The expected winnings are $3 for each time that you play the game.
What is expected winnings?
The expected value is a generalization of the weighted average in probability theory. Informally, the expected value is the arithmetic mean of a significant number of outcomes of a random variable that were independently chosen.
For an event with the outcomes {x₁, x₂, x₃,...} each one with correspondent probabilities {p₁, p₂, ...}
The expected value (here is equivalent to the expected winnings) is given by:
EV = x₁*p₁ + x₂* p₂ + ...
Here the outcomes are:
Winning $20, this happens if you draw a green marble, and there are:
7 green ones
3 yellow ones
10 black ones.
So 7 out of 20, then the probability is p₁ = 7/20
The second outcome is win $30 if you get a yellow one, there are 3 yellow ones, so the probability is p₂ = 3/10
Finally, you lose $15 if you get a black one, the probability now is
p₃ = 10/20
Then the expected winnings (remember that costs $1 to play, so we need to take that in consideration) is:
W = -$1 + $20*(7/20) + $30*(3/20) - $15*(10/20) = $3
Hence, the expected winnings are $3 for each time that you play the game.
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Find the value of q for which the equation
qx² - 6x + 18 = 0
has one repeated real root
q = ______
Answer:
q = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
given a quadratic equation in standard form
ax² + bx + c = 0 ( a ≠ 0 )
then the nature of the roots can be found using the discriminant
Δ = b² - 4ac
• if b² - 4ac > 0 then roots are real and irrational
• if b² - 4ac = 0 then the roots are real and equal
• if b² - 4ac < 0 then the roots are not real
qx² - 6x + 18 = 0 ← is in standard form
with a = q , b = - 5 , c = 18
for one repeated (equal) real root , then
b² - 4ac = 0 ( substitute values )
(- 6)² - (4 × q × 18) = 0
36 - 72q = 0 ( subtract 36 from both sides )
- 72q = - 36 ( divide both sides by - 72 )
q = [tex]\frac{-36}{-72}[/tex] = [tex]\frac{1}{2}[/tex]
I dont understand this problems
The value of x = 7 (blue)
The value of x = 6 (yellow)
The value of x = 4 (marron)
The value of x = 20 (black)
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
1,
The two angles are equal.
The sides opposite to the angles are also equal.
x = 7 (blue)
2.
The given triangle is an equilateral triangle.
All angles are equal.
The sides opposite to the angles are also equal.
x = 6 (yellow)
3.
Alternate angles are equal.
The sides opposite to the alternate angles are also equal.
x = 4 (marron)
4.
The given triangle is an isosceles triangle.
Two sides are equal.
One angle is 40.
The sum of the angles is 180.
x + x + 40 = 180
2x + 40 = 180
2x = 140
x = 20 (black)
Thus,
x = 7 (blue)
x = 6 (yellow)
x = 4 (marron)
x = 20 (black)
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Suppose that the functions g and h are defined as follows.
g(x)=5-4 x²
h(x)=5-4 x
(b) Find all values that are NOT in the domain of g/h
If there is more than one value, separate them with commas.
By using the concept of function, it can be calculated that-
a) [tex]\frac{g}{h}(-3) = -\frac{31}{17}[/tex]
b) The point [tex]\frac{5}{4}[/tex] is not in the domain of [tex]\frac{g}{h}[/tex]
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here,
a) The given functions are
g(x) = 5 - 4x²
h(x) = 5 - 4x
[tex]\frac{g}{h}(x) = \frac{g(x)}{h(x)} = \frac{5-4x^2}{5-4x}[/tex]
[tex]\frac{g}{h}(-3) = \frac{g(-3)}{h(-3)} = \frac{5 - 4(-3)^2}{5 - 4(-3)} = -\frac{31}{17}[/tex]
b) [tex]\frac{g}{h}(x)[/tex] is not defined if 5 - 4x = 0
[tex]\frac{g}{h}(x)[/tex] is not defined if [tex]x = \frac{5}{4}[/tex]
So the point [tex]\frac{5}{4}[/tex] is not in the domain of [tex]\frac{g}{h}[/tex].
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1 Look at parallelogram EFGH shown below. 10+ y E 10-9-8-7-6-5-4-3-2 H 9996 NYMNA 7 512 45679 -10k What is its perimeter? F 34 G fin 6 IN 00 of 10
The perimeter of the parallelogram is 24 units
How to determine the perimeter of the parallelogramFrom the question, we have the following parameters that can be used in our computation:
The parallelogram is added as an attachment
When the number of units on each side of the parallelogram is counted, we have the following representation
EH = FG = 7 units
EF = GH = 5 units
The perimeter of the parallelogram is the sum of the side lengths
So, we have the following representation
Perimeter = EH + EF + FG + GH
Substitute the known values in the above equation, so, we have the following representation
Perimeter = 7 + 7 + 5 + 5
Evaluate the sum
Perimeter = 24
Hence, the perimeter is 24 units
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Calculate how much you would have in 20 years if you saved $3,000 a year at an annual rate of 8 percent with the company contributing $750 a year. Use Exhibit 1-B. (Round time value factor to 3 decimal places and answer to the nearest whole dollar.)
Calculate how much you would have in 20 years if you saved $3,000 a year at an annual rate of 8 percent with the company contributing $750 a year. Use Exhibit 1-B. (Round time value factor to 3 decimal places and answer to the nearest whole dollar.)
Answer:69/100 you would save since it decreased in value
(20x³ - 15x² -15x+16) / (5x ²-5x)
Answer:
4x + 1 - 2/x + 6/(20x³ - 15x² -15x+16)
Step-by-step explanation:
4x + 1 - 2/x + 6/(20x³ - 15x² -15x+16)
________________
5x ²-5x | 20x³ - 15x² -15x+16
1 -(20x³ - 20x²) ==> -15x²-(-20x²)= -15x²+20x² = 5x²
5x² - 15x
2 -(5x² - 5x) ==> -15x-(-5x)= -15x+5x = -10x
-10x+16
3 -(10x+10)
6 ==> 16-10 = 6
1: At step 1, (4x) * (5x²-5x) = (20x³ - 20x²)
2: At step 2, 1 * (5x² - 5x) = 5x² - 5x
3: At step 3, (2/x) * (5x² - 5x) = 10x+10
: question 13 a teacher has decided to implement a curve to calculate grades for her class. her class average grade is a 65,
The minimum grade require to get grade of B is 78.6.
In the given that;
μ = 65 (average grade)
σ = 20 (standard deviation)
X ≈ N(μ, σ^{2})
Let c be the minimum grade to required to get grade of B
Percentage of data below c = 10% + 15% + 50% =75%
If we convert the percentage to probability = 75%/100% = 0.75
Now to get the value of c we solve the equation
P(X < c) = 0.75
⇒P{(X-μ)/σ < (c-μ)/σ)=0.75
Here z = (X-μ)/σ follows normal (0,1)
z is the standard normal variable
⇒P(z<(c-μ)/σ)=0.75
⇒P(z< (c-65)/20)=0.75
From z table we get, (c-65)/20 = 0.68
⇒(c-65)/20 = 0.68
⇒c= 78.6
So, minimum grade require to get grade of B is 78.6.
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The right question is given below:
1. The first letter of the suspect's name matches the variable with the greatest value.
7J=105 OR g-16=2
The name starts with letter g as the variable has highest value.
What is variable?
A variable is associate degree alphabet or term that represents an unknown variety or unknown worth or unknown amount. The variables square measure specially utilized in the case of algebraical expression or pure mathematics.
Main body:
according to question:
7j = 105
simplifying the value , we get
j = 105/7
j = 15
similarly
g - 16 = 2
simplifying the value , we get
g = 18
value of g is greater than j .
Hence the name starts with letter g.
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A sample of 200 g of an isotope decays to another isotope according to the function A(t}=200 e^{-0.054t}, where t is the time in years.
(a) How much of the initial sample will be left in the sample after 25 years?
(b) How long will it take the initial sample to decay to half of its original amount?
(a) After 25 years, about ? g of the sample will be left.
(Round to the nearest hundredth as needed.)
According to exponential equation 52 g sample will be left in the sample after 25 years
What is exponential equation?
The exponential function may be a function denoted by f(x)=\exp or e^. Unless otherwise fixed, the term usually refers to the positive-valued operate of a true variable
Main Body:
Given =
A(t}=200 e^{-0.054t}
A)
t = 25 years
A(25}=200 e^{-0.054*25}
A(25}=200 e^{-1.35}
A(25}=200 *0.26
A(25}= 52 g
B) A = 100
A(t}=200 e^{-0.054t}
100 =200 e^{-0.054t}
e^{-0.054t} = 1/2
taking logarithm on both sides , we get
t = 12.83 years
Hence the value for each parts are as follows.
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A grocery store bought milk for $2.30 per half gallon and stored it in two refrigerators. During the night, one refrigerator malfunctioned and ruined 14 half gallons. If the remaining milk is sold for $3.90 per half gallon, how many half gallons did the store buy if they made a profit of $105.40?
The number of half gallons that that store bought with the amount of profit they made would be = 41 half gallons.
What is a refrigerated milk?A refrigerated milk is the milk that is preserved in a refrigerator to prevent spoilage and prolong the shelf life of the milk.
A refrigerator is an electrical electronic device that is used for the preservation and storage of food and food products such as milk.
The amount that half gallon of milk was bought = $2.30 per half gallon.
The amount of half gallons of milk that was ruined= 14
The remaining milk was sold at = $3.90 per half gallon.
The profit made by the store = $105.40
The amount of half gallons that was bought,
= 105.40/3.90
= 27 + 14 ruined half gallon= 41 half gallons.
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Find the slope and y- intercept of the line -x + y = -10
Answer:
y-intercept | -10
slope | 1
Step-by-step explanation:
plane curve | Cartesian equation -x + y = -10 | y-intercept
slope
y-intercept | -10
slope | 1
2) Solve for m: 2.6m = 8.06
Answer: m = 3.1
Step-by-step explanation:
To solve for m you must divide 2.6m by 2.6m. Therefore, you must do the same on the other side of the equation.
2.6m/2.6m = 8.06/2.6m
m= 3.1
[tex]m=3.1.[/tex]
Step-by-step explanation:1. Write the equation.[tex]2.6m = 8.06[/tex]
2. Divide by 2.6 in both sides of the equation.[tex]\frac{2.6}{2.6} m=\frac{8.06}{2.6}\\ \\(1)m=\frac{8.06}{2.6}\\ \\m=\frac{8.06}{2.6}[/tex]
3. Simplify the fraction.[tex]m=\frac{8.06}{2.6}\\ \\m=3.1[/tex]
4 Verify the answer by substituting the calculated value by x in the original equation.[tex]2.6(3.1) = 8.06\\8.06=8.06[/tex]
That's correct!
5. Express the final result.[tex]m=3.1.[/tex]
What way can you simplify this equation?
Answer: 8√2
Step-by-step explanation:
What is the maturity date of a loan taken out on June 6, for 73 days?
The number of days in June is 30
The number of days in July = 31
The number of days in August = 31
The maturity date for a loan taken out on June 6 for 73 days is August 28.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The date on which the loan was taken = June 6.
The number of days for the loan to mature = 73 days.
Now,
The number of days in June is 30
The number of days in July = 31
The number of days in August = 31
Now,
There are (30 - 6) = 24 days remaining in the month of June.
So,
24 + 31(July) = 45 days.
Now,
73 - 45 = 28 days need to be taken from August.
So,
45(July) + 28(August) = 73 days.
This means,
The maturity date is August 28.
Thus,
The maturity date for a loan taken out on June 6 for 73 days is August 28.
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I thought of a number. If I add 30/7 to it, then subtract 22/7 from the result, and then subtract that difference from 59/7, I get 19/7. What is my number
Answer: 10
Step-by-step explanation:
x + 30/7-22/7-59/7 = 19/7
Add 59/7 to both sides:
x + 30/7-22/7 = 19/7 + 59/7
Add 22/7 to both sides
x + 30/7 = 19/7 + 59/7 + 22/7
Subtract 30/7 from both sides
x = 19/7+59/7+22/7-30/7
Simplify
x = 10
A line's y-intercept is 9, and its slope is 5. What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
y=____ x +____
The equation of the line that has a slope of 5 and y-intercept of 9 will be y = 5x + 9.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The slope of the line is 5. Then the equation is given as,
y = 5x + c
The y-intercept of the line is 9. Then the equation of the line is given as,
y = 5x + 9
The equation of the line that has a slope of 5 and y-intercept of 9 will be y = 5x + 9.
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Find the midrange for the following group of data items.
17, 14, 13, 12, 18, 15 11, 13
(Type an integer or a decimal)
Ahmed is planning to cook his family dinner and needs to purchase several food items. He is able to purchase these items either at the local grocery store or the farmer's market. Given in the table are the items and their prices.
Grocery Store Farmer's Market
8 tomatoes for $14 10 tomatoes for $16.50
4 cups of mozzarella cheese for $4.40 3 cups of mozzarella cheese for $3.45
12 eggs for $2.40 7 eggs for $1.75
Part A: Choose one of the food items offered at the grocery store and the farmer's market and determine the unit price of the item at each location. Show all necessary work, including the name of the item chosen. (6 points)
Part B: Based on your answer in part A, which location offers a better deal? Explain. (4 points)
Answer: Better Deals: for tomatoes--Farmer's Mkt., for cheese--Grocery, for eggs--Grocery
Step-by-step explanation:
Unit prices:
tomatoes: $14/8 = $1.75/tomato (grocery); $16.50/10 = $1.65 (farmers)
cheese: $4.40/4 = $1.10/cup (grocery); $3.45/3 = $1.15 (farmers)
eggs: $2.40/12 = $0.20/egg (grocery); $1.75/7 = $0.25/egg (farmers)
HELP I BEG
Which statement correctly applies mathematical reasoning to find the possible values for x in the equation x − 1.4 = 1.8?
x is between 0.2 and 1.8
x is greater than 1.8
x is less than 1
x is less than 0.2
Answer:
[tex]x[/tex] is greater than 1.8
Step-by-step explanation:
Adding 1.4 to both sides of the equation yields [tex]x=3.2>1.8[/tex].
The required reasoning for the given expression is that x is greater than 1.8. Option B is correct.
What is the expression?The expression is the relationship between variables and represented as y = ax + b is an example of a polynomial expression.
here,
Given expression,
x - 1.4 = 1.8
The above expression refers that, when we subtract 1.4 from x it gives 1.8, which implies that x is a number greater than 1.8.
So the reasoning can be complied as x is greater than 1.8.
Thus, the required reasoning for the given expression is that x is greater than 1.8. Option B is correct.
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Thomas has devised a scheme for splitting up the test and training set. For each row from coordinates : • Rows for Stanford students have a 50% chance of being placed in the train set and 50% chance of placed in the test set. • . Rows for Berkeley students have a 80% chance of being placed in the train set and 20% chance of placed in the test set.Given that a row is in the test set, what is the probability that it corresponds to a Stanford student? Assign that probability to prob_furd. Hint: Remember that there are 77 Berkeley students and 23 Stanford students in coordinates Hint 2: Thomas' last name is Bayes (15 points)
The probability that a row in the test set belongs to a Stanford student is 0.4167.
Given that,
Thomas has come up with a plan for dividing the training and test set. From the coordinates, for each row:
Students from Stanford have a 50% chance of being assigned to the test set and a 50% chance of being assigned to the train set for their rows.
20% of Berkeley students' rows are assigned to the test set, while 80% are assigned to the train set.
We have to find what is the probability that a row in the test set belongs to a Stanford student.
We know that,
Let us define events are as
B: Student in the coordinate is Berkeley student
S: Student in the coordinate is Stanford student
Tr: Rows is in the train set
Ts: Rows is in the test set
Since there are 77 Berkeley student and 23 Stanford student in coordinate
Hence,
P(B) = Probability that Student in the coordinate is Berkeley student
= 77/(77+23) = 77/100 = 0.77
P(S) = Probability that Student in the coordinate is Stanford student =23/(77+23) = 23/100 = 0.23
Conditional probability,
P(Ts|B) = Probability that Student placed in the test set when the student is Berkeley student = P(Ts|B) = 0.20
P(Ts|S) = Probability that Student placed in the test set when the student is Stanford student = P(Ts|S) = 0.5
Required probability,
Given that a row is in the test se, Probability that it corresponds to a Stanford student =
Probability of Stanford students = P(S|Ts) =
By Bayes theorem,
P(S|Ts) = P(Ts|S)×P(S)/P(Ts|S)×P(S)+P(Ts|B)×P(B)
P(S|Ts) = 0.22×0.5/0.22×0.5+0.20×0.77
P(S|Ts) = 0.4167
Therefore, The probability that a row in the test set belongs to a Stanford student is 0.4167.
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The Chungs recorded their monthly budget in a table. Complete the table. The first category is done for you.
7. Create a circle graph of the Chungs' budget.
To view the circle graph (pie chart) of the chungs' budget check the attached file.
What is pie chart?
A pie chart is a graphical representation technique that displays data in a circular-shaped graph.
Pie charts are often used to represent sample data with data points belonging to a combination of different categories.
Chung's budget in percentage:
Charity = 30/2145 x 100%
= 1.39%
= 1.4%
Clothes = 185/2145 x 100%
= 8.62%
Entertainment = 178/2145 x 100%
= 8.29%
Food = 424/2145 x 100%
= 19.76%
Rent = 1050/2145 x 100%
= 48.95%
Transportation = 213/2145 x 100%
= 9.93%
Others = 65/2145 x 100%
= 3.03%
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please help with this it is a final
Use the Pythagorean theorem to find the side of the right triangle. Length 3m, With 2m+14, 5m
The side lengths of the triangle are 11.1, 21.4, and 18.5 units.
What is the Pythagorean theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.
The given sides of the right triangle are 3m, 2m+14, and 5m.
As per the Pythagorean theorem, it follows:
(2m + 14)² = (3m)² + (5m)²
4m² + 196 + 56m = 9m² + 25m²
30m² -56m - 196 = 0
15m² - 28m - 98 = 0
[tex]m=\frac{-(-28)\pm\sqrt{(-28)^2-4(15)(-98)}}{2(15)}\\\\m=\frac{28\pm\sqrt{6664}}{2(15)}\\\\m =\frac{28\pm81.6}{2(15)}\\\\m=3.7\text{ or } m=-1.8[/tex]
Since the lengths cannot be negative, the value of m is m = 3.7.
Therefore, the side lengths of the triangle are:
3m = 3(3.7)
= 11.1
2m + 14
= 2(3.7) + 14
= 21.4
and,
5m
=5(3.7)
= 18.5
Hence, the side lengths of the triangle are 11.1, 21.4, and 18.5 units.
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(-2/3, 1/4); y - 2 = -2/3(x+1)
Answer:
10?
__________________
Hope this helps? C:
A plumber's helper is ordering drainpipe. Here is the list the
plumber gave him:
Fixture Feet of pipe
Kitchen sink 5
Bath tub 4
Lavatory 3
Laundry tub 5
Second lavatory 2
7:3/4
GREAT
ROOM
2/8 15 LITE
VAULT
What is the total number of feet of drainpipe he should
order?
The total number of feet that the plumber's helper should order for drain pipes is 19 feet.
How to find the number of feet of pipes?The plumber's helper has been given the list of places in the house that will need a drain pipe. The total number of feet of pipes that he should buy should therefore be the total number of pipes that each of these places in the house need.
The number of feet of pipes is therefore:
= Kitchen sink + Bath tub + Lavatory + Laundry tub + Second lavatory
= 5 + 4 + 3 + 5 + 2
= 19 feet
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For options A– E choose all of the expressions that are equivalent to 3(4x + 3).
A. 12x + 3
B. 3(3 + 4x)
C. 7x + 6
D. 4x + 3 + 4x + 3 + 4x + 3
E. 12x + 9
The equivalent expression for the given expression is 3(4x + 3) will be 12x+3. Option A is correct.
What is distributive property?The distributive property is the property that expresses the distributive law of algebraic multiplication. Similarly, in polynomial expression we can use the distributive property, for example, we can write a(c+b) in the form of (ac+bc).
It is given that the expression is,3(4x + 3)
We have to find the equivalent expression for the given expression,
Expressions that function identically but have a different appearance are called equivalent expressions. When we enter the same value for the variable, two algebraic expressions that are equivalent will have the same result.
=3(4x + 3)
=12x+3
Thus, the equivalent expression for the given expression is 3(4x + 3) will be 12x+3. Option A is correct.
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Analysis of variance is the most common inferential statistical procedure used to analyze experiments because O there are several different versions of it, and so it can be used to compare the effect of many different groups and variables there is one version of it and it is better for comparing two group more accurately than the two-sample tests. O it is the only statistical procedure that can test either between-subjects factors or within- subjects factors. O most researchers are more interested in differences between the population and one sample
Option-A is It comes in a variety of forms, making it possible to compare the effects of numerous groups and variables satisfy the statement.
Given that,
The most typical inferential statistical method used to evaluate trials is analysis of variance because
We have to find which of the options are suitable for the given statements.
Option-A is It comes in a variety of forms, making it possible to compare the effects of numerous groups and variables satisfy the statement.
Option-B is It comes in one form, and compared to two-sample tests, it is more accurate for comparing two groups does not satisfy the statement.
Option-C is It is the only statistical method that can test both within- and between-subjects factors does not satisfy the statement.
Option-D is The majority of academics are more focused on differences between one sample and the population as a whole does not satisfy the statement.
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In a multiple regression problem involving two independent variables, if b1 is computed to be +2.0. It means that a. the estimated mean of Y increases by 2 units for each increase of 1 unit of X1, without regard to X2.
b. the estimated mean of Y increases by 2 units for each increase of 1 unit of X1. holding X2 constant.
c. the estimated mean of Y is 2 when XI equals zero.
d. the relationship between X1 and Y is significant
In multiple regression problem with two independent variables, value of one varible , b₁ is 2 then it means that the estimated mean of Y increases by 2 units for each increase of 1 unit of X₁, holding X₂ constant. So, second option is correct option.
Multiple Regression: Multiple regression is a statistical technique that can be used to analyze the relationship between a single dependent variable and multiple independent variables. The goal of multiple regression analysis is to use independent variables with known values to predict the value of each dependent value.
Y = b₁x₁+ b₂x₂ + … bₙxₙ + a
Here Y is the dependent variable, and X₁,…,Xₙ are the n independent variables. In calculating the weights, a, b₁,…,bₙ,
In the multiple regression b1 shows the coeffcient of independent variable X₁ in fitted model.
Here b₁ =+2.0 shows that for each unit increase in X₁, dependent variable Y is increased by 2 keeping other things constant.
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among all simple closed curves in the plane oriented counterclockwise find the one alon which the work done
Using the Green's Theorem, the one along which the work done by the force is 11π/16.
In the given question we have to find the one along which the work done by the force is the greatest.
The given closed curves in the plane is
[tex]F(x,y)=\left(\frac{x^{2}y}{4} + \frac{y^3}{3}\right)\hat{i}+x\hat{j}[/tex]
Suppose C be a simple smooth closed curve in the plane. It is also oriented counterclockwise.
Let S be the interior of C.
Let P = [tex]\frac{x^{2}y}{4} + \frac{y^3}{3}[/tex] and Q = x
So the partial differentiation is
[tex]\frac{\partial P}{\partial y}=\frac{x^2}{4}+y^2[/tex] and [tex]\frac{\partial Q}{\partial x}[/tex] = 1
By the Green's Theorem, work done by F is given as
W= [tex]\oint \vec{F}d\vec{r}[/tex]
W= [tex]\iint_{S}\left ( \frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y} \right )dxdy[/tex]
W= [tex]\iint_{S}\left ( 1-\frac{x^2}{y}-y^2 \right )dxdy[/tex]
Let C = x^2+y^2 = 1 and
x = rcosθ, y = rsinθ
0≤r≤1; 0≤θ≤2π
There;
W = [tex]\int_{r=0}^{1}\int_{\theta=0}^{2\pi}\left ( 1-\frac{r^2\cos^2\theta}{4}-r^2\sin^2\theta \right )\left|\frac{\partial(x,y)}{\partial{r,\theta}}\right|d\theta dr[/tex]
and [tex]\frac{\partial (x,y)}{\partial(r, \theta)}=\left|\begin{matrix}\cos\theta &-r\sin\theta \\ \sin\theta & r\cos\theta\end{matrix} \right |[/tex] = r
Thus;
W = [tex]\int_{r=0}^{1}\int_{\theta=0}^{2\pi}\left ( 1-\frac{r^2\cos^2\theta}{4}-r^2\sin^2\theta \right )rd\theta dr[/tex]
After solving
W = 11π/16
Hence, the one along which the work done by the force is 11π/16.
To learn more about Green's Theorem link is here
brainly.com/question/28384298
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The right question is:
Among all simple smooth closed curves in the plane, oriented counterclockwise, find the one along which the work done by the force:
[tex]F(x,y)=\left(\frac{x^{2}y}{4} + \frac{y^3}{3}\right)\hat{i}+x\hat{j}[/tex]
is the greatest. (Hint: First, use Green’s theorem to obtain an area integral—you will get partial credit if you only manage to complete this step.)
Which answer choice correctly complete the sentence?
Asking the “Did you Check” questions is an important step in the Problem Solving Plan because you can
A.
determine if your answers are
reasonable.
B. organize your thoughts.
C. understand the problem better.
D. define your strategy easier.