complete the statements about the closure of sets

Let S be the sum of the integers 25-210:

S = 25 + 26 + 27 + … + 208 + 209 + 210

Let S₃, S₄, and S₁₂ denote the sums of the integers in S that are multiples of 3, 4, or 12, respectively. We'll also count how many terms each sum involves; it'll be useful later.

S₃ = 27 + 30 + 33 + … + 204 + 207 + 210 … … … (62 terms)

S₃ = 3 (9 + 10 + 11 + … + 68 + 69 + 70)

S₄ = 28 + 32 + 36 + … + 200 + 204 + 208 … … … (46 terms)

S₄ = 4 (7 + 8 + 9 + … + 50 + 51 + 52)

S₁₂ = 36 + 48 + 60 + … + 180 + 192 + 204 … … … (15 terms)

S₁₂ = 12 (3 + 4 + 5 + … + 15 + 16 + 17)

Let's look at S₃ :

S₃ = 3 (9 + 10 + 11 + … + 68 + 69 + 70)

By reversing the order of the sum, we get

S₃* = 3 (70 + 69 + 68 + … + 11 + 10 + 9)

Of course S₃ = S₃*, I'm just calling it something else temporarily. Notice that every term in the same position of either sum adds up the same number.

9 + 70 = 79

10 + 69 = 79

11 + 68 = 79

and so on. Then

S₃ + S₃* = 3 (79 + 79 + 79 + … + 79 + 79 + 79)

or

2S₃ = 3 × 62 × 79   ==>   S₃ = 7,347

We can compute the other two sums in the same way.

S₄ = 4 (7 + 8 + 9 + … + 50 + 51 + 52)

S₄* = 4 (52 + 51 + 50 + … + 9 + 8 + 7)

==>   2S₄ = 4 × 46 × 59  ==>   S₄ = 5,428

S₁₂ = 12 (3 + 4 + 5 + … + 15 + 16 + 17)

S₁₂* = 12 (17 + 16 +15 + … + 5 + 4 + 3)

==>   2S₁₂ = 12 × 15 × 20   ==>   S₁₂ = 1,800

Then the sum you want is

S₃ + S₄ - S₁₂ = 10,975

We subtract S₁₂ because each of its terms is counted twice (once in S₃ and again in S₄).

Answer:

x = 60

2x = 120

2x + 30 = 150

2x - 30 = 90

Step-by-step explanation:

2x + 2x - 30 + 2x + 30 = 360

2x + 2x + 2x + 30 - 30 = 360

6x + 0 = 360

6x = 360

x = 360 / 6

x = 60

2x

= 2 x 60

= 120

2x + 30

= 120 + 30

= 150

2x - 30

= 120 - 30

= 90

Answer:

7.07143

Step-by-step explanation:

Diameter: 18

Angle: 45

Radius: 9

Answer:

below

Step-by-step explanation:

that's is the solution above

From the given number line, we have inequality as {x|x≤4.5}. Therefore, option B is the correct answer.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Inequalities on a number line allow us to visualize the values that are represented by an inequality. To represent inequalities on a number line we show the range of numbers by drawing a straight line and indicating the end points with either an open circle or a closed circle.

From the given number line, we have inequality as {x|x≤4.5}

Therefore, option B is the correct answer.

To learn more about the inequalities visit:

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Answer:

x=-3

Step-by-step explanation:

Answer:

Please see the attached pictures for the full solution.

[tex]\boxed{ \frac{d}{dx} ( {x}^{n} ) = n {x}^{n - 1} }[/tex]

Answer:

if it's area the area would be the length of the diameter of the semi circle which is the height of the triangle multiplied by the base of the triangle to find the area of the triangle then to find the area of the circle would be pie multiplied by the diameter divided by two squared

[tex]\pi \ \times 7 {}^{2} [/tex]

then the total area would be the area of the triangle plus the area of the half circle

Answer:

Min = -16; max = 0

Step-by-step explanation:

I plotted the inequalities for the constraints (see pic).

Sub in the coordinates of the vertices into the optimisation equation.

z = -(-4) + 5(-4) = -16

z = 0

z = -3 + 5(-1) = -8

Therefore, the max value of z is 0, and the min value is -16

To find the missing value divide both sides by -7:

28/-7 = 4

The missing value is 4

Answer= -4

Step-by-step explanation:

negative × negative = positve. therefore if 7×4=28 , then -7×-4=28

Answer:

V = 24.28 in ^3

Step-by-step explanation:

The area of the base is

A =5/2 × s × a  where s is the side length and a is the apothem

A = 5/2 ( 2.13) * .87

A = 4.63275

The volume is

V = Bh  where B is the area of the base and h is the height

V = 4.63275 ( 5.24)

V =24.27561 in^3

Rounding to the  hundredth

V = 24.28 in ^3

Answer:

y =(x-9)^2 +2

Step-by-step explanation:

The vertex form of a quadratic is

y = a(x-h)^2 +k  where (h,k) is the vertex and a is a constant

y = a(x-9)^2 +2

We can choose a if not given another point so I choose a = 1

y =(x-9)^2 +2

The volume of this pipe considering the thickness of the pipe is 154 cubic inches.

The general formula to calculate the volume of a cylindric object such as a pipe is:

In this formula, d represents the diameter and h represents the height.

The external diameter is 6 inches; however, the pipe is 1.25 inches thick, which implies the real internal diameter is 3.5.

Now, let's calculate the volume:

Learn more about cylindric in: https://brainly.com/question/14965384

Answer:

D. 154 cubic inches

Step-by-step explanation:

Answer:

4/2

Step-by-step explanation:

Rise/Run

4/2

Answer:

2

Step-by-step explanation:

y2 - y1 / x2 - x1

-1 - (-3) / 6 - 5

= 2/1

= 2

Answer:

a = 1/42, b = 1/7, c = 1/3 and d = 1/2

Step-by-step explanation:

a = bcd (1)

a + b = cd (2)

a + b + c = d (3)

a + b + c + d = 1  (4)​

Substituting equation (3) into equation (4), we have

a + b + c = d (3)

a + b + c + d = 1  (4)​

(a + b + c) + d = 1  (4)​

d + d = 1  (5)

2d = 1

dividing through by 2, we have

d = 1/2

Taking equation (2) and equation (3), we have

a + b = cd (2)

a + b + c = d (3)

substituting equation (2) into equation (3), we have

a + b = cd (2)

(a + b) + c = d (3)

cd + c = d

Factorizing, we have

c(d + 1) = d

dividing through by d + 1, we have

c = d/(d + 1)

substituting d = 1/2 into the equation, we have

c = d/(d + 1)

c = 1/2 ÷ (1/2 + 1)

c = 1/2 ÷ 3/2

c = 1/2 × 2/3

c = 1/3

Taking equations (1) and (2), we have

a = bcd (1)

a + b = cd (2)

Substituting equation (1) into (2), we have

a = bcd (1)

a + b = cd (2)

bcd + b = cd (2)

Factorizing, we have

b(cd + 1) = cd

dividing through by (cd + 1), we have

b = cd/(cd + 1)

substituting the values of c and d into the equation,, we have

b = cd/(cd + 1)

b = 1/3 × 1/2/(1/3 × 1/2 + 1)

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

b = 1/6 ÷ 7/6

b = 1/6 × 6/7

b = 1/7

Since a = bcd, substituting the values of b,c and d into the equation, we have

a = bcd

a = 1/7 × 1/3 × 1/2

a = 1/42

So, a = 1/42, b = 1/7, c = 1/3 and d = 1/2

Answer:

D 2/3

Step-by-step explanation:

Rise over run. The x values is -3 and 9 which is the distance or run between the dots. Find the distance by finding which number is between then so -3+x=9 where x is 12. The y values are -7 and 1. Find y where -7+y=1 where y is 8. That is the rise. So the rise is 8 and that is over the run, 12, gives you 8/12 which can be simplified to 2/3.

Answer:

option D is false it's not parallelogram

Answer:

-70

Step-by-step explanation:

keep adding -4 until you reach the 18th term for example

-2

-6

-10

-14

-18

-22

-26

-30

-34

-38

-42

-46

-50

-54

-58

-62

-66

-70

Answer:

14

Step-by-step explanation:

[tex]angle \: b = angle \: c \: thus \: ab = ac[/tex]

[tex]2x = 3x - 7 \\ 2x - 3x = - 7 \\ - x = - 7 \\ x = 7[/tex]

[tex]ac = 3x - 7 = 14[/tex]

Answer:

i think the answer is 126cm

Answer:

idea how to tell your loved one how you feel? How about a love song?

Answer:

Step-by-step explanation:

[tex]\frac{g}{f} (x)=\frac{g(x)}{f(x)} \\=\frac{3x^2+x}{4x} \\=\frac{x(3x+1)}{4x} \\=\frac{3x+1}{4}[/tex]

Answer: 196πcm²

Given

Diameter = 14

Radius = d/2

= 14/2

= 7

Surface area = 4πr²

Take π = 22/7

= 4×22/7×7×7

= 616 cm²

Must click thanks and mark brainliest

[tex] \large\begin{gathered} {\underline{\boxed{ \rm {\purple{Formula \: \: Using \: = \: 4 \: \pi \: {r}^{2} }}}}}\end{gathered}[/tex]

[tex]\bf \ \implies \: \: r \: = \: \frac{Diameter}{2} \\ [/tex]

[tex]\bf \ \implies \: \: r \: = \: \frac{14}{2} \\ [/tex]

[tex]\bf \ \implies \: \: r \: = \: \cancel\frac{14}{2} \: \: \large ^{7} \: \\ [/tex]

[tex]\bf \ \implies \: \: r \: = \: 7 \: cm[/tex]

[tex]\bf \large \longrightarrow \: \: 4 \: \pi \: {r}^{2} [/tex]

[tex]\bf \large \longrightarrow \: \: 4 \: \times \: \pi \: \times {7} \: ^{2} [/tex]

[tex]\bf \large \longrightarrow \: \: 4 \: \times \: \pi \: \times 49[/tex]

[tex]\bf \large \longrightarrow \: \: 196 \: \pi \: {cm}^{2} [/tex]

Hence , the surface area of sphere is 196 π cm²

Answer:

w^-2 = 1/w^2

a^6

Step-by-step explanation:

We know that a^b * a^c = a^( b+c)

w^3 * w^ -5 = w^(3-5) = w^-2

We know that a^-b = 1/a^b

w^-2 = 1/w^2

We know that a^b ÷ a^c = a^( b-c)

a^4 ÷ a^-2 = a^(4 - -2) = a^6

Answer:

[tex]\frac{1}{ w^{2} }[/tex]

[tex]a^{6}[/tex]

Step-by-step explanation:

x^n * x^m = x ^ (n+m)

w^3 * w^ -5 = w^ -2 = [tex]\frac{1}{ w^{2} }[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

x^n ÷ x^m = x^ n-m

a^4 ÷ a^-2 = a^ 4 -(-2) = [tex]a^{ 6}[/tex]

Answer:

13-3=10

10-4=6

Step-by-step explanation:

man id hate to have to do this work literally just use your fingers or something

Answer:

search it in internet.hope you'll find the answer

Answer:

The surface area of the rectangular prism is 814[tex]in^{2}[/tex]

Step-by-step explanation:

In order to find the surface area for a rectangular prism you have to solve using the following formula

A=2(wl+hl+hw)

Hope this helps!

Using the function concept, it is found that the result would not be a function, as for each month, there would be multiple possible number of days.

In a function, one value of the input can be related to only one value of the output.

In this problem, the input is the month and the output is the possible number of days in the month.

Since there is a month with either 28 or 29 days, and the other months have either 30 or 31 days, the are multiple outputs for each input, hence, the result is not a function.

You can learn more about the function concept at https://brainly.com/question/12463448

Answer:

56 m³

Step-by-step explanation:

Base area = 8×6/2 = 24 m²

Height = 7 m

Volume = 24×7/3

= 56 m³

Answered by GAUTHMATH