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Suppose we want to choose 5 colors, without replacement, from 18 distinct colors.
(a) If the order of the choices does not matter, how many ways can this be done?
(b) If the order of the choices matters, how many ways can this be done?
Considering the definition of permutation and combination:
the number of ways of choosing 5 colors from 18 distinct colors (the order doesn't matter) is 8,568.the number of ways of choosing 5 colors from 18 distinct colors (the order of choices matters) is 1,028,160.Definition of PermutationPermutation is placing elements in different positions. So, permutations of m elements in n positions are called the different ways in which the m elements can be arranged occupying only the n positions.
In other words, permutations (or Permutations without repetition) are ways of grouping elements of a set in which:
take all the elements of a set.the elements of the set are not repeated.order matters.To obtain the total of ways in which m elements can be placed in n positions, the following expression is used:
[tex]mPn=\frac{m!}{(m-n)!}[/tex]
where "!" indicates the factorial of a positive integer, which is defined as the product of all natural numbers before or equal to it.
Definition of combinationCombinations of m elements taken from n to n (m≥n) are called all the possible groupings that can be made with the m elements in such a way that not all the elements enter; the order does not matter and the elements are not repeated.
To calculate the number of combinations, the following formula is applied:
[tex]C=\frac{m!}{n!(m-n)!}[/tex]
This caseIn this case, you know we want to choose 5 colors, without replacement, from 18 distinct colors. This is:
We want to choose 4 colors: n= 5The total number of distinct colors: m= 18(a) If the order of the choices is not taken into consideration, you use a combination as follow:
[tex]C=\frac{18!}{5!(18-5)!}[/tex]
Solving:
[tex]C=\frac{18!}{5!13!}[/tex]
C= 8,568
Finally, the number of ways of choosing 5 colors from 18 distinct colors (the order doesn't matter) is 8,568.
(b) If the order of the choices matters, you use a permutation as follow:
[tex]18P5=\frac{18!}{(18-5)!}[/tex]
Solving:
[tex]18P5=\frac{18!}{13!}[/tex]
18P5= 1,028,160
Finally, the number of ways of choosing 5 colors from 18 distinct colors (the order of choices matters) is 1,028,160.
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What is the slope? (5,6) and (-1, 4)
Answer:
1/3
Step-by-step explanation:
y2-y1/x2-x1
4-6/-1-5
-2/-6
1/3
Find the equation of the line in SLOPE-INTERCEPT form if the slope is 3 and passes through the point (3,5)
A.y = 3x - 4
B.y = 3x -5
C.y = 3x + 5
D.y-5 = 3(x-3)
rational numbers
-2 + -([tex]\frac{1}{2}[/tex]+[tex]\frac{1}{3}[/tex]+[tex]\frac{1}{5}[/tex])
a)-[tex]\frac{1}{30}[/tex]
b)[tex]\frac{-29}{30}[/tex]
c)[tex]\frac{29}{30}[/tex]
d)1[tex]\frac{1}{30}[/tex]
Answer in fraction
The fraction is simplified to - 29/30 . Option B
What is a fraction?
A fraction is simply known as the part of a whole.
Types of fractions;
Mixed fractionsSimple fractionsProper fractionsImproper fractionsGiven the fraction;
-2 + ( 1/ 2 + 1/ 3 + 1/ 5 )
Find the lowest common multiple
- 2 + ( 15 + 10 + 6 /30 )
-2 + ( 31/30)
expand the bracket by finding the lowest common multiple, we have;
-60 + 31 / 30
Add the numerators
- 29/30
Thus, the fraction is simplified to - 29/30 . Option B
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Find the area.
5 cm
4 cm
3 cm
Answer:
The area is 60
Step-by-step explanation:
You had to multiply 5×4×3
Answer:
my math teacher said that to find the area multiple all the numbers together so I got 47
This one as well please
Answer:
1/11
Step-by-step explanation:
If there are 11 counters and there's only 1 white one, that makes it to where there's only a 1 in 11 chance of you choosing that one white counter.
How do you solve this equation step-by-step? (below)
4a + 8 - 2a - 3 = 45
Answer:
a=20
Step-by-step explanation:
4a+8-2a-3=45
-8 on both sides
4a-2a-3=37
+3 on both sides
4a-2a=40
2a=40
a=20
Answer:
a = 20
Step-by-step explanation:
Let's understand it quickly,
4a + 8 - 2a - 3 = 45
Gather the like terms on RHS and LHS,
4a - 2a = = 45 - 5
2a = 40
a = 40/2
a = 20
Hope it helps!<3
Let U = { 14, 15, 16, 17, 18, 19, 20 },
A = { 16, 17, 18, 19 }.
Use the roster method to write the set A′.
Complement of A set in roster form will be {14,15,20}.
U = { 14, 15, 16, 17, 18, 19, 20 },
A = { 16, 17, 18, 19 }.
A'= {14,15,20}
A set is mathematically represented in a straightforward way using roster notation. The elements (or members) of a set are listed in a row inside the curly brackets in the roster form. If the set contains more than one element, a comma is used in a roster notation to indicate the separation of every two elements. A list of the elements of a set, each separated by a comma, enclosed in a set of curly brackets, can be used to describe the contents of the set. Roster form is the term for this method of setting forth a set.
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What is the value of the expression below?
(12^1/6)^6
A. 8
B. 64
C. 12
D. 1
Calculate the radicand of f(x)=x^2+20x+97 and state what it tells you about the roots of the function. Then solve the function using the quadratic formula.
Answer: The roots are x=-10 +- root 3.
Step-by-step explanation:
Write 7 9/10 as an improper fraction
Answer:
7910=7910
Step-by-step explanation:
7 9/10 as an improper fraction is 79/10.
Given is a mixed fraction 7 9/10 we need to convert it into improper fraction,
To convert the mixed number 7 9/10 into an improper fraction, you need to follow these steps:
Step 1: Multiply the whole number (7) by the denominator (10): 7 x 10 = 70.
Step 2: Add the numerator (9) to the result from Step 1: 70 + 9 = 79.
Step 3: Write the sum from Step 2 as the numerator of the fraction.
Step 4: Keep the denominator (10) the same.
Therefore, 7 9/10 as an improper fraction is 79/10.
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verify -(-x)=x for x =12/15 please answer fast
Answer:
-(-12/15) = 12/15
Step-by-step explanation:
-(-x) = x
Two minuses, one minus outside the bracket and one inside, make a positive. Thus:
-(-12/15) = 12/15
the double number line shows that 4 bottles of water cost 10 dollars at a music festival
Answer:
That means that each water is $2.50, das crazy tho
Step-by-step explanation:
-6x+15=45
what does x equal/
Answer:
6x Would not be considered as a answer but it is known as a unknown so the answer would be -60
Step-by-step explanation:
This is because it is
What are the slopes of the graphs
Answer:
1. 1/3
2. -2
3. 0
4. -2
5. 2/3
6. 0
Step-by-step explanation:
I'm going left to right for each graph just for clarification so you don't get confused.
I hope this helps and if it did I would appreciate it if you marked me Brainliest. thank you and have a nice day!
Find the value of x.
Answer:
27.5
Step-by-step explanation:
Answer:
(8-2)180
6*180= 1080
1080- 119- 140- 124- 132- 132- 102 = 331
6x +6x = 331
12x= 331
x= 27.5833
6(x)= 165.5
165.5 +165.5 + 119+ 140 + 124+ 132 + 132+ 102= 1080
I
Line segment LN has endpoints L(-2, -3) and N(3, 7).
Which of the following determine the coordinates of point M located at the
of LN?
Answer:
(1/2, 2)
Step-by-step explanation:
Use Midpoint Formula
Label points L and N
M = (x1 + x2/2, y1 + y2/2)
M = ( -2 +3/2, -3 + 7/2)
M = (1/2, 2)
I really do not understand and need the answer!
You have just been hired as New York’s premier Real Estate Agent! In your company, you will make a 7% commission. The real estate market in New York is booming! As the realtor calculates your potential commission if you sell the property for the list price.
If the listing price for Candy Cane Creek is $864, 550, how much commission would you receive?
Answer: $60,518.50
Step-by-step explanation: Multiply 864,550 and 0.07 because you need to find the commision.
Answer:
Hello
Step-by-step explanation:
Joey made a deposit into
an account that earns 6%
simple interest. After 3
years, Joey had earned $400.
How much was Joey’s initial
deposit? __________________
Write a real world problem that you can model with the two step equation 5x+7=10.
The equation can be expressed as the product of 5 and a number increased by 7 is equal to 10.
Solving linear equationLinear equation are equations that has a leading degree of 1. The standard linear equation is given as y = mx + b
Given the expression 5x + 7 = 10
Subtract 7 from both sides to have:
5x+ 7 - 7 = 10 -7
5x = 10 - 7
5x = 3
5x - 3 = 0
5x = 3
x = 3/5
The equation can be expressed as the product of 5 and a number increased by 7 is equal to 10.
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what are the slope and the y-intercept of the linear function that is represented by the table
Answer:
D: The slope is 3, and the y-intercept is 3/2
A display has
6
66 packs of marbles with a total mass of
629
g
629g629, start text, g, end text. The packaging of each pack has a mass of
2
3
g
3
2
gstart fraction, 2, divided by, 3, end fraction, start text, g, end text and each marble has a mass of
4
1
2
g
4
2
1
g4, start fraction, 1, divided by, 2, end fraction, start text, g, end text.
Which equation can we use to determine
m
mm, the number of marbles per pack?
Answer:
D) 6(4 1/2 m + 2/3)=629Step-by-step explanation:
A display has 6 packs of marbles with a total mass of 629g. The packaging of each pack has a mass of 2/3 g and each marble has a mass of 4 1/2 g.
Which equation can we use to determine m, the number of marbles per pack?
A 6*4 1/2 m+ 2/3=629 B 6 m(4 1/2+ 2/3)=629 C 6 m+4 1/2+ 2/3=629 D 6(4 1/2 m + 2/3)=629================================
A total mass is the sum of 6 packs and each pack is:
m marbles + packaging = 4 1/2 m + 2/3We can put it as equation:
6(4 1/2m + 2/3) = 629Correct option is D
Answer:
D. 6(4 1/2 m + 2/3)=629
Step-by-step explanation:
I did it on khan academy so theres no way this is incorrect.
Lynne needs to borrow $9500 for cosmetic surgery she obtains a loan from her grandmother for 24 months at a simple interest rate of 9.3% what is the loans future value?
Answer:
$11267
Step-by-step explanation:
Loan Future value = amount borrowed + interest
Amount borrowed = 9500
Interest = Principal * Rate * Time/100
Interest = 9500*9.3 * 2/100
Interest = 95*9.3 * 2
Interest = $1767
Loan Future amount = 9500 + 1767
Loan Future amount = $11267
A recipe for chocolate chip cookies with toffee bits and walnuts serves 8 people and needs 3 cups of flour. If Zachary wants to make the recipe for 14 people, how many cups of flour should he use?
I will mark you as the brainliest IF answered correctly.
Answer:
Im pretty sure it's 5.25 cups of flour
Step-by-step explanation:
so we know that it takes 3 cups for 8 people and we don't know the amount for 14 people so write it as a fraction and cross multipy
For the equation
8/3=14/x
The cross product is
8*x=3*14
Solving for x
x=3×14/8
and reducing
x=5.25
Cost price of an item is Rs 600. If the selling price is Rs 780, then the profit percent is
Answer:
Profit percentage=30%
Step-by-step explanation:
The profit percentage=profit/cost price×100%
but we can calculate profit as=selling price-cost price
profit=Rs780-Rs600=Rs180
Now substitute the profit value into the formula
Profit percentage=Rs180/Rs600×100%=30%
C.P of an item= Rs.600
S.P of an item = Rs. 780
Profit = SP- CP
= Rs. 780- Rs.600
=Rs.180
Now, profit percent= profit÷ CP × 100%
= 180 ÷ 600 × 100%
=30%
SOLVED! I HOPE ITS RIGHT!
PLEASE HELP ME????!!!?
Step-by-step explanation:
what is the question ?
check everything that applies to the angles 1 and 2 ?
in that case :
two angles are adjacent angles, when they share a vertex and side.
so, yes, adjacent angles is true
vertical angles are angles that are opposite of each other when two lines cross.
so, no, vertical angles is false.
two angles are complementary, when they are adjacent and have combined 90°.
so, yes, complementary angles is true.
2 angles are supplementary, when they are adjacent and have combined 180°.
so, no, supplementary angles is false.
a linear pair of angles is basically the same as supplementary angles.
they are formed when two lines intersect each other (at a single point). The angles at the intersection point are linear if they are adjacent to each other, and their sum is always equal to 180°.
so, no, linear pair is false.
PLS HELP!!! I am gonna fail
Answer:
Help with what? You didn't post anything.
Step-by-step explanation:
Rank the following tools for measuring length from those that give the least precise results to the most precise results.
Highway mile marker
A yardstick
A length of a person's foot
A five - foot long branch from a tree
Answer:
option 3,4,2,1
Step-by-step explanation:
Look at my picture, what’s the missing statement in step 4?
Answer:
Step-by-step explanation:
∠ACE=∠ BCD (reflexive property )
It is common to both the angles or both the angles represent the same angle.
We have to prove two triangles are similar.
Here we show two angles of different triangles are equal.
Hence similar by AA
Answer:
m<CBD is congruent to m<DBC
Step-by-step explanation:
Reflexive property states that any real number, for example a, is equal to itself. < cbd is congruent to < dbc :)
Passenger trains leave the station every
40 minutes. Freight trains leave every
30 minutes. If a passenger train and a
freight train just left at the same time, how
long will it be before one of each train
departs at the same time again?
When Passenger trains leave the station every 40 minutes and Freight trains leave every 30 minutes, If a passenger train and a freight train just left at the same time, then it will take 120 minutes for one of each train departs at the same time again
Given,
The passenger trains leave the station every 40 minutes
Freight trains leave every 30 minutes
We have to find the LCM
Prime factorization
30=2×3×5
40=2×2×2×5
LCM(30,40)= 2×2×2×3×5=120
Hence, when Passenger trains leave the station every 40 minutes and Freight trains leave every 30 minutes, If a passenger train and a freight train just left at the same time, then it will take 120 minutes for one of each train departs at the same time again.
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