How many distinct subsets of the set $s=\{1,8,9,39,52,91\}$ have three-digit sums?

Answers

Answer 1

The number of distinct subset of the set is an illustration of combination

There are 34 distinct subset of the set that have three digit sums

How to determine the number of distinct subsets?

The set is given as:

S = {1,8,9,39,52,91}

Group the elements

S = {(1,8),9,39,52,91}

So, we have:

S ={s1,s2,s3,s4,s5}

To have a three-digit sum, the sum of the selected elements must be 100 or above.

The number of ways the above set can be selected is:

[tex]n_1 = 4 * [^3C_1 + ^3C_2 + ^3C_3] + 1[/tex]

Evaluate

[tex]n_1 = 4 * [3 + 3 + 1] + 1[/tex]

[tex]n_1 = 29[/tex]

The set can be further rearranged as:

S = {(52,39),9,(8,1)}

i.e.

S = {b1,b2,b3}.

The number of ways the above set can be selected such that the sum is 100 or above is:

[tex]n_2 = 2 * [^2C_1] + 1[/tex]

Evaluate

[tex]n_2 = 2 * 2 + 1[/tex]

[tex]n_2 = 5[/tex]

So, the total number of ways is:

[tex]n = n_1 +n_2[/tex]

This gives

[tex]n = 29 +5[/tex]

[tex]n = 34[/tex]

Hence, there are 34 distinct subset of the see that have three digit sums

Read more about combination at:

https://brainly.com/question/11732255

Answer 2

There are 34 distinct subsets of the see that have three-digit sums.

What are distinct subsets of the set?

When we know that S is a subset of T, we place the circle representing S inside the circle representing T.

The set is given as:

S = {1,8,9,39,52,91}

Group the elements

S = {(1,8),9,39,52,91}

S ={s1,s2,s3,s4,s5}

To have a three-digit sum, the sum of the selected elements must be 100 or above.

The number of ways the above set can be selected is:

[tex]\rm n_1=4\times (^3C_1+^3C_2+^3C_3)+1\\\\n_1=4(3+3+1)+1\\\\n_1=4 \times 7+1\\\\n_1=28+1\\\\n_1=29[/tex]

The set can be further rearranged as:

S = {(52,39),9,(8,1)}

S = {b1,b2,b3}.

The number of ways the above set can be selected such that the sum is 100 or above is:

[tex]\rm n_2=2\times ^2C_1+1\\\\n_2= 2\times 2+1\\\\n_2=4+1\\\\n_2=5[/tex]

The distinct subsets of the set are;

[tex]\rm n_1+n_2=29+5 =34[/tex]

Hence, there are 34 distinct subsets of the see that have three-digit sums.

Read more about combination at:

brainly.com/question/11732255

#SPJ4


Related Questions

solve ps brainliest!

Answers

Answer:

W = 17

Step-by-step explanation:

Hi! Ok so the equation is: 24=2w-10

24=2w-10 First add =10 to each side

10+24= 2w +10 -10 the tens on the right cancel.

34=2w then divide each side by negative two

(34/2)=(2/2)w can be simplified to 17=w

Now say you invest the $7,500 and the highest interest rate you can find is 4.5% compounded annually,
but you would have to leave the investment in the account for a minimum of 4 years. If you decide to
wait 4 years to buy the car, how much more money will you have to save to buy a car at the $9,500
price? Use the compound interest formula A = P (1 + i)". (Round final answer to the nearest cent, but
otherwise don't round any intermediate values)

Answers

the answer is a i hope this helps

Step-by-step explanation:

hope this helps

In 20 years Lillian will be three years older than twice her current age. Set up an equation that
can be used to solve for x, Lillian's current age.

Answers

Answer:

ok so x is her currect age y is her age in 20 years

2x+6=y

x+20=y

that means that both sides are equal

2x+6=x+20

-6

2x=x+14

-x

x=14

so her currect age is 14 and lets plug in

14+20=34

her currect age is 14 and her age in 20 years is 34

Hope This Helps!!!

Find the area of the circle

Answers

Step-by-step explanation:

78.50 in^2 I am pretty sure

Answer:

78.50 in squared

Step-by-step explanation:

To find the area of a circle, you need to use the equation area = pi * r^2, or pie multiplied by the radius squared. The radius is half of the diameter, which means the radius is 5. 5 squared is 25. Pi times 5 is about 78.50 inches squared.

A food truck did a daily survey of customers to find their food preferences. The data is partially entered in the frequency table. Complete the table to analyze the data and answer the questions:


Likes hamburgers Does not like hamburgers Total
Likes burritos 38 77
Does not like burritos 95 128
Total 134 71


Part A: What percentage of the survey respondents do not like both hamburgers and burritos? (2 points)

Part B: What is the marginal relative frequency of all customers that like hamburgers? (3 points)

Part C: Use the conditional relative frequencies to determine which data point has strongest association of its two factors. Use complete sentences to explain your answer. (5 points)

Answers

Answer:

A:

18.5% 

B:

124 / 205

C:

75 / 113. 66.4% Strongest 

49 / 92. 53.2% Middle

38 / 81 46.9% Weakest

75  / 113 is the strongest because it has the highest percentage fore the  conditional relative frequencies. The others are weaker because they have as high of a percentage.

Step-by-step explanation:

The answers are shown below:

What is Conditional relative frequency?

A conditional relative frequency compares a frequency count to the marginal total that represents the condition of interest.

a) Out of 205 people, 38 like neither, hence:

Percentage= 38/ 205 *100= 18.54%

b) Out of the 205 participants, 205 - 81 = 124 like hamburgers, hence:

= 124 / 205

=0.6049

c)The table is, dis considering the totals:

49 - 43

75 - 38

Due to the higher total, the data that has the strongest association of its two factors is liking hamburgers and not liking burritos.

Learn more about this concept here:

https://brainly.com/question/28011510

#SPJ2

Solving distance problems-
10 points

Answers

Answer:

1.  54 and 9/20 km

2. 80 mm

3. 1.142 mi

4.0.83333 cm

Step-by-step explanation:

Do them all  by the butterfly method.

Ramona went to a theme park during spring break she was there for 7 hours and rode 21 rides at what rate did I Ramona ride rides in rides per hour

Answers

Answer:

57393487

Step-by-step explanation:

un kilo por hora espero que te ayude

Answer:

3 rides/hour

Step-by-step explanation:

Not sure what ^^ guy was saying... And I don't understand why?

The correct answer is number of rides / hours.

21 / 7 = 3


I need the answer please

Answers

Answer: sqrt(182)

Step-by-step explanation:

I went to the store with $20. After buying all my groceries, I spent $15.87. How much money do I have left?

Answers

you would have 4.13 left

20-15.87=4.13

Answer:

The answer is $4.13

Step-by-step explanation:

It is easier to do this if we add two zeros at the end of 20 to make it 20.00 so the decimal places line up. Lets take it one place at a time. first is the hundreths, which is 0-7. This is not possible, so we borrow from the tenths, but the tenths is also a zero. The tenths zero has to borrow from the ones zero. Basically, the 2 in 20 becomes 1, and the zeros in the ones and tenths place become nines, and the last zero becomes 10. 10 minus 7 is 3, 9 minus 8 is 1, 9-5 is 4, and 1-1 is 0.

Hope this helps!


[tex] \sf \large \: find \: \frac{dy}{dx} \: if \: x=a ( \Theta + sin \Theta ) , y= a (1- Cos \Theta ) \: at \: \Theta = \frac{π}{2} \\ \\ \\ \\ \\ [/tex]

Kindly Don't Spàm!
Thanks!!!!​

Answers

Given :

[tex] \: \: \: [/tex]

[tex] \rm \large \: x = a ( \Theta + Sin \Theta )[/tex]

[tex] \: \: \: [/tex]

[tex] \rm \large y = a ( 1 - cos \: \Theta )[/tex]

[tex] \: \: [/tex]

Now , x = a ( θ + sin θ )

[tex] \: \: [/tex]

Diff w.r.t " θ "

[tex] \: \: \: [/tex]

[tex] \rm \large\frac{dx}{dθ } = a \: \frac{d}{dθ} (θ + \sin\theta )[/tex]

[tex] \: \: [/tex]

[tex] \boxed{ \rm \large\underline{ \frac{dx}{d \theta} = a(1 + \cos \theta ) }}[/tex]

[tex] \: \: [/tex]

Now y = a ( 1-cosθ)

[tex] \: \: [/tex]

Diff w.r.t " θ " we get .

[tex] \: \: [/tex]

[tex] \rm \large \frac{dy}{d \theta} = a \frac{d}{d \theta} (1 - cos \theta) [/tex]

[tex] \: \: \: [/tex]

[tex] \boxed{ \rm \large \underline{ \frac{dy}{d \theta} = a \sin \theta}}[/tex]

[tex] \: \: \: [/tex]

From eqn ( 1 ) & ( 2 )

[tex] \: \: [/tex]

[tex] \rm \large \frac{dy}{dx} = \frac{ \frac{dy}{d \theta} }{\frac{dx}{d \theta}} [/tex]

[tex] \: \: \: [/tex]

[tex] \: \: \: \rm \large = \frac{ \cancel{a} \: sin \theta}{ \cancel a \: (1 + cos \theta)} [/tex]

[tex] \: \: [/tex]

[tex] \rm \large \: = \frac{sin \theta}{1 + \cos \theta } [/tex]

[tex] \: \: \: [/tex]

[tex] \rm \large \: \frac{2 \sin( \frac{\theta }{2} ) cos\frac{\theta }{2} }{2 \: cos ^{2} \frac{\theta }{2}} \: \: ......(sin \: a \: = 2 \: sin \frac{a}{2} \: cos \frac{a}{2} 1 + \: cos \: a \: = 2cos ^{2} \frac{a}{2} )[/tex]

[tex] \: \: [/tex]

[tex] \rm \large \: \frac{dy}{dx} = \frac{sin \frac{ \theta}{2} }{cos \frac{ \theta}{2} } [/tex]

[tex] \: \: [/tex]

[tex] \rm \large \: \frac{dy}{dx} = tan \frac{ \theta}{2} [/tex]

[tex] \: \: [/tex]

[tex] \rm \large \: ( \frac{dy}{dx} ) = tan \frac{ \frac{ \theta}{2} }{2} [/tex]

[tex] \: \: [/tex]

[tex] \rm \large \: = tan( \frac{ \theta}{4} )[/tex]

[tex] \: \: [/tex]

[tex] \boxed{ \rm \large \underline{ ( \frac{dy}{dx} ) = \frac{\pi}{2} = 1}}[/tex]

[tex] \: \: [/tex]

Hope Helps!:)

Julio makes a scale drawing of the kitchen floor to determine how
many square feet of flooring he needs to buy. the scale of his drawing
is 1 inch:4 feet.
what is the area of julio's actual kitchen floor?
27
step 1 is to convert 3. to
step 2 is to convert 4. to
step 3 is to multiply each improper fraction by 4
step 4 is to multiply your answers to step 3 together to find the
answer

Answers

The scale drawing of Julio's kitchen would change the kitchen size

The actual area is 243 square feet

How to determine the actual area of Julio's kitchen?

The parameters are given as:

Length = 4.5 inchesWidth = 3.375 inches

Start by converting the dimensions to feet using the scale ratio

Actual length = 4.5 inches/ (1 inch/ 4 feet) = 18 feetActual width = 3.375 inches/ (1 inch/ 4 feet) = 13.5 feet

The area is then calculated as:

Actual Area = Actual length * Actual Width

This gives

Actual Area =18 feet * 13.5 feet

Evaluate the product

Actual Area = 243 square feet

Hence, the actual area is 243 square feet

Read more about scale drawings at:

https://brainly.com/question/8975579

Please help I'm giving 40 points.

Answers

Answer:

Please see explanation

Step-by-step explanation:

look at the photo

Write a numerical expression to represent the phrase.

5 more than the product of 12 and 8

Answers

Answer:

(12x8) + 5

Step-by-step explanation:

The product of 12 and 8 would be multiplication, so you can represent that as. (12x8) or 12x8.

Hello!

First of all, "the product" of 2 numbers means you multiply these 2 numbers.

Then, "5 more" means we add 5.

This is how the phrase "5 more than the product of 12 and 8" is written as a numerical expression:

(12×8)+5

[In case you need to simplify it]

96+5

101

Hope everything is clear.

Let me know if you have any questions!

Always remember: Knowledge is power!

which shapes best model the surface areas of the object? What is the surface are of each object, based on it’s model?

Answers

1) Sphere 804
2) cylinder 704


what is (x^-2 y^10)^2/x^5 y^-3 using only positive exponents

Answers

Answer:

[tex] \frac{(x^{ - 2}{y}^{10})^{2} }{ {x}^{5} {y}^{ - 3} } \\ \frac{ {x}^{ - 4} {y}^{20} }{ {x}^{5} {y}^{ - 3 } } \\ {x}^{ - 9} {y}^{23} \\ \frac{ {y}^{23} }{ {x}^{9} } \\ ans \: c[/tex]

Tina's teacher wrote 7/8 on the whiteboard. What percentage is equivalent to the fraction that Tina's teacher wrote on the whiteboard?

Answers

I think it's like 0.88, but I believe that's it rounded up.

Jestions: 5
5. Which of the following fractions makes this statement true?
4
12
er
3
7
dio
2
7
4.
5
panol
7
12

Answers

Answer:

I believe 2/7

Step-by-step explanation:

When you make them the same denominator they look like 48/84 > 24/84 and that's how you get the answer

Write a word problem to match the shaded fraction bar 3/4

Answers

Answer:

shaded part=3/4

unshaded part=1/4

Total=1

X2-7x+6; x2-5x-6 please help

Answers

Answer: (x−6)(x−1)(x+1)

What is 9 to the of 3

Answers

Answer:

729

Step-by-step explanation:

What shapes have only one pair of parallel sides?

Answers

Answer:

A TRAPEZOID!!

Step-by-step explanation:

Answer:

Trapezoids have only one pair of parallel sides

Help literally fast at possibly

Answers

Answer:

Yes you want to do it again soon

(Use distributive property)
6 (5x + 3)

Answers

Answer:

30x + 18

Step-by-step explanation:

Using distributive property, you can find the answer like so.

Multiply 6 and 5x first

6(5x + 3)

30x + 3

Now multiply 6 by 3

6(5x + 3)

30x + 18

Hope I explained this well to you. :)

HELP!!!! I can’t figure this out

Answers

Answer:

A

Step-by-step explanation:

Part A
What are the possible outcomes of rolling a six-sided dle?

Answers

Answer:

1, 2, 3, 4, 5, 6

Step-by-step explanation:

6 sided dice, and each side has a number on it. 6 numbers from 1-6. This also means it has 6 possible outcomes if thrown once, so the Probability of each number is [tex]\frac{1}{6}[/tex] because there are 6 sides. It also helps if you visualise a dice, or know how one looks like.

Hope this helps! Let me know if you have any further questions.

- profparis :)

if I helped you, I would appreciate a brainliest :D

Answer:

⅙ or 1 out of 6

Step-by-step explanation:

This is because a die has 6 sides which when rolled will give you one side of its six sides which is ⅙

I need help

Imagine that you designed a firework. When the firework first explodes, it splits into eight sparkles. Each of those sparkles then explodes and splits into eight new sparkles.

How many sparkles would the second explosion produce? Explain how you determined your answer.

Answers

Answer:

8 x 8 = 64

Step-by-step explanation:

Just including the second explosion, each of the 8 sparks bursts into 8, that means 8 sparks were produced 8 times, or 8x8

Answer:

1 sparkle Burst it produces 8 sparkles so you say 8×8×8×8×8×8×8×8

it takes 120 unit cubes to completely fill a rectangular prism. the prism is 10 units cubes high


how would i answer this ?

Answers

Answer:

12

Step-by-step explanation:

Well, I am pretty sure you are looking for the length.

Since area = length x width, I would say that you could divide as well.

120 = 10 x 12

I am pretty sure the length is 12.

:)

an unknown number is increased by -3. the result is -8
find the unknown number

Answers

Answer:

The unknown number is -5.

Step-by-step explanation:

-3 + -5 = -8

-8 - -3 = -5

-8 - -5 = -3

The perimeter of the triangular park shown on the right is 15x+2 . What is the missing​ length? The other two lengths are 5x-1 and 4x+4

Answers

Answer:

6x - 1

Step-by-step explanation:

Side 1: 5x - 1

Side 2: 4x + 4

Side 3: Unknown, y

Perimeter: 15x + 2

Perimeter = Side 1 + Side 2 + Side 3

15x + 2 = 5x - 1 + 4x + 4 + y

15x + 2 = 9x + 3 + y

6x - 1 = y

y = 6x - 1

Side 3 = 6x - 1

Identify the set as finite or infinite.

{1, (1/4), (1/16), (1/64), ...}

Answers

It is an infinite set
Other Questions
Where was Cuneiform developed?A) IndiaB) EgyptC) MesopotamiaD) Iraq Does anyone know how much does a Toyota AE86 car gets for monthly car payments??not math-related sorry BetterCook, a profit-maximizing firm, has a patent on a kitchen appliance, making it the only producer of that appliance. The graph above shows BetterCooks demand, marginal revenue, average total cost, average variable cost, and marginal cost curves. Solve the equation.10x + 1 + 7x = 37x = 15x = 12x = 12x = 15 19 pints converted to gallons If the total profit per month is Rs 200,000 and the revenue per month can be obtained twice the cost per month minus 50,000, find the revenue and cost per month #3 Match the term with the area of the body commonly affected. Find the area of triangle Identify whether the underlined clause is an adjective clause, adverb clause, or noun clause.I don't understand what she was thinking.NounAdverbAdjective Mrs culpeppers and and mr Cochran s class recorded the number of books each student read in a week Which of the following statements is true about the data sets? Which expression is equivalent to (o)(5)?Of(5) g(5)Of(5) + g(5)O5f(5)05g(5) Sarah took out a 4-year loan for $17,000 to purchase a car. If the interest rate on the loan is 1.3% compounded monthly, how much will she pay in total over the 4 years? Round your answer to the hundredths place. The primary force encouraging the entry of new firms into a purely competitive industry is. 27.Scientists believe that Earth's early atmospherechanged in composition as a result ofA. the appearance of oxygen-producing organismsB.the drifting of the continentsC.the changes in Earth's magnetic fieldD.a transfer of gases from the Sun A construction crew has just built a new road. They built the road at a rate of 3 kilometers per week. They built 18.75 kilometers of road. How many weeks did it take them? When women are hired in coaching and administrative positions in sport organizations, they may have low levels of job satisfaction due to What do latitude and longitude lines help us find?A. The area of a region.B. The absolute location of a place.C. How tall a mountain range is.D. The distance between the Earth and Sun. Brainliest if correct What does "I hate life" mean in Zulu PLS HELP FAST!! WILL GIVE THE BRAINLIEST!!! 25 POINTS!!! You have just read several theories about the causes of crime, and seen examples of how those theories might be used to prevent crime.Which of these theories makes the most sense to you? Why?Which of these theories made the least sense to you? Why?