Answers
Short answer (I write nPr = P(n, r) and nCr = C(n, r) ):
P (6, 4) = 6! / (6 - 4)! = 6! / 2! = 720 / 2 = 360
C (6, 4) = P (6, 4) / 4! = 6! / (4! (6 - 4)!) = 360 / 24 = 15
Long answer:
P(n, r) counts the number of permutations of n objects taken r at a time, given by
P(n, r) = n ! / (n - r )!
A permutation is a unique arrangement of objects such that the order in which they are arranged is taken into account. For example, if the objects in question are the numbers in the set {1, 2, 3}, then
• there are 3! = 6 total possible permutations if we take all 3 numbers at once:
123, 132, 213, 231, 312, 321
• there are 3!/(3-2)! = 3!/1! = 6 total permutations if we only take 2 numbers at once:
12, 13, 21, 23, 31, 32
• there are 3!/(3-1)! = 3!/2! = 3 total permutations if we take only 1 number at a time:
1, 2, 3
• and there is 3!/(3-0)! = 3!/3! = 1 way of permuting the 3 numbers without taking any of them:
(the permutation itself is just empty space)
By contrast, C(n, r) counts the combinations of n items taken r at a time, given by
C(n, r) = P(n, r) / r !
A combination is like a permutation, but the order of the objects doesn't matter. Continuing with the previous example of arrangements of the numbers from {1, 2, 3}, we have
• 3! / (3! (3-3)!) = 1 combination taking all 3 numbers at once:
123
(the other 5 permutations listed earlier are made up of the same numbers, so we consider them duplicates)
• 3! / (2! (3-2)!) = 3 combinations taking only 2 numbers at once:
12, 13, 23
• 3! / (1! (3-1)!) = 3 combinations taking only 1 number:
1, 2, 3
• 3! / (0! (3-0)!) = 1 combination taking none of them:
(again, empty space)
The main point is that the order of objects is considered across permutations, while it's ignored across combinations.
Related Questions
Use the distance that these 9 students skimmer cars traveled in inches to calculate the MIDDLE 50%
468, 376, 540, 198, 230, 531, 281, 426, 346
a. 458 - 353.3
b. 255.5 - 499.5
c. 281 - 468
d. 230 - 531
Answers
9514 1404 393
Answer:
b. 255.5 to 499.5
Step-by-step explanation:
The middle 50% is the range between the first and third quartiles. In this group of 9 numbers, the first quartile is the average of numbers 2 and 3 when the numbers are listed from smallest to largest.
first quartile = (230 +281)/2 = 255.5 . . . . . . matches answer choice B
The third quartile is the average of numbers 7 and 8:
third quartile = (468 +531)/2 = 499.5 . . . . . also matches answer choice B
The middle 50% is 255.5 to 499.5.
_____
When I put the numbers in order, I get ...
198 230 ^ 281 246 376 426 468 ^ 531 540
^ indicates that the quartile here is the average of the adjacent numbers
bold indicates the median (2nd quartile)
Question 5 (1 point)
Solve the inequality for x.
- 3x + 6 < 15
Ox>-3
Ox<-3
0x<-7
Ox>-7
Answers
Answer:
x > -3
Step-by-step explanation:
-3x + 6 < 15
-3x < 15 - 6
-3x < 9
-x < 3
x > -3
A. x > -3
Step-by-step explanation:
Step 1: Subtract 6 from both sides.
−3x + 6 − 6 < 15 − 6
−3x < 9
Step 2: Divide both sides by -3.
−3x/−3 < 9/−3
x > −3
Can someone help me pls
Answers
Answer:
57°
Step-by-step explanation:
180-56=114
114÷2=57
Answer:
57°
Step-by-step explanation:
AO and BO are both the radius of the circle, so they are equal. Since it makes an iscosoles triangle, angles A and B are equal.
180-66=114
114/2=57
Please help, I’m not sure if I’m doing this right (math). 9 says 9x-47 btw.
Answers
Answer:
<1 = 43
<2= 17
<3= 120
<4=60
<5= 60
<6= 60
<7 =17
<8= 120
<9= 43
Step-by-step explanation:
< 4, <5, <6 are all 60
<3 and <4 are a linear pair, so they add to 180. Since <4 is 60, <3 is 180-60= 120
<6 and <8 are a linear pair, so they add to 180. Since <6 is 60, <8 is 180-60= 120
Angles 1 and 9 are congruent
4x+3=9x-47
50=5x
10=x
<1= 4(10)+4= 43
<9-9(10)-47=43
Now you have 2 angles for the triangle A B D- subtract the 2 known from 180
<2= 180-43-120=17
<7= 180-43-120=17
find the given polynomial by finding the greatest common monomial factor or the ñegative of the greatest common monomial factor and rewrite the expression.
Answers
Answer:
1. The greatest common monomial factor is xy
2. xy(6 + 2y² + 3x²)
Step-by-step explanation:
6xy + 2xy³+ 3x³y
1. Determination of the greatest common monomial (GCM) factor.
6xy + 2xy³+ 3x³y
6xy => 2 × 3 × x × y
2xy³ = 2 × x × y × y × y
3x³y = 3 × x × x × x × y
GCM => xy
2. Rewrite the expression
6xy + 2xy³+ 3x³y
GCM => xy
6xy + 2xy³+ 3x³y = xy(6 + 2y² + 3x²)
During a certain epidemic, the number of people that are
infected at any time increases at a rate proportional to the
number of people that are infected at that time. If 1,000 people
are infected when the epidemic is first discovered, and 1,200
are infected 7 days later, how many people are infected 12 days
after the epidemic is first discovered?
Answers
9514 1404 393
Answer:
1367 people
Step-by-step explanation:
The wording "a rate proportional to the number" indicates the function is exponential. The growth factor is 1200/1000 = 1.2 in 7 days, so the exponential function can be written ...
i(t) = 1000(1.2^(t/7))
After 12 days, the number infected is modeled as ...
i(12) = 1000(1.2^(12/7)) ≈ 1367
About 1367 people are infected 12 days after discovery.
The given lines are rotated 90°. Which choice describes the lines resulting from the transformation?
A)
intersecting
B)
parallel
C)
perpendicular
D)
skew
Answers
Answer:
there still parallel even if they rotated
Cellular phone service is available for $37 per month for 1847 minutes. What is the monthly cost per minute? Round your answer to the nearest tenth of a cent.
The cost for the phone service is cents per minute.
Answers
solve x + 1 > 3. graph the solution. can someone help me out??
Answers
Answer:
x>2
Step-by-step explanation:
x+1>3
x>3-1
x>2
I hope this helps
y = 3x - 1 Let x = 6. The ordered pair is (6,_).
Answers
Answer:
Step-by-step explanation:
y = 2x - 1
x = 6
y = 3*6 - 1
y = 18 - 1
y = 17
(6,17)
First answer gets brainest. 8th grade math root question
Answers
Answer:
9
Step-by-step explanation:
Answer: 9
Step-by-step explanation:
Square Rooting is basically going down to the origins of the number, trying to figure out what times (x) would give you your current number. In order it get 81, you would need to do 9*9, therefore making the square root 9
a sunglasses store bought $5,000 worth of glasses the store made $9,000 making a profit of $20 per sunglasses there were How many pairs of sunglasses involved?
Answers
Answer:
150 pairs
Step-by-step explanation:
so total money spent Is equal to 5000
profit is equal to 3000
profit on each pair is equal to 20
so 3000 divided by 20
which gives 150
so 150 pairs of sunglasses were involved
pls give me brainliest I need it
Answer:
The sunglasses involved are 200
Point O is the center of the square ABCD. Point E is the midpoint of line segment CD. The area of square ABCD is 24, what is the are of the quadrilateral BCEO?
Answers
Answer: You divided 24 by 3 then you take the answer
Step-by-step explanation:I hope it help
Hey, I need help!
What is 56/2?
Answers
Answer:
28
Step-by-step explanation:
Answer:
56 divided by 2 would be 28.
Step-by-step explanation:
[tex]\frac{56}{2}[/tex] is the same thing as half of 56, since two 28s added together is 56, which means [tex]\frac{56}{2}[/tex] is equivalent to 28.
michelle has four credit cards with the balances and interest rates listed below. She wants to pay off her credit cards one at a time, based on the interest rate. In which order should Michelle pay off her credit cards
Answers
Answer:
3,2,1,4
Step-by-step explanation:
Calcula el área y perímetro de un rectángulo que tiene como base (x+y) y altura (x-1).
Answers
Answer:
A = x^2 - x + xy - y
P = 4x + 2y - 2
Step-by-step explanation:
[tex]a = (x + y)(x - 1) \\ a = {x}^{2} - x + xy - y \\ \\ p = 2((x + y) + (x - 1)) \\ p = 2(2x + y + - 1) \\ p = 4x + 2y - 2[/tex]
I hope that is useful for you :)
PLEASE HELP! IM GIVING BRAINLIEST!
Answers
Answer:
1/2 x 1/2= 2/4
Step-by-step explanation:
Answer:
Nicoles pattern is correct
Ians pattern is 0,1,3,7,15,
Coordinate pairs
1,0
5,1
17,3
53,7
161,15
Step-by-step explanation:
Pencil and paper
Solve for y please will mark brainly
Answers
Answer:
y = -4
Step-by-step explanation:
since f(y) = 9, you know the equation is equal to 9
9 = [tex]\sqrt{y+29}[/tex] - y
81 + 18y + y^2 = y + 29
y = -4
Someone please answer this correctly!!
Answers
Answer:
1.98 × 10^10
Step-by-step explanation:
First solve for how many text messages were sent out per one month:
22,000,000 × 900
19,800,000,000
Convert into scientific notation:
1.98 × 10^10
In scientific notation, there can only be one number before the decimal. The rest of the numbers must be after the decimal; hence, why I put the numbers 9 and 8 after the decimal. If the rest of the numbers are zeros, you do not have to add them after the decimal. Instead, starting from right to left, count the number places until you reach your decimal. The number you have counted will be your exponent. I counted nine 0's, one 8, and one 9 which made this exponent 10 as there were 10 decimal placements.
Florida Fish and Wildlife is having problems with the growing population of Pythons in the Everglades. The graph below shows the annual growth of the python population from beginning 2000 to 2010. What is the domain of the graph that is shown?
Answers
Answer:
x≥0
Step-by-step explanation:
the domain is anything above 0
The domain of the graph is [0, 10] or 0 ≤ x ≤ 10 when the annual growth of the python population from the beginning of 2000 to 2010.
What is a function?It is defined as a special type of relationship and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
Florida Fish and Wildlife is having problems with the growing population of Pythons in the Everglades.
As we can see in the graph the annual growth of the python population from the beginning of 2000 to 2010 is continuously increasing between 0 to 10,
Mathematically,
x ∈ [0, 10] or
0 ≤ x ≤ 10
Thus, the domain of the graph is [0, 10] or 0 ≤ x ≤ 10 when the annual growth of the python population from the beginning of 2000 to 2010.
Learn more about the function here:
brainly.com/question/5245372
A ratio of the number of boys to the number of girls in a choir is 5 to 4. There are 60 girls in the choir
Answers
solve for x using the quadratic formula. x^2+9x+20=0
Answers
Answer: x= -4,-5
Step-by-step explanation:
Answer:
Step-by-step explanation:
I can help
Step 1
factor the left sides of the equation
Then you will get (x+4)(x+5)=0
Step 2
You will have to set the factors equal to 0
x=-4 or x=-5
Hope this helped
Use the ALEKS calculator to find 35% of 65. Do not round your answer.
Answers
Answer:
35 % of 65 is 22.75 %
Step-by-step explanation:
35/100 = 0.35
0.35 x 65 = 22.75
therefore 35% of 65 is 22.75%
The picture shows two sections of Mrs. Jones's art supply drawer.
Paints
Brush’s
What is the total area of both sections of the drawer? Enter the answer in the box.
Answers
I WILL MARK YOU AS BRAINLIEST IF YOU ANSWER CORRECTLY!!! Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(-8, 3), B(-3, 3), C(-3, 6), and D(-8, 6)
What is the area of rectangle ABCD
Answers
Answer:
15 square units
Step-by-step explanation:
So who’s tryna help me ☝
Answers
Answer:
4
Step-by-step explanation:
5+3=8 and 5-3=2 which is 8/2=4
Answer: 4
1. Simplify 5 + 3 to 8.
8 / 5 - 3
2. Simplify 5 - 3 to 2.
8 / 2
3. Simplify.
4
solve the system using substitution x=-4y y=2x+9
Answers
Answer: x=-4
Step-by-step explanation:
Given
x=-4y
y=2x+9
Rephrase equation to find y value in terms of x
y=-x/4
y=2x+9
Use substitution (substitute value of y)
2x+9=-x/4
Multiply -4 on both sides
-4(2x+9)=-4(-x/4)
-8x-36=x
Add 8x on both sides
-8x-36+8x=x+8x
-36=9x
Divide 9 on both sides
-36/9=9x/9
x=-4
Hope this helps!! :)
Please let me know if you have any questions
What is the perimeter of a square with an area of 256 cm^2
Answers
Answer:
16cm
Step-by-step explanation:
The area of a square is calculated by perimeter * perimeter. 256 is made of 16*16
Answer:
you know that the Area of a square is calculated as S^2 or SxS
to find the side length just do square root of 256
wich is 16 cm
multiply by 4 and the perimeter is 16*4= 64
if the square roots of the natural numbers from 1 to 200 are calculated what will be the whole numbers
Answers
Answer:
f
Step-by-step explanation:
Green vines attached to the trunk of the tree had wound themselves toward the top of the canopy. Ants used the vine as their private highway, avoiding all the creases and crags of the bark, to freely move at top speed from top to bottom or bottom to top depending on their current chore. At least this was the way it was supposed to be. Something had damaged the vine overnight halfway up the tree leaving a gap in the once pristine ant highway.
The whole numbers will be:
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}
How to find the whole numbers?
Remember that a square root will have a whole number as an outcome only if the input is a square number.
Then, what we can do here is just find all the square numbers smaller than 200.
1*1 = 1
2*2 = 4
3*3 = 9
4*4 = 16
5*5 = 25
6*6 = 36
7*7 = 49
8*8 = 64
9*9 = 81
10*10 = 100
11*11 = 121
12*12 = 144
13*13 = 169
14*14 = 196
Then, if we take the square roots of all the natural numbers from 1 to 200, we will have 14 whole numbers as outcomes, and these will be:
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}
If you want to learn more about square roots, you can read:
https://brainly.com/question/8952483
The diagram shows a rhombus inside a regular hexagon
Work out the size of x
Answers
Answer:
add a picture
Step-by-step explanation: