Using the concepts of probability, we got that book is independent variable in the experiment in which I randomly assign one group of angelenos to read a book about the history of the Seattle supersonics, and the other to read a book about cheese.
The independent variable is the condition that you actually change in an experiment. It is the variable you control. It is known as independent because its value does not depend on the value and is not affected by the state of any other variable in the experiment.
Hence, when i randomly assign one group of Angelenos to read a book about the history of the Seattle supersonics, and the other to read a book about cheese and then give them a quiz about basketball history (including recent events such as the Los Angeles Lakers then the independent variable in this experiment is the book given by me.
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f(x) = (1 + =)",
k, n EN,
Given that the coefficient of x³ is twice the coefficient of x² in the binomial expansion of f(x),
(a) prove that n = 6k + 2.
Given also that the coefficients of x4 and x5 are equal and non-zero,
(b) form another equation in n and k and hence show that k = 2 and n = 14.
Using these values of k and n,
(c) expand f(x) in ascending powers of x, up to and including the term in x5.
Give each coefficient as an exact fraction in its lowest terms
n>2
Given that the coefficient of x³ is twice the coefficient of x² in the binomial expansion of f(x)
(a) It is proved that n = 6k + 2
(b)k = 2 and n=14
(c) After expansion, the equation is
1 + 14x + 91/4x^2 + 1001/2x^3 + 1001/16x^4 + 1001/16x^5
What is the binomial theorem?
The algebraic expansion of a binomial's powers is described by the binomial theorem (also known as binomial expansion) in elementary algebra.
The theorem states that the polynomial (x + y)n can be expanded into a sum including terms of the form axbyc, where the exponents b and c are nonnegative integers and b + c = n, and the coefficient an of each term is a particular positive integer dependent on n and b.
Solution Explained:
f(x)= (1+x/k)^n
Given that the coefficient of x^3 is twice the coefficient of x^2 in the binomial expansion of f(x)
a)
Coeff of x^3 = 1/6[n(n-1)(n-2)/k3]
Coeff of x^2 = 1/2[n(n-1)/k2]
1/6[n(n-1)(n-2)/k3] = 2* 1/2[n(n-1)/k2]
Canceling on both sides gives:
(n-2)/(6k) = 1
n = 6k+2 Hence proved
Given also that the coefficients of x^4 and x^5 are equal and non-zero,
b)
Coeff x^4 = 1/24 [n(n-1)(n-2)(n-3)/k4
Coeff x^5 = 1/120 [n(n-1)(n-2)(n-3)(n-4)/k5
1/120 [n(n-1)(n-2)(n-3)(n-4)/k5 = 1/24 [n(n-1)(n-2)(n-3)/k4
Canceling gives:
(n-4)/(120k) = 1/24
n = 5k+4
From previous:
n = 6k+2 = 5k+4
k = 2
n=14
Using these values of k and n,
c)
Give each coefficient as an exact fraction in its lowest terms
1 + 14x + 91/4x^2 + 1001/2x^3 + 1001/16x^4 + 1001/16x^5
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Express as a trinomial.
(2x-8)(2x-2)
Answer:
Step-by-step explanation:
:
The answer is 4x^{2}+12x-16. correct me if im not ty!
Answer:
4x^2 - 20x + 16
Step-by-step explanation:
4x^2 - 4x - 16x + 16
4x^2 - 20x + 16
Hudson goes to a store an buys an item that costs x dollars. He has a coupon for 20%
off, and then a 5% tax is added to the discounted price. Write an expression in terms
of a that represents the total amount that Hudson paid at the register.
If Hudson having a discount coupon of 20% off, wants to buy an item having a printed price of "x" dollars, and a 5% tax is added to the discounted price in the end, then the expression that can represent the final amount Hudson paid for the item will be [(4x/5) + (x/25)].
As per the question statement, Hudson goes to a store an buy an item that costs "x" dollars, with the intention of using his 20% flat discount coupon, and then, a 5% tax is added to the final discounted price.
We are required to determine an expression that can represent the final amount Hudson paid for the item as per the above case.
Since Hudson gets a discount of 20% over the cost price of his desired item, the discounted cost price of the item becomes, [x - {(20/100) * x}]
= [x - {(1/5) * x}]
= [x - (x/5)]
= (4x/5).
And then, a 5% tax is added to the final discounted price, which takes the final amount to [(4x/5) + {(5/100) * (4x/5)]
= [(4x/5) + {(1/20) * (4x/5)]
= [(4x/5) + (x/25)]
= (21x/25)
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over the past month, george the tortoise has been flipped onto his back 146 times by angie the tortoise. george has been able to get back on his feet without help 3 times. what's the empirical probability that george will be able to get back on his feet without help the next time angie flips him over?
The empirical likelihood that George can stand up on his own the very next time Angie knocks him over would be 3/146.
Describe the term empirical probability?The likelihood of an event is closely related to an empirical probability, also described as an experimental probability. Empirical probability bases its evaluation of the likelihood that a specific result will recur on the number of instances of that outcome together within sample set.For the given question.
We include George the turtle, who Angie has successfully turned over 146 times the turtle.3 times George has used the assistance to get back up on his feet. The empirical probability is really what we seek.Therefore, it follows that we are doing an experimental calculation based on the observation whether George will indeed be able to stand again the following time.
empirical probability = 3/146
Thus, the empirical likelihood that George can stand up on his own the very next time Angie knocks him over would be 3/146.
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On the southeast corner of Millennium Park, there is a garden walk. It is marked off in red in the drawing below. Side C, the hypotenuse of the triangle, shows the row along which flowers will be planted.
a) If side a measures 90 feet and side b measures 120 feet, how many feet of flowers will be planted along side c, the hypotenuse of the triangle? Show your work and explain your reasoning.
b) Calculate the area of the red triangle to find the area of the garden. Show your work.
c) Millennium Park has an outdoor concert theater. Before a concert, the area reserved for special seating is roped off in the shape of a triangle as shown below. How can the converse of the Pythagorean theorem help you determine whether the roped off area is in the shape of a right triangle?
a. Using the Pythagorean Theorem, side c = 150 feet
b. Area = 5,400 ft²
c. Applying the converse of the Pythagorean Theorem, the triangle would be a right triangle if the sum of the squares of two sides equals the square of the other side.
What is the Converse of the Pythagorean Theorem?The converse of the Pythagorean theorem states that if the sum of the squares of the two smaller sides of a triangle is equal to the square of the longer side, then the triangle is a right triangle.
a. Apply the Pythagorean theorem:
c = √(a² + b²)
c = ?
a = 90 feet
b = 120 feet
Substitute
c = √(90² + 120²)
c = 150 feet
b. Area = 1/2(a)(b) = 1/2(90)(120)
Area = 1/2(10,800)
Area = 5,400 ft²
c. Using the converse of the Pythagorean Theorem, we can check if the sum of the squares of two sides equals the square of the other side.
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use the following to answer the next 2 questions. solar-heat installations successfully reduce the utility bill 60% of the time. suppose 10 houses with solar-heat installations are selected at random and the outcome between houses is independent. suppose x is the number of houses that successfully reduced the utility bill out of the 10. 14. which discrete distribution will appropriately model x? explain. binomial 15. what is the probability that at least 9 out of 10 solar-heat installations are successful and will reduce the utility bill? a. 0.0464 b. 0.9432 c. 0.0403 d. 0.8429
The probability that at least 9 out of 10 solar-heat installations will succeed and reduce the utility bill is 0.0464.
What is a binomial distribution?
The probability distribution known as the binomial distribution, which is used in statistics, quantifies the chances that a value will take one of two independent values given a particular set of conditions or hypotheses.
Formula to calculate the binomial distribution
P(X = x) =ⁿCₓ× pˣ×(1-p)ⁿ⁻ˣ
Here, we know that
Solar-heat installations successfully reduce the utility bill 60% of the time.
We have to calculate the probability that at least 9 out of 10 solar-heat installations will succeed and reduce the utility bill.
We have 60% = 0.6 = p and n = 10.
We have a binomial distribution: X : (10, 0.6).
We use the binomial distribution formula to calculate the probability
P(X = x) =ⁿCₓ× pˣ×(1-p)ⁿ⁻ˣ, we get
P(x ≥ 9) = 1 - P(x < 9)
P(x ≥ 9) = 1 - P(x ≤ 8)
P(x ≥ 9) = 1 - ∑⁸₀ P(x = x)
P(X ≥ 9) = 1 - ∑⁸₀¹⁰Cₓ × (0.6)ˣ × (1-0.6)¹⁰⁻ˣ
P(X ≥ 9) = 1 -( 0.00011 + 0.00157 + 0.01062 + 0.04247 + 0.11148 + 0.20066 + 0.25082 + 0.21499 + 0.12093)
P(X ≥ 9) = 1 -0.95365
P(X ≥ 9) = 0.04635
Hence, the probability that at least 9 out of 10 solar-heat installations will succeed and reduce the utility bill is 0.0464.
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After raining for 3/4 of an hour, a rain gauge is of 2/5 the way full. If it continues to rain at the same rate for 15 more minutes, what fraction of the rain gauge will be filled?
Answer:
8/15
Step-by-step explanation:
You want the fraction of a rain gauge filled after 15 more minutes when the rain rate is 2/5 of the gauge in 3/4 of an hour.
Proportion15 minutes is 1/4 hour, so 15 more minutes brings the total time to 1 hour. The fraction (x) of the gauge that is filled will be ...
x/1 = (2/5)/(3/4)
x = (2/5)(4/3) = 8/15
After a total of 1 hour, the rain gauge will be 8/15 of the way full.
A football team receives the ball on their
own 10 yard line.
a. They make a gain of 15 yards in the first play. What yard line is the ball on?
b. What represents zero in this situation? Explain.x
The summation of 10 yards line and 15 yard is 25 yards and the ball represents zero situation when the ball is in net and goals.
Given,
The team receives the ball on their own yards = 10 yards.
that is,
initial position of the ball = 10 yards.
Using summation, (the summation is to add or subtract any two numbers or more terms by doing operation, to get answer).
They make a gain of 15 yards in the first play.
Their final position in 10 yards plus 15 yards
= 10 + 15
=25 yards.
Therefore, the yard line is 25 yards.
The zero situation of the game is when the ball is in net and the player make a goal.
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Find quotient of 1/3 divided by 5/6
Answer:
2/5
Step-by-step explanation:
flip 5/6 to become 6/5 then cross reduce then cross multiply
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The function has a maximum value of 30 at x = 3.
Given Function:
f(x) = -3[tex]x^{2}[/tex]+18x+3
here a = -3 , b = 18 , c = 3
a is negative so it has maximum value
x = -b/2a
= -18/2*(-3)
= -18/-6
= 18/6
= 3
f(x) = -3*[tex]3^2[/tex] + 18*3 + 3
= -3*9+54+3
= -27+54+3
= 27+3
= 30
Therefore the function has a maximum value of 30 at x = 3.
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If y=8 when x=4, write the direct variation equation and find y when x=5
HELPP
Kenneth has c toy cars. Jennifer has 3 times as many toy cars as Kenneth. Write an expression that shows how many toy cars Jennifer has.
Answer:
3c
3c mean 3xc
but just write 3c
The table shows the probabilities that a biased dice will land on 2, on 3,
on 4, on 5 and on 6.
Number on dice
Probability
1
2
0.1
3
0.17
4
5
6
0.08 0.16 0.14
Paulo rolls the biased dice 300 times.
Work out an estimate for the total number of times the dice will land on 1 or on 5
The total number of times the dice will land on 1 or on 5 is 153.
What is probability?
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.All of the probabilities will add up to 1. This gives us the equation.
P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1
P(1) + 0.17 + 0.08 + 0.16 + 0.14 + 0.1 = 1
P(1) + 0.65 = 1
P(1) = 1 - 0.66
P(1) = 0.35
We now need to find the probability of 1 or 5.
P( 1 or 5) = P(1) + P(5)
= 0.35 + 0.16
= 0.51
We now use the predicting outcomes formula
Expected = P( 1 or 5) * No. of times
= 0.51 * 300
= 153
Hence, the total number of times the dice will land on 1 or on 5 is 153.
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What is the least common multiple of 8, 29, and 22?
Answer:
1
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
What is the slope of a line perpendicular to the line whose equation is 2x-12y=-120? Fully simplify your answer.
The slope of the line perpendicular to the line 2x - 12y = 120 will be -6.
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line can be also written as -
Ax + By + C = 0
By = - Ax - C
y = (- A/B)x - (C/A)
We have the following equation -
2x - 12y = - 120
Rearranging the equation, we get -
2x - 12y = 120
12y = 2x - 120
6y = x - 60
y = (1/6)x - 10
The slope of the line perpendicular to the line 2x - 12y = 120 will be -
m[2] = -1 / (1/6) = - 6
m[2] = - 6
Therefore, the slope of the line perpendicular to the line 2x - 12y = 120 will be -6.
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Solve the following system of equations. Show your work.
y=−3x+5
5x−4y=−3
Solution:
A triangle has sides with lengths of 26 inches, 36 inches, and 46 inches. Is it a right triangle?
yes or no
Answer:
no
Step-by-step explanation:
You want to know if side lengths 26 in, 36 in, 46 in form a right triangle.
Pythagorean tripleThe integer side lengths will form a right triangle if they are a Pythagorean triple, or a multiple of one.
We notice that these side lengths have a common difference of 10 in. That makes them an arithmetic sequence. The only Pythagorean triples that are an arithmetic sequence are {3, 4, 5} and its multiples. The shortest side is 3 times the common difference.
The lengths {26, 36, 46} cannot form a right triangle. The attachment shows the triangle is an obtuse triangle.
No, the triangle is not a right triangle.
__
Additional comment
The side lengths will form a right triangle if and only if they satisfy the relation a² +b² = c², where a, b are the two short sides.
26² +36² = 1972 ≠ 2116 = 46²
Simplifique la siguiente expresión.
(3²) 4.3³.
Is this rat correct tell me tell me NOWWWW teehee
Answer:
No , x = -2
Step-by-step explanation:
When Dividing the Equation by a Constant , all terms in both sides must be divided by this Constant.
So here we divided both sides by 2 , but -6 is not divided , so this step is incorrect
The correct Answer is
[tex]\frac{-6}{2}+\frac{2x}{2} =\frac{-10}{2} \\-3+x=-5\\x=-5+3=-2[/tex]
Write 2^40 as a pwer with the following base (2^8)
By algebra properties, the resulting expression of the power 2⁴⁰ is (2⁸)⁵.
How to rewrite a power expression according algebra properties
In this problem we must rewrite a power expression in terms of the power 2⁸, which is the base of the resulting expression. This can be done by applying algebra properties:
Step 1 - Write the original expression presented in the statement.
2⁴⁰
Step 2 - By definition of multiplication between real numbers.
2⁽⁸⁾⁽⁵⁾
Step 3 - By the definition of the power of a power.
(2⁸)⁵
The resulting expression is (2⁸)⁵.
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precipitation data was compiled and discretized into three states. 1. dry, 2. light rain, and 3. wet. given these states the tratisition matrix chain model of davis rainfall was computed as. what is the probability a dry day is followed by a light rain day
The probability a dry day is followed by a light rain day is 0.07.
Define probability.Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
Given.
Here, the markov chain's three possible states are listed as dry, light rain, and wet.
From the second number in the first row, the chance of a dry day followed by a light rain is calculated as follows: P(dry⇒ light) = 0.01.
Therefore, the necessary probability in this case is 0.01.
We currently have (wet⇒ light) - 0.07
Therefore, the necessary probability in this case is 0.07.
The probability a dry day is followed by a light rain day is 0.07.
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I need some help with this question about graphed functions
The equation of the function graphed for 0 ≤ x ≤ 360 is
y = -1 + cos 2xWhat is transformation?Transformation is a term used in mathematics to refer to the movements made by objects.
Transformation that took place in the graph is of two types namely
translationvertical stretchThe translation involves moving the graph downward by 1 unit. This movement shifts the graph from running across the x axis to making x axis the crest
The vertical stretch is by a factor of 2. A complete cycle would have been rom 0 to 180. however two cycles are now covered within this period.
The graph is of showing cos x (blue) and y = -1 + cos 2x (red) is attached
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g the center for medicare services reported that there were 295,000 reported appeals for hospitalization and other medicare part a services. for this group, 40% of the first round appeals were successful. suppose ten first round appeals were just received. the results follow a binomial distribution. what is the probability of getting more than two heads? enter answer to four decimal places.
The probability that of getting more than two heads is 0.9537.
Describe the binomial probability?There are just two options for each appeal: either it has been accepted or it wasn't. A binomial probability is employed to answer this question since the chances that one appeal will be permitted is independent of the possibility that any other appeals will be granted.The probability of precisely x successes per n repeated trials is known as a binomial probability, and X has only two possible outcomes.
P(X = x) = Cn,ₓ.pˣ(1 - p)ⁿ⁻ˣ ...eq 1
Where Cn,ₓ represents the number of distinct combinations of x items drawn from a group of n elements, as determined by the formula below.
Cn,ₓ = n!/x!(n - x)!
Where p is the likelihood that anything will happen.
10 appeals are necessary; n = 10.
Because 40% of appeals are successful; p = 0.4.
For the probability of getting at least two heads.
P(X ≥ 2) = 1 - P(X < 1)
P(X < 2) = P(X = 0) + P(X = 1)
Put the values in eq 1 and get the values for X.
P(X < 2) = 0.006 + 0.0403 = 0.0463
Now,
P(X ≥ 2) = 1 - 0.0463
P(X ≥ 2) = 0.9537
Thus, the probability that of getting more than two heads is 0.9537.
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Example 2 5. WALKING Lily has walked 2 miles. Her goal is to walk 6 miles. Lily plans to reach her goal by walking 3 miles each hour h for the rest of her walk. Write an equation to find the number of hours it will take Lily to reach her goal.
Answer:
y=3x-2
Step-by-step explanation:
y is for how many miles she wants to walk which is 6. she walks 3 miles per hour which is 3x (x is for hours) and -2 because she already walked 2 miles
I NEED HELP ASAP PLS I NEED TO FINISH MY OTHER ASSIGMENTS TYSM
The value of x by setting up equation is 16.
Given in question,
∠VZW = (2x + 32)°
∠RZY = (3x + 16)°
∠VZW = ∠RZY
2x + 32 = 3x + 16
2x - 3x = 16 - 32
-x = -16
x = 16
Hence, x = 16.
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the probability that an individual without a college education earns more than $100,000 is 0.4, whereas the probability that a person with a b.s. or higher degree earns more than $100,000 is 0.6. the probability that a person chosen at random has a b.s. degree is 0.4. what is the probability that a person has at least a b.s. degree if it is known that he or she earns more than $100,000? (round your answer to four decimal places.)
The Probability that someone holds b.s. degree if it is known that he or she earns more than $100,000 is 0.75.
Considering the values given in the question,
P(earns more than $100000 without college education) = 0.2
P(earns more than $100000 with a B.S. or higher degree) = 0.6
P(Has a B.S. degree) = 0.5
P(earns more than $100000) = P(earns more than $100000 | without college education) × P(without college education) + P(earns more than $100000 | with a B.S. or higher degree) × P(has a B.S. degree)
= 0.2 × (1 - 0.5) + 0.6 × 0.5
= 0.4
P(at least a B.S. degree | earns more than $100,000) = P(earns more than $100000 | with a B.S. or higher degree) × P(has a B.S. degree) / P(earns more than $100000)
= 0.6 × 0.5 / 0.4
= 0.75
Therefore, If a person's income above $100,000 is known, there is a 0.75 probability that they have at least a b.s. degree.
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30 POINTS IF ANYONE GETS THIS RIGHT AND BRAINLSIT.
1st image
angle 5 is 31 degrees alternate interior angles
2nd image
angle8=angle9, alternate interior angles
Help! What is the domain of the graph shown below?
A. All real numbers greater than 0.
B. All real numbers greater than -2
C. All real numbers between -5 and 4
D. All real numbers
Answer:
D
Step-by-step explanation:
there are no restrictions on the domain and
- ∞ < x < ∞
That is the domain is all real numbers
the human resources department at a major high-tech company recently conducted an employee satisfaction survey of 100 of its 3000 employees. data were collected on such variables as age, gender, marital status, current salary, level of overall satisfaction on a scale from 1 to 5, number of years with the company, and job title. which of the variables listed are considered to be ratio level data?
Gender and marital status and Job title.
What are edtech companies?Computer hardware, software, educational theory, and practice are all used in conjunction with educational technology, also known as edutech or edtech, to facilitate learning. The sector of businesses that produce educational technology is frequently referred to by its abbreviation, edtech.EdTech companies can approach the consumers, this can be done via the schools that are convinced to use a product for free. Then, if the families want to continue to use the offering they can be charged for its usage at home. Here, schools act as lead generators for consumer adoption.They design contemporary learning spaces that enable digital immersion.They provide individualized instruction that is catered to the learning style and circumstances of each student.They offer access to a variety of information and educational opportunities without regard to location.learn more about edtech companies click here:
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the mpg (miles per gallon) of a certain compact car is normally distributed with a mean of 31 and a standard deviation of 1.2. what is the probability that the mpg for a randomly selected compact car would be more than 30?
The probability that a compact car's randomly chosen mpg would be higher than 30 is 0.797.
Given data;
A certain compact car's mpg (miles per gallon) has a mean of 31 and a standard deviation of 1.2 and is regularly distributed.
We need to get the probability that the mpg for a randomly selected compact car would be more than 30.
Therefore;
Mean = μ = 31
Standard deviation = σ = 1.2
Let;
P(X > 30) = P(X - 31/1.2 > 30 - 31/1.2)
= P(Z > -0.833)
= 0.797
Hence, the probability that the mpg for a randomly selected compact car would be more than 30 is 0.797.
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