Copy Central prints grayscale and colored copies. Yesterday they printed 9 grayscale copies for every 2 colored copies. If they printed 20 color copies how many grayscale copies were printed?

Evaluating the given expressions, A) 10^14 (option a), B) 10^-6 (option b), C) 10^27 (option b) D) 10^-8 (option c).

A) 10^5 x 10^9

Using the product of power rule, when the base is same, the exponents are added together. Hence,

10^5 x 10^9 = 10^(5 + 9) = 10^14

B) 10^4 x 10^-10

Using the product of power rule,

10^4 x 10^-10 = 10^(4 – 10) = 10^-6

C) 10^30 ÷ 10^3

Using the quotient power rule, when the base is the same, the exponents are subtracted.

10^30 ÷ 10^3 = 10^(30 – 3) = 10^27

D) 10^-12 ÷ 10^-4

Using the quotient power rule,

10^-12 ÷ 10^-4 = 10^(-12 –(-4) = 10^(-12 + 4) = 10^-8

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Answer: Simplified

Step-by-step explanation: The question is already as simplified as it can get.

The estimated value of y when x1=12, x2=1, and x3=-1 is -204. This is calculated by substituting the given values into the equation ˆy=−184−7x1+47x2+20x3.

ˆy=−184−7(12)+47(1)+20(-1)

ˆy=−184-84+47-20

ˆy=−204

In the multiple regression equation

ˆy=−184−7x1+47x2+20x3

the estimated value of y can be determined by substituting the given values of x1, x2, and x3 into the equation. For example, given

x1=12, x2=1, and x3=-1,

the estimated value of y can be calculated as follows: ˆy=−184−7(12)+47(1)+20(-1). This simplifies to

ˆy=−184-84+47-20, or ˆy=-204.

The equation takes the form of a linear equation, with each independent variable x1, x2, and x3 multiplied by a coefficient, and then added together to give the estimated value of y. In this example, the coefficient for x1 is -7, for x2 is 47, and for x3 is 20. This means that if x1 increases by 1 unit, then the estimated value of y will decrease by 7 units; if x2 increases by 1 unit, then the estimated value of y will increase by 47 units; and if x3 increases by 1 unit, then the estimated value of y will increase by 20 units. Using the multiple regression equation, therefore, the estimated value of y can be calculated when the values of the independent variables are known. In this example, given x1=12, x2=1, and x3=-1, the estimated value of y is -204.

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The complete question is

In the following multiple regression equation, what is the value of x2 when x1 = 15.5 and ˆy is estimated to be -412?ˆy=78−20x1−10x2x2=2)Given the following multiple regression equation:ˆy=−184−7x1+47x2+20x3Determine the estimated value of y whenx1=12x2=1x3=−1ˆy=−204

Answer:

Step-by-step explanation:

positive

Answer:

None

Step-by-step explanation:

Evaluate each answer option, following the order of operations (PEMDAS).

[tex]\begin{aligned}\textsf{A.} \quad (6^2+2)-18\sqrt{81}&=(36+2)-18\sqrt{81}\\&=(36+2)-18(9)\\&=38-18(9)\\&=38-162\\&=-124\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{B.} \quad 6^2(2-8)\sqrt{81}&=36(2-8)\sqrt{81}\\&=36(2-8)(9)\\&=36(-6)(9)\\&=(-216)(9)\\&=-1944\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{C.} \quad (6^2+2-8)\sqrt{81}&=(36+2-8)\sqrt{81}\\&=(36+2-8)(9)\\&=(38-8)(9)\\&=(30)(9)\\&=270\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{D.} \quad 6^2 +2(8\sqrt{81})&=36+2(8\sqrt{81})\\&=36+2(8\cdot 9)\\&=36+2(72)\\&=36+144\\&=180\end{aligned}[/tex]

Therefore, none of the answers has a value of -18.

The graph of the resulting line of y = 1/2 x + 4 will be a line passing through P(0, 4), Q (-8, 0) and R (2, 5).

A graph is a pictorial representation of a figure formed by connecting set of points.

We have to find the points through which the line y = 1/2 x + 4 passes through to draw the graph of the line.

Let x = 0 ⇒ y = 4

A point P is found as P (0, 4), which is the y intercept where the line touches with the Y axis.

Let y = 0, then 1/2 x = -4 or x = -8

A point Q is found as Q (-8, 0) which is the x intercept where the line touches with the X axis.

Let x = 2, then y = 5

A point R is found as R (2, 5).

So graph of y = 1/2 x + 4 will be a line passing through P(0, 4), Q (-8, 0) and R (2, 5).

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The solution to the system of equations is x = 0, y = 0.

What is substitution algebraic expression?

Substitution means replacing the variables in an algebraic expression with their numerical values. We can then work out the total value of the expression.

To use algebraic substitution to solve for x and y, we can substitute one equation into the other and solve for one of the variables.

Given that y = -8x, we can substitute this into the second equation, 2x + 4y = 0

So, 2x + 4(-8x) = 0

Simplifying this we get,

2x - 32x = 0

30x = 0

Dividing both sides by 30

x = 0

Now we have x = 0, we can substitute this value back into the equation y = -8x

So y = -8(0)

y = 0

Hence, the solution to the system of equations is x = 0, y = 0.

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No, we cannot draw a triangle with sides 3 cm, 3.5 cm, and 6.5 cm.

Let's understand the concept behind this:

Apply the triangle's length-of-sides property, which stipulates that the total of any two sides should be more than the value of the third side. Such a triangle cannot exist if there is any pair of sides whose sum is equal to or less than the third side.

We must determine whether the supplied side lengths constitute a triangle. We now understand that the triangle's third side should be greater than the sum of any two of its sides. Such a triangle cannot exist if there is any pair of sides whose sum is equal to or less than the third side. So, we'll try every combination and see if it meets the criteria.

Let’s assume AB = 3 cm, BC = 3.5 cm and AC = 6.5 cm.

AB + AC = 3 + 6.5 cm = 9.5 cm > 3.5 cm = BC.

AC + BC = 6.5 + 3.5 = 10 cm > 3 cm = AB.

AB + BC = 3 + 3.5 cm  = 6.5 cm = AC.

However, in this case, the length of the third side is equal to the total lengths of the other two sides, which renders the triangle's condition incorrect.

Therefore, there does not exist any triangle with sides of 3 cm, 3.5 cm, and 6.5 cm.

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Both Teresa and Leon have constructed regular hexagons. Teresa drew a circle and marked a point on it, then used a compass set to the radius to construct a regular hexagon. Leon drew a segment, then used a circle with the segment as the radius and a compass set to the length of the segment to construct a regular hexagon.

It is important to note that a regular hexagon is a polygon with six congruent sides and six congruent angles, and is constructed by using a compass to draw six equidistant points on a circle, connecting the points with straight lines, forming the hexagon. In both cases described above, it appears that Teresa and Leon were using a compass and the appropriate measurements to construct regular hexagons.

The distance between the two cities located at latitude 19 degrees N, and the other has a latitude 26 degrees S is 5011 km

The distance between the two cities is calculated using the formula

= x/360 * 2 * pi * r

where

r = radius

x = the angle subtended by the distance

From the question we have that

x = 19 degrees N + 26 degrees S

x = 45 degrees

radius of the earth = 6380 km

distance between the points = x/360 * 2 * pi * r

distance between the points = 45/360 * 2 * pi * 6380

distance between the points = 0.125 * 12760 * pi

distance between the points = 5010.84 km

distance between the points = 5011 km

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2x< x+22 is the inequality equation which satisfy that x=20 the other inequality equation does not satisfy the condition.

Given that,

We have to find which inequality is true for x=20

The inequality equations are

a. x-5 < 2x-35

b. 2x < x+22

c. x/4 > x-12

d. x+30 >3x

We know that,

We have to substitute x=20 in the inequality equation to check which equation is true.

a. 20-5 < 2(20)-35

15 < 40-35

15< 5

NO, the inequality is not true

b. 2(20) < 20+22

40 < 42

Yes, the inequality is true

c. 20/4 > 20-12

5>8

NO, the inequality is not true

d. 20+30 > 3(20)

50 > 60

NO, the inequality is not true

Therefore, 2x< x+22 is the inequality equation which satisfy that x=20 the other inequality equation does not satisfy the condition.

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Answer:

Foci:  (±5, 0)

Vertex: ( ±4 , 0)

Eccentricity: e = 5/4

Step-by-step explanation:

   Write the equation of hyperbola in the form,

              [tex]\boxed{\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1}[/tex]

9x² - 16y² = 144

Divide the entire equation by 144,

          [tex]\sf \dfrac{9x^2}{144}-\dfrac{16y^2}{144}=\dfrac{144}{144}\\\\\\ \dfrac{x^2}{16}-\dfrac{y^2}{9}=1\\\\\\\dfrac{x^2}{4^2}-\dfrac{y^2}{3^2}=1[/tex]

a = 4 and b =3

  Eccentricity: e

           [tex]\boxed{e=\sqrt{1+\dfrac{b^2}{a^2}}}[/tex]

                [tex]\sf = \sqrt{1+\dfrac{9}{16}}\\\\=\sqrt{\dfrac{16}{16}+\dfrac{9}{16}}\\\\=\sqrt{\dfrac{25}{16}}=\sqrt{\dfrac{5*5}{4*4}}\\\\\\=\dfrac{5}{4}[/tex]

Foci:

         (ae, 0)  & (-ae , 0)

          [tex]\sf \left(4*\dfrac{5}{4},0 \right) \ ; \ \left( -4*\dfrac{5}{4},0 \right)\\\\\\(5, 0) \ ; \ (-5,0)[/tex]

Vertex of hyperbola:

       The vertex of the hyperbola is a point where the hyperbola cuts the axis.  (-a , 0)  ; (a , 0)

 Vertex : (-4 , 0) ; (4 , 0)

The solution for this question is as follows:

Vertices ≈ (±4 , 0)

Foci ≈ (±5 , 0)

Eccentricity: e = 5/4

Asymptotes: y=  ±(3/4)x

Hyperbola:

The location of all the points on a plane where the distance between them and two fixed points in the plane is always equal to zero is called a hyperbola.

Step by step solution:

Given: [tex]9x^{2} -16y^{2} =144[/tex]      

The given equation of hyperbola can be written as:

⇒[tex]\frac{x^{2} }{16} -\frac{y^{2} }{9} =1[/tex]

On comparing with standard equation of hyperbola; [tex]\frac{x^{2} }{a} -\frac{y^{2} }{b} =1[/tex]

We get; a=4 and b=3

The eccentricity of hyperbola is given by:

      9=16(e^2 - 1)

So; e^2 = (9/16) + 1

       e^2 = 25/16

       e = 5/4

The vertices of hyperbola are given by (±a , 0) ≈ (±4 , 0)

The foci of hyperbola are given by (±ae , 0) ≈ (±5 , 0)

The asymptotes of hyperbola are given by y= ± (b/a)x  

                                                                        y=  ±(3/4)x

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Using ratio, the length of the tree is 1.9m

Ratio is a comparison of two or more related quantities, expressed as a fraction or a proportion. Ratios are used to compare values and to look for relationships between them. For example, if you have five friends and two of them are girls, the ratio of girls to boys is 2:3 (2 out of 5).

We can set up two ratio as a proportion to find the length of the tree.

1.2 / x = 4.2 / 6.5

Cross multiply both sides and solve for x

x = (1.2 * 6.5) / 4.2

x = 1.85m ≅ 1.9m

The height of the tree is 1.9m

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1) Remainder is 2 and sum of 4 consecutive square numbers is divisible by 4.

2) Their difference will be divisible.

The amount that remains after division is known as the Remainder. The result of division is a value if a number (dividend) cannot be divided entirely by another number (divisor).

1. Suppose the a random number is x and 4 consecutives number are x, x+1, x+2, x+3

Given that,

x² + (x+1)²+ (x+2)²+ (x+3)²

x² + (x² +2x+1) + (x² +4x+4)+ (x²+6x+9)

4x² + 12x + 14

is divisible by 4 with remainder 2

[tex]$ \frac{4x^2 + 12\text x + 14}{4} $[/tex]

[tex]$ \frac{4x^2 + 12\text x + 12 +2}{4} $[/tex]

[tex]$ \frac{4x^2 + 12\text x + 12 }{4} $[/tex] [tex]$+\frac{2}{4}[/tex]

Hence proved, remainder is 2 and sum of 4 consecutive square numbers is divisible by 4.

2. As both 14 and 21 is divisible by seven, their difference is also divisible by 7, i.e. 70-42 = 28, all the numbers are divisible by 7 and hence the squares of the number are also divisible by seven as well as their numbers.

14²⁰ - 21²

(7 × 2)²⁰ - (7 × 3)²

Thus, their difference will be divisible.

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Answer:

10x^2 - 11x -6

Step-by-step explanation:

1/ First, distribute the brackets:

( multiply 5x to the other bracket, then 2 multiply it also to the other bracket)

After the distribution you'll get this:

10x^2 - 15x + 4x - 6

2/ finally, to simplify you'll have to combine the like terms:

( as you can see the only like terms we have are -15x and +4x)

combine them and you'll get:

10x^2 - 11x -6  ( this is the final answer)

The formula for Area of Hexagon is written as : [tex]\frac{3\sqrt{3} a^{2} }{2}[/tex]

The formula for Perimeter of Hexagon is written as : [tex]6a[/tex] .

A Regular Hexagon is defined as a two dimensional shape which has 6 sides, 6 angles and 9 diagonals, and sum of its interior angles is 720°.

When one side length of the regular hexagon is given as "a" units ,

A regular hexagon comprises of six equilateral triangles, formula for finding area of a hexagon is derived from formula of area of equilateral triangle .

So,  the Area can be calculated by the formula : [tex]\frac{3\sqrt{3} a^{2} }{2}[/tex]  square units ;

and Perimeter of hexagon be calculated by the formula : [tex]6a[/tex] units .

The given question is incomplete , the complete question is

What is the formula for area and perimeter of a hexagon ?

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Dilating the given triangle with a magnitude of 3, the number corresponding to the question mark is 18.

Therefore the answer is 18.

Dilating a triangle means to scale it up or down by a certain factor, in this case, by a factor of 3. To dilate a triangle, you need to multiply the each elements of the matric by the dilation factor.

On multiplying a matrix by a scalar number, each element of the matrix is multiplied by that scalar number.

3 × [3 6 3 | -3 3 3] =  [3×3 6×3 3×3 | -3×3 3×3 3×3]

=[ 9 18 9 | -9 9 9]

That is

[tex]3\left[\begin{array}{ccc}3&6&3\\-3&3&3\end{array}\right] = \left[\begin{array}{ccc}-3*3&6*3&3*3\\-3*3&3*3&3*3\end{array}\right][/tex]

[tex]= \left[\begin{array}{ccc}9&18&9\\-9&9&9\end{array}\right][/tex]

So the element corresponding to the question mark is 18.

--The question is incomplete, complete question is given below--

"Dilate the given triangle with a magnitude of 3.

[tex]\left[\begin{array}{ccc}3&6&3\\-3&3&3\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}9&?&-\\-9&-&-\end{array}\right][/tex]"

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The rate of change of the amount of gasoline in a storage tank at t=3 hours is -0.75 thousand gallons per hour, and the amount of gasoline in the storage tank is increasing at an increasing rate between t=5 and t=10.

(a) To estimate the rate of change of the amount of gasoline in the storage tank at time t=3 hours, we can use the formula for the average rate of change over an interval: (G(b) - G(a)) / (b - a).

We can choose two points on the table that are closest to t=3 hours, such as t=2 and t=4. Using these points, we have:

G(2) = 22

G(4) = 20.5

Substituting these values into the formula, we get:

(G(4) - G(2)) / (4 - 2) = (20.5 - 22) / (4 - 2) = -1.5 / 2 = -0.75

The units of measure for this rate of change would be thousands of gallons per hour.

(b) Since G′′(t)>0 for 5≤t<10, this means that the second derivative of G(t) is positive for all values of t within this interval. The second derivative represents the rate of change of the rate of change, or the acceleration. A positive second derivative indicates that the rate of change is increasing, or that the function is accelerating. This means that the amount of gasoline in the storage tank is increasing at an increasing rate between t=5 and t=10.

We can also conclude that G′(t)>0 for 5≤t<10 since the second derivative represents the rate of change of the first derivative, which is positive. This means that the first derivative, or the rate of change of the function, is also positive for this interval. This confirms that the amount of gasoline in the storage tank is increasing between t=5 and t=10.

Complete Question:

'A gasoline storage tank is filled by a pipeline from a refinery. At the same time, gasoline flows from the tank into trucks that will make deliveries to gasoline stations. The amount of gasoline in the storage tank at time t is given by the twice-differentiable function G, where t is measured in hours and 0≤t≤10. Values of G(t), in thousands of gallons, at selected times t are given in the table above. It is known that G′′(t)>0 for 5≤t<10.

(a) Use the data in the table to estimate the rate of change of the amount of gasoline in the storage tank at time t=3 hours. Show the computations that lead to your answer. Indicate units of measure.

(b) For 0 t (hours) 0 5 8 10 G (0 (thousands of gallons 22 18.5 19.5 22 24'

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Funsters inc. , the largest toy company in canada, sells its most popular doll for $35. It has just learned that its leading competitor toysorama is mass producing an excellent copy and plans to flood the market with their $10 doll in 6 weeks. Funsters should increase the supply of its doll now before the other doll hits the market.

1. Addressing Customer Needs

Often business competition motivates brands and businesses to meet customer needs, vying to be more effective than their competitors. This encourages brands to develop an understanding of audience needs.

This competition resulted in a focus on meeting customer needs including higher quality products, increased service value, and increased customer satisfaction.

2. Analyze Strengths and Weaknesses

Business competition can drive an evaluation of strengths and weaknesses, as well as optimizing sales strategies based on these findings. This enables a business to maximize resources, make informed decisions about marketing and sales strategies, and tailor offerings according to their strengths.

3. Increasing Demand

Business competition is an effective way to increase demand for a product or service. As more companies invest in their marketing and advertising efforts, the consumer demand for their products and services may increase as brand awareness increases.

3. Encouraging Innovation

In order to gain an advantage in the market, business competition can drive to innovate strategies and improve their products or services in creative ways. This is an important contribution to continuously improving the quality of goods and services, advancing product and service technology, and adapting to changing consumer needs.

4. Show Excellence

A business often tracks and analyzes competitors' performance to gain insight into their business strategy. By studying competitors' tactics, a business will be able to demonstrate their superiority in the market. So that many businesses can develop strategies that will result in success.

5. Promoting Business

Continuous business development can be an important factor in long-term success. Business competition is often challenging to continue to increase brand awareness, promote, analyze success, and develop new methods to achieve even bigger goals.

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Answer:

Step-by-step explanation:

p=12 q=4 r=10

The difference between the diameters of the two cells G and H will be;

⇒ 70.43 × 10⁻² centimeters

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

Two cells are measured using this method,

Cell G: 1.87 x 10⁻² centimeters

Cell H: 7.23 x 10⁻³ centimeters

Now,

Since, Two cells are measured as;

Cell G: 1.87 x 10⁻² centimeters

Cell H: 7.23 x 10⁻³ centimeters

Hence, The difference between the diameters of the two cells G and H is,

⇒ 7.23 x 10⁻³ - 1.87 x 10⁻²

⇒ 72.3 × 10⁻² - 1.87 × 10⁻²

⇒ (72.8 - 1.87) × 10⁻²

⇒ 70.43 × 10⁻² centimeters

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Answer:

The shadow cast by the building is of the length 11.8 m.

Step-by-step explanation:

We consider the height of the building as the height of the triangle and the length of the shadow as the base of the triangle, then the distance from the top of the building to the tip of the shadow would be the hypotenuse of the triangle.

Using the Pythagorean theorem:

c^2 = a^2 + b^2

Where c is the hypotenuse, which is 36m, a is the height of the building, which is 34m and b is the base of the triangle, which is the length of the shadow.

So by plugging the given numbers in:

b^2 = c^2 - a^2

b^2 = 36^2 - 34^2

b = √(36^2 - 34^2)

b ≈ 11.8m (if rounded to the nearest tenth)

So the length of the shadow in this scenario is approximately 11.8 m.

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the volume of rectangular shape is 8 cm³ and density is 4 gm/cm³

What is cube?

The term "cube" refers to a solid three-dimensional shape in mathematics or geometry that has six square faces, eight vertices, and twelve edges. It is also asserted to be a conventional hexahedron. You must be familiar with the three-by-three Rubik's cube, which is the most prevalent example in daily life and can help to increase brain capacity. Similar to this, you'll run into a lot of real-world examples, like 6-sided dice, etc. Solid geometry is the study of three-dimensional objects with surface areas and volumes. Cube, cylinder, cone, and sphere are some of the other solid shapes. Here, we'll talk about its definition, attributes, and relevance to mathematics.

Given sides of the rectangular cube are 1 cm, 2c.m, and 4c.m

The volume will be the product of all three sides = 1*2*4 = 8 cube cm

The density will be mass/volume.

= 32gm/8 = 4 gm/cm³

Hence volume of the rectangular shape is 8 cm³ and density is 4 gm/cm³

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Answer:

what is the regular price of the soda? 1.59$

A line segment has two specific endpoints in a line. The length of the line segment is set, that is the distance between two fixed points.

The length here can be measured by metric units such as centimeters (cm), and millimeters (mm), or by conventional units like feet or inches.

A closed line segment contains both endpoints, but an open line segment is exclusive of the two endpoints. A line segment that has just one endpoint is called a half-open line segment.

A line segment has two endpoints. Now if we know the coordinates of the endpoints, then we calculate the length of the line segment by distance formula.

[tex]D = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} -y_{1})^{2} }[/tex]

Let a line segment has coordinates (2, –3) and (–1, –2). What is the length of a line segment?

Therefore, by distance formula,

[tex]D = \sqrt{(2 - (-1))^{2} + (-3 -(-2)^{2} }[/tex]

[tex]D = \sqrt{(2 + 1))^{2} + (-3 +2)^{2} }[/tex]

[tex]D = \sqrt{(3)^{2} + (-1)^{2} }[/tex]

[tex]D = \sqrt{10}[/tex] = 3.16

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Answer:

45%

Step-by-step explanation:

5% owns both so you remove that 5% from both the 40% and 10% because it's already in the "both" category. For example if Sara has both, then it also means that Sara is among the 5% that has both but also in the 40% that owns a bike and the 10% that owns a skateboard. You need to remove Sara from those two categories (skateboard and bike) because she's already in the "both" category.

So when you remove it, it's not 40 and 10 percent but 35 and 5 percent.

The answer is 35+5+5 = 45%

The amount to be paid by Chet if The flight he selected was $229.99, but he got 20% off because he booked it online through a new travel website, is $184.

A percentage, often known as percent, is a division by 100. Percentage, which means "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance.

Given:

The flight he selected was $229.99 but he got 20% off because he booked it online through a new travel website,

Calculate the amount of discount as shown below,

Discount = 20% of 229.99

Discount = 20 / 100 × 229.99

Discount = 0.2 × 229.99

Discount = 45.998

Thus, the amount to be paid = 229.99 - discount

the amount to be paid = 229.99 - 45.99

the amount to be paid = 184

Thus, the amount to be paid is $184.

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The payments each month do not cover all interest and no principal. The correct answer would be an option (B).

A credit card trap occurs when the minimum payments required each month do not cover all the interest charges and do not reduce the principal balance. This means that even if the cardholder makes the minimum payments on time, they will still be paying only the interest charges and not reducing the amount of debt. This can result in a cycle of high-interest debt that is difficult to escape from.

Option A is incorrect as it's describing a common way payments work on credit cards.

Option C is not a trap, as it's describing a credit card issuer with a low-interest rate.

Option D is also incorrect, as it's describing a common way payments work on credit cards.

Hence, the correct answer would be an option (B).

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