Box A has a length of 5 feet, height of 1 foot, and width of 3 feet. Box B has a length of 4 feet, height of 3 feet, and width of 2 feet. Box C has a length of 7 feet, height of 2 feet, and width of 1 foot. Box D has a length of 3 feet, height of 3 feet, and width of 3 feet.
Lucas wants to use the box with the greatest volume. Which shipping box should he use?

Box

⇒ Supplementary angles are angles that add up to 180°

⇒ ∠1+∠2=180°(angles on a straight line)

∠2=∠4( Corresponding angles are equal m||n)

⇒*NOTE THE FOLLOWING STATEMENT IS TO MAKE YOU UNDERSTAND,IT MUST NOT BE INCLUDED IN YOUR ANSWERBOOK)

If ∠2=∠4

in the place of ∠2 in the equation ∠1+∠2=180° we can substitute ∠4 since the two angles (∠2 and ∠4) are equal by corresponding angles

______________________________________________________

⇒You may include this step now as you now know how ∠4 came up.

∴∠1+(∠4)=180°

∠1+∠4=180°

Now from the above equation we can see that ∠1 and ∠4 are supplementary angles as they both add up to 180°

Answer:

Step-by-step explanation:

the answer is 4

An equation that shows how the total number of diplomas signed depends on the number of seconds the principal spends signing them is y = 37 + 0.5x.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, let x be number of seconds the principal spends signing them. The principal already signed 37 diplomas. Th equation to illustrate this is 37 + 0.5x.

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The length of the other two sides of the rectangular garden is 6 meters and the perimeter of the garden is 18 meters.

According to the question,

We have the following information:

Two sides of a rectangular garden are 3 meters long. The area of the garden is 18 square meters.

We know that the following formula is used to find the area of rectangle:

Length*width = 18

Length*3 = 18

Length = 18/3

Length of the rectangular garden = 6 meters

Now, perimeter of the rectangular garden:

2(length+width)

2(6+3)

2*9

18 meters

Hence, the length of the other two sides of the rectangular garden is 6 meters and the perimeter of the garden is 18 meters.

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Answer:cap

Step-by-step explanation:C A P

Answer:

C. -16

Step-by-step explanation:

Hope this helps you! :))

16

Step-by-step explanation:

the answer is c

just took a test and I got it right

The exponential function that approximates the number of fruit flies on the banana after x days is y = 7 x 1.3ˣ.

An exponential function is a mathematical function form of y = aⁿ or y = abˣ, where b is a constant or the base of the function, a is a variable, and n is the variable exponent.

Exponential functions must always contain an exponent, which is an integer raised to some power.

When the exponent is positive, it implies the function is increasing in value and vice versa.

Percentage increase per day = 30%

The number of fruit flies found = 7

The number of days = x days

Let the number of flies after x days = y

y = 7 x 1.3ˣ

Thus, an exponential representation of the function which Emma can use to model the number of fruit flies after x days is y = 7 x 1.3ˣ.

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The percent of Americans that had central heterochromia is A. 0061%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this case, it's estimated that only around 200,000 Americans have central heterochromia and the population of the United States

was 327,750,000 people.

The percent of Americans that had central heterochromia will be:

= Those with the disease / Total population × 100

= 200,000 / 327,750,000 × 100

= 0.0061%

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The solution to the system graphed is (2, 0).

The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.

In a line graph, the information or data is plotted as a series of markers, or dots, and is then connected to one another by a straight line.

Usually, data that changes over time is represented by a line graph.

Given:

From the graph we have two line red and purple.

The intersecting point for both line is (2, 0).

Hence, the solution to the system graphed is (2, 0).

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The factor pairs of 30 are (1, 30), (2, 15), (3, 10), (5, 6), (6, 5), (10, 3), (15, 2) and (30, 1)

The number is 30

The factors pair of a number is the numbers that when we multiply them together we will get the number

Here the  number is 30

The factors of 30 are

1, 2, 3, 5, 6, 10, 15, 30

The factor pairs of 30 are

1 × 30 = 30

2 × 15 = 30

3 × 10 = 30

5 × 6 = 30

6 × 5 = 30

10 × 3 = 30

15 × 2 = 30

30 × 1 = 30

Hence, the factor pairs of 30 are (1, 30), (2, 15), (3, 10), (5, 6), (6, 5), (10, 3), (15, 2) and (30, 1)

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There can be 2184 ways in which three posts can be selected using permutation.

What is permutation?

An arrangement of things in a specific order is referred to as a permutation. In this arrangement, the components or components of sets are arranged in a linear or sequential order.

Main Body:

Total members =14

total posts =3

As one person can not hold more than 1 post ,

total ways are = ¹⁴P₃

Therefore total ways = 14!/11!  

                                   = (14*13*12*11!)/11!

                                   = 14*13*12

                                   = 2184 ways

Hence answer is 2184 ways to select 3 members out of 14.

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Answer:

The numbers in which 7 appears are. 7, 17, 27, 37, 47, 57, 67, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 87, 97, 107. So, counting all. ∴ Number of times 7 appears = 21

Answer:

equal to

Step-by-step explanation:

4 + 1/2= 4+ 0.5= 4.5

4.5=4.5

12 and 30 are the two numbers are greater than 6 with HCF  6 and LCM  60.

What is Highest common factor and Least Common Multiple?

Least Common Multiple is the entire name of LCM in mathematics, whereas Highest Common Factor is the full name of HCF. When two or more numbers are given, the HCF identifies the largest factor present, while the LCM defines the least number that is exactly divisible by two or more numbers.

Assume that the two numbers with HCF of 6 are 6a and 6b, where a and b are co-prime and a, b > 1.

HCF x LCM = Product of the numbers.

6 x 60 = 6a x 6b

10 = a x b

10 can be written as, 1 x 10 and 2 x 5.

But a and b > 1.

So, 10 = 2 x 5

a = 2, b = 5

Therefore, the two numbers are,

6a = 6(2) = 12 and

6b = 6(5) = 30

Hence, the two numbers with HCF  6 and LCM  60 are 12 and 30.

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The equation that shows a proportional relationship between x and y is y=6x

The options represent the given parameters

As a general rule

A proportional relationship is represented as y = kx

Where k represents the constant of proportionality

So, we check the options for equations that has the same form as y = kx

We have

y = 6x

The above equation is a linear equation

In fact, it is a linear equation that shows a proportional relationship

Note that all linear equations have a constant rate of change

So, the proportional relationship is given as

y = 6x

Where the constant of proportion is 6

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Answer:

-5/7, 10/7

Step-by-step explanation:

The slope of an equation in standard form is -a/b

so -5/7

Set x to 0 to find the vertical intercept

5(0)+7y=10

7y=10

y=10/7

The running total is  $95.27.

There are two types of records, Active and Inactive. There are also two major classifications, Vital and Important.

He opened the account with $299.88. He subsequently wrote many cheques, from which you deduct the sum of 299,88.

He deposited a check, thus 299.88-90.48= 209.40, 209.40 - 65.00= 144.40, and then he added $381.33 to 144.40 to get 525.73.

then you need to deduct more since he wrote more checks.

Consequently, 525.73-54.47=471.26, and 471.26-375.99=95.27, giving him a balance of $95.27.

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The current total is $95.27. Active and Inactive records are the two types of records. There are two major classifications as well: Vital and Important.

Good records are required to create reliable financial statements. Balance sheets and income (profit and loss) statements are included. These statements may help you manage your company and deal with your bank or creditors.

Good Records are documents that contain recorded data that demonstrate the effectiveness of the quality management system, regardless of format or feature.

Given,

He deposited into the account = $299.88

He then wrote a number of cheques, from which you deduct = $299,88.

He deposited a check, thus 299.88 - 90.48

= 209.40, 209.40 - 65.00

= 144.40

and then he added $381.33 to 144.40 to get 525.73.

then you need to deduct more since he wrote more checks.

Consequently,

525.73 - 54.47

=471.26  

and 471.26-375.99

= 95.27

As a result, The gives him a balance of $95.27.

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The measures of the remaining three angles of the decagon are 40, 50 and 130 degrees.

A decagon simony means a polygon with 10 sides. In a regular decagon, the interior angles add up to 1440 degrees, and the exterior angles add up to 360 degrees.

Complementary angles sum up to 90 degrees while supplementary angles sum up to 180 degrees.

Therefore,

1440 - 1220 = 220

Let the angles be a, b and c.

Therefore,

a + b + c  =220

a + b = 90

b + c = 180

Hence,

a = 220 - 180

a = 40°

b = 90 - 40

b = 50°

c = 180 - 50

c = 130°

The angles are 40°, 50° and 130°.

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The situation can be represented using the equation 3g + 7 = 40

From the question, we have the following parameters that can be used in our computation:

Length of three sides = g

Length of the fourth side = 7

Perimeter = 40

The perimeter of a quadrilateral is the sum of the sides of the shape

This means that

P = sum of the 4 sides

So, we have

P = g + g + g + 7

Evaluate

P = 3g + 7

Rewrite as

3g + 7 = 40

Hence. the equation that represents the situation is 3g + 7 = 40

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Answer:

x=3

Step-by-step explanation:

Answer: x=3

Step-by-step explanation:

First, you need to subtract x and x by itself, and do the same with the 3x. Your equation should now look like 6 = 2x. Now, divide each side of the equation with 2, and now your equation should look like 3 = x!

-----------------------

So, to double check, replace the x's with 3. The equation should be 3 + 6 = 3(3). If you do the math, it equals 9 = 9!

Answer:

  see attached (red)

Step-by-step explanation:

You want the graph of the transformed triangle defined by the lines y=x, x=6, y=-1/3x+4 after rotation 270° and reflection across the y-axis.

A graph of the lines shows the vertices of the triangle are ...

  A(3, 3), B(6, 6), C(6,2)

Rotation 270° is described by the transformation ...

  (x, y) ⇒ (y, -x)

Reflection across the y-axis is described by ...

  (x, y) ⇒ (-x, y)

Then the composition of these transformations is ...

  (x, y) ⇒ (-y, -x) . . . . . . . . equivalent to reflection over y=-x

Applying this composition to the triangle vertices, we find its final location to be ...

  A(3, 3) ⇒ A''(-3, -3)

  B(6, 6) ⇒ B''(-6, -6)

  C(6,2) ⇒ C''(-2, -6)

The triangle with these vertices is shown in red in the attachment.

The x-intercept of the table of values is 12 or (12, 0).

To find the x-intercept of a table that represents a linear relationship between x and y, first write the equation that models the table.

To write the equation, first find the slope (m) using two pairs of values, say, (22, 36) and (27, 54)

Slope (m) = (54 - 36)/(27 - 22)

Slope (m) = 18/5

Write the equation that represents the table of values by substituting (a, b) = (22, 36) and m = 18/5 into y - b = m(x - a):

y - 36 = 18/5(x - 22)

To find the x-intercept, substitute y = 0 into the equation, y - 36 = 18/5(x - 22) to find the value of x:

0 - 36 = 18/5(x - 22)

-36 = 18/5(x - 22)

5(-36) = 18(x - 22)

-180 = 18(x - 22)

-180/18 = x - 22

-10 = x - 22

-10 + 22 = x

12 = x

x = 12

The x-intercept is 12 or (12, 0).

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The total number of students going on a trip is 375 students.

Given that,

The entire third through fifth graders are taking a field trip to Coney Island. There are 125 pupils each grade. The cafeteria should provide lunches.

We have to find how many students will be travelling on the trip.

So,

In Grade 3 we have 125 students.

In Grade 4 we have 125 students.

In Grade 5 we have 125 students.

So,

Total number of students going on trip = Number of students in Grade 3 + Number of students in Grade 4 + Number of students in Grade 5

= 125 + 125 + 125 = 375.

Therefore, The total number of students going on a trip is 375 students.

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Answer:

Answer is b

Step-by-step explanation:

Because

Answer:

The slope of this line is undefined.

38 sets

474 - 246 = 228

228 ÷ 6 = 38

Step-by-step explanation:

to eliminate the always positive absolute value at the end let's set y = -3x

that makes the absolute value term = 0 in all cases.

then we have

sqrt((x - 8)² + (-3x + 4)²)

the x-value that makes this a minimum result also makes

(x - 8)² + (-3x + 4)²

a minimum.

x² - 16x + 64 + 9x² - 24x + 16

10x² - 40x + 80

the x that makes this a minimum, also makes

x² - 4x + 8

a minimum.

we get the extreme value as zero of the first derivative :

0 = 2x - 4

4 = 2x

x = 2

so, we get the minimum of all these expressions for x = 2.

as y = -3x, we get y = -3×2 = -6.

the minimum value for the expression is with

x = 2

y = -6

so, the minimum value is

sqrt((2 - 8)² + (-6 + 4)²) + |-6 + 3×2| =

= sqrt((-6)² + (-2)²) + |-6 + 6| =

= sqrt(36 + 4) + 0 =

= sqrt(40) = 6.32455532...

The value of v from the given equation v=u+at is 42

An equation is a mathematical expression that contains an equals symbol

From the given equation v=u+at

u=18

a=6

t=4

Substituting for u,a and t in the equation

v=18+6(4)

expanding the bracket

v=18+24

v=42

Hence, the the v in the equation v=u+at is 42

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The number of parks per capita when there is the total population of 870,000 people and there are 212 parks is 4,103.77358.

“Per capita” is a Latin term that means “per head.” This term is used to express the average per person, the term “per capita” is occasionally used in statistics instead of “per person.”

On a given case, the per capita parks for population can be calculated by dividing total population by total parks.

According to the given illustration,

Total population of city = 870,000

Total Parks= 212

Calculation of parks per capita in the city of Indianapolis:

Per capita shops = Total population/ Total shops

Per capita shops =870,000/212

Per capita shops = 4,103.77358

Therefore, the number of parks per capita is 4,103.77358.

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