To generate a series of 100 numbers uniformly distributed in the interval [0,1] using a linear congruential generator, we can use the parameters a = 41, c = 33, m = 100, and Z0 = 48.
A linear congruential generator is a simple method for generating pseudo-random numbers. It uses a recurrence relation of the form Zₙ₊₁ = (aZₙ + c) mod m, where Zₙ is the current random number, a is a multiplier, c is an increment, and m is the modulus. In this case, we start with an initial seed value of Z0 = 48 and generate subsequent numbers using the given parameters. To compute the mean and standard deviation of the generated series, we calculate the sample mean and sample standard deviation of the 100 numbers. The sample mean is the average of the numbers, while the sample standard deviation measures the spread or dispersion of the numbers around the mean. We can then compare these computed values with the expected theoretical values for a continuous uniform distribution on the interval [0,1]. The theoretical mean of a continuous uniform distribution is (a + b) / 2, where a and b are the endpoints of the interval. In this case, the mean is (0 + 1) / 2 = 0.5. The theoretical standard deviation of a continuous uniform distribution is (b - a) / sqrt(12), which for the interval [0,1] is 1 / sqrt(12) ≈ 0.2887. Any differences between the computed and theoretical mean and standard deviation may arise due to the nature of pseudo-random number generation. Linear congruential generators are deterministic and have certain limitations in terms of randomness. Deviations from the expected theoretical values can be attributed to the algorithm used and the chosen parameters. If the generated numbers deviate significantly from the expected mean and standard deviation, it may indicate that the linear congruential generator is not adequately simulating a continuous uniform distribution.
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Aside from the Gini index and Entropy, explain two other parameters to measure purity (best split) in a decision tree.
In addition to the Gini index and Entropy, there are other parameters that can be used to measure purity or determine the best split in a decision tree. Two commonly used parameters are: Classification Error , Gini Gain.
Classification Error (Misclassification Error):
The classification error, also known as the misclassification error, measures the fraction of misclassified instances in a node. It calculates the probability of misclassification by assigning the majority class label to all instances in the node. The classification error is given by the formula:
Classification Error = 1 - (max(p1, p2, ..., pk))
where p1, p2, ..., pk are the proportions of each class in the node.
A lower classification error indicates a purer node, where the majority of instances belong to a single class.
Gini Gain:
Gini gain is a measure of the reduction in the Gini index achieved by splitting a node based on a particular feature. It quantifies how much the impurity or randomness decreases after the split. Gini gain is calculated by subtracting the weighted average of the Gini indices of the resulting child nodes from the Gini index of the parent node. The feature with the highest Gini gain is chosen as the best split.
Gini Gain = Gini Index(parent) - (Weighted Average of Gini Indices of Child Nodes)
A higher Gini gain indicates a better split that maximizes the reduction in impurity.
These parameters, like the Gini index and Entropy, help in determining the purity of nodes and finding the optimal splits in a decision tree algorithm. By evaluating multiple parameters, the decision tree can make informed choices about the features and splits that lead to the most homogeneous and informative subsets of data.
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A candy bar cost the store $0.79. The store wants a 65% mark up. What would the price of the candy bar be to have a 65% mark up?
Answer:
1.30$
Step-by-step explanation:
The price of the candy bar to have a 65% mark up is $1.3035.
What is Markup Percentage?Markdown percentage is defined as the increase in the price which is calculated as a percent of the selling price.
Given that,
Markup percentage = 65% = 65/100 = 0.65
Let x be the price of the candy bar be to have a 65% mark up.
(x - 0.79) / 0.79 = 0.65
x - 0.79 = 0.5135
Adding 0.79 to both sides,
x = 1.3035
Hence the price of the candy bar would need to be $1.3035.
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Define the problem k-independent set. b) Explain why the brute force method for solving k-clique runs in polytime if k is constant but in Ω(2
n
) time when k=n/2. c) Give a polytime answer-preserving transformation T from k-clique to k-independent set (so T takes as input an instance of k-clique and gives as output an instance of k-independent set). Prove that T is polytime. Prove that T is answer-preserving.
The transformation T preserves the answer: if G has a k-clique, then G' has a k-independent set, and vice versa.
a) **Problem Definition: K-Independent Set**
A k-independent set is a subset of vertices in a graph such that no two vertices in the set are adjacent (i.e., there is no edge connecting them). Formally, given an undirected graph G = (V, E), a k-independent set S is a subset of V where for every pair of vertices u and v in S, there is no edge (u, v) in E. The goal is to find the largest k-independent set in the given graph.
b) **Brute Force Method for Solving K-Clique**
The brute force method for solving the k-clique problem involves examining every possible subset of k vertices in the graph and checking if each subset forms a complete subgraph (clique) of size k. If the size of the graph is n and k is constant, then the number of possible subsets to examine is a polynomial function of n. Thus, the brute force method runs in polynomial time when k is constant.
However, when k=n/2, the brute force method becomes inefficient. The number of subsets of k vertices to examine becomes 2^n/2, which grows exponentially with the size of the input graph. This exponential growth makes the brute force method impractical for larger values of n.
c) **Transformation from K-Clique to K-Independent Set**
To transform an instance of the k-clique problem to the k-independent set problem, we define the following polynomial-time transformation T:
Given an instance of k-clique G = (V, E), construct a new graph G' = (V, E'), where E' consists of all the edges in G that are not in E. In other words, the edges in G' are complementary to the edges in G.
The transformation T is polynomial-time because constructing G' from G can be done in polynomial time since the size of E' is at most the size of E.
**Proving T is Polynomial-Time:**
The transformation T runs in polynomial time because constructing G' from G requires checking each edge in E, which can be done in polynomial time.
**Proving T is Answer-Preserving:**
Let C be a clique of size k in G. If we apply the transformation T to G and obtain G', then the vertices in C will not be adjacent in G', as they form a clique in G. Hence, C becomes a k-independent set in G'.
Conversely, if S is a k-independent set in G', then the vertices in S are not adjacent in G'. This means that there is no edge connecting any pair of vertices in S in G'. Thus, S forms a clique of size k in G.
Therefore, the transformation T preserves the answer: if G has a k-clique, then G' has a k-independent set, and vice versa.
In conclusion, the transformation T from k-clique to k-independent set is polynomial-time and answer-preserving.
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What is the correct way to describe 1 inch and 4/16.
Answer:
say it is 4/16th of an inch
Step-by-step explanation
Louisa has 4 yards of fabric. She uses a 2/5 yard of fabric to make a doll dress.
How many doll dresses can Louisa make with the fabric?
Answer:
Louisa can make 10 doll dresses with 4 yards of fabric.
Step-by-step explanation:
We know that one doll dress requires 2/5 yard of fabric. The question is asking find how many dresses can be made from 4 yards of fabric, in which this equation can represent:
4 = 2/5x
Find x:
4 ÷ 2/5
= 4/1 x 5/2
= 20/2 or 10 (SIMPLIFIED)
So, Louisa can make 10 doll dresses with 4 yards of fabric.
I hope I helped!
.In a recent survey of people aged 50-71 in the United States, during a follow-up period the annual probability of lung cancer occurrence was about 0.00023 for people who had never smoked and about 0.01284 for current smokers who smoked more than two packs per day. (a) Find and interpret the relevant difference in proportions. (b) Find and interpret the relevant relative risk. (c) Which measure would you say is more informative, and why? (d) For a different type of cancer, the relative risk for smokers vs. non-smokers is 3.10. Can we say this is a concerning increase in risk from a practical point of view? Explain why or why not.
a) The probability of lung cancer occurrence in current smokers who smoke more than two packs per day is 0.01261 more than that of people who have never smoked.b) The probability of lung cancer occurrence in current smokers who smoke more than two packs per day is 57.08 times more than that of people who have never smoked. c) The relevant relative risk is more informative as it compares the probability of lung cancer occurrence in current smokers who smoke more than two packs per day to that of people who have never smoked.d) smokers have a 3.10 times higher risk of developing this type of cancer compared to non-smokers.
a) The relevant difference in proportions: Firstly, we need to determine the difference between the probability of lung cancer occurrence between the non-smokers and smokers who smoke more than two packs per day. The difference between the two proportions is as follows:P(X1) = 0.00023 (Probability of lung cancer occurrence in people who have never smoked)P(X2) = 0.01284 (Probability of lung cancer occurrence in current smokers who smoke more than two packs per day)
Therefore, the difference in proportion can be calculated as follows:P(X2) - P(X1) = 0.01284 - 0.00023 = 0.01261 (Answer)Interpretation: The probability of lung cancer occurrence in current smokers who smoke more than two packs per day is 0.01261 more than that of people who have never smoked.
b) The relevant relative risk:Relative risk = [P(X2)/1 - P(X2)] / [P(X1)/1 - P(X1)] = (0.01284/1 - 0.01284) / (0.00023/1 - 0.00023) = 57.08 (Answer)Interpretation: The probability of lung cancer occurrence in current smokers who smoke more than two packs per day is 57.08 times more than that of people who have never smoke
c) Which measure is more informative: The relevant relative risk is more informative as it compares the probability of lung cancer occurrence in current smokers who smoke more than two packs per day to that of people who have never smoked. It highlights the significant risk factor associated with smoking.
d) Concerning increase in risk from a practical point of view: Yes, a relative risk of 3.10 for a different type of cancer suggests a concerning increase in risk from a practical point of view. A relative risk of more than 1 suggests an increased risk associated with a particular factor. In this case, smokers have a 3.10 times higher risk of developing this type of cancer compared to non-smokers.
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What is 5 3/8 - 3 2/5 ( like fractions w a whole number )
Answer:
1.97500=1 and 39/40
Step-by-step explanation:
please give me brainliest
PLEASE HELP! WILL GIVE BRAINLIEST IF CORRECT!
Answer:
first mark brainliest
Answer:
its is b, supplementary angles
Step-by-step explanation:
–3b + –9 = –3
what is b
Given that, -3b + (-9) = (-3)
We have to find value of b[tex].[/tex]
⭆ -3b + (-9) = (-3)
⭆ -3b - 9 = -3
⭆ -3b = -3 + 9
⭆ -3b = 6
⭆ 3b = -6
⭆ b = -6/3
⭆ b = -2 [Final answer]
Hope It Helps!Solve the system by substitution:
Quincy wants to go to the movies with his friends
he has 20 dollars, 5 for the movie ticket and the rest for snacks. he wants to purchase 4 snacks, these snacks include 2$pizza,3$candy, what can he buy?
Answer:
2=pizza$
3=candy$
4 pizzas 2 cndys
Step-by-step explanation:
its hard to explain but he has 20 dollars -5 for ticket thats 15
helppp ill mark u as brainlist
Answer:
More work space
Step-by-step explanation:
Parameterize the plane that contains the three points (-4,-2, 2), (8. - 12. -6), and (40,0,0). F(s, t) - (Uses and for the parameters in your parameterization, and enter your victor as a single wctor, with angle brackets eg, as)
the parameterization of the plane that contains the three points (-4, -2, 2), (8, -12, -6), and (40, 0, 0) is: F(s, t) = (-4 + s, -2 + t, 2)
How to find the parameterization of the planeTo parameterize the plane that contains the three points (-4, -2, 2), (8, -12, -6), and (40, 0, 0), we can use two vectors that lie in the plane and find their cross product. The cross product will give us the normal vector to the plane, which we can then use to parameterize the plane.
Let's take the vectors formed by the points (-4, -2, 2) and (8, -12, -6), and (-4, -2, 2) and (40, 0, 0).
Vector v1 = (8, -12, -6) - (-4, -2, 2) = (12, -10, -8)
Vector v2 = (40, 0, 0) - (-4, -2, 2) = (44, 2, -2)
Now, let's calculate the cross product of v1 and v2:
Normal vector N = v1 x v2 = (12, -10, -8) x (44, 2, -2)
To find the cross product, we can use the following formula:
N = (v1.y * v2.z - v1.z * v2.y, v1.z * v2.x - v1.x * v2.z, v1.x * v2.y - v1.y * v2.x)
Calculating the cross product:
N = ( (-10 * -2) - (-8 * 2), (-8 * 44) - (12 * -2), (12 * 2) - (-10 * 44) )
= ( -16, -400, -568 )
Now, we have the normal vector N = (-16, -400, -568) which is perpendicular to the plane. We can use this vector to parameterize the plane.
Let's define a point on the plane as P0 = (-4, -2, 2).
The parameterization of the plane can be given by the equation:
F(s, t) = P0 + s * U + t * V
Where U and V are two linearly independent vectors lying in the plane.
Let's choose U = (1, 0, 0) and V = (0, 1, 0) as the vectors lying in the plane.
Substituting the values, we get:
F(s, t) = (-4, -2, 2) + s * (1, 0, 0) + t * (0, 1, 0)
= (-4 + s, -2, 2) + (0, t, 0)
= (-4 + s, -2 + t, 2)
Therefore, the parameterization of the plane that contains the three points (-4, -2, 2), (8, -12, -6), and (40, 0, 0) is:
F(s, t) = (-4 + s, -2 + t, 2)
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HELP ME PLEASE WILL MARK
Answer:
Step-by-step explanation:
The points lie on a straight line and go through the origin
Plz help me and solve step by step
Thank you.
Answer:
p ≥ 13
13 pizzas at least
Step-by-step explanation:
$107 + $4 = $111
$111/$9 = 12.3333 round it to 13
now we know he needs to sell at least 13 pizzas so the inequality p= 13 or p > 13.
This is my go at it, I am not sure though.
Find the slope of (-12,3) (16,-11)
Answer:
the slope is -1/2
Step-by-step explanation:
the formula for slope is m= y2-y1/x2-x1 (m is the slope)
the points are (-12,3) and (16,-11)
label the numbers
x1: -12
y1: 3
x2: 16
y2: -11
Now plug everything in
m=-11-3/16--12
m=-14/28
m= -1/2
Hope this helps!
Easy with a lot of points
Help me solve these three problems!!
Step-by-step explanation:
4y=12x+20
4y=32x
4y/4=32x/4
=8x
plsss help!! i would greatly appreciate it
Answer:
1.
A) Corresponding angles
B) Alternate Exterior angles
C) Interior Angles
I can't figure out #2.
Step-by-step explanation:
expand (3m+1/3n)^3 pls explain step by step
Answer:
[tex]\bold{\underline{(3m+\frac13n)^3=27m^2+9m^2n+mn^2+\frac1{27}n^2}}[/tex]
Step-by-step explanation:
[tex](3m+\frac13n)^3=(3m+\frac13n)(3m+\frac13n)(3m+\frac13n)=\\\\=\left[(3m)(3m)+(3m)\left(\frac13n\right)+\left(\frac13n\right)(3m)+\left(\frac13n\right)\left(\frac13n\right)\right]\left(3m+\frac13n\right)=\\\\=\left[9m^2+mn+mn+\frac19n^2\right]\left(3m+\frac13n\right)=\\\\=\left[9m^2+2mn+\frac19n^2\right]\left(3m+\frac13n\right)=\\\\=9m^2(3m)+9m^2(\frac13n)+2mn(3m)+2mn(\frac13n)+\frac19n^2(3m)+\frac19n^2(\frac13n)=\\\\=27m^3+3m^2n+6m^2n+\frac23mn^2+\frac13mn^2+\frac1{27}n^2=\\\\=27m^2+9m^2n+mn^2+\frac1{27}n^2[/tex]
Solve each problem using quadratic functions. 1. The sum of two positive integers is 35. What is the minimum sum of their squares? 2. A rectangle has a perimeter of 100 cm. Find the greatest possible area for the rectangle.
1. The minimum sum of their squares is achieved when the two integers are 8 and 9, resulting in a sum of 793.
2. The greatest possible area for the rectangle is 625 square centimeters, which occurs when the length is 25 cm and the width is also 25 cm.
The sum of two positive integers is 35. To find the minimum sum of their squares, let's assume the two integers are x and y.
Given: x + y = 35
We want to minimize the sum of their squares, which can be represented as:
S = x^2 + y^2
To solve this problem using quadratic functions, we need to express one variable in terms of the other and then substitute it into the equation for S.
From the given information, we have:
x = 35 - y
Substituting this into the equation for S, we get:
S = (35 - y)^2 + y^2
Expanding and simplifying, we have:
S = 1225 - 70y + y^2 + y^2
S = 2y^2 - 70y + 1225
Now, we have a quadratic function for S in terms of y. To find the minimum value of S, we can use the vertex formula:
The x-coordinate of the vertex of a quadratic function in the form f(x) = ax^2 + bx + c is given by x = -b / (2a).
In our case, a = 2, b = -70. Substituting these values into the formula, we get:
y = -(-70) / (2 * 2)
y = 35 / 4
y = 8.75
Since the variables represent positive integers, we will consider the nearest integer values of y, which are 8 and 9.
Checking the values of S at y = 8 and y = 9:
For y = 8:
S = 2(8^2) - 70(8) + 1225
S = 128 - 560 + 1225
S = 793
For y = 9:
S = 2(9^2) - 70(9) + 1225
S = 162 - 630 + 1225
S = 757
Therefore, the minimum sum of their squares is achieved when the two integers are 8 and 9, resulting in a sum of 793.
A rectangle has a perimeter of 100 cm. To find the greatest possible area for the rectangle, let's assume the length of the rectangle is x and the width is y.
Given: 2x + 2y = 100
We want to maximize the area of the rectangle, which can be represented as:
A = xy
To solve this problem using quadratic functions, we need to express one variable in terms of the other and then substitute it into the equation for A.
From the given information, we have:
x = (100 - 2y) / 2
x = 50 - y
Substituting this into the equation for A, we get:
A = (50 - y) * y
A = 50y - y^2
Now, we have a quadratic function for A in terms of y. To find the maximum value of A, we can again use the vertex formula:
The x-coordinate of the vertex of a quadratic function in the form f(x) = ax^2 + bx + c is given by x = -b / (2a).
In our case, a = -1, b = 50. Substituting these values into the formula, we get:
y = -(50) / (2 * -1)
y = 25
Checking the value of A at y = 25:
A = 50(25) - (25)^2
A = 1250 - 625
A = 625
Therefore, the greatest possible area for the rectangle is 625 square centimeters, which occurs when the length is 25 cm and the width is also 25 cm.
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Plz answer it’s timed
Answer:
(-2, 0), (0, -1), (-3, 0)
Step-by-step explanation:
if you know coordinates, just find it on the graph and see if it falls in the region, if it falls on a solid line, it is ok, and if it falls on a dashed line, it is not in the region
so the okay ones are
(-2, 0)
(0, -1)
(-3, 0)
If Hal multiplies one side of the equation below by 7, what does he need to do to balance the equation? 56 + 124 = 180 A Add 7 to the other side. B Subtract 7 from the other side. C Divide each side by 7. D Multiply the other side by 7.
Answer:D
Step-by-step explanation: All equations should be balanced and equal. What you do to one side, must be done to the other.
Solve for C. a(c+b)=d
Answer:
a=db+c
Step-by-step explanation:
a(c+b)=d
Step 1: Factor out variable a.
a(b+c)=d
Step 2: Divide both sides by b+c.
a(b+c)b+c=db+c
a=db+c
Alexandra is a head librarian in a city with a population of 1.8×106 residents. When her library system conducted a survey, they found that the average resident visits a library 1.5 times per year. How many total library visits per year does that work out to?
Answer:
1.8 x 166 = 190.8
190.8 divided by 1.5 = 127.2
Step-by-step explanation:
The total library visits per year work out to 2700000.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
To find the total number of library visits per year, we can multiply the number of residents by the average number of visits per resident per year:
total library visits per year = (number of residents) x (average visits per resident per year)
= 1.8 x 10⁶ x 1.5
= 2.7 x 10⁶
= 2700000
Therefore, the total number of library visits per year is 2.7 x 10⁶.
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Can someone please help me asap ?!? I’ll mark brainlist
Answer:
Step-by-step explanation:
Classify the pair of the numbered angles. Select the correct choice under each figure.
Alternate Exterior Angles Alternate Interior Angles Corresponding Angles Consecutive Interior Angles
Answer/Step-by-step explanation:
First figure:
<2 and <1 lie outside the two lines cut across by the transversal, and they also lie in opposite sides of the transversal. Therefore:
<1 and <2 are Alternate Exterior Angles
Second figure:
<3 and <4 lie within the two lines cut across by the transversal. And also lie on the same side of the transversal. Therefore:
<3 and <4 are Consecutive Interior Angles
Third Figure:
<5 and <6 both lie in the same position on the two lines cut by the transversal. Therefore:
<5 and <6 are Corresponding Angles
Fourth Figure:
<7 and <8 lie inside the two lines cut across by the transversal, and also lie in opposite directions of the transversal, therefore:
<7 and <8 are Alternate Interior Angles
If m∠1 equals (4x + 2)° and m∠2 equals 110°, what is the value of x?
Answer:
x = 17
Step-by-step explanation:
Assuming that the sum of the two angles is equal to 180 degrees, then the equation to solve for angle 1 is
4x + 2 + 110 = 180
4x + 112 = 180
Then solve for x
4x = 68
x = 17
Then to find angle 1 just plug x into the equation for angle 1
4x + 2
4(17) + 2
Angle 1 = 70
The productive activities of a producer can have one of the
following effects on the supply side of a market:
A. A positive external effect on other producers, where MSC
> MPC
B. A positive
The productive activities of a producer can have a positive external effect on other producers, where the Marginal Social Cost (MSC) is greater than the Marginal Private Cost (MPC). This means that the producer's actions generate positive externalities that benefit other producers in the market.
The productive activities of a producer can have different effects on the supply side of a market. One effect is a positive external effect on other producers, where the Marginal Social Cost (MSC) is greater than the Marginal Private Cost (MPC).
A. Positive external effect on other producers: In this case, the producer's activities generate positive externalities, which benefit other producers in the market. The Marginal Social Cost (MSC), which includes both the private cost to the producer and the external cost imposed on others, exceeds the Marginal Private Cost (MPC), which represents only the private cost to the producer. This indicates that the producer's actions have a broader positive impact beyond their own costs and benefits.
Positive external effects can arise in various situations. For example, a producer implementing environmentally friendly production methods that reduce pollution can benefit other producers by improving the overall quality of the environment. The cleaner environment may lead to better health conditions for workers, reduced production costs for other producers, and increased productivity in the market as a whole.
These positive external effects highlight the importance of considering the broader social costs and benefits associated with production activities. By accounting for externalities and taking actions to promote positive spillover effects, policymakers and producers can work towards a more efficient and socially beneficial allocation of resources.
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3. Consider the following system: →0.85→0.85→ Determine the probability that the system will operate under each of these conditions: a. The system as shown. (Do not round your intermediate calculations. Round your final answer to 4 decimal places.) b. Each system component has a backup with a probability of .85 and a switch that is 100 percent reliable. (Do not round your intermediate calculations. Round your final answer to 4 decimal places. c. Each system component has a backup with a probability of .85 and a switch that is 90 percent reliable. (Do not round your intermediate calculations. Round your final answer to 4 decimal places.)
a. The probability that the system will operate as shown is approximately 0.6141.
b. Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.
c. The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.
a. To find the probability that the system will operate as shown, we multiply the probabilities of each component. Since the system is shown to have three components with a probability of 0.85 each, we can calculate:
Probability = 0.85 × 0.85 × 0.85
Probability ≈ 0.6141
The probability that the system will operate as shown is approximately 0.6141.
b. In this case, each system component has a backup with a probability of 0.85 and a switch that is 100% reliable. Since the backup has a probability of 0.85, and the switch is 100% reliable (probability = 1), we can calculate the probability as:
Probability = 0.85 × 0.85 × 0.85
Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.
c. In this scenario, each system component has a backup with a probability of 0.85, but the switch is 90% reliable (probability = 0.90). We can calculate the probability as:
Probability = 0.85 × 0.90 × 0.85
Probability ≈ 0.6485
The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.
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help? Please jdjxjc
Answer:
4
Step-by-step explanation:
Solve the quadratic equation using square roots method.Leave the answer in irrational form. 15-6x-2x^2=0 HELP
Answer:
Solve Quadratic Equation by Completing The Square
Solving 2x2-6x-15 = 0 by Completing The Square .
Divide both sides of the equation by 2 to have 1 as the coefficient of the first term :
x2-3x-(15/2) = 0
Add 15/2 to both side of the equation :
x2-3x = 15/2
Now the clever bit: Take the coefficient of x , which is 3 , divide by two, giving 3/2 , and finally square it giving 9/4
Add 9/4 to both sides of the equation :
On the right hand side we have :
15/2 + 9/4 The common denominator of the two fractions is 4 Adding (30/4)+(9/4) gives 39/4
So adding to both sides we finally get :
x2-3x+(9/4) = 39/4
Adding 9/4 has completed the left hand side into a perfect square :
x2-3x+(9/4) =
(x-(3/2)) • (x-(3/2)) =
(x-(3/2))2
Things which are equal to the same thing are also equal to one another. Since
x2-3x+(9/4) = 39/4 and
x2-3x+(9/4) = (x-(3/2))2
then, according to the law of transitivity,
(x-(3/2))2 = 39/4
Step-by-step explanation:
Basically, the answer is -1.622 and 4.622.
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