
Case 4: 3 people standing = [tex]_{8}C_{3}[/tex] = [tex]\frac{8!} {3! 5!}[/tex] = [tex]\frac{6 \times 7 \times 8} {6}[/tex] = 56 arrangements. In this case, three people standing are next to each other = [tex]_{8}C_{1}[/tex] = 8 arrangements. Two people standing are next to each other and the third person is not = [tex]_{8}C_{1} \times _{4}C_{1}[/tex] = 8 × 4 = 32. So, it will be 56 - 8 - 32 = 16 arrangements.
Case 5: 4 people standing but no two adjacent people = 2 arrangements.
The number of arrangements that no two adjacent people will stand.
n(A) = 1 + 8 + 20 + 16 + 2 = 47
The probability that no two adjacent people will stand is
P(A) = n(A)/n(S)
P(A) = 47/256
Hence, the probability that no two adjacent people will stand is 47/256.
Learn more about finding probability with combination here:
brainly.com/question/3901018
#SPJ4
A group of 4 people go to a restaurant and the bill without tax comes to $105.73. Tax is 6%. Remember to round to the nearest hundredth because this is money. After tax is added, you want to leave a 20% tip on the new total. The group of 4 people decides to split the total cost equally. How much will each person pay?
i need the answer fasttttt
Each person need to pay $ 80.88345.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Bill without tax = 105.73
Tax = 6%
So, bill amount after tax = 105. 73 + 105. 73 x 6/100
= 105.73 + 6.3438
= $112.0738
Addition of 20% tip = 112.0738 + 211.46 = $323.5338.
If the amount is divided among 4 people, each will pay
= 323.5338/4
= $ 80.88345
Learn more about Unitary Method here:
https://brainly.com/question/22056199
#SPJ1
3. Martin finishes a swim race in 78.934 seconds. His teammate, Abby finishes the race in 83.978 seconds and their last teammate finishes the race in 84.765 seconds.
CHALLENGE: How many minutes in total did they spend completing the race?
Help me pkleasee :((
The number of minutes in total that the three swimmers spent in completing the race is; 4.12795 minutes
How to carry out units conversion?We are given;
Time taken by Martin to finish swimming = 78.934 seconds
Time taken by Abby to finish swimming = 83.978 seconds
Time taken by the last teammate to finish the race = 84.765 seconds
Thus;
Total time taken by the three swimmers to finish the race = 78.934 + 83.978 + 84.765 = 247.677 seconds
Now, we want to know the total time they spent in minutes and we know that the unit of conversion is;
60 seconds = 1 minute
Thus;
247.677 seconds = (247.677 * 1)/60 = 4.12795 minutes
Read more about units conversion at; https://brainly.com/question/13994383
#SPJ1
an isosceles triangle has a base that measures x 2 with legs that measure 4x - 3 and 2x 5. what is the value of x? an isosceles triangle has a base that measures x 2 with legs that measure 4x - 3 and 2x 5. what is the value of x?
The value of x is 4 for the isosceles triangle has a base that measures x+2 with legs that measure 4x-3 and 2x+5.
What is an isosceles triangle?Therefore, an isosceles triangle has two equal sides as well as two equal angles. An equilateral triangle is one in which all of its sides are equal, and a scalene triangle is one in which none of its sides are equal. The characteristics of an isosceles triangle are as follows: There is agreement between two sides. The base of an isosceles triangle refers to the third side of the triangle, which is unequal to the other two sides. The two angles that are opposite the equal sides line up perfectly.
Here,
Since the adjacent sides of isosceles triangles are equal,
4x-3=2x+5
4x-2x=5+3
2x=8
x=4
The isosceles triangle has a base that measures x+2 and legs that measure 4x-3 and 2x+5, so x is equal to 4.
To know more about isosceles triangle,
https://brainly.com/question/28412104?referrer=searchResults
#SPJ4
13.ERROR ANALYSIS Describe and correct the error in
the student's reasoning.
Answer:
Step-by-step explanation:
The table shows a set of values for x and y
y is inversely proportional to the square x.
a) Find an equation for y in terms of x. (2)
b) Find the positive value of x when y = 25 (2)
Answer:
see explanation
Step-by-step explanation:
(a)
given y is inversely proportional to x² then the equation relating them is
y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation
to find k use any ordered pair from the table
using (2, 4 ) , then
4 = [tex]\frac{k}{2^2}[/tex] = [tex]\frac{k}{4}[/tex] ( multiply both sides by 4 )
16 = k
y = [tex]\frac{16}{x^2}[/tex] ← equation of variation
(b)
when y = 25 , that is
25 = [tex]\frac{16}{x^2}[/tex] ( multiply both sides by x² )
25x² = 16 ( divide both sides by 25 )
x² = [tex]\frac{16}{25}[/tex] ( take square root of both sides )
x = ± [tex]\sqrt{\frac{16}{25} }[/tex] = ± [tex]\frac{4}{5}[/tex]
the positive value of x is then [tex]\frac{4}{5}[/tex]
You are a prep cook in a restaurant. A particular
recipe uses 4 cups sugar. You only need to
make 1/3 of the normal amount. How many cups of sugar should you measure?
3. Functions f and g are shown below. Which
best represents
function g?
a. g(x) = f(x) - 3
b. g(x) = -f(x)
c. g(x) = f(x)
d. g(x) = f(x - 2)
Answer:
i think it might be c
Step-by-step explanation:
ERROR ANALYSIS Describe and correct the error. QRS=VWX by the ASA Congruence Theorem
Answer:
The error made is that the ASA theorem cannot be used here because the congruent side is not directly in between the two congruent angles in either triangle. Really, the information we are given is Angle-Side-Side, not Angle-Side-Angle, and this is not a congruence theorem unless the triangles given are right triangles.
you roll a six-sided die 20 times. what is the probability of having exactly 8 rolls land on a number greater than 4?
The probability of getting a number greater than 4 when the dice is rolled 20 times is 7.
The number on dice greater than 4 is 2 (that is 5 and 6 on dice) thus the probability of getting a number greater than 4 is
P = 2/6
P = 1/3
This is the probability if the dice were rolled once but if the dice were rolled 20 times thus the probability, in this case, needs to be multiplied by 20
P = 1/3*20
P = 6.66
equivalents to 7
For more information on probability kindly visit to
https://brainly.com/question/20312769
#SPJ4
1. A typical Chinese restaurant will often feature a Special Dinner, in which the customer has the choice of ordering one appetizer and one entree.
a. If there are 8 appetizers and 11 entrees, how many different Special Dinners
are there?
b. If there are 12 appetizers and 7 entrees, how many different Special Dinners
are there?
a) 88 unique special dinners are there if there are 8 appetizers and 11 entrees.
b) 84 unique special dinners are there if there are 12 appetizers and 7 entrees.
Given that,
In a typical Chinese restaurant, the Special Dinner is frequently offered, allowing the customer to select one appetizer and one entrée.
We have to find
a) How many unique special dinners are there if there are 8 appetizers and 11 entrees.
b) How many unique special dinners are there if there are 12 appetizers and 7 entrees.
We solve
a) We just multiply
8×11=88
b) 12×7=84
Therefore, a) 88 unique special dinners are there if there are 8 appetizers and 11 entrees.
b) 84 unique special dinners are there if there are 12 appetizers and 7 entrees.
To learn more about unique visit: https://brainly.com/question/14957572
#SPJ1
assume the state of arkansas placed a tax on playing cards of 6 cents per pack. if the state generated $48600 in revenue, how many packs of cards were sold?
The number of pack of cards sold at the state of Arkansas is 8100.
Describe the term division?Multiplication is the complete reverse of division. If participants of 4 add up to 12, then 12 divided into three classes of equally sized results in 4 in each group.For the values given in question.
The tax on playing card in state of Arkansas = 6 cents per pack.
Total revenue generated = $48600.
Divide total revenue by one pack price to get the number of packs.
Number of pack = Total revenue/price of each pack
Number of pack = $48600/6
$48600.Number of pack = 8100
Thus, the number of pack of cards sold at the state of Arkansas is 8100.
To know more about the division, here
https://brainly.com/question/28449912
#SPJ4
The area of rectangle abcd is 28 cm a) what is the length of side ab in terms of x? length of ab = 4 cm x cm 6 cm x cm b) if the area of rectangle abcd is 28 cm?, we can show that x2 + ax = b where a and b are integer values. work out the values of a and b. a : (1) b= (1) total marks: 3
The length AB of rectangle in terms of x is (4 + x) and values of a and b are 10 and 4.
The side AB measures (4 + x). Hence, the length of AB in terms of x is (4 + x).
The area of rectangle is calculated by the formula-
Area = length × breadth
Keep the values in formula -
28 = (4 + x) (6 + x)
Performing multiplication of both brackets with each other
28 = 24 + 4x + 6x + x²
Solving and rewriting the equation
x² + 10x = 4
Equation in question - x² + ax = b
Comparing both the equations, we get a = 10 and b = 4.
Thus, length of AB is (4 + x) and value fo a is 10 and b is 4.
Learn more about rectangle -
https://brainly.com/question/25292087
#SPJ4
What is the area of the parallelogram shown?
A= In^2
one class period at lily's school lasts for an hour and fifteen minutes, or $\frac{5}{4}$ hours. however, her biology class usually spends the first five minutes of that time talking and the next ten minutes reviewing old homework problems before they begin the lesson, which goes until the end of class. what fraction of lily's time is spent on the lesson itself?
Lily's time is spent in biology class on lesson is 1 hour or 60 minutes.
Time of one class = 1 hour and fifteen minutes
As we know, 1 hour = 60 minutes
So, time of a class = 60 + 15
Performing addition
Time of a class = 75 minutes
Time spent in talking in biology class = 5 minutes
Time spent in reviewing old homework = 10 minutes
Total time spent = 15 minutes
Remaining time = 75 - 15
Performing subtraction
Remaining time = 60 minutes
Hence, 60 minutes or 1 hour is spent on the lesson.
Learn more about addition and subtraction -
https://brainly.com/question/20460320
#SPJ4
Find the Area of the figure below, composed of a parallelogram and two semicircles. Round to the nearest tenth place.
Answer:
550.4 square units.
Step-by-step explanation:
This problem is easier than it seems.
To find the area of the parallelogram, multiply 11 and 32 to get 352 sq. units
The two semicircles must be equal because the sides of a parallelogram must be equal.
So if you add the semicircles together, you get a circle.
So we're really finding parallelogram+circle.
The area of a circle is [tex]\pi[/tex]x[tex]r^{2}[/tex], and the circle's radius is 8 because the radius is half of the diameter.
[tex]\pi[/tex]≈3.1 because you're rounding to the nearest tenth.
3.1x64=198.4 sq. units
198.4+352=550.4 square units.
Solve for x:
[tex]\sqrt{x-3} =\sqrt{x} +3[/tex]
A. -2
B. 2
C. no solution
D. 4
Answer: The answer is C: No solution
Step-by-step explanation:
By squaring the other side (to therefor remove the square off X) you get [tex]x-3=x+6\sqrt{x} +9[/tex]
You then cancel out the equal terms, in this case x, to reach the equation:
[tex]-3=6\sqrt{x} +9[/tex]
This equation, has no solution, as the left side is always negative, and the right side will always be positive, making any statement for x false.
Give the numerical coefficient of the term.
−7x
The numerical coefficient is _____.
The numerical coefficient is -7
How to determine the numerical coefficient?From the question, the expression is given as
-7x
Considering an expression given as
Ax
The numerical coefficient of the above expression is A
When compared to the expression -7x, we have
The numerical coefficient is -7
So, we can conclude that the numerical coefficient of -7x is -7
Read more about expressions at
https://brainly.com/question/4344214
#SPJ1
Answer:
-7
Step-by-step explanation:
The numerical coefficient is -7
Solve the system of equations.
Answer:
(7,5)
Step-by-step explanation:
[tex]-3y+4x=13 \implies -15y+20x=65 \\ \\ -5y-6x=-67 \implies 15y+18x=201 \\ \\ \therefore 38x=266 \implies x=7 \\ \\ \implies -3y+4(7)=13 \implies y=5 \\ \\ \therefore (7,5)[/tex]
If f(x)=4x^3+5, then what is the remainder when f(x) is divided by x−3?
Using Remainder theorem
Answer:
113
Step-by-step explanation:
Finding a remainder seems like you should be dividing. Remember everything is a shortcut for something else in math. So first you learn Long Division, but that's too much writing, so then you learn Synthetic Division, but there's an even shorter shortcut. It is called Remainder Theorem. If you just substitute 3 (because x-3 in the question) into the function, and you calculate it, you get the remainder.
f(x) = 4x^3 + 5
f(3) = 4(3)^3 + 5
f(3) = 4(27) + 5
= 108 + 5
= 113
See image.
A model of a car is 1 feet wide and 3 feet long. If the actual car is 15 feet long, what is the width of the actual car?
A. 3 feet
B. 5 feet
C. 15 feet
D. 45 feet
Answer:
5 feet.
Step-by-step explanation:
if we see that 3 feet is the model and 15 feet is the actual, we find the ratio is 3:15 or 1:5. since the width is 1 foot, then we see the actual is 5 feet long.
Which step contains a mistake in solving for the system of equations?
x + 2y = 5
y = 3x - 8
1. x + 2(3x) - 8 = 5
2. x + 6x - 8 = 5
3. 7x = 13
4. x = 13/7
5. 7x 8 5
Answer:
First step, correct answer is (3,1)
Step-by-step explanation:
1.it should be x+2(3x-8)=5
2. x+6x-16=5
3.7x=21
4. 7x/7=21/7
5. x=3
then you can eitheir take x+2y=5 or y=3x-8 i suggets taking second option as it is easier, just input values for x in
) 3x-8=y
6. 3(3)-8= 1
7. x=3, y=1
passes through A (2, "-5)" parallel to BC with (1, 3) and ( 4, 5) PLS HURRRY!!!!!
The equation for the linear equation parallel to BC is:
y = (2/3)*x - 19/3
How to get the linear equation?
A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through two points (x1, y1) and (x2, y2), then the slope is:
slope = (y2 - y1)/(x2 - x1)
And two lines are parallel if both lines have the same slope and different y-intercept.
So if we want to et a line parallel to BC whose endpoints are (1, 3) and ( 4, 5), the slope should be:
slope = (5 - 3)/(4 - 1) = 2/3
So our line is like:
y = (2/3)*x + b
And this must pass through (2, -5)
Replacing these values we get:
-5 = (2/3)*2 + b
-5 - 4/3 = b
-15/3 - 4/3 = b
-19/3 =b
Then the linear equation is:
y = (2/3)*x - 19/3
Learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
Complete the function table. Function: t = 5d − 2
The table for the linear equation is summarized below:
d t
3 13
4 18
5 23
6 28
How to complete a table related to a linear function
In this problem we have a two-column table associated to a linear function, the first column of the table represent a set of values of the domain (d) of the function and the second column of the table is for the set of values of the range (t) of the same. We need to fill the second column of the table with the values associated with the range:
d = 3
t = 5 · 3 - 2
t = 15 - 2
t = 13
d = 4
t = 5 · 4 - 2
t = 20 - 2
t = 18
d = 5
t = 5 · 5 - 2
t = 25 - 2
t = 23
d = 6
t = 5 · 6 - 2
t = 30 - 2
t = 28
To learn more on linear functions: https://brainly.com/question/9330192
#SPJ1
Rewrite in simplest terms: 6(8v-7)-10v
Step-by-step explanation:
[tex]6(8v - 7) - 10 \\ 48v - 42 - 10 \\ 48v - 52[/tex]
125.8% of £188.83
Give your answer rounded to 2 DP.
The answer is 237.55
Define Percentage
A ratio or figure stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
Given expression is,
125.8% of £188.83
Rewrite it as,
⇒ 125.8 / 100 * 188.83
⇒ 1.258 * 188.83
⇒ 237.54814
⇒ 237.55 (rounded to 2 Decimal places)
Hence, the answer is 237.55
To read more about Percentage
https://brainly.com/question/24304697
#SPJ13
Decide whether each equation is true for all, one, or no values of x.
Answer:
Theres nothing to see?
Step-by-step explanation:
Answer:
First is one value of x
Second is no values of x
Third is all values of x
Step-by-step explanation:
Please give brainliest!
What is the slope of a line that is perpendicular to y=4/5x+15 and passes through point (−3, 4)?
Answer:
Step-by-step explanation:
The slope of the line y = -5x-4 is -5 or -5/1 so the slope of the perpendicular line is +1/5 eg…
y = x/5 + c
To find c we substitute x=15, y=-2
-2 = 15/5 + c
-2 = 3 + c
C = -5
So the equation is
Y = x/5 - 5
Write and graph linear equations
The equation of linear equation is y = -5x +3.
What is equation of linear equation?
A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line. This is the reason why it is named as a 'linear equation'.
The standard form or the general form of linear equations in one variable is written as, Ax + B = 0; where A and B are real numbers, and x is the single variable. The standard form of linear equations in two variables is expressed as, Ax + By = C; where A, B and C are any real numbers, and x and y are the variables.
The slope intercept form of linear equation is
y = mx + b
where m is the slope.
Given,
The slope = -5
and the points are (4, -17)
y = -17, x = 4, m = -5
-17 = -5(4) + b
-17 = -20 + b
-17 + 20 = b
b =3
The equation of linear equation is y = -5x + b
To know more about linear equation, visit:
https://brainly.com/question/28307569
#SPJ1
express (3) - (2tan^2 x) in terms of cos x
The expression of [tex]3-2tan^2x\\[/tex] in terms of [tex]cosx[/tex] is [tex]3-2(\frac{1-cos^2x}{cos^2x})[/tex]. Similarly, any tirigonometric equation can be convereted into other forms of trigonometric functions.
What is trigonometric functions?
Denoting the relation between a right-angled triangle's angle and sides are trigonometric functions, which are periodic functions.
Consider the given expression.
[tex]3-2tan^2x\\[/tex]
Now, substitute [tex]\frac{sinx}{cosx}[/tex] for [tex]tanx[/tex] as follows:
[tex]3-2tan^2x=3-2(\frac{sinx}{cosx})^2\\=3-2(\frac{sin^2x}{cos^2x})[/tex]
Now, all the terms are converted into cos x except the sin x terms in the numerator. Hence, using the relation between sin x and cos x. Substitute [tex]1-cos^2x[/tex] for [tex]sin^2x[/tex].
[tex]3-2tan^2x=3-2(\frac{1-cos^2x}{cos^2x})[/tex]
Now, all the terms are in cos x. Hence, the expression of [tex]3-2tan^2x\\[/tex] in terms of [tex]cosx[/tex] is [tex]3-2(\frac{1-cos^2x}{cos^2x})[/tex]. In the similar way any function can be conveted into other trigonometric functions.
Learn more about trigonometric functions from the following link:
https://brainly.com/question/25618616
#SPJ1
HELPP!!!1 i'm rushing like i need to summit that ASAP!!
The missing expression in step 2 should be [(6² + 2)/0.5] - 14.8 ÷ 8.
The missing expression in step 6 should be 76 - 1.85.
How to evaluate and solve the given expression?In order to evaluate this expression, we would apply the PEMDAS rule, where mathematical operations within the parenthesis are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the expression to the right. Lastly, the mathematical operations of addition or subtraction would be performed from left to right.
For step 1, we have the following:
[(6² + 2)/|-0.5|] - 14.8 ÷ 8.
In step 2, we would take the absolute value of -0.5:
[(6² + 2)/0.5] - 14.8 ÷ 8.
Therefore, we would have the quantity of the sum of six squared (6²) plus two (2) divided by 0.25, minus 14.8 ÷ 8
In step 3, we would take the exponent of 6:
[(36 + 2)/0.5] - 14.8 ÷ 8.
In step 4, we would add 36 and 2 together:
[(38)/0.5] - 14.8 ÷ 8.
In step 5, we would divide 38 by 0.5:
76 - 14.8 ÷ 8.
In step 6, we would divide 14.8 by 0.5:
76 - 1.85
In step 7, we would subtract 1.85 from 76 as follows:
Solution = 76 - 1.85 = 74.15.
Read more on step here: https://brainly.com/question/28313300
#SPJ1