Answer:
Step-by-step explanation:
-3x - 2y = -20
3x + y = 10
-y = -10
y = 10
3x + 10 = 10
3x = 0
x = 0
(0, 10)
Let X1, …, Xn be a random sample from a gamma(α, β) population.
(a) Find the MLE of β, assuming α is known.
(b) If α and β are both unknown, there is no explicit formula for the MLEs of α and β, but the maximum can be found numerically. The result in part (a) can be used to reduce the problem to the maximization of a univariate function. Find the MLEs for α and β for the data in Exercise 7.10(c).
the logarithm of the likelihood function and differentiate it with respect to both alpha and beta.
(a) The MLE of β is given by [tex]$$\hat{\beta} = \frac{\sum_{i=1}^n X_i}{n \alpha}.$$[/tex]
(b) The likelihood function for the data in Exercise 7.10(c) is given by [tex]$$L(\alpha, \beta) = \alpha^n \beta^{-n\alpha} \prod_{i=1}^n X_i^{-\alpha}.$$[/tex]We can take the logarithm of both sides to obtain[tex]$$ \ell(\alpha, \beta) = n \log \alpha - n \alpha \log \beta - \alpha \sum_{i=1}^n \log X_i.$$[/tex]Taking the partial derivatives of the log-likelihood function and setting them to 0 yields [tex]$$\frac{\partial \ell}{\partial \alpha} = \frac{n}{\alpha} - n \log \beta - \sum_{i=1}^n \log X_i = 0 \quad \text{and} \quad \frac{\partial \ell}{\partial \beta} = -\frac{n \alpha}{\beta} = 0.$$[/tex]Sol
Using the data from Exercise 7.10(c), we take the logarithm of the likelihood function and differentiate it with respect to both alpha and beta. We then set the partial derivatives to 0 to obtain equations for alpha and beta which can be solved to find the MLEs.
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In evaluating a double integral over a region D. a sum of iterated integrals was obtained as follows: Sketch the region D and express the double integral as an iterated integral with reversed order of integration.
Let D be the region bounded by the lines y = 0, y = x, x = 1, and x = 2. In order to express the double integral as an iterated integral with reversed order of integration, we first need to sketch the region D.
The double integral could be expressed as an iterated integral with reversed order of integration as follows:
[tex]$\int_{1}^{2}\int_{0}^{x}f(x,y)dydx$[/tex]
The region is bounded by the lines y = 0, y = x, x = 1, and x = 2. This forms a triangle-like shape with 1 and 2 being the x-coordinates of the vertices and y = 0 being the base of the triangle. Then, we can express the double integral as: [tex]$\int_{1}^{2}\int_{0}^{x}f(x,y)dydx$[/tex], where the order of integration is reversed from the original double integral. This means that first we are integrating with respect to y from 0 to x, and then we are integrating with respect to x from 1 to 2.
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In a study where the least squares estimates were based on 34 sets of sample observations, the total sum of squares and regression sum of squares were found to be: SST = 4.35 and SSR = 4.18. What is the error sum of squares?
Multiple Choice
1.07
0.17
0.320
8.74
In a study where the least squares estimates were based on 34 sets of sample observations, the total sum of squares and regression sum of squares were found to be: SST = 4.35 and SSR = 4.18. What is the error sum of squares is 0.17.
What do you meant by squares?A square is a figure with four equal sides and four right angles. It's a popular shape for windows and record albums, among many other things.Square has many different metaphorical uses. Old towns had square open areas for meetings, so now "town square" means meeting place, even if it's not shaped exactly like a square. If you settle your debts, you square them, and if someone calls you a square, they mean you're boring, rule-abiding, and lame. In math, a square is the product of something multiplied by itself. If you square your plans with someone, you line them up.To learn more about square refer to:
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with the given vertices.
4. E(-3, 3), F(1, 3), G (3, -3), H(-5, -3)
Answer:
sorry new don't understand the app
Round the answer to the nearest tenth please
Answer:
19.9 m
Step-by-step explanation:
Cone: r= 1m Height= 2m (You will use the radius for the Cylinder)
1/3 x π x 1^2 × 2 = 2.0943951023932
2.0943951023932 x 2 = 4.1887902047864 (Just use the hundreths place if writing down.)
Cylinder: r= 1m Height= 5m
π x 1^2 x 5 = 5π = 15.707963267949
Now add both together then round to tenths.
4.1887902047864 + 15.707963267949 = 19.8967534727354
(Remember use hundreths place if writing down)
19.8967534727354 --> 19.9 m
a current i(t) with arbitrary time dependence is around a circular ring. derive the general formula for the power radiated,
P = ∫(i^2 dl / 6πε0 c^3) × a^2
where q is the charge, ε0 is the permittivity of free space, c is the speed of light, and a is the acceleration of the charge.
Now consider a small element of length dl around the ring through which the current i flows. The power radiated from this element can be written as
dP = (i^2 dl / 6πε0 c^3) × a^2
where a is the acceleration of the charge in the element due to the changing magnetic field.
The total power radiated from the entire ring is obtained by integrating this expression over the length of the ring.
P = ∫(i^2 dl / 6πε0 c^3) × a^2
This is the general expression for the radiated power of the current distribution around the ring.
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Your company creates haircare and skincare products in large quantities. You have a cylindrical storage tank that’s going to be used for a new batch of shampoo. The tank is 170 feet across in diameter and 60 feet high.
Use this formula sheet for your calculations.
Part A
To calculate the volume of this cylindrical tank, what preliminary calculations must be done with the information given in the problem?
To calculate the volume of a cylindrical tank, you will need to use the formula for the volume of a cylinder, which is:
V = πr^2h
Where V is the volume, r is the radius of the base of the cylinder, and h is the height of the cylinder.
To use this formula, you will need to first calculate the radius of the base of the tank. To do this, you will need to divide the diameter of the tank (170 feet) by 2.
Once you have calculated the radius, you can plug the value into the formula along with the height of the tank (60 feet) to find the volume of the tank.
Answer:
Step-by-step explanation:
height of the tank= 60 feet
diameter = 170 feet.
as we know, radius = 2 *diameter
therefore radius = diameter /2
= 170/2
=85 feet
volume of cylinder = πr²h
π =3.14
= 3.14 ×85×60
=10927.2 feet²
you are measuring a process, and you are given the following information: overall average: 131 population stdev: 5 sample size: 11 determine the upper control limit if your desired confidence interval is 99.73%. enter your answer to one decimal place. it's ok if you get a negative number; in that case, just enter the minus sign in front of it.
The upper control limit is 16.4 if our desired confidence interval is 99.73%.
What is Confidence interval?In statistics, a confidence interval describes the likelihood that a population parameter will fall between a set of values for a given percentage of the time.
Given 131 population
Standard deviation = 5
sample size = 11.
mean = 131/11 = 11.9.
Determine the upper control limit if desired confidence interval is 99.73%
Confidence interval = sample mean ± margin of error
Upper limit = sample mean + margin of error.
Margin of error = z* * population of standard deviation/[tex]\sqrt{n}[/tex]
Margin of error = 3.00 * 5/[tex]\sqrt{11}[/tex].
Value of z* for 99.73% confidence interval is 3.00.
So margin of error = 4.5.
Upper limit = 11.9 + 4.5
Upper limit = 16.4
If we want a confidence level of 99.73%, the top control limit is 16.4.
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what is the area of this triangle
30POINTS
Answer:
81.74 cm²
Step-by-step explanation:
Use tan(x) to find x
tanθ = opposite/adjacent
tan(36) = x/15
15tan(36) = x
area of triangle = [tex]\frac{1}{2}[/tex]*b*h
[tex]\frac{1}{2}[/tex]*15tan(36)*15 = 81.74 cm² (2 d.p.)
write an equation of the line that passes through the given point and is parallel to the given line. (see example 2.) 7. (0, 2); x
Equation of the line parallel to the given line and passing through the given point = 2x+5y=18.
What is EQUATIONS?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
The meanings of the word equation and its cognates in various languages can vary slightly.
For instance, in French, an equation is defined as having one or more variables, whereas in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign.
Finding the values of the variables that result in the equality is the first step in solving an equation with variables.
The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfill the equality are known as the equation's solutions.
Equations come in two varieties: identities and conditional equations.
According to our question-
Given line: 2x+5y−7=0
the mid - point of the line segment joining point (2,7) and (−4,1) is
( 2(2−4 )2(7+1))=(−1,4)
the equation of the line will be
y−y 1=m(x−x 1)y−4=( 5−2 )(x+1)
5y−20=−2x−2
2x+5y=18
Hence, Equation of the line parallel to the given line and passing through the given point = 2x+5y=18.
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let $d$ be any positive integer not equal to $2, 5$ or $13$. show that one can find distinct $a,b$ in the set $\{2,5,13,d\}$ such that $ab-1$ is not a perfect square.
The statement given in the question holds true . We get this result after analyzing the given data set .
Given , hypothesis is ,
Let d be any positive integer not equal to2 , 5 or 13 .
Show that one can find distinct a , b in the set {2,5,13,d} such that ab-1 is not a perfect square.
Using the modular way to solve this question we get ,
d = 0 , 3 = | 4 |
Then , we get the result as ,
13d - 1 , which is not a perfect square.
d = 2|4|
we get , 2d -1
which again is not a perfect square.
Similarly after checking the value for all the possible cases , we will get the result that the hypothesis is correct.
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Last year, Alan opened an investment account with $7200. At the end of the year, the amount in the account had increased by 6.5%. How much is this increase in dollars? How much money was in his account at the end of the year?
Answer:
1) $468
2) 7668
Step-by-step explanation:
1) 6.5% of 7200 is 468. Therefore, this is the amount it had increased.
2) 7200+468=7668 Total for the end of the year
Select all of the equations for the line that passes through (5, −2) and (0, 18).
Multiple select question.
A)
y+2=−4(x−5)
B)
x+4y=−12
C)
y−6=−4(x+1)
D)
y=−4x−12
E)
y=−4x+18
F)
4x+y=18
Answer:
Need more info please
Step-by-step explanation:
Armando divided 6 and 258
Answer:
43
Step-by-step explanation:
258 divided by 6 equals 43
Look below
Armando divided 6 and 258
258 is the bigger number, so we will keep that on the right, and then add the dividing symbol. Next, we will add the 6. That should look like this:
258÷6
then just put it on a calculator and you get the answer 43. hope that helps
maya spent a total of 80% at the grocery store. of this amount, she spent $44 on fruit. what percentage of total did she spend on fruit
The percentage of total that Maya spend on fruit is 55%.
How to calculate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, Maya spent a total of $80 at the grocery store. of this amount, she spent $44 on fruit. The percentage of total that she spend on fruit will be:
= Amount on fruit / Total amount × 100
= 44/80 × 100
= 55%
The percentage is 55%.
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Complete question
maya spent a total of $80 at the grocery store. of this amount, she spent $44 on fruit. what percentage of total did she spend on fruit
A rivet is to be inserted into a hole. If the standard deviation of hole diameter exceeds 0.02 mm, there is an unac- ceptably high probability that the rivet will not fit. A random sample of n = 15 parts is selected, and the hole diameter is measured. The sample standard deviation of the hole diameter measurements is s = 0.016 mm. (a) Is there strong evidence to indicate that the standard deviation of hole diameter exceeds 0.02 mm? Calculate a P-value to draw conclusions. State any necessary assumptions about the underlying distribution of the data. (b) Construct a 95% lower confidence bound for o. (c) Use the confidence bound in part (b) to test the hypothesis.
Since our test statistics ( 8.96 ) is less than the critical value ( 29.141 ),
there is no strong evidence to indicate that the standard deviation of hole diameter exceeds 0.02 millimeters.
Given that;
H₀ : σ = 0.02
H₁ : σ > 0.02
The test statistics is;
X² = ( n-1 )s² / σ² = ( 15 - 1)(0.016)² / (0.02)²
= 0.003584 / 0.0004
= 8.96
degree of freedom
df = n - 1 = 15 - 1 = 14
For right tailed test, critical value at 0.01 level of significance is 29.141.
Now since our test statistics ( 8.96 ) is less than the critical value (29.141 ),
Therefore, there is no strong evidence to indicate that the standard deviation of hole diameter exceeds 0.02 millimeters.
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Question
Newton's Law of Universal Gravitation: The gravitation attraction, f , between two objects of masses x and y is proportional to the product of the masses and inversely proportional to the square of the distance, d , between the objects.
Write an equation for the constant of variation, k, in terms of f, x, y, and d.
Complete the equation in the space below (do not enter “k=“)
The required equation for the variation of k is given as k = Fd² / xy.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Newton's Law of Universal Gravitation states that the gravitational attraction, f, between two objects with masses x and y is proportional to the product of their masses and inversely proportional to the square of their distance, d.
So,
F ∝ x × y - - - - (1)
And
F ∝ 1 / d² - - - - - (2)
Combining equations 1 and 2
F ∝ xy / d²
Or
F = kxy / d²
Now,
Formulate the above expression with subject to constant k.
K = Fd² / xy
Thus, the required equation for the variation of k is given as k = Fd² / xy.
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scenario 2: an analyst wants to know if the proportion of smokers in the population is the same in usa and canada. in order to test this hypothesis she collects data from individuals, both smokers and non-smokers, living in these countries. your task is to help the analyst perform her hypothesis test. in order to do this you need to compute various statistics using excel. use 5% level of significance. [scenario 2: q1] the proportion of smokers in the us sample is . 0.17 0.06 0.16 0.12 0.40
The conclusion statement of the hypothesis is to reject the null hypothesis and accept the alternative hypothesis and the z score of -121.70 is in the rejection area
How to calculate the hypothesis?
In order to calculate, the hypothesis test we have to make inferences about the population data. It is also used to check if the results of an experiment are valid.
Here we have given that an analyst wants to know if the proportion of smokers in the population is the same in USA and Canada. in order to test this hypothesis she collects data from individuals, both smokers and non-smokers, living in these countries. your task is to help the analyst perform her hypothesis test. in order to do this you need to compute various statistics using excel. use 5% level of significance.
Here we have the following sample of data,
0.17 0.06 0.16 0.12 0.40
Through the given samples, we have identified the following values,
Count, N: 5
Sum, Σx: 0.91
Mean, μ: 0.182
Variance, σ2: 0.013376
Then the hypothesis test is written as,
The critical value (cutoff point) is 2.132. In left-tail hypothesis testing, any z score less than the critical value will be rejected. Since -121.70 is less than 2.132, we reject the null hypothesis. We accept the alternative hypothesis.
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PLEASE HELP ASAP!!!
A machine at a bakery poured out flour for 16 minutes. At the end of that time, the machine was empty. The graph shows the amount of flour (in grams) remaining in the machine versus time (in minutes). Find the range and the domain of the function shown.
Answer:
R = 0≤ y ≤ 800
D = 0≤ x ≤ 16
.
.
.
.
Solve:
b. m∠1=
m∠2=
m∠3=
The measure of the angles in the given figure of the triangle is given by: m∠1= 56 ,m∠2= 56 and m∠3= 74.
As given in the question,
In the given triangle MPQ we have,
Sum of all the interior angles in the triangle is 180 degrees.
m ∠P + m ∠M + m∠1 =180°
⇒58° + 66° + m∠1=180°
⇒m∠1= 180° - ( 58° + 66°)
⇒m∠1=56°
From the figure , ∠1 and ∠2 are vertically opposite angles:
⇒m∠1= m∠2
⇒m∠2=56°.
In triangle QNO we have,
m ∠O + m∠2 + m∠3 =180°
⇒50° + 56° +m∠ 3=180°
⇒106° + m∠3= 180°
⇒m∠3= 180° - 106°
⇒m∠3=74°
Therefore, the measure of the required angles in the given triangles are m∠1= 56 ,m∠2= 56 and m∠3= 74.
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Liam accidentally charged more on his debit card than he had in his checking account. His balance is now -$12.75. He is charged a $10 overdraft fee each day his account balance is below $0. He makes no other withdrawals or deposits. Which equation accurately represents his balance, y, after x days?
Answer:
The equation that accurately represents Liam's balance, y, after x days is y = -12.75 - 10x.
This equation takes into account the fact that Liam's balance is already -$12.75 and that he is charged a $10 overdraft fee each day his balance is below $0. As the number of days, x, increases, the total amount of overdraft fees he is charged will also increase, resulting in a decrease in his balance.
For example, if Liam's balance is -$12.75 after 0 days, his balance will be -$22.75 after 1 day (y = -12.75 - 10(1) = -22.75), and his balance will be -$32.75 after 2 days (y = -12.75 - 10(2) = -32.75).
For which equation would x = 12 be a solution?
Ox+4≤12
12 x < 200
012-x24
O 12÷x>12
Answer:
the second solution would be correct 12x < 200
Step-by-step explanation:
12x < 200
12(12) <200
144 < 200
If Ethan has $40, what's the most amount of games he could bowl at Happy Bowl (after he rented shoes)?
Answer:
he could play 4 games and have some change left over
Step-by-step explanation:
renting shoes cost 5 dollars and each game costs 8 dollars so 40-5=35 35/8=4.375
Which of the following represents a nonlinear function?
y=x²
y=x
y=-2 x
y=5 x+7
The equation that represents a non linear function is y = x² , the correct option is (a) .
In the question ,
four functions are given ,
we have to select the option that is non linear ,
we know that ;
A Linear Function is an equation in which the the highest degree of the equation is 1 , and the graph is a straight line . and
A Non Linear Function ,is an equation in which the highest degree of the equation is more than 1 , and the graph is not a straight line .
So , from the given options
we can see that all the options have degree 1 except the equation y = x² which has highest degree 2 .
Therefore , The Non Linear Function is (a) y = x² .
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please help me answer this math question
Answer:
k>0: ]-∞, 1[ v ]9 , +∞[
Step-by-step explanation:
we know that D > 0 because the anwser has to have two outcomes so:
b²-4.a.c>0 => (k-3)²-4.k.1>0 <=> k²-6k+9-4k>0 <=> k²-10k+9>0
=> D=8² : x1 = 9 v x2 = 1
k>0: ]-∞, 1[ v ]9 , +∞[
Each of the faces of a fair six-sided number cube is numbered with one of the numbers 1 through 6, with a different number appearing on each face. Two such number cubes will be tossed, and the sum of the numbers appearing on the faces that land up will be recorded. What is the probability that the sum will be 4, given that the sum is less than or equal to 6 ?
A
2/36
B
3/36
C
3/15
D
2/9
E
4/6
Answer:
e
Step-by-step explanation:
because it's number is common
Select the correct answer. When using the binomial formula, which of the following is a correct step in the expansion of (x + y)? 4(4-1)(4-2) (4-³)³ + 31 24 + 24 + 24 + ○ D. x + Ο Α. OB. C. x(4-¹)y + 4(4-¹) (4-2) y² + 2(4-¹)y + 4(4-¹) x(4-2) y² + x(4-1)y + 4(4-¹)(4-2)² + (4-1)(4-2)(4-3)3 + 4(4-1)(4-2)(4-3) (4-4) z 4(4 − 1)(4 − 2)(4 — 3) (4-4) - 3 4(4-1)(4-2) (4-3)³ + 3 4(4-1)(4-2)(4-3) (4-4) 41 4(4 − 1)(4 − 2)(4 — 3) (4-4) (4-1)y + 4(4-1)(4-2) (4-3)³ +
The probability generating function of the dis- crete nonnegative integer valued random variable X having probability mass function pj, j = 0, is defined by ø(s) = E[s] =Σp;si j=0 Let Y be a geometric random variable with param- eter p 1 s, where 0 < s < 1. Suppose that Y is independent of X, and show that ø(s) = P{XY}
The probability generating function of a discrete nonnegative integer valued random variable X is defined by ø(s) = E[s] = Σp;si j=0, where pj is the probability mass function of X. P{XY} = P{X=i,Y=j} = P{X=i}P{Y=j} = pi pj sij,Therefore, ø(s) = Σ pi pj sij = P{XY}
In this problem, we are also given a geometric random variable Y with parameter p 1 s, where 0 < s < 1. Y is independent of X. To show that ø(s) = P{XY}, we must show that the two expressions are equal.
First, we note that the probability of X and Y being equal to i and j, respectively, is given by P{X=i,Y=j} = P{X=i}P{Y=j} = pi pj sij. This is because the probability of X being equal to i is pi, and the probability of Y being equal to j is pj (where p is the parameter of the geometric distribution). Since sij is the product of i and j, the probability of both X and Y being equal to i and j, respectively, is pi pj sij.
We can now substitute this expression into the probability generating function for X. We have that ø(s)
= E[s] = Σp;si j=0
= Σ pi pj sij
= P{XY}
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If a linear regression equation predicts more than 25% of the variance in the Y scores, then the correlation between X and Y must be greater than r = ________.
b. 0.50
c. 0.35
d. 0.40
Using correlation and it's value of coefficient , The answer is b. 0.50
What do you mean by regression?A statistical method called regression links a dependent variable to one or more independent (explanatory) variables. A regression model can demonstrate whether changes in one or more of the explanatory variables are related to changes in the dependent variable.
What do you mean by correlation?A statistical measure called correlation shows how much two or more variables fluctuate in connection to one another.
we have 25% variance confidence.
[tex]r ^ {2} = 0.25[/tex]
[tex]r=\sqrt {0.25}[/tex]
[tex]r=0.50[/tex]
The answer is b.0.50
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If a linear regression equation predicts more than 25% of the variance in the Y scores, then the correlation between X and Y must be greater than (c) r = 0.35.
Correlation (r) quantifies the strength and direction of the linear relationship between two variables. A correlation of 0.35 indicates a moderate positive linear association, suggesting that as X increases, Y tends to increase as well, and vice versa.
When the correlation surpasses this threshold, it implies that a substantial portion of the variability in Y can be explained by changes in X. However, it's important to interpret the correlation value within the context of the specific data and the field of study.
Other factors like sample size and potential outliers can also influence the significance of the correlation. In summary, a correlation greater than (c) 0.35 signifies a meaningful connection between X and Y, contributing to the prediction of Y scores using the linear regression equation.
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Elizabeth was flying from Dallas to Chicago to visit her grandmother. The plane left the airport at 10:15 a.m. Lunch was served 1 hour and 42 minutes into the flight. If it took Elizabeth 23 minutes to eat, at what time did she finish her lunch?
Answer:
15 ñ
Step-by-step explanation: