how many 3 element subsets of {1, 2, 3, 4, 5, 6, 7, 8, ,9, 10, 11} are there for which the sum of the elements in the subset is a multiple of 3

Answers

Answer 1

Answer:

There are 155 ways in which these elements casn occur.

Step-by-step explanation:

We want 3 element subsets whose sum are multiples of 3

1+2+3= 6

1+2+6= 9

1+2+9= 12

1+9+11=21

1+3+5=9

1+4+8=12

1+5+6=12

1+6+8=15

1+7+10=18

1+8+9=18

1+9+11=21

2+3+7=12

2+4+6=12

2+4+9=15

2+5+11=18

2+6+7=15

2+7+9=18

2+8+5=15

2+8+11=21

2+9+10=21

3+6+9= 18

3+9+11=21

3+10+11=24

6+9+10=27

6+8+11=27

6+7+11=24

7+8+9= 24

8+9+10=27

7+9+11=27 .........

We have 11 elements

We need a combination of 3

The combinations can be in the form

even+ even+ odd

odd+odd+odd

even + odd+odd

So there are 3 ways in which these elements can occur

Total number of combinations with  3 elements =11C3= 165

There are 6 odd numbers and 5 even numbers.

Number of subsets with 3 odd numbers = 6C3= 20

Number of two even numbers and 1 odd number = 5C2*6C1=10*6= 60

Number of 2 odd and 1 even number = 6C2* 5C1= 5*15= 75

So 20+60+75=155

There are 155 ways in which this combination can occur


Related Questions

can you help me please?​

Answers

Answer:

it is a it the first one. 7/13

Answer:

A.

Step-by-step explanation:

The bottom number is the same so leave then and just add the top.

Makes 7/13

What is the area of the building below? *

Answers

you’ll need to split the shape into 2 rectangles then find the area of both the rectangles and add them together.
30*10=300
20*10=200
area=500

Kyle is making a frame for a rectangular piece of art. The length of the frame is 3 times the width, as shown below.

A rectangle with a length of 3 x and height of x.

If Kyle uses 18 feet of wood to make the frame, what is the length of the frame?

Answers

Answer:

D

Step-by-step explanation:

Answer:D

Step-by-step explanation: got it right

Find the slope of the line
that goes through the given
points
t
(1,2) (3,-4)
I
1

Answers

Answer:

Step-by-step explanation:

y2-y1=

x2-x1

2--4=6(negatives cancel out)

3-1=2

so 6/2 =3

3 is slope

A company loses $5,400 as the result of a manufacturing defect. Each of the 8 owners have agreed to contribute an equal amount, x, to help pay for the losses.

Part A
Which expression shows the total loss after the owners contribute some money?

Answers

Answer:

x=$5400:8

$5400:8x = total loss after the owners contribution

The expression shows the total loss after the owners contribute some money is 8x = 5400

Equation

An equation is an expression used to show the relationship between two or more numbers and variables.

Let x represent the amount contributed by each owner as loss.

Since there are 8 owners sharing a loss of $5400, hence:

8x = 5400

x = 675

The expression shows the total loss after the owners contribute some money is 8x = 5400

Find out more on equation at: https://brainly.com/question/13763238

 Can someone pleaseeee help if you’re correct I’ll give u brainlist

Answers

Answer:

p=65

Step-by-step explanation:

180-50=130

130/2=65

I believe p= 65 degrees

What time is it exactly 1,440,000 minutes after 10 pm

Answers

Answer:

The answer is 11 PM

Step-by-step explanation:

1,440,000 minutes is the same as 24,000 hours. Then, you add that to 10pm of that day and you get 11 pm. It is the same as multiplying 24 x 1000 hrs. it is like adding 1000 days to that since it is 24 hrs in one day. Hope this helped!!

Answer:

11:00 pm

Step-by-step explanation:

1,440,000 minutes, convert it into hours and you get 24,000 hours. Since 24 hours equal a day 24,000 is 1,000 days. Attach 10:00 pm since its exactly 1,000 days after and you get 11:00 pm.

When 17 is divided by K ; where k is a positive integer less than 17 the remainder is 3 .What is the remainder when the sum of the beta possible values of Kivided by 17.

Answers

Answer:

The remainder is 4.

Step-by-step explanation:

Note: This question is not correctly stated. It is therefore correctly restated before answering the question as follows:

When 17 is divided by k; where k is a positive integer less than 17, the remainder is 3. What is the remainder when the sum of the possible values of k is divided by 17?

The explanation of the answer is now given as follows:

Since k < 17, it implies that the possible values of k must be from between 1 and 16 inclusive.

Between 1 and 16, only 7 or 14 will give a remainder of 3 when either of them is used to divide 17. Therefore, 7 and 14 are the possible values of k.

Therefore, we have:

Sum of the possible values of k = 7 + 14 = 21

Also, we have:

Sum of the possible values of k divided by 17 = 21 / 17 = 1 with a remainder of 4.

Therefore, the remainder is 4 when the sum of the possible values of k is divided by 17.

9. Determine which of the following sequences is a geometric sequence. Check all that apply.
3,9, 27, 81, ...
100, 90, 80, 70, ...
5, 10, 20, 40, ...
2, 10, 18, 26,...
625, 125, 25, 5, ...
-2, 6, -18, 54, ...

Answers

Step-by-step explanation:

first geometric sequence

3^1, 3^2 ,3^3, 3^4,......

3, 9, 27, 81.......

second

5^1, 5^2, 5^3, 5^4,........

5, 25, 125, 625,........

third

2, 10, 18, 26,.....

which has the difference of 8

fourth

100, 90, 80, 70,......

​If ​y ​= 80 when ​x ​= 32, find ​x ​when ​y ​= 100.

Answers

Answer:

when y=80 the value of x is 32 and when y=100 what is the value of x so Criss cross 80=32

and 100= x so the answer will be 32*100 divided by 80 is equal to 40 I guess it's 40 the value of x is 40 in my guess

How can you best describe how to determine if a sequence is arithmetic or geometric?

Answers

Maybe finding out through calculator

Help me please. I need helpppppoooooopppppopopppp

Answers

Answer:

0

Step-by-step explanation:

The minimum number of cavities a patient had was 0 cavities.

Answer:

0

Step-by-step explanation:

The smallest number that indicates cavity is '0' therefore it is the minimum number of cavities

What is the solution to the equation -6x + 9 – 4x = 14?

Answers

[tex] - 6x + 9 - 4x = 14 \\ - 6x - 4x = 14 - 9 \\ - 10x = 5 \\ x = \frac{5}{ - 10} \\ x = - \frac{1}{2} \\ x = - 0.5[/tex]

A cube has a side length of 6 cm. What is the volume of the cube, in cubic centimeters ​

Answers

Answer:

V=216cm³

Step-by-step explanation:

V=216cm³

There are 20 sweets in a box.
x of the sweets are red.
The rest of the sweets are yellow.
Tom takes at random a sweet from the box.
Write down an expression, in terms of x, for the probability that Tom takes a yellow sweet.

Answers

Answer:

[tex]probability \: of \: getting \: red \: sweets = \frac{x}{20} \\ probability \: of \: getting \: yellow \: sweets \: = \frac{(20 - x)}{20} [/tex]

The probability of getting red sweets is x/20 and the probability of getting yellow sweet is (20-x)/20.

What is a probability?

Probability is about estimating or calculating how likely or 'probable' something is to happen.

Given that x is the number of red sweets.

The total number of sweets is 20.

The number of yellow sweets = 20 - x.

The probability of getting a red sweet is given by

P(x) = x/20

The probability of getting a yellow sweet is given by

P(20-x) = (20-x)/20

Hence, x/20 is the probability of getting a red sweet and (20-x)/20 is the probability of getting yellow sweet.

To learn more about probability, use the link given below:

https://brainly.com/question/11234923

#SPJ2

PLEASE HELPpppppppppppppppp

Answers

Answer: 140%

Step-by-step explanation:

Cost of the coats = $45 each

Selling price of the coat = $63 each

The percent of the purchase price that is the sales price would be:

= 63/45 × 100

= 7/5 × 100

= 140%

Therefore, the answer is 140%.


Need help with question

Answers

Your answer is gonna be the second one!

Enter numbers into the table so that the paired values are in a proportional relationship. x 2 6 8 20 y 3 4 6 10

Answers

Answer: X 2,6,8,12,20

Y 1,3,4,6,10

Step-by-step explanation:

Divided by 2 too get the answers  or add 10 + 10 you’ll get the answer

Answer:

Y 1,3,4,6,10

Step-by-step explanation:

took the test c:

I have a half-full bottle of water and it has more than 8 ounces in it. What would be the expression

Answers

Answer:

The equivalent expression is [tex]\frac{1}{2}\cdot V_{max} > 8\,oz[/tex].

Step-by-step explanation:

The best approach consists in translating the sentence given in the question into mathematical terms until an expression is complete:

(i) I have a half-full bottle of water

Translation: I use a bottle with a maximum volume capacity [tex]V_{max}[/tex], measured in ounces, a half of it is full of water:

[tex]\frac{1}{2}\cdot V_{max}[/tex]

(ii) And it has more than 8 ounces in it

Translation: The volume occupied by the water is greater than 8 ounces. Hence, we get the following inequation:

[tex]\frac{1}{2}\cdot V_{max} > 8\,oz[/tex]

PLS HELP THIS IS TIMED

Answers

C because you divide both sides first

Find the nth term of this quadratic sequence
4,9, 16, 25, 36,​

Answers

Answer:

[tex]a_{n}[/tex] = (n + 1)²

Step-by-step explanation:

The terms are square numbers with each term shifted to the right by 1

That is 1, 4, 9, 16, 25, 36, .....

Thus to obtain 4 in the first position, then

n = 1 → (1 + 1)² = 2² = 4

To obtain any term add 1 to its position in the sequence, that is

[tex]a_{n}[/tex] = (n + 1)²

Is -4 a integer yes or no

Answers

Answer:

Yes

Step-by-step explanation:

A integer is any number that's not a fraction.

Answer:

yes

Step-by-step explanation:

integer are numbers that aren't a fraction

what would be the slope of (1,-2) and (3,0)

Answers

Answer:

1

Step-by-step explanation:

Hello :)

So to answer this problem, we can use the rise over run formula.

The rise is the difference of any two y values.

The run is the difference of the x values from the same two y values.

This question gives us 1,-2 and 3,0

We can use them for the formula:

-2 - 0 divided by 1 - 3

-2/-2 = 1

Answer:

[tex]m=1[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step-by-step explanation:

Step 1: Define

Point (1, -2)

Point (3, 0)

Step 2: Find slope m

Substitute [Slope Formula]:                    [tex]m=\frac{0+2}{3-1}[/tex]Evaluate Addition/Subtraction:              [tex]m=\frac{2}{2}[/tex]Evaluate Division:                                   [tex]m=1[/tex]

A friend purchases items from a website and resells them on her own website. She typically marks up her merchandise 40%. If she purchased an item for 15$, what price should she set for the item?

Answers

Answer:

$21

Step-by-step explanation:

Step one:

given

she purchased an item for $15

marks up her merchandise 40%.

let us find 40% of $15

and add the answer to the initial price of the item

Step two:

40/100*15

=0.4*15

=$6

Hence the price should she set for the item is

=15+6

=$21

What is the length of AC?

A. Square root of 2
B. Square root of 5
C. 3
D. 5

Answers

Answer:

B. √5 units

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra II

Distance Formula: [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point A (-3, 2)

Point C (-1, 3)

Step 2: Find distance d

Substitute [DF]:                    [tex]d = \sqrt{(-1+3)^2+(3-2)^2}[/tex]Add/Subtract:                       [tex]d = \sqrt{(2)^2+(1)^2}[/tex]Exponents:                           [tex]d = \sqrt{4+1}[/tex]Add:                                      [tex]d = \sqrt{5}[/tex]

Choose the number sentence whose product is 5.85.
A. 1.7 x 3.5
B. 26 x 2.25
C. 4.5 x 2.3
D. 1.3 x 4.5

Answers

Answer:

D

1.3 times 4.5 is 5.85

Answer:

D

Step-by-step explanation:

BRAINLYEST please

5x^2+2x-3=0 by factorisation method​

Answers

Answer:

x = - 1, 0.6

Step-by-step explanation:

[tex]5 {x}^{2} + 2x - 3 = 0 \\ \\ 5 {x}^{2} + 5x - 3x - 3 = 0 \\ \\ 5x(x + 1) - 3(x + 1) = 0 \\ \\ (x + 1)(5x - 3) = 0 \\ \\ x + 1 = 0 \: \: or \: 5x - 3 = 0 \\ \\ x = - 1 \: \: or \: \: x = \frac{3}{5} \\ \\ x = - 1 \: \: or \: \: x = 0.6 \\ \\ x = - 1, \: \: 0.6[/tex]

Answer:

X= -1 or X=3/5

Step-by-step explanation:

5x^2+2x-3=0

(x+1)(5x-3)=0

x= -1 or 5x/5=3/5

x=3/5

In the worlds coolest freezer sodium gas was cool to temperature of 78.5 below zero and then called 194.65 more what was the new temperature of the sodium gas

Answers

Answer:

[tex]-273.15^{\circ}\text{C}[/tex]

Step-by-step explanation:

[tex]T_i[/tex] = Initial temperature of sodium gas = [tex]-78.5^{\circ}\text{C}[/tex]

[tex]\Delta T[/tex] = Change in temperature of sodium gas = [tex]-194.65^{\circ}\text{C}[/tex]

[tex]T_f[/tex] = Final temperature of sodium gas

Change in temperature of gas is given by

[tex]\Delta T=T_f-T_i\\\Rightarrow T_f=\Delta T+T_i\\\Rightarrow T_f=-194.65+(-78.5)\\\Rightarrow \Delta T=-273.15^{\circ}\text{C}[/tex]

The new temperature of sodium gas is [tex]-273.15^{\circ}\text{C}[/tex].

What is the answer to it?

Answers

Answer:

The answer is

[tex] - 6x + 17[/tex]

A restkaurant worker is able to clean 32 dishes in 8 minutes. How many minutes would it take to clean 58 dishes?

Answers

Answer:

14.5

Step-by-step explanation:

Find the unit rate

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