Using the permutation and the combination formula, we have that:
a) The first three finishers can be awarded medals in 504 ways.
b) They can be arranged in 252 ways.
c) In how many ways can 4 students form a team from a set of 8.
If the order is important, the permutation formula is used.If the order is not important, the combination formula is used.Combination formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Permutation formula:
The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
Item a:
Order is important, as the finishers are ranked, hence:
[tex]P_{(9,3)} = \frac{9!}{6!} = 504[/tex]
The first three finishers can be awarded medals in 504 ways.
Item b:
The order is not important, hence:
[tex]C_{10,5} = \frac{10!}{5!5!} = 252[/tex]
They can be arranged in 252 ways.
Item c:
Situation in which the order is not important, hence, for example, in how many ways can 4 students form a team from a set of 8.
For more on permutation/combination, you can take a look at https://brainly.com/question/25247153
Sarah is buying gifts for her friends. She is purchasing phone cases and chargers. The phone cases cost $25 and the charges cost $30. She
plans on spending no more than $100 and wants to buy at least 4 gifts. Which inequalities would be used to model this situation?
Answer:
Step-by-step explanation:
Let P be the number of phone cases and C the number of chargers.
p($25) + C($30) ≤ $100
and
P + C ≥ 4
plz help its taxes!!! just questions not real lol
Answer:
pay: 32,000*12 ( since its per month) =384,000
income tax: 384,000*0.45 = 172,800
EI: 384,000*0.0173=6,643.20
CPP: 384,000*0.0495=19,008
Yearly Pay will be 384,000-172,800-6,643.20-19,008= $185,584.80
Weekly pay (paycheck) = 42320.91/52 = $ 3,568.25
Step-by-step explanation:
numbers in order from least to greatest?
35%, 3/5, 0.27, 2/7
Answer:
0.27, 2/7, 35%, 3/5
Step-by-step explanation:
please help finals study guide
Answer this question.
You get a thank you and 5 stars if it's the correct answer.
Answer:
w = 5, x = 7, y = 6, z = 12
Step-by-step explanation:
Evaluate each row by solving the corresponding equation, that is
row 1
4w = 20 ( divide both sides by 4 )
w = 5
row 2
2w + 2x = 24 ( substitute w = 5 )
2(5) + 2x = 24
10 + 2x = 24 ( subtract 10 from both sides )
2x = 14 ( divide both sides by 2 )
x = 7
row 3
w + 2x + y = 25 , that is
5 + 2(7) + y = 25
5 + 14 + y = 25
19 + y = 25 ( subtract 19 from both sides )
y = 6
row 4
w + x + y + z = 30 , that is
5 + 7 + 6 + z = 30
18 + z = 30 ( subtract 18 from both sides )
z = 12
If -11 + N = -11, then N is the
a. additive identity
b. additive inverse
c. multiplicative inverse
d. multiplicative identity
Answer:
Step-by-step explanation:
eeuduehuheuhd hbu h
Jane wrote all natural numbers from 5 to 12. including 5 and 12.
how many numbers did Jane write?
PLS ANSWER FAST
Answer:
5, 6, 7, 8, 9, 10, 11 and 12 are the natural numbers between 5 and 12 including them, therefore Jane wrote 8 numbers. natural numbers start at positive 1 and go up by whole numbers infinitely, hope this helps
A piece of timber is
x
cm long.
How long would 3 pieces of timber be put together in a line?
Answer:
3x cm long.
Step-by-step explanation:
If one piece is x cm
and there are 3 together, presumeabley the same length
then you'd just need to multiply the length 3 times, therefore 3x respresents multiplying x 3 times.
Have a good day!
Answer:
3x cm long
Step-by-step explanation:
3 times x is 3x
Factorize 81xsquared+180x+100
Answer:
81x²+180x+1009x²+180x+10²using (a+b)²=a²+b²+2ab9x²+2(9x)(10)+10²(9x+2)²=(9x+2)(9x+2)Consider a parallelogram with vertices at (0, 3), (2, 0), (4, 2), and (2, 5).
2) Suppose the parallelogram is reflected over the x-axis, which vertex of the parallelogram will have the same coordinate before and after the reflection?
A) (0, 3)
B) (2, 0)
C) (2, 5)
D) (4, 2)
Answer:
B
Step-by-step explanation:
So a reflection over the x is a change in the y value.
Only point (2,0) is on the x-axis, so it will not move.
Calculate the distance between the points M=(-1, -2) and C=(-9, 2) in the coordinate plane.
Round your answer to the nearest hundredth.
Answer:
nearest hundredth 8.944
Step-by-step explanation:
d = √((x2-x1)2 + (y2-y1)2)
Step by step procedure:
Find the difference between coordinates:
(x2-x1) = (-9 - -1) = -8
(y2-y1) = (2 - -2) = 4
Square the results and sum them up:
(-8)2 + (4)2 = 64 + 16 = 80
Now Find the square root and that's your result:
Exact solution: √80 = 4√5
Approximate solution: 8.944
Question 7 of 15 Which is an equation of the line through (0,0) and (5,-2)? O A. y = 3 B. y = ja c. y = - 30 D. y=- Y
Answer:
b po sana po maka tulong
Step-by-step explanation:
pa brainliest po
A baseball team won about 62% of 162 games in a season.
About how many games did they win?
Answer:
the one about 100 games
Step-by-step explanation:
62 percent *162 =
(62:100)*162 =
(62*162):100 =
10044:100 = 100.44
this rounds to 100
Answer:
About 100 games
Step-by-step explanation:
162 * 0.62 = 100.4
100.4 rounded is 100
Help a sis out ??
Write a function rule for the area of a triangle whose height is 4 in, more than twice the length
of its base. What is the area of the triangle when the length of its base is 16 in.?
A. A = 262 + b
C. A = 262 + b
A = 144 in?
A = 528 in.
B. A = b2 + 2b
A = 288 in
D. A = 262 + 4b
A = 576 in
O
D
B.
C
SES
Answer:
B
Step-by-step explanation:
let base be b then height h = 2b + 4
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height ) , then
A = [tex]\frac{1}{2}[/tex] b(2b + 4) ← distribute parenthesis
A = b² + 2b
When b = 16 , then
A = 16² + 2(16) = 256 + 32 = 288 in²
PLS HELP ASAP ILL GIVE BRAINLKEST THANKS
Answer:
y = 5/6 x
Step-by-step explanation:
rise/run = slope
rise = 5
run = 6
so, 5/6 = slope
Which graph best represents the solution to this system of inequalities?
A.
B.
C.
D.
Answer:
letter A po
Step-by-step explanation:
thanks for brain less
if 10 seeds are planted, what is the probability that exactly 3 don't grow?
Answer:
10:7
Step-by-step explanation:
take 10 as it is and it becomes 10
then,10-3 it is because when 3 don't grow it subtracts and becomes 7
Eva took a taxi from her house to the airport. The taxi company charged a pick-up fee of $4.10 plus $0.50 per mile. The total fare was $9.60, not including the tip. Write and solve an equation which can be used to determine mm, the number of miles in the taxi ride.
Here we must write and solve a linear equation to find the number of miles that Eva traveled in the taxi. We will find that Eva traveled 11 miles.
So we know that the taxi charges a fee of $4.10 and then a plus of $0.50 per mile.
So if you travel for m miles, the cost equation is:
C(m) = $4.10 + $0.50*m
Now, we know that for Eva the total fare (total cost) was $9.60, then we need to solve:
$9.60 = C(m) = $4.10 + $0.50*m
$9.60 = $4.10 + $0.50*m
$9.60 - $4.10 = $0.50*m
$5.50 = $0.50*m
$5.50/$0.50 = m = 11
This means that Eva traveled 11 miles in the taxi.
If you want to learn more about linear equations, you can read:
https://brainly.com/question/19045223
Answer:
11
Step-by-step explanation:
Pls help with question 3 and below
Step-by-step explanation:
now find the area of triangle and add with the area of square and subtract with the area of circle
hope it will help you
A rectangular poster is 3 times as long as it is wide. A rectangular banner is 5 times as long
the banner and the poster have perimeters 24 inches. What are the lengths and of widths of the poster and the banner?
Rectangular Poster:
Length = 9
Width = 3
Rectangular Banner:
Length = 10
Width = 2
Hope this is helpful!
Does (2, –2) make the equation y = –2x + –2 true?
Answer: no it doesn’t because -2 doesn’t equal to -6
Step-by-step explanation:
all you have to do is plug 2 for x value and -2 for y
-2= -2(2)+ -2
so -2= -4+ -2 and -4+ -2 is -6
therefor -2 doesn’t equal to -6
Can someone please help?
Answer:
Well a midpoint makes the cutter segment or Line in exactly in half. So the two lines cutted are equal. In this case t is the midpoint. PT and TQ are equal. So you have two expressions, make then equal to each other since they are congruent.
6x+4=8x-8
12=2x
x=6
Now PT is 6x+4
So we subsitute x for 6 since x=6
6*6+4
40
PT is 40
How do I solve this
please help due any minute
Answer:
A the system has no solution
Step-by-step explanation:
Simplifying 2x + -5y = -8
Solving 2x + -5y = -8
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '5y' to each side of the equation. 2x + -5y + 5y = -8 + 5y
Combine like terms: -5y + 5y = 0 2x + 0 = -8 + 5y 2x = -8 + 5y
Divide each side by '2'. x = -4 + 2.5y Simplifying x = -4 + 2.5y
Solution for 2x-5=12 equation:
2x - 5 = 12
2x = 12 + 5
2x = 17 (divide both sides by 2 to get x)
2x/2 = 17/2
x = 8.5
please answer i'll mark brainliest
Answer:
X=-10 Y=-3
Step-by-step explanation:
one more time what 4 + 4 × 4 + 4 ÷ 4=
Answer:
I think probably 21
Step-by-step explanation:
4+16+1 = 21
Someone helppp pls due in 5 min
I will thank
After a power failure, the temperature in a freezer increased at an average rate of 3.5 °F per hour. The total
increase was 10.5 °F. Enter and solve an equation to find the number of hours until the power was
restored. Let x represent the number of hours it takes for the temperature to increase to 10.5 °F.
x=hours
7.5=2.5x
3=x
x=3
3 hours until the power was restored
60 points!!! Please answer immediately and the entire page please I will also give you five stars
Answer:
Step-by-step explanation:
9. Correct, D
-3Y + 9X <= 12
3Y - 9X => -12
3Y => -12 + 9X
Y => -4 + 3X
10. D
11. D
12. Correct, B
13. Correct, E
14. A
15. B
A swim team with 41 members decided to buy T-shirts that cost $15.75 each. 3. ___
What was the cost of the 41 T-shirts?