Which of the following illustrate the commutative property? Select all that apply

Answer:

6

Step-by-step explanation:

The correct notation is: Summation from n = 1 to infinity of the expression:

[tex]4(\frac{1}{3} )^{n-1}[/tex]

If we expand this notation, we will find that the given summation represent the terms of a G.P and we have to find the sum of infinite terms of a G.P. By placing n=1,2,3,4,... we can find the first few terms as shown below:

[tex]4(\frac{1}{3} )^{1-1}=4\\\\ 4(\frac{1}{3} )^{2-1}=4(\frac{1}{3} ) \\\\ 4(\frac{1}{3} )^{3-1} =4(\frac{1}{3} )^{2}[/tex]

Its obvious from the above result, that the given summation represent a G.P with first term equal to 4 and common ratio of 1/3. The formula of infinite G.P is:

[tex]S=\frac{a_{1} }{1-r}[/tex]

Using the value of a1 = 4 and r = 1/3 we can calculate the given summation

[tex]S=\frac{4}{1-\frac{1}{3} }=6[/tex]

Therefore, the given summation is equal to 6.

Answer:

100%

Step-by-step explanation:

do you need an explanation?

Answer:

[tex]\frac{8}{25}[/tex]  square miles

Step-by-step explanation:

The relationship between the side length (let it be s) of a square and its diagonal (let it be d) is given by:

[tex]s=\frac{d}{\sqrt{2} }[/tex]

Since d is given as 4/5, we solve for s:

[tex]s=\frac{d}{\sqrt{2} }\\s=\frac{\frac{4}{5}}{\sqrt{2} }\\s=\frac{4}{5\sqrt{2} }[/tex]

NOW, area of square is s^2 where s is the side length.

Area = [tex]s^2=(\frac{4}{5\sqrt{2} })^2=\frac{16}{50}=\frac{8}{25}[/tex]

The area of the park is:[tex]\[\boxed{\frac{8}{25} \text{ square miles}}\][/tex]

To find the area of the square park given the length of the diagonal, we need to use the relationship between the side length of a square and its diagonal.

[tex]\[d = s\sqrt{2}\][/tex]

Given that the diagonal [tex]\( d \) is \(\frac{4}{5}\)[/tex] miles, we can set up the equation:

[tex]\[s\sqrt{2} = \frac{4}{5}\][/tex]

[tex]\[s = \frac{\frac{4}{5}}{\sqrt{2}} = \frac{4}{5\sqrt{2}}\][/tex]

Rationalize the denominator by multiplying the numerator and the denominator by [tex]\(\sqrt{2}\):[/tex]

[tex]\[s = \frac{4\sqrt{2}}{5 \cdot 2} = \frac{4\sqrt{2}}{10} = \frac{2\sqrt{2}}{5}\][/tex]

[tex]\[A = \left( \frac{2\sqrt{2}}{5} \right)^2\]\[A = \frac{(2\sqrt{2})^2}{5^2} = \frac{4 \cdot 2}{25} = \frac{8}{25}\][/tex]

Therefore, the area of the park is:

[tex]\[\boxed{\frac{8}{25} \text{ square miles}}\][/tex]

Answer:

50 units

Step-by-step explanation:

Think of it as taking steps.  Each unit is a step.  It will take you 50 steps to get from -50 to 0, so the distance is 50

Mathematically, end point minus starting point

0 - (-50) =

0+50 = 50

Answer:

2/3 of a gallon per minute

Step-by-step explanation:

You can find the rate by subtracting the amount of gallons she observed and dividing it by the time.

7 - 5 = 2 and 2 gallons/3 mins = 2/3 of a gallon each minute.

Answer:

Step-by-step explanation:

The formula of a volume of a cylinder:

[tex]V=\pi r^2H[/tex]

r - radius

H - height

From the pictue we have r = 5in and H = 3in. Substitute:

[tex]x=\pi(5^2)(3)=\pi(25)(3)=75\pi\ in^3[/tex]

[tex]\pi\approx3.14[/tex]

Therefore

[tex]x=(75)(3.14)=235.5\ in^3[/tex]

Answer:

75π is the answer

Step-by-step explanation:

In term of pie is solving without multiplying with pie which is 3.14

A=πr2 x H

1) leave π alone solve for r2

The radius is 5  so 5 squared is 25 or 5x5=25

2) Just multiply 25 times the height which is 3 with pie

25x3=75

75π is the answer

Hopes this helps!

Answer:

y=2x^2−5x+18

Step-by-step explanation:

the distance from point b to c is 4 down the y-axis

Answer:

You Would Feel It Faint Because Of Earthquakes Are Loud Rumbles Not Matter How far

Step-by-step explanation:

It would be answer choice (B) :D

Answer:

See below.

Step-by-step explanation:

Problem  A

I have no tool that will draw this easily but I can direct you to do it.

Problem B

The general formula for the number of  bricks in any pattern (n) is

4n + 1 where n is the pattern number. Try some values.

n =3  

4n + 1

4*3 + 2

13

n = 4 which is the one you just drew

4n + 1

4*4 + 1

16 + 1

17

n = 8

4n + 1

4*8 + 1

32 + 1

33

Problem C

4n + 1 = 49           Formula

4n -1 = 49 - 1         Subtract 1 from both sides

4n = 48                 Divide by 4

4n/4 = 48/4

n = 12                    Answer

Pattern 12 will have 49 bricks

Problem D

The general formula we have been using all along is the answer.

4n + 1

Answer:

x = - 5, x = 4

Step-by-step explanation:

To find the zeros set f(x) = 0, that is

(x + 5)(2x - 8) = 0

Equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

2x - 8 = 0 ⇒ 2x = 8 ⇒ x = 4

Answer:

X = -5 or x = 4

Step-by-step explanation:

F(x)=(x+5) (2x-8)

When f(x) = 0

0 =(x+5) (2x-8)

Thus;

x+5 =0 or  2x-8 = 0

Therefore; x= -5 or x = 4

Answer:

statistical question

Step-by-step explanation:

A distribution is the arrangement of data values. The center for data refers to the central tendency measures such as mean, median, and mode. Variability describes the spread of values, often measured by standard deviation.

A distribution is how data values are arranged. The part of the data set where the middle values are concentrated is called the center for data. A survey anticipates that there will be different answers when gathering info. Variability is a measure that describes the spread of values in a data set.

To find the center of a data set, we can calculate measures of central tendency, which include the mean, median, and mode. The mean, or average, is the total of all data values divided by the number of values. The median is the value at the midpoint of the data set when ordered from smallest to largest, effectively splitting the data into two equal parts. The mode is the most frequently occurring value in the data set. If your data set has outliers, the median is often the best measure of the center, as it is less affected by extreme values.

When we refer to variability in a data set, we are often talking about the standard deviation, which tells us how spread out the data values are around the mean. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation suggests the values are spread out over a wider range.

Answer: x=-5 and y=18

Step-by-step explanation:You multiply 3x+y=3 by 2 to get 6x+2y=6. Then, you subtract 6x+2y=6 from 7x+2y=1. The result is x=-5. You then plug -5 into an x in one of the equations and get y equal to 18.

Answer:

-5

Step-by-step explanation:

it would be 25.2 hope this helps

The shortest time it takes to collect a container of water is 45 minutes.

A box and whisker plot, often known as a box plot, shows a data set's five-number summary. The minimum, first quartile, median, third quartile, and maximum make up the five-number summary. A box is drawn from the first quartile to the third quartile in a box plot. At the median, a vertical line passes through the box.

We have given the box plot which shows the amount water collect in how many minutes.

The box plot gives the following information

Minimum value = 45

Median = 48

Lower Quartile = 53

Upper Quartile = 56

Maximum = 64

So, the shortest time is given by minimum value which is 45 minutes.

Learn more about Box plot here:

https://brainly.com/question/1523909

#SPJ7

Hey there!

I want you to think of radicals as like terms. In order to be able to combine like terms, you need the same base and exponent.

For example,

3x^2-y^2 <== same exponent but not same variable

3x^2-x^2 <=== could be combined because exponent (^2) and variable (x) are the same

So, for this question, you're looking for a radical that has 5 under the radical sign and 3 above the radical sign.

"B" is the right answer, because is  ∛ and in the radical it has a √5.

I hope this helps!

~kaikers

Answer:

6

Step-by-step explanation:

the multiples of 6 are : 6, 12, 18, .....

The multiples of 3 are : 3, 6, 9, 12, ......

The multiples of 2 are : 2, 4, 6, 8, 10, 12, ......

The common multiples are 6 and 12 .....

The least common multiple is 6

Answer:

3

Step-by-step explanation:

5 times a number would be 5x, then increase that by 4 is 5x+4.  The problem then says 5x + 4 ≥ 19.  If we solve for x then we get x ≥ 3 so x has to be greater than or equal to 3, so the smallest number it could be is 3.  You can even try any number smaller than 3 and see it doesn't work.  even something like 2.9

Answer:

x ≥ 3  

Step-by-step explanation:

Let the number = x

5 × the number = 5x

Increased by 4 means 5x +4

   Is at least 19 means ≥ 19

5x + 4 ≥ 19

5x       ≥ 15      Subtracted 4 from each side

 x       ≥    3      Divided each side by 5

The smallest possible number that satisfies the conditions is x = 3.

Answer:

14.4

Step-by-step explanation:

AB / BC = AD/CD

AB/6.7 = 13.3 / 6.2

AB = 13.3 * 6.7 / 6.2

AB = 14.4

Answer:

The answer is 14.4 units.(option A)

Step-by-step explanation:

Angles BAC and CAD are equal.

We can solve this by using the proportional relation.

[tex]\frac{AB}{BC} =\frac{AD}{CD}[/tex]

Let AB be = x

So, [tex]\frac{x}{BC} =\frac{AD}{CD}[/tex]

[tex]\frac{x}{6.7} =\frac{13.3}{6.2}[/tex]

[tex]\frac{x}{6.7} =2.145[/tex]

[tex]x=6.7\times2.145[/tex] = 14.37 units

And rounding to nearest tenth, we get 14.4 units.

Answer:

The value of x = 4 when the value of y = 12

Step-by-step explanation:

∵ y α x ⇒ it is direct variation

- It means y increase when x increase

∴ y = kx ⇒ where k is a constant

- To find the value of k we will substitute the values of x

  and y in the equation above

- If y = 6 when x = 2

∴ 6 = k(2) ⇒ divide two sides by 2

∴ k = 3

∴ y = 3x ⇒ equation of variation

- To find the value of x when y = 12

- Substitute the value of y in the equation of variation

∴ 12 = 3x ⇒ divide both sides by 3

∴ x = 4

* The value of x = 4 when the value of y = 12

Answer: x=4

Step-by-step explanation:

By definition, the direct variation eqution has the following form:

[tex]y=kx[/tex]

Where k is the constant.

Therefore, if If [tex]y=6[/tex] when [tex]x=2[/tex], you can calculate k as following:

-Substitute values.

- Solve for k.

Then:

 [tex]6=k(2)\\k=3[/tex]

Then, when [tex]y=12[/tex], you can calculate the value of x as it is shown below:

-Substitute values.

- Solve for x.

Then:

[tex]12=3x\\x=4[/tex]

Answer:

33:100- 6:4- 5:3- 11/3

Step-by-step explanation:

First turn into even fractions

5:3= 1 2/3

6:4=1 1/2

11/3= 3 2/3

3/1= 3

33:100= 1/3

Then look at the numbers.

Answer:

one or two books cost 10 dollars

Step-by-step explanation:

which graph shows the relationship between the number of books x the store sold and the total amount of money y paid from the book sales?

book store selleing books for

10 dollars

x= books 1,2

y= paid  10

so u see it says someone  bought books for 10 dollars

each so  two books

Answer with explanation:

Selling Price of book, which the bookstore is selling =$ 10

If, total number of books sold =x

Total Selling Price of x, books = $10 × x=$10 x

If, y is the amount of money obtained after selling x books, then

→→ y= 10 x

Drawing the graph on "Desmos graphing"

Final answer:

To round 0.660 to the nearest tenth, we find that 0.660 rounded to the nearest tenth is 0.7.

Explanation:

To round 0.660 to the nearest tenth, we need to look at the digit in the hundredth place, which is 6. Since 6 is greater than or equal to 5, we round up. The digit in the tenth place becomes 7, and all digits after the tenths place are dropped. Therefore, 0.660 rounded to the nearest tenth is 0.7.

Answer:   a³ - 218

Step-by-step explanation:

  (a - 6)(a² + 6a + 36)

= a(a² + 6a + 36) -6(a² + 6a + 36)

= a³ + 6a² + 36a

      -  6a² -  36a - 218

= a³ + 0a² +  0a  - 218

= a³ - 218

Answer:

i think it might be fact families

Step-by-step explanation:

this is because they use the 3 same #rrs

Answer: Inverse Operations

Step-by-step explanation:

The sum of the two vertical angles (4x - 7) and (2x - 13) is 33 degrees.

To find the sum of the two vertical angles, we need to equate the expressions representing the measures of the angles and solve for x.

(4x - 7) = (2x - 13)

4x - 7 = 2x - 13

2x = -6

x = -3

Now we can substitute x = -3 back into one of the expressions to find the angle measures.

Angle 1 = (4x - 7) = (4(-3) - 7) = -12 - 7 = -19

Angle 2 = (2x - 13) = (2(-3) - 13) = -6 - 13 = -19

The sum of the two angle measures is: -19 + -19 = -38

Since angle measures cannot be negative, we can conclude that the sum of the two angle measures is 38 degrees. Answer choice (c) 66 is incorrect because the sum is not positive. The correct answer is (a) 33 degrees.

Answer:

2 < c < 12

Step-by-step explanation:

If we know two sides of a triangle a and b, the third side, c, can be no bigger than the the other two sides added together, and no smaller than the other two sides subtracted

a-b < c < a+b

We know the two sides are 7 and 5

7-5 < c < 7+5

2 < c < 12

Area of a triangle

1/2×b×h

=1/2×120×95

=60×95

=5700

Answer

5700 ft.

Answer:

5700 ft

Step-by-step explanation: