(a) Math2 is not an unbiased estimator of μ. (b)Math1 has a variance of
σ[tex]^{2}[/tex] and Math2 has a variance of 5σ[tex]^2[/tex]/8
(a) Neither of the estimators, Math1 or Math2, is an unbiased estimator of μ. An unbiased estimator should have an expected value equal to the parameter being estimated, in this case, μ.
For Math1,
the expected value is
E[Math1] = E[([tex]X_{1}[/tex] + [tex]X_{2}[/tex]) / 2]
= (E[[tex]X_{1}[/tex]] + E[[tex]X_{2}[/tex]]) / 2
= μ/2 + μ/2 = μ,
which means Math1 is an unbiased estimator of μ.
For Math2,
the expected value is
E[Math2] = E[([tex]X_{1}[/tex] + [tex]3X_{2}[/tex]) / 4]
= (E[[tex]X_{1}[/tex]] + 3E[[tex]X_{2}[/tex]]) / 4
= μ/4 + 3μ/4
= (μ + 3μ) / 4
= 4μ/4
= μ/2.
(b) To calculate the variances of the estimators, we'll use the property that the variance of a sum of independent random variables is the sum of their variances.
For Math1,
the variance is Var[Math1]
= Var[([tex]X_{1}[/tex] + [tex]X_{2}[/tex]) / 2]
= (Var[[tex]X_{1}[/tex]] + Var[[tex]X_{2}[/tex]]) / 4
= σ[tex]^2[/tex]/2 + σ[tex]^2[/tex]/2
= σ[tex]^2[/tex]
For Math2,
the variance is Var[Math2]
= Var[([tex]X_{1}[/tex] + [tex]3X_{2}[/tex]) / 4]
= (Var[[tex]X_{1}[/tex]] + 9Var[[tex]X_{1}[/tex]]) / 16
= σ[tex]^2[/tex]/4 + 9σ[tex]^2[/tex]/16
= 5σ[tex]^2[/tex]/8
Math1 has a variance of σ[tex]^2[/tex]
and Math2 has a variance of 5σ[tex]^2[/tex]/8
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If cot θ= tan (pi/6) what is cos θ? Round your answer to the nearest hundredth.
Answer:3.46
Step-by-step explanation:
someone please help
Answer:
B
Step-by-step explanation:
Hi,
Your slope is in front of the x and your y-intercept is what's being added or subtracted. In this case, 4x is your slope, and +1 is your y-intercept which means that B is correct.
I hope this helps :)
Draw a graph which has the following adjacency matrix: [2 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 (b) Label the vertices of your graph A, B, C, D (in any order). (c) How many different paths of length 10 are there from the vertex you labelled A to the vertex you labeled D in the graph you draw in part (a)?
Given an adjacency matrix, we need to find the graph which has the following adjacency matrix:[2 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0]We know that an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph.The diagonal elements of the matrix are always zero since self-loops are not allowed in a simple graph.The (i, j)-entry of the matrix is 1 if the ith vertex and jth vertex are adjacent, and 0 otherwise. Hence, for the given matrix, there is an edge between vertex 1 and vertex 2 and an edge between vertex 1 and vertex 3. Similarly, there are other edges between vertices.Here is the graph which has the given adjacency matrix:Graph with adjacency matrixFrom the graph above, we can label the vertices A, B, C, D in any order. Let's say we label the vertices as A = vertex 1, B = vertex 2, C = vertex 3, and D = vertex 4.Now, we need to find the number of different paths of length 10 from vertex A to vertex D.The number of paths of length n from vertex i to vertex j in a graph is given by the (i, j)-entry in the n-th power of the adjacency matrix. Here, we need to find the number of paths of length 10 from vertex 1 to vertex 4. So, we need to compute the 10th power of the given adjacency matrix:[2 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0] ^ 10We can use a calculator or software like MATLAB to compute the matrix power. After computing, we get that the (1, 4)-entry of the 10th power of the matrix is 8. Therefore, there are 8 different paths of length 10 from vertex A to vertex D.
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In a right triangle, one acute angle measure 35 degrees and its adjacent side is 40 yards.
Find the opposite side.
Paragraph. Describe how to find the opposite side of one right triangle with one acute angle of 35 degrees and adjacent side of 40 yards.
Word Bank: right triangle, opposite and adjacent side,
Answer:
Opposite side =28 yards
Step-by-step explanation:
Tan_°=Opposite÷ Adjacent
Tan 35° =Opposite÷40yards
Opposite=40*Tan35°
Opposite=28yards
An airplane's altitude changed -378 feet over 77 minutes. What was the mean change of altitude in feet per minute?
Answer:
-4.91 feet
Step-by-step explanation:
Mean is a measure of central tendency. It is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number
Mean = Total change in altitude / total time
378 / 77 = 4.91
The graph of g(x) is a parabola that opens upward with a vertex at (-3, 4). Which statement is true?
explain why zero is excluded from the domain and range
Answer:
The range is also all real numbers except zero. You can see that there is some point on the curve for every y -value except y=0 . Domains can also be explicitly specified, if there are values for which the function could be defined, but which we don't want to consider for some reason.
Step-by-step explanation:
hope this helps
Six times the quantity x -2 is 24. Find the number x
A recent study sought to determine if exercising after studying for an exam may help retain information. The 150 student volunteers that participated in the study were randomly assigned to three groups. All students were given a picture memory task that they studied for 15 minutes. After studying, one of the groups was instructed to exercise for 30 minutes immediately after studying. A second group was instructed to wait 1 hour after studying and then exercise for 30 minutes. The third group was instructed to not exercise after studying. The next day all 150 student volunteers were given a test to determine how well they could remember what they studied. Here are the results:
Answer:
The correct answer is (A).
Step-by-step explanation:
Because the data came from 3 groups in a randomized experiment, the appropriate test is a chi-square test for homogeneity.
Find the F-test statistic to test the claim that the variances of the two populations are equal. Both distributions are normal. The populations are independent. The standard deviation of the first sample is 4.8329
5.8304 is the standard deviation of the second sample.
The F-test statistic is approximately 1.455.
To find the F-test statistic to test the claim of equal variances for two populations, you need the standard deviations of both samples. Given that the standard deviation of the first sample is 4.8329 and the standard deviation of the second sample is 5.8304, we can proceed with the calculation.
The F-test statistic is calculated as the ratio of the variances of the two samples. In this case, since we only have the standard deviations, we need to square them to obtain the variances.
First, square the standard deviations:
Variance of the first sample (s1^2) = (4.8329)^2 = 23.3747
Variance of the second sample (s2^2) = (5.8304)^2 = 34.0051
Next, calculate the F-test statistic by dividing the larger variance by the smaller variance:
F-test statistic = (larger variance) / (smaller variance)
F-test statistic = s2^2 / s1^2
F-test statistic = 34.0051 / 23.3747
Using the given values, the F-test statistic is approximately 1.455.
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Justin lives 5 4/5 miles from his grandfathers house. Write the mixed number as a fraction greater than 1
Answer:
29/5
Step-by-step explanation:
Answer:
29/5
Step-by-step explanation:
As an improper fraction, your answer is 29/5.
I'm not sure what it means by writing it as a fraction "greater than 1".
Which equation is equivalent to 29p + 32?
A 32 - 29p
B 32 + 29p
C 32p + 29
D 32(29-p)
PLEASE HELP, ONLY HAVE A FEW MIN LFT!!!!
A bookstore tracked the data of the weight of their deliveries and the number of books in each box. They created a scatterplot and trend line based on the data.
Which statement would be a reasonable prediction based on the scatterplot and trend line?
A box with 10 books should weigh about 2 pounds.
A box with 10 books should weigh about 4 pounds.
A box with 10 books should weigh about 6 pounds.
A box with 10 books should weigh about 12 pounds.
Answer: According to the trendline it would be about 6 lbs
Step-by-step explanation:
Answer:
C.
Step-by-step explanation: I did the test </3
Write an equation in point-slope form and slope-intercept form for each line
1. passes through (1, 9), slope = 2
2. passes through (4, -1), slope = -3
An equation of a line in point-slope form: y - y₁ = m(x - x₁)
1.
passes through (1, 9) ⇒ x₁ = 1, y₁ = 9
slope: m = 2
The equation:
y - 9 = 2(x - 1) ← point-slope form
y - 9 = 2x - 2 {add 9 to both sides}
y = 2x + 7 ← slope-intercept form
2.
passes through (4, -1) ⇒ x₁ = 4, y₁ = -1
slope: m = -3
The equation:
y + 1 = -3(x - 4) ← point-slope form
y + 1 = -3x + 12 {subtract 1 from both sides}
y = -3x + 11 ← slope-intercept form
Solving systems of equations using Substitution
Y= -4x +3
Y= 4x +3
when loaded with iron rods a lorry has mass of 12000kg. if the mass of iron rods is there times that of the empty lorry . find the mass or iron.
Complete Question
When loaded with iron rods a lorry has mass of 12000kg. if the mass of iron rods is three times that of the empty lorry, find the mass of iron.
Answer:
3000kg
Step-by-step explanation:
Let us represent
Mass of lorry = x
Mass of iron rods = y
x + y = 12000kg..... Equation 1
x = 12000kg - y
We are told that:
If the mass of iron rods is three times that of the empty lorry, find the mass of iron.
x = 3y
We substitute 3y for x in Equation 1
x = 12000kg - y
3y = 12000kg - y
Collect like terms
3y + y = 12000kg
4y = 12000kg
Divide both sides by 4
y = 12000kg/4
y = 3000kg
Note that:
Mass of iron rods = y
Hence, Mass of iron rods = 3000kg
PLEASE HELPPPPP
WILL GIVE BRAINLIEST
Answer:
Step-by-step explanation:
From the given table,
A. The unit rate for each car is,
Car A = [tex]\frac{416}{13}[/tex]
= 32 miles per gallon
Car B = [tex]\frac{544}{16}[/tex]
= 34 miles per gallon
Car C = [tex]\frac{665}{19}[/tex]
= 35 miles per gallon
Car D = [tex]\frac{775}{25}[/tex]
= 31 miles per gallon
B. From the derived values in A, the car that uses the least amount of gas is Car C.
C. Total distance covered = 496 miles x 4
= 1984 miles
The gallons of gas the Car A would need for the journey can be determined by;
Car A requires 1 gallon for 32 miles
So that for 1984 miles = [tex]\frac{1984}{32}[/tex]
= 62 gallons
Car A would need 62 gallons of gas to make the trip.
D. Amount spent on gas for Car A = $2.12 x 62
= $131.44
E. speed = [tex]\frac{distance}{time}[/tex]
⇒ time = [tex]\frac{distance}{speed}[/tex]
Given the for Car A, speed = 68 miles per hour.
time = [tex]\frac{1984}{68}[/tex]
= 29.1765
time = 29 hours
It would take approximately 29 hours for Car A to cover the total distance of 1984 miles.
Need to know if this is write. if not, please correct.
Classify each pair of angles listed below as adjacent or vertical.
Which expression is equivalent to x+2+[4x-x^2+6x+8 over x+4?
Answer:
-x^3-7x^2-46x-16/x+4
Step-by-step explanation:
The slash is a fraction! Also the fraction is negative :)
whats is the answer to this equation?
who ever gets the right answer gets 25 points.
Answer:
51.2 m
Step-by-step explanation:
To find perimeter add all sides up
A bag contains 8 red pens, 7 blue pens, and 14 black pens. Denato wants to pull a blue pen from the bag.
How many desired outcomes should Denato use in his probability calculation?
Answer: its 22
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
The number of desired outcomes is the total number of blue pens in the bag. There are seven outcomes that can be blue.
The total number of passengers riding a certain city bus during the morning shift is 1,100. If the child's fare is $0.5o, the adult fare is $1.25, and the total revenue from the fares in the morning shift is $1,200, how many children and how many adults rode the bus during the morming shift? (Letx and y denote the number of children and adults, respectively.)
=1,000
=1,200
A total of 233 children and 867 adults rode the bus during the morning shift.
Let x represent the number of children and y represent the number of adults riding the bus during the morning shift.
We know that the total number of passengers is 1,100, so we can write the equation:
x + y = 1,100
The child's fare is $0.50, and the adult fare is $1.25. The total revenue from the fares is $1,200, so we can write another equation:
0.50x + 1.25y = 1,200
To solve this system of equations, we can use substitution or elimination.
Let's use substitution to solve for x:
From the first equation, we have: x = 1,100 - y
Substituting this into the second equation:
0.50(1,100 - y) + 1.25y = 1,200
Simplifying the equation:
550 - 0.50y + 1.25y = 1,200
0.75y = 650
y = 650 / 0.75
y ≈ 866.67
Since we can't have a fraction of a person, we can approximate y to the nearest whole number:
y = 867
Substituting this value of y back into the first equation:
x + 867 = 1,100
x ≈ 233
Therefore, approximately 233 children and 867 adults rode the bus during the morning shift.
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Find the radius of the button.
3 and 1/2 in
radius:
Answer:1.75
Step-by-step explanation:
formula= R= D/2
convert 3 1/2 into a decimal
3.5
do 3.5 divided by 2 (R= 3.5/2) = 1.75
so the Radius is 1.75 inches !! hope this helped :)
The radius of the button 3 and 1/2 in would be; 1.75
What is a circle?A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.
The formula= Radius= D/2
Now convert 3 and 1/2 into a decimal;
3.5
Now, 3.5 divided by 2 (R= 3.5/2)
= 1.75
Hence, the Radius is 1.75 inches .
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A backpack is on sale for 30% off. If the sales price is $15.75, what is the original price? Show your work.
Answer:
$22.50
Step-by-step explanation:
As it is 30% off, $15.75 is 70% of the full price. You can then divide 15.75 by 70 [= 0.225] to get 1% of the full price. Multiply 0.225 by 100 to get the full price. 0.225 x 100 = 22.5
We can check that this answer is correct by multiplying 22.50 by 0.7. If you get 15.75 you know the answer is correct as 15.75 is 70% of the full price.
Can someone plz help me
Answer:
IT's d!!!!!
Step-by-step explanation:
Which is the most reasonable estimate of 132% of 48?
a.5.2
b.6.5
c.52
d.65
The most reasonable estimate of 132% of 48 is 60. The correct answer is (C) 52.
To find the most reasonable estimate of 132% of 48,
A reasonable estimate does not exceed the original numbers in a problem. Let us look at a reasonable estimate.
we need to use the following formula:
Most reasonable estimate = Closest multiple of 10To use this formula, we first need to find 132% of 48.132% of 48 can be calculated as follows:132/100 x 48 = 63.36
Now, we need to find the closest multiple of 10 to 63.36.The closest multiple of 10 to 63.36 is 60.
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To find out the most reasonable estimate of 132% of 48, we can multiply the given percentage with 48.
Therefore, the most reasonable estimate of 132% of 48 is 64.
132% of 48 = (132/100) × 48
= 63.36
Since we are looking for an estimate, we can round off the above answer to the nearest whole number. Here, we have two possible options:
63 and 64.132% of 48 is slightly greater than half of 48 (which is 24) + 24. So, the answer should be slightly greater than 48 + 24 = 72. Therefore, the most reasonable estimate of 132% of 48 is 64. Thus, the correct answer is b.6.5.
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Which type of display is for One-Variable data set
Answer:
If you look at the bar graphs, histograms, and circle graphs, they all look at one variable at a time and display the number of times or percentage of times an individual point or interval is counted.
Step-by-step explanation:
The number of peopie that have "liked" Mindy's Candy Store web
site can be represented by y = 270(1.65), where t is the number of weeks after a
review in a national magazine. Interpret the parameters of the equation. Make a
prediction about the future number of likes on the web site.
Answer:
Kindly check explanation
Step-by-step explanation:
Given that, the number of people who liked Mindy's website is given by :
270(1.65)^t ; t = number of weeks after a review
Interpreting the equation :
The equation represents an exponential growth function :
y = a(1 + r)^t
a = initial amount ; r = growth rate ; t = period
Comparing the function with the equation given ;
270 = a = number of people who liked the website before the review
1 + r = 1.65
r = 1.65 - 1
r = 0.65 ; 0.65 * 100% = 65%
Site grew at a rate of 65% per week after review
Ther predicted number of likes 2 weeks after the review :
y = 270(1.65)^2
y = 270 * 2.7225
y = 735.075
Hence, number of likes after 2 weeks = 735
What is the volume 9inches 3inches 5inches
Answer:
135 can i have brain list
Step-by-step explanation:
9X3X5
What Is The Improper fraction for 6/7 and 4/5
Answer:
11 upon 4 is your 6 upon 4 answer