Let P denote the set of primes and E the set of even integers. As always, Z and N denote the integers and natural numbers, respectively. Find equivalent formulations of each of the following statements using the notation of set theory that has been introduced in this section. (a) 0 is an integer but not a natural number.

Answers

Answer 1

Answer:

{0} ∈ Z ∧ {0} ∉ N

Step-by-step explanation:

The notations we can use here are:

∈ = belongs

∉ = does not belong.

∧ = and

So, if we want to say that 0 is an integer, we use:

{0} ∈ Z

if we want to say that 0 is not a natural number, we use:

{0} ∉ N

And, if we want to say both in the same statement, we can use the "and" symbol:

{0} ∈ Z ∧ {0} ∉ N


Related Questions


1. The table represents values when input into a function f(x). What is the average rate of change of f(x)
from x = 2 to x=6? Show your work.

Answers

Answer:

Step-by-step explanation:

[tex]Rate \ of\ change =\frac{f(6)-f(2)}{6-2}[/tex]

                         [tex]=\frac{11-(-5)}{6-2} =\frac{11+5}{4}=\frac{16}{4}=4[/tex]

Find the area of a trapezium which has 6cm,5cm and 4cm

Answers

Answer:

28 sq. cm

Step-by-step explanation:

Area of a trapezium

= height * (base + top)/2

= 4 (6+8)/2

=28 sq. cm.

What is the value of x?

Answers

Answer:

i think its 29

Step-by-step explanation:

180-64=116

116/2=58

58/2=29

Answer:What is the value of x?

Step-by-step explanation: x" is often used in algebra to mean a value that is not yet known. It is called a "variable" or sometimes an "unknown". In x + 2 = 7, x is a variable, but we can work out its value if we try! A variable doesn't have to be "x", it could be "y", "w" or any letter, name or symbol.

Please help! What is the area in square units?

Answers

9514 1404 393

Answer:

  103 square units

Step-by-step explanation:

There is a way to find the area by counting grid points, but the fairly large number of them suggests that could be both tedious and prone to error. Instead, we'll chop up the figure into a trapezoid and two triangles.

From the top corner of the right edge draw a horizontal line across the figure. This will make the bottom portion a trapezoid and the top portion two triangles. The length of that horizontal line is 13 units, the height of the trapezoid, and the sum of the triangle bases.

The bottom trapezoid has a left-side base of 7 units and a right-side base of 6 units. Its area is ...

  A = 1/2(b1 +b2)h

  A = 1/2(7 +6)(13) = 1/2(13)(13) = 169/2 = 84.5 . . . square units.

The right top triangle has a base of 11 and a height of 3, so its area is ...

  A = 1/2bh

  A = 1/2(11)(3) = 33/2 = 16.5 . . . square units

The left top triangle has a base and height of 2 units each, so its area is ...

  A = 1/2(2)(2) = 2 . . . square units

Then the total area of the figure is ...

  84.5 +16.5 +2 = 103 . . . square units

_____

Check

Here is the check by counting grid points. The number of grid points on the outline of the figure is i=22. The number of grid points inside the figure appears to be b=93. Then the area by Pick's theorem is ...

  b +i/2 -1 = 93 + 22/2 -1 = 103 . . . square units

ANSWER ASAP IM BEING TIMED
WILL GIVE BRAINLIEST IF UR CORRECT AND IF I GET AN A ILL DO A FREE POINT GIVEAWAY

Choose the polynomial written in standard form.
xy2 + 4x4y + 10x2
x4y2 + 4x3y + 10x
x4y2 + 4x3y5 + 10x2
x6y2 + 4x3y8 + 10x

Answers

Answer:

Standard form means that you write the terms by descending degree.

x^4y^2 + 4x^3y + 10x^2

The degree of the first term x^4y^2 is 4+2=6

The degree of the second term 4x^3y is 3+1=4

The degree of the third term 10x^2 is 2

The terms are written by descending degree. Therefore, polynomial x^4y^2 + 4x^3y + 10x^2 is written in standard form.

Step-by-step explanation: I hope this helps <3

A formula for finding the perimeter of a rectangle is P=2L+2W. If you know the perimeter (P) and width (W) of a rectangle, which formula can you use to find the length (L)?

Answers

Step-by-step explanation:

→ P = 2L + 2W

→ P = 2(L + W)

→ P ÷ 2 = L + W

(P ÷ 2) - W = L

We can use this formula to to calculate the length.

the answer to this questions is “hey girl”

Dena borrowed $75,000 to buy a used car. The credit union charged 9% simple interest per year. She paid $2,025 in interest. For what period of time did she borrow the money?
Whats the...
Principal_____
Rate____
Intrest_____
PLSSSS ITS DUE IN 10 MINS

Answers

Pricipal- $75000
Rate- 9%
Interest- $2025

Hope this helps ;)

If so mark as brainliest

Evaluate the expression when t is 4.
Equation: 3 x 2t

Answers

Answer:

Step-by-step explanation:

3*2t

substitute the value of t

=3*2*4

=24

Answer:

24

Step-by-step explanation:

so you do

3x 2(4) subsuite the t for the 4

then  do 2*4= 8

then d0 3x8= 24

4. Select all the ways that describe the
graph of the function in interval 2.
ty
(2)
(1)
(3)
The function is increasing.
The slope is negative.
The function is decreasing.
The function is constant.
The slope is positive.

Answers

Answer:

all

Step-by-step explanation:

have the awnserbbbnnnnnnnnnnnn

For each of the following right triangles, set up a trigonometric ratio involving angle A and then find the
measure of Angle Aby using the appropriate inverse trigonometric ratio. Round to the nearest whole degree.

Answers

Answer:

Step-by-step Explanation:

(a) sinA= 7/18 A= sin ^-1( 7/18 ) = 23 (b) A=99°(c) A = 53°(d) A= 36°

HOPE IT HELPS!!!!

Answer:

Step-by-step explanation:

(a) A = 23°

(b) A=99°

(c) A = 53°

(d) A= 36°

Computer World has all computers on sale
for 20% off. If the regular price of a laptop is
$750, what is the sale price?

Answers

the sale price would be $150

Answer:

The sale price is $150

Step-by-step explanation:

1. Turn your percent into a decimal.

20% = 0.20 or 0.2

2. Multiply the decimal by 750.

0.2 x 150 = $150

(i usually use a calculator for this part)

The coordinate grid represents the school playground. Which of the following accurately describes the location of a playground area? Select all that apply.

Answers

Answer:

the answer is the first one

Step-by-step explanation:

the slide is 2 under left and 4 units up from the soccer field

1 N 3 4 5 6 7 00 9 10 The fastest that a seahorse can travel is 2,640 feet per hour. What is its top speed in m 0.05 miles per hour 0.2 miles per hour 0.5 miles per hour O 2 miles per hour​

Answers

Step-by-step explanation:

1 mile=5280 feet

0.5 mile=2640 feet.

The fastest that a seahorse can travel is 2,640 feet per hour. The top speed in miles per hour is 0.5 miles per hour.Can be also.

If the answer is correct plz mark me as brainliest.

What is 66.143 rounded to the nearest tenth?
QUICK

Answers

Answer:

66.1

Step-by-step explanation:

Answer:

66.1

Step-by-step explanation

To round the decimal number to its nearest tenth, look at the hundredth number. If that number is greater than 5, add 1 to the tenth value. If it is less than 5, leave the tenth place value as it is, and remove all the numbers present after the tenth’s place.

Find the perimeter of the figure below, in feet.
8.eft
6.6 ft
16.6A
6.6 ft
6.6 ft
eft
2 ft
6.6 ft
6.6 ft
12.4ft
12.4ft
8.2 ft

Answers

Answer:

not entirely sure but my answer is 87.6ft.

for the perimeter of the shape.

Step-by-step explanation:

I cut out the extra square-ish pieces of the sides and found

that both are 17.2 for their perimeter. so 17.2×2= 34.4

then I found the perimeter of the sides of the rectangular shape and the sides were both 18.4ft. so 2(18.4+8.2)= 53.2.

so 53.2+34.4 = 87.6ft.

What is filtration??​

Answers

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

[tex]\pmb{\qquad{\qquad{\qquad{\underline{\green{\underline{\sf{Filtration}}}}}}}}[/tex]

Filtration is a physical or chemical separation process that separates solid matter and flu.id from a mixture using a filter medium that has a complex structure through which only the flu.id can pa.ss.

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

Calculate the surface area of a solid box in the shape of a cube with
side length 3cm.

Answers

Answer:

54 cm^2

Step-by-step explanation:

side ( a ) = 3 cm

Formula : -

Surface area ( cube ) = 6a^2

Surface area ( cube )

= 6 x ( 3 )^2

= 6 x 9

= 54 cm^2

Answer:

54cm^2

Step-by-step explanation:

There are 6 sides in a cube. One of the sides should have the area of 9, because it's a cube and 3 * 3 is 9.

Considering that one side is [tex]9cm^{2}[/tex], the surface area should be 9 * 6, which is 54.

The surface area is 54cm^2.

Please can you help with no 5

Answers

Answer:

0.0046

Step-by-step explanation:

1/6 *1/6 *1/6 = 0.00462963

What is the circumference, using 3.14 for pi.

Answers

Answer:

circumference=2πr

2×3.14×637.68m

its yr correct ans.

hope it helps

stay safe healthy and happy...

Answer:

Option 4:  37.68 m

Step-by-step explanation:

The formula for finding this equation is C = 2πr

So to find our answer we will first multiply 2 by 3.14 and we get 6.28.  Now multiply 6.28 by 6 and we get 37.68.  Therefore, 37.68 is our answer.

Which number completes the table?
n
63
91
119
147
n7
9
?
21

Answers

Answer:

The answer is 13.

Step-by-step explanation:

n ÷ 7

= 91 ÷ 7

=13

which digit have the same place value and face value in 6782 1904​

Answers

4 and 0 has the same place value and face value.

Hope this is helpful :)

Answer:

0 and 4 are the digit which have same place and face value.

Which first step most directly leads to the solution of the equation below?
x^2 – 16 = 65

A. Add 16 to both sides of the equation.

B. Add -x^2 to both sides of the equation.

C. Rewrite the left-hand side as (x - 4)(x+4)

D. Rewrite the left-hand side as (x - 4)^2​

Answers

C the Promised and I have put in both of them for a few weeks but they have to do a better job on

2 7/9 divided by 5/6 in fraction.

Answers

The fraction after the division is A = 46 / 15

What is a Fraction?

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given data ,

Let the first fraction be p = 2 7/9

Let the second fraction be q = 5/6

Now , A = p/q

On simplifying the equation , we get

A = 2 7/9 / 5/6

A = ( 25/9 ) / ( 5/6 )

A = ( 25/9 ) x ( 6/5 )

On simplifying , we get

A = 138/45

A = 46 / 15

Hence , the fraction is A = 46/15

To learn more about fractions click :

https://brainly.com/question/29766013

#SPJ2

Determine the scale factor.

NEED HELP ASAP

Answers

Answer:

3

Step-by-step explanation:

so you can see it more boldly

explained in the comment thing.

What is the least number of bottles that can be packed in 4-packs or 6-packs without a remainder?

Answers

Answer:

4 bottles i think but you should check with someone else too

Answer:

4 bottles i think but you should check with someone else too

Step-by-step explanation:

The measure of angle NOP is 140
Which of the equations could be used to find the measure of angle NOQ?

Answers

Answer:

a) 23 + x = 140

Step-by-step explanation:

140 - 23 = 117

the angle x = 117°

You are building a fence and have 540 inches left to go. The fencing comes in sheets of 3 yards. How many sheets of fencing do you need to complete the fence?

Answers

Answer:

Step-by-step explanation:

243

Question 5 of 10
What is the slope of the line x = 3?
Answer here

Answers

Answer:

Undefined

Step-by-step explanation:

This equation is just a vertical line, so the slope is undefined.

Which is the endpoint of a ray?
Point R
Point S
Point T
Point U

Answers

9514 1404 393

Answer:

  Point S

Step-by-step explanation:

A ray extends in one direction from its end point. Point S is the only point shown in the diagram that does not have parts of a line extending in opposite directions from it.

Point S is a ray!!

Hope this help!!

You invested $11,000 in two accounts paying 3% and 7% annual interest, respectively. If the total interest earned for the year was $730, how much was invested at each rate? The amount invested at 3% is $​

Answers

Answer:

I invested $ 10,000 at 7% per year, and $ 1,000 at 3% per year.

Step-by-step explanation:

Given that I invested $ 11,000 in two accounts paying 3% and 7% annual interest, respectively, if the total interest earned for the year was $ 730, to determine how much was invested at each rate, the following calculation must be performed:

5,000 x 0.07 + 6,000 x 0.03 = 530

8,000 x 0.07 + 3,000 x 0.03 = 650

10,000 x 0.07 + 1,000 x 0.03 = 730

Therefore, I invested $ 10,000 at 7% per year, and $ 1,000 at 3% per year.

Answer:

A 3% = 1000 and B 7% = 10000

Step-by-step explanation:

A + B = 11000

A * 0.03 + B * 0.07 = $730

A = 11000 - B

(11000 - B)*0.03 + B*0.07 = 730

330 - 0.03B + 0.07B = 730

330 + 0.04B = 730

0.04B = 400

B = 10000

A = 11000 - B = 11000 - 10000

A = 1000

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