Answer:
Step-by-step explanation:
A reflection across the line y = x will not carry the square onto itself, since the vertex (0, 2) would be reflected to (2, 0) which is not a vertex of the original square.
A reflection across the line y = -x would also not carry the square onto itself, since the vertex (0, 2) would be reflected to (−2, 0) which is not a vertex of the original square.
However, a reflection across the x-axis would carry the square onto itself since all of the vertices lie in the same quadrant, and reflecting across the x-axis does not change their signs.
A 45° or 90° rotation about the origin would also carry the square onto itself since the square has rotational symmetry of order 4.
Therefore, the correct answers are C, D, and E.
If a driver travels 40 mph, what is his ratio of miles to minutes?
If a driver travels at the speed of 40 mph, then the ratio of his speed in miles to minutes would be equal to 2/3 miles per minute.
The problem is based on simple conversion of units of speed from SI system to imperial system (it is named so because it was discovered in Britain). The speed of the driver is 40 mph that is 40 miles per hour. It means that to convert it into the ratio of miles and minutes, the relation between minutes to hours is to be known.
It is known that one hour is equal to 60 minutes. Therefore speed of driver is calculated as 40/60 miles per minute, which is equal to 2/3 miles per minute.
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Find the missing base of the parallelogram described.
There has been a 3% change in the money supply and a 1% change in velocity. In order to balance the exchange equation, what percentage of change needs to occur on the right side of the equation?
A. 1%
B. 4%
C. 7%
To balance the equation, the right side of the equation must also change by 4%.
What is equation?
An equation is a mathematical statement that asserts the equality of two expressions. It consists of two sides, a left-hand side (LHS) and a right-hand side (RHS), separated by an equals sign (=)
To balance the exchange equation, the percentage change on the left side of the equation [tex](\% \triangle M + \% \triangle V)[/tex] must equal the percentage change on the right side of the equation [tex](\% \triangle P + \% \triangle Q)[/tex].
Given that there has been a 3% change in the money supply [tex](\% \triangle M)[/tex] and a 1% change in velocity [tex](\% \triangle V)[/tex], the left side of the equation can be written as:
[tex]\%\triangle M + \%\triangle V = 3\% + 1\% = 4\%[/tex]
To balance the equation, the right side of the equation must also change by 4%. Therefore, the correct answer is:
B. 4%
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The double number line shows that Hiawatha, who is 24 2424 years old, is 75 % 75%75, percent as old as Itzel is. A double number line with 2 tick marks. The line labeled Age, years, reads from left to right: 0, 24. The line labeled Percentage, reads from left to right: 0 percent, 75 percent. A double number line with 2 tick marks. The line labeled Age, years, reads from left to right: 0, 24. The line labeled Percentage, reads from left to right: 0 percent, 75 percent. Complete the table to show different percentages of Itzel's age.
The double number line shows that Hiawatha is 75% as old as Itzel. This means that Hiawatha's age is 75% of Itzel's age. If we let Itzel's age be x, then Hiawatha's age is 0.75x.
What is double number line?A double number line is a visual representation of two related numerical quantities, such as distance and time or cost and quantity.
It consists of two parallel lines that are divided into equal segments or tick marks.
Each line represents one of the quantities, and the tick marks show the values or measurements of that quantity.
To complete the table showing different percentages of Itzel's age, you can choose different values of x and then calculate 75% of that value to find Hiawatha's age. For example:
If Itzel is 20 years old, then Hiawatha is 0.75 x 20 = 15 years old (since he is 75% as old as Itzel).
If Itzel is 40 years old, then Hiawatha is 0.75 x 40 = 30 years old.
If Itzel is 60 years old, then Hiawatha is 0.75 x 60 = 45 years old.
You can continue this pattern for different values of Itzel's age to complete the table.
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The double number line demonstrates that Itzel is 75% older than Hiawatha, who is 24 years old.
Itzel is 25% older than Hiawatha, who is 8 years old.
Itzel is 100% older than Hiawatha, who is 32 years old.
What is double number line?The visual representation of two linked numerical quantities, such as length and time or price and quantity, is called a double number line.
Two parallel lines that have been separated into equal pieces, or tick marks, make up the object.
The tick marks on each line denote the values or measurements of each quantity, and each line represents one of the quantities.
You can select various numbers of x and then multiply that number by 75% to determine Hiawatha's age in order to finish the table that displays various percentages of Itzel's age.
The double number line demonstrates that Itzel is 75% older than Hiawatha, who is 24 years old.
(24/3) = 8 => 25% of Itzel's age
(8*4) = 32 => 100% of Itzel's age
From the double number line
Age (years) Percentage
[24] 75% of Itzel's age
[ 8] 25% of Itzel's age
[32] 100% of Itzel's age
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The complete question is attached below,
The ratio of boys to girls is 3:2, if the total number of children in the class is 35, how many boys are there?
PLSSS HELPP NOWW!!!!!
Answer:
21 boys
Step-by-step explanation:
girls 3+3=6+3=9+3=12+3=15+3=18+3=21
boys 2+2+2=6+2=8+2=10+2=12+2=14
3times 7=21
2 times 7 equals 14
so 21+14=35
Rewrite each equation in vertex form by completing the square. Then, give the key features revealed by both equations.
Question 7.
The vertex form of the equation is:
y = a(x - h)² + k, where a = 1, h = 1, and k = -16
How to explain the equationIt should be noted that to rewrite the equation in vertex form by completing the square, we first need to factor out the coefficient of x²:
y = x² - 2x - 15
y = (x² - 2x + 1) - 16
y = (x - 1)² - 16
Here, the vertex form of the equation is:
y = a(x - h)² + k, where a = 1, h = 1, and k = -16
The key features revealed by both equations are:
Vertex: The vertex of the parabola is (1, -16).
Axis of symmetry: The axis of symmetry is the vertical line x = 1.
Minimum/Maximum: Since the coefficient of x² is positive, the parabola opens upwards, and the vertex represents the minimum point of the graph.
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Keith took a four question test. He got 1 and a half of a question wrong. What is his final score?
Keith took a four question test and got 1 and a half questions wrong. His final score is 2.5 out of 4, or 62.5%.
To calculate Keith's final score, you need to divide the number of correct answers by the total number of questions. In this case, Keith answered 2.5 out of 4 questions correctly. Therefore, his final score is 2.5 divided by 4, which equals 0.625. This is equal to 62.5%.
To summarize, Keith took a four question test and got 1 and a half questions wrong, giving him a final score of 62.5%.
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The area of a square garden is 300 m². How long is the diagonal?
5√6 m
150 m
10√6 m
900 m
Answer:10root6
Step-by-step explanation:
what is the radical equivalent to s^3/2
Answer:
√1.5
Step-by-step explanation:
As a fraction, the square root of 3/2 can be expressed as √1.51 or just as √1.5.
A sports scout for a team is looking for the more consistent player. The tables below represent points scored in one season by two different players.
Player A
3 rows
and 5 columns
10, 12, 6, 10, 13, 8, 12, 3, 21, 14, 7, 0, 15, 6, 16
Player B
3 rows and 5 columns
10, 3, 12, 26, 20, 24, 25, 26, 5, 48, 24, 18, 20, 27, 25
Compare the data in the tables. Which player should the scout choose? Explain your answer.
Based on the given information, the scout should choose Player A if they are looking for consistency.
What are range and standard deviation?
Range is the difference between the highest and lowest scores in the set.
Standard deviation measures how spread out the scores are from the mean.
To determine which player is more consistent, we need to look at the variability in their scores. One way to measure variability is to calculate the range and the standard deviation of each player's scores.
The smaller the range, the more consistent the player's scores are.
A smaller standard deviation indicates that the scores are closer together, which means the player is more consistent.
Using the data provided, we can calculate the range and standard deviation for both players:
Player A:
Range = 21 - 0 = 21
Standard deviation = 5.70
Player B:
Range = 48 - 3 = 45
Standard deviation = 10.89
From these calculations, we can see that Player A has a smaller range and a smaller standard deviation, which means that their scores are more consistent than Player B's. Therefore, the scout should choose Player A if they are looking for consistency.
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given the arithmetic sequence what is the domain for N?
The domain for n in the arithmetic sequence is the one in the first option:
all integers where n ≥1
What is the domain of N?We have a arithmetic sequence defined by the general formula:
aₙ = 4 - 3*(n - 1)
And we want to find the domain for the possible values of n that we can use in that formula.
Remember that the terms of a sequence are defined as:
a₁, a₂, a₃,...
So the values of n are positive whole numbers, in this case the first one is n = 1.
a₁ = 4 + 3*(1 - 1)
a₁ = 4
And then we can keep using any positive integer, then the correct option is:
all integers where n ≥1
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Determine whether the relation is a function (3,0),(6,-2),(2,-1),(-7,0)
Yes, this relation is a function and here the domain and range are:
domain = {3,6,2,-7} and range ={0,-2,-1,0}
Domain and Range:
The domain and scope of a function are part of the function. The domain is the set of all input values of a function, and the range is the possible outputs given by the function. Field → Function → Sequence. If there is a function f : A → B such that each element of set A corresponds to an element of set B, then A is the field and B is the codomain. The graph of an element "a" under a relation R is given by "b", where (a,b) ∈ R.
The scope of the function is the set of images. The domain and range of a function are usually expressed as:
Domain(f) = {x ∈ R: State} and range(f)={f(x): x ∈ domain(f)}
According to the Question:
The given function is:
{(3,0),(6,-2),(2,-1),(-7,0)}
It is a function as every input has a single output.
So, 3,6,2,-7 are the elements of the domain of the given relation.
Here domain = {3,6,2,-7} and range ={0,-2,-1,0}
Therefore, this relation is a function.
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A small circle is centered inside of a larger circle. The large circle has a radius of 10 inches. The small circle has a radius of 3 inches.
Answer: 126in
Step-by-step explanation:
ftc6yhunum8im
huju7kt6r
5+10=24
g5ghykn
an airplane 32,000 feet above the ground begins to descend at a rate of 2,250 feet per minute .Assuming the plane continues the descend at the same rate write an equation to model the height h of the plane ,t minutes after it began its descent. Then find the height of the plane after 6 minutes
After answering the presented question, we can conclude that equation Therefore, the height of the plane after 6 minutes of descending is 19,500 feet.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
h(t) = 32,000 - 2,250t
h(6) = 32,000 - 2,250(6) = 19,500 feet
Therefore, the height of the plane after 6 minutes of descending is 19,500 feet.
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the depth of water in a tank oscillates once every 6 hours. if the smallest depth is 5.5 feet and the largest depth is 8.5 feet, find a possible formula for the depth in terms of time in hours.
The depth of water in a tank oscillates once every 6 hours, with a smallest depth of 5.5 feet and a largest depth of 8.5 feet. This can be expressed in a formula as a function of time in hours. The formula is: Depth = 5.5 + (3/2) * sin(2πt/6)
The formula is: Depth = 5.5 + (3/2) * sin(2πt/6), where t is the time in hours. This formula expresses the oscillating nature of the water level, which ranges from 5.5 to 8.5 feet. The sine function used in the formula reflects the oscillation of the depth. The frequency of the oscillation is determined by the factor (2πt/6) and the range is determined by the amplitude (3/2).
To better understand this formula, consider the example of a tank with a depth of 5.5 feet when the time is 0 hours. After 6 hours, the time has increased to t = 6 and the formula yields a depth of 8.5 feet. This shows that the formula is correctly representing the oscillation of the water level, with an amplitude of 3/2.
To summarize, the formula for the depth of water in a tank oscillating once every 6 hours with a smallest depth of 5.5 feet and a largest depth of 8.5 feet is given by the expression Depth = 5.5 + (3/2) * sin(2πt/6). This formula incorporates a sine function with a factor (2πt/6) and an amplitude of 3/2. The factor determines the frequency of the oscillation, while the amplitude determines the range of the oscillation.
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The assets and liabilities of a local surf shop are listed below. Building Mortgage $100,650 Other Debt $45,780 Accounts Receivable $11,261 Property Value $181,975 Long Term Investments $138,000 Small Business Loan $22,698 Long Term Liabilities $35,000 Owned Inventory $32,990 Cash $219,783 Savings Account $148,321 Owned Equipment $35,872 The surf shop owner receives notice that the property value has increased by $20,000. What is the net worth of the surf shop?
The net worth of the surf shop is $585,074.
What is total cost?The variable and fixed cost of providing commodities are combined to create a total using the total cost formula.
First, we need to add the $20,000 increase in property value to the existing value to get the new property value:
$181,975 + $20,000 = $201,975
Next, we can add up the values of all the assets:
Owned inventory + Cash + Savings account + Accounts receivable + Owned equipment + Property value + Long-term investments
= $32,990 + $219,783 + $148,321 + $11,261 + $35,872 + $201,975 + $138,000
= $788,202
Then we can add up the values of all the liabilities:
Building mortgage + Small business loan + Other debt + Long-term liabilities
= $100,650 + $22,698 + $45,780 + $35,000
= $203,128
Finally, we can subtract the total liabilities from the total assets to find the net worth of the surf shop:
Net worth = Total assets - Total liabilities
= $788,202 - $203,128
= $585,074
Therefore, the net worth of the surf shop is $585,074.
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what is the polynomial of the shaded region?
The polynomial that represents the area of the shaded region is 7x-1 ( optionA)
What is area of a shape?The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares
Therefore, the area of the shaded region = area of the big rectangle - area of the small rectangle
area of the big rectangle = l×b
= (x-1)(x+5)
= x²+5x -x -5
= x²+4x-5
area of the small rectangle = l×b
=( x+1)(x-4)
= x²-4x+x-4
= x²-3x-4
therefore area of the shaded part
= x²+4x-5 - (x²-3x-4)
= x²+4x-5-x²+3x+4
collect like terms
x²-x²+4x +3x+4-5
= 7x -1
therefore the polynomial that represents the area of the shaded part is 7x-1
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the square region shown has been partitioned into 5 identical rectangular regions. if the perimeter of each of the rectangular regions is 30, what is the perimeter of the square region?
Given that the square region has been partitioned into 5 identical rectangular regions, and the perimeter of each rectangular region is 30. We are to find the perimeter of the square region.
As we know that the perimeter of a rectangle is given by P= 2 (l + b)
Let's say the length of the rectangle is 'l' and the breadth of the rectangle is 'b'. Since the five rectangular regions are identical, all of them will have the same length and breadth. Let's take the length and breadth of each rectangular region as x and y respectively. So, the perimeter of each rectangular region is given by P = 2(x + y) = 30Given P = 30, we get2(x + y) = 302x + 2y = 30x + y = 15... equation (1)
We know that the square region is partitioned into 5 identical rectangular regions. Therefore, the length of the square region will be 5 times the length of the rectangular region and the breadth of the square region will be the same as the breadth of the rectangular region. So, length of the square region = 5x, and breadth of the square region = y.
The perimeter of the square region = 2(5x + y) = 10x + 2yAs we know that x + y = 15 (from equation 1)So, 10x + 2y = 10(x + y) + 8y= 10(15) + 8y= 150 + 8y. Therefore, the perimeter of the square region is 150 + 8y.
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pls answer quickly will give brainlyist
Answer:12/25=sind*cosd
3/5=sinc
4/5=sind
16/15=tand*cosc
Step-by-step explanation:
please mark brainliest
123000000 as a power of 10
Answer:
123,000,000 as a multiple of a power of 10 is
1.23 x 10⁸ .
in 1996, a total of 40,257,000 taxpayers in the united states filed their individual tax returns electronically. by the year 2015, the number increased to 241,364,256. what is the geometric mean annual increase for the period? (round your answer to 2 decimal places.)
The information indicates that the correct answer is 9.76% annually.
What do you mean by geometric?The area of mathematics that deals with the characteristics of surrounding space, spatial interactions between distinct objects, and the shape of particular items.
It would take 19 years between 1996 and 2015 in all.
We are aware that the equation: gives a geometric mean of a collection of n positive numbers.
GM = [tex]((x1)(x2)(x3).............)^{1/n}[/tex]
This would provide us with the product of these values' nth roots.
Thus, the following would be the formula indicating rate of rise over time: -
GM = [tex](value at the end of the period / value at the start of the period)^{1/n} -1[/tex]
[value at the end of the period / value at the start of the period
Value at the conclusion of the time is equal to 241,364,256, hence the statement stands.
The initial value was 40,257,000.
n = 19
Using values, we obtain:
=[tex](241,364,256/40,257,000)^{1/19} -1[/tex]
= (5.995)1/19 - 1
= 0.0976
= 9.76% per year
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The triangle below is equilateral. Find the length of the side x to the nearest tenth.
To the nearest tenth, the length of each side of the equilateral triangle is roughly [tex]10(\sqrt{(3) - 1)[/tex].
What characteristics define equilateral?An equilateral triangle has the following three characteristics: identical lengths on all three sides. The three angles are identical. Three symmetry lines may be seen in the figure.
All of the triangle's sides are equal in length since it is equilateral. Call this length "s" for short.
The distance from vertex A to side x, measured in altitude, is equal to the length of side x. Call the intersection of the altitude and side x "P" for short.
The length of AP is [tex](s/2) * \sqrt{}[/tex] because we know that the altitude from vertex A creates a triangle with sides of 30-60-90. (3).
Since side BP is half the length of side AB, we also know that its length is (s/2).
As a result, x's length equals the product of AP and BP:
x = AP + BP
= (s/2) * [tex]\sqrt{(3) + (s/2)[/tex]
= [tex](s/2)(\sqrt{(3) + 1)[/tex]
We are told that x equals 10. We may put the formula we discovered for x equal to 10 and do the following calculation to find s:
[tex](s/2)(\sqrt{(3) + 1)[/tex] = 10
The result of multiplying both sides by two is:
[tex]s(\sqrt{(3) + 1) = 20[/tex]
When you divide both sides by [tex](\sqrt{(3) + 1)[/tex], you get:
[tex]s = 20/(\sqrt{3) + 1)[/tex]
The result of multiplying the numerator and denominator by the conjugate of [tex](\sqrt{(3) + 1), (\sqrt{(3) - 1)[/tex], is as follows:
s = [tex]20(\sqrt{3) - 1)/(3 - 1)[/tex]
= [tex]10(\sqrt{(3) - 1[/tex]
As a result, to the nearest tenth, the length of each side of the equilateral triangle is about [tex]10(\sqrt{(3) - 1[/tex].
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Use the formula V = s³, where V is the volume and s is the edge length of the cube, to solve this problem.
A cube-shaped box has an edge length of 45 meter.
What is the volume of the container?
Enter your answer, as a fraction in simplest form, in the box.
The volume of the container is 91125 cubic meters.
What is volume?
A measurement of three-dimensional space is volume. It is frequently expressed numerically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are related.
A sphere is the most basic and typical form of a three-dimensional shape. A sphere's radius is the simplest parameter to measure. The radius of the sphere is used to determine its volume.
Given the edge of a cube is 45 meters.
The formula of volume is V = s³.
The volume of the container is
45³
= 91125 cubic meter.
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. in a classroom of 30 students, 3 of the students wear wrist watches. (a) if 14 students are selected with replacement, what is the probability that exactly 2 of them wear wrist watches? (b) if 14 students are selected without replacement,
Probability of
=0.0403.
The probability that exactly two of the 14 students selected with replacement will wear wrist watches is 3/30 * 2/29 * 27/28 * 26/27 = 0.0437.
The probability that exactly two of the 14 students selected without replacement will wear wrist watches is 3/30 * 2/29 * 26/28 * 25/27 = 0.0403.
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Which values are in the solution set of the compound inequality? Select two options. 4(x + 3) ≤ 0 or x+1>3 –6 –3 0 3 8
The two values that are in the solution set are -6 and 4, since both of these values satisfy at least one of the inequalities in the compound inequality.
What is inequality equation?
An inequality is a mathematical statement that compares two values or expressions using one of the inequality symbols: < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).
To solve the compound inequality 4(x + 3) ≤ 0 or x + 1 > 3, we can first simplify the left-hand side of the first inequality:
4(x + 3) ≤ 0
4x + 12 ≤ 0
4x ≤ -12
x ≤ -3
Now we can solve the second inequality:
x + 1 > 3
x > 2
Therefore, the solution set for the compound inequality is all values of x that are less than or equal to -3 or greater than 2. This can be written in interval notation as:
(-∞, -3] ∪ (2, ∞)
Therefore, the two values that are in the solution set are -6 and 4, since both of these values satisfy at least one of the inequalities in the compound inequality.
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write the center of radius of the circle
To write the center and radius of a circle, we need to have the equation of the circle in standard form, which is: (x - h)² + (y - k)² = r² where (h, k) is the center of the circle and r is the radius.
What is circle?A circle is a geometrical figure that is defined as a closed shape where all the points on the boundary of the shape are at an equal distance from the center point. The center of a circle is the point which is equidistant from all points on the circumference of the circle. To determine the center of a circle, we need to follow some steps:
Step 1: Identify the coordinates of three points on the circle
To find the center of a circle, we need to know the coordinates of at least three points on the circumference of the circle. The coordinates of these points can be determined by measuring the distance of the points from the x-axis and y-axis.
Step 2: Find the perpendicular bisectors of two chords
Once we have identified three points on the circle, we need to find the perpendicular bisectors of two chords. A chord is a line segment that connects two points on the circumference of the circle. The perpendicular bisector of a chord is a line that is perpendicular to the chord and passes through the midpoint of the chord.
Step 3: The intersection of perpendicular bisectors is the center of the circle
The perpendicular bisectors of two chords will intersect at a single point. This point is the center of the circle. To verify that this point is indeed the center, we can measure the distance from the center point to the three points on the circle. If the distances are equal, then the point is indeed the center of the circle.
In summary, to find the center of a circle, we need to identify the coordinates of at least three points on the circumference of the circle, find the perpendicular bisectors of two chords, and then find the intersection of the two perpendicular bisectors. This point is the center of the circle.
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The circumference of a circle is 23π cm.
What is exact the area of the circle?
Do not round. Include correct units.
Show your process
Unit 10: Circles Homework 6: Tangent Lines (Can I please have this rounded to the nearest tenth Thank You)
A tangent line is a straight line that intersects a circle at only one point, and it is perpendicular to the radius that goes through that point.
Tangent lines are important because they help us determine the relationship between circles and other geometric shapes.
To find the tangent line to a circle, we need to first identify the point of intersection between the circle and the line.
A tangent line to a circle is a line that intersects the circle at exactly one point, called the point of tangency. The tangent line is perpendicular to the radius that intersects the point of tangency.
m = [tex]\frac{-1}{r}[/tex]
where m is the slope of the tangent line, and r is the radius of the circle.
The equation of a tangent line to a circle can be found using the point-slope form of the equation:
y - y1 = m(x - x1)
where (x1, y1) is the point of tangency and m is the slope of the tangent line.
The length of the tangent segment from the point of tangency to the point of intersection with a secant line can be found using the formula:
[tex]t^2[/tex] = s1 * s2
where t is the length of the tangent segment, and s1 and s2 are the lengths of the two segments of the secant line that intersect the circle.
In terms of calculating the tangent line, we can use the point-slope formula.
Let's say we have a circle with equation [tex]x^2[/tex] + [tex]y^2[/tex] = [tex]r^2[/tex] and we want to find the tangent line at the point (a,b).
We can start by taking the derivative of the equation with respect to x, which gives us 2x + 2yy' = 0.
Solving for y', we get y' = -x/y.
Then, we substitute the values of x and y at the point of intersection (a,b) to get the slope of the radius at that point.
Finally, we take the negative reciprocal of that slope to get the slope of the tangent line, and use the point-slope formula to find the equation of the tangent line.
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p(x) = 4x; Find p(-6)
p(x)= (x-4)²-(x-6)². ... 4X - 20 = 0 => X = 20/4 => X= 5.
suppose the first and the last page of the document must be printed in color, and only two printers are able to print in color. the two color printers can also print black-and-white. how many ways are there for the 100 pages to be assigned to the four printers?
If the first and last pages of a document must be printed in color, and only two printers can print in color, then there are a total of 4⁹⁹ ways that 100 pages can be assigned for printing to four printers.
The fundamental principle of counting says that if there are p ways to do one thing and q ways to do another thing, then there are p×q ways to do both things. Number of printers that is able to print in color = 2
Number of colors printed by printers = 2
We have to determine the number of ways are there for the 100 pages to be assigned to the four printers. Now, consider there are no restrictions. Let's break this problem into two parts. First, we have to print 2 pages in color and there are only two color printers. So, number of ways to print the first and the last page of the document = 2²
= 4
Number of remaining pages of document = 98
Number of avaliabile printers = 4
Now, second part, we have only 98 pages (out of 100 pages, 2 colors pages are already printed). Each of these 98 pages can be assigned to a printer in 4 ways. So, number of ways to print remaining 98 pages of document = 4⁹⁸.
Using the counting principle, number of ways for printing the 100 pages by four printers = 2² × 4⁹⁸
= 4 × 4⁹⁸ = 4⁹⁹
Hence, required number of ways are 4⁹⁹.
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