Door prizes for entrants in a young inventors competition are $100, $50, $25 and $10. In how many ways can the door prizes be awarded if there are 23 entrants?.

Answer: g/15 = 3 ; g = 45 gifts.

Step-by-step explanation: You would basically have to multiply 15 by 3, and it equal 45. This answer choice shows an equation that will make the answer 45, so it is right.

g/15 will equal 3.

Then, you would break them apart and do the denominator (15) multiplied by the numerator (3).

This will get you the answer 45.

So, you will get the answer choice A.

Answer:

1/12

Step-by-step explanation:

See attached worksheet.

Answer:

3(x-5) =3x - x - 8

3x-15 = 2x - 8

3x-2x= -8+15

x=7

Step-by-step explanation:

first 3 will multiply by x and -5,which are in bracet like this

                                         3(x-5)= 3x - x -8

after they would became 3x-15 = 2x (because 3x will be subtracted by x) -8

                                           so it will become like this

                                             3x-15=2x-8

after that 3x will be subtracted by 2x like this 3x-2x and -8 will be add in +15 so it would be

                                    x=7

Explanation

Step 1

the sum of the internal angles in a triangle equals 180, then

for triangle CDE

Step 2

as we can see, in poitn c, we have a 180 degrees angle(ACD)

so

I hope this helps you

Answer:

SAS

Step-by-step explanation:

Answer:

-0.5f - 4.52 = -25.52 + 1f

-1.5f = 21

f = 14

Answer:

14

Step-by-step explanation:

-4.52 + 25.52 = f + 0.5f

21 = 1.5f

f = 14

Answer:

Its A

Step-by-step explanation:

that's literally what a segment is

Answer: its associative property Hope I helped

Step-by-step explanation:

The product of the given expression is 1,30,200.

Given expression:-

(−310)(4.2)(−100)

We have to find the solution of the given expression by using either the commutative property or the associative property.

We will use the associative property of multiplication to find the product.

(−310)(4.2)(−100) = (-310)*(4.2*(-100)) = (-310)*(-420) = 1,30,200

Associative property

The associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result.

Hence,

(a*b)*c = a*(b*c) , where a, b and, c are real numbers.

Commutative property

Commutative property In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.

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Yes , there can be a Right triangle with two side lengths as simple fraction and other side length as an integer .

In the question ,

we have to find , whether a Right Triangle can be made by two fractions and an integer length .

yes, we can make a Right Triangle with two lengths as fractions and other length as integer .

let us prove it with the help of an example .

Consider the triplet 7 , 24 , 25 .

let the two fractions side be 7/25 and 24/25 , and the hypotnuse of the right triangle be  1 .

We know that for the Right Triangle

(side1)² + (side2)² = hypotnuse²

(7/25)² + (24/25)² = 1²

49/625 + 576/625 = 1

(49+576) / 625 =1

625/625 = 1

1 = 1

hence ,it is a Right Triangle .

Therefore , Yes , there can be a Right triangle with two side lengths as simple fraction s and other side length as an integer .

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Given:

Required:

To

Taking into account the definition of a system of linear equations, the number of adult tickets sold was 50.

A system of linear equations is a set of linear equations in which two or more variables are related.

In the systems of equations, the values of the unknowns must be found, with which when replacing, they must give the solution proposed in the  equations.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

3c + 5a= 340

c + a= 80

From the several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable "c" from the second equation:

c= 80- a

Replacing this expression in the first equation:

3×(80- a) + 5a= 340

Solving:

3×80- 3a + 5a= 340

3×80- 3a + 5a= 340

240- 3a + 5a= 340

- 3a + 5a= 340- 240

2a= 100

a=100÷ 2

a= 50

Finally, 50 adult tickets were sold.

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A few properties of a parallelogram.

1) Opposite sides are always equal.

2) Opposite angles are always equal.

3) The sum of all the angles is 360.

In part 2, we are given the angles. Therefore, we can apply the 2nd property.

11x = 55

5y = z (lets say the unknown is z).

Now, 11x = 55

x = 55/11

x = 5

Now, we have to angles of 55 degrees but we don't know about y and z. Therefore, we have to apply the third property.

55 + 55 + 5y + z = 360

110 + 5y + z = 360

5y + z = 360 -110

5y + z = 250. (i)

According to property 2, 5y = z. Hence, put the value of 5y in the equation (i), we get

5y + z = 250

z + z = 250

2z = 250

z = 250/2

z = 125

From the value of z, we can find the value of y using z = 5y

125 = 5y

5y = 125

y = 125/5

y = 25

Hence, x = 5 and y = 25

The state income tax owed on a $90,000 per year salary is $5,175.

Tax is a compulsory amount that is levied by the government on the income of individuals or on certain goods and services. Progressive tax is when the amount of tax paid by individuals increases as the amount of income earned increases. The amount paid as tax can be determined by multiplying the appropriate tax rate by the total income.

Tax paid = income x tax rate

$90,000 x 5.75%

$90,000 x 0.0575 = $5,175

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The state income tax owed on an $90,000 per year salary is  $5,175.

Taxes are mandatory contributions levied on individuals or corporations by a government entity

Given,

A certain state uses the following progressive tax rate for calculating individual income tax: Income Progressive Range ($) Tax Rate 0 - 3000 2% 3001 - 5000 3% 5001 - 17,000 5% 17,001 and up 5.75%

We need to find the state income tax owed on an $90,000 per year salary.

Tax paid = income x tax rate

$90,000 x 5.75%

5.75% should be converted to decimal by dividing with 100.

5.75/100=0.0575

So $90,000 x 0.0575 = $5,175

Hence the state income tax owed on an $90,000 per year salary is  $5,175.

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The average rate of change of the given graph is 31.3

The graph of the function is represented as the given parameter

From the graph, we have the following points

(x, y) = (10, 313) and (20, 626)

The average rate of change is the slope of the function and the average rate of change is calculated as

Average rate = [f(b) - f(a)]/[b - a]

Where

(a, f(a)) = (10, 313) and (b, f(b)) = (20, 626)

Substitute the known values in the above equation

So, we have

Average rate = [626 - 313]/[20 - 10]

Evaluate

Average rate = 31.3

Hence, the average rate is 31.3

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When the radius is 10 inches and the height is 20 inches

(a) rate change of the volume of the cylinder is 5340.7 inch²/min.

(b) rate of change of the surface area of the cylinder is 1068.14 inch²/min.

Volume and surface area of the closed cylinder both increase with time.

Let r be the Radius and h be the height of the cylinder in inches at time t.

[tex]\frac{dr}{dt} =5[/tex] inch/min and [tex]\frac{dh}{dt} =-3[/tex] inch/min

Let V be the volume of the cylinder then

Differentiating with respect to t,

[tex]\frac{dV}{dt} =2\pi r(\frac{dr}{dt} )h+\pi r^{2} \frac{dh}{dt}[/tex]

At r=10 inch and h=20 inch,

[tex]\frac{dV}{dt} =1700\pi =[/tex] 5340.7 inch²/min ≈ 5000 inch²/min

Thus, it is increasing with time as it has a positive sign.

Let S be the surface area of a closed cylinder

[tex]\frac{dS}{dt} =2\pi r(\frac{dr}{dt} )h+2\pi r(\frac{dr}{dt} )+4\pi (\frac{dr}{dt} )r[/tex]

At r=20 inch and h=20 inch

[tex]\frac{dS}{dt} =340\pi =[/tex] 1068.14 inch²/min ≈ 1000 inch²/min

It is also increasing with time as it is also having a positive sign.

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I WILL FIND THE GRADIENT FIRST

[tex]m = \frac{y2 - y1}{x2 - x1} \\ = \frac{5 - ( - 8)}{8 - 4} \\ m = \frac{5 + 8}{4} \\ m = \frac{13}{4} [/tex]

THE GENERAL EQUATION OF A STRAIGHT LINE IS y=mx+c

I will use the point (8,5)

to find the value of c

[tex]5 = \frac{13}{4} (8) + c \\ 5 = \frac{104}{4} + c \\ c = 5 - \frac{104}{4} \\ c = - \frac{84}{4} \\ c = -21[/tex]

THE EQUATION IS

[tex]y = \frac{13}{4} x - 21[/tex]

The width of the paper in the smaller notebook is 4 1/4 inches.

When two shapes are similar, the ratio of their corresponding sides are equal, and their corresponding angles are equal.

For two notebooks in the shape of a rectangle, the ratio of their lengths must be equal to the ratio of their widths.

If one sheet of paper in a notebook is 8 1/2 inches by 11, and the pages of the smaller similar notebook are 5 1/2 inches long, then the width of the paper in the smaller notebook is

11 inches / 5 1/2 inches = 8 1/2 inches / width of smaller notebook

width of smaller notebook = 4 1/4 inches

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The multiplication we need to make is:

To answer this question we need to use the following rules for multiplications with signs:

We can see that in our expression we have the last case: a negative number multiplied by a positive number. In this case, the negative number is -6 and the positive number is 1.

So, we know from the rule that the result will be negative.

And finally, we multiply just the numbers: 6 by 1 is 6.

In summary, the result is:

Answer: -6

Answer:

-6

Step-by-step explanation:

hope this helps

The coordinate of the midpoint AB is (1/2, 1/2)

From the question, the coordinates of the points are given as

A = (-2, 2)

B = (3, -1)

The midpoint of a line or points is then calculated using the following midpoint formula

Midpoint = 1/2 * (x₂ + x₁, y₂ + y₁)

Where x and y are the coordinates of A and B

Substitute the known values in the above equation

So, we have the following equation

AB = 1/2 * (-2 + 3, 2 - 1)

Evaluate the sum

AB = 1/2 * (1, 1)

Evaluate the products

AB = (1/2, 1/2)

Hence, the midpoint is (1/2, 1/2)

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3) [tex]\angle BCA \cong \angle CAD[/tex] (alternate interior angles theorem)

4) [tex]\triangle ABC \cong \triangle CDA[/tex] (AAS)

Answer:

Explanation:

The slope-intercept form of the equation of a line can be written as;

where m = slope of the line

b = y-intercept of the line

So if Joanne graphed a linear function with a slope(m) of -4 passing through (0, -2), let's go ahead and determine the y-intercept of the line as shown below;

Therefore, the equation of line will be y = -4x - 2 as graphed below;

Given Nick's function as y = -2x - 4, combining both graphs, we'll have the below;

The red line is Joanne's line while the blue line is Nick's line.

We can see from the above graph of both lines that Joanne's line intersects the y-axis above Nick's line's

Of the functions listed in the options the ones that are linear are:

a. y = -2x

b. -4y = 3x

d. 2x - 3y = 12

Linear equations are equations of the first order. These equations are defined for lines in the coordinate system.

The correct solution of the expressions are;

1. (14⁴)² × 14⁻⁶ / 14² = 1

2. 14⁻⁵ (14³)² 14⁻² = 1 / 14

3. (14³)⁴ (14⁻⁷)² = 1 / 196

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The expressions are,

1. (14⁴)² × 14⁻⁶ / 14²

2. 14⁻⁵ (14³)² 14⁻²

3. (14³)⁴ (14⁻⁷)²

Now,

The solutions of the expressions are find as;

1. (14⁴)² × 14⁻⁶ / 14² = 14⁸ × 14⁻⁶ / 14²

                            = 14⁸⁻⁶ / 14²

                            = 14² / 14²

                            = 14²⁻²

                            = 14⁰

                            = 1

And,

2. 14⁻⁵ × (14³)² × 14⁻² = 14⁻⁵ × 14⁶ × 14⁻²

                               = 14⁻⁵⁺⁶⁻²

                               = 14⁻¹

                               = 1 / 14

And,

3. (14³)⁴ (14⁻⁷)² = 14¹²  14⁻¹⁴

                     = 14¹²⁻¹⁴

                     = 14⁻²

                     = 1 / 14²

                     = 1 / 196

Therefore,

The correct solution of the expressions are;

1. (14⁴)² × 14⁻⁶ / 14² = 1

2. 14⁻⁵ (14³)² 14⁻² = 1 / 14

3. (14³)⁴ (14⁻⁷)² = 1 / 196

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By the Distributive Property, the expression is 7h - 70

From the question, the expression is given as

7(h − 10)

As a general rule, the Distributive Property of algebra states that

a(b - c) =a * b - a * c

Using the above as a guide, we have

a = 7, b = h and c = 10

Substitute a = 7, b = h and c = 10 in the equation a(b - c) =a * b - a * c

So, we have

7(h − 10) =7 * h - 7 * 10

Evaluate

7(h − 10) =7h - 70

Hence, the simplified expression is 7h - 70

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The range is the difference between the largest and the smallest and the range is 5.2

This is a graph that is divided into two vertical axes such that one axes represent the stem and the other axis represents the leaf

From the question, we have the following parameters:

Stems = 12, 13, 14, 15, 16, and 17

Each of these stem elements have their own leaves

So, the complete stem and leaf plot is as follows

12     |  3, 3, 6, 7, 9, 9.

13     |  1, 1, 4, 5, 5.

14     |  0, 0, 2, 3, 3, 8, 8, 9.

15     |  2, 2, 2, 2, 2, 3, 5, 5, 7.

16     | 4, 5, 5, 9, 9.

17      | 3 5.

Key

12 | 3 means 12.3.

To determine the range, we simply take the smallest number and the largest number represented by the plot and calculate the difference

In (a), we have

The range is calculated from the smallest number and the largest number represented by the plot

So, we have

Smallest = 12.3

Largest = 17.5

So, the range is

Range = 17.5 - 12.3

Evaluate

Range = 5.2

Hence, the range is 5.2

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Answer:

$134.50

Step-by-step explanation:

4200 x .035 = 134.50

3.5% Percent means per 100

3.5/100 when you divide by 100, you move the decimal two places to the left.

The commission amount is $147

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Mr. Webster sells vacation rentals and earns a 3.5% commission on every vacation rental he sells.

He sold $4200.

So, 3.5% of commission:

4200 x 3.5  / 100

= 147

Therefore, the commission is $147.

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The equation will be used for solving the retail price is y = 1.8x

Given,

The equation will be used for solving the retail price is y = 1.8x

A local shoe store buys shoes at a wholesale price.

and mark up 80%

The table is:

Quantity                                              Wholesale Price

0-20 pairs                                                  $25.00

21-40 pairs                                                 $23.00

41-60 pairs                                                 $21.00

61-80 pairs                                                 $19.00

81 or more pairs                                         $17.00

To find the retail price for each range.

Now, According to the question:

An equation will be used :

the equation for all of them would be :

y = new price

x = wholesale price

y = 1.8x

Quantity of :0 - 20 pairs.

= 25 x 1.80

= $45.00

Quantity of: 21 - 40 pairs

= 23 x 1.80

= $41.40

Quantity of: 41 - 60 pairs

= 21 x 1.80

= $37.80

Quantity of: 61 - 80 pairs

= 19 x 1.80

= $34.20

Quantity of: 81 or more pairs

= 17 x 1.80

= $30.60

Hence, The equation will be used for solving the retail price is y = 1.8x

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