An engineer selected 30 components at random and measure their strengths. 34,54,73,38,89,52,75,33,50,39,42,42,40,66,72,85,28,71,52,47,41,36,33,38,49,51,55,63,72,78 Does this data suggest that the population mean strength of the components differs from 50? Set up an appropriate hypothesis test to answer this question.
Answers
The population mean strength of the components differs from 50 is 0.304.
In the given question, an engineer selected 30 components at random and measure their strengths. 34,54,73,38,89,52,75,33,50,39,42,42,40,66,72,85,28,71,52,47,41,36,33,38,49,51,55,63,72,78
We have to check does this data suggest that the population mean strength of the components differs from 50 and we have to set up an appropriate hypothesis test to answer this question.
Sample size n = 30
Claim : The population mean strength of the components differs from 50.
Null and alternative hypothesis:
H(0): μ = 50
H(A): μ≠50
As the population standard deviation is unknown (not given) , t-test can be used .
Test Statistic :
t = (X-μ)/(S/√n)
To find the sample mean we find the average of the given sample.
So
X = 34 + 54 + 73 + 38 + 89 + 52 + 75 + 33 + 50 + 39 + 42 + 42 + 40 + 66 + 72 + 85 + 28 + 71 + 52 + 47 + 41 + 36 + 33 + 38 + 49 + 51 + 55 + 63 + 72 + 78/ 30
X = 53.267
Now finding the standard deviation using the excel.
SD = 17.1101
To find the SD we use the formula =STDEV(B1:C15)
Now putting the value in the formula of Test Statistic
t = (X-μ)/(S/√n)
t = (53.267-50)/(17.1101/√30)
After solving:
t=1.046
P-value :
As the alternative hypothesis H(A) is of not equal to type , this is two tailed test.
Degrees of freedom = n-1 = 30 -1 = 29
df =29
Using Excel function , =TDIST( t , df , number of tails )
=TDIST( 1.046 , 29 , 2 )
=0.304201657
Rounding to three decimal places
= 0.304
P-value = 0.304
Hence, the population mean strength of the components differs from 50 is 0.304.
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Related Questions
The exponential function f with base b is defined by f(x) = ___ , b > 0 and b != 1. Using interval notation, the domain of this function is _____ and the range is _____.
Answers
The exponential function of f with base b is defined by f(x) = bˣ, b>0
and b≠1. Using interval notation, the domain of this function is (−∞, ∞)
and the range is (0, ∞).
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = aˣ in mathematics, where x is the independent variable
According to the given question, the required solution would be as:
The exponential function of f with base b is defined by f(x) = bˣ, b>0
and b≠1. Using interval notation, the domain of this function is (−∞, ∞)
and the range is (0, ∞).
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50 POINTS!!!! Amy is attending a trekking camp. She walks from her tent to a hilltop in 3 hours. She has a picnic with her friends on the hilltop for 5 hours. Amy walks back to her tent in 2 hours. Which graph best represents the distance, y, in miles, traveled by Amy for a certain amount of time, x, in hours?
Answers
Answer: B
Step-by-step explanation: We know that Amy took three hours to get to the hilltop, so A and D are out because they are saying she reached the hilltop in 2 hours, instead of 3. Then we have C and B left. The difference between them is that C is saying that they had a picnic for 4 hours instead of 5.
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Answer:
B
Step-by-step explanation:
The given graphs are distance-time graphs, where:
Time is on the x-axis.Distance is on the y-axis.As Amy walks from her tent to a hilltop in 3 hours, the first part of the graph should be a straight line with a positive gradient, where the x-values of its endpoints are:
x = 0 and x = 3.Therefore, we can immediately discount answer options A and D as they suggest that this part of Amy's journey takes only 2 hours.
Amy stops and has a picnic at the top of the hilltop for 5 hours. Therefore, her distance from the tent during this time does not change as she is not moving. This will be represented on the graph by a horizontal line that has endpoints at:
x = 3 and x = 8.Therefore, the graph that displays the given parameters is graph B.
suppose the college administrator was only able to survey a random sample of 50 students. she finds that 32 of these students report having a full- or part-time job. find the sample proportion.
Answers
The sample proportion of the random sample of 50 students is 64% or 0.64.
Given:
the college administrator was only able to survey a random sample of 50 students.
she finds that 32 of these students report having a full- or part-time job.
we are asked to determine the sample proportion = ?
Based on the given conditions, we formulate:
32÷50
simplify:
16/25
= 64% or 0.64
hence we get the required sample proportion.
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A force of 8 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 0.8 times the instantaneous velocity.
(a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position.
Answers
The equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position is [tex]\frac{\frac{-sin(8t)}{2} - cos(8t) }{e^{4t} }[/tex] at x = 0, y = -1.
Here, we have been told that the force has a magnitude of = 8 pounds (i)
It stretches a spring to a length of = 1 foot (ii)
The damping force is 0.8 times the instantaneous velocity. (iii)
We use the differential equation of motion of damping force which is =
= mx₂ +λx₁+kx
Using the formula and the values of (i), (ii), and (iii), we get -
= [tex]\frac{\frac{-sin(8t)}{2} - cos(8t) }{e^{4t} }[/tex]
This is the required equation of motion.
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Merrill is completing homework problems where they need to determine whether graphs show proportional relationships. Merrill’s dog bit the corner off of the page so they cannot see whether this graph goes through the origin. Explain how to determine whether the graph shows a proportional relationship. Please have an actual answer or do not answer this cause it is due 8am Monday
Answers
In order to determine whether this graph shows a proportional relationship, you should determine if the ratios of the two variables plotted on the graph have a constant of proportionality.
What is a proportional relationship?In Mathematics, the graph of a proportional relationship between two variables is always characterized by a straight line with its data points passing through the origin (0, 0).
Mathematically, a proportional relationship can be modeled by the following linear equation:
y = kx
Where:
y and x are the variables.k represents the constant of proportionality.In conclusion, the ratio of the two variables plotted on the graph of a proportional relationship is always constant.
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Identify the factor and levels in the following scenario: The Hyppo (a gourmet ice pop store) is trying to test out new dip flavors in which customers can dip their popsicles (strawberry, orange, and banana). All of the popsicles are made the same, utilizing the same simple chocolate flavoring for experimental purposes, but the dips are randomly applied. Twenty regular customers are given the popsicles with the dips on them in a random order, and are asked to rate them from 1-3.
Group of answer choices
Factor = dip flavor. Levels = ratings 1-3
Factor = strawberry, orange, and banana. Levels = dip flavor
Factor = the hyppo location. Levels = 20 regular customers
Factor = dip flavor. Levels = strawberry, orange, and banana
Answers
The factor and levels in the scenario is,
Factor = dip flavor. Levels = strawberry, orange, and banana.
What is popsicles?
A frozen treat on a stick made of liquid is known as an ice pop. An ice pop is "quiescently" frozen, or frozen when at rest, and turns into a solid block of ice, unlike ice cream or sorbet, which are churned while freezing to prevent ice crystal formation. It is held by the stick, which serves as a handle.
There is only one factor (independent variable) involved in above case, i.e. dip flavor is only factor mentioned in given case.
We can see that dip flavor has three categories or levels, i.e. strawberry, orange, and banana
Therefore, we have
factor = dip flavor and levels = strawberry, orange, and banana.
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b. calculate the mean and standard deviation of the number of people with blood type a-positive in 100 randomly selected us people using the binomial model. use r or a calculator.
Answers
The mean and standard deviation of the number of people with blood type a-positive in 100 randomly selected is μ=85, σ=3.5707
What is meant by standard deviation?The standard deviation is a statistic that measures the amount of variation or dispersion of a group of values.
Standard deviation is usually abbreviated SD and is most commonly represented in mathematical texts and equations by the lower case Greek letter (sigma) for population standard deviation or the Latin letter s for sample standard deviation.
A low standard deviation indicates that the values are close to the mean of the set (also known as the expected value), whereas a high standard deviation indicates that the values are spread out over a broader range.
Given, The population proportion of success is p=0.85
And also given that the sample size is n=100
b) The population mean is:
μ=np
μ=100(0.85)
μ=85
Therefore, mean=85
And the population standard deviation is:
σ=√np(1-p)
σ=√100(0.85)(1-0.85)
σ=3.5707
Therefore, standard deviation=3.5707
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The complete question is:
" Rh - positive blood appears in 85% of the population in the USA. a) Verify that it's possible to use the normal approximation to binomial distribution if a sample size is 100 randomly selected people. b) Find the mean and standard deviation of the normal distribution."
a club elects a president vice-president and secretary treasurer how many sets of officers are possible if there are members and any member can be elected to each position? no person can hold more than one office.
Answers
2730 sets of officers are possible if there are members and any member can be elected to each position.
Permutations Without Repetition: Permutation repetitions select a set of items from a set of choices that can be distinguished, with each item only being selected once in each set. All collections with unique sets and unique orders of elements in a set are included in the total permutations.
The idea of permutations without replacement must be used because each member can only hold one office and each position holds a specific office.
The formula of permutation is,
p = n! / (n - r)!
where r denotes the number of elements to be selected and n denotes the number of selections.
From a selection of 15 candidates, there are the following options for electing 3 members to fill a particular position:
p = 15! / (15 - 3)!
= 15! / 12!
= 2730
thus, there are 2730 sets of officers possible.
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Write a two column proof for the following statement.
“Given that 2( -x + 4) = 3 , prove that x = 5/2.
Answers
The two column proof for the statemen is as follows
Statement Reason
2(-x + 4) = 3 given
-2x + 8 = 3 Distributive property of multiplication
-2x = 3 - 8 Collection of similar terms
-2x = -5 Subtraction property of equality
-2x/-2 = -5/-2 Division property of equality
x = 5/2 Definition of equality
What is algebra?The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions.
In algebra, we utilize integers with fixed or definite values, such as 2, 13, 0.5, etc. combined with variables like x, y, and z
An instance of algebra is 2( -x + 4) = 3
What is distributive property of multiplication?The distributive property of multiplication is applied when there is multiplication over addition of terms like exemplified here
2(-x + 4)
= -2x + 4
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer: The correct results are shown below by plugging in the values.
f(x)=[tex]3^{x}[/tex]
X Y
-2 1/9
-1 1/3
0 1
1 3
2 9
Step-by-step explanation: Confirmed correct.
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FILL IN THE BLANK. in bayes theorem, you have some starting information, then you collect some new information so that you can___the original probabilities so you now have better information.
Answers
In bayes theorem, you have some starting information, then you collect some new information so that you can UPDATE the original probabilities so you now have better information.
What is Baye's theorm ?The Bayes' theorem, commonly referred to as the Bayes' rule, is a mathematical formula used in statistics and probability theory to calculate the conditional probability of events. The Bayes theorem essentially describes the likelihood of an event based on prior knowledge of any circumstances that might be relevant to the event.
P(A|B) = [tex]\frac{ P(A) P(B|A)}{P(B)}[/tex]
How often A happens given that B already happens, written as P(A|B),How often B happens given that A already happens, written as P(B|A)How likely A is on its own, written as P(A)How likely B is on its own, written as P(B)So it is always the case of conditional probability.
Hence, the original probability is always updated in case of Baye's theorm.
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Determine a series of transformations that would map polygon ABCD onto polygon A'B'C'D'?
Answers
The transformations that would map the polygon ABCD onto polygon A'B'C'D' is
dilation followed by a translation
How to determine the transformationsThe original coordinate of the polygon, from the graph using a position as an instance
A (1. -1)
There was a dilation with a scale factor of 2, transformation rule for dilation is
(x, y) for a scale factor of r → (rx, ry)
followed by a translation three units down, the transformation rule for translation 3 units down is
(x, y) → (x, y - 3)
following similar procedure for the given problem we have
preimage image (dilation) image (translation)
A (1, -1) → (1 * 2, -1 * 2) → A' (2, -2) → (2, -2 - 3) → A'' (2, -5)
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Write the equation of the line in fully simplified slope-intercept form. pls help
Answers
Answer:y=-5x-5
Step-by-step explanation:
(0,-5) and (1,-10)
-10-(-5)= -5
1-0=1
-5/1 = -5
y = -5x - 5
Explanation:
y-intercept is (0,-5) on the graph
calculate slope by rise/run —> -5/1 = -5
Solve x^2-3x=-8. Please explain
Answers
Answer:
No solution.
Step-by-step explanation:
1. Move terms to the left side
x² - 3x = -8
x² - 3x - (-8) = 0
2. Use the quadratic formula
x = [tex]\frac{-b + \sqrt{b^2 - 4ac} }{2a}[/tex]
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
x² - 3x + 8 = 0
a = 1
b = -3
c = 8
x = [tex]\frac{-(-3) + \sqrt{(-3)^2 - 4 * 1 * 8} }{2*1}[/tex]
3. Simplify
After simplifying:
x = [tex]\frac{3 + \sqrt{-23} }{2}[/tex]
4. No real solutions because the discriminant is negative.
The square root of a negative number is not a real number.
d = -23.
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How many 2-digit special numbers are there?.
Answers
Four special two digit numbers exist: 1, 2, 145, and 40585.
A special two-digit number is one in which the original two-digit number is equal to the sum of the number's digits plus the product of its digits. Take the number's initial and last digits out, then add and multiply each digit independently. After that, multiply the two-digit number by the sum and product of its digits and then compare the result to the original value. If they match, it qualifies as a special two-digit number; otherwise, it does not.
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Which equation has no solution 4x 6?.
Answers
It only produces favorable results. |3x - 6| = -5, etc., will not have solutions for x. |4x - 2| = -6 has a negative value of -6. Therefore, there is no answer to the equation |4x - 2| = -6.
How do you tell if an equation doesn't have a solution?Result of an equation with no solutions 4x-2 =-6 equations without answers. These equations don't have a value for the variable that would make them true. If you attempt to solve an equation and the result is false, the problem has no solutions.
There are certain equations with no answers. These equations don't have a value for the variable that would make them true. If an equation has no solutions, you can tell.
[tex]5x+7 \s= 3x+4+2x\s5x+7[/tex]
=[tex]5x+4[/tex]
meld the phrases 3x and 2x together.
[tex]7 \s= 4[/tex]
Take 5 times off of each side.
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What is the mean number of 5 11 2 12 4 2?.
Answers
explanation: mean is the average and all numbers add to be 36 and divided by the amount of numbers which is 6. the solution is 6
Answer: 6
Step-by-step explanation:
(P.S.: Everything in italics are numbers.)
Add all of the numbers. (5+11+2+12+4+2=36)Divide 36 by the amount of numbers in the problem. There are 6 numbers in the problem. (36 divided by 6=6)So the answer will be 6! You're welcome!
What is the mean deviation method?.
Answers
The step-by-step method of mean deviation given below.
What is the mean deviation method?
When calculating the average departure from the mean value of a particular data set, statisticians employ a measure known as the mean deviation. Following the steps below will make it simple to determine the mean deviation of the data values.
In statistics, the term "deviation" refers to the discrepancy between the observed value of a data point and its expected value. As a result, mean deviation, also known as mean absolute deviation, is the typical departure of a data point from the mean, median, or mode of the data collection.
MAD = (∑ f1 |xi - x⁻|) / ∑ f1
fi is the frequency of repetition xi, xi of denotes the mid-value of the class interval.
Example, Say your data set is: 9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4.
The Mean is: 9 + 2 + 5 + 4 + 12 + 7 + 8 + 11 + 9 + 3 + 7 + 4 + 12 + 5 + 4 + 10+ 9 + 6 + 9 + 4. Over 20. That equals 104 over 20 = 7.
Statistics refers to deviation as the difference between the observed value of a data point and the expected value. The average deviation of a data point from the mean, median, or mode of the data collection is known as the mean deviation, sometimes known as the mean absolute deviation. Mean deviation is indicated by the acronym MAD.
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can you guys please answer this? its timed so dont take too long!
Answers
The expression -2x³ + 13x² + 3x + 50 is equivalent to 10 - (2x³ + 11x² - 2x - 35) + (x + 5) + 6(4x²
Equivalent ExpressionAn algebraic expression is an expression which consists of variables, coefficients, constants, and mathematical operators such as addition, subtraction, multiplication and division. Generally, if two things are the same, then it is called equivalent. Similarly, in mathematics, the equivalent expressions are the expressions that are the same, even though the expression looks different. But if the values are plugged in the expression, both the expressions give the same result.
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
In the given expression;
10 - (2x³ + 11x² - 2x - 35) + (x + 5) + 6(4x²); this can be reduced or simplified to -2x³ + 13x² + 3x + 50
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A construction company is setting up signs on 5 miles of road. If the company places one sign every 1/3 mile, how many signs will it use?
Answers
Answer:
75
Step-by-step explanation:
1) Divide 5 by 1/3.
Use the rule ---> [tex]a\div\frac{b}{c} =a\times\frac{c}{b} .[/tex]
5 * 3
15
Due to this being a proportional equation, you multiply 15 by 5.
5:(1/3)=75
Please help me with this problem!
Answers
Answer:
van can carry 15 people
Bus can carry 30 people
Step-by-step explanation:
we can make a system of equation for these 2 schools
15v+16b=705
8v+6b=300
isolate a variable
8v+6b=300
-8v. -8v
6b=300-8v
/6. /6. /6
b=50-8/6v
Now substitute
15v+16(50-8/6v)=705
15v+800-21 1/3v=705
-6 1/3v+800=705
-800. -800
-6 1/3v=-95
/19/3. /-19/3
v=-95*3/-19
v=-285/-19
v=15
Now fill in v to find b
8(15)+6b=300
120+6b=300
-120. -1#0
6b=180
/6. /6
b=30
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4 ^ p * 4 ^ 5 = 4 ^ 15
Answers
Answer:
p = 10
Step-by-step explanation:
4 ^ 10 x 4 ^ 5 = 4 ^ 10+5 = 4 ^ 15
p = 10
Find the value of x. then find the angle measures of the polygon.
Answers
The value of x is 125.
what angle sum property of hexagon?
The formula for the angle sum property is, S = ( n − 2) × 180°, where 'n' represents the number of sides in the polygon.
The sum of all interior angles is equal to 720 degrees, where each interior angle measures 120 degrees. The sum of all exterior angles is equal to 360 degrees, where each exterior angle measures 60 degrees.
Using angle sum property
120+120+120+100+x+x+10=720
2x+470= 720
2x= 720-470
2x= 250
x=125
hence, the value of x is 125.
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after running which of the following code segments would the robot end up in the same place facing the same direction as after running the code segment below?
Answers
The solution for the code is can be followed by breaking the loop twice.
Given,
After running which of the following code segments would the robot end up in the same place facing the same direction as after running the code segment below;
Below is the trace that robot takes ,
| - <---
|
---> |
This means it moves forward twice and rotate left and this repeat for 3 times.
Same steps can be followed by breaking the loop twice which is being done by,
REPEAT 2 TIMES
{
MOVE_FORWARD ( )
}
ROTATE_LEFT ( )
REPEAT 2 TIMES
{
MOVE_FORWARD ( )
}
ROTATE_LEFT ( )
REPEAT 2 TIMES
{
MOVE_FORWARD ( )
}
ROTATE_LEFT ( )
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Assuming QF is the full employment equilibrium then in Figure 11.2, if the level of spending is equal to AD1 , the AD shortfall would be
A) Equal to XZ.
B) Greater than XZ.
C) Equal to XY.
D) Equal to YZ
B) Greater than XZ.
Answers
Assuming QF is the full employment equilibrium then in the Figure, if the level of spending is equal to AD1, the AD shortfall would be greater than XZ. The answer is B.
The respective figure as referred in the question is as attached.
What is the full employment equilibrium?Full employment equilibrium refers to the equilibrium where all resources in the economy are fully utilized (employed). Full employment is a situation in which all available labor resources are being used in the most economically efficient way, so there is no cyclical or deficient-demand unemployment.
When the natural rate of unemployment is equal to the unemployment rate, this means the cyclical rate of unemployment is zero. So, when this relationship happens, the economy is considered to be at full employment.
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compared to the distance between earth and mars, the distance between jupiter and saturn is .
Answers
Compared to the distance between Earth and Mars, the distance between Jupiter and Saturn is much larger. (Option B)
Planetary distance is the measure of distance between two planets which vary based on the placement of the planet in an orbit. An orbit is the path where planets revolve around the Sun in the solar system. The planets’ orbits form an elliptical shape. To measure the distance between two planets in the solar system an astronomical measure used is astronomical unit (AU). An Astronomical Unit (AU) is the average distance between Earth and the Sun and is used to measure distances within our solar system. The distance between Mars from Earth is equivalent to 0.52 AU while the distance between Jupiter and Saturn is 4.32 AU. Hence, compared to the distance between Earth and Mars, the distance between Jupiter and Saturn is much larger.
Note: The question is incomplete as it is missing options which are a) much smaller b) much larger c) about the same d) just slightly less.
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in the fixed effects regression model, you should always exclude one of the binary variables for the entities independent of whether an intercept is present in the equation or not.
Answers
To avoid any perfect multicollinearity we need to exclude any one of the binary class variables for all the entities which are independent of whether an given intercept is present across the given equation or not.
Fixed outcomes is a statistical regression version wherein the intercept of the regression version is authorized to differ freely throughout people or groups. It is frequently implemented to panel information with the intention to manage for any individual-unique attributes that don't range throughout time. Use fixed-outcomes (FE) each time you're most effective inquisitive about reading the effect of variables that fluctuate over time.
FE discover the connection among predictor and final results variables inside an entity (country, person, company, etc.). In many packages which includes econometrics and biostatistics a set outcomes version refers to a regression version wherein the organization method are fixed (non-random) instead of a random outcomes version wherein the organization method are a random pattern from a population.
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What are rational roots examples?.
Answers
An example of rational roots can be given as:
Let the polynomial be: 4x³ + 3x² + 6x + 9;
Then,
coefficient of the variable with the highest degree = 4
coefficient having the variable with degree 0 = 9
Factors of 4 are: 1, 2;
Factors of 9 are: 1, 3;
The possible rational roots for such an equation will be: 3, 1, 1/2, 3/2, -3, -1, -1/2, -3/2;
Rational roots are the roots or solutions of equations of any polynomial consisting of one variable of any power.
Where all the coefficients are integers.
Let the solution/root of a polynomial be p/q. Then the root would be rational if and only if the coefficient of the variable with the highest degree is divisible by 'q' , and the coefficient independent of the variable or having the variable with degree 0 is divisible by 'p'
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How do the Midsegments of a triangle compare to its sides?.
Answers
you have the choice of choosing a number between 0 and 100. the winner is the group that guesses 2/3s of the average guesses of all groups. for example, if all other groups choose 100 and your group chooses 63, 2/3 of the average guesses would be 62.4 and your team would win.
Answers
Using the Dominant strategy and Nash equilibrium, helps you to choose a number between large sample (0-100) such that the choosing number is 2/3 of average guess of all and become a winner.
Dominant Strategy:
A dominant strategy refers to a player's preference for a particular choice of action, independent of the actions and decisions of other players in a strategy game. A dominant strategy is based on the playoffs the player wins.
The concept of Nash Equilibrium is not too difficult to understand. Imagine any combination of player choices. For example, everyone picks 34 in the hope that it matches her 2/3rds of other people's guesses. Nash proved that every game has at least one such equilibrium if randomized strategies are allowed.
Zeroth order - If everyone was a zero-order thinker, just guess randomly between 0 and 100 and pick a random number. Average = ( 0 + 100 ) / 2 = 50.
1st order thinkers guess 2/3 of 0th order thinkers = (2 / 3) × 50 = 33.
2nd order thinkers guess/3 primary thinkers
= (2 / 3) × 33 = 22.
3rd order - 3rd order thinkers guess 2/3 of 1st order thinkers = (2 / 3) × 22 = 15.
Distribution of k order thinkers and sophisticated thinkers. If the population he is a 0th, 1st, 2nd, 3rd thinker, we can estimate
(2/3) ×(50 + 33 + 22 + 15) / 4 = 20.
Thus, different strategies for different opposing thinkers are discussed here.
To learn more about Nash equilibrium,
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