Answer:
1,968
Step-by-step explanation:
Let x₁ and x₂, y₁ and y₂, and z₁ and z₂ represent the 3 pairs of siblings, and let;
Set X represent the set where the siblings x₁ and x₂ sit together
Set Y represent the set where the siblings y₁ and y₂ sit together
Set Z represent the set where the siblings z₁ and z₂ sit together
We have;
Where the three siblings don't sit together given as [tex]X^c[/tex]∩[tex]Y^c[/tex]∩[tex]Z^c[/tex]
By set theory, we have;
[tex]\left | X^c \cap Y^c \cap Z^c \right |[/tex] = [tex]\left | X^c \cup Y^c \cup Z^c \right |[/tex] = [tex]\left | U \right | - \left | X \cup Y \cup Z \right |[/tex]
[tex]\left | U \right | - \left | X \cup Y \cup Z \right |[/tex] = [tex]\left | U \right | - \left (\left | X \right | + \left | Y\right | + \left | Z\right | - \left | X \cap Y\right | - \left | X \cap Z\right | - \left | Y\cap Z\right | + \left | X \cap Y \cap Z\right | \right)[/tex]
Therefore;
[tex]\left | X^c \cap Y^c \cap Z^c \right | = \left | U \right | - \left (\left | X \right | + \left | Y\right | + \left | Z\right | - \left | X \cap Y\right | - \left | X \cap Z\right | - \left | Y\cap Z\right | + \left | X \cap Y \cap Z\right | \right)[/tex]
Where;
[tex]\left | U\right |[/tex] = The number of ways the 3 pairs of siblings can sit on the 7 chairs = 7!
[tex]\left | X\right |[/tex] = The number of ways x₁ and x₂ can sit together on the 7 chairs = 2 × 6!
[tex]\left | Y\right |[/tex] = The number of ways y₁ and y₂ can sit together on the 7 chairs = 2 × 6!
[tex]\left | Z\right |[/tex] = The number of ways z₁ and z₂ can sit together on the 7 chairs = 2 × 6!
[tex]\left | X \cap Y\right |[/tex] = The number of ways x₁ and x₂ and y₁ and y₂ can sit together on the 7 chairs = 2 × 2 × 5!
[tex]\left | X \cap Z\right |[/tex] = The number of ways x₁ and x₂ and z₁ and z₂ can sit together on the 7 chairs = 2 × 2 × 5!
[tex]\left | Y \cap Z\right |[/tex] = The number of ways y₁ and y₂ and z₁ and z₂ can sit together on the 7 chairs = 2 × 2 × 5!
[tex]\left | X \cap Y \cap Z\right |[/tex] = The number of ways x₁ and x₂, y₁ and y₂ and z₁ and z₂ can sit together on the 7 chairs = 2 × 2 × 2 × 4!
Therefore, we get;
[tex]\left | X^c \cap Y^c \cap Z^c \right |[/tex] = 7! - (2×6! + 2×6! + 2×6! - 2 × 2 × 5! - 2 × 2 × 5! - 2 × 2 × 5! + 2 × 2 × 2 × 4!)
[tex]\left | X^c \cap Y^c \cap Z^c \right |[/tex] = 5,040 - 3072 = 1,968
The number of ways where the three siblings don't sit together given as [tex]\left | X^c \cap Y^c \cap Z^c \right |[/tex] = 1,968
Graph the equation of
= 1/3 − 4
Answer:my uncle john told me D
Step-by-step explanation:Beacause john have a brain
2x²+10x+12 اريد مساعده
Answer:
2(x+2)(x+3)
Step-by-step explanation:
The Venn diagram shows three types of numbers: odd (O), even (E), and prime (P).
Circles O and P overlap, and circle P also overlaps with circle E.
Which is represented by Ø?
Answer:
Null set
Step-by-step explanation:
Odd(0)
Even (E)
Prime (P)
Answer:
Its A since the other person didnt say it
Step-by-step explanation:
Which is the graph of the equation y-1=- f (x-3)?
Express tan J as a fraction in simplest terms
Answer:
SOH-CAH-TOA
tan = opposite/adjacent
tan J = 15/20 = 3/4
Step-by-step explanation:
A standard deck of cards contains 52 cards. Of these cards there are 13 of each type of suit (hearts, spades, clubs, diamonds) and 4 of each type of rank (A – K). Two cards are drawn from the deck and replaced each time back into the deck. What is the probability of drawing the King of Clubs and a heart from the deck of cards?
Answer: 13%
Step-by-step explanation:
khairul order one set meal at a restaurant which offer a 20% discount. there is a service charge of 10% and GST is at 7% given that he pays a total of 23.54 find the marked price of the set meal
Answer:
Market price of set = 25.14
Step-by-step explanation:
Given:
Discount percentage = 20%
Service charge = 10%
GST = 7%
Amount pays = 23.54
FInd:
Market price of set
Computation:
Assume;
Market price of set = a
Market price of set after discount = a(1-20%)
Market price of set after discount = 0.80a
Market price of set after discount + (Market price of set after discount)(Service charge) + (Market price of set after discount)(GST) = Amount pays
0.80a + (0.80a)(10%) + (0.80a)(7%) = 23.54
0.80a + 0.08a + 0.056a = 23.54
0.936a = 23.54
a = 25.14
Market price of set = 25.14
Zachary's art club ordered a giant sub sandwich for a party. It was 6 feet long! When the sandwich arrived, Zachary cut it into 16 equal pieces.
How long was each piece?
Write your answer as a proper fraction or mixed number.
Answer:
3/8 feet long
Step-by-step explanation:
Find how long each piece was by dividing 6 by 16:
6/16
Simplify this by dividing each number by 2:
6/16
= 3/8
So, each piece was 3/8 feet long
What is the slope of the graph?
write a function rule for the table
f (x) = 3x
The only function rule that works is A.
Instead of using f(x) - use y
Then place the numbers in for x and see which are true. The answer is A
given the nth term of geometric expression is (as in the diagram)
a) state the value of k
b) the first term of progression
Step-by-step explanation:
a) k = 1
b) geometric progression formula:
Tn = ar^(n-1)
first term, a = 3/2
Let f be defined as shown. What is f^-1(6)
Hello,
[tex]f^{-1}(6)=5[/tex]
A savings account for a car is set up with an initial balance of $3000, and 125 is added every
month (no other transactions occur on the account).
1. Write the expression:
2. Write the equation equal to the $5,000 car goal:
3. M=
4. How long will it take:
Answer:
1) 3000 + 125m
2) 3000 + 125m = 5000
3) M= 16
4) It would take 16 months
Step-by-step explanation:
Okay so no since there are no other transaction and you already have a balance of 3000 with a monthly Fee of 125 the equation shpuld be like this.
So every month you add 125,we dont know how much months we have to pay so we can use the variable given to us in this case “M”. So your base expression should look like this,
3000 + 125m (3000 base fee that doesnt change, and 125 every month fee)
Then it asked us to put it as the final balance as 5000, so using the base expression we can do this
3000 + 125m = 5000
Now to solve it you would solve it like any other equation
5000-3000=2000
2000=125m
2000/125= 16
Okay so m = 16
M in this case stands for months so the final answer would be it would take 16 months to reach the final balance of 5000
Select the correct product. (x^2+4)(x^2-4)
1. X^4-16
2. X^4+16
3. X^2+8x+16
4. X^2-8x-16
Answer:
[tex] ({x}^{2} + 4 )( {x}^{2} - 4) \\ 1)( {x}^{2} - 16) \\ = (x - 4)(x + 4) \\ 2)( {x}^{2} + 16) \\ = (x - 4)(x + 4) \\ 3) {x}^{2} + 8x + 16 \\ {x}^{2} + (4 + 4)x + 16 \\ {x}^{2} + 4x + 4x + 16 \\ x(x + 4) + 4(x + 4) \\ (x + 4)(x + 4) \\ 4) {x}^{2} - 8x - 16 \\ {x}^{2} - (4 + 4)x - 16 \\ {x}^{2} - 4x + 4x - 16 \\ x(x - 4) + 4(x - 4) \\ (x - 4)(x + 4)[/tex]
Please answer this to the best of your ability please
Answer:
B) 17 games.
Step-by-step explanation:
Let g represent the number of games Mark played.
Since there is a $5 entrance fee and each game costs an additional $1.25, we can write the expression:
[tex]1.25g+5[/tex]
Which represents that total cost after g games.
Since we know that Mark spent a total of $26.25:
[tex]1.25g+5=26.25[/tex]
Solve for g. Subtract five from both sides:
[tex]1.25g=21.25[/tex]
And divide both sides by 1.25. Hence:
[tex]g=17[/tex]
So, Mark played a total of 17 games.
Our answer is B.
Answer:
Mark played 17 games
Step-by-step explanation:
26.25-5 = 21.25
21.25 divided by 1.25 is 17
~hope this helps~
:)
Solve -5x + 5y = 15 and 3x – 2y=-8 by elimination
If someone can help that’d be brilliant
Step-by-step explanation:
-5x+5y=15(multiply by 2)
3×-2y=-8(multiply by 5)
-10×+10y=30
15×-10y=-40
5x=-10
x=-2
Here,
-5x+5y=15.......(I)
and
3x-2y=8.....(II)
Now,
adding 3 in eqn (II)
so, 6x-5y=8
Now,
combining eqn (I) &(II)
-5x+5y=15
+6x-5y=8
[both 5y is cancelled ]
or, x=7
Now,
in eqn(i)
-5x+5y=15
or, -5*7+5y=15
or, -35+5y=15
or, -35-15=-5y
or, -50=-5y
or, -50/-5=y
[minus is cancelled ]
Therefore, y=10 and x=7
rosa brought (d) drawings to an art show, after selling 17 of them, she had 22 left.identify the equation that represents this situation and the correct solution.
A. d-17=22; d=39
B. d+17=22; d=5
C. d+17=22; d=39
D. d-17=22; d=5
Answer:
A
Step-by-step explanation:
Rosa started with d amount of drawings. After selling 17, she has 22 left. So the equation is d-17=22. 17+22=39, so d must equal 39.
A line has slope 3 and y–intercept 4.
Answer:
1. 4x + y= 3
Step-by-step explanation:
im sure that is the right answer
please help me please
Answer:
that thing is not seeing properly and you can capture it again and resend it
Explain why the probability that the critical path will be finished in 22 weeks or less is not necessarily the probability that the project will be finished in 22 weeks orless.
Answer:
The question is very not detailed but I assume that because the path will finish does not mean that the whole thing/project will finish.
Step-by-step explanation:
The value of the expression 10 - 1/2^4 x 48
A = 2
B = 4
C = 5
D = 7
Answer:
option d is correct answer
PLEASE HELP!!! What is the volume of the solid? Let π=3.14.
A. 5,425.92 m3
B. 2,1714.7 m3
C. 8,131.09 m3
D. 3,214.54 m3
Answer:
A. 5,425.92 m3
Step-by-step explanation:
Radius = 24m
Length = 12m
Volume = Area * Length
Area = π * (radius ^2)
Radius = Diameter / 2
Radius = 24m / 2 = 12m
Area = π * (12m^2)
Area = 3.14 * 144 = 452.16m
Volume = 452.16m * 12m
Volume = 5425.92m3
Find the probability of exactly three successes in six trials of a binomial experiment in which the the probability of is 50%.
Start by doing the binomial expansion of (x+y)^6 where x represents success. This is
(x^6y^0) + 6(x^5y^1) +15(x^4y^2) +20(x^3y^3) +15(x^2y^4) +6(x^1y^5) +(x^0y^6)
We are interested in the x^3y^3 term which represents exactly 3 sucesses. Since the probalbility of sucess and failure are both .5 we should be able to figure this out just using the coefficients of the terms which is
20/64 = .3125 which is 31.25%
The probability of exactly three successes in six trials of a binomial experiment in which the the probability of is 50% is 31.25%.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
Here,
Probability =(³₆×(50%)³×(1-50%)⁶⁻³
= 20×(1/2)³×(1/2)³
= 20× 1/64
= 20/64
= 5/16
= 0.3125
= 0.3125×100
= 31.25%
Therefore, the probability of exactly three successes in six trials of a binomial experiment in which the the probability of is 50% is 31.25%.
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car travels at an average speed of 40 km/h for 0.5 hours.
How far did the car travel in km?
Given :-
A car travels at an average speed of 40 km/h for 0.5 hours.To Find :-
The distance travelled.Solution :-
We know that ,
→ Distance = Speed × Time
So that ,
→ Distance = 40 km/hr × 0.5 hr
→ Distance = 40km/hr × 1/2 hr
→ Distance = 20km .
Hence the required answer is 20km .
how many divisors does 56 have?
Answer:
1,2,4,7,8,14,28,56 those are the divisors for 56
Step-by-step explanation:
hope that helps >3
56 7*2^3 1,2,4,7,8,14,28,56
Helen drives 195miles in 3 hours
what is her average speed in mph
Answer:
65 mph is the correct answer
Answer:
s=d/t
=195/3
=65 mph
Solve for x. Round to the nearest tenth of a degree, if necessary.
Answer:
[tex]x\approx 49.6^{\circ}[/tex]
Step-by-step explanation:
In any right triangle, the tangent of an angle is equal to its opposite side divided by its adjacent side.
For angle [tex]x[/tex]:
Opposite side is 40Adjacent side is 34Therefore, we have:
[tex]\tan x^{\circ}=\frac{40}{34}[/tex]
Take the inverse tangent of both sides to solve for [tex]x[/tex]:
[tex]\tan^{-1}(\tan x)=\tan^{-1}(\frac{40}{34}),\\x=\tan^{-1}(\frac{40}{34}),\\x=49.63546343\approx \boxed{49.6^{\circ}}[/tex]
*Recall [tex]\tan^{-1}(\tan x)=x\text{ for } x\in (-90^{\circ}, 90^{\circ})[/tex]
Write the following expression in exponential form:
16x16x16x1.6
0416
0164
16x4
O 16+ 4
Answer:
16x16x16x1.6
Step-by-step explanation:
here's your answer hope it helps you
What is the value of cose in the diagram below?
Answer:
[tex]cos \theta = 0.6[/tex]
Step-by-step explanation:
Draw a line from point ( 0.6, 0.8 ) to the X - axis, forming a right triangle with hypotenuse = r = 1 , adjacent = 0.6, opposite = 0.8
[tex]cos \theta = \frac{adjacent}{hypotenuse} , \ where \ adjacent = 0.6 ,\ hypotenuse \ = r= 1[/tex]
[tex]cos \theta = \frac{0.6}{1}\\\\cos \theta = 0.6\\\\\theta = cos^{-1} \ 0.6\\\\\theta = 53.13^\circ[/tex]
The value of cos θ is,
⇒ cos θ = 0.6
What is mean by Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Now, We can Draw a line from point ( 0.6, 0.8 ) to the X - axis, forming a right triangle with hypotenuse = r = 1 , adjacent = 0.6, opposite = 0.8
Hence, We can formulate;
⇒ cos θ = 0.6 / 1
⇒ θ = cos ⁻¹ 0.6
⇒ θ = 53.13°
Thus, The value of cos θ is,
⇒ cos θ = 0.6
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Sofia has 25 coins in nickels and dimes in her pocket for a total of $1.65 how many of each type of coin does she have?
Answer:
She has 23 nickels and 5 dimes.
Step-by-step explanation:
Let n = the number of nickles and d = the number of dimes.
The number of each = 28. Set up the equation:
n + d = 28
Solve for n:
n = 28 - d
The total amount is $1.65 or 165 cents:
5n + 10d = 165
Substitute:
5(28 - d) + 10d = 165
140 - 5d + 10d = 165
140 + 5d = 165
5d = 165 - 140
5d = 25
d = 5, the number of dimes.
Solve for n:
n = 28 - d
n = 28 - 5 = 23, the number of nickles.
Proof:
5n + 10d = 165
5(23) + 10(5) = 165
115 + 50 = 165
165 = 165
Hope this Helps! Have an Awesome Day!!! <3
Step-by-step explanation:
Answer:
Sofia has 23 nickles & 5 dimes
Step-by-step explanation:
The number of each is 28
Form an equation:
[tex]n+d=28[/tex]
Solve for n:
[tex]n=28-d[/tex]
The total amount is $1.65 for 165 cents:
[tex]5n+10d=165[/tex]
Substitute:
[tex]5(28-d)+10d=165[/tex]
[tex]140-5d+10d=165[/tex]
[tex]140+5d=165[/tex]
[tex]5d=165-140[/tex]
[tex]5d=25[/tex]
[tex]d=25/5[/tex]
[tex]d=5[/tex]
Solve for n:
[tex]n=28-d[/tex]
[tex]n=28-5=23[/tex] ⇒ the number of nickles
CHECK:
[tex]5n+10d=165[/tex]
[tex]5(23)+10(5)=165[/tex]
[tex]115+50=165[/tex]
[tex]165=165[/tex]
hope this helps....