Suppose there are 100 items, numbered 1 to 100 , and 100 baskets, also numbered 1 to 100 . Item i is in basket b if and only if i divides b with no remainder. Thus, item 1 is in all the baskets, item 2 is in all fifty of the even-numbered baskets, and so on. Basket 12 consists of items {1,2,3,4,6,12}, since these are all the integers that divide 12. Answer the following questions: (a) If the support threshold is 5 , which items are frequent? (b) If the support threshold is 5 , which pairs of items are frequent? (c) What is the confidence of the following association rules? 1. {5,7}→2 2. {2,3,4}→5 (d) For the item-basket data specified here, which basket is the largest? Explain. (e) [bonus] (15 points) Describe all the association rules that have 100% confidence. 3. (40 points) Apply the A-Priori Algorithm with support threshold 5 to the data in question 2 (the above question). Show your work.
If the support threshold for given integers is 5 , then (1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 25, 30, and 60) items are frequent.
The following pairs of items will be frequent: (1,2), (1,3), (1,4), (1,5), (1,6), (1,10), (1,12), (1,15), (1,20), (1,30), (2,4), (2,6), (2,10), (2,12), (2,20), (3,6), (3,12), (4,12), (5,10), and (5,20).
The confidence of the following association rules are 100% and 50%.
(a) The items that are frequent, if the support threshold is 5, can be found by counting the number of baskets that contain each item. The following items will be frequent: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 25, 30, and 60. These are the items that appear in at least five baskets.
(b) The pairs of items that are frequent if the support threshold is 5 can be found by counting the number of baskets that contain each pair of items. The following pairs of items will be frequent: (1,2), (1,3), (1,4), (1,5), (1,6), (1,10), (1,12), (1,15), (1,20), (1,30), (2,4), (2,6), (2,10), (2,12), (2,20), (3,6), (3,12), (4,12), (5,10), and (5,20).
(c) The confidence of the following association rules is as follows:
1. {5,7}→2 has a confidence of 100%, since 2 appears in all baskets that contain both 5 and 7.
2. {2,3,4}→5 has a confidence of 50%, since 5 appears in only half of the baskets that contain 2, 3, and 4.
(d) The basket that is the largest is basket 60, which consists of the following items: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. This is because 60 is divisible by all of these items.
(e) The association rules that have 100% confidence are those where the antecedent and consequent are the same. For example, the following rules have 100% confidence: {1}→1, {2}→2, {3}→3, and so on.The steps for the Apriori Algorithm with support threshold 5 is as follows:
Step 1: Create a list of frequent 1-itemsets. This list includes all items that appear in at least five baskets. {1,2,3,4,5,6,8,10,12,15,20,25,30,60}
Step 2: Generate candidate 2-itemsets by joining frequent 1-itemsets. {1,2}, {1,3}, {1,4}, {1,5}, {1,6}, {1,10}, {1,12}, {1,15}, {1,20}, {1,30}, {2,4}, {2,6}, {2,10}, {2,12}, {2,20}, {3,6}, {3,12}, {4,12}, {5,10}, {5,20}
Step 3: Count the support of each candidate 2-itemset. Discard those with support less than 5. {1,2}: 100, {1,3}: 44, {1,4}: 44, {1,5}: 36, {1,6}: 28, {1,10}: 12, {1,12}: 20, {1,15}: 12, {1,20}: 12, {1,30}: 8, {2,4}: 36, {2,6}: 20, {2,10}: 12, {2,12}: 20, {2,20}: 12, {3,6}: 12, {3,12}: 20, {4,12}: 20, {5,10}: 12, {5,20}: 12
Step 4: Generate candidate 3-itemsets by joining frequent 2-itemsets. {1,2,4}, {1,2,6}, {1,2,10}, {1,2,12}, {1,2,20}, {1,3,12}, {1,4,12}, {2,4,6}, {2,4,10}, {2,4,12}, {2,6,12}
Step 5: Count the support of each candidate 3-itemset. Discard those with support less than 5. {1,2,4}: 20, {1,2,6}: 12, {1,2,10}: 12, {1,2,12}: 20, {1,2,20}: 12, {1,3,12}: 20, {1,4,12}: 20, {2,4,6}: 12, {2,4,10}: 12, {2,4,12}: 20, {2,6,12}: 12
Step 6: Continue generating candidate k-item sets and counting their support until no frequent item sets of length k can be found.
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non-rivalry and non-excludability apply to group of answer choices private goods public goods goods produced by monopolies natural resources
Non-rivalry and non-excludability apply to public goods. Public goods are goods or services that are non-excludable,
meaning that it is impossible or impractical to exclude people from using them, and non-rivalrous, meaning that consumption of the good by one individual does not diminish its availability to others.
Examples of public goods include national defense, clean air and water, and scientific research. Because of their non-excludable and non-rivalrous nature, public goods often suffer from under-provision in a market economy.
Private goods, on the other hand, are both rivalrous and excludable. This means that only one person can consume the good at a time, and individuals can be prevented from consuming the good if they do not pay for it.
Goods produced by monopolies and natural resources can be either private or public goods depending on their excludability and rivalrousness.
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i) Given that a = 1, b = 3, c = 7, evaluate abc
Hope it helps
If we weren't given the values of the variables, it would be impossible to simplify the expression any further.
Luckily, we are given the value of each of the three variables.
The value of a is 1 :
1bc
or
bc
The value of b = 3 :
3c
Finally, the value of c is 7 :
3*7
21
Evaluated Expression ↓21
Using Euler's formula, how
many edges does a polyhedron
with 5 faces and 5 vertices have?
[?] edges
Euler's Formula: F + V = E + 2
Answer:
8 edges
Step-by-step explanation:
Form the formula F+V=E+2
U make E the subject by moving everything thing else to the left hand side
F+V-2=E
this implies 5+5-2=E
10-2=E
therefore Edges = 8
The polyhedron with 5 faces and 5 vertices has 8 edges.
To determine the number of edges in a polyhedron with 5 faces and 5 vertices using Euler's formula (F + V = E + 2).
we need to substitute the given values into the equation.
Given:
Number of faces (F) = 5
Number of vertices (V) = 5
Substituting these values into Euler's formula, we have:
5 + 5 = E + 2
Simplifying the equation:
10 = E + 2
Subtracting 2 from both sides:
E = 10 - 2
E = 8
Therefore, the polyhedron with 5 faces and 5 vertices has 8 edges.
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Assume that when human resource managers are randomly selected, 42% say job applicants should follow up within two weeks. If 7 human resource managers are randomly selected, find the probability that at least 2 of them say job applicants should follow up within two weeks. The probability is ___
(Round to four decimal places as needed)
The probability of at least 2 of them say job applicants should follow up within two weeks is 0.8291.Therefore, the required probability rounded to four decimal places is 0.6882.
That p = 0.42, q = 0.58 and n = 7We need to find the probability that at least 2 of them say job applicants should follow up within two weeks.This is a binomial probability problem. We can solve this problem using Binomial Distribution formula:P(X ≥ 2) = 1 - P(X = 0) - P(X = 1)Where,P(X ≥ 2) = Probability of at least 2 people say job applicants should follow up within two weeks.
P(X = 0) = Probability that no one says job applicants should follow up within two weeks.P(X = 1) = Probability that only one person says job applicants should follow up within two weeks.P(X = x) = nCx px q^(n-x)Where,nCx = n! / x! (n - x)!Where,n = 7, x = 0, 1, 2, 3, ...., 7, p = 0.42, q = 0.58Let's substitute the given values in the formula:P(X ≥ 2) = 1 - P(X = 0) - P(X = 1)P(X = 0) = 7C0 (0.42)^0 (0.58)^7 = 0.0266P(X = 1) = 7C1 (0.42)^1 (0.58)^6 = 0.1443P(X ≥ 2) = 1 - 0.0266 - 0.1443 = 0.8291
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20 times the difference of a number, z, and 7
Answer:
20(z-7)
Step-by-step explanation:
I am so sorry if you keep seeing me ask for help
Answer:
67°-------------------
Given three interior angle measures of a triangle:
38°, 75° and xUse the triangle sum theorem to find the missing angle:
38 + 75 + x = 180x + 113 = 180x = 180 - 113x = 67So the missing angle is 67°.
If 1 inch = 2.54 cm, how many centimetres (cm) are there in 5 inches (in.)? *
Answer:
5 inches = 12.7 cm
Step-by-step explanation:
Answer:
12.7
Step-by-step explanation:
if x = 2.54
then 5x = 12.7
5 x 2.54 = 12.7cm
The probability that a foot ball team will win a game is 2/11.The probability that they will lose is 3/11.What is the probability the game will be a draw
Answer:
6/11
Step-by-step explanation:
Since there are 3 possible outcomes for the game (win,lose and draw) and the total probability for the three outcomes must be equal to 1.
Then;
The probability that the game will be a draw Pd = 1 - (probability that they will lose Pl + probability that they will win Pw)
Pd = 1 - (Pl + Pw) ........1
Given;
Pl = 3/11
Pw = 2/11
Substituting the values into equation 1;
Pd = 1 - (2/11 + 3/11)
Pd = 6/11
The probability that the game will be a draw Pd = 6/11
asking to graph y-5 = -3/4 (x+3)
Answer:
Slope -3/4
y-intercept (0, 11/4)
Step-by-step explanation:
please help easy math!! 8th grade math Storypromblem answer number 9
Answer: Chris's Gym pays $2.75
Step-by-step explanation:
So i was glancing at this question wondering how I was gonna figure it out then flipped it upside down in my head and figred out what I was missing
So basically we know that Tyrell pays $2.00 for court reservations
Chris on the other hand according to the table pays $52.75 for court reservation in addition to his monthly fee. Now we have to find out how much is just the court fee. So if we look at the next box I realized that a second court recomendation costs $55.5 and I realized that to find the court reservation costs I needed to subtract so 55.5-52.755= 2.75 which means Chis has a monthly costs of 50 and pays $2.75 for a court holding
find the exact value of sin(0) when cos(0) =3/5 and the terminal side of (0) is in quadrant 4
When the cosine of an angle (0) is 3/5 and the angle lies in quadrant 4, the exact value of the sine of that angle is -4/5.
To find the exact value of sin(0), we can utilize the Pythagorean identity, which states that \(sin^2(x) + cos^2(x) = 1,\) where x is an angle in a right triangle. Since the terminal side of the angle (0) is in quadrant 4, we know that the cosine value will be positive, and the sine value will be negative.
Given that cos(0) = 3/5, we can determine the value of sin(0) using the Pythagorean identity as follows:
\(sin^2(0) + cos^2(0) = 1\\sin^2(0) + (3/5)^2 = 1\\sin^2(0) + 9/25 = 1\\sin^2(0) = 1 - 9/25\\sin^2(0) = 25/25 - 9/25\\sin^2(0) = 16/25\)
Taking the square root of both sides to find sin(0), we have:
sin(0) = ±√(16/25)
Since the terminal side of (0) is in quadrant 4, the y-coordinate, which represents sin(0), will be negative. Therefore, we can conclude:
sin(0) = -√(16/25)
Simplifying further, we get:
sin(0) = -4/5
Hence, the exact value of sin(0) when cos(0) = 3/5 and the terminal side of (0) is in quadrant 4 is -4/5.
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Note the correct and the complete question is
Q- Find the exact value of sin(0) when cos(0) =3/5 and the terminal side of (0) is in quadrant 4 ?
What is the number of different ordered 3-tuples such that each item of each one of these ordered 3-tuples is an element of A
The number of different ordered 3-tuples, where each item is an element of set A, can be determined by calculating the Cartesian product of set A with itself three times.
In general, the Cartesian product of two sets A and B is the set of all possible ordered pairs where the first element is from set A and the second element is from set B. Extending this concept to three sets, the Cartesian product will consist of ordered triples.
To find the number of different ordered 3-tuples, we need to consider the cardinality (number of elements) of set A. Let's denote the cardinality of A as n.
The number of different ordered 3-tuples can be calculated as n raised to the power of 3, since each position in the tuple can be filled with any element from set A. In other words, it is equivalent to finding the number of combinations with repetition.
Therefore, the number of different ordered 3-tuples is n^3.
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PLES HALP POINTS PIC DOWN BELOW
Answer:
The answer is D
Step-by-step explanation:
Answer:
D) Quadrant IV (quadrant 4)
Step-by-step explanation:
Point C is in quadrant IV because its point is (4,-4)
For points that have a positive x-coordinate and a negative y-coordinate, that means they are in quadrant IV.
Another way to figure this out is by looking at this graphically:
y
|
Quadrant | Quadrant
II | I
|
------------------------------|----------------------------- x
|
Quadrant | Quadrant
III | IV
|
I hope this helps!
What is the mean and MAD of 23,28,32,31,21
Answer:
So there are 6 numbers
The mean is 14.83
and the mean absolute deviation is 7.83
Step-by-step explanation:
Prove : ABCD is a parallelogram. (need help fast I will mark you brainiest!)
Answer:
Parallelogram = 2 pairs of parallel sides and opposite angles are equal
Triangle BEA and triangle DFC are equivalent by side angle side
Therefore, angle DCF is equivalent to angle BAE
Angles FEB and DFE are right angles due to them being supplementary angles with angles BEA and DFC, respectively.
This means triangles BEC and DFA are equivalent.
This means angles FCB and EAD are equivalent, which means angles BCD and DAB are equivalent.
This also means angles ABC and ADC are equivalent.
Opposite angles equivalent = parallelogram
A 15 foot ladder is leaning against a house. How far is the top of the ladder from the ground if the ladder is 12 feet away from the house?
Answer:
9 feet
Step-by-step explanation:
Use the Pythagorean Theorem:
\( {x}^{2} + {12}^{2} = {15}^{2} \)
\( {x}^{2} + 144 = 225\)
\( {x}^{2} = 81\)
\(x = 9\)
(4)find a basis for r4 that includes v0 and v1. (b) (4)using the results of part (a) find an orthonormal basis {w0,w1,w2,w3} for r4. in your basis, w0 should be parallel to v0 and {w0,w1} should span the same subspace as {v0,v1}. (c) (4)let b be your basis from part (b) and b′be the standard basis for r4 ({e1,e2,e3,e4}). write the matrix m that converts from b′-coordinates to b-coordinates. (d) (2)express [1 2 3 4]t in terms of your orthonormal basis from part (b).
(a) A basis for R4 that includes v0 and v1 can be found by adding two linearly independent vectors to {v0, v1}.
To find a basis for R4 that includes v0 and v1, we need to add two linearly independent vectors to the set {v0, v1}. Let's call these vectors v2 and v3. As long as v2 and v3 are linearly independent from v0 and v1, they will form a basis for R4.
The choice of v2 and v3 can vary, but they must be chosen carefully to avoid linear dependence. Once v2 and v3 are determined, we will have a basis {v0, v1, v2, v3} for R4 that includes v0 and v1.
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1. Constrained optimization a. (5 points) Draw a budget constraint using the following information: P
x
=$2,P
y
= $4,I=$100. Label the X-intercept, Y-intercept, and the slope of the budget constraint. b. (5 points) Suppose the MRS=Y/(2X). Solve for the optimal bundle of X and Y. c. ( 3 points) Label the optional bundle "A" that you found in part b on the graph above and draw an indifference curve that shows the optimal bundle. d. (5 points) Now suppose that the income decreases to $80. Draw the new budget constraint on the graph above. What is the new optimal bundle (i.e., X
∗
= and Y
∗
= ) ? Label this point "B" and draw another indifference curve that corresponds to this optimal bundle. 2. Income pffects a. (5 points) Label the optimal bundle " A " on the graph above. Now, suppose that income decreases. Assuming that X is a normal good and Y is an inferior good, what happens to the optimal amount of X and Y after the change?
In this scenario, we have a budget constraint and an indifference curve representing preferences. By analyzing the given information, we can determine the optimal bundle of goods and how it changes with a decrease in income.
a. The budget constraint can be represented graphically. The X-intercept is found by setting Y = 0, giving us X = I/Px = 100/2 = 50. The Y-intercept is found by setting X = 0, giving us Y = I/Py = 100/4 = 25. The slope of the budget constraint is determined by the ratio of the prices, giving us -Px/Py = -2/4 = -1/2. Thus, the budget constraint line can be drawn connecting the X and Y intercepts with a slope of -1/2.
b. The optimal bundle of X and Y can be found by maximizing utility subject to the budget constraint. Given the marginal rate of substitution (MRS) of Y/(2X), we set the MRS equal to the slope of the budget constraint, -Px/Py = -1/2. Solving for X and Y, we can find the optimal bundle.
c. Labeling the optimal bundle found in part b as "A," we can draw an indifference curve passing through this point on the graph. The indifference curve represents the combinations of X and Y that provide the same level of utility.
d. If the income decreases to $80, the new budget constraint can be drawn with the same slope but a lower intercept. We can find the new optimal bundle, labeled "B," by maximizing utility subject to the new budget constraint. Similarly, we can draw another indifference curve passing through point B to represent the new optimal bundle.
If X is a normal good and Y is an inferior good, a decrease in income will generally lead to a decrease in the optimal amount of Y and an increase in the optimal amount of X. This is because as income decreases, the demand for inferior goods like Y tends to decrease, while the demand for normal goods like X remains relatively stable or may even increase. The specific changes in the optimal amounts of X and Y would depend on the specific preferences and income elasticity of the goods.
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A storage tank consist of a hemisphere and a cylinder which share a common base. The tank has a height of 16.5 m and the cylinder has a base diameter of 4.7m. Find the total capacity of the tank.
The total capacity of the tank is 272.675 cubic meters.
Given that,
A storage tank consist of a hemisphere and a cylinder which share a common base.
The base of both hemisphere and cylinder will be the same circle with the same radius.
Also, we have,
Height of the tank = 16.5 m
Base diameter of the cylinder = 4.7 m
Radius of the base of the cylinder = 4.7 / 2 = 2.35 m
Radius of the hemisphere = 2.35 m
Height of the cylinder = Total height of the tank - Height or radius of the hemisphere
Total capacity of the tank = Volume of hemisphere + Volume of cylinder
= 2/3 π r³ + π r² h
= 2/3 π (2.35)³ + π (2.35)² (16.5 - 2.35)
= 8.652π + 78.143π
= 272.675 cubic meters
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Rectangle a b c d is rotated around line m. line m bisects the rectangle and splits side a b into 2, 6 inch pieces. sides a d and b d are 5 inches. what solid will be produced if rectangle abcd is rotated around line m? assume that the line bisects both sides it intersects. what will the dimensions of the three-dimensional solid be? rectangular prism; length = 12 in.; width = 6 in.; height = 5 in. triangular prism; length = 12 in.; width = 6 in.; height = 5 in. cylinder; radius = 12 in.; height = 5 in. cylinder; radius = 6 in.; height = 5 in.
A cylinder with a radius of 6 inches and a height of 5 inches is produced if rectangle ABCD is rotated around line m.
A solid figure is a 3-dimensional shape (length, width, and height) so that it has a volume inside. Examples of solid figures are prism, cylinder, cone, pyramid, and so on.
From the question we get the following information:
- rectangle ABCD
- line m divides side AB into 2, each 6 inches
- the length of side AD and BD is 5 inches
So, when we rotate rectangle ABCD around line m, it will produce a cylinder, with:
- cylinder height = AD = BD = 5 inches
- cylinder diameter = 1/2 AB = 6 inches
To get the best illustration of the problem, we can draw rectangle ABCD and line m.
So the solid figure produces if we rotate rectangle ABCD around line m is a cylinder with a radius of 6 inches and a height of 5 inches.
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Answer: D) cylinder; radius = 6 in.; height = 5 in.
Step-by-step explanation:
Edege 2023
The length of one of the parallel sides of a trapezium is 5 more than the other parallel side. The perpendicular height is 7 cm. Write an expression for the area
Answer:
7x+35/2
Step-by-step explanation:
The area of a trapezoid is \(\frac{(b_1+b_2)}{2}\cdot h\), where b1 and b2 are the two bases and h is the height. Because b2 is 5 more than b1, which we will represent as x, we have the two bases as x and x + 5 respectively. Plugging into the equation, we have \(\frac{2x+5}{2}\cdot 7\) .We have this as (x+5/2)(7), which is 7x+35/2
Hey can you help me pls
Answer:
B
Step-by-step explanation:
in a certain lottery, three numbered balls are randomly drawn from a large basket without replacement. to win, a player's ticket must have each of the numbers drawn in no particular order. the balls are numbered from one to one hundred. if jack buys twenty-one tickets, what is the probability that he will win?
The probability that Jack will win is 0.00015. The result is obtained by dividing the number of tickets that Jack has by the total number of events.
How to calculate the probability?Probability of an event is calculated by dividing the number of favorable outcomes by the total number of events in the sample space.
In a certain lottery are 100 balls numbered from 1 - 100 in a large basket. Three numbered balls are randomly drawn without replacement. To win the lottery, a player's ticket must have each of the numbers drawn in no particular order.
If jack buys 21 tickets, find the probability that he will win!
In any the order, the different triples of tickets that a player can have can be found by a combination.
The total number of events would be
\(= \: _{100}C_{3}\)
\(= \frac{100!}{3! \:97!} }\)
\(= \frac{98 \times 99 \times 100}{2 \times 3}\)
= 161700 different triples
Jack has 21 tickets. So, the probability that Jack will win is
P = 21/161700
P = 0.00013
Hence, Jack will win with the probability of 0.00013.
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In ΔRST, r = 530 cm, s = 530 cm and t=950 cm. Find the measure of ∠T to the nearest 10th of a degree.
Usted debe resolver los siguientes triángulos rectángulos empleando las
relaciones dadas para funciones trigonométricas, teorema de Pitágoras y teorema
de ángulos interiores de un triángulo. La suma de las medidas de los ángulos
interiores de un triángulo es 180°.
1. a =340 u.l. y α = 30°28
2. c = 458 u.l. y α =65°35'
3. a =202,56 u.l. y b = 337,98 u.l.
4. a = 2.867 u.l. y c = 8.234 u.l.
5. c = 305,02 u.l. y α = 58°10.6'
6. b = 4,310 u.l. y c = 6,320 u.l.
Answer: watch this video it will help a lot
ures+of+the+angles+interiors+of+a+triangle+is+180%C2%B0.+1.+a+%3D340+u.l.+and+%CE%B1+%3D+30%C2%B028+2.+c+%3D+458+u.l.+and+%CE%B1+%3D65%C2%B035%27+3.+a+%3D202.56+u.l.+and+b+%3D+337.98+u.l.+4.+a+%3D+2.867+u.l.+and+c+%3D+8.234+u.l.+5.+c+%3D+305.02+u.l.+and+%CE%B1+%3D+58%C2%B010.6%27+6.+b+%3D+4%2C310+u.l.+and+c+%3D+6%2C320+u.l.&aqs=chrome..69i57j69i64l2.386j0j7&sourceid=chrome&ie=UTF-8#fpstate=ive&vld=cid:af82eef0,vid:i3bjEOA5_zc
Step-by-step explanation:You must solve the following right triangles using the
relations given for trigonometric functions, Pythagorean theorem and theorem
of interior angles of a triangle. The sum of the measures of the angles
interiors of a triangle is 180°.
1. a =340 u.l. and α = 30°28
2. c = 458 u.l. and α =65°35'
3. a =202.56 u.l. and b = 337.98 u.l.
4. a = 2.867 u.l. and c = 8.234 u.l.
5. c = 305.02 u.l. and α = 58°10.6'
6. b = 4,310 u.l. and c = 6,320 u.l.
What is The Value Of X
Answer:
X = 92 degrees
Step-by-step explanation:
the angles of a triangle all add up to 180 degrees, so 40 plus 180-132 = 88
180-88= 92 so X = 92
The area of a rectangle is given by the equation 2*l (squared) -5*l = 18 , in which l is the rectangle's length. what is the length of the rectangle.
Answer: L=4.5
Step-by-step explanation:
\(2L^2-5L=18 \ \ \ \ \ L > 0\\2L^2-5L-18=18-18\\2L^2-5L-18=0\\2L^2-5L-4L+4L-18=0\\(2L^2-9L)+(4L-18)=0\\2L*(L-4.5)+4*(L-4.5)=0\\(L-4.5)*(2L+4)=0\\L-4.5=0\\L_1=4,5\\2L+4=0\\2L+4-4=-4\\2L=-4\\\)
Divide both parts of the equation by 2:
\(L_2=-2\notin\ (L > 0)\)
Level 4: Solve linear systems in real-world applications and word problems.
12. Real-World Application World Problem
Again, Mr.X is selling donuts and bagels for a school fundraising event. But the prices changed to
battle against inflation. For donuts, the price is now $3 each. For Bagels, the price is now $4.50.
This time, he sold 26 donuts and bagels together and the money raised is $94.50.
How many donuts and bagels he sold?
(Hint: First, define your variables.
Let x be
Let y be
Then, this particular problem can be modeled by system of linear equations in standard form.)
Mr. X sold 20.5 donuts and 5.5 bagels. X is selling donuts and bagels for a school fundraising event. But the prices changed to battle against inflation.
Let x be the number of donuts sold, and y be the number of bagels sold. Then we can set up a system of linear equations to represent the given information:
x + y = 26 (the total number of donuts and bagels sold is 26)
3x + 4.5y = 94.5 (the total money raised is $94.50)
To solve for x and y, we can use elimination or substitution method. Here, we will use substitution method:
x + y = 26 (multiply both sides by 3 to eliminate x's coefficient)
3x + 4.5y = 94.5
3x + 3y = 78
3y = 16.5
y = 5.5
Substitute y = 5.5 into either equation to solve for x:
x + 5.5 = 26
x = 20.5
Therefore, Mr. X sold 20.5 donuts and 5.5 bagels. However, since he cannot sell half a donut or half a bagel, we can round the values to the nearest whole number. Thus, he sold 21 donuts and 6 bagels.
Learn more about selling donuts here
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Anita has saved $43.75 of the $112.50 that she needs for a new snowboard.She saves $13.75 from her paper route each week. The equation13.75w + 43.75 = 112.50 can be used to represent the number of weeksit will take her to reach her goal. In how many more weeks will Anita havesaved enough money for the snowboard?
In order to find the number of weeks w it will take Anita to reach her goal, we need to solve the following equation for w:
\(13.75w+43.75=112.50\)So, we can apply the same operations on both sides of the equation, until we isolate the variable w and find its value.
We obtain:
\(\begin{gathered} 13.75w+43.75-43.75=112.50-43.75 \\ \\ 13.75w=68.75 \\ \\ \frac{13.75w}{13.75}=\frac{68.75}{13.75} \\ \\ w=5 \end{gathered}\)Therefore, Anita will have saved enough money for the snowboard in 5 weeks.