Reduce the numbers in the list modulo 3 to get the set
{1, 2, 0, 1, 2, 0, …, 1, 2, 0}
containing [tex]k[/tex] copies each of 1, 2, and 0.
Take any 3 elements from the list. Their sum is divisible by 3 if those elements' residues also sum to 3 ≡ 0 (mod 3). To get a sum of 0, we must make one of the following choices:
3 elements each with the same residue, so0 + 0 + 0 ≡ 0 (mod 3)
1 + 1 + 1 ≡ 3 ≡ 0 (mod 3)
2 + 2 + 2 ≡ 6 ≡ 0 (mod 3)
1 element each with different residues, so0 + 1 + 2 ≡ 3 ≡ 0 (mod 3)
There are
[tex]\dbinom k3 \dbinom k0 \dbinom k0 = \dfrac{k(k-1)(k-2)}6[/tex]
ways of choosing 3 elements with a given residue and 0 elements with any other residue, hence
[tex]3\dbinom k3\dbinom k0\dbinom k0 = \dfrac{k(k-1)(k-2)}2[/tex]
ways of choosing any 3 elements with the same residue, and there are
[tex]\dbinom k1 \dbinom k1 \dbinom k1 = k^3[/tex]
ways of choosing any 3 elements with distinct residues.
So, the total number of ways of making the selection is
[tex]3\dbinom k3\dbinom k0^2 + \dbinom k1^3 = \boxed{\dfrac32 k^3 - \dfrac32 k^2 - k}[/tex]
Which is a correct classification for the triangle?
O obtuse triangle
O right triangle
O acute triangle
O equiangular triangle
Answer:
obtuse triangle is the correct classification for the triangleThe correct classification of the triangle should be considered as the obtuse triangle.
What is the obtuse triangle?In the obtuse triangle here one of the angle should be considered as the obtuse angle.
In the case when the sum of the squares of the two shorter sides of a triangle should be smaller than the square of the longest side so it considered as the obtuse triangle.
Learn more about triangle here: https://brainly.com/question/22176005
What is the percentage of sugar in the syrup made of 10kg of water and 5kg of sugar? Thx!
Answer:
total=15 kg
so 5/15*100
=33.3
Step-by-step explanation:
Please help me to solve this!
Answer:
7 days im not sure
Step-by-step explanation:
can you trying giving us the answer that comes with the question if they have them
f(-4) = 3x^2-2x pls help i dont know this question
Step-by-step explanation:
f ( - 4) = 3 ( - 4) ² - 2( - 4)
=. 3 ( 16) + 8
=. 48 + 8 = 56
plz mark my answer as brainlist plzzzz.
hope this will be helpful to you.
Which of these ordered pairs is a solution to the inequality y - 2x < -3? ( (2,4) (-2, 3) (3, 4) (1,-1)
Answer:
(3, 4)
Step-by-step explanation:
Twice the complement of an angle is 24 degrees less than its supplement. What is the measure of the angle?
Answer:
2(90-x)=180-x-24
solve this
180-2x=156-x
solve the rest on your own
Hope it helps!
The measure of the angle will be 24 degree.
What is Complementary angle?
When sum of two angles are 90 degrees then the two angles are called Complementary angles.
Given that;
The expression is,
''Twice the complement of an angle is 24 degrees less than its supplement.''
Now,
Let measure of an angle = x degree
The complement of an angle x = (90 - x) degree
The supplement of an angle x = (180 - x) degree
Then, By the given condition we can formulate;
2 ( 90 - x) = (180 - x) - 24
180 - 2x = 180 - x - 24
180 - 2x = 156 - x
Subtract 180 both sides;
180 - 2x - 180 = 156 - x - 180
- 2x = - x - 24
Take negative sign common,
2x = x + 24
Subtract x both side,
2x - x = 24
x = 24
Thus, The measure of the angle will be 24 degree.
Learn more about the complement angles visit:
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Tell weather each pair is parallel, perpendicular, or neither: 8x – 2y = 3
x + 4y = -1
Joel reflected point P over the y-axis to get P'(–1, 5). Find the original coordinates of P.
Answer:
The original point P is (-1, -5)
Since the original point was reflected over the y axis then you would reflect over the x axis to get the original point and when you reflect over the x axis the x coordinates stay the same and you change the y coordinates to the opposite of what it is
You have two cans of paint, Can A and Can B. Can A contains 80% red paint and 20% blue. Can B contains half blue and half red. How much blue paint should be added to 3 liters of Can A to make it the same as Can B?
Answer:
0.9 liters.
Step-by-step explanation:
The difference between 20% of 3 and 50% of 3 is 30%. 30% of 3 liters is 0.9 liters so this is what you add to can A.
Celia used celery, carrots, and tomatoes in a recipe. Use the clues to find the amount of each ingredient she used. CLUE 1: The amounts were 2/5 cup, 3/4 cup, and 5/8 cup. CLUE 2: There is less celery than tomatoes. CLUE 3: There is less tomatoes than carrots.
Answer:
Celery = 3/8 cups
Tomatoes = 2/5 cups
Carrot = 5/4 cups
Step-by-step explanation:
CLUE 1: The amounts were 2/5 cup, 3/4 cup, and 5/8 cup
CLUE 2: There is less celery than tomatoes.
CLUE 3: There is less tomatoes than carrots
From clue 2 and 3:
Tomato > Celery ; Carrots > tomatoes
From least to highest :
Celery < Tomatoes < Carrot
Arranging clue 1 in ascending order :
2/5 = 0.4
3/8 = 0.375
5/4 = 1. 25
Hence,
3/8 < 2/5 < 5/4
Celery = 3/8 cups
Tomatoes = 2/5 cups
Carrot = 5/4 cups
Nancy was baking a cake for her mom's birthday. She spent
of her time measuring
the ingredients and of her time mixing. If Nancy spend 35 minutes on these two
4.
activities, how many total minutes did she spend baking?
34 divided by 4 is 8.5 minutes in all 4 activities.
When h(1)=-2, and h(n)=h*(n-1)+n, what is h(2)=
Answer:
h(2)=0
Step-by-step explanation:
That’s what I got when I got it wrong and I asked for the answer and I promise it’s 0
Answer:
its 0
Step-by-step explanation:
a student has a savings account with $475 in in it. She deposits $125 of her paycheck into the account every week. Her goal is to save 7,000 for college. How long will it take her to reach her goal of $7000?
Answer:
52.2 weeks
Step-by-step explanation:
7000 - 475 = 6,525
6525 ÷ 125 = 52.2
Answer:
It will take her 53 weeks to get her goal of 7,000$
Step-by-step explanation:
I subtracted 475 from 7,000 to see how much she needed to save for. I got 6525. I multiplied 125 times 52 and got 6500. To get to her goal she needs 25 more dollars so, she'll have to work another week to get to that goal.
:)
please help for brainlist ASAP and explain or no brainlist
Answer:
A
Step-by-step explanation:
because as you see the odd number is 1 its A
Answer:it’s 1/3 because it would be 1/2 to get two even number or odd so it’s 1/3
Step-by-step explanation:there’s 3 even numbers on one dice and it’s 1/2 a chance to get even and same for odds so with two dices it’s 1/3 because it’s 1/3 to get both evens and 1/3 to get both odds so it’s 1/3
Diego hosted a spaghetti dinner for the soccer team. He made 6 boxes of spaghetti to feed the 20 people that came. Next time, 50 people are coming! How many boxes of spaghetti should Diego buy to feed all those people? Explain or show your reasoning.
can someone please help me
y=5x+1
Answer:
X= [tex]\frac{1}{5\\}[/tex] y+ 1[tex]\frac{-1}{5}[/tex]
Step-by-step explanation:
y=5x+1
Step 1: Flip the equation.
5x + 1
Step 2: Add -1 to both sides.
5x + 1 + −1 = y+ −1
Step 3:
Divide both sides by 5.
[tex]\frac{5x}{5\\}[/tex]= [tex]\frac{y-1}{5}[/tex]
Which of the values in the set {2, 3, 4, 5} is a solution to the equation 2x + 4 = 10? (4 points) a 2 b 3 c 4 d 5
Answer:
B: 3
Step-by-step explanation:
2x
x=3 3times2= 6
6+4 =10
Hope this helps
A ladder is leaning against a vertical wall. The distance from the top of
the ladder to the base of the wall is 23 feet. The distance from the base
of the wall to the bottom of the ladder is 5 feet. What is the length of the
ladder (nearest tenth)?
Answer:
23.5(to the nearest tenth)
Step-by-step explanation:
pythagoras theorem states
c^2= a^2+ b^2
a= 23
b=5
c^2= 529+25
c^2= 554
c= square root of 554
c = 23.5 (approximately)
this took me a lot of time
giving me brainliest will make me happy
The present age of Arun’s father is three times that of Arun. After 5 years,
what will be their ages?
Answer:
Arun father age will be 3X+5 and his age will be X+5
I really need help with this
Answer:
3
Step-by-step explanation:
I recall seeing this question. If I'm wrong, let me know.
please help me i need to get this done
Answer:
15 students are wearing sneakers.
Step-by-step explanation:
There are 33 students in total, which will compare to 11 (5+6).
33 ÷ 11 = 3
The scale factor is 3.
Sneakers: 3 x 5 = 15 students
Please answer the pictures provided
Answer:
-6-3
Step-by-step explanation:
April wrote two equations to represent this system of equations. She wrote: y = 5x +
I and y = 14x - 10. Do you agree or disagree with April?
Answer:
Disagree
Step-by-step explanation:
The lines are parallel, which means they have different y-intercepts but the same slope.
April's two equations have different slopes (5 and 14), so they do not properly represent two parallel lines.
Consider the quadratic function: f (x) = 5x2 + 20x + 20. What are the zeros of the function using completing the square?
Step-by-step explanation:
step 1. f(x) = 5x^2 + 20x + 20
step 2. f(x) = 5(x^2 + 4x + 4)
step 3. f(x) = 5(x + 2)^2
step 4. 0 = 5(x + 2)^2
step 5. zeros: -2
Calculus. Find the area.
Answer:
8/3 square units.
Step-by-step explanation:
First, visualize the area. You can refer to the attachment below.
To find the area then, we will integrate y from x = 0 to x = 2. Therefore:
[tex]\displaystyle A=\int_0^2x^2\, dx[/tex]
Integrate:
[tex]\displaystyle A=\frac{1}{3}x^3\Big|_{0}^2[/tex]
Evaluate:
[tex]\displaystyle A=\frac{1}{3}[2^3-0^3]=\frac{1}{3}(8)=\frac{8}{3}[/tex]
The area is 8/3 square units.
Answer:
A = [tex]\frac{8}{3}[/tex] units²
Step-by-step explanation:
8•3=(n divided by 3)
Answer:
N= 72
Step-by-step explanation:
8x3= 24
24x3=72
check: 72/3= 24
Which transformation would take Figure A to Figure B
Answer:
6 squares to right and 6 squares down
Step-by-step explanation:
Go with the coordinate (-1, 5) on shape A
Hope it helps :)
Move 6 squares to right and 6 squares down.
The initial coordinate that is the x value is -5 and the transformation figure has x value 5.
So move figure A 6 squares to the right . And then move 6 squares to the down we get the transformation figure B.
Therefore, by moving 6 squares to right and 6 squares to down we get the transformation figure B.
Learn more:https://brainly.com/question/7161333
If a bag contains 18 red, 6 yellow, 24 blue, and 8 white balloons, what is the part-lo-whole ratio of white balloons to
all balloons?
A)
1:5
B)
1:6
C)
1:7
D)
1:8
Answer:
1:6
Step-by-step explanation:
1:6
I hope this answer is correct
HELP!! im using the last of my points for this, im really bad at math and im stressed trying to do this.
Answer:
D. 19.6in
Step-by-step explanation:
ΔAFC is similar o ΔA'FC'. Therefore, their sides are in ration to one another:
FA/F'A'=AC/A'C'
9/(9+12)=8.4/A'C'
9/21=8.4/A'C'
3/7=8.4/A'C'
A'C'=8.4/(3/7)=19.6
Answer:
D. 19.6in have a good rest of yo life :)
Bella has a cell phone plan in which she pays for each call minute and text message she sends. The total number of minutes used and text messages sent last month was 561. If call minutes cost 8 cents each and text messages cost 5 cents each and her bill was $34.26. how many minutes did she use?
Answer:
⇒Let the no. of call minute be = x
⇒& no. of text messages be = y
⇒As total number of minutes used and text messages sent last month was 561
So x + y = 561.................................(1)
⇒Now as call minutes cost 8 cents each and text messages cost 5 cents each and her bill was $34.26
So 8x + 5y = 3426............................(2)
On solving equation 1 & 2 we have
we got x = 354 cent
& y = 207 cent
Answer:
Step-by-step explanation:
x (354,307)