After covering a distance of 160-mile rental cost of both company will become same.
How to solve inequalities?Mathematical expressions with the symbols >,<, ≥ and ≤ are known as inequality. Finding a range, or ranges within ranges, of values that an unknown x can have while still satisfying the inequality is referred to as "solving" an inequality. Inequalities are resolved using graphs and algebra. It is imperative that you practice the techniques described here a lot so they become second nature if you want to master them.
An inequality still exists if the same amount is added to both sides. The inequality still holds true if the same amount is subtracted from each side. An inequality still holds true if both sides are multiplied or divided by the same positive value. However, if both sides of an inequality are multiplied or divided by a negative value, the inequality is no longer valid. In actuality, the inequity is turned around.
Solving according to ques,
Let us represent distance covered be X miles.
$100+($0.30) X = $20 + ($0.80) X
subtracting $20 and ($0.30) X from both sides, we get
$80 = ($0.50) X
X = 160 mile.
So, rental costs for company will be same when bot the trucks will cover a distance of 160 mile.
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Can someone help me with this question?
Consider the mathematical sentence 2 = 2.
Is there any variable or constant that you could add to or subtract from both sides, or
multiply or divide both sides by using the Properties of Equality to make this true sentence false? Choose variables and constants to create new mathematical sentences to justify your conclusion.
If a statement is true, then it cannot be falsified no matter what.
A true statement will yield a true statement.
A false statement can yield a true or false statement.
The answer to your question is no, we cannot do anything to make the statement "2=2" false
pls help me with this problem
Answer:
Step-by-step explanation:
Hi
Answer:
The mean price for this sample is $1,385.00
Step-by-step explanation:
⭐What is the "mean" of a sample?
The mean of a sample is another word for the average of said sampleYou add up all the values and divide that sum by the number of values presentTo find the mean for this data, we need to divide the sum of the prices for the computers bought by the total number of computers bought.
Sum of the prices for the computers:
[tex]14(1400)+12(1050)+5(2150)[/tex]
[tex]= 19,600 + 12,600 + 10,750[/tex]
[tex]= 42,950[/tex]
Total number of computers bought:
[tex]14+12+5[/tex]
[tex]= 31[/tex]
Mean price:
[tex]\frac{42,950}{31}[/tex]
[tex]= 1,385.00[/tex]
How do you prove two overlapping triangles are congruent?
If the two triangle are overlapping , then they are congruent.
The term congruent refers the triangles that have three sets of corresponding congruent sides and three sets of corresponding congruent angles.
Here we have to prove that the two overlapping triangles are congruent.
Here we know that the two triangle are overlappling.
Now we have to do the following process to prove that the overlapping triangles are also congruent.
As per the reflexive property of congruence, here when overlapping triangles share a common side or angle because the reflexive property of congruence states that a segment or angle is congruent to itself. Therefore, according to the geometry when two triangles share a side or angle this can be used to prove one set of congruent sides/angles.
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S Ivy deposited $530 into a savings account
9 years ago. The account earns 33%
interest, compounded annually. How much
interest has she earned? Answer in dollars
and round to the nearest cent.
Interest earn is $6,371.45 ≅ $6,370 (round to the nearest cent)
What is earned?To receive as return for effort and especially for work done or services rendered. : to bring in by way of return.
What is compound interest?When you earn interest on your interest earnings as well as the money you have saved, this is known as compound interest. A = P is the compound interest formula.
A = P[tex](1 + r/n)^{nt}[/tex]
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
$530 for 9 years at 33% interest each year using the compound interest formula, where t = number of time periods elapsed
A = P[tex](1 + r/n)^{nt}[/tex]
A= 530 (1 + 0.33/1)^9
A = $6,901.45
So to find interest I = A-P
I = $6901.45 -$530
I = $6,371.45
Interest earn is $6,371.45 ≅ $6,370 (round to the nearest cent)
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How many solutions does y 0 and y =- 6 has?
The system of equations has no solution because they are parallel lines.
What is the equation?The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.
In general, any equation of the form y = k, where k is a constant, represents a horizontal line that extends indefinitely in both directions.
The system of equations y=0 and y=-6 describes two lines in the coordinate plane.
The first equation, y=0, is the x-axis.
The second equation, y=-6, is a horizontal line 6 units below the x-axis.
As we know, y = 0 and y = -6 are two parallel lines.
Therefore, no solution exists.
Hence, the system of equations has no solution.
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What are the 3 possible solution that you can obtain when solving a system of linear equations
There are three ways to solve systems of linear equations in two variables:
graphing.substitution method.elimination method.System of Linear Equations :
A system of linear equations is two or more linear equations that are being solved simultaneously.
Solution of a System :
In general, a solution of a system in two variables is an ordered pair that makes BOTH equations true. In other words, it is where the two graphs intersect, what they have in common. So if an ordered pair is a solution to one equation, but not the other, then it is NOT a solution to the system.
A consistent system is a system that has at least one solution.
An inconsistent system is a system that has no solution.
There are three ways to solve systems of linear equations in two variables:
graphing substitution methodelimination method
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help???????????????????
The equation with a solution s = 3/4 is the second option:
4s = 3
Which equation has the given solution?We want to see which of the given equations has a solution s = 4/3.
What you can do is take all the given equations and solve them, for example, if I solve the first one:
s - 1 = 1/4
We will get:
s = 1 + 1/4 = 5/4
So this one is not the correct one.
The second equation is:
4s = 3
Dividing both sides by 4:
s = 3/4
So this is the correct option.
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What is the sum of roots of 3x² 10x 8 0?
The sum of the roots of 3x² 10x 8 0 is -2.
The given equation, 3x² 10x 8 0, is a quadratic equation with two roots. To find the sum of the roots of this equation, we must first solve the equation. To do this, we use the quadratic formula, which states that the roots of the equation are x = [-b ± √(b² - 4ac)]/2a. Here, a = 3, b = 10 and c = 8.
Therefore, the roots of the equation are x = [-10 ± √(10² - 4(3)(8))]/2(3). This simplifies to x = [-10 ± √(-4)]/6. Since the square root of a negative number is not a real number, the roots of the equation are not real numbers, and the sum of the roots is undefined. Therefore, the sum of the roots of 3x² 10x 8 0 is -2.
x = [-10 ± √(10² - 4(3)(8))]/2(3)
x = [-10 ± √(-4)]/6
x = [-10 ± √(-4)]/6
Since the square root of a negative number is not a real number, the roots of the equation are not real numbers, and the sum of the roots is undefined.
Therefore, the sum of the roots of 3x² 10x 8 0 is -2.
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Annie scored 29 out of 35 marks in a test.
What percentage of the test did Annie get correct?
Give your answer to 1 decimal place.
If x has a percentage of 10 and that is equal to y at 100 percent. Then if x is at 100 percent, what is the percentage of y?
If x has a percentage of 10% and that is equal to y at 100%, then x is equal to 10% of y. If x is at 100%, then the percentage of y would be 1000%.
Here's how to arrive at this answer:
First, let's set up the equation to represent the given information:
x = 10% * y
If we solve for y in this equation, we get:
y = x / (10%)
Now, if we set x equal to 100%, we get:
y = (100%) / (10%)
Simplifying this fraction gives us:
y = 10
Since y is equal to 10, the percentage of y is 1000%.
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given triangle ABC find the values of x and y. In your final answer, include all of your calculations.
Answer:
Step-by-step explanation:
X = ?
y = ?
The big triangle ABC is a right triangle, we can use Pythagoras theorem to find side y, then use SOH CAH TOA to find angles :)
also, there is a special rule for a triangle set up like this one
2CD = BD
for this triangle then,
2CD = 9
CD = 4.5
X = 13.5
now use Pythagoras to find y
[tex]13.5^{2}[/tex] = [tex]6^{2}[/tex] + [tex]y^{2}[/tex]
182.25 -36 = [tex]y^{2}[/tex]
[tex]\sqrt{146.25}[/tex] = y
12.093386 = y
now that you have all 3 sides of the big triangle, use which ever trig function you are most comfy with to find angle B or C, i'll find C
CAH = Cos(C) = Adj / Hyp
Cos(C) = 6 / 13.5
arcCos(Cos(C)) = arcCos(6/13.5)
C = 63.6122°
now find B
180 = 90 + 63.6122 + B
26.3877° = B
got it?
Can we use AAA congruence criteria to make two congruent triangle give reason?
The sides of a triangle with all respective angles equal, i.e. AAA condition, may or may not be equal. Only if two triangles with the same respective angles are identical would the congruence stay true.
Knowing only angle-angle-angle (AAA) does not work because it can produce similar but not congruent triangles. When you're trying to determine if two triangles are congruent,
there are 4 shortcuts that will work. Because there are 6 corresponding parts 3 angles and 3 sides, you don't need to know all of them. If the three angles (AAA) between two triangles are congruent, that does not imply that the triangles must be congruent. They have the same shape (and can be considered comparable), but we don't know how big they are.
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C. P. =Rs 50,s.p.=Rs 65
Answer: Profit = Rs 15, Profit %= 30%
Step-by-step explanation: When S.P.( Selling Price) is greater than C.P.(Cost Price), there is a Profit.
Profit= S.P-C.P
Hence Rs 15 is the profit.
To calculate Profit %, we use the formula Profit ÷ C.P. × 100%
Hence, the Profit % is 30%.
a group of seven people are attending the movies together. (a) two of the seven insist on sitting side-by-side. in how many ways can the seven be seated together in a row? (b) two of the people do not like each other and do not want to sit side-by-side. now how many ways can the seven be seated together in a row?
The probability of 2 people insists on sitting side by side is 2/7. In the next, the probability of 2 people insists on sitting side by side is 2/5
What is probability?The possibility of occurring a particular events is called probability.
it is expressed in ratio of two data. The probability has no unit to measure.
how to calculate probability?Number of students =7, among them 2 are insists on sitting side by side
now probability to sit in such a way = 2/7
again, 2 students will never sit side by side so the number became 5.
probability to sit side by side = 2/5
hence, the result is 2/7 and 2/5
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find sin2theta and cos2theta and tan2theta if cos theta is 1/3 and theta is less than 360 but greater than 270
someone help!!
Answer:
sin2theta
= (4root2)/9
cos2theta = -7/9
tan2theta
= (4root2)/-7
Step-by-step explanation:
see image.
Draw a picture to help see your angles and the triangle trigonometry. Use Pythagorean theorem and triangle trig to find sintheta and tantheta. Use Double Angle Formulas to find the answers to the question. See image.
The value of the sin 2θ, cos 2θ, and tan 2θ will be - 0.628, -0.778, and 0.808, respectively.
What is trigonometry?Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
The trigonometric equation is given below.
cos θ = 1/3
cos θ = 0.3333
θ = 289.47°
The value of the sine of angle 2θ will be given as,
sin 2θ = sin (2 × 289.47°)
sin 2θ = sin 578.94°
sin 2θ = -0.628
The value of the cosine of angle 2θ will be given as,
cos 2θ = cos (2 × 289.47°)
cos 2θ = cos 578.94°
cos 2θ = -0.778
The value of the tangent of angle 2θ will be given as,
tan 2θ = tan (2 × 289.47°)
tan 2θ = tan 578.94°
tan 2θ = 0.808
The value of the sin 2θ, cos 2θ, and tan 2θ will be - 0.628, -0.778, and 0.808, respectively.
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Three sisters each purchase a dress of equal value. One of the sisters purchased a purse for $26.00. If the grand total was $249.50, how much did each dress cost?
Answer:
you would take 249.50 and subtract 26.00 from it. then you would divide it by 3 for the initial cost of each dress
Step-by-step explanation:
249.50-26.00=223.05 then divide
223.05÷3= 74.05
hope that helped !
Eight people of various ages were polled and asked to estimate the number of cds they had bought in the previous year. The following table contains the collected data. The variable x represents the age. The variable y represents the number of cds. Age number of cds 18 12 20 17 24 10 25 6 28 4 30 4 32 2 34 3 using the data in the table, choose which set of axes and which set of ordered pairs should be used in making a scatter plot of the data.
The ordered pairs of the data that should be used to plot the points on the scatter plot are (18, 12), (20, 17), (24, 10), (25, 6), (28, 4), (30, 4), (32, 2), and (34, 3).
The appropriate set of axes to make a scatter plot of the data is a horizontal x-axis and a vertical y-axis. The horizontal x-axis would represent the age of the people while the vertical y-axis would represent the number of CDs bought. The ordered pairs of the data that should be used to plot the points on the scatter plot are (18, 12), (20, 17), (24, 10), (25, 6), (28, 4), (30, 4), (32, 2), and (34, 3).
A scatter plot is a graph that is used to represent the relationship between two variables. It is a graphical representation of data that shows the relationship between two variables by plotting a set of ordered pairs on a coordinate plane. The ordered pairs of the data are represented by a mark, usually a dot, on the graph. The horizontal x-axis is usually used to represent the independent variable and the vertical y-axis is used to represent the dependent variable. In this case, the x-axis is the age of the people and the y-axis is the number of CDs purchased.
A scatter plot can be used to find patterns in data and to identify relationships between two variables. By plotting the ordered pairs of the data on the coordinate plane, the scatter plot will show any correlations or trends that are present in the data. For example, if there is a positive correlation between age and the number of CDs purchased, the scatter plot will show a line of points that goes up and to the right. On the other hand, if there is a negative correlation between the two variables, the scatter plot will show a line of points that goes down and to the right. By plotting the data points on a scatter plot, it is possible to identify any patterns or trends that are present in the data.
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What is median in 7th grade math?
The median is the middle point in a dataset—half of the data points are smaller than the median and half of the data points are larger.
The data set's median is the value in the center. Put all the numbers in ascending or descending order, and then choose the middle number to determine the median. There will only be one middle integer if the number of data points is odd. If the number of data points is even, you must choose the middle two numbers, add them together, and divide by two. Your median will be that value.
Example: The median of 4, 1, and 7 is 4 because when the numbers are put in order (1,4,7)the number 4 is in the middle.
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What is the coefficient of the variable in the expression 2 − 5x − 4 8?
The coefficient of the variable x in the expression 2-5x-4+8 is -5
Given that,
The expression is 2-5x-4+8 which can be simplified as -5x+6
To find : The coefficient of the variable x in the expression
The coefficient of x in 2-5x-4+8 is -5
A number multiplied by a variable is referred to as the coefficient of a number. For instance, the x2 coefficient in the formula 6x2+99 is 6
Coefficient is the number that is beside the variable in the equation.
As we can see that the term that is in multiplication with x is -5.
Hence, the coefficient of x in the equation is -5.
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Which shows one way to determine the factors of x³ 4x² 5x 20 by grouping?
The one way of determining the factors of x³ + 4x² + 5x + 20 by grouping is (b) x²(x + 4) + 5(x + 4) .
The Grouping in a polynomial is done by the taking the GCF( greatest common factors) from the different terms .
the expression is given as : x³ + 4x² + 5x + 20 ;
in order to determine the factors by grouping ,
we first take x² common from the first two terms and 5 common from the last two terms .
we get ;
⇒ x²(x + 4) + 5(x + 4)
Therefore , the one way of determining the factors is x²(x + 4) + 5(x + 4) .
The given question is incomplete , the complete question is
Which shows one way to determine the factors of x³ + 4x² + 5x + 20 by grouping ?
(a) x(x² + 4) + 5(x² + 4)
(b) x²(x + 4) + 5(x + 4)
(c) x²(x + 5) + 4(x + 5)
(d) x(x² + 5) + 4x(x² + 5)
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36) The table below shows the growth rate of a vine over several weeks:
Week
1
3
6
9
11
Length (inches)
5
6
9
11
14
What is the average rate of change from weeks 3 to week 9?
A) 0.83
B) 0.9
C) 1.2
D) 1.1
0.83 is the average rate change of length of vine from weeks 3 to 9.
What is an average?In mathematics, the average value of a set of integers is the middle value, which is determined by dividing the sum of all values by the number of values.
When we need to get the average of a set of data, we add all the values and then divide this sum by the number of values.
Calculation:The length of the plant at the end of the third week is 6 inches.
At the conclusion of week nine, the length of the vine is 11 inches.
So the change in the length of the plant is 11-6 = 5 inches.
The change in weeks is 9-3 = 6 weeks.
We know that average growth = [tex]\frac{change in x}{ change in y}[/tex] = Δx÷Δy
∴ change in length/ change in time = [tex]\frac{5}{6}[/tex] = 0.833
0.83 is the average rate change of length of vine from weeks 3 to 9.
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What is the 3 step process in math?
Identifying the issue, considering potential solutions, and selecting the best course of action are the three primary components of problem-solving.
How the 3 step process work on mathematics?Mathematical issues can be solved in a variety of methods; however, a three-step technique is a streamlined approach that can assist anybody in solving even the most challenging problem.
Three steps is here:
1. Create a mental image of the issue
Daydreaming and the mental imagery that takes place when reading a book are two frequent instances of mental pictures. The images that athletes conjure up during practice or before a competition, describing each step they will take to achieve their objective, are another example.
2. The strategy should be used to solve the issue
A strategy is a way to manipulate numbers, use connections and interactions between numbers to solve an issue. For each procedure, there are a few key tactics. The first thing you do with the statistics is frequently used to label a technique.
3. Conclude by fixing the issue
A conclusion is a claim made after a set of premises and a set of logical principles known as syllogisms have been considered. Deduction is the process of inferring conclusions from premises and syllogisms.
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Mrs. Jain went for lunch with her friends at a restaurant which offers her a 20% discount
The total amount she needs to pay is ₹6396
What is discount?A reduction made from the gross amount or value of something.
Given that, Mrs. Jain goes to lunch with her friends at a restaurant which offers her a 20% discount. The cost of the food that they order is 6,480. Given that there is a service charge of 5% and GST is at 18%
Discount Offered is 20%, so price after discount will be-
= ₹6480-₹(20% of 6480)
= ₹5200
Service Charge she has to pay:
5% of ₹5200
= ₹260-Answer
Total Amount of Bill:
= ₹5200+Service Charge+GST
= ₹5200+₹260+₹(18% of ₹5200)
= ₹(5200+260+936)
= ₹6396
Hence, The total amount she needs to pay is ₹6396
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as a third-grade teacher, you receive the standardized test scores for mary and learn that she has gotten a stanine of 1 on the spelling subtest and a stanine of 3 on the math subtest. you should conclude that mary:
Performed at about average on spelling, but about one standard deviation below average on math.
Any test that (1) requires all test takers to answer the same questions, or a set of questions from a common bank of questions, in the same way and (2) is scored in a "standard" or consistent manner, allowing for comparison of the relative performance of individual test takers, is considered to be standardized.
Students are frequently chosen for certain programs using standardized assessments. For instance, norm-referenced examinations like the SAT (Scholastic Assessment Test) and ACT (American College Test) are used to decide whether high school students get admitted to elite institutions.
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Find the missing angles
Angle 1 is 35°, angle 2 is 65°, angle 3 is 29°, angle 4 is 115°, angle 5 is 65°, angle 6 is 36° and finally angle 7 is 144° considering the shape triangle whenever possible.
What is a triangle and what are its properties?A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.
Calculation:Considering the triangle that is containing angle 3 along with the angles 90° and 61° and as we know the sum of angles in a triangle = 180° so the angle 3 is 29°
As we know that opposite angles are equal we can say that angle 4 is 115°
Now considering the triangle that contain angle 3 which is 29° and angle 4 which is 115° we can say that angle 6 is 36° by applying sum of angles in a triangle.
Considering the triangle that consists of angles 1 , 6 and 80°+ angle 3 we can say that angle 1 is 35°
now considering the trinaglewith angles 1, 2 and 80° we can say that angle 2 is 65°
As we know that opposite angles are equal we can that angle 5 is same as angle 2 which is 65°.
Finally as angle 6 + angle 7 sum = 180° as they are on the straight line
we can say that angle 7 is 144°
Angle 1 is 35°, angle 2 is 65°, angle 3 is 29°, angle 4 is 115°, angle 5 is 65°, angle 6 is 36° and finally angle 7 is 144° considering the shape triangle whenever possible.
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HEL HELP HELP ITS DUE TODAY 700 students attend Ridgewood Junior High School. 10% of students bring their lunch to school everyday. How many students brought their lunch to school on Thursday?
Answer:
If 10% of the students at Ridgewood Junior High School bring their lunch to school every day, and there are 700 students at the school, then 10% of 700 students is equal to 0.1 * 700 = <<10*.01*700=70>>70 students.
Therefore, on Thursday, 70 students brought their lunch to school.
Is high school easy or hard?
Although it won't necessarily be harder, this will consume more of your time.
What is Workload?How much work performed by an element in a given timeframe, or the typical measure of work took care of by a substance at a specific moment of time. An estimate of an organization's performance and efficiency can be derived from the amount of work it handles. This term is used in computer science to describe the capacity of computer systems to handle and process work.
At the time of creation, components like databases and servers frequently receive an anticipated workload. Following that, a time-based comparison of their performance to the anticipated workload is carried out.
There is always more work to do in high school classes. You might have assignments that are more difficult, more homework, or more classes than you did in middle school. Although it won't necessarily be harder, this will consume more of your time.
Classes naturally become more challenging over time. After all, year after year, you tackle more difficult concepts. A component of education is that. Theoretically, middle school was "harder" than elementary school. There will be classes that are harder, and you might have to put in more work for some of them. But you should be able to handle these classes as long as you have a solid foundation. You can join the thousands of students who have made it this far.
Therefore, This will take up more of your time, despite the fact that it will not necessarily be harder.
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find a and b if the point p (6,0) and Q 3 2 lie on the graph of ax+ by
Answer:
a=b=0
Step-by-step explanation:
y=(ax)/b so now plug in the points
first 0=6a/b
next 2=3a/b
0=6a
2b=3a
a,b =0
You probably put the wrong problem but this is what I got.
b. a new ground-approach radar system approved by the federal aviation administration is being considered as a means of reducing congestion. under this system, planes can be processed at a constant rate of 15 per hour (i.e., the variance is zero). what would be the expected number of airplanes circling the airport, waiting in queue for clearance to land, if this system were to be used?
The expected number of airplanes circling the airport, waiting in queue for clearance to land, if this new radar system were to be used is zero.
The new radar system is being considered as a means of reducing congestion, which implies that there is currently an issue with congestion at the airport. One way to reduce congestion is to process planes at a faster rate, which is exactly what the new radar system aims to do.
The statement "planes can be processed at a constant rate of 15 per hour (i.e., the variance is zero)" indicates that the system is able to process planes at a consistent rate of 15 per hour, with no variation in this rate. This means that there should be no planes waiting in queue for clearance to land, as they can all be processed at the constant rate of 15 per hour. Therefore, the expected number of airplanes circling the airport and waiting in queue for clearance to land is zero.
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If all possible rearrangements of the word REVISIONS are sorted alphabetically, the n-th word is VISIONERS. What is the remainder when n is divided by 100?
Answer:
75
Step-by-step explanation:
You want the remainder when n is divided by 100, where VISIONERS is the n-th word in the alphabetically-ordered list of the permutations of REVISIONS.
Lexicographical orderThe letters of the word REVISIONS are, in alphabetic order, are EIINORSSV. We notice there are two each of the letters I and S.
When the permutations of the letters of REVISIONS are written in lexicographical order, the list will first have all of the permutations beginning with E, then those beginning with I, and so on until the permutations beginning with S are exhausted.
Counting permutationsTo find the rank (number n) of the first permutation beginning with V, we must count the number of permutations ahead of it in the list. This will be the sum of the numbers of permutations beginning with E, I, N, and so on through S.
The straightforward way to do this is to consider the letters individually, and the number of permutations associated with each one. For example, the letters following E will be the 8 letters IINORSSV, which have two repeat pairs. The number of permutations of these 8 letters is 8!/(2!·2!) = 10080.
The next leading letter in the list is I, which can be followed by any of the letters EINORSSV, for a total of 8!/2! = 20160 permutations.
The letter N will be the next leading letter, and it will have a number of permutations equal to the number for the letter E, 10080.
At this point, we have exhausted 4 of the 8 letters that must precede V in the ordered list, and have counted 10080 +20160 +10080 = 40320 permultations. We notice this is, in effect, 10080 permutations per letter, the number of permutations of the letters not including V.
If we were to work through the remaining letters (including the repeated S), we would find the total to be 8·10080 = 80640 permutations before any starting with V.
Effectively, our formula for the number of added permutations preceding words matching up to the k-th letter of our target word is ...
p(9-k)!/q
where p is the number of letters in the (remaining) ordered letter list preceding the k-th letter of VISIONERS, and q is the factor that compensates for repeated letters among those remaining. "q" is the product of the factorials of the number of times a letter is repeated. For 2 letters, each repeated once, q = 2!·2! = 4.
Application of the formulaV is the 9th letter of EIINORSSV; there are 8 letters preceding, including 2 repeated twice. k=1, so there are 8·(9-1)!/(2!·2!) = 80640 permutations preceding ones starting with V.
I is the 2nd letter of EIINORSS; there is 1 letter preceding, including 2 repeated twice. k=2, so there are 1·(9-2)!/(2!·2!) = 1260 permutations preceding ones starting with VI.
S is the 6th letter of EINORSS; there are 5 letters preceding, including 1 repeated twice. k=3, so there are 5·(9-3)!/2! = 1800 permutations preceding ones starting with VIS.
I is the 2nd letter of EINORS; there is 1 letter preceding, with no repeats. k=4, so there are 1·(9-4)! = 120 permutations preceding ones starting with VISI.
O is the 3rd letter of ENORS; there are 2 letters preceding. k=5, so there are 2·(9-5)! = 48 permutations preceding ones starting with VISIO.
N is the 2nd letter of ENRS; there is 1 letter preceding. k=6, so there are 1·(9-6)! = 6 permutations preceding ones starting with VISION.
We note that the remaining letters, ERS, are in alphabetical order, so there are no additional permutations preceding VISIONERS.
RankThen the number of permutations preceding VISIONERS is ...
80640 +1260 +1800 +120 +48 +6 = 83874
and the rank of VISIONERS is 83875.
RemainderThe remainder when this is divided by 100 is 75.
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Additional comment
The usual counting method goes into more detail than the one described here. For problems of reasonable size, it is often easier to count the permutations generated ahead of the one of interest using a "next permutation" function.
In the attachment, we generated them all, and searched for the one of interest.