The number of games, the friends have to play is an illustration of combination.
They have to play 28 games to ensure that they all play
Given
[tex]n = 8[/tex] --- number of friends
[tex]r = 2[/tex] --- only two friends can play at a time
For everyone else to play, we will make use of the following combination formula;
[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]
So, we have:
[tex]^8C_2 = \frac{8!}{(8 - 2)!2!}[/tex]
[tex]^8C_2 = \frac{8!}{6!2!}[/tex]
Expand
[tex]^8C_2 = \frac{8 \times 7 \times 6!}{6! \times 2 \times 1}[/tex]
[tex]^8C_2 = \frac{8 \times 7}{2 \times 1}[/tex]
[tex]^8C_2 = 4 \times 7[/tex]
[tex]^8C_2 = 28[/tex]
Hence, the 8 friends have to play 28 games to ensure that everyone else plays
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All dimensions of a cylinder are multiplied by 1.5. Which statement is true?
A. The total surface area is multiplied by 3.375.
The volume is multiplied by 2.25.
B. The total surface area is multiplied by 2.25.
The volume is multiplied by 3.375.
C. The total surface area is multiplied by 3.
The volume is multiplied by 4.5.
D. The total surface area is multiplied by 4.5.
The volume is multiplied by 3.
Answer:
The true statement is;
B. The total surface area is multiplied by 2.25
The volume is multiplied by 3.375
Step-by-step explanation:
By scale drawing proportionality, we have;
The amount by which all the dimensions of the cylinder are multiplied to create an image of the cylinder = 1.5
∴ The scale factor between the original cylinder and the image of the cylinder, S.F. = 1.5
By rule, we have;
The area factor of the surface area = S.F.² = 1.5² = 2.25
Therefore;
The total surface area of the original cylinder is multiplied by 2.25 to get the total surface area of the image of the cylinder
By rule, we have;
The volume factor = S.F.³ = 1.5³ = 3.375
Therefore;
The volume of the original cylinder is multiplied by 3.375 to find the volume of the image of the cylinder.
Answer:
B
Step-by-step explanation:
7/8 = m - 5/12 What is m?
Answer:
31/24 or 1.29
Step-by-step explanation:
First isolate m to one side of the equation
7/8+5/12=m
21/24 + 10/24=m
31/24=m or you can simplify to get 1.29
The fun guys game rental store charges an annual fee of $5 plus $5.50 per game rented. The game bank charges an annual fee of $20 plus $2.50 per game. for how many game rentals will the cost be the same at both stores?
Use Pythagorean theorem to solve the following right triangles, put your answer in simplest radical form:
Answer:
Step-by-step explanation:I found the answer on this web[tex]^{}[/tex]site. It seems correct! Link Below!ly/3fcEdSx
bit.[tex]^{}[/tex]
PLSSSSS HELPPPPP REWARD BRAINLEISTTT
ANSWER:
number 1 is D, it moves to the right 4 times
number 2 is B, its a vertical stretch of 2
Can someone plz help me plz I beg u plz
Answer:
A.... X=3
Step-by-step explanation:
The net of a solid figure is shown below:
The net of a solid figure is shown below:
Which calculation will give the total surface area of the solid figure?
A) 3 x 6 x 6 square inches
B) 6 x 3 x 3 x 3 square inches
C) 3 x 6 x 6 x 6 square inches
D) 6 x 3 x 3 square inches
Answer:
D, 6 x 3 x 3
Step-by-step explanation:
One area of a square is 3 x 3 there are 6 squares so we multiply by 6 too.
Find the circumference of the circle to the nearest hundredth
11cm
Question: Find the circumference of the circle to the nearest hundredth
d = 11cm
Answer:
34.54 cm
Step-by-step explanation:
Applying,
P = πd...................... Equation 1
Where P = Circumference of perimeter of the circle, d = diameter of the circle, π = pie
From the question
Given: d = 11 cm
Constant: π = 3.14
Substitute these values into equation 1
P = (3.14×11)
P = 34.54 cm
HELPPPPPPPPPPPP THIS IS A MEGA TEST Felicia pours 3/4 of a 2 1/2-liter bottle of chlorine solution into a swimming pool. Then, she measures out the liter of the remaining solution to use to clean the pool filter. How much chlorine solution is left in the bottle?
Answer:
1/4 L
Step-by-step explanation:
2 1/2=10/4 10/4*3/4=30/16= 1 7/8
1 7/8=15/8 10/4*2=20/8 20/8-15/8=5/8
5/8-3/8=2/8 or 1/4 L
Answer: 1/4 L
In bottle 1/4 of chlorine solution is left in bottle.
What is an expression?
Expression in math is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that;
Felicia pours 3/4 of a 2 1/2-liter bottle of chlorine solution into a swimming pool.
And, then she measures out 3/8 liters of the remaining solution to use to clean the pool filter.
Now,
Chlorine solution in bottle = 2 1/2 × ( 1 - 3/4 ) - 3/8
= 5 / 2 × 1/4 - 3/8
= 5 / 8 - 2 / 8
= 1 / 4
Thus, In bottle 1/4 of chlorine solution is left in bottle.
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The complete question is this;
Felicia pours 3/4 of a 2 1/2-liter bottle of chlorine solution into a swimming pool then she measures out 3/8 liters of the remaining solution to use to clean the pool filter how much chlorine solution is left in the bottle?
estimate 12 8/9 - 10 1/6
Answer: 49/18
Step-by-step explanation:
3 feet
4 feet
inches
6 inches
Is Inches
What is the volume, in cubic feet, of the
cement used to make the steps? Show or
explain all of the steps you used to determine
your answer.
Answer: 12 for the main square
Step-by-step explanation:
take the 4 and the 3 and multiply it, makes 12. you see how each stair is 6 inches and there is 3 full steps which makes it 1.50 feet. 12 x 1.50 is 18. that makes your main square. I'm sorry but I cant really help you with the steps but that was also confusing to me.
laura has a 3-digit combination lock on her briefcase and has forgtten the combination. If she knows that the first digit is a 3, and the second digit is a prime, how many numbers must Laura try before the lock is sure to open?
Answer:
Laura needs to try 36 more times before the lock is sure to open.
Step-by-step explanation:
Alright, with a three digit lock, there are 9 possible numbers for each digit:
1, 2, 3, 4, 5, 6, 7, 8, and 9.
Since the first one is 3, lets move onto the second digit, which is prime.
Of the numbers between 1-9,
2, 3, 5, and 7 are prime.
With the last digit, it can be any number 1-9.
With all of this, there are 4 combos left for the second digit then 9 combos for the third digit. Therefore, there would be 36 possible combinations as 4 * 9 =36.
Use elimination/linear combination to solve the following.
please help
Answer:
Step-by-step explanation:
3x + 4y = 17
5x - 4y = 7
you can thus cancel out 4y
Hence
8x = 24
Hence x = 3
Substituting’
3(3) + 4y = 17
9 + 4y = 17
Hence 17 - 9/4
= y = 2
Hope this helps
Jim and Carol recorded gas prices at five stations for their own towns in the table below. Gas Prices Name Station 1 Station 2 Station 3 Station 4 Station 5 Jim $3.45 $3.54 $3.71 $3.62 $3.49 Carol $3.89 $3.65 $3.39 $3.48 $3.49 Which person's town had the lower mean for gas prices and by about how much?
A Jim, by $0.02
B Carol, by $0.02
CJim, by $0.06
D. Carol, by $0.06
Norma needs to find the sum of the fractions below. 3/8 +5/6 Norma starts by multiplying the first fraction by 3/3.
By which number should she multiply the second fraction?
A.8/8
B.4/4
c.3/3
d.undefined
Answer:
Its A
Step-by-step explanation:
Because if you add 3+5 that is 8 so 8/8
Pls, help me with this math question
Answer:
Perimeter [tex]\sqrt{26}+\sqrt{5}+\sqrt{10}+\sqrt{17}[/tex] units. Area 12 square units.
Step-by-step explanation:
Perimeter: total distance around the figure.
Distance Formula: the distance between points [tex]\left(x_1,y_1\right) \text{ and } \left(x_2,y_2\right)[/tex] is
[tex]d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
[tex]AB=\sqrt{(6-1)^2+(2-1)^2}=\sqrt{25+1}=\sqrt{26}[/tex]
[tex]BC=\sqrt{(5-6)^2+(4-2)^2}=\sqrt{1+4}=\sqrt{5}[/tex][tex]CD=\sqrt{(2-5)^2+(5-4)^2}=\sqrt{9+1}=\sqrt{10}[/tex][tex]DA=\sqrt{(1-2)^2+(1-5)^2}=\sqrt{1+16}=\sqrt{17}[/tex]
The perimeter is the sum of all those segment lengths.
One way to find the area of the figure is to surround it with a rectangle, insert some lines so that the areas you do not want can be found and subtracted from the rectangle's area. (See attached image.)
The area of the large rectangle around the figure is 5 x 4 = 20 square units.
The triangles have areas 1/2 (base) (height):
A. (1/2)(1)(4) = 2 square units
B. (1/2)(3)(1) = 1.5 square units
D. (1/2)(1)(2) = 1 square unit
E. (1/2)(5)(1) = 2.5 square units
Square C. (1)(1) = 1 square unit
Total of all the area you don't want to include:
2 + 1.5 + 1 + 2.5 + 1 = 8 square units
Subtract 8 from the surrounding rectangle's area of 20, and you get the area of the figure is 20 - 8 = 12 square units.
simplify 3+4(y-7)+5y
Answer:
9y-25
Step-by-step explanation:
Answer:
9y-25
Step-by-step explanation:
Math
Tomorrow the last day of school how ya feel?
-franz:)
Answer:
Ours is today. Feels weird how we came a long way with the pandemic presiding our academic studies.
Step-by-step explanation:
find the volume of the irregular figure
Answer:
V = 672cm^3
Step-by-step explanation:
V of irregular figure = lwh + lwh
V = 7(3)(2) + 10(7)(9)
V = 42 + 630
V = 672cm^3
Select all the sets of conditions that will create only one unique triangle.
Find the area of the given regular polygon
Round your answer to the nearest tenth, if necessary.
A. 221.7
B. 665.1
C. 280.6
D. 2660.4
Answer:
A.221.7Step-by-step explanation:
god bless
[tex]a[/tex]
7 1/2 divided by 3/4 =
Help please ;-;
Answer:
10
Step-by-step explanation:
convert mixed number into improper fraction
15/2÷3/4
to divide by a fraction multiply by the reciprocal of that fraction
15/2×4/3
reduce the numbers with the greatest common factor 3
5/2×4
reduce the numbers with the greatest common factor 2
multiply the numbers
5×2=10
10 is your answer
Asif and Ben share $2100 in the ratio Asif: Ben = 3:7.
Work out how much Asif receives.
$2100
Answer:
$630 for Asif
Step-by-step explanation:
Asif gets 3/10ths
So
2100 x 3/10 = $630 for Asif
Ravi and Hasan bought 13⁄4 of pies , Ravi ate 1/3 and Hasan ate 2/3 of it
. How much pie is left?
Answer:
The final answer is 0
Step-by-step explanation:
1/3 + 2/3 = 1 which means Ravi and Hasan ate the whole thing
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!
Three boys were playing balls. Ben's ball bounced eight more times than Menard's . Menard's ball bounced half as many times as Diego's. Diego's ball bounced eight times. How many times did Ben's ball bounced?
Answer:
12 bounce
Step-by-step explanation:
Let :
Number of Menard's bounce = x
Ben's bounce = x + 8
Diego's bounce = 2x
If Diego's bounce = 8
Then ;
2x = 8
x = 8/2
x = 4
Ben's bounce = x + 8
Ben's bounce = 4 + 8 = 12
How many reflectional symmetries does this figure have?
Enter your answer in the box.
_ reflectional symmetries
How many rational symmetries does this figure have?
Enter your answer in the box.
_ rotational symmetries
Answer:
1 & 1
Step-by-step explanation:
can i have help please i don't know the answer
Answer: 1.75=5n
Step-by-step explanation:
1.75 is being divided by n 5 times
The product ( the result of a multiplication problem ) of 2 rational expressions is x+22x−3 with the restrictions x≠– 3, x≠32, x≠4 and x≠ 5. Find an expression that meets the criteria. You may leave your answer in factored form.
Answer:
x + 22x - 3 = 4 (5x) + 3 (x-1)
Step-by-step explanation:
x + 22x - 3
23x - 3
20x + 3x - 3
5x + 15x + 3x - 3
5x (1 + 3) + 3 ( x - 1)
4 (5x) + 3 (x-1)
Which of the following are solutions to the equation below?
Check all that apply.
(3x - 5)2 = 19
Answer:
Take the square root of each side of the equation to set up the solution for
x
(
3
x
−
5
)
2
⋅
1
2
=
±
√
19
Remove the perfect root factor
3
x
−
5
under the radical to solve for
x
.
3
x
−
5
=
±
√
19
The complete solution is the result of both the positive and negative portions of the solution.
Tap for more steps...
x
=
√
19
3
+
5
3
,
−
√
19
3
+
5
3
The result can be shown in multiple forms.
Exact Form:
x
=
√
19
3
+
5
3
,
−
√
19
3
+
5
3
Decimal Form:
x
=
3.11963298
…
,
0.21370035
…
The solutions of the of the equation are,
⇒ x = 3.12
⇒ x = 0.21
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ (3x - 5)² = 19
Now,
We can simplify the expression for the solutions as;
⇒ (3x - 5)² = 19
Take square root both side,
⇒ √(3x - 5)² = √19
⇒ (3x - 5) = √19
Add 5 both side,
⇒ 3x - 5 + 5 = √19 + 5
⇒ 3x = √19 + 5
⇒ 3x = ± 4.36 + 5
⇒ 3x = 4.56 + 5
⇒ 3x = 9.36
Divide by 3;
⇒ x = 9.36 / 3
⇒ x = 3.12
And, 3x = - 4.56 + 5
3x = 0.64
x = 0.64/3
x = 0.21
Thus, The solutions of the of the equation are,
⇒ x = 3.12
⇒ x = 0.21
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Help with this please!!
Answer:
the first answer
Step-by-step explanation:
well first ofc u have to graph both equations to be able to compare them and if u don't have a graphing calculator just search up Desmos graphing calculator it will help A LOT