The graph below represents the result of a survey in which a number of students
reported how many letters were in their last names.
What was the range of name lengths?

Hi student, let me help you out! :)

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We are asked to find the solution to the inequality:

[tex]\star~\large\pmb{\cfrac{x}{9}+3 < 4}[/tex]

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

Step 1.

[tex]\star~\large\pmb{\cfrac{x}{9} < 4-3}[/tex]

[tex]\star~\large\pmb{\cfrac{x}{9} < 1}[/tex]

Step 2.

[tex]\star~\large\pmb{\cfrac{x}{9}\times9 < 1\times9}[/tex]

Notice that on the left, the 9s cancel, and we're left with x.

Step 3.

[tex]\star~\large\pmb{x < 9}[/tex]

This is the solution.

Hope it helps you out! :D

Ask in comments if any queries arise.

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Answer:

x < 9

Step-by-step explanation:

Given:  

[tex]\dfrac{x}{9} + 3 < 4[/tex]

1. Subtract 3 from both sides of the inequality

[tex]\dfrac{x}{9} + 3 - 3 < 4 - 3\\\\\implies\dfrac{x}{9} < 1[/tex]

2. Multiply both sides of the inequality by 9

[tex]9\left(\dfrac{x}{9}\right) < 1(9)\\\\\implies x < 9[/tex]

Learn more about finding the solution of an inequality:

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Answer:

Below in bold.

Step-by-step explanation:

4/2 = 2

8/4 = 2

Each term is obtained by multiplying the previous one by 2.

This is a geometric sequence with common ratio r = 2

the nth term

= a1r^(n-1)    where a1 = the first term

= 2(2)^(n-1).

[tex] a_{n} = 2_{n}[/tex]

Step-by-step explanation:

[tex]a_{1} = 2[/tex]

[tex]d = a_{2} - a_{1}[/tex]

[tex] = 4 - 2 = > 2[/tex]

Getting the nth term

[tex]a_{n} = a_{1} + (n - 1)d[/tex]

[tex] a_{n} = 2 + (n - 1)2[/tex]

[tex] a_{n} = 2 + (2n - 2)[/tex]

[tex]a_{n} = 2 + 2n - 2[/tex]

[tex] a_{n} = 2n[/tex]

Answer:

x=2

9+2=11

6+2=8

8x11+88

Step-by-step explanation:

Answer:

(5√x) / [(3√x)-4]

Step-by-step explanation:

You cannot solve this because 5, 3, and 4 are not factors/multiples of one another

I simplified it though

when the exponent is 1/2, it is the same as taking the square root of something

5x^1/2 is the same as 5√x

3x^1/2 is the same as 3√x

Answer: (1, 2) (The third option)

Step-by-step explanation: A solution has to be on the line. (1, 2) is the only point that isn't on the line.

An equation is formed of two equal expressions. The correct option is C.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The given statement in the form of equations can be written as,

1. The sum of m and n is 32 ⇒ m + n = 32

2. The value of m is three times the value of n ⇒ m=3n

Hence, the correct option is C.

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Problem 9

r+h = 9

SA = 2*pi*r^2 + 2*pi*r*h = 54pi

2*pi*r^2 + 2*pi*r*h = 54pi

2pi*r(r + h) = 54pi

r(r+h) = 27

r(9) = 27

9r = 27

r = 27/9

r = 3

r+h = 9

h = 9-r

h = 9-3

h = 6

Answers:  r = 3 and h = 6 are the radius and height respectively.

==========================================================

Problem 10

d = diameter = 68 mm

r = radius = d/2 = 68/2 = 34 mm

SA = surface area of a sphere

SA = 4*pi*r^2

SA = 4*pi*34^2

SA = 4264pi

Answer:  4264pi square mm

==========================================================

Problem 11

Plug V = 3000 into the sphere volume formula and isolate r.

V = (4/3)pi*r^3

3000 = (4/3)pi*r^3

(4/3)pi*r^3 = 3000

4pi*r^3 = 3*3000

4pi*r^3 = 9000

r^3 = 9000/(4pi)

r = cube root(  9000/(4pi)  )

r = ( 9000/(4pi) )^(1/3)

r = 8.947002 approximately

Now we can determine the surface area of this sphere.

SA = 4pi*r^2

SA = 4*pi*( 8.947002 )^2

SA = 1005.923451

Answer:  1005.923451 square feet approximately

==========================================================

Problem 12

We'll follow the same idea as problem 11, but in reverse.

SA = 4*pi*r^2

400pi = 4pi*r^2

r^2 = (400pi)/(4pi)

r^2 = 100

r = sqrt(100)

r = 10

Luckily we get a nice whole number for the radius r. Use it to find the volume.

V = (4/3)*pi*r^3

V = (4/3)*pi*10^3

V = (4000/3)pi

Answer:   (4000/3)pi   cubic inches exactly

==========================================================

Problem 13

The diagram is missing. I don't have enough info to be able to answer.

Answer:

B. 3.5

Step-by-step explanation:

I believe this is correct :')

The attached diagram represents the tree diagram for three consecutive mornings.

The probability of arriving on time is given as:

P(On Time) = 65%

Assume that the bus would definitely show up.

Then it means that the event is a binomial event and the possible outcomes are:

On Time and Late

The above means that the number of possible outcomes is 2.

For three consecutive mornings, the total outcome is:

Total = 2³

Evaluate

Total = 8

This means that the tree diagram would have 8 outcomes

Next, we draw the tree diagram (see attachment)

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Triangle EFG has vertices E(-2, 1), F(-1, 4), and G(3, 4). Graph the figure and its image after a clockwise rotation of 90° about vertex F. Then write the coordinates of triangle E'F'G'.

Answer:

expected value is $4.5

Step-by-step explanation:

expected value is $4.5

Based on the preferred dividends, the dividends for preferred and common stock in each year are:

Preferred stock dividends:

Common stock dividends:

Preferred shares have a specific dividend, and as these are cumulative shares, the dividends that are not paid in one year, will be paid in the next.

Dividends per year:

= 20,000 x 2% x 150

= $60,000

20y1 dividend per share:

= 60,000 / 20,000

= $3.00 per share

20y2 dividend per share:

= 24,000 / 20,000

= $1.20 per share

20y3 dividend per share:

The remaining dividend from 20y2 will have to be paid here:

= (60,000 + (60,000 - 24,000)) / 20,000

= 96,000 / 20,000

= $4.80 per share

Preferred dividends are paid first:

Common dividends are:

= (Amount distributed as dividends - Preferred dividends) / Number of common shares

In 20y1:

= (120,000 - 60,000) / 50,000

= $1.20

In 20y2:

= (45,000 - 45,000) / 50,000

= $0 per share

In 20y3:

= (180,000 - 96,000) / 50,000

= $1.68 per share.

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Answer:

12.5

Step-by-step explanation:

x = 2.5, 5x = ?

5(2.5) = 5 x 2.5 = 12.5

Answer:

the answer  to your question is 10

Step-by-step explanation:

if you divide 40 by 25% then you will get 10

Answer:

c=1 and c=3

Step-by-step explanation:

If x>0 and y>0, then

\sqrt{\dfrac{50x^6y^3}{9x^8}}=\sqrt{\dfrac{25\cdot 2y^2\cdot y}{9x^2}}=\dfrac{5y\sqrt{2y}}{3x}.

9x

8

50x

6

y

3

=

9x

2

25⋅2y

2

⋅y

=

3x

5y

2y

.

If

\dfrac{5y\sqrt{2y}}{3x}

3x

5y

2y

is equal to

\dfrac{5y^c\sqrt{2y}}{dx},

dx

5y

c

2y

,

then

\begin{gathered}y=y^c\Rightarrow c=1,\\ \\3x=dx\Rightarrow d=3.\end{gathered}

y=y

c

⇒c=1,

3x=dx⇒d=3.

Answer:

x = √41  which is 6.40 to the nearest hundredth.

Step-by-step explanation:

x^2 = 4^2 + 5^2      (By the Pythagoras theorem)

x^2 = 16 + 25 = 41

x = √41.

Answer:

x = 97

y = 83

Step-by-step explanation:

y = 83 (being the vertically opposite angle )

y + x = 180 (being co-interior angle)

or,

83 + x = 180

or,

x = 180 - 83

.•. x = 97

Answer:

8

Step-by-step explanation:

[tex]P = \{3,6,9\}\\\\\text{Number of elements,}~ n = 3\\\\\text{Number of subset} = 2^n = 2^3 = 8[/tex]

The median is 6.5.

The first quartile is 5.

The third quartile is 8.

The interquartile range is 3.

The numbers in the dot plot are: 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 22

Median is the number in the middle of the dataset.

Median = 1/2 ( n + 1)

1/2 x 21 = 11.5th number = (6+ 7) / 2 = 6.5

First quartile = 1/4 x (n + 1)

1/4 x 21 = 5.25th number = 5

Third quartile = 3/4 x (n + 1)

3/4 x 21 = 15.75th number = 8

Interquartile range = 8 - 5 = 3

Please find attached the dot plot. To learn more about interquartile range, please check:  https://brainly.com/question/3966385

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The y-intercept of f(x) has the same value as the x-intercept. The function f⁻¹(x) has a range including all values greater than or equal to 0; function f(x) does also.

Functions are found all across mathematics and are required for the creation of complex relationships.

A function and its inverse are shown on the same graph.

Complete the sentences to compare the functions.

The y-intercept of f(x) has the same value as the x-intercept.

The function f⁻¹(x) has a range including all values greater than or equal to 0; function f(x) does also.

More about the function link is given below.

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Answer:

decimal form; 0.22222...

exact form; 2/9

Step-by-step explanation:

Answer:

(12x12)+(12x8)+(12x12)=

Step-by-step explanation:

add that up on ur calculator for the answer

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's evaluate ~

[tex]\qquad \sf  \dashrightarrow \:2x(2x - 3) - 3x(x - 2)[/tex]

[tex]\qquad \sf  \dashrightarrow \:(2x \sdot2x) - (2x \sdot3) - (3x \sdot x) - (3x \sdot - 2)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 4 {x}^{2} - 6x- 3 {x}^{2} - ( - 6x)[/tex]

[tex]\qquad \sf  \dashrightarrow \:4 {x}^{2} - 3 {x}^{2} - 6x + 6x[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} [/tex]

I hope the Step were clear to you ~

Answer:

x²

Step-by-step explanation:

Given: 2x(2x - 3) - 3x(x - 2)

Distributive Property: a(b + c) = ab + ac

1. Distribute

⇒ 2x(2x) + 2x(-3) + -3x(x) + -3x(-2)

⇒ 4x² - 6x - 3x² + 6x

2. Combine like terms

⇒ 4x² - 3x² - 6x  + 6x

⇒ x²

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Answer:

360 degrees

Step-by-step explanation:

The sum of the INTERior angles of a pentagon equal

      (n-2)(180) = 540

          each angle is then   540/5 = 108

               each is a supplementary angle to the exterior angle

                       so EACH exterior angle is    180 - 108 = 72

         there are 5 of these    5 * 72 = 360 degrees

Answer:

1522.584

Step-by-step explanation:

1500(1+.09/12)^2=1522.584

[tex]\text{Let the number be x.}\\\\\text{According to the condition,}\\\\~~~~~4+2x=3x-8\\\\\implies 3x-2x = 4+8\\\\\implies x = 12\\\\\text{Hence, the number is 12.}[/tex]

Answer:

you do 5 multiplied by 4 and plus 3 I hope this helps

Answer:

Under Islamic law, land ownership is classified into two main categories, frrstly, according to the mode of acquisition or how land came into the possession and ownership of the individual and secondly according to the type of taxation.

Answer:

Are you Muslim I think Pakistan or Saudi