Explain how the Venn diagrams in this lesson show that all integers and all whole numbers are rational numbers

Answers

Answer 1

The Venn diagram shows that rational numbers include all integers (-3, -2, -1, 0, 1, 2, 3,) and all whole numbers (0, 1, 2, 3, 4, 5). Inside the rational numbers circle is the integer circle, and the whole numbers circle, which concludes that all integers and whole numbers are rational numbers.

Explain How The Venn Diagrams In This Lesson Show That All Integers And All Whole Numbers Are Rational

Answer 2

All integers in which real numbers are involved can be written as p/q such that p and q are integers so they will be a rational number.

What is an irrational number?

Any real number that cannot be written as the quotient of two integers, p/q, where p and q are both integers, is referred to as an irrational number.

In another word, irrational numbers are those numbers that can not terminate.

For example, √2, and √3 are irrational numbers because they cannot be written as p/q where p and q both should be integers.

All integers are non-decimal numbers so they can be written as p/q such that p and q both will be integers so they will be a rational number.

The whole number is a positive integer so it will be in the category of integers only.

So,

In the given Venn diagram it is clear that in the real number all rational and irrational numbers are included in the rational number integer and in which the whole number is shown.

Hence "All integers in which real numbers are involved can be written as p/q such that p and q are integers so they will be a rational number".

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Related Questions

PLEASE HELP FAST!!!!!!!!!!!!!!!!!

Tomas asked 15 students whether summer break should be longer. He used his calculator ti divide the number of students who said yes by the total number if students. His calculator showed the result as 0.9333......

a. Write this number as a fraction.

b.How many students said that summer break should be longer

PLEASE AWNSER THEM

Answers

Answer:

A: [tex]\frac{14}{15}[/tex]

B: 14

Step-by-step explanation:

Let the number of students who said that summer break should be longer be x.

Total number of students = 15

The result showed = 0.9333....

We can calculate this like :

[tex]\frac{x}{15}=0.93333.....[/tex]

This gives x = 14 approx

So, in fraction form it can be written like = [tex]\frac{14}{15}[/tex]

14 students said the summer break should be longer.

If Gabby wants to make an octagon with a side length of 20 inches using a wire how much wire does she need

Answers

Answer: She Will Need 160 Inches Of Wire.

Step-by-step explanation: 20x8=160

360 km is 24% of blank km

Answers

the answer 1500 hope it helped

Our answer would be 1,500km did it on the calculator

What is the value of x? x+4/5=11 Enter your answer in the box in simplest form.

Answers

I think it is 10.2. because 4/5 is 0.8. then subtract 0.8 from 11 to get 10.2. so x=10.2.

Lines a and b are parallel.
What is the measure of angle m?

m = ?

Answers

Since the lines are Parallel 125 degrees are the same for angles like 125 degrees so the measure of line m is 55 degrees.
180-125=55

The answer is : m=55
180-125=55

how can you use mental math to determine if a ratio is simplified

Answers

You can see if it is simplified by checking if the numbers can be divided with the same number. Typically, this is done mentally.
Ex: You can mentally determine that 10:4 is not simplified, because both can be divided by 2.
You can then determine that 5:2 is simplified.

3. List all measurements that you can make with the 10-oz and 6-ov glasses. You can combine both cups for this process. If the measurements were not included in your process to solve, prove how you can make specific measurements. 4. Make observations about your findings Is there anything that you notice? Make a conjecture. Do you think what you found will work in all cases (for example if you were to use odd measurements rather than even)? 5. Vary the problem in an attempt to prove your conjecture. You can vary the problem by changing the target amount to find or changing the size of the glasses. Since you have already found all possible measurements for the 10-oz and 6-oz glass, your task is to change the glass sizes.

Answers

The ways that can be used to illustrate the measurement will be:

Use an object as a reference pointChoose an appropriate vessel to pour your liquid into. Place your vessel on a flat surface and bring yourself down to eye level.

How to illustrate the information?

It should be noted that the measurements that one can make with the 10-oz and 6-ov glasses include measuring cups of water, etc.

It is important to have some visual aids as a reference for the correct amount. It is important to clearly see the amount being poured as the fluid is slowly poured into the vessel.

In mathematics, the conjecture is a conclusion or a proposition which is proffered on a tentative basis without proof.

In conclusion, use an object as a reference point, choose an appropriate vessel to pour your liquid into, and then place the vessel on a flat surface and bring yourself down to eye level.

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Mira's kitchen sink holds up to 103.468 liters of water. Round this amount to the nearest liter.

Answers

103 nearest liter is one place.

The nearest liters is 103 L(liters).

While rounding a figure to the nearest whole number, the figure closest to the decimal point is considered.

If the figure that is closest to the decimal point is more than 5, it would be taken as one and added to the first unit of the figures which is 3.

But if the figure is less than 1, it's taken as Zero.

From the liters given, 4 which is closest to the decimal point is less than 5. This is therefore taken as 0

Therefore, the nearest liters is 103 L(liters).

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how do you write 10 less than half a number as 27 as an equation

Answers

Let

x--------> the number

we know that

The expression is equal to

[tex]\frac{x}{2} -10=27\\ \\\frac{x}{2}=27+10\\ \\\frac{x}{2}=37\\ \\x=74[/tex]

therefore

the answer is

[tex]\frac{x}{2} -10=27[/tex]

paul owes his father $10.75. he borrows $5.50 more from his father. what is paul's debt to his father

Answers

he first owes 10.75 He then borrows 5.50

10.75 + 5.50 = 16.25

Paul owes his father $16.25

hope this helps

16.25 hope this helps

An amphitheater charges $75 for each seat in Section A, $55 for each seat in Section B, and $30 for each lawn seat. There are three times as many seats in Section B as in Section A. The revenue from selling all 23,000 seats is $870,000. How many seats are in each section of the amphitheater?

Answers

Section A seats = 1500 Section B seats = 4500 Lawn seats = 17000 Let's write a few equations to express what we know. A = number of seats in section A B = number of seats in section B L = number of law seats "There are three times as many seats in Section B as in Section A" B = 3A "all 23,000 seats" L = 23000 - A - B L = 23000 - A - 3A "The revenue from selling all 23,000 seats is $870,000" 870000 = 30L + 55B + 75A Now let's substitute 3A for B 870000 = 30L + 55(3A) + 75A And substitute (23000 - A - 3A) = (23000 - 4A) for L 870000 = 30(23000 - 4A) + 55(3A) + 75A And solve for A 870000 = 30(23000 - 4A) + 55(3A) + 75A 870000 = 690000 - 120A + 165A + 75A 870000 = 690000 + 120A 180000 = 120A 1500 = A So we know that section A has 1500 seats. Because of B = 3A = 3*1500 = 4500, section B has 4500 seats. Finally, L = 23000 - A - B = 23000 - 1500 - 4500 = 17000 seats

Final answer:

Explaining how to determine the number of seats in each section based on seat pricing and total revenue.

Explanation:

Analyzing seat pricing and revenue:

Let the number of seats in Section A be x.Then, the number of seats in Section B is 3x.Set up equations based on the given information and total revenue to find the number of seats in each section.

what are the answers??

Answers

2x + 5x + 4 = 25
7x + 4 = 25
7x +4 (-4) = 25 (-4)
7x = 21
7x/7 = 21/7
x = 3

26 = 3b - 2 - 7b
26 = 4b - 2
26 + 2 = 4b - 2 (+2)
28/4 = 4b/4
b = 7

5m/8 - 6/8 +3m/8 = 2/8
8m/8 = 8/8
m = 1

hope this helps

The ratio of girls to boys in Liza’s classroom is 5
to 4
. How many girls are in her classroom if there is a total of 27
students?

Answers

There are 15 girls in the classroom

Answer:

15 girls

Step-by-step explanation:

Let

x-----> the number of girls

y-----> the number of boys

we know that

-----> equation A

isolate the variable y

-----> equation B

Substitute equation B in equation A

you welcome

A full can fly at a speed of 22 miles per hour about how many feet per hour can the gull fly?

Answers

First you need to know how many feet are in a mile.
5280 feet in a mile.
SO then you need to multiply 22*5280 and you get 116,160.
I hope that this helps!

drew adds 1/2 cup of wheat flour and 2 3/4 cup of white flour to his muffin batter. how many cups of flourdoes drew add

A 1 1/4
B 2 2/3
C 3 1/4
D 3 3/4

Answers

Answer:3 and 1/4 is the answer

Step-by-step explanation:

Suppose the leftmost digits of two numbers are 8 and 3 can u tell which number is greater? Explain

Answers

No because although 8 is a greater number than 3 it could be 300 and 80, therefore the 3 number would be greater. But it could just as easily be 30 and 800. You cannot tell by a single digit.

What is the true statement

Answers

D. No integers are irrational.
All intergers are rational

It would be D.

Whole numbers are numbers that are positive and don't have a decimal, which therefore, all are integers.

Integers are numbers that don't have a decimal, and are either negative or positive, so around half of them are whole numbers.

Um, all numbers are real, that's why we're talking about them.

Irrational numbers are numbers that can't be expressed as fractions. All integers can be expressed as fractions. Therefore, D is true.

An angle has a measure of 47 degrees. Find the measure of its supplement

Answers

hello :
the measure of supplement An angle has a measure of 47 is : x
x°+47°=180
x° = 180° - 47°
x° = 133°

The table below shows the combination of a dry prepackaged mix and water to make concrete. The mix says for every 1 gallon of water stir 60 pounds of dry mix. We know that 1 gallon of water is equal to 8 pounds of water. Using the information, finish the table. NEED HELP ON FINISHING THE TABLE.

Dry mix lbs water lbs total lbs
________ _________ 14 1/6
________ _________ ________

Answers

Let's assign a variable x to the number of multiples for each pound of dry mix and water. With that being the said, the question for finding the total pounds would be:

Total pounds = x*Pounds of dry mix + x*Pounds of water
Total pounds = 60x + 8x = 68x = 14 + 1/6 = 85/6
x = 85/6 / 68
x = 5/24

Thus, the pounds of dry mix is 60*5/24 = 25/2 lbs, while the pounds of water is 8*5/24 = 5/3 pounds.

You would like to make orange juice for the Queen of Canada but her tastes are very particular. She requires 400mL of orange juice, but it has to be the correct concentration, which is 23% concentrate. You have some 250mL cans of Windsor Delight OJ concentrate, which asks for 3 cans of water to every can of concentrate. You also have 250mL cans of Budget Brit OJ concentrate, which requires 4 cans of water for every can of concentrate. How much Windsor Delight mixture, and how much Budget Brit mixture will go into every 400mL of Her Majesty's Royal

Answers

32 ml of Budget Brit OJ concentrate 60 ml of Windsor Delight OJ concentrate Let's look at what you have available. There are two types of concentrate one of them is 1 can of concentrate to 3 cans of water, or 25% concentrate. The other is 1 can of concentrate to 4 cans of water, or 20% concentrate. What you want is a mixture that has 23% concentrate. Assuming you mixed both concentrates in separate containers and then in turn mixed those together in the proper ratio, the equation to express this is 0.20x + 0.25(400-x) = 0.23*400 Solving for x, first distribute the 0.25, and do the multiplications 0.20x + 0.25(400-x) = 0.23*400 0.20x + 100 - 0.25x = 92 Merge terms -0.05x + 100 = 92 Subtract 100 from both sides -0.05x = -8 And divide by -0.05 on both sides x = 160 So you now know that you need 160 ml of the 20% solution and 240 ml of the 25% solution. So you can now work backwards to determine how much of each concentrate you need. 0.20 * 160 = 32 ml of Budget Brit OJ concentrate 0.25 * 240 = 60 ml of Windsor Delight OJ concentrate

To create 400mL of orange juice with a 23% concentrate for the Queen of Canada, use a specific combination of Windsor Delight and Budget Brit OJ concentrates.

To make 400mL of orange juice with a 23% concentrate for the Queen of Canada:

Use 200mL of Windsor Delight OJ concentrate (which needs 3 cans of water per can).Use 200mL of Budget Brit OJ concentrate (which requires 4 cans of water per can).This combination meets the required concentration of 23% for the 400mL of orange juice.

Mr. and Mrs. Patton and their daughter Carolyn own three cars. Carolyn drives 10 miles per week farther with her car than her father does with his. Mr. Patton does twice as many miles per week as Mrs. Patton. If their total mileage per week is 160 miles, how many miles per week does each drive?

Answers

x = mr. pattons miles, y = mrs. patton's miles, z = carolyn's miles

x + y + z = 160
z = x + 10 ......z = 2y + 10
x = 2y

2y + y + 2y + 10 = 160
5y + 10 = 160
5y = 160 - 10
5y = 150
y = 150/5
y = 30 <=== mrs. patton drives 30 miles

x = 2y
x = 2(30)
x = 60....mr. patton drives 60 miles

z = x + 10
z = 60 + 10
z = 70 <== carolyn drives 70 miles

Answer: They drive 60 miles, 70 miles, 30 miles respectively.

Step-by-step explanation:

Since we have given that

Total mileage per week = 160 miles

Let the number of miles that her father does be x

Let the number of miles that she does be x+10

let the number of miles that her mother does be [tex]\dfrac{x}{2}[/tex]

so, our equation becomes,

[tex]x+x+10+\dfrac{x}{2}=160\\\\2x+\dfrac{x}2}=160-10\\\\\dfrac{4x+x}{2}=150\\\\\dfrac{5x}{2}=150\\\\x=\dfrac{150\times 2}{5}\\\\x=60\ miles[/tex]

So, her father drives 60 miles.

She drives 60 +10 = 70 miles.

Her mother drives [tex]\dfrac{60}{2}=30\ miles[/tex]

Hence, they drive 60 miles, 70 miles, 30 miles respectively.

A butter block weighs 200g the dimension of the block is 8cm by 5cm by 6cm what is the density to 3 decimal places?

Answers

Density = mass/volume
mass = 200g
volume = 8x5x6 = 240 cm^3

Density = 200g/240cm^3

Density = 0.833 g/cm^3

Hope I helped!!

Density of butter block is 0.833 g/cm³

Given that;

Weight of butter block = 200 g

Dimension of Butter block = 8cm by 5 cm by 6 cm

Find:

Density of butter block

Computation:

Density of butter block = Weight of butter block / Volume of butter block

Weight of butter block

Density of butter block = 200 / [(8)(5)(6)]

Density of butter block = 200 / 240

Density of butter block = 0.833 g/cm³

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sum of two numbers is 39. the greater number is 7 more than the smaller number. ( set up an equation )

Answers

Let the two numbers be x and y with x being the greater number.

Given,

x = 7 + y

Also given,

x + y = 39

Substituting the value of x from above,

7 + y + y = 39

7 + 2y = 39

2y = 39 - 7

2y = 32

y = [tex] \frac{32}{2} [/tex]

y = 16

x = 7 + y

x = 7 + 16

x = 23

Hence, the two numbers are 23 and 16.

x + y =39

x = y+7

y+7 +y = 39

2y +7 = 39

2y =32

y = 32/2 = 16

x = 16+7 = 23

start at 125. create a pattern that subtracts 6 from each number. stop when you have 5 numbers.

Answers

125-6= 119 119-6= 113 113-6=107 107-6= 101 101-6= 95

119 113 107 101 95

Answer:

The pattern is as follows:

125 119 113 107 101 95

Step-by-step explanation:

We are asked to create a pattern such that each digit is 6 less than the previous digit of the pattern.

Now, we have to start with 125.

The next term will be:

125-6=119

The next term of the pattern will be:

119-6=113

The next term will be:

113-6=107

The next term will be:

107-6=101

The next will be:

101-6=95

How to rewrite 3x4-1+2

Answers

If you want to solve it the answer is 13...
If you want multiple ways to write that here are some:
3x4+2-1
3x4+1
12+2-1
12+1
Etcetera

Angela is competing in a dance competition. If dance move is done correctly, the dancer earns points. If a dance move is done incorrectly the dancer loses points. Angela currently has 200 points. Angela then loses 30 points and earns 70 points. Write and evaluate an expression to find Angela’s final score

Answers

you have to do (200-30) + 70 =240

Answer:

(200-30) + 70 =240

Step-by-step explanation:

Shona is buying a rug for her room. Store A has the rug for $45 with a 10% discount. Store B has the same rug for $46 and is offering a $10 off coupon. The sales tax is 6% on either purchase. If Shona only has $40 to spend, which store will she purchase the rug from, and how much will she have left over?

Answers

store is is cheaper by just a little bit less

Store A= with discount it is 40.50 (45 x 0.10 and then subtract the answer from 45) and with tax it is 42.93 (40.5 x 0.06 and then add the answer to 40.5). so she doesn't have enough money for that one.

Store B= with coupon it is 36.00 (46-10). with tax it is 38.16 (36 x 0.06 and then add the answer to 36). She has enough money for this one.

40-38.16= 1.84 left over

that seems right to me

Find the remaining trigonometric ratios of θ based on the given information.
csc θ = 2 and cos θ is positive

Answers

Here is what I got. Hope it helps.

Final answer:

To find the remaining trigonometric ratios of θ given that csc θ = 2 and cos θ is positive, we calculate sin θ, cos θ, tan θ, cot θ, and sec θ.

Explanation:

To find the remaining trigonometric ratios of θ, we are given that csc θ = 2 and cos θ is positive. Based on this information, we can determine the values of the other trigonometric ratios.

The reciprocal of sin θ is csc θ, so we can find sin θ by taking the reciprocal of 2. Therefore, sin θ = 1/2.

Since cos θ is positive and sin θ is positive (since 1/2 is positive), we know that θ is in the first quadrant. In the first quadrant, all the trigonometric ratios are positive. Therefore, cos θ = √(1 - sin²θ) = √(1 - (1/2)²) = √(1 - 1/4) = √(3/4) = √3/2.

Finally, we can find the remaining trigonometric ratios:

tan θ = sin θ / cos θ = (1/2) / (√3/2) = 1/√3 = √3/3cot θ = 1/tan θ = √3/3sec θ = 1/cos θ = 2/√3 = 2√3/3cos θ = √3/2

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the selling price for a refrigerator is 584 if the mark up is 25% of the dealers cost, what is the dealers cost of the refrigerator?

Answers

25% of 584 is 146. If you meant to say "25% off of the dealer's cost", the answer would be $438, since you're finding what 25% of the original price is (146) and subtracting it from the original price. The equation would be 584 - 146 = 438. I hope this helped <3

To calculate the dealer's cost of a refrigerator, you can use the selling price and the mark-up percentage by following a step-by-step process.

Mark Up Calculation:

Let the dealer's cost be x.Mark up = 0.25x.Selling price = Dealer's cost + Mark up = x + 0.25x = 1.25x = $584.Solve for x: 1.25x = 584, x = $467.20.

Therefore, the dealer's cost of the refrigerator is $467.20.

Why do you subtract exponents when dividing powers with the same base?

Answers

Let's see why that happens by evaluating an expression with exponents.

[tex]\frac{a^{20}}{a^{10}}[/tex] <-- Now expand the exponent
[tex]\frac{a^{20}}{a^{10}} = \frac{(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)}{(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)}[/tex]

Now simplify the fraction by canceling out any common factors on the numerator and denominator.

[tex]\frac{(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)}{(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)} = \frac{(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)}{1} = a^{10}[/tex]

So, it's the same thing as subtracting the powers.

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