1. In your own words, describe the following:

a.) Cartesian Coordinate System

b.) The uses of the system

c.) Who developed the system?

d.) Historically, why is the system unique?

2. Use the list below to write the correct term for each definition on the line provided.

axes (of a graph) coordinates coordinate grid intersection number line ordered pair

origin quadrant x-axis

x-coordinate y-axis y-coordinate

a.) the first number of an ordered pair

b.) the second number of an ordered pair

c.) any of four regions formed by the axes in a rectangular coordinate system

d.) the point at which two lines meet

e.) numbers that correspond to points on a graph in the form (x, y)

f.) the intersection of the x-axis and y-axis in a coordinate plane, described by (0,0)

g.) the horizontal and vertical number lines used in a rectangular graph or coordinate grid system as a fixed reference for determining the position of a point

h.) the vertical ( ) axis on a coordinate plane

i.) the horizontal ( ) axis on a coordinate plane

j.) a line on which numbers can be written or visualized

k.) the location of a single point on a rectangular coordinate system where the digits represent the position relative to the x-axis and y-axis Example: (x, y) or (3, 4)

l.) network of evenly spaced, parallel horizontal and vertical lines especially designed for locating points, displaying data, or drawing maps

Quadrilateral ABCD can be dilated by a scale factor 1.25 to create a smaller image and by a scale factor 1.5 to create a bigger image.

To calculate the scale factor of a given shape for its dilation or reduction, the formula that should be used is given as follows:

Scale factor = bigger dimension/smaller dimension.

To create a smaller image;

bigger dimension length AB = 22in

smaller dimension length AB = 17.6in

Scale factor = 22/17.6 = 1.25

To create a bigger image:

Bigger dimension length = 33in

Smaller dimension length = 22in

scale factor = 33/22 = 1.5

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Answer:

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the initial principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, P = $100, r = 9% = 0.09, n = 1 (compounded annually), and t = 16. We want to find A.

A = 100(1 + 0.09/1)^(1*16)

A = $397.42

Therefore, Javae will have $397.42 in his account on his 30th birthday. The answer is option D.

After Jenny invested the $1900 in a 5-year CD,

A) Given principal money (P) = $1900

Rate of interest (r) = 1.47% / 100 = 0.047

number of times interest compounded per year (n) = 4

number of years (t) = 5

Amount Jenny will have after 5-years (A) = [tex]p(1+r/n)^{nt}[/tex]

A = [tex]1900(1+0.047/4)^{4*5}[/tex]

A = [tex]1900(1 + 0.01175)^{20}[/tex]

A = [tex]1900(1.01175)^{20}[/tex]

A = 1900(1.2631) ≅ $2400

B) Interest earned after 5 years = $2400 - $1900 = $500.

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Answer:

(i) Calculation:

1 GB = 1000 MB

Number of videos that could be stored = (1 GB / 100 MB) = 10

Therefore, William can store 10 videos on his computer if each video is 100MB in size.

(ii) Algorithm using pseudocode:

Ask the user to input the file size in megabytes.

Multiply the file size by 1,000,000 to convert it to bytes.

Print the result in a user-friendly format by dividing the bytes by 1,048,576 and rounding to two decimal places, and adding "MB" and "bytes" to the output.

Pseudocode:

Input file_size_in_mb

Set bytes = file_size_in_mb * 1000000

Set result = round((bytes / 1048576), 2)

Output "There are " + result + " MB " + bytes + " bytes".

Answer:

Quotient=23 and remainder=14

Answer: s = p - 0.25p; $30

Step-by-step explanation:

      First, we need to know that a percent divided by 100 becomes a decimal.

          25% / 100 = 0.25.

      Next, we will use this equation because it takes 25% off of the original price (p) by subtracting 0.25p from p.

          s = p - 0.25p

      Lastly, we will substitute 40 in for 0 and solve.

          s = ($40) - 0.25($40)

          s = $30

The volume of the cylinder is 90π cubic units.

To calculate the volume of a cylinder with a radius of 3 and a height of 10, you can use the following formula:

Volume = π × r² × h

Where:

- Volume represents the volume of the cylinder,

- π (pi) is a mathematical constant approximately equal to 3.14159,

- r is the radius of the cylinder (in this case, 3), and

- h is the height of the cylinder (in this case, 10).

Now, plug in the given values:

Volume = π × (3)² × 10

Simplify the expression:

Volume = π × 9 × 10

Volume = 90π

So, the volume of the cylinder is 90π cubic units.

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The expression for the number of slices Harris ate is [tex](n/44) - 11.[/tex]

Let s be the number of slices each friend received.

Then the total number of slices on the pizza is n and we have: 44s = n because pizza was evenly divided among the 44 friends). Harris ate 11 fewer slices than he received, so he ate s - 11 slices.

The no of slices he  received is s and we have:

s = (s - 11) + Harris's slices eaten

Substituting 44s = n, we will solve for s:

44s = n

s = n/44

So, the expression for the number of slices Harris ate is [tex](n/44) - 11.[/tex]

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Answer:

240 tickets sold

Step-by-step explanation:

first, you would set up the proportion by writing [tex]\frac{228}{95} =\frac{x}{100}[/tex]

with "x" being the number of seats that needs to be sold

then, you would cross multiply

and you get

[tex]95x=228*100[/tex]    next, you simplify to get the inequality [tex]95x=22800[/tex]

then divide both sides by 95

[tex]x=240[/tex]

so 240 tickets to fill all the seats

hope this helps ;)

Step-by-step explanation:

[tex] - 3 = \frac{3}{4} (2) + b[/tex]

[tex] - \frac{6}{2} = \frac{3}{2} + b[/tex]

[tex]b = - \frac{9}{2} [/tex]

[tex]y = \frac{3}{4} x - \frac{9}{2} [/tex]

Alternately, starting at (2, -3), go up 3 units, then right 4 units, to (6, 0). Draw a line that goes through these points.

The lateral surface area of the rectangular prism is 308 units² and the total surface area is 398 units²

The formula of lateral surface area of the rectangular prism is given as;

LSA = 2(l +b)h

substituting the values into the formula;

LSA = 2(5 + 9) * 11

LSA = 308 units²

The total surface area is given by

TSA = 2(lb + bh + lh)

TSA = 2[(5*9) + (9*11) + (11*5)

TSA = 398 units²

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The simple interest earned after 3 years on $500 at an interest rate of 6% is $90.

Simple interest is a type of interest that is calculated based only on the initial amount borrowed or invested, called the principal amount, and does not take into account any additional interest earned on the interest over time.

To find the simple interest earned on $500 at an interest rate of 6% after 3 years, we can use the formula:

Simple Interest = Principal x Rate x Time

Where

Principal = $500

Rate = 6% = 0.06 (in decimal form)

Time = 3 years

Plugging these values into the formula, we get

Simple Interest = $500 x 0.06 x 3

= $90

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I have solved the question in general, as the given question is incomplete.

The complete question is:

Find the simple interest earned after 3 years on $500 at an interest rate of 6%.

John will be able to fill 8 glasses with iced tea.

To convert quarts to cups, we need to multiply the number of quarts by 4, since 1 quart is equal to 4 cups. So, 3 quarts of iced tea is equivalent to 3 x 4 = 12 cups of iced tea.

Since each glass holds 1½ cups of iced tea, John will need to divide the total cups of iced tea by the capacity of each glass: 12 cups / 1.5 cups/glass = 8 glasses.

Therefore, John will fill 8 glasses with iced tea.

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a) The depreciation expenses for Year 1 to Year 4 using the straight-line method are $2,632, $5,263, $4,211, and $2,632, respectively.

b) Using the units-of-activity method, the depreciation expenses are $7,000, $14,000, $11,900, and $7,000, respectively.

c) Using the double-declining-balance method, the depreciation expenses are $4,658, $11,172, $7,302, and $2,640, respectively.

a) To calculate the depreciation expense for each year using the straight-line method, the company needs to first determine the depreciable cost of the equipment. This is the cost of the equipment minus its estimated residual value.

The depreciable cost is $41,550 - $1,650 = $39,900.

To calculate the annual depreciation expense using the straight-line method, divide the depreciable cost by the useful life of the equipment, which is three years.

Year 1: ($39,900 ÷ 3) × (1,000 ÷ 5,700) = $2,632

Year 2: ($39,900 ÷ 3) × (2,000 ÷ 5,700) = $5,263

Year 3: ($39,900 ÷ 3) × (1,700 ÷ 5,700) = $4,211

Year 4: ($39,900 ÷ 3) × (1,000 ÷ 5,700) = $2,632

b) To calculate the depreciation expense using the units-of-activity method, the company needs to first determine the depreciation rate per unit of activity. This is the depreciable cost of the equipment divided by its total estimated hours of use.

The depreciation rate per unit of activity is $39,900 ÷ 5,700 hours = $7 per hour.

Year 1: $7 × 1,000 hours = $7,000

Year 2: $7 × 2,000 hours = $14,000

Year 3: $7 × 1,700 hours = $11,900

Year 4: $7 × 1,000 hours = $7,000

c) To calculate the depreciation expense using the double-declining-balance method, the company needs to first determine the straight-line depreciation rate. This is the depreciable cost of the equipment divided by its useful life.

The straight-line depreciation rate is $39,900 ÷ 3 years = $13,300 per year.

The double-declining-balance depreciation rate is twice the straight-line rate, or $13,300 × 2 = $26,600.

Year 1: $26,600 × (1,000 ÷ 5,700) = $4,658

Year 2: ($39,900 - $4,658) × (2,000 ÷ 5,700) = $11,172

Year 3: ($39,900 - $4,658 - $11,172) × (1,700 ÷ 5,700) = $7,302

Year 4: ($39,900 - $4,658 - $11,172 - $7,302) × (1,000 ÷ 5,700) = $2,640

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Answer:

x = 18°

Step-by-step explanation:

7x - 6° = 120°

7x = 126°

x = 18°

So, the answer is x = 18°

option B is correct: [tex](x+2)^2+(y+7)^2=36[/tex]

The general equation of the circle is given by:

[tex](x-h)^2+(y-k)^2=r^2[/tex]              

where,

(h, k) is the center of the circle and r is the radius of the circle.

As per the statement:

The center of a circle is at (−2, −7) and its radius is 6.

[tex]\implies (h, k) = (-2, -7)[/tex] and [tex]r = 6[/tex] units

Substitute these we have:

[tex](x-(-2))^2+(y-(-7))^2=6^2[/tex]

[tex]\implies(x+2)^2+(y+7)^2=36[/tex]

Therefore, the equation of circle is, [tex]\bold{(x+2)^2+(y+7)^2=36}[/tex]

The slope and derivative of a vertical tangent are both undefined due to the vertical nature of the tangent line.

The slope/derivative of a vertical tangent.
A vertical tangent occurs when a curve has a point where its tangent line is vertical.

In terms of the slope and derivative, the following is true about the vertical tangent:
Slope:

The slope of a vertical tangent is undefined because the vertical line has no run (change in x). Slope is calculated as the rise (change in y) divided by the run (change in x), and division by zero is not possible.
Derivative:

The derivative of a function at a point represents the slope of the tangent line to the curve at that point.

When the tangent is vertical, the derivative is also undefined because the slope is undefined.

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We have (0, 1) and (3, 5) as two points on the line y = 4/3x + 1.

The equation y = 4/3x + 1 represents a line in slope-intercept form, where the coefficient of x (4/3) represents the slope of the line and the constant term (1) represents the y-intercept.

To select two points on the line, we can choose any values for x and use the equation to find the corresponding values of y.

For example, let's choose x = 0:

y = 4/3x + 1

y = 4/3(0) + 1

y = 1

So one point on the line is (0, 1).

Now let's choose x = 3:

y = 4/3x + 1

y = 4/3(3) + 1

y = 5

So another point on the line is (3, 5).

Since both equations hold true, we can conclude that (0, 1) and (3, 5) are two points on the line y = 4/3x + 1.

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Answer:

  15.0 in

Step-by-step explanation:

You want the height of a cone with radius 8 in and slant height 17 in.

The right triangle shown in the figure has height h, base x = 8 in, and slant height y = 17 in. The Pythagorean theorem tells you the relationship between these side lengths:

  x² +h² = y²

  8² +h² = 17²

  h² = 17² -8² = 289 -64 = 225

  h = √225 = 15.0

The height of the cone is 15.0 inches.

__

Additional comment

A triple of 3 integers that form the sides of a right triangle is called a "Pythagorean triple." The triple in this problem is one of those: {8, 15, 17}. Other Pythagorean triples you will often see in algebra, trig, and geometry problems are {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {9, 40, 41}. You will also see multiples of these, for example 3×{3, 4, 5} = {9, 12, 15}.

It can be worthwhile to remember some of these. For this problem, recognizing 8 and 17 as part of the triple {8, 15, 17} means you can write down the answer with no further work.

The picture below shows the graph of the inequality of x² ≤ 4

Option B is correct.

In mathematics, an inequality is described as a relation which makes a non-equal comparison between two numbers or other mathematical expressions which is used most often to compare two numbers on the number line by their size.

A graph of inequality denotes that the variables is the set of points that represents all solutions to the inequality.

A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality.

Therefore, the correct option is B. x² ≤ 4

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The maximum number of mail swaps that Bagelbot can perform between officials from A and officials from B can be 150 .

It can be determined by calculating the maximum number of edges possible for a bipartite graph between A and B. A bipartite graph is a graph in which the vertices can be divided into two disjoint sets such that every edge connects a vertex in one set to a vertex in the other set.

In this case, the officials from A and officials from B represent the two disjoint sets.

The maximum number of edges in a bipartite graph between A and B can be calculated as the product of the number of officials in A and the number of officials in B. Therefore, if there are n officials in A and m officials in B, the maximum number of mail swaps that Bagelbot can perform is n x m.

For example, if there are 10 officials in A and 15 officials in B, the maximum number of mail swaps that Bagelbot can perform is 10 x 15 = 150.

This means that Bagelbot can potentially redirect up to 150 pieces of mail between officials from A and officials from B.

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The Median and IQR are most appropriate to describe the measures of center and variability of distribution. The histogram depicts the distribution of time is positively skewed. So, option(b) is right one.

We have a graph present in above figure, which showes the amount of time in hours spent on homework per week for a sample of students. We have to select correct measures of center and variability. The graph is a histogram. From the graph we can see that the data is positively skewed. Now for skewed distribution we prefer median over mean as mean is more sensitive to the outliers. As the data(time) is in ratio scale we can use any of the measures of dispersion; but for skewed distribution IQR is preferred because of its robustness. In a word both median and IQR can handle outliers. Thus the appropriate answer is Median and IQR, option (c).

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Complete question :

The above figure complete the question

the graph below displays the amount of time to the nearest hour spent on homework per week for a sample of students. which measures of center and variability would be most appropriate to describe the given distribution? group of answer choices

a) mean and standard deviation

b) mean and iqr

c) median and standard deviation

d) median and iqr

e) median and range

The two quantities needed to determine the total amount of money Monte paid his employees this month are:

A. the hourly salary of each employee

C. the number of hours each employee worked this month.

With four employees at the Monte Bakery, who earn a different hourly wages, to work out the total salary for the month, Monte needs to multiply the hourly wage of each employee by the total number of hours each worked.

Thus, in this mathematical operation, we first use multiplication and then add each individual employee's total salary to sum the total salary for the month.

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The power of -1 to a function, or [tex]((f^{-1})(x)),[/tex]represents the inverse function of f. In other words, if f(x) produces a certain output y, then the inverse function[tex]f^{-1}(y)[/tex]will produce the input x. It is important to note that not all functions have an inverse, and if they do, they may only be valid for certain inputs and outputs.

In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f1. The inverse of f exists if and only if f is bijective.

[tex]((f^{-1})(x)),[/tex]

The inverse function of f is denoted by. For a function, its inverse admits an explicit description: it sends each element to the unique element such that f(x) = y1.

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The correct answer is false. A reduced echelon matrix [tex]T(x) = 0[/tex] with a row of [tex][0 . . 0 | 0] or [0 . . . 0 | b][/tex], where[tex]b \neq 0[/tex], is not considered one-to-one.

Let's first define what it means for a matrix to be one-to-one.

A matrix is said to be one-to-one if each column of the matrix is linearly independent.

This means that for any given input, there is only one possible output.
Now, let's consider the reduced echelon matrix T(x) = 0. If this matrix has a row of [tex][0 . . 0 | 0] or [0 . . . 0 | b][/tex], b ≠ 0, it means that one of the variables in the system of equations represented by the matrix is a free variable.

This free v[tex]T(x) = 0.[/tex]ariable can take on any value, and the other variables will adjust accordingly.
If the reduced echelon matrix is [tex][1 0 | 2; 0 0 | 0],[/tex] the system of equations would be [tex]x = 2[/tex] and y can be any value.

This means that the matrix is not one-to-one, because there are multiple outputs for the same input.
the correct answer is false.

A reduced echelon matrix[tex]T(x) = 0[/tex] with a row of [tex][0 . . 0 | 0] or [0 . . . 0 | b][/tex], where [tex]b \neq 0[/tex], is not considered one-to-one.

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Answer: The answer is 84

The total of the angels of the triangle always equals 180. So 62+34=96 therefor 96-180=84.

Answer:

[tex]f(x) = (x + 2)(x - 12)[/tex]

[tex]f(x) = {x}^{2} - 10x - 24[/tex]

A four members of the Harrison family save  $896 on airfare by vacationing in Vancouver.

Here, the airplane tickets to Fairbanks Alaska will cost $958 each.

⇒ c₁ = $958

where c₁ represents the airfare to Fairbanks Alaska

and the airplane tickets to Vancouver Canada will cost $734.

⇒ c₂ = $734

Let us assume that s represents the amount of savings per ticket.

⇒ s = c₁ - c₂

⇒ s = 958 - 734

⇒ s = $224

Since there are four members in the family.

So using unitary method the total savings would be,

⇒ t = 4 × s

⇒ t = 4 × 224

⇒ t = $896

Therefore, the total savings =  $896

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The complete question is:

Airplane tickets to Fairbanks Alaska will cost $958 each. Airplane tickets to Vancouver Canada will cost $734. How much can the four members of a Harrison family save on airfare by vacationing in Vancouver?

Step-by-step explanation:

We can use trigonometry to solve this problem. The grade of the road is given as an angle of 9.5°. This means that for every 1 unit of horizontal distance traveled, the elevation changes by the tangent of 9.5°.

We want to find the change in elevation for a car descending the 4-mile stretch. To do this, we can multiply the length of the road by the tangent of the grade angle:

Change in elevation = 4 miles x tan(9.5°)

Using a calculator, we can find that tan(9.5°) = 0.1664. Substituting this value into the equation, we get:

Change in elevation = 4 miles x 0.1664 ≈ 0.67 milesTo convert this to feet, we can multiply by the number of feet in a mile:

Change in elevation = 0.67 miles x 5,280 feet/mile ≈ 3,539 feetTherefore, the change in elevation for a car descending the 4-mile stretch is approximately 3,539 feet.

The total surface area of the prism is  177.2 m².

The total surface area of the prism is calculated by applying the formula for total surface area of prism.

S.A = bh + (s₁ + s₂ + s₃)L

where;

The surface area of the prism is calculated as;

S.A = 4 m (3 m) + (3.8 m + 4 m + 4 m) x 14 m

S.A = 177.2 m²

Thus, the surface area of the prism is calculated using the formula for surface of right prism.

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