The account balance of each of three children at the end of a month is shown below:

Kyle has −$2.25
Jason has −$2.00

Sue has as much savings in her account as the amount Kyle owes the bank.

Part A: On a blank paper, draw a number line from −4 to +4. Plot points on the number line to show the account balances of the three children. Label the points using the name of each child. Describe in detail how you created and labeled this number line, and what it looks like in detail. (5 points)

Part B: Determine whether Kyle or Jason owes the bank more. Use absolute values and inequalities to write statements that justify your conclusion. (5 points)

The rates aren't equivalent based on the information given regarding the games.

It should be noted that 16 points were scored in 4 games. Therefore, the points per game will be:

= 16 / 4

= 4 points.

Also, 48 points scored in 8 games. Therefore, the points per game will be:

= 48 / 8

= 6 points.

Therefore, the rates aren't equivalent.

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16 points scored in 4 games.

48 points scored in 8 games.

Are the rates equivalent?

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

Reason:

Let's go through the four answer choices to see which are true and which are false. We'll rule out the ones that are true.

The percentage is 42.8571%.

Percentage, a relative value indicating hundredth parts of any quantity. One percent  is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.

All of something is 100 percent, half of it is fifty percent, none of something is zero percent. To determine a percentage, you divide the portion of the whole by the whole itself and multiply by 100.

Given fraction:

3/7

To convert the fraction into percentage we have multiply 100

3/7*100

=300/7

= 42.8571%

Hence, the percentage of fraction 3/7 is 42.8571%.

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The appropriate journal entries for year 4 depreciation is:

Dr. depreciation                      $52,210

Cr. Accumulated depreciation                 $52,210

What is depreciation?

Depreciation is the gradual systematic allocation of the cost of asset over its useful years, the fact that the machine in this case would be used for 4 years means that its initial cost needs to be allocated over the 4 years.

Depreciation(straight-line method)=(cost-salvage value)/useful life

Depreciation(straight-line method)=( $214,200-$19,000)/4=$48,800 per year

Depreciation rate per unit=($214,200-$19,000)/488000

Depreciation rate per unit=$0.40

Depreciation in year 4=130,300*$0.40

Depreciation in year 4=$52,210

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Additional information provided by the student in the comment section:

How do I record the 4th year?

Answer:

$1.92

Step-by-step explanation:

The corresponding row to 6 ounces is this

The function is decreasing on the interval [-5 < x < -1] (segment 1),

The function is increasing  on the interval [-1 < x < 4] (segment 2),

The function is decreasing on the interval [4 < x < 9] (segment 3).

A graph can be defined as a pictorial representation or a diagram that represents data or values.

As per the given graph,

The function is decreasing from the interval from -5 to  -1 in its domain

The function is increasing  from the interval from -1 to  4 in its domain

The function is decreasing  from the interval from 4 to  9 in its domain

Therefore, the function is decreasing on the interval [-5 < x < -1] (segment 1), increasing  on the interval [-1 < x < 4] (segment 2), and decreasing on the interval [4 < x < 9] (segment 3).

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Answer:

D. d= -3.6

Step-by-step explanation:

12.6= -1.8 -4d

Add the negative 1.8 to the left side and then divide by -4

The expression to illustrate the information when Maria bought the tickets is C = (5 × $20) + ($2 × 5) and the total amount paid is $110.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. A mathematical expression shows the value of something by combining numbers, variables, and operators. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Mathematical operators like addition, subtraction, multiplication, and division are used to create expressions in writing. For instance, the mathematical equation for "4 added to 2" will be 2+4.

From the information, Maria bought 5 tickets for $20 each. Each ticket had a $2 fee.

The expression that can be used to illustrate this will be:

C = (5 × $20) + ($2 × 5)

where C = Total cost

C = $100 + $10

C = $110

Therefore the expression to illustrate the information when Maria bought the tickets is C = (5 × $20) + ($2 × 5) and the total amount paid is $110.

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Answer:

B and C

Step-by-step explanation:

B = 4y - 3 + 3 = -2y + 1 + 3

  = 4y = -2y + 4

C = 4y - 3 -4y = -2y + 1 -4y

   = 3 = -6y +1

The equation to represent the growth of the trees is given by

AA=32+6t and BB=20+9t and both the trees will be of equal height after 3 years.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

Equation is defined as the quality of being equal and is frequently represented by a mathematical statement with equal values on either side or by a problem requiring consideration of a number of factors.

Given that tree A is 32 inches tall and tree B is 20 inches tall.

Tree A grows 6 inches per year.

Length of the tree A after t years = 32 + 6t

Tree B grows 9 inches per year

Length of the tree B after t years = 20 + 9t

Now let us consider that both trees grows equal after a certain period of time.

If we equate both the expressions then we can form an equation to calculate the value of t.

∴ 32+6t = 20+9t

or, 6t - 9t = 20 - 32

or, -3t = -12

or,  t = 4 years

The trees will be of equal length after 4 years.

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x = 1/2 is the simplify answer of linear equation .

What in mathematics is a linear equation?

18/4 - 36x/4  = 0

18 - 36x / 4 = 0

18 - 36x = 0

18 = 36x

x = 18/36

x = 1/2

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The translation of the statement is 7x - 7 = 147 and the numerical value of x is 22.

Given the statement in the question?

"Seven subtracted from seven times a number is 147"

Translate the statement into an equation;

Let x represent the unknown number.

Now, combine

7x - 7 = 147

Therefore the translation of the statement is 7x - 7 = 147.

Next, we solve for x

7x - 7 = 147

Add 7 to both sides

7x - 7 + 7 = 147 + 7

7x = 154

x = 154/7

x = 22

Therefore, the translation of the statement is 7x - 7 = 147 and the numerical value of x is 22.

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An item is $55 before sale, and bought for 45 percent off the regular price. therefore the sale price of item is  $30.25.

Markup is the amount that will be increased in the original price of the considered thing.

Markdown is the amount that will be decreased from the original price of the considered thing.

Think of "up" and "down" as increasing and decreasing prices respectively.

Given that item is $55 before sale, and bought for 45 percent off the regular price.

WE have to do that as; 45% off $55 implies subtract 45% from $55

= 45/100 × 55 = $24.75

therefore the item bought at $55 - $24.75= $30.25.

Hence, the sale price of item is  $30.25.

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The complete question is

An item is regularly priced at $55. It is on sale for 45% off the regular price. What is the sale price?

Based on the number of freshwater fish per s-a-l-t-water fish, the ratio for s-a-l-t-water fish to freshwater fish is 5 : 7.

The ratio between the s-a-l-t-water fish and the freshwater fish putting both figures against each other as a ratio.

The ratio would be:

Number of s-a-l-t-water fish : Number of freshwater fish

Putting in the quantities gives:

5 s-a-l-t-water fish fish : 7 freshwater fish

5 : 7

In conclusion, the ratio is 5 : 7.

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Answer:

How about this: A bag of 8 oranges is $6.50 and you want to know the price per orange? Or how about this:  You have a soda vending machine and each soda is $2.00.  A case of soda (24 cans) costs you $15.00.  You need to know how much the case costs per can to see if you will make a profit.

Step-by-step explanation:

A unit rate is a type of ratio that compares one unit of some quantity to a different number of units of a quantity.

The value of x from the given figure is 8/3

The sum of all the ides of the parallelogram is perimeter. According to the given figure;

2(3x-8)+2(16) = 32.2

Expand to have:

6x-16 + 32 = 32.2

6x + 16 = 32.2

Subtract 16 from both sides

6x = 16

x = 16/6

x = 8/3

Hence the value of x from the given figure is 8/3

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Answer:

Step-by-step explanation:

The area of the composite shape that is given in the image below = 40 in.².

In the diagram given below, the shape can be decomposed into a triangle and a rectangle, since it is composed of both shapes.

Thus:

The area of the composite shape = area of rectangle + area of triangle.

Area of the triangle = 1/2(b)(h)

base = 12 - 7 = 5 in.

height = 5 - 3 = 2 in.

Area of the given triangle = 1/2(5)(2)

Area = 5 in.²

Area of the given rectangle = (l)(w)

length = 7 in.

width = 5 in.

Area of the given rectangle = (7)(5) = 35 in.²

The area of the composite shape given = 35 + 5 = 40 in.².

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Answer:

are u sure this is the question ⁉️

Answer:

x=10 or 4

Step-by-step explanation:

square root of x-7²=x-7

x=3+7 or -3+7=10 or4

Answer:

y = - [tex]\frac{\sqrt{111} }{20}[/tex]

Step-by-step explanation:

using Pythagoras' identity in the right triangle formed by the radius 1 and the given point, then

y² + (- [tex]\frac{17}{20}[/tex] )² = 1²

y² + [tex]\frac{289}{400}[/tex] = 1

y² = 1 - [tex]\frac{289}{400}[/tex] = [tex]\frac{111}{400}[/tex] ( take square root of both sides )

y = ± [tex]\sqrt{\frac{111}{400} }[/tex] = ± [tex]\frac{\sqrt{111} }{20}[/tex]

since the point is in the third quadrant then y < 0

y = - [tex]\frac{\sqrt{111} }{20}[/tex]

The journal entries to record the materials requisitions, labor costs, and applied overhead is: Debit Work in process inventory $16,300, Credit Manufacturing overhead $1,300, Credit Raw materials inventory.

1. Debit Work in process inventory   $16,300

($15,000+$1,300)

Credit Manufacturing overhead   $1,300

Credit Raw materials inventory    $15,000

(To record material acquisition)

2. Debit Work in process inventory   $17,550

($19,690-$2,140)

Debit Manufacturing overhead   $2,140

Credit Factory payroll     $19,690

(To record labor costs)

3. Debit Work in process inventory   $26,325

Credit Manufacturing overhead    $26,325

($17,550×150%)      

(To record applied overhead)

Therefore the journal entries to record the materials requisitions, labor costs, and applied overhead is: Debit Work in process inventory $16,300, Credit Manufacturing overhead $1,300, Credit Raw materials inventory.

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The value of n which is a constant representing number of innings is equal to 50.

What is ERA or earned run average ?

Earned runs without the help of passed ball, are represented by the earned run average, which is the number of earned runs a pitcher allows per nine innings.

It is given that In 2020, the pitcher had an ERA of 2.70.

A rate of earned runs to a fixed number of innings, n, which is also known as ERA.

Let's check it.

To determine a pitcher's earned run average or (ERA), multiply the runs by nine, then divide it by the number of innings pitched.

The runs earned in 2020 is 15 , let's multiply it by 9.

So , we get 15 × 9 = 135.

Now , divide it by number of innings which is 50.

So , the value of ERA will be equal to : 135 ÷ 50 = 27 which is also given in the question.

Now we will calculate the value of n.

So ,

n = (9 × Earned runs) / ERA

or

n = ( 9 × 15 ) / 2.7

n = 135 / 2.7

n = 50 innings

Therefore , value of n which is a constant representing number of innings is 50.

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The weight of apple that Sandy has left after one week is 2.1 pounds.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the number of apple remaining after x days. Sandy collected 10 pounds of apples at an apple orchard and eat 20% daily, hence:

y = 10(1 - 0.2)ˣ

y = 10(0.8)ˣ

After 1 week, x = 7:

y = 10(0.8)⁷ = 2.1 pounds

The weight of apple that Sandy has left after one week is 2.1 pounds.

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The probability that a person chosen at random uses both internet connections is 1/9

Total number of people = 27

Number of people who use ADSL lines = 16

Number of people who use wireless internet = 15

Number of people who use neither of the two = 3

Let the number of people who use only ADSL lines and wireless internet be denoted by A and B respectively.

Then A + B + A∩B + 3 must be equal to 27

A + B + A∩B = 24

further, we can see that

(A + A∩B) = 16  

B + 16 = 24

B = 8

Also, (B + A∩B) = 15

8+ A∩B = 15

A∩B = 7

Thus, the number of people who use both internet connections = 7

Now, P(A∩B) = 7/27

= 1/9

Hence, probability that a person chosen at random uses both internet connections is 1/9.

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Answer:

The circumference of a circle with diameter 9.36 is 29.41

Step-by-step explanation:

the circumference of a circle is

2×pi×r

with r being the radius and therefore, 2×r being the diameter.

2×pi×r = 9.36 cm

2r = diameter = 9.36/pi = 2.979380535... ≈ 2.98 cm

The term that explains the relationship between angles C and D is: A. Adjacent angles.

When two angles share a common vertex and a common side, the two angles are referred to as adjacent angles.

In the diagram given, lines JK and JM intersect at point J to form 4 angles of which angles C and D share a common side and a common vertex (point J).

Therefore, the term that explains the relationship between angles C and D is: A. Adjacent angles.

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Answer:

A

i took the test and got it right

Answer:

235.4

Step-by-step explanation:

7% more than 220 would be 235.4

First you would turn 7% as a decimal which would be .07. Then, you would multiply .07 times 220 which would give you 15.4. Lastly, you would add 15.4 plus 220 which would equal 235.4.

7%=.07

.07×220=15.4

15.4+220=235.4

The total volume of the ocean in litres is [tex]1.332\times10^{21}[/tex] litres.

Given that, the depth of an ocean =[tex]3.7\times 10^{3}[/tex] m and the area of the ocean = [tex]3.6\times10^{14}[/tex] m².

We need to find the total volume of the ocean in litres.

Volume is defined as a capacity occupied by a three-dimensional solid shape. Any shape is hard to visualize but can be compared between shapes. The volume of any object is the product of the area of a base and the height of the object.

Now, the volume of the ocean=[tex]3.6\times10^{14}[/tex]×[tex]3.7\times 10^{3}[/tex]

=[tex]13.32\times10^{17}[/tex] m³

=[tex]13.32\times10^{17}\times1000[/tex]

=[tex]1.332\times10^{21}[/tex] litres

Therefore, the total volume of the ocean in litres is [tex]1.332\times10^{21}[/tex] litres.

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Let

[tex]S = \displaystyle \sum_{1\le j<k\le673} z_jz_k[/tex]

and

[tex]p_{\mu,\nu}(x) = (x-z_1)^\mu (x-z_2)^\mu \cdots (x-z_\nu)^\mu[/tex]

The [tex]z_jz_k[/tex] terms occur in the coefficient of the [tex]x^{\mu\nu-2}[/tex] term, given by

[tex]\displaystyle \left[x^{\mu\nu-2}\right] p_{\mu,\nu} = \binom\mu2 \sum_{r=j}^\nu z_j^2 + \mu^2 \sum_{1 \le j < k \le \nu} z_jz_k[/tex]

(essentially due to Vieta's formulas)

With [tex]\mu=3[/tex] and [tex]\nu=673[/tex], we have

[tex]\displaystyle \left[x^{2017}\right] p_{3,673} = \binom32 \sum_{j=1}^{673} z_j^2 + 3^2 S \\\\ ~~~~ \implies S = \frac{19}9 - \frac13 \sum_{j=1}^{673} z_j^2 \\\\ ~~~~ \implies S = \frac{19}9 - \frac13 \left(\left(\sum_{j=1}^{673} z_j\right)^2 - 2 S\right) \\\\ ~~~~ \implies S = \frac{19}3 - \left(\sum_{j=1}^{673} z_j\right)^2[/tex]

The remaining sum on the right is the sum of the roots of [tex]\sqrt[3]{p_{3,673}(x)} = p_{1,673}(x)[/tex].

Recall that the sum of the roots of a polynomial

[tex]P_n(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_0[/tex]

is [tex]-\frac{a_{n-1}}{a_n}[/tex]. Then the sum of the roots of [tex]p_{3,673}(x)[/tex] is -20, which is 3 times the sum of the roots (counting multiplicity) of [tex]p_{1,673}[/tex], so

[tex]\displaystyle \sum_{j=1}^{673} z_j = -\dfrac{20}3 \\\\ ~~~~ \implies S = \frac{19}3 - \left(-\frac{20}3\right)^2 = -\frac{343}9 \\\\ ~~~~ \implies |S| = \frac{343}9, m=343, n=9 \implies m+n = \boxed{352}[/tex]

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