Type the correct answer in each box. Use numerals instead of words. The domain of this function is {-12, -6, 3, 15}. Complete the table based on the given domain. x y -6 5 15 15

The volume of a cuboid implies the product of its length, width, and height. So that the fraction of the original cuboid that would remain is [tex]\frac{7}{15}[/tex].

A cuboid is a solid derived from a rectangle, thus it has rectangular faces. Its volume can be determined by;

volume of a cuboid = length x width x height

In the given question, the volume of the original cuboid can be determined as;

  volume = 3 x 4 x 5

                = 60 Cubic units

Since holes can not be drilled at the intersection of the holes, then the volume of the hole has to be determined.

To determine the volume of the hole drilled, we have:

(6 x 3) + (3 x 2) + (2 x 2) = 28 Cubic units

So that the fraction of the original cuboid that would remain = [tex]\frac{28 cubic units}{60 cubic units}[/tex]

                                                                   = [tex]\frac{7}{15}[/tex]

Therefore,  [tex]\frac{7}{15}[/tex] of the original cuboid would remain.

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360

Step-by-step explanation:

The quadratic equation is y = 1/2x^2 - 3x + 4

A quadratic equation is represented as:

y = ax^2 +bx + c

Using the values on the table, we have:

a(0)^2 + b(0) + c = 4 ---- when x = 0

a(2)^2 + b(2) + c = 0 ---- when x = 2

a(4)^2 + b(4) + c = 0 ---- when x = 4

Evaluate these equations

c = 4

4a + 2b + c = 0

16a + 4b + c = 0

Substitute c = 4

4a + 2b + 4 = 0

16a + 4b + 4 = 0

Divide through by 2 and 4

2a + b + 2 = 0

4a + b + 1 = 0

Subtract both equations

2a -1 = 0

Solve for a

a= 1/2

Substitute a= 1/2 in 4a + b + 1 = 0

4 * 1/2 + b + 1 = 0

Evaluate

2 + b + 1 = 0

Solve for b

b = -3

So, we have:

y = ax^2 +bx + c

This gives

y = 1/2x^2 - 3x + 4

Hence, the quadratic equation is y = 1/2x^2 - 3x + 4

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The maximum data rate of that modem is doubled if the number of points in its constellation were doubled

According to statement

Modem has a data rate is 14,400 bps

we know that the data rate can be calculated by T=A/S

If a is Doubled then the data rate is also doubled.

Because A is directly proportional to the T and S is inversely proportional to T.

So, The maximum data rate of that modem is doubled if the number of points in its constellation were doubled

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The value of (-12) . 8 is -96 and the value of 14.(-5).(-11) is 770

The question implies that we calculate the expressions in two different ways.

1) (-12).8

Way 1:

We have:

(-12).8

This means

(-12) . 8 = -12 * 8

Evaluate

(-12) . 8 = -96

Way 2

We have:

(-12).8

This means

(-12) . 8 = -12 * 8

Express 8 as 4 + 4

(-12) . 8 = -12 * (4 + 4)

Expand

(-12) . 8 = -12 * 4 -12 * 4

Evaluate the products

(-12) . 8 = -48 - 48

Evaluate the sum

(-12) . 8 = -96

Hence, the value of (-12) . 8 is -96

2) 14.(-5).(-11)

Way 1:

We have:

14.(-5).(-11)

This means

14.(-5).(-11) = 14 * -5 * -11

Evaluate

14.(-5).(-11) = 770

Way 2

We have:

14.(-5).(-11)

This means

14.(-5).(-11) = 14 * -5 * -11

Multiply -5 and -11

14.(-5).(-11) = 14 * 55

Multiply 14 and 55

14.(-5).(-11) = 770

Hence, the value of 14.(-5).(-11) is 770

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Answer: A

Step-by-step explanation:

Let's first review how turning about the origin changes a point's coordinates:

After rotating and translating some points, one can see the following pattern:

Using these patterns will make it much easier to find the correct series of transformations than graphing each one.

A: A 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left

Using the patterns found above, this set of transformations would make (x,y) move first to (-y, x), then (-y-1, x).

B: A translation 1 unit to the left followed by a 90-degree counterclockwise rotation about the origin

This would make (x,y) move first to (x-1,y), then to (-y, x-1)

C: A 270-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left

This would make (x,y) move first to (y, -x), then (y-1, -x)

D: A translation 1 unit to the left followed by a 270-degree counterclockwise rotation about the origin

This would make (x,y) move first to (x-1,y), then (y, -x+1)

Therefore, the answer is A, as only it correctly matches to polygon A'B'D'C'.

The dimensions are 16  ft by 32 ft

The quadratic equation is w^2-256=0

We have given that,

Todd and his brother Robert are going to use 512 square feet of their backyard for skateboard ramps. the shape of the backyard is rectangular, with the length twice as long as the width.

The area of a rectangle is equal to

A=WL

Where L is the long side of the rectangle

W is the width side of the rectangle

in this problem we have

A=512ft^2

S0,512=LW -----> equation A

L=2W ------> equation B

substitute equation B in equation A

512=2W(W)

512=2w^2

2w^2-512=0

W^2=512/2

W=\sqrt(256)

W=16

Find the value of L

L=2W

L=2(16)

L=32ft

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Answer:

C)512 = 2w2

Step-by-step explanation:

trust

Answer:

$15

Step-by-step explanation:

Range is the difference of the highest and lowest data.

Based on the given $20 is the highest and $5 is the lowest.

$20 - $5 = $15

Answer:

15

Step-by-step explanation:

you can think of this table as a data set--and you could even write it out

5, 5, 5, 10, ......... 20, 20 {I did not write it out in full of course}

so, when thinking about the range, we can think of it as a range of our data set.

We find the range of a data set by finding the difference between the highest and lowest values

So, we know that our highest data value (amount) is 20, and the lowest is 5:

20 - 5 = 15

meaning that there is a range of $15 in this data set of allowance amounts

hope this helps!! have a lovely day! :)

Answer:

If you ever see a big word like greatest,biggest,largest,etc,that stands for Greatest Common Divisor(GCD) and therefore,you have to find prime numbers that can divide the two numbers each equally.

the greatest number of trees Abe can have in each row would be 9

3| 54|27

3 | 18| 9

3|. 6|3

you take the prime factors and multiply which would give you 9

Answer:

  6 +7x

Step-by-step explanation:

To write an English expression as an algebraic one, you must first understand what the English is telling you. Then the translation is straightforward.

A plus sign (+) signifies addition. Multiplication is signified several different ways. The simplest is writing the factors next to each other.

The objects involved in the addition are 6 and a product:

  6 + product

The product is said to consist of two factors: 7 and "a number". The instructions say to use "x" for "a number", so the product can be written ...

  7x

Then the complete algebraic expression is ...

  6 +7x

Answer:

45

Step-by-step explanation:

the number of ones expected is

probability × number of rolls

= 0.3 × 150

= 45

Using proportions, the coordinates of point R are given as follows: R(1.2, 0.4).

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Segments pr and pq are partitioned in the ratio 3:2, hence:

[tex]PR = \frac{3}{5}PQ[/tex]

[tex]R - P = \frac{3}{5}(Q - P)[/tex]

The points are:

For the x-coordinate, we have that:

[tex]R - P = \frac{3}{5}(Q - P)[/tex]

[tex]x - 6 = \frac{3}{5}(-2 - 6)[/tex]

x - 6 = -4.8

x = 1.2.

For the y-coordinate, we have that:

[tex]R - P = \frac{3}{5}(Q - P)[/tex]

[tex]y + 5 = \frac{3}{5}(4 + 5)[/tex]

y + 5 = 5.4.

y = 0.4.

The coordinates are: R(1.2, 0.4).

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Answer: the attachment i put with this file

Step-by-step explanation:

to graph this linear function, you can use the mantra "rise and run" to plot the points on the graph, and draw a line through the points.

The smallest possible length of the hypotenuse is 118

The given parameters are:

The non-degenerate implies that the right triangle has a positive area.

Since at least one length is 84, then both lengths can also be 84.

The hypotenuse is then calculated using the following Pythagoras theorem.

h^2 = 84^2 + 84^2

Evaluate the sum

h^2 = 14112

Take the square root of both sides

h = 118.8

Round down

h = 118

Hence, the smallest possible length of the hypotenuse is 118

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Answer:

a: -13º

b: 83º

Step-by-step explanation:

- a: [tex]-27 + 14 = -13[/tex]º

- b: [tex]68 + 15 = 83[/tex]º

- the equation would originally be written as 68 - -15 but 2 negatives make a positive so -- becomes +

hope this helps :)

Answer:

77

Step-by-step explanation:

Based on the question, we can deduce the arrangement of the plants is in a form of a square. (Number of rows = Number of Columns).

In that case, the answer is very straightforward, just square root the number of plants to be planted:

[tex]\sqrt{5,929} \\= 77[/tex]

This means there would be 77 rows of 77 plants per row.

The perimeter of the top of the basket is 20 in.

Perimeter of square is defined as addition the lengths of the  square's four sides.

Diagonal = 6

Let,  side of square = a

a²+a² = 6²

2a² = 36

a² = 18

a = 3√2

Perimeter of the square = 4 × side of square

Perimeter of the square = 4 × 3√2

Perimeter of the square = 12√2 ≈ 20 in

Hence, the perimeter of the top of the basket is 20 in.

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Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

Hello!

We can find the graph by finding the roots of the equation.

Since the equation is already in factored form, we can use the Zero Product Property to find the roots. The roots of an equation are the value(s) of x when y is 0 (x-axis).

The roots of the equation are 2 and 3. That means the graph intersects the x-axis at points 2 and 3. Looking at the graphs shown, the answer is Option A.

Answer:

3474

Step-by-step explanation:

To determine the difference in the amount sold, take the amount sold today and subtract the amount sold yesterday

46453-42979

3474

Answer:

307 paces

Step-by-step explanation:

First, lets convert Robert's pace to metres. (cm > m)

75cm = (75/100)m

= 0.75m

Number of Full Paces = Length of Bridge / 1 Full Pace

=

[tex] \frac{230m}{0.75m} \\ = 306 \frac{2}{3} paces[/tex]

See , we must have full paces, and in this case we are finding the minimum number of paces, so we will be looking at the lowest possible whole number, which in this case, is 307 paces.

Answer:

6/5 or 1.2, they're the same value

Step-by-step explanation:

When it says "rate of change", it's really just asking for the slope. If you don't know what the slope is, essentially how much the y-value increases by whenever x increases by 1. This can be formally defined using the equation: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] which is essentially [tex]\frac{rise}{run}[/tex]. The subtraction is finding the difference between the two numbers to see how much it's changed by. Btw the order doesn't matter, I could plug in (-3, -2) as (x2, y2) or I could plug it in as (x1, y1) as long as I make sure to input it in correctly. In this example I'll just say (-3, -2) = (x1, y1) and (2, 4) = (x2, y2). Plugging these values into the equation gives you: [tex]\frac{4- (-2)}{2- (-3)} = \frac{6}{5}[/tex] that's the rate of change

Answer:

Step-by-step explanation:

The equation that best represents the set-up is (d) 9^2 + x^2 = 16^2

The complete question is in the image

The value of x is calculated using the following Pythagoras theorem

16^2 = x^2 + 9^2

Rewrite as:

9^2 + x^2 = 16^2

Hence, the equation that best represents the set-up is (d) 9^2 + x^2 = 16^2

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For the given sentences, the algebraic expressions are:

a) N = 110*c - 300

b) N = 12*b

For the first statement:

A 3-digit number, where the tens digit is c, can be written as:

N = 100*a + 10*c + b

Then the hundreds digit is a, and here we know that is 3 less than the tens digit, then:

a = c - 3

The ones digit is b, here we know that it is 0, then b = 0.

Replacing that in our number we get:

N = 100*(c - 3) + 10*c = 110*c - 300

N = 110*c - 300

That is the algebraic expression.

b) A two-digit number can be written as:

N = b*10 + a

Where b is the tens digit and a is the ones digit.

Here we know that the units digit is twice as bit as the tens digit, then:

a = 2b

Replacing that we get:

N = b*10 + a = b*10 + 2b = 12*b

N = 12*b

That is the algebraic expression.

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The correct statement is the distribution is unimodal.

A Stem plot is a table where each data value is split into a stem which is the first digit or digits and a leaf which is the last digit.

Mode refers to a value that appears most frequently in a data set. A unimodal data set is a distribution with one clear most frequent values. There are only one set of modes in the data. They are 76.

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