After a data set was partitioned, the first partition contains 43 cases that belong to Class 1 and 12 cases that belong to Class 0, and the second partition contains 24 cases that belong to Class 1 and 121 cases that belong to Class 0.
a. Compute and list the Gini impurity index for the root node. (Round your answer to 4 decimal places.)
b. Compute and list the Gini impurity index for partition 1. (Round your answer to 4 decimal places.)
c. Compute and list the Gini impurity index for partition 2. (Round your answer to 4 decimal places.)
d. Compute and list the Gini impurity index for the split. (Round your answer to 4 decimal places.)
Answers
a. The Gini impurity index for the root node is 0.469
b. The Gini impurity index for partition is 0.3208
c. The Gini impurity index for partition 2 is 0.2249
d. The Gini impurity index for the split is 0.2514.
a. The Gini impurity index for the root node can be calculated as follows:
Total cases in both partitions = 43 + 12 + 24 + 121 = 200
Proportion of Class 1 cases in root node = (43 + 24) / 200 = 0.335
Proportion of Class 0 cases in root node = (12 + 121) / 200 = 0.665
Gini impurity index = \(1 - ((0.335)^2 + (0.665)^2) = 0.469\)
b. The Gini impurity index for partition 1 can be calculated as follows:
Total cases in partition 1 = 43 + 12 = 55
Proportion of Class 1 cases in partition 1 = 43 / 55 = 0.782
Proportion of Class 0 cases in partition 1 = 12 / 55 = 0.218
Gini impurity index =\(1 - ((0.782)^2 + (0.218)^2) = 0.3208\)
c. The Gini impurity index for partition 2 can be calculated as follows:
Total cases in partition 2 = 24 + 121 = 145
Proportion of Class 1 cases in partition 2 = 24 / 145 = 0.1655
Proportion of Class 0 cases in partition 2 = 121 / 145 = 0.8345
Gini impurity index =\(1 - ((0.1655)^2 + (0.8345)^2) = 0.2249\)
d. The Gini impurity index for the split can be calculated as follows:
Weighted average of the Gini impurity index for partition 1 and partition 2:
[(55/200) × 0.3208] + [(145/200) × 0.2249] = 0.2514
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Related Questions
when writing a decimal number that is less than 1, you must apply the _________ zero rule, to clarify the decimal point is there.
Answers
When writing a decimal number that is less than 1, you must apply the leading zero rule to clarify the decimal point is there.
What is leading zero rule ?The leading zero rule states that when writing a decimal number that is less than 1, you should include a leading zero before the decimal point to indicate that the number is less than 1. For example, if you want to write the decimal number 0.75, you should write it as "0.75" with a leading zero, rather than just "75", to indicate that it is a decimal number and not a whole number.This is important because it helps to clearly indicate the place value of each digit in the number. Without the leading zero, it might be difficult to tell whether the number is a decimal or a whole number. The leading zero rule helps to avoid confusion and ensures that decimal numbers are written clearly and accurately.To learn more about decimal number refer :
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A manufacturing press costs $63959 and it depreciates in value 1.3% per month. What is its value 3 years after its purchase date? (Hint: use a geometric series.) Please answer as a number. Do not include the dollar sign.
Answers
The manufacturing press costs $63959 and depreciates in value by 1.3% per month.
Here is the calculation that will help to find its value in three years using a geometric series and its value as a number. The initial cost of the press is $63959.
The depreciation in value of the press per month is 1.3% or 0.013 of its initial value.
Since the press depreciates every month, the number of times that it has depreciated after three years is 36 (3 years x 12 months per year).
To calculate the value of the press after 3 years, we use the formula for a geometric series that is:Where, a is the first term, r is the common ratio, and n is the number of terms.
The first term is the initial value of the press (a = $63959), and the common ratio is (1 - 0.013), which is 0.987.The number of terms is 36 (n = 36), which is the number of times the press depreciates after three years.
After substituting the values in the above formula, we get:Therefore, the value of the press three years after its purchase date is $47822.56 (rounded to the nearest cent).
Summary: The value of the press three years after its purchase date is $47822.56 (rounded to the nearest cent) using a geometric series formula.
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Hi, does anyone mind helping me with this pls?
Answers
Answer:
a and b
Step-by-step explanation:
they're both equal to 25%; 100 reduced by 75 is 25
3) Justin made some cookies for the holiday. She baked 10 sugar cookies, 18 chocolate chip cookies, and 15 ginger cookies. What is the ratio of sugar cookies to ginger cookies in simplest form?
Answers
Divide each by GCF of 3
6:5 ——> answer
Which is greater 9/2 or 8/3
Answers
Answer:
9/2 is greater than
Step-by-step explanation:
Help me with this!!!!
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Well the half point of 427 and 428 is 427.5 so 427.5.
what do you call the result of this opperation 2x+5
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Answer:
addition?
Step-by-step explanation:
How to find the critical points of a function.
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An automobile manufacturing plant produced vehicles today: were sedans, were trucks, and were motorcycles. Plant managers are going to select two of these vehicles for a thorough inspection. The first vehicle will be selected at random, and then the second vehicle will be selected at random from the remaining vehicles. What is the probability that two motorcycles will be selected
Answers
Answer:
120 / 561
Step-by-step explanation:
An automobile manufacturing plant produced 34 vehicles today: 16 were motorcycles, 9 were trucks, and 9 were vans. Plant managers are going to select two of these vehicles for a thorough inspection. The first vehicle will be selected at random, and then the second vehicle will be selected at random from the remaining vehicles.What is the probability that two motorcycles will be selected
16/34 X 15 X 33
quick and easy plz help
Answers
If m∠AED = 35°, what is m∠ABC?
Answers
The measure of angle ABC is given as follows:
m < ABC = 145º.
What are supplementary angles?Two angles are defined as supplementary angles when the sum of their measures is of 180º.
In a parallelogram, we have that the opposite angles are supplementary.
The opposite angles for this problem are given as follows:
<AED.<ABC.Hence the measure of angle ABC is given as follows:
m < ABC + 35º = 180º.
m < ABC = 145º.
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if two significant main effects emerge in a two-factor anova, then the interaction between factors must be significant.T/F
Answers
False. In a two-factor ANOVA, if two significant main effects emerge, it does not necessarily mean that the interaction between factors is significant. Main effects and interaction effects are independent of each other and can have different levels of significance.
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The presence of significant main effects does not necessarily indicate a significant interaction between factors in a two-factor ANOVA. It is possible for there to be significant main effects without a significant interaction.
Therefore, it is important to examine both the main effects and the interaction effects in a two-factor ANOVA to fully understand the relationship between the variables being studied.
False
In a two-factor ANOVA, there are three possible significant effects: two main effects for each factor and one interaction effect between the factors. When two significant main effects emerge, it means that there are significant differences in the levels of both factors. However, this does not automatically mean that the interaction between the factors must also be significant. The interaction effect is an entirely separate effect and can be significant or non-significant regardless of the significance of the main effects.
If two significant main effects emerge in a two-factor ANOVA, it does not necessarily mean that the interaction between factors must be significant.
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a) Find the maximum value of f(x,y) = x^{3}y^{4} for x,y \geq 0 on the unit circle.
Answers
The maximum value of f(x,y) on the unit of circle is \(\frac{48 \sqrt{21}}{2,401}\).
The full question is in the attachment. From the unit circle
x² + y² = 1y² = 1 - x²Substitute to f(x,y)
f(x,y) = x³y⁴ = x³ (y²)² = x³ (1 - x²)²
f(x,y) = x³ (1 - 2x² + x⁴)
f(x,y) = x³ - 2x⁵ + x⁷
df/dx = 3x² - (2 × 5)x⁴ + 7x⁶
df/dx = 3x² - 10x⁴ + 7x⁶
df/dx = x² (3 - 10x² + 7x⁴)
To find the maximum or minimum value, the derivated equals zero.
0 = x² (7x⁴ - 10x² + 3)
0 = x² (x - 1) (x + 1) (7x² - 3)
x² = 0x = 0
f(x,y) = x³ - 2x⁵ + x⁷ = 0³ - (2 × 0⁵) + 0⁷ = 0x - 1 = 0
x = 1
f(x,y) = 1³ - (2 × 1⁵) + 1⁷ = 1 - 2 + 1 = 0x + 1 = 0
x = - 1
f(x,y) = (- 1)³ - (2 × (- 1)⁵) + (- 1)⁷ = - 1 + 2 - 1 = 0
7x² - 3 = 0
Using ABC formula
a = 7b = 0c = - 3\(x_{1,2} \:=\: \frac{-b \pm \sqrt{b^2 \:-\: 4ac}}{2a}\)
\(x_{1,2} \:=\: \frac{-0 \pm \sqrt{0^2 \:-\: (4 \times 7 \times - 3)}}{2 \times 7}\)
\(x_{1,2} \:=\: \frac{\pm \sqrt{4 \times 21)}}{14}\)
\(x_{1,2} \:=\: \frac{\pm 2 \sqrt{21}}{14}\)
\(x_{1,2} \:=\: \frac{\pm \sqrt{21}}{7}\)
\(x_1 \:=\: \frac{\pm \sqrt{21}}{7}\)f(x,y) = x³ - 2x⁵ + x⁷
\(f \:=\: (\frac{\sqrt{21}}{7})^3 \:-\: (2 \times (\frac{\sqrt{21}}{7})^5) \:+\: (\frac{\sqrt{21}}{7})^7\)
\(f \:=\: \frac{21 \sqrt{21}}{7^3} \:-\: \frac{2 \times 21 \times 21 \sqrt{21}}{7^5} \:+\: \frac{21 \times 21 \times 21 \sqrt{21}}{7^7}\)
\(f \:=\: \frac{7^4 \times 21 \sqrt{21} \:-\: 7^2 \times 2 \times 21 \times 21 \sqrt{21} \:+\: 21 \times 21 \times 21 \sqrt{21}}{7^7}\)
\(f \:=\: \frac{7^5 \times 3 \sqrt{21} \:-\: 7^4 \times 2 \times 3 ^2 \sqrt{21} \:+\: 7^3 \times 3^3 \sqrt{21}}{7^7}\)
\(f \:=\: \frac{7^3 \: (7^2 \times 3 \sqrt{21} \:-\: 7 \times 2 \times 3 ^2 \sqrt{21} \:+\: 3^3 \sqrt{21})}{7^7}\)
\(f \:=\: \frac{147 \sqrt{21} \:-\: 126 \sqrt{21} \:+\: 27 \sqrt{21}}{7^4}\)
\(f \:=\: \frac{48 \sqrt{21}}{2,401}\)\(x_2 \:=\: - \frac{\sqrt{21}}{7}\)
\(f \:=\: (- \frac{\sqrt{21}}{7})^3 \:-\: (2 \times (- \frac{\sqrt{21}}{7})^5) \:+\: (- \frac{\sqrt{21}}{7})^7\)
\(f \:=\: \frac{- 147 \sqrt{21} \:+\: 126 \sqrt{21} \:-\: 27 \sqrt{21}}{7^4}\)
\(f \:=\: \frac{- 48 \sqrt{21}}{2,401}\)
The maximum value from x₁.
The minimum value from x₂.
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3(4j+1) = 2(6j +3/2)
Helpp
Answers
One hundred pyramid-shaped chocolate candies with a square base with 12 mm sides and height of 15 mm are melted in a cylindrical pot. If the pot has a radius of 75 mm, what is the height of the melted candies in the pot?
Answers
Step-by-step explanation:
Volume of 100chocolates:
((12^2 x 15)/3) x 100 =72000
volume of cylinder:
base area x height
base area= πr^2= 5625π
height=volume/base area
height=72000/5625π=4.07 (3sf)
ans: 4.07mm
what is the range of the function f(x)=7-3x when the domain is -4, -2, 0, 2?
pls help asap. i’m giving 75 points
Answers
f(4) = 7-3(4) = -5
f(-2) = 7-3(-2)= 13
f(0) = 7-3(0)= 7
f(2) = 7-3(2) = 1
I need these answers please, I have a D this'll bring up my grade alot.
Answers
Answer: a=-1, -3
h=-3, 0
k=8, -4
Step-by-step explanation:
find the value of x. PLEASE HELP
The answer is 14, teacher gave us the answer, but I need to show my work
Answers
Answer:
14*
Step-by-step explanation:
5x+4*=74*
-4 -4
5x=70*
x=14*
*dont mind the asterisks they are my temporary degree signs
hope this helps
brainliest?
2. (15 marks) On September 10 the Moon's phase was full, called a "harvest Moon" because of the time of year, and its distance from Earth was 370,746 km. (a) The Moon's average radius is 1737.4 km. What Kas the Moon's angular diameter on September 10? Express your answer in minutes of are, (b) The Moon's orbit around Earth is elliptical, and its average distance from Earth is 384,400 km. On September 10, what was the percentage difference between the Moon's actual angular diameter and its average angular diameter? (c) The Moon's angular diameter on September 10 found in part (a) was calculated either exactly using trigonometry or using the small angle approximation. What is the percentage error from using the small angle approximation? percent error ≡
θ
exact
(θ
exact
−θ
approx
)
×100
Answers
(a) The Moon's angular diameter on September 10 was approximately 16.92 minutes of arc.
(b) On September 10, the Moon's actual angular diameter was approximately 43.6% smaller than its average angular diameter.
(a) To find the Moon's angular diameter on September 10, we can use the formula:
Angular diameter = 2 * arctan (Moon's radius / Moon-Earth distance)
Moon's average radius (r) = 1737.4 km
Moon-Earth distance (d) = 370,746 km
Substituting these values into the formula, we have:
Angular diameter = 2 * arctan (1737.4 / 370,746)
Using a calculator, we find the angular diameter to be approximately 0.282 degrees.
To express this in minutes of arc, we multiply by 60 (since there are 60 minutes in a degree):
Angular diameter = 0.282 degrees * 60 minutes/degree ≈ 16.92 minutes of arc
Therefore, the Moon's angular diameter on September 10 was approximately 16.92 minutes of arc.
(b) To find the percentage difference between the Moon's actual angular diameter and its average angular diameter, we can use the formula:
Percentage difference = [(Actual angular diameter - Average angular diameter) / Average angular diameter] * 100
Average angular diameter (θ_average) = 0.5 degrees (since the Moon's average diameter is approximately 0.5 degrees)
Actual angular diameter (θ_actual) = 0.282 degrees (as calculated in part a)
Substituting these values into the formula, we have:
Percentage difference = [(0.282 - 0.5) / 0.5] * 100
Calculating this, we find the percentage difference to be approximately -43.6%.
Therefore, on September 10, the Moon's actual angular diameter was approximately 43.6% smaller than its average angular diameter.
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On September 10 the Moon's phase was full, called a "harvest Moon" because of the time of year, and its distance from Earth was 370,746 km. (a) The Moon's average radius is 1737.4 km. What Kas the Moon's angular diameter on September 10? Express your answer in minutes of are, (b) The Moon's orbit around Earth is elliptical, and its average distance from Earth is 384,400 km. On September 10, what was the percentage difference between the Moon's actual angular diameter and its average angular diameter?
How many teaspoons are in 400 milliliters? 1tsp=5ml
Answers
Answer:
80 tea spoons
Step-by-step explanation:
400÷5=80
hope it helps
\( \frac{1}{5} \frac{x}{400} \)
1x400/5=80/400
what is the probability that a 2-card hand (drawn from a standard deck of 52) has two queens, two kings, or one of each?
Answers
2/221 is the probability that a 2-card hand has two queens, two kings, or one of each.
What is probability?Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or the probability that a statement is true.Probability varies between zero and 1, wherein zero approaches are not possible and 1 approach is certain.Now, calculate the probability as follows:
There are 4 kings and 4 queens in a deck of cards.Then, it can be either KK or QQ.
Select 2 kings from 4 king cards that can be done in 4c₂=6 ways.Select 2 queens from 4 queen cards that can be done in c₂ = 6 ways.Total ways = 52c₂ = 1326So required probability = 2king or 2 queen
= 6/1326 + 6/1326= 12/1326= 2/221Therefore, the probability that a 2-card hand (drawn from a standard deck of 52) has two queens, two kings, or one of each is 2/221.
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What are the 5 steps in dividing rational expressions?.
Answers
The 5 steps in dividing rational expressions are explained below.
What are rational expressions?Rational expression seem to be parts that have factors in their denominators (and frequently numerators as well). For instance, x 2 x + 3 \dfrac{x^2}{x+3} x+3x2 start part, x, squared, separated by, x, furthermore, 3, end portion is a reasonable articulation.
Steps to divide the rational expression,1) Take the rational expression.
2) Rewrite the division as the product of the first rational expression then, the reciprocal of the second.
3) Factor the numerators and denominators of rational expression completely.
4) Multiply the numerators and denominators together.
5) Simplify by dividing out common factors.
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A strawberry farmer will receive $33 per bushel of strawberries during the first week of harvesting. Each week after that, the value will drop $0.80 per bushel. The farmer estimates that there are approximately 125 bushels of strawberries in the fields, and that the crop is increasing at a rate of four bushels per week. When should the farmer harvest the strawberries (in weeks) to maximize their value? (Assume that "during the first week of harvesting" here means week 1.) weeks How many bushels of strawberries will yield the maximum value? bushels What is the maximum value of the strawberries (in dollars)? $
Answers
To find the week when the farmer should harvest strawberries to maximize their value, we need to use quadratic equations. The equation for the value of strawberries is y = -0.8x^2 + 33x, where y is the value in dollars and x is the number of weeks after the first week of harvesting. To find the maximum value, we need to use the formula x = -b/2a, where a is -0.8 and b is 33. The maximum value occurs at x = 20.625 weeks. Plugging this into the equation, we can find that the maximum value is $527.81. To find the number of bushels that yield the maximum value, we can plug x = 20.625 into the equation for the number of bushels, which is y = 4x + 125. Therefore, the farmer should harvest strawberries in week 21 to maximize their value, and the maximum value is $527.81 for 205 bushels of strawberries.
To solve the problem, we need to use quadratic equations because the value of strawberries decreases linearly each week. The equation for the value of strawberries is y = -0.8x^2 + 33x, where y is the value in dollars and x is the number of weeks after the first week of harvesting. To find the maximum value, we need to use the formula x = -b/2a, where a is -0.8 and b is 33. Plugging these values into the formula, we get x = -33/(2*(-0.8)) = 20.625 weeks. This means that the maximum value occurs at week 21 since we started counting from the first week of harvesting.
To find the maximum value, we need to plug x = 20.625 into the equation for the value of strawberries. Therefore, y = -0.8*(20.625)^2 + 33*(20.625) = $527.81. This is the maximum value of the strawberries.
To find the number of bushels that yield the maximum value, we can plug x = 20.625 into the equation for the number of bushels, which is y = 4x + 125. Therefore, y = 4*(20.625) + 125 = 205 bushels of strawberries.
The farmer should harvest strawberries in week 21 to maximize their value, and the maximum value is $527.81 for 205 bushels of strawberries. The farmer can use this information to plan their harvesting schedule and maximize their profits.
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What is the 92nd term of 11,19,27
Answers
Answer:
the 92nd term of the arithmetic sequence is 731 because the common difference between them is 8.
How Do i get the correct answer for this?
Answers
Simple way :-
If a function has co-ordinates (x,y) then it's inverse has co-ordinates (y,x)
Now
(0,4)->(4,0)(1,6)->(6,1)(2,8)->(8,2)(3,10)->(10,3)Kofi is 5years older than Ama now. Two years ago, Kofi was twice as old as Ama. Find their ages now.
Answers
Answer:
Ama is an elephant so she is 2 years old
Step-by-step explanation:
Perform The Indicated Operation & Simplify. Express The Answer In Terms Of I (As A Complex Number) : (7 + 12 i ) . (7 + 12 i)
Answers
The simplified expression of (7 + 12i) × (7 + 12i) is -95 + 168i.
To perform the indicated operation and simplify, we'll multiply the expression (7 + 12i) by itself
(7 + 12i) × (7 + 12i)
Using the distributive property, we can expand this expression
= 7 × (7 + 12i) + 12i × (7 + 12i)
= 49 + 84i + 84i + 144i²
Since i² is equal to -1, we can simplify further:
= 49 + 168i + 144(-1)
= 49 + 168i - 144
= -95 + 168i
Therefore, the simplified expression is -95 + 168i.
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For the second application, 3.2 MB has been downloaded. How much is left to download?
Answers
The amount left to download is given by (x - 3.2) megabytes.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that for the second application, 3.2 MB has been downloaded.
Assume that the size of the second application is [x] MB. Then, if we
denote the amount left to download is denoted by [y], then we can
write -
y = x - 3.2
Therefore, the amount left to download is given by (x - 3.2) MB.
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Is this a function or not a function?
(6, 3) (5, 3) (4, 3) (3, 3)
Answers
express the integral ∭ef(x,y,z) dv∭ef(x,y,z) dv as an iterated integral in the three different ways below, where ee is the solid bounded by the surfaces y=225−9x2−25z2y=225−9x2−25z2 and y=0
Answers
The value of the triple integral is ∫0¹⁵∫-√(225-9x²-25z²)¹/²/(5)√9-x²/5∫(225-9x²-25z²-9y)¹/²ef(x,y,z) dy dx dz
The given integral to express as an iterated integral is ∭ef(x,y,z) dv in the solid EE bounded by the surfaces y=225−9x²−25z2y=225−9x²−25z² and y=0.
We can write the integral as an iterated integral in three different ways; in terms of dx dy dz, dz dy dx and dx dz dy. Let's derive the three different iterated integrals below:Using the first iterated integral formula:dx dy dz∭∭∭ef(x,y,z)
dv = ∫0¹⁵ ∫-3√(5-y/9)¹/²/3√5 ∫-√(225-9x²-25z²)¹/²/(5)√9-x²/5ef(x,y,z) dx dz dyUsing the second iterated integral formula:dz dy dx∭∭∭ef(x,y,z)
dv = ∫-3√5∫(225-9x²-25z²)¹/²/5 ∫(225-9x²-25z²-9y)¹/²ef(x,y,z) dy dx dz
Using the third iterated integral formula:dx dz dy∭∭∭ef(x,y,z)
dv = ∫0¹⁵∫-√(225-9x²-25z²)¹/²/(5)√9-x²/5∫(225-9x²-25z²-9y)¹/²ef(x,y,z) dy dx dz
Hence, the three iterated integrals for the given function in the given solid are as derived above.
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