There are more than 30 students in Benedict's math
class.
Graph and check the solutions of the inequality. Then
complete the statements,
S> 30
Draw
circle at
0
10
20
30
40
Shade all numbers
Check the graph of the solution by substituting in
for the variable.

Answer:

4 to 3

Step-by-step explanation:

First, we need to know how many nonfiction books there are and how many mystery books there are

Well, there are 24 mystery books and 18 nonfiction ones

To find the ratio between them, we need to compare how much 18 is to 24

To do this, let's find a common factor of 18 and 24

Both 18 and 24 have a common factor of 6

6 x 3 = 18

6 x 4 = 24

So, we know that there are 4 6's in 24 and 3 6's in 18

That means the ratio of 24 to 18 is the same as 4 to 3

Because 18 is 3 fourths of 24

So, the ratio of mystery books to nonfiction ones is 4:3

Answer:

4 to 3

Step-by-step explanation:

No.of mystery books= 24

No.of non - fiction = 18

Ratio= 24:18 (or) 24/18

Simplification of 24/18 is 4/3 (or) 4 to 3

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The GCD of 5! and 7! is 2^3 * 3^1 * 5^1 = 120.

the greatest common divisor of 5! and 7! is 120.

To find the greatest common divisor (GCD) of 5! and 7!, we need to factorize both numbers and identify the common factors.

First, let's calculate the values of 5! and 7!:

5! = 5 * 4 * 3 * 2 * 1 = 120

7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040

Now, let's factorize both numbers:

Factorizing 120:

120 = 2^3 * 3 * 5

Factorizing 5,040:

5,040 = 2^4 * 3^2 * 5 * 7

To find the GCD, we need to consider the common factors raised to the lowest power. In this case, the common factors are 2, 3, and 5. The lowest power for 2 is 3 (from 120), the lowest power for 3 is 1 (from 120), and the lowest power for 5 is 1 (from both numbers).

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To accurately determine the amount they would have to buy, we would need the specific measurements of the pool, the desired fence height and any other requirements they have.

To determine how much Gwen and Lisa would have to buy to replace the fence on their pool, we would need more specific information about the pool's dimensions, the type of fence they want, and any other relevant details.

Let's consider some factors that could affect the amount they would need to purchase:

Perimeter of the pool:

The length of the fence required would depend on the perimeter of the pool.

If we know the dimensions of the pool, we can calculate its perimeter by adding up the lengths of all sides.

Fence height:

The height of the fence is another important factor. Depending on local regulations or personal preferences, Gwen and Lisa might need a specific height for their pool fence.

This would determine the length of fencing material they need to purchase.

Fence type and style:

Different types of fences, such as chain-link, wood, vinyl, or wrought iron, have varying costs and installation requirements.

The choice of fence material and style will impact the amount they would have to buy.

Gates and openings:

If Gwen and Lisa require gates or openings in the fence, they would need to account for these as well.

The number and size of gates would affect the total amount of fencing material needed.

With these details, we can calculate the perimeter, account for gates and openings and factor in the material type and style to provide an estimate of the amount of fencing they need to purchase.

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Hello and Good Morning/Afternoon:

The table shows a linear function:

 \(\hookrightarrow \text{This means that the slope is consistent between all the points}\\\)

Thus we can use any point to help us find our slope:

 \(\hookrightarrow \text{let's pick two points}\)

       \(\hookrightarrow \text{Slope} = \dfrac{y_2-y_1}{x_2-x_1} = \dfrac{16-7}{5-2} =\dfrac{9}{3} =3\)

Answer: 3

Hope that helps!

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Answer:

C

Step-by-step explanation:

13-8x =-18 with x being a random number apart from zero

Answer:

60°

Step-by-step explanation:

As we can see it is an equilateral triangle so all angles are equal so

x = 60°

Hope it will help :)

The number of ways to choose the colors is 36

The given parameters are:

Colors = 9

Colors to choose = 7

Since order does not matter, then it is combination

This is calculated using:

\(^nC_r = \frac{n!}{(n - r)!r!}\)

This gives

\(^nC_r = \frac{9!}{7!2!}\)

Evaluate

\(^nC_r = 36\)

Hence, the number of ways is 36

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A more modern explanation would be, "Parallel lines are two lines within a given plane that never intersect."

Two lines on a sphere are an illustration that defies the notion of parallel lines. Meridians are the name given to longitude lines on spheres like the Earth.

Meridians are lines that run parallel to one another from the North Pole to the South Pole. However, if we take into account two meridian lines, they will cross at the North and South Poles. Two lines that are originally parallel will, therefore, eventually intersect at the poles on a sphere, defying the notion of parallel lines.

We can change the original definition of parallel lines to read, "Parallel lines are two lines that do not intersect within a given plane."

This adjustment accounts for the fact that lines can exist in many geometrical contexts, such as on a sphere or in three-dimensional space, where the idea of parallelism may be different. By including the phrase "within a given plane," we restrict the concept to the typical geometry seen in Euclidean geometry, where parallel lines do not meet.

A newer definition may therefore read, "Parallel lines are two lines within a given plane that never intersect." This updated definition makes clear that parallel lines must be taken into account inside a certain plane in order to maintain their validity, while also acknowledging the limitations of the idea.

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Given:

The equation of a line is:

\(2y+3x=10\)

The line is dilated by factor 3.

To find:

The result of dilation.

Solution:

The equation of a line is:

\(2y+3x=10\)

For \(x=0\),

\(2y+3(0)=10\)

\(2y+0=10\)

\(y=\dfrac{10}{2}\)

\(y=5\)

For \(x=2\),

\(2y+3(2)=10\)

\(2y+6=10\)

\(2y=10-6\)

\(2y=4\)

Divide both sides by 2.

\(y=\dfrac{4}{2}\)

\(y=2\)

The given line passes through the two points A(0,5) and B(2,2).

If the line dilated by factor 3 with origin as center of dilation, then

\((x,y)\to (3x,3y)\)

Using this rule, we get

\(A(0,5)\to A'(3(0),3(5))\)

\(A(0,5)\to A'(0,15)\)

Similarly,

\(B(2,2)\to B'(3(2),3(2))\)

\(B(2,2)\to B'(6,6)\)

The dilated line passes through the points A'(0,15) and B'(6,6). So, the equation of dilated line is:

\(y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\)

\(y-15=\dfrac{6-15}{6-0}(x-0)\)

\(y-15=\dfrac{-9}{6}(x)\)

\(y-15=\dfrac{-3}{2}x\)

Multiply both sides by 2.

\(2(y-15)=-3x\)

\(2y-30=-3x\)

\(2y+3x=30\)

Therefore, the equation of the line after the dilation is \(2y+3x=30\).

Answer:

the actual sales be $31,132

Step-by-step explanation:

The computation of the actual sales is as follows:

Let us suppose the actual sales be x

Now the sales tax be 0.06x

Now the total sales would be

x + 0.06x = $33,000

1.06x = $33,000

x = $33,000 ÷ 1.06

= $31,132

hence, the actual sales be $31,132

The same is to be considered by applying the above equation

Answer:

actual sales be $31,132

Step-by-step explanation:

1/3 - inch cubes across the bottom layer = 30

the number of layers is 9

Total number of 1/3-inch cubes 270 cubes

The small cube inside has a dimension of 1/3

The area of the cube is 1/3 * 1/3 = 1/9

the area of the bottom layer is 2 * 1 2/3 = 10/3

the number of small cubes across the bottom is

=  10/3 / 1/9

= 30

The number of layers is calculated by division

= total height of layers / 1/3-inch side of the cube

= 3 / 1/3

= 9 layers

Total number of 1/3-inch cube

= 30 * 9

= 270 cubes

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A graph of the exponential function \(f(n)=37000(1.06)^n\) is shown in the image attached below.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

\(f(x)=a(b)^x\)

Where:

Based on the information provided above, your salary can be modeled or represented by the following exponential function;

\(f(n)=37000(1.06)^n\)

Lastly, we would use an online graphing calculator to plot the given exponential function as shown in the graph attached below.

In conclusion, the rate of change of this exponential function is equal to 1.06.

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Step-by-step explanation:

7! = 5040 ways

The surface area of the prism include the following: C. two hundred seventy-five and one-eighth cm².

In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:

Surface area of a rectangular prism = 2(LH + LW + WH)

Where:

By substituting the given side lengths into the formula for the surface area of a rectangular prism, we have the following;

Surface area of rectangular prism = 2[(23/4 × 4) + (23/4 × 47/4) + (4× 47/4)]

Surface area of rectangular prism = 2[23 + 1081/16 + 47]

Surface area of rectangular prism = 275 1/8 cm².

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Answer:

21

Step-by-step explanation:

PEMDAS : Parenthesis, Exponent, Multiplication/Division, Addition/Subtraction.

First, we want to deal with the parenthesis within the parenthesis.

(4.6/2) = 2.3

Rewrite it into the equation.

[3 * 2.3] + 14.1 = ?

Now, do the work in the parenthesis again.

[6.9] + 14.1 = ?

There isn't anymore parenthesis, exponents, or multiplication/division, so we move onto addition now and add both terms.

6.9 + 14.1 = 21

? = 21

The answer is 21.

We have to use the slope formula.

Let's replace the given points in the formula.

Then, we use the point-slope formula to find the equation.

Remember that the y-intercept is always the independent term.

Answer:

Step-by-step explanation:

From the picture attached,

Graph (A)

Domain of the function : (-∞, ∞) or a set of real numbers

Range of the function : (-∞, ∞) or a set of real numbers

Graph (B),

Domain : (-∞, ∞) Or a set of real numbers

Range : (-∞, 6] Or x ≤ 6

Graph (C),

Domain : [-2, ∞) or x ≥ -2

Range : (-∞, ∞) Or a set of real numbers

Therefore, Graphs (A), (B) have the domain of all real numbers and Graph (C) has the range of all real numbers.

Since all the parabolas are not the functions,

Therefore, Graph (C) is not a function. Graphs (A) and (B) are the functions.

Answer:

50°

Step-by-step explanation:

\(m\angle RST = \frac{1}{2} \times (150\degree - 50\degree) \\\\

m\angle RST = \frac{1}{2} \times 100\degree \\\\

\purple{ \bold{m\angle RST =50\degree}} \\\\\)

Answer:

57

Step-by-step explanation:

Together both angles equal 90

(3x - 15) + (5x -23) = 90

Combine like terms

8x - 38 = 90

Add 38 to both sides

8x = 128

Divide by 8

x = 16

You can check by replacing x with 16 and seeing if it still equals 90.

To find angle MON... replace x with 16

5(16) - 23

Angle MON = 57

I hope this helps!!

Answer:

y=-\(\frac{1}{4}\)x

Step-by-step explanation:

Answer:

y=-1/4x

Step-by-step explanation:

Answer:

AB = 97

Step-by-step explanation:

AB is half of mABD.

Answer:60mm

Step-by-step explanation:

288,000 π = (4/3)πr³

Divide both sides by π

288,000 = (4/3)r³

Multiply both sides by 3/4

216,000 = r³

Take the cube root of both sides

60 = r

It should be noted that the addition of the variables give in the expression will be 11✓2.

It should be noted that the information is incomplete. Therefore, an overview will be given. In this case, let a = ✓2, b = ✓8 and c = ✓128.

This can be illustrated as:

= a + b + c

= ✓2 + ✓8 + ✓128

= ✓2 + 2✓2 + 8✓2

= 11✓2

Therefore, it should be noted that the should be noted that the addition of the variables give in the expression will be 11✓2

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Answer:

DEMOS LSO

Step-by-step explanation:

Answer:

64cm³

Step-by-step explanation: