2. Write an expression using fractions to show how to determine the amount that each person will pay. Then calculate each person's contributions showing all steps in long division.

The equivalent expression of the given expression is 5n/4 -3/8

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

Here, the given expression is :

(-2 ¹/₂n + ¹/₄) + (3 ³/₄n - 5/8)

simplifying the above expression by taking like considering like terms :

= -2 ¹/₂n + 3 ³/₄n +  ¹/₄- 5/8

= (15/4)n - (5/2)n + (2-5)/8

= (15-10)n/4 -3/8

= 5n/4 -3/8

Therefore, the equivalent expression of the given expression is 5n/4 -3/8.

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Answer: bacteria 100 in a petri dish

Step-by-step explanation: every 30 min the bacteria doubles

Graph of g is a translation where g(x) = (x+2)^2 - 2x – 1

f(x) = x^2 - 2x

g(x) = f(x+2) + 3

Translation is a movement of the graph either horizontally parallel to the x-axis or vertically parallel to the y-axis. A translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction. A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. In a Euclidean space, any translation is an isometry.

Hence , g(x) = (x+2)^2 -2(x+2) + 3 = (x+2)^2 - 2x - 1. When we graph the equations, we can confirm that our answer is correct.

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Answer:

[tex]r > 2[/tex]

Step-by-step explanation:

1) Rearrange the terms

-6 > 10 - 8r

2) Calculate

8r > 10 + 6

3) Divide both sides

8r > 16

4) Simplify (Cross out the common factor)

[tex]r >[/tex] [tex]\frac{16}{8}[/tex]  

5) r > 2

[tex]p(a \: \cup \: b) = p(a) + p(b) - p(a \: \cap \: b) \\ p(a \: \cup \: b) = 0.2 + 0.4 - p(a \: \cap \: b) \\ p(a \: \cup \: b) = 0.6 - p(a \: \cap \: b) \\[/tex]

[tex]but \: \: p(a \: \cap \: b) = p(a /b) \times p(b) \\ p(a \: \cap \: b) = 0.25 \times 0.4 = 0.1[/tex]

[tex]p(a \: \cup \: b) = 0.6 - p(a \: \cap \: b) \\ p(a \: \cup \: b) = 0.6 - 0.1 \\p(a \: \cup \: b) = 0.5[/tex]

The expression that represents the statement is a - 15

The mathematical statement is given as:

The​ age, a, decreased by 15 years

The variable in the above mathematical statement is

Variable a

This means that the decrease the variable in the above mathematical statement by 15

When the variable in the above mathematical statement is decreased by 15 years, we have the following expression

a - 15

This means that the representation of the the variable in the above mathematical statement is a - 15

Hence, the expression that represents the statement is a - 15

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Answer:

because he is human and human like to dance and eat

Answer:

2.75

Step-by-step explanation:

A in a 4-unit class will be 4 x 4 = 16 points

B in a 3-unit class will be 3 x 3 = 9

C in a 3-unit class will be 2 x 3 = 6

D  in a 2-unit class will be 1 x 2 = 2

Total points = 16 + 9 + 6 + 2 = 33

Total credit hours = 4 + 3 + 3 + 2 = 12

GPA = 33/12 = 2.75

For every 21 liters of petrol a car can run for 80 km- 58.2 liters of petrol would be required to ensure the car has enough petrol of a trip that is 224 km unitary method

It is provided that to run 80km car requires 21 liters of petrol

To know how much petrol is required for a trip of 224 km, we first would require to know how much petrol is required to run 1 km

This is called unitary method

Petrol required by car to run 1 km would be petrol required by car to cover 80kms of distance divided by 80 km of distance = 21 liters of petrol/ 80 km distance

                                                      = 21/80

                                                      =0.26 liters

So, petrol required by car for a trip of 224 km= 0.26 liters  ×224km

                                                                          = 0.26× 224

                                                                           =  58.24 liters

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Based on the amount the winner receives, the interest rate to be compounded annually, and the number of years, the amount that should be invested to award the price is $35,720.80.

The amount that should be invested is the present value of the $8,000 for the next 5 years. This amount would be the present value of an annuity due because constant payments that come at the beginning of a period are annuity dues.

Present value of annuity due = Annuity due x (Present value interest factor of annuity due, 6%, 5 years)

Solving for the amount to be invested to award the price gives:

= 8,000 x 4.4651

= $35,720.80

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Answer:D

Step-by-step explanation::

Answer:

123.88

Step-by-step explanation:

Answer:

  (-7, 5)

Step-by-step explanation:

You want to know the image of the point (-4, -6) after reflection in the x-axis and translation 3 left and 1 down.

The composition ...

  [tex]T_{-3,-1}\circ r_{\text{x-axis}}[/tex]

is interpreted to mean reflection in the x-axis occurs first, then translation by (-3, -1).

That is, a composition of transformations is evaluated right to left.

Reflection in the x-axis moves a point from below the x-axis to the same distance above the x-axis. That is, the sign of the y-coordinate changes:

  (-4, -6) ⇒ (-4, 6) . . . reflection in the x-axis

The translation vector is added to the coordinates of the point:

  (-4, 6) +(-3, -1) = (-4-3, 6-1) = (-7, 5)

The image of the point is located at (-7, 5).

We may infer from the number line that A and B are separated by 8 units (AB).

Let AB stand for the separation between points A and B, and let AC stand for the separation between points A and C. Let B stand for the separation between points B and C. Hence:

Point B being halfway between A and C, we can infer:

AB + BC Equals AC (Postulated segment addition)

As a result, since the distance between points A and B is equal to 1/3 of AC:

AC/3 = AB = 1/3(AC)

But as shown in the accompanying image:

AC equals 16 – (–8) to 24 units.

Therefore:

AB = 1/24 = 8 unit

A and B are separated by 8 units.

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On the number line, Point B is between points A and C. The distance between points A and B is 1/3 of AC. What is AB?​

Answer:

$191.29

Step-by-step explanation:

Use the formula
[tex]A = P(1 + \dfrac{r}{100})^n[/tex]

where P is amount deposited, A the accrued amount, n number of years and r the interest rate in % compounded annually

The division by 100 is necessary to convert r% to a decimal for calculations

We have P = 850, r = 7% and n = 3

Plugging these in we get
[tex]A = 850\cdot (1 + (\dfrac{7}{100})^3\\\\A= 850\cdot(1 + 0.07)^3\\A = 850\cdot1.07^3\\\A = \$1,041.29[/tex]

Interest = A - P = 1041.29 - 850 = $191.29

Answer:

10.25

Step-by-step explanation:

Define the variable

Let x be the unknown number.

Therefore:

[tex]\begin{aligned}& \textsf{Four times a number}: \quad & 4x\\& \textsf{Twenty less than four times a number}: \quad & 4x-20\\& \textsf{Twenty less than four times a number is twenty one}: \quad & 4x-20=21\end{aligned}[/tex]

To find the number, solve the found equation for x:

[tex]\begin{aligned}\implies 4x-20&=21\\4x-20+20&=21+20\\4x&=41\\\dfrac{4x}{4}&=\dfrac{41}{4}\\x&=10.25\end{aligned}[/tex]

Therefore, the unknown number is 10.25.

As an improper fraction, this is ⁴¹/₄.

As a mixed number, this is 10 ¹/₄.

Answer:

x = 10.25

Step-by-step explanation:

Given that,

→ Twenty less than four times a number is twenty one.

The equation we form,

→ 4x - 20 = 21

Now the value of x will be,

→ 4x - 20 = 21

→ 4x = 21 + 20

→ x = 41/4

→ [ x = 10.25 ]

Hence, the number is 10.25.

If Singer B took in ​$29 million less than Singer​ A, it means that Singer A generates $236 million and singer B generates $207 million in tickets sale.

The fact that singer B generated $29 million less than singer A means that if singer A generates x million , singer would generate (x-29) million in tickets salessingers:

443=2x-29

443+29=2x

472=2x

x=472/2

x=236singer

B's earnings=236-29

singer B's earnings=207

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Answer:

a) The fact that corresponding angles are equal

b) The fact that alternate angles are equal

Step-by-step explanation:

I hope this helps

a) Measure of corresponding angles are equal.

b) Pair of alternate interior angles are of equal measure.

We know when a transversal intersects two parallel lines at two distinct points,

Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.

From the given figure the fact used to fund the measure of the angle r is

corresponding angles.

The fact that is used to find the angle t is in a parallelogram measure of opposite angles are equal.

Also, r and t are pairs of alternate interior angles so they measure the same.

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Answer:

$70

Step-by-step explanation:

$50 to start do 2*10 to get 20 add those 50+20=70

Next, $30 to start do 4*10 to get 40 add those 30+40=70

They both come out o $70

Answer:

c

Step-by-step explanation:

8 telephone calls per hour

The expression to know many magazines kadien have left will be 60 - 5x.

From the information, Kadien had 60 magazines and he sells x magazines per day for 5 days.

The expression to calculate the number that will be left will be:

= 60 -(5 × x)

= 60 - 5x

The expression is 60 - 5x.

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The measure of the supplementary angles are 34.3 and 145.7 degrees.

Supplementary angles are those angles that sum up to 180 degrees.

In other words, two angles are Supplementary when they add up to 180 degrees.

Therefore, the angles measures 111.4° more than the measure of it's supplementary angle.

Hence,

let

x = measure of the other angle

x + x + 111.4 = 180

2x + 111.4 = 180

subtract 111.4 from both sides

2x + 111.4 - 111.4 = 180 - 111.4

2x = 68.6

divide both sides by 2

x = 68.6 / 2

x = 34.3

Other angle  = 34.3 + 111.4 = 145.7°

Therefore, the measure of the supplementary angles are 34.3 and 145.7 degrees.

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Answer:

64

Step-by-step explanation:

because you use 8+8+8+8=32 so you multiply 8x8 to get 64

for perimeter you add all four side with the same number ad the four sides is 8

but for area you multiply the 2 side  and the two sides is 8

Answer:

20 bags

Step-by-step explanation:

400/4 = 100, because it takes four apples to make a pound

100/5 because each bag holds 5 pounds,

20, bags filled with 5 pounds of apples

7. e = 2A - f

72. Area = 615.8 in.²

Circumference = 88.0 in.²

73. Area = 615.8 in.²

Circumference = 88.0 in.²

74. Missing length = √40 ≈ 6.3

75. Missing length = √45 ≈ 6.7

76. Scale factor = 18/6 = 3

77. Scale factor = 12/4 = 3

Area = πr²

Circumference = 2πr

7. A = (e + f)/2

2A = e + f

2A - f = e

e = 2A - f

72. r = 14 in.

Area = πr² = π(14²) = 615.8 in.²

Circumference = 2π(14) = 88.0 in.²

73. r = 30.2/2 = 15.1

Area = πr² = π(15.1²) = 615.8 in.²

Circumference = 2π(15.1) = 88.0 in.²

74. Missing length = √(6² + 2²) [Pythagorean Theorem]

Missing length = √40 ≈ 6.3

75. Missing length = √(6² + 3²) [Pythagorean Theorem]

Missing length = √45 ≈ 6.7

76. Scale factor = 18/6 = 3

77. Scale factor = 12/4 = 3

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Side of the given square room  flooring is 12 foot  

What is a square and its area?

A Square is a closed, two dimensional shape which has four sides and all four sides are equal and at 90 degree angle to each other .

As  all four sides are equal, Let each of the side of a square is a

Area of the square is given by = a*a

Given that a designer paid $4 per square feet for a square flooring

Total amount spent by the designer = $600

Total area of flooring = total amount spent /rate of per unit area

                                  = $600/$4 square foot =150 sq foot

Let the side of the given square flooring be x

Then area of the floor = [tex]x^{2} =150\\[/tex]

Thus side of the room floor = [tex]x=\sqrt{150}[/tex] = 12.25 = 12 foot

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Answer:

1, 2 and 3

Step-by-step explanation:

The numbers are 1, 2 and 3

When we add together : 1+ 2+ 3 = 6 and

When we multiply: 1 × 2 × 3 = 6

Answer:

269 R 15

Step-by-step explanation:

R means remainder

So if u divide 4857 by 18 you will get 269 reminder 15.

Answer: 24

Step-by-step explanation: HI = 2 times KL

-8x + 120 = 2(-8x + 96)

-8x + 120 = -16x + 192

8x = 72

x = 9

KL = -8x + 96

KL = -8(9) + 96

KL = 24