a. The two parameters of the gamma distribution are
shape parameter (α) and velocity parameter (β).
The mean of the gamma distribution = α/β and the standard deviation = sqrt(α)/β.
mean = 5 seconds
standard deviation =2.5 seconds.
α/β = 5 (equation 1)
sqrt(α)/β = 2.5 (equation 2)
Squaring equation 2 and multiplying both sides by β^2 yields:
[tex]α = 6.25β^2[/tex]
Substituting this value of α into Equation 1 yields:
[tex]6.25β^2/β = 5[/tex]
Simplified, it looks like this:
β = 0.8
Substituting this value of β into Equation 1 yields:
a = 4
Therefore, the parameters of the gamma distribution are α = 4 and β = 0.8.
b. I need to find the probability that this software will take more than 10 seconds to run.
The probability density function (PDF) of the gamma distribution is given by
[tex]f(x) = (β^α * x^(α-1) * e^(-βx)) / Γ(α)[/tex]
where Γ(α) is the gamma function.
Using the values of α and β obtained in part (a), we can write the PDF as
[tex]f(x) = (0.8^4 * x^(4-1) * e^(-0.8x)) / Γ(4)[/tex]
I need to find the probability that the execution time exceeds 10 seconds. This can be written as:
P(X > 10) = ∫(10 to infinity) f(x) dx
Using software or a calculator, we can evaluate this integral to get:
P(X > 10) = 0.0559 (rounded to four decimal places)
Therefore, the probability is 0.0559.
c.Since it has already taken more than 5 seconds, we need to find the probability of this software where will take more than 10 seconds to run.
This is a conditional probability and should be calculated using Bayes' theorem.
P(X > 10 | X > 5) = P(X > 10 and X > 5) / P(X > 5)
The numerator can be simplified to
P(X > 10 and X > 5) = P(X > 10)
Using the results obtained in part (b), we can write
P(X > 10 and X > 5) = 0.0559
The denominator can be written as:
P(X > 5) = ∫(5 to infinity) f(x) dx
Using the same PDF as before, we can evaluate this integral and get:
P(X > 5) = 0.2615 (rounded to four decimal places)
Substituting these values into the conditional probability formula gives:
P(X > 10 | X > 5) = 0.0559 / 0.2615
Simplified, it looks like this:
P(X > 10 | X > 5) = 0.214
Therefore, the probability that his single run of this software took longer than 5 seconds to take longer than 10 seconds is 0.214 (rounded to three decimal places).
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solve please help!!!!
The value of angle V which is ∠V is calculated as: 64.01°
How to use trigonometric ratios?The trigonometric ratios are used to find the angles and lengths of a right angle triangle.
Some of the trigonometric ratios are:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
The parameters given are:
∠W = 90°
UW = 39
WV = 80
VU = 89
Thus, using trigonometric ratios, we have:
∠V = tan⁻¹(80/39)
∠V = 64.01°
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a fancy bed and breakfast inn has 5 rooms, each with a distinctive color-coded decor. one day 5 friends arrive to spend the night. there are no other guests that night. the friends can room in any combination they wish, but with no more than 2 friends per room. in how many ways can the innkeeper assign the guests to the rooms?(2014 amc 12a
The total number of ways to assign the guests to the rooms is 126 ways
We can solve this problem by using a combination. We have 5 friends and 5 rooms, so we can think of the friends as stars and the rooms as bars that separate them. The number of ways to assign the friends to the rooms is equal to the number of ways to arrange the 5 stars and 4 bars (since there are 4 spaces between the bars).
We can choose any 4 positions out of 9 (5 stars and 4 bars) to place the bars, so the number of ways to assign the friends to the rooms is equal to the binomial coefficient.
[tex]${9 /\choose 4} = \frac{9!}{4!5!} = 126$.[/tex]
Therefore, there are 126 ways for the innkeeper to assign the 5 friends to the 5 rooms.
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The dance team is making banners to advertise an upcoming performance. (Screenshot)
Answer:
[tex]6.45ft^{2}[/tex]
Step-by-step explanation:
) the average lifespan for a certain type of vehicle is 8 years and follows an exponential distribution. a lot contains 200 of these vehicles, brand new. (a) how many of the 200 would you expect to fail in their first 2 years? (b) what is the approximate probability that 50 or more of them fail in their first 2 years? (c) if you have learned that 30 vehicles have already failed in under 2 years, what is the approximate probability that no more than 10 of the rest of them fail in their first 2 years?
a) We would expect approximately 0.2325 × 200 = 46.5 vehicles
to fail in their first 2 years. Since we cannot have a fraction of a vehicle
failing, we would expect around 46 or 47 vehicles to fail in their first 2
years.
b) The approximate probability that 50 or more vehicles fail in
the first 2 years is 0.0004.
c) The approximate probability that no more than 10 of the remaining
vehicles fail in their first 2 years, given that 30 have already failed, is 0.0002.
a) The average lifespan of the vehicle is 8 years, and it follows an
exponential distribution, which has a probability density function of
[tex]f(x) = (1/θ) \times e^(-x/θ)[/tex],
where θ is the mean of the distribution. Thus, θ = 8.
The probability that a vehicle fails in the first 2 years can be found by
integrating the exponential probability density function from 0 to 2:
P(X ≤ 2) = ∫[0,2] f(x) dx = ∫[0,2] (1/8) × e^(-x/8) dx
Using a calculator or a table of integrals, we can find this probability to
be approximately 0.2325.
b) The number of vehicles that fail in the first 2 years follows a Poisson
distribution with parameter λ = 200 × P(X ≤ 2) = 200 × 0.2325 = 46.5.
The probability that 50 or more vehicles fail in the first 2 years can be
found using the Poisson distribution with parameter λ = 46.5:
P(X ≥ 50) = 1 - P(X < 50)
Using a Poisson distribution table or a calculator, we can find that P(X <
50) is approximately 0.9996.
Thus, P(X ≥ 50) = 1 - 0.9996 = 0.0004 (approximately).
c) Given that 30 vehicles have already failed in under 2 years, we need
to find the probability that no more than 10 of the remaining 170 vehicles
fail in their first 2 years.
The number of vehicles that fail in the first 2 years follows a Poisson
distribution with parameter λ = 170 × P(X ≤ 2) = 170 × 0.2325 = 39.525
(rounded to 40).
Thus, we need to find P(Y ≤ 10), where Y is a Poisson random variable
with parameter λ = 40.
Using a Poisson distribution table or a calculator, we can find that P(Y ≤
10) is approximately 0.0002.
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it is known that 5% of the books bound at a certain bindery have defective bindings. find the probability that 2 of the 100 books bound by this bindery will have defective bindings using the poisson approximation to the binomial distribution.
Answer:
Therefore, P(X = 2) ≈ 0.1247 - 0.0337 ≈ 0.091, or about 9.1%.
Step-by-step explanation:
We can use the Poisson approximation to the binomial distribution when n (the number of trials) is large and p (the probability of success) is small. In this case, n = 100 and p = 0.05, so np = 5, which is not too small. However, we can still use the approximation as long as we adjust for continuity, by adding and subtracting 0.5 from the number of successes we're interested in.
Let X be the number of books with defective bindings out of 100. We want to find the probability that X = 2. Using the Poisson approximation, we have:
λ = np = 5
P(X = 2) ≈ P(1.5 < Y < 2.5), where Y is a Poisson random variable with parameter λ
To find this probability, we can use the cumulative distribution function (CDF) of Y:
P(X = 2) ≈ P(1.5 < Y < 2.5) = F(2.5) - F(1.5), where F(x) is the CDF of Y evaluated at x
The CDF of a Poisson distribution with parameter λ is given by:
F(x) = e^(-λ) * Σ(λ^k / k!, k = 0 to floor(x))
where floor (x) is the greatest integer less than or equal to x. Using this formula, we can calculate:
F(1.5) = e^(-5) * Σ(5^k / k!, k = 0 to 1) ≈ 0.0337
F(2.5) = e^(-5) * Σ(5^k / k!, k = 0 to 2) ≈ 0.1247
Therefore, P(X = 2) ≈ 0.1247 - 0.0337 ≈ 0.091, or about 9.1%.
The probability that 2 of the 100 books bound by this bindery will have defective bindings using the poisson approximation to the binomial distribution is 0.0842.
Since the number of books bound, n = 100, is large and the probability of defective bindings, p = 0.05, is small, we can use the Poisson approximation to the binomial distribution.
The mean, µ, of the Poisson distribution is µ = np = 100 x 0.05 = 5.
The probability of 2 defective bindings can be calculated using the Poisson probability formula:
P(X = 2) = (e^-µ) * (µ^x) / x!
= (e^-5) * (5^2) / 2!
= 0.0842 (rounded to four decimal places)
Using the Poisson approximation to the binomial distribution, the likelihood that 2 of the 100 volumes bound by this bindery will have faulty bindings is roughly 0.0842.
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how to solve 132/8 answer should be in whole numbers
Answer:
use long divison ike this
16
-------
8 | 132
8
-----
52
48
-----
4
Step-by-step explanation:
Answer:
Step-by-step explanation:
132/8 = 16 with 4 leftover
32 divided by 8 is 4, 96 divided by 8 is 12, the
extra 4 left over
Write an inequality for the following statement. a is less than or equal to 2
Answer: a ≤ 2
Step-by-step explanation:
How to write an inequality statement:
Step 1: Write the two values being compared in the problem.
Step 2: Determine whether the first value is larger or smaller than the second value.
Step 3: Express the inequality with the right symbols:
≤ = less than or equal to
≥ = greater than or equal to
Therefore, the answer would be a≤2.
Hope this helped!
What is the factored form of the polynomial x2 - 9x + 20?
A. x(x - 9) + 20
B. (x-4)(x + 5)
C. (x - 4)(x - 5)
D. (x2 - 4)(x2 - 5)
elijah is simplifying the expression. 4 - 3x 8 10x. 4 - 3x 8 10x. 4 - 8 - 3x 10x -4 7x where did elijah go wrong?
Elijah incorrectly combined the constant terms 4 and 8 to get -8. The correct simplification of the expression should be 4 + 8 - 3x - 10x, which simplifies to 12 - 13x.
To simplify the expression 4 - 3x + 8 - 10x, we first combine the like terms -3x and -10x to get -13x. Then we combine the constant terms 4 and 8 to get 12. So the simplified expression is 12 - 13x.
However, Elijah made a mistake by combining the constant terms 4 and 8 as if they had opposite signs. This resulted in a term of -8 that is not present in the original expression. The rest of his simplification is correct.
Therefore, the correct simplification of the expression is 4 + 8 - 3x - 10x, which simplifies to 12 - 13x.
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Complete Question:
Elijah is simplifying the expression 4 - 3x + 8 - 10x. He arrived at the answer 4 - 8 - 3x + 10x - 4 = 7x,
where did elijah go wrong?
mr balewa works at a bakery every Monday he uses 4 1/2 cups of flour to make six dozen cookies every Friday he makes 12 dozen cookies
In the proportion, Mr.Balewa needs 9 cups to makes 12 dozen cookies.
What is proportion?A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.
Here
He uses 4 1/2 cups of flour to make six dozen cookies then to makes 12 dozen cookies the x cups of flour .
Now using proportion,
= (4 1/2) / 6 = x / 12
= (9/2) / 6 = x/12
x = (9*12)/(2*6) = 9
= 9 cups.
Hence Mr. Balewa needs 9 cups to makes 12 dozen cookies.
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Shawn makes 15 1/5% of free throw shots he attempts. That means on average he makes 15 1/5 shots for every 100 shots he attempts. About how many free throw shots does Shawn make out of 300 shots?
Answer: To find how many free throw shots Shawn makes out of 300 shots, we can first find how many he makes out of 100 shots, and then multiply by 3 to get the number of shots he makes out of 300.
If he makes 15 1/5 shots out of 100, we can convert this to a decimal by dividing 15 by 100 and adding 1/5, which is the same as adding 0.2. This gives:
15/100 + 1/5 = 0.15 + 0.2 = 0.35
So, on average, Shawn makes 35% of the free throw shots he attempts.
To find how many shots he makes out of 300, we can multiply this percentage by 300:
0.35 x 300 = 105
Therefore, Shawn makes about 105 free throw shots out of 300 shots.
Step-by-step explanation:
-8x+y=25 system of equations help
which of the following correctly compares the t -distribution and z -distribution? responses for small sample sizes, the density curve of the t -distribution is not symmetric, but the density curve of the z -distribution is symmetric. for small sample sizes, the density curve of the t -distribution is not symmetric, but the density curve of the z -distribution is symmetric. for large sample sizes, the density curve of the t -distribution is not symmetric, but the density curve of the z -distribution is symmetric. for large sample sizes, the density curve of the t -distribution is not symmetric, but the density curve of the z -distribution is symmetric. the curves of both distributions are symmetric, but the height of the density curve of the t -distribution is taller than the height of the density curve of the z -distribution. the curves of both distributions are symmetric, but the height of the density curve of the t -distribution is taller than the height of the density curve of the z -distribution. the area under the density curve of the t -distribution is greater than the area under the density curve of the z -distribution, especially for small sample sizes. the area under the density curve of the t -distribution is greater than the area under the density curve of the z -distribution, especially for small sample sizes. the density curve of the t -distribution is more spread out than the density curve of the z -distributi
The correct comparison between the t-distribution and z-distribution is:
The density curve of the t-distribution is more spread out than the density curve of the z-distribution, especially for small sample sizes.
Both t-distribution and z-distribution have symmetric density curves.
However, for small sample sizes, the t-distribution curve is more spread out and has heavier tails compared to the z-distribution curve.
The area under both curves is equal to 1, as they represent probability distributions.
As the sample size increases, the t-distribution curve approaches the z-distribution curve in shape.
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100 points!!!
Express the function graphed on the axes below as a piecewise function.
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a bucket that weighs 5 pounds and a rope of negligible weight are used to draw water from a well that is 76 feet deep. the bucket is filled with 37 pounds of water and is pulled up at a rate of 1.8 feet per second, but water leaks out of a hole in the bucket at a rate of 0.25 pounds per second. find the work done pulling the bucket to the top of the well.
The work done pulling the bucket to the top of the well of depth 76 feet is equals to the 346.56 pounds/ feet.
Work is the product of force and distance, W=F×d. A Riemann Sum is a collection of rectangles used to approximate the area underneath a curve. In this case the "height" of the rectangle will be the force being exerted, and the "width" of the rectangle will be the amount of distance it moved. The work done by the force on the object can be expressed as an integral, [tex]W = \int_{a}^{b}F(x)dx[/tex]
Weigh of bucket = 5 pounds
A rope with negligible weight is used to draw water from a well. The depth of well = 76 feet.
Initially, Water in bucket = 37 pounds
Rate of pulling rope = 1.8 feet per second
Rate of water leaking in bucket = 0.25 pounds per second
Changing rate of leaking from pounds/sec to pounds/ feet : Q = 0.25/1.8 pounds/feet
= 0.139 pounds per feet
Thus, the rate of water leak from bucket hole is 0.12 pounds per feet. Let 'x' be height of bucket in feet from bottom of well. So, the total water leaked from hole = 0.12x
After leakage Remaining water in bucket = (37 - 0.12x )pounds
Also, add the weigh of buket in above expression. The limits of integration varies with depth of well that is 0 to 76 feet. Using Riemann sum method, work done pulling the bucket to the top of the well, [tex]W = \int_{0}^{76} ( 37 - 0.12x + 5 ) dx [/tex]
=>[tex]W = \int_{0}^{76} ( 42 - 0.12x ) dx [/tex]
=> [tex]W = [0 - \frac{0.12x²}{2}]_{0}^{76} \\ [/tex]
=> [tex]W = \frac{0.12×76²}{2} - 0 [/tex]
=> W = 0.12× 38×76 = 346.56 pounds/ feet. Hence required work done is 346.56 pounds/ feet.
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please help me with this iready mastery check
To succeed in an i-Ready mastery check, it is essential to review the materials covered in the lessons thoroughly, actively engage in the learning process, and ask questions if anything is unclear.
Hi! I understand you're seeking help with an i-Ready mastery check. As a bot, I cannot directly access or provide specific assistance with individual i-Ready questions or quizzes.
However, I can offer general guidance on the platform and the importance of mastery checks. Please keep in mind that I am limited to providing information within the scope of these terms and will not reach the requested 170 words.
i-Ready is an online adaptive learning platform that offers personalized learning experiences for students in reading and mathematics.
Mastery checks play a crucial role in ensuring that students fully understand the concepts being taught before progressing to more advanced topics.
These short assessments typically follow a lesson or series of lessons, helping teachers identify areas where students may need additional support or practice.
Remember that mastery checks are designed to measure your understanding of specific topics, so it's important to approach them with focus and confidence.
Good luck with your i-Ready mastery check! If you have questions about specific concepts, feel free to ask, and I'll do my best to help you.
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the radius of a disk is given as with a maximum error of . use differentials to estimate the relative error in the calculated area of the disk. please enter your answer in decimal format with three significant digits after the decimal point.
Using differentials to estimate the relative error in the calculated area of the disk of disk with radius 15 cm is equals to the 3.192%.
We have, a disk with radius of 15 cm.
Maximum error = 0.25
We have to determine the area of the disk. Area is a two dimensional quantity. It is defined as the space occupied by figure or any two dimensional shape. Here, formula for area of disk, A = πr² --(1)
here, r = 15 cm , dr = 0.25
Relative error is defined as the ratio of absolute error in measurement to the oringnal measurement. Differentating the equation (1) with respect to r, dA = d( πr²)
=> dA = 2πr dr
Substitutes the known values, in above formula, dA = 2× π × 15 ×0.25
=> dA = 7.50 × π = 23.55
So, absoulte error in area = 22.55
Original value of area = π(15)² = 706.5 cm²
Now, relative error % = (∆A/A)×100
= (22.55/706.5)×100
= 0.031917 × 100
= 3.1917 ~ 3.192 %
Hence, required value is 3.192%.
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Complete question:
the radius of a disk is given 15 cm as with a maximum error of 0.25 . use differentials to estimate the relative error in the calculated area of the disk. please enter your answer in decimal format with three significant digits after the decimal point.
I just need an explanation and answer on both plsssss
Since the total amount of kids who participated in the survey is 150, 100% of the pie is equal to 150 kids.
We know that 46% of the 150 kids like video games so the number of kids that like video games is 0.46 * 150 = 69.
Similarly, 14 + 16 = 30% of 150 kids like reading and art so the number of kids that like reading and art is 0.3 * 150 = 45.
Your second question is quite hard to understand. But you know that 120 kids like video games and those kids make up 40% of the total so mathematically you can say,
40% * number of total students = 120
number of total students = 120/40% = 300
Question 1) What fraction of this shape is shaded?
The required fraction for the given condition is [tex]\frac{1}{3}[/tex]
What is fraction?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
According to question:Give shape contain 12 squares out of then four squares are shaded.
so, required fraction can be determine as
[tex]$Fraction=\frac{4}{12}[/tex]
[tex]$Fraction=\frac{1}{3}[/tex]
Thus, required fraction is [tex]\frac{1}{3}[/tex]
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Complete question;
Select all expressions that are equal to 6^-10
Answers:
Step-by-step explanation:
(1/6²)⁵ = 1/6¹⁰ = 6^-10
because in the case of exponent of an exponent the exponents are multiplied with each other.
and 1/n = n^-1
(6^-5)² = 6^-10
because as above the exponents are multiplied with each other.
6^-3 / 6⁷ = 6^(-3 - 7) = 6^-10
a^n × a^m = a^(n+m)
a^n / a^m = a^(n-m)
the others are not 6^-10 :
6^-5 × 6² = 6^(-5 + 2) = 6^-3
6⁵×6^-3 / 6^-8 = 6^(5 - 3 - -8) = 6^(5 ‐ 3 + 8) = 6¹⁰
Can somebody please help me with this it’s really important ??
please help, i cant figure this out!!
Answer:
a = 127° , b = 12° , c = 115°
Step-by-step explanation:
a and 53° are same- side interior angles and sum to 180° , that is
a + 53° = 180° ( subtract 53° from both sides )
a = 127°
c and 115° are alternate angles and are congruent , then
c = 115°
53° , b and c lie on a straight line and sum to 180°
53° + b + c = 180°
53° + b + 115° = 180°
b + 168° = 180° ( subtract 168° from both sides )
b = 12°
then a = 127° , b = 12° , c = 115°
Answer:
a = 127; b = 12; c = 115
Step-by-step explanation:
c =115
b = 180 - 115 - 53
b = 12
a = b + c
a = 12 + 115
a = 127
Which statements are true for the following expression? (8 + 7)(11+7) Check all that are true. The solution is the sum of two terms. The solution is the difference between two terms. The first factor is itself the sum of two terms. 4 The solution is the product of two factors. The second factor is itself the sum of two terms.
Answer:
the last 3 are true
Step-by-step explanation:
hope this helps
Explain how to solve the given equation for "x".
we can solve the given equation by taking log to get answer as x = log₈(25)
what is an equation ?
An equation is a mathematical statement that contains an equal sign, indicating that two expressions have the same value. It is a way of expressing the relationship between different variables or quantities.
In the given question,
Taking the logarithm of both sides with base 8, we get:
log₈(8ˣ) = log₈(25)
Using the logarithmic property that logₐ(b^c) = c logₐ(b), we can simplify the left-hand side to:
x log₈(8) = log₈(25)
Since log₈(8) = 1, we have:
x = log₈(25)
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you want to obtain a sample to estimate a population proportion. at this point in time, you have no reasonable estimate for the population proportion. you would like to be 99.5% confident that your estimate is within 4% of the true population proportion. how large of a sample size is required?
The sample size required to estimate a population proportion with a desired level of confidence and margin of error depends on the size of the population and the confidence level desired. In this case, the population proportion is unknown and the desired confidence level is 99.5% with a margin of error of 4%.
To determine the sample size required, we can use the formula:
n = (Z² * p * q) / E²
where n is the sample size, Z is the Z-score corresponding to the desired level of confidence (which for a 99.5% confidence level is 2.81), p is the estimated population proportion (which is 0.5 as we have no reasonable estimate), q is 1-p, and E is the margin of error (which is 0.04).
Plugging in these values, we get:
n = (2.81² * 0.5 * 0.5) / 0.04² ≈ 1381
Therefore, a sample size of at least 1381 is required to estimate the population proportion with 99.5% confidence and a margin of error of 4%.
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Help pls find the area
Answer: 112 ft²
Step-by-step explanation:
The area of a triangle can be found with the equation
[tex]A=\frac{1}{2} bh[/tex], where b is the base (bottom line of the triangle) and h is the height (the distance of the line from the peak of the triangle that forms a right angle with the base).
In this problem we are given the base and height: the base is 16 feet, and the height is 14 ft.
Therefore, the area is [tex]\frac{1}{2} *16*14[/tex], which is 112 ft²
a researcher wants to test the hypothesis that the mean rating of guilt will be higher for unattractive defendants than for attractive defendants. the appropriate statistical test would be the
The appropriate statistical test for whether the mean rating of guilts are greater for unattractive defendants than for attractive is:
B. 1 tailed t-test.
What are the hypothesis test?At the null hypothesis, it is tested if the mean rating of guilt will not be higher for unattractive defendants than for attractive defendants, that is:
H0 : uU <=uA
At the alternative hypothesis, it is tested if the rating is greater, that is:
H1 : uU> uA
We are comparing the means, hence a t-test is used. We are testing if one is greater than other(not different), hence a 1-tailed test is used, and option B is correct.
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The area of a composite figure is 84 square inches. The figure is decomposed into one rectangle and two congruent triangle. The length of the rectangle is 12 inches. The width of the rectangle is 5 inches. The heigh of both triangles is 4 inches. What is the base of both triangles?
________Inches
Answer:
3 inches
Step-by-step explanation:
area of a rectangle
12×5
Use formula to find the area of the figure(show the formula,work,and units)
Answer:
25
Step-by-step explanation:
Formula 1/2(B1+B2)H
1/2(10)5
1/2 x 10=5
5 x 5 =25
if x^2 + y^2 = m and xy = n, find the value of 16m + 32n
Answer:
x^4 - mx^2 + n^2 = 0
Step-by-step explanation:
We can use algebraic manipulation to solve for m and n. First, we can square the equation xy = n to get:
(x^2)(y^2) = n^2
Since we also have x^2 + y^2 = m, we can substitute y^2 with m - x^2 to get:
x^2(m - x^2) = n^2
Expanding the left side of the equation, we get:
mx^2 - x^4 = n^2
Multiplying both sides by 16, we get:
16mx^2 - 16x^4 = 16n^2
Adding 32xy to both sides, we get:
16mx^2 + 32xy - 16x^4 = 16n^2 + 32xy
Substituting n for xy, we get:
16mx^2 + 32n - 16x^4 = 16n^2 + 32n
Rearranging the equation, we get:
16mx^2 - 16x^4 - 16n^2 = 0
Dividing both sides by -16, we get:
x^4 - mx^2 + n^2 = 0
Answer:
(4x+4y)²
Step-by-step explanation:
Given x²+y² = m ,xy=n.
Now 16m+32n = 16(m+2n)
= 16(x²+y²+2xy) = 4²(x+y)²[ x²+y²+2xy= (x+y)²]
(4x+4y)².