The pieces are reassembled into a triangulation of the original polygon.
What is inductive hypothesis?In a proof by strong induction, the inductive hypothesis is a statement that assumes the desired property is true for all cases up to some fixed size, and then uses that assumption to prove that the property is also true for the next case.
According to information:For the proof that every simple polygon with at least three sides can be triangulated, the inductive hypothesis would be something like,
"Assume that every simple polygon with up to k sides can be triangulated for some fixed k >= 3."
In other words, we are assuming that the property is true for all polygons with up to k sides, where k is some fixed number greater than or equal to 3.
The proof then proceeds by showing that if the property is true for all polygons with up to k sides, then it must also be true for polygons with k+1 sides. This usually involves breaking the (k+1)-sided polygon into smaller pieces (using a diagonal), each of which has fewer sides and can therefore be triangulated by the inductive hypothesis. Finally, the pieces are reassembled into a triangulation of the original polygon.
By completing this proof, we have shown that the property is true for all simple polygons with at least three sides.
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The following graph represents a function.
-8-6-4
39
8
Domain: [Select]
6
P
P
-2-
-4
-6
-8
2019 StrongMind
What are the domain and range of the function?
The domain of the function is: Domain = {-8, -6, -4, -2, 1, 2} and range of the function is :- Range = {-8, -6, -4, -2, 0}.
Define function?A function is a rule that maps each element in one set, called the domain, to a unique element in another set, called the range.
It is a relation between two sets where each input in the domain corresponds to a unique output in the range.
Functions are often represented by equations, graphs, or tables, and they are used to model real-world phenomena and solve mathematical problems in various fields such as science, engineering, economics, and more.
The domain of the function is the set of all possible input values, which in this case are the x-coordinates of the given points on the graph. So, the domain is:
Domain = {-8, -6, -4, -2, 1, 2}
The range of the function is the set of all possible output values, which in this case are the y-coordinates of the given points on the graph. So, the range is:
Range = {-8, -6, -4, -2, 0}
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In a set of three lines, a pair of parallel lines is intersected by a transversal. The intersection forms eight special angles. Two of the special angles, ∠A and ∠B, are corresponding angles.
For the set of parallel lines intersected by a transversal,A = 4x andB = 2(x+14).
Use an equation to represent the corresponding angle relationship betweenA and B.
Use the equation to find the measures ofA andB.
We can solve this equation by using corresponding angle relationship between A and B , to get A= 56° and B=56°
What is corresponding angle ?
In geometry, when two lines are intersected by a transversal, the angles formed at each intersection point are called the corresponding angles. Corresponding angles are angles that occupy the same relative position at each intersection point where the transversal intersects two parallel lines.
What is equation?
In mathematics, an equation is a statement that shows the equality between two mathematical expressions using an equals sign (=). An equation can contain variables (represented by letters) and constants (fixed values).
In the given question,
The corresponding angle relationship between angle A and angle B can be represented by the equation:
angle A = angle B
Substituting the given values of angle A and B we get
4x = 2(x+14)
4x = 2x + 28
2x = 28
x = 14
Therefore angle A = 4x = 4(14) = 56°
Therefore angle B = 2(x+14) = 2(14+14) = 56°
So both angle A and B have a measure of 56°.
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A music store is selling records for $3. 00 each and cds for $1. 50 each. Write and algebraic expression to represent the cost of buying r (records) and c (cds)
The algebraic expression to represent the cost of buying r records and c CDs is given as, Cost = 3r + 1.5c
The music store is selling the records for a price of $3.00 and the CDs for $1.50 each. Let us say someone buys r number of record and c number of CDs.
So, the final algebraic expression that we will get from the above mentioned information is Cost = 3r + 1.5c.
Here, 3r represents the cost of buying "r" number of records at $3.00 each, and 1.5c represents the cost of buying "c" number of CDs at $1.50 each. By adding these two costs together, we can find the total cost of buying r number of records and c number of CDs.
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in a large population, 64% of the people have been vaccinated. if 3 people are randomly selected, what is the probability that at least one of them has been vaccinated?
The probability that at least one of three randomly selected people has been vaccinated in a large population where 64% of people have been vaccinated is 0.784.
The probability that at least one of three randomly selected people has been vaccinated in a large population where 64% of people have been vaccinated can be calculated using the binomial probability formula.
The binomial probability formula is used to calculate the probability of a given number of successes from a given number of trials when the probability of success is constant. In this case, the number of trials is 3 (i.e. the three randomly selected people) and the probability of success is 64% (i.e. the probability that each of the randomly selected people has been vaccinated).
To calculate the probability that at least one of the three randomly selected people has been vaccinated, we first calculate the probability of none of them having been vaccinated:
P(none) = (1 - 0.64)^3 = 0.216
Then, the probability of at least one of them having been vaccinated is 1 - P(none) = 1 - 0.216 = 0.784.
In conclusion, the probability that at least one of three randomly selected people has been vaccinated in a large population where 64% of people have been vaccinated is 0.784.
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In the figure, each side of square ABCD has length 1, the length of line Segment CE is 1, and the length of line segment BE is equal to the length of line segment DE. What is the area of the triangular region BCE?
A. 1/3
B. \(\frac{\sqrt{2}}{4}\)
C. 1/2
D. \(\frac{\sqrt{2}}{2}\)
E. 3/4
Thus, the area of triangular region BCE is √(1/2) / 2.
The area of triangular region BCE can be found using the formula for the area of a triangle: (1/2) * base * height. In this case, the base of triangle BCE is equal to the side length of square ABCD, which is 1. To find the height, observe that triangle BEC is a right triangle with right angle at vertex B.
Since the length of line segment BE is equal to the length of line segment DE, and CE has a length of 1, we can deduce that triangle BED is an isosceles right triangle. Therefore, the angle BEC is 45 degrees, and the angle BED is also 45 degrees.
Using the Pythagorean theorem on triangle BED, we have:
[tex]BE^2 + DE^2 = CE^2[/tex]
Since BE = DE, we can rewrite the equation as:
[tex]2(BE^2) = 1[/tex]
[tex]BE^2 = 1/2[/tex]
[tex]BE = √(1/2)[/tex]
Now that we know the length of BE, we can use it as the height of triangle BCE. Therefore, the area of triangle BCE is:
Area = (1/2) * base * height
[tex]Area = (1/2) * 1 * √(1/2)[/tex]
[tex]Area = √(1/2) / 2[/tex]
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I need the answer for 4x+8<24 it is for my homework
Answer:
Step-by-step explanation:
x = 8
Question 11
Aiguo rode his bike twice as many miles as Xavier. Together, they rode a total of 22.5 miles. How many miles did
Xavier ride?
Part A
Write a system of equations that represents the situation.
y =
x + y =
Part B
Solve the system of equations. Express the coordinates as decimals if necessary.
Done and
I’m literally so confused
Xavier rode 7.5 miles and Aiguo rode twice as much, or 15 miles.
How many miles did Xavier ride?Let x be the number of miles Xavier rode. Since Aiguo rode twice as many miles as Xavier, let 2x be the number of miles Aiguo rode.
Together, they rode a total of 22.5 miles, so we have the equation:
x + 2x = 22.5
Simplifying, we will get:
3x = 22.5
x = 22.5/3
x = 7.5
We can check our answer by verifying that the sum of their distances is indeed 22.5 miles:
= 7.5 + 15
= 22.5
Therefore, the solution is x = 7.5 and y = 15.
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select a random sample of size 2 by writing the five numbers in this population on slips of paper, mixing them, and then selecting two. calculate the mean for your sample.
The mean for the sample is 14.5.
We are asked to select a random sample of size 2 by writing the five numbers in this population on slips of paper, mixing them, and then selecting two. We then have to calculate the mean for the sample. The given numbers are: 12, 17, 8, 13, and 20. Therefore, there are five numbers in the population.
Now, we have to choose any two numbers randomly from the population. Let us suppose that we select 12 and 17 randomly from the population. Therefore, the sample will be {12, 17}. Now, we have to calculate the mean of the sample.
The formula to calculate the mean is: mean = sum of all numbers in the sample / total number of items in the sample. The sum of 12 and 17 is 12 + 17 = 29. Therefore, the sum of all numbers in the sample is 29. Also, the total number of items in the sample is 2.
Therefore, we can calculate the mean as: mean = 29 / 2mean = 14. 5. Therefore, the mean for the sample is 14.5.
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A number is equal to 3 times a smaller number. Also, the sum of the smaller number and 4 is the larger number. The
situation is graphed on the coordinate plane below, where x represents the smaller number and y represents the larger
number.
Which two equations represent the situation?
A. y= 1/3x and y = x-4
B. Y = 1/3x and y= x +4
C. Y= 3x and y= x +4
D. Y= 3x and y = x- 4
Please and thank you! <3
Answer:
3x = y
x + 4 = y
Step-by-step explanation:
Letter C
in a relation r over a set of people, we have that a person x is related to person y if x's birth date is prior to y's birth date. no two people in the group have the same birth date. indicate the choice that correctly describes the relation r.
The relation R is a partial order for the given set of data regarding over the set of people. (Option 1)
A partial order is a binary relation that is reflexive, antisymmetric, and transitive. In this case, the relation R is reflexive since a person is always born before themselves. It is also transitive since if person A is born before person B, and person B is born before person C, then person A must be born before person C.
However, the relation R is not symmetric, since if person A is born before person B, then person B cannot be born before person A. Therefore, the relation R is not a total order.
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Complete Question:
in a relation r over a set of people, we have that a person x is related to person y if x's birth date is prior to y's birth date. no two people in the group have the same birth date. indicate the choice that correctly describes the relation r.
partial ordersymmetricasymmetrictotal orderWhich of the following shows an example of two irrational numbers being multiplied to get a rational number?
Responses
3×9
0×5√
2√ ×8√
2√×3√
Step-by-step explanation:
Which of the following shows an example of two irrational numbers being multiplied to get a rational number?
Responses
option c
Find the sales tax. Then find the total cost of the item. Sales Tax Selling Price Rate of Sales Tax Sales Tax $90.00 5%
Answer:
Sales tax: $90 × .05 = $4.50
Total cost: $90 + $4.50 = $94.50
Nicholas and three other members from the Culinary Team had 100 fliers to post
around the school. Last week, they posted 1/4 of them. This week, they posted 2/4
of the remaining fliers. How many fliers have they still not posted?
The number of fliers that Nicholas and three other Culinary Team members have not still posted is 37 fliers.
How is the number determined?The remaining number of fliers not yet posted is a function of mathematical operations.
Basically, mathematical operations involve addition, subtraction, division, and multiplication.
The total number of fliers, Nicholas and three other Culinary Team members are posting around the school = 100
The fraction posted last week = 1/4
= 25 fliers (100 x 1/4)
The remaining fliers after posting 25 fliers = 75 (100 - 25)
The fraction posted this week = 2/4 = 1/2
1/2 of 75 = 37.5 or 38 fliers
The remaining fliers they still have not posted = 37 (75 - 38)
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What is the answer to this? Pls help
(9x10^4)+(7x10)
Answer:
(9x10^4)+(7x10) = 90,000 + 70 = 90,070
What are the values of x and y? *
The values of sides x and y of the triangle are 6.75 and 11.25 units respectively.
The Pythagorean TheoremThe square of the hypotenuse side of the right-angled triangle equals the sum of the squares of the other two sides, according to Pythagoras' Theorem. The three sides of this triangle are referred to as the perpendicular, base, and hypotenuse.
by using the Pythagorean theorem:
Equation1: y ² =x ² + 9²
Equation2: (12 + x) ² =1 5 ² + y ²
Putting values of equation1 in 2 we get
(12 + x) ² =1 5 ² +x ² + 9²
144 + x²+ 2×12x = 225 + x²+ 81
x=6.75
Putting value of x in equation1
y ² =6.75 ² + 9²
y=11.25
Hence, the values of x and y are
x = 6.75 unit
y =11.25 unit
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I have a pool in shape of a rectangle with a length of 28 feet and a width of 14 feet. I also have the stairs that form a trapezoid with the measurements of a=4 feet and b=6 feet and the height is 2 feet. what is the total area of both shapes combined for the pool? *(rectangle area = A=b x h) *Trapezoid Area =A = 1/2 (a+b)xh
Answer:
Step-by-step explanation:
28x14x4x6x2+18816
about 10% percent of workers (ages 16 years and older) in the united states commute to their jobs by carpooling. you randomly select eight workers. what is the probability that exactly four of them carpool to work?
Probability that exactly four workers carpool to work is 0.214990847, or approximately 21.5%.
We must apply the binomial distribution formula to resolve this issue. The number of successes in a certain number of independent trials that all have the same chance of success are described by the binomial distribution, which is a type of probability distribution. In this scenario, the number of successes is the number of workers who carpool, and the probability of success is 0.1.
The binomial distribution's formula is:
[tex]P(X=k) = to (n pick k) * p*k*1-p (n-k)[/tex]
Where n is the total number of trials (in this case, 8), p is the success probability (0.1), and (n choose k) is the binomial coefficient, which is equal to [tex]n! / (k! * (n-k)![/tex] and P(X=k) is the probability of obtaining exactly k successes.
This formula can be used to determine the likelihood that four employees will carpool to work:
[tex]P(X=4) = (8 pick 4) * 0.14 * 0.94 * 0.214 = 0.214990847.[/tex]
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a local county has an unemployment rate of 4%. a random sample of 19 employable people are picked at random from the county and are asked if they are employed. round answers to 4 decimal places.
The probability that exactly 8 of the 19 people in the random sample are employed is 27.93%.
We need to calculate the probability that exactly 8 of the 19 people in the random sample are employed. The probability of a single person being employed is 4%, or 0.04.
To calculate the probability of 8 people being employed out of the 19, we can use the binomial distribution formula:
P(X=8) = nCx * (p^x) * (1-p)^(n-x) Where n = 19, x = 8, p = 0.04, and 1-p = 0.96
So, P(X=8) = 19C8 * (0.04^8) * (0.96^11) = 0.2793 or 27.93%.
Therefore, the probability that exactly 8 of the 19 people in the random sample are employed is 27.93%.
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What is the measure of each interior angle of a regular 20-gon?
Answer:
162°
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 20 , then
sum = 180° × (20 - 2) = 180° × 18 = 3240°
The interior angles of a regular polygon are congruent
then each interior angle = 3240° ÷ 20 = 162°
13xy^2 - 12x^2y + 5x^2y simplify
there is a population of 15,500 bacteria in a colony. if the number of bacteria doubles every 234 hours, what will the population be 936 hours from now?
If the number of bacteria doubles every 234 hours, we can use the exponential growth formula to find the population at a future time t:
N(t) = N0 * 2^(t/T)
where N(t) is the population at time t, N0 is the initial population, T is the doubling time (234 hours in this case), and t is the time elapsed.
We are given that the initial population is 15,500 bacteria. We want to find the population 936 hours from now. Therefore, we can substitute the values into the formula:
N(936) = 15,500 * 2^(936/234)
N(936) = 15,500 * 2^4
N(936) = 15,500 * 16
N(936) = 248,000
Therefore, the population of bacteria in the colony will be 248,000 after 936 hours.
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3. What is the distance between the points (4, 5) and (-3, 5)?
7 units
8 units
1 units
10 units
Answer:
7
Step-by-step explanation:
you use your fingers and count down from 4 to -3 and you get 7.
Seven bananas weigh 1 3/4 pounds and are on sale for $3 .How much does Luke pay for 28 bananas?How much do the 28 bananas weigh?Assume each banana weighs about the same.
Answer:
The 28 bananas weigh 7 pounds
Step-by-step explanation:
We can start by figuring out the price per banana by dividing the total price by the number of bananas:
Price per banana = $3 / 7 bananas
Price per banana = $0.43 per banana (rounded to the nearest cent)
Next, we can use the price per banana to find the cost of 28 bananas:
Cost of 28 bananas = 28 bananas x $0.43 per banana
Cost of 28 bananas = $12.04
Therefore, Luke pays $12.04 for 28 bananas.
To find the weight of 28 bananas, we can use the fact that seven bananas weigh 1 3/4 pounds:
Weight of one banana = 1 3/4 pounds / 7 bananas
Weight of one banana = 1/4 pound per banana
Then we can multiply the weight of one banana by 28 to find the total weight of 28 bananas:
Weight of 28 bananas = 1/4 pound per banana x 28 bananas
Weight of 28 bananas = 7 pounds
Therefore, the 28 bananas weigh 7 pounds.
The list below represents the number of novels written
by each of Amir's 10 favorite authors.
1 3 3 4 5 7 8 10 12 23
What is the interquartile range of the number of novels
written by each of Amir's 10 favorite authors?
The interquartile range of the number of novels
written by each of Amir's 10 favorite authors would be = 7
How to calculate the interquartile range of the novels?The total number of the novels written by the 10 favorite authors of Amir = 1 +3 +3 +4+ 5 +7+ 8+ 10+ 12+ 23 = 76
The interquartile range of the number of novels = Q3-Q1
Where Q3 = median of second half = 10
Q1 = median of the first half = 3
The interquartile range of the number of novels = 10-3 = 7
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Select the best answer for the question.
4. A large facility that manufacturers send large quantities of product to then be distributed to stores is called:
O A. Store
B. Distribution Center
C. Carton
D. Garage
The statement that describe the term in the question is (b) the distribution center
How to determine the statement that describe the statementA distribution center is a large facility used by manufacturers to store and send out large quantities of products to be distributed to retail stores or directly to customers.
The products are often received in bulk and then sorted, packaged, and shipped to their final destination. The distribution center may also handle other tasks such as inventory management, quality control, and returns processing.
The purpose of the distribution center is to streamline the distribution process, reduce shipping costs, and ensure that products are delivered to their final destination in a timely and efficient manner.
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a rectangle's length is 5cm more than its width, if it has an area of 336 cm squared find the length
The length of the rectangle is 19 cm.
The formula for the area of a rectangle,
Area = Length x Width
Given that the area is 336 cm squared.
So, we can set up an equation,
⇒ 336 = (w + 5)w
where w represents the width of the rectangle.
Expanding this equation,
⇒ 336 = w² + 5w
Moving all terms to one side:
⇒ w² + 5w - 336 = 0
This is a quadratic equation that we can solve using the quadratic formula,
⇒ w = (-5 ± √(5² - 4(1)(-336))) / (2(1))
⇒ w = (-5 ± 23) / 2
We'll take the positive value,
⇒ w = 14
So, the width of the rectangle is 14 cm.
We also know that the length is 5 cm more than the width,
Therefore,
⇒ l = w + 5
⇒ l = 14 + 5
⇒ l = 19
Therefore, the length of the rectangle is 19 cm.
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a display of cans on a grocery shelf consists of 20 cans on the bottom, 18 cans in the next row, and so on in an arithmetic sequence, until the top row has 4 cans. how many cans, in total, are in the display?
In total, there are 126 cans in the showcase.
We will use the method for the sum of an arithmetic sequence to solve this problem. The formulation is:
S = (n/2)(a + l)
Wherein S is the sum of the sequence, n is the range of terms, a is the first term, and l is the last term.
In this example, the primary time period is 20, and the closing term is 4. The common difference among the terms is -2, given that we are subtracting 2 cans from each row. we will discover the number of terms using the formulation:
l = a + (n-1)d
Wherein d is the common distinction. solving for n, we get:
n = (l - a)/d + 1
n = (4 - 20)/(-2) + 1
n = 9
Now we can plug within the values for a, l, and n into the system for the sum:
S = (n/2)(a + l)
S = (9/2)(20 + 4)
S = 126
Thus, there are 126 cans in the display in total.
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how to determine if we can apply the existence and uniquness theorem to guarantee that there is exactly one unique soltuion
The Existence and Uniqueness Theorem states that if a system of linear equations has a unique solution, then the solution can be found by solving the associated augmented matrix.
To determine whether a system of linear equations has a unique solution, the number of equations must equal the number of unknowns. Additionally, the equations must not be linearly dependent. If these criteria are met, then the Existence and Uniqueness Theorem guarantees that there is exactly one unique solution.
To illustrate, consider the system of equations:
x1 + x2 - x3 = 2
2x1 - x2 + 2x3 = 8
3x1 + 2x2 - 4x3 = 0
= 4. Therefore, the Existence and Uniqueness Theorem guarantees that there is exactly one unique solution for this system.
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Help me on this please
Answer:
x = -4
y = 1
Step-by-step explanation:
I added a photo of my solution
midpoint of 0 and 2/7
Answer: 0, 4.5
Step-by-step explanation:
The answer in decimal form is 0 and 4.5. :)