Sets A and B, shown in the Venn diagram, are such that the total number of elements in set A is twice the total number of elements in set B. Altogether, there are 3011 elements in the union of A and B, and their intersection has 1000 elements. What is the total number of elements in set A?

Answers

Answer 1
Hi there,
Let's solve your problem step by step. First off, we need to assign variables to each set. Here's how you do that:

Let a represent set A and let b represent set B.

Now that we have that down, we can move on. Our next step is to translate our given information to numbers. We are given that set A has twice the total number of elements than in set B. This is what we get after the translation:

[tex]a=2b[/tex]

We are also given that there are 1000 elements in the two sets' intersection. Hence, we get:
[tex]a-1000[/tex] and [tex]b-1000[/tex]
The total number of elements combined in set A and set B can be represented as: 
[tex](a-1000)+(b-1000)+1000[/tex]
The question gives us that there are 3011 total elements in the union of A and B, so we can equate the expression above to 3011. This is our resulting product:
[tex](a-1000)+(b-1000)+1000 = 3011[/tex]
We can simplify this equation to [tex]a+b=4011[/tex]. In the beginning, we found that a = 2b, or b = 1/2a, so we can substitute that into the equation. Here is the process:
[tex]a+b=4011[/tex]
[tex]a+ \frac{1}{2}a=4011[/tex]
[tex] \frac{3}{2} a=4011[/tex]
[tex]a=2674[/tex]
Therefore, the total number of elements in set a is 2674.


Related Questions

Solve the equation.
5p/7 - 18 = -43

A. -35
B. -31
C. -85 2/5
D. -50

Please explain your answer.

Answers

Hello! So the first thing we need to do is add 18 to both sides. When you do that, it should be 5p/7 = -25. Now, we must multiply both sides by 7/5 to isolate the “p”. -25 * 7/5 is -35. If you want to check to make sure it’s right, plug in the alleged “p” value to make sure it’s right. When we substitute “p” for -35 and we solve it by doing order of operations, we get -43. The answer is A: -35.

Answer:

-35

Step-by-step explanation:

If the length between points on a map is 6 inches, 8 inches, and 9 inches, and the scale is one inch equals 5 miles, find the distances in miles.

a.) 1.2, 1.6, and 1.8 miles
b.) 11, 13, and 14 miles
c.) 30, 40 and 45 miles

Answers

c) because you multiply the conversion by the number of inches. Therefore, 6x5=30, 8*5=40, and 9*5=45

Answer:

Option c is correct

Distance in miles are; 30, 40, 45 miles

Step-by-step explanation:

As per the statement:

If the length between points on a map is 6 inches, 8 inches, and 9 inches.

It is also given that:

1 in. = 5 miles

We have to find the distance in miles:

For 6 inches.

1 in. = 5 miles

6 in. = [tex]6 \cdot 5 = 30[/tex] miles

Similarly, for 8 inches:

8 inches = [tex]8 \cdot 5 = 40[/tex] miles

For 9 inches:

9 inches = [tex]9 \cdot 5 = 45[/tex] miles

Therefore, distance in miles are; 30, 40, 45 miles

Bank get most of the money to loan out to people from
A taxes charged by banks
B the government
C other banks
D people that deposit money in the bank for safekeeping

Answers

correct answer: "D people that deposit money in the bank for safekeeping"

The bank uses people's savings to loan money. They usually keep a fraction of what they have in store in case the person that has the money in the bank ask it back. For example, if $5000 are deposited in the bank, for savings, the bank could lend out $4500 of it.
The taxes charged by banks are used for the bank keeping.

Answer:

D!!

Step-by-step explanation:

There are 912 yellow chairs and blue chairs altogether in an auditorium. The blue chairs are arranged in 36 rows with 12 chairs in each row. The yellow chair are arranged in rows of 20. How man rows of yellow chairs are there?

Answers

You would do 36X12= 432 then 912 - 432=480. then you would 480÷20=24. So there are 24 rows of yellow chairs
First you have to do 36 times 12 which is 432, then subtract that from the total which is 480 then divide that by 20 and you get 24. Plz give this a thanks

Write 7.085 × 10-14 as an ordinary number 0.000 000 000 007 085 0.000 000 000 000 708 5 0.000 000 000 000 0708 5 0.000 000 000 000 0070 85

Answers

7.085x10-14 would simplify to 70.85-14, which equals 56.85

The ordinary number for the given Scientific notation is 0.00000000000007085.

Given that, [tex]7.085\times10^{-14}[/tex].

What is scientific notation?

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as [tex]1.57\times10^7[/tex].

The given number can be written as [tex]\frac{7.085}{10^{14}}[/tex]

= 0.00000000000007085

Therefore, the ordinary number for the given Scientific notation is 0.00000000000007085.

To learn more about the Scientific notation visit:

https://brainly.com/question/18073768.

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(−5k
​3
​​ −6k+1)+(−6k
​2
​​ +5k)

Answers

Remove unnecessary parenthesis.

-5k 3 - 6k +1 - 6k 2 + 5k (simplify each term) -15k - 6k + 1 - 12k +5k = -28k +1

Answer: 28k + 1

Step-by-step explanation:

−5k

3

−6k

2

−k+1

If n + 3 = 13, then n = 4.33333... B

Answers

Solve the equation, N=13-3=10

Can u simplify and convert these please and thank you

Answers

5 free points just claimed. thx :D

match the top cards to the bottom cards to show doubles plus 1

Answers

This question is all about doubles. The given bottom cards 5 2 3 4 and the top cards are 1 4 3 2.

The problem is asking to match the top cards to the bottom ones then adding 1 to get the doubles.

So 1 should be corresponding to two. Since 1 + 1 = 2

4 should be corresponding to 5. Since 4 + 1 = 5

3 should be corresponding to 4. Since 3 + 1 = 4

And lastly, 2 should be corresponding to 3. Since 2 + 1 = 3 

If josh spends 4,000 a year on tuition and fees, 1,200 a year on books, and forgoes earning 10,000 a year, how much will his four year degree cost

Answers

his four years of college will cost $8800
Final answer:

The total cost of the four-year degree for Josh, when considering tuition and fees, book costs, and his foregone earnings, would be 60,800 dollars.

Explanation:

The cost of a four-year degree would be the sum of tuition and fees, book costs, and forgoing potential earnings per year, multiplied by the four years of the degree. Let's break it down:

Tuition and fees cost: 4000 dollars/yearBook costs: 1200 dollars/yearForgone earnings: 10000 dollars/year

Therefore, the annual cost would be the sum of these, which is 4000 + 1200 + 10000 = 15200 dollars/year. Then we multiply this by the 4 years, 15200 * 4 = 60800 dollars. So, the four-year degree would cost Josh 60800 dollars, considering the provided expenses and forgone earnings.

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The repeating decimal, 0.27..., is converted to the fraction 0.27..=3/x

what is the value for x in the fraction

Answers

i think the answer to your question is 11.11 I hope this helps

Answer:

The required number in the fraction is x=11

Step-by-step explanation:

Given : The repeating decimal, 0.27..., is converted to the fraction  [tex]0.27....=\frac{3}{x}[/tex]            

To find : What is the value for x in the fraction ?

Solution :

Let [tex]y=0.272727...[/tex] ....(1)

Multiply both side by 100,

[tex]100y=27.2727...[/tex] .....(2)

Subtract (1) and (2),

[tex]100y-y=(27.2727....)-(0.272727...)[/tex]

[tex]99y=27[/tex]

[tex]y=\frac{27}{99}[/tex]

[tex]y=\frac{3}{11}[/tex]

On comparing with [tex]0.27....=\frac{3}{x}[/tex]

The value of x is 11.

Therefore, The required number in the fraction is x=11.

if (7,2) is an ordered pair of the function f(x) which of the following must be an ordered pair of the inverse of f(x)?

(2,7)
(2,2)
(7,2)
(7,7)

Answers

All you have to do is to reverse the order of the x and y components of (7,2):
(2,7).

Answer:

(2,7)

Step-by-step explanation:


Here is an example just to show that it works.

3x+2y=25

3(7) + 2(2) = 21 + 4 = 25

3y+2x=25

25-2x=3y

25/3 - 2/3x = y

25/3 -2*2/3=25-4/3=21/3=7



Merritt is driving to mount Shasta. On her map, she is a distance of 7.75 inches away. The scale on the map is .5 inch = 50 Miles. How far must Merritt travel to reach her destination?

Answers

193.75 miles cause 7.75 * .5 = 3.875 and 3.875* 50 = 193.75

Consider two identical iron nails: one nail is heated to 95 °c, the other is cooled to 15 °c. the two nails are placed in a coffee cup calorimeter and the system is allowed to come to thermal equilibrium. what is the final temperature of the two nails

Answers

Final answer:

In this case, the final temperature of the two nails will be an average of their initial temperatures, which is 55 °C.

Explanation:

When two objects at different temperatures come into contact, heat is transferred from the object with higher temperature to the object with lower temperature until they reach thermal equilibrium.

In this case, the heated iron nail at 95 °C will transfer heat to the cooled iron nail at 15 °C when they are placed in the coffee cup calorimeter.

The final temperature of the two nails will be an average of their initial temperatures, which is (95 °C + 15 °C) / 2 = 55 °C.

A towns election commitee expects 5 out of every 7 registered voters to vote in the next

Answers

Where is the rest of the problem?

What is the domain and the range of the relation represented by the ordered pairs? {(6,6),(−1,3),(3,6),(0,4)}{(6,6),(−1,3),(3,6),(0,4)} Select each correct answer.

Answers

Hello,

Let's review: The domain is all the possible x values of a relation/function. To get the domain, we look at the x values in the ordered pairs.

The domains are: {-1, 0, 3, 6} - as you can see these are the x values of each pair.

Let's review: The range is all the possible y values in a relation/function. To find the rang, we look at the y values of the pairs.

The ranges are: {3, 4, 6} - notice how there are two "6" in those pairs, and when writing the range, you don't need to repeat the number if it's already written.


I hope this helps! =)

May

Which shows the expressions in the order they would appear on a number line from least to greatest?

17 over 9, square root of 6, square root of 15, square root of 30, 3 to the power of 3

3 to the power of 3, square root of 30, square root of 15, square root of 6, 17 over 9

3 to the power of 3, square root of 6, square root of 15, 17 over 9, square root of 30

17 over 9, square root of 30, square root of 15, 3 to the power of 3, square root of 6
SOMEONE PLEASE HELP!!

Answers

[tex] \frac{17}{9} =1.888888889 [/tex]
[tex] \sqrt{6} =2.449489743[/tex]
[tex] \sqrt{30}=5.477225575[/tex]
[tex] 3^{3}=27 [/tex]

Answer:

A

Step-by-step explanation:

Write a real-life situation that can be modeled by the expression 5 x 3/4

3/4 is a fraction

Answers

Hello there! You can do something like this:
Kelly has 3/4 cup of a bottle of water. She likes to drink 5 times the amount of that every day. How many cups of water does Kelly like to drink every day?
Hope this helped you!
Good luck!
Bob has
3/4 cup of flour but he would need to use it 5 times this week..
How many cups of flour would Bob need each day?

There are 130 calories in a cup of whole milk and only 74 in a cup of skim milk. In switching to skim milk, find the percent decrease in number of calories.

Answers

Do 130 divided by 74 and you will probably get 1.74 and round it off

Ted used a $150 check to pay for some books. Where in his checkbook register should he write this amount? in the PAYMENT or WITHDRAWAL AMOUNT column in the DEPOSIT AMOUNT column in the BALANCE column in the FEE column NextReset

Answers

I would think that the answer would be the payment column. It wouldn't be the withdrawal amount column because he is not taking the money out of a bank account. 

Answer:

Ted should write the amount in the PAYMENT column of the checkbook register.

Step-by-step explanation:

When we want to withdraw money from the account then we need to mention the amount in the WITHDRAWAL column of the checkbook register.

When we want to deposit money to the account then we need to mention the amount in the DEPOSIT column of the checkbook register.

When we want to pay money to the someone else's  account then we need to mention the amount in the PAYMENT column of the checkbook register.

So, Ted must write the amount in the PAYMENT column of the checkbook register.

Find factors of 15y^2-50y+35=

Answers

First, factor out the common factor 5.

15y^2-50y+35 =

= 5(3y^2 - 10y + 7)

Now we need to factor the trinomial.
3 can be factored as 3 * 1
7 can be factored as 1 * 7 or (-1) * (-7)
Since the middle term is negative, we need to use -1 and -7 as the factors of 7

= 5(3y - 7)(y - 1)
I would first factor out that 5:    15y^2-50y+35  =   5(3y^2 - 10y + 7)
and then focus on factoring 3y^2 - 10y + 7.  Looking at the first and last coefficients 3 and 7, I'd form possible rational roots, which would include 7/3 and -7/3.

Using synthetic division, I'd determine whether either 7/3 or -7/3 is a root of 3y^2 - 10y + 7:

          ____________
(7/3)  /   3    -10    7
                     7     -7
          --------------------
             3      -3     0

Since there is no remainder, I'd conclude that 7/3 is a root of 3y^2 - 10y + 7, and that (3x-7) is a factor.    Look at the coefficients 3   -3; they tell us that (3x-3) is another factor.

Now let's take back that '5' we factored out earlier.

Factors of  15y^2 - 50y + 35 are   5, (3x-7) and (x-1).  

Multiply these 3 factors together as a check.  I found that (3x-7)(x-1) comes out to 3x^2 - 10x + 7, and that multiplying this by 5 produces

         15y^2 - 50y + 35, which is the expression we started with.

A jar holds 128 fluid ounces of juice. The label says the jar has 16 servings. How many fluid ounces are needed for 80 servings?

Answers

There are 16 servings for each 128 fluid ounces of juice. 

Divide 80 servings by 16 servings, and 5 should be the quotient. Therefore, there are 5 jars of juice. Multiply 128 by 5 since 128 fluid ounces are in one jar. The answer should be 640 fluid ounces. 

Answer: 640 fluid ounces

Step-by-step explanation:

We assume that the fluid ounces in jar is directly proportional to the number of servings.

Given : A jar holds 128 fluid ounces of juice. The label says the jar has 16 servings.

Ratio of  fluid ounces of juice to number of servings =[tex]\dfrac{128}{16}[/tex]  (1)

Let x denotes the fluid ounces are needed for 80 servings.

Ratio of  fluid ounces of juice to number of servings =[tex]\dfrac{x}{80}[/tex]   (2)

From (1) and (2) , we have

[tex]\dfrac{x}{80}=\dfrac{128}{16}[/tex]   [in direct variation ration  remains constant.]

[tex]x=\dfrac{128\times80}{16}=640[/tex]

Hence, 640 fluid ounces are needed for 80 servings.

what is the value of n (9x23) +(3 ×39) - 28 = n

Answers

9*23=207
3*39=117
117+207=324
324-28=296
(9*23)+(3*39)-28  
207+117-28
324-28
296




During the 1998-1999 Junior Hockey League season, the Sharks played 66 games. Together, their wins and losses totaled 59. They tied 14 fewer games than they lost. How many games did they win that season?

Answers

We make [tex]w[/tex] an integer that represents the Sharks' wins, [tex]l[/tex] represent the losses, and [tex]t[/tex] represent the ties. 

We know that [tex]w+l+t=66[/tex], [tex]w+l=59[/tex], and [tex]t+14=l[/tex]. 

We subtract the first two equations, to get [tex]t=7[/tex]. If we plug this into the third equation, we get [tex]l=21[/tex]. 

We plug this into the first equation and get [tex](w)+(21)+(7)=66[/tex]. Simplifying, we find that [tex]w=\boxed{38\text{ games}}[/tex]. 

The Leukemia and Lymphoma Society sponsors a 5K race to raise money. It receives $55 per race entry and $10,000 in donations, but it must spend $15 per race entry to cover the cost of the race. Write and solve an inequality to determine the number of race entries the charity needs to raise at least $55,000.

Answers

The goal for the 5K charity race is to raise 55, 000. The charity makes 40.00 for every entry. Additionally , the charity received 10,000 dollars in donations which brings the amount needed to 45,000 . They would need 1,125 entries to make their goal.

which expression would give the thirteenth term Given the sequence 8, 16, 32, 64, ...,
813
8 · 213
8 · 212 ? 813 8 · 213 8 · 212

Answers

if you notice, 8, 16, 32, 64 <--- 8 * 2 is 16, 16 * 2 is 32 and so on.

so, you get the next term's value by simply multiplying the "current term" by 2.  So is a geometric sequence then.

therefore, the "common ratio" or multiplier is 2, and the first term's value is 8.

[tex]\bf n^{th}\textit{ term of a geometric sequence}\\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ r=2\\ a_1\\ n=13 \end{cases} \\\\\\ a_{13}=8\cdot 2^{13-1}\implies a_{13}=8\cdot 2^{12}\implies a_{13}=8\cdot 4096 \\\\\\ a_{13}=32768[/tex]

What is the equation of the line in standard form? (-3, 1) (3, 2)

Answers

Final answer:

The equation of the line passing through the points (-3, 1) and (3, 2) in standard form is (1/6)x - y = 5/6.

Explanation:

The equation of a line in standard form is Ax + By = C, where A, B, and C are constants. To find the equation of the line passing through the points (-3, 1) and (3, 2), we need to find the values of A, B, and C.

To do this, we can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept. First, let's find the slope using the formula:

m = (y2 - y1) / (x2 - x1)

Plugging in the values, we get:

m = (2 - 1) / (3 - (-3)) = 1/6

Now, we can substitute the slope (m) and one of the given points (x, y) into the slope-intercept form to find the y-intercept (b). Using (-3, 1) as the point:

1 = (1/6)(-3) + b

Simplifying, we get:

b = 5/6

Now, we can substitute the values of m and b into the standard form equation to get:

(1/6)x - y = 5/6

What is X+.07x=44.94

Answers

X+.07x=44.94
Combine like terms.
1.07x=44.94
Divide both sides by 1.07 to isolate the variable.
x=42

What is a solution to (x + 6)(x + 2) = 60?

A. x = −6
B. x = −4
C. x = 4
D. x = 12

Answers

THE SOLUTION FOR THIS QUESTINS WILL BE 
X=4, -12 

D.x=12 this is your answer

the difference of a given month's rainfall from the average monthly rainfall is called the deviation. What is the deviation for each month shown?
average monthly rainfall 3.6
given month may 2 3/5; june 7/8; July 4 1/4

Answers

If you add all of them up you will get 43/2

Answer:

Deviation:

may : 1

june: 0.875

july: 0.65

Step-by-step explanation:

It's given that the difference of a given month's rainfall from the average monthly rainfall is called the deviation .

To find : deviation for each month: may 2 3/5; june 7/8; July 4 1/4:

Solution :

Average monthly rainfall = 3.6

Rainfall in may = [tex]2\frac{3}{5}[/tex] = 2.6

Deviation = Average monthly rainfall -  month's rainfall ( may ) = 3.6 - 2.6 = 1

Rainfall in june = 3.6 - 0.875 = [tex]\frac{7}{8}=2.725[/tex]

Deviation = Average monthly rainfall - month's rainfall ( june ) = 0.875

Rainfall in july = [tex]4\tfrac{1}{4}=\frac{17}{4}=4.25[/tex]

Deviation = Average monthly rainfall - month's rainfall ( july ) = 4.25 - 3.6 = 0.65

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