what is the vertex for y = x2 - 4x
Answers
vertex is at (2, -4)
Explanation:
\(\bold{x}_{\bold{vertex}}=-\dfrac{b}{2a};\bold{y}_{\bold{vertex}} =f\huge \text{(}-\dfrac{2}{ba}\huge \text{)}\) given the equation in the standard form of
\(ax^2+bx+c\)
Given :
\(y=x^2-4x+0\)
\(a=1, \ b=-4, \ c=0\)
\(\bold{x}_{\bold{vertex}}=\dfrac{-(-4)}{2\times1} =\dfrac{4}{2} =2\)
\(\bold{y}_{\bold{vertex}}=f(2)=(2)^2-4(2)=4-8=-4\)
\(\bold{Vertex}:(x,y)=(2,-4)\)
Related Questions
Using a rule, describe a single transformation that has the same effect as the composition of translations.
Translation (x, y) - (x - 4, y - 2) followed by
translation (x, y) - (x - 3,y + 1)
Answers
The single transformation that has the same effect is (x, y) - (x - 7 , y - 1)
How to determine the single transformationFrom the question, we have the following parameters that can be used in our computation:
Translation (x, y) - (x - 4, y - 2) followed byTranslation (x, y) - (x - 3,y + 1)To determine the single transformation, we add the translation rules
Using the above as a guide, we have the following:
(x, y) - (x - 3 - 4 , y + 1 - 2)
Evaluate the like terms
(x, y) - (x - 7 , y - 1)
Hence, the rule is (x, y) - (x - 7 , y - 1)
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4. Factor Completely *
(1 Point)
5x3 + 40x2 - 2x - 16
Answers
Answer:
(x+8)(5x2−2)
Step-by-step explanation:
Hope this helps have a nice day :)
The value of investments in the stock market change daily. Suppose you buy a stock for $1,000. It increases in value by 4.5% and then falls 4.5%. What is the new value
Answers
After the stock's value increases by 4.5% and then falls by the same percentage, the new value would be approximately $997.975.
Let's calculate the new value of the stock after the increase and decrease.
Starting with $1,000, a 4.5% increase in value would be calculated as (4.5/100) * 1000 = $45. This brings the value up to $1,045.
Next, a 4.5% decrease in value would be calculated as (4.5/100) * 1045 = $47.025. This amount is subtracted from the increased value of $1,045.
Subtracting $47.025 from $1,045 gives us $997.975, which is slightly less than $1,000.
Therefore, after the stock's value increases by 4.5% and then falls by the same percentage, the new value would be approximately $997.975. It's important to note that this calculation assumes a simple percentage increase and decrease without considering other factors that can affect stock market fluctuations.
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Rewrite the equation in terms of x.
y =4/7(x-13)
Answers
Answer:
y=(47)xy=(47)x
Rewrite the equation as 47x=y47x=y.47x=y47x=y
Multiply both sides of the equation by 7474.74(47x)=74y74(47x)=74ySimplify both sides of the equation.Tap for more steps...x=7y4
Step-by-step explanation:
confusing bro
Answer:
x = (4/7y) + 13
Step-by-step explanation:
y = 4/7( x -13)
cross multiply
y x 7( x -3) = 4
(x - 3) = 4/7y
x = (4/7y) + 13
help me pls someone
Answers
Answer:
c
Step-by-step explanation:
Really do not want to know
Select the correct answer. A linear function has a y-intercept of -12 and a slope of 3/2 . What is the equation of the line? A. B. C. D.
Answers
Answer:
y = 3/2x-12
Step-by-step explanation:
The slope-intercept form of a line is
y = mx+b where m is the slope and b is the y-intercept
The slope is 3/2 and the y-intercept is -12.
y = 3/2x-12
Answer:
\(\sf y = \dfrac{3}{2}x - 12\)
Step-by-step explanation:
The equation of a linear function can be written in the form y = m x + c, where,
m → slope → 3/2
c → y-intercept → -12
we can substitute these values into the equation.
The slope, m, is 3/2, so the equation becomes:
y = (3/2)x + c
The y-intercept, c, is -12, so we can replace c with -12:
\(\sf y = \dfrac{3}{2}x - 12\)
Therefore, the equation of the line is y = (3/2)x - 12
Select the domain and range of F.
F={(x, y) Ix+y=10].
1. Set F is not a function and does not contain a domain or range
2. Domain: [10] Range: (10)
3. Domain: All Real Numbers Range: All Real Numbers
Answers
The domain and range of F is F={(x, y) Ix+y=10] is: 3. Domain: All Real Numbers Range: All Real Numbers
The given set F={(x, y) | x+y=10} represents a linear equation where the sum of x and y is always equal to 10.
To determine the domain and range of F, we need to consider the
possible values of x and y that satisfy the equation.
Domain: The domain represents the set of all possible values for the independent variable, which in this case is x. Since there are no restrictions on the value of x, the domain is All Real Numbers.
Range: The range represents the set of all possible values for the dependent variable, which in this case is y. By rearranging the equation x+y=10, we can solve for y to get y=10-x. Since x can take any real value, y can also take any real value. Therefore, the range is also All Real Numbers.
The correct answer is: 3. Domain: All Real Numbers Range: All Real Numbers
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How much money do I need now if I am going to recieve $5000 every 6 months (starting in 6 months) for 10 years if the interest rates are 4%/a compounded semiannually?
Answers
He needs to have $205783 amount of money to receive $5000 every 6 months for 10 years.
What is Interest ?Interest is the amount of money received , when a certain lump sum amount is deposited.
It is given that the person is receiving ,
Interest = $5000 ,
after six months , every six month
Time Period = 10 years
Interest Rate = 4%
Compounded Semiannual
Let the principal amount be $x
Compound Interest is given by
Amount = P[ 1 + r/n]ⁿˣ
Here x is the time period
Therefore the Amount = x{ 1 +0.04/2}²⁰
x + 5000 *20 = x{ 1 +0.04/2}²⁰
x + 100000 = 1.486 x
x = $205783
Therefore he needs to have $205783 amount of money to receive $5000 every 6 months for 10 years.
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PLEASE HELP These box plots show daily low temperatures for a sample of days in two
different towns.
Town A
15 20
30
40
45
Town B
2
35 40 45 48
0
5
10
15
20
45
50
55
60
25 30 35 40
Degrees (F)
Which statement is the most appropriate comparison of the spreads?
O A. The interquartile range (IQR) for town A, 30°, is less than the IQR
for town B, 46º.
B. The standard deviation for town A, 20°, is greater than the
standard deviation for town B, 10°.
C. The interquartile range (IQR) for town A, 20°, is greater than the
IQR for town B, 10°.
D. The interquartile ranges (IQRs) for towns A and B are both 20°.
Answers
Answer: D: The median for town A, 30 Degrees, is greater than the median for town B, 25 Degree.
Step-by-step explanation:
The median means the middle number. Town A median is 30 and Town B median is 25.
Step-by-step explanation:
Answer:
C. The interquartile range (IQR) for town A, 20°, is greater than the IQR for town B, 10°Step-by-step explanation:
The IQR is about middle 50% of data range. This is the difference between Q3 and Q1.
Town A
Q3 = 40, Q1 = 20IQR = 40 - 20 = 20Town B
Q3 = 45. Q1 = 35IQR = 45 - 35 = 10Correct choice is C
the difference of a number and 7
Answers
Answer:
x-7
Step-by-step explanation:
kylie works for a large nursery and is investigating whether to use a new brand of seeds. the new brand of seeds advertises that 93% of the seeds germinate, which is higher than the germination rate of the seeds she is currently using. she will change over to this new brand unless the actual germination rate is less than what is advertised. kylie conducts an experiment by randomly selecting 76 seeds of the new brand and plants them. she finds that 70 of those seeds germinated. what are the null and alternative hypotheses for this hypothesis test?
Answers
The null and alternative hypotheses for this hypothesis test is H₀ : p = 0.93, Hₐ : p > 0.93.
What is Hypothesis ?A hypothesis in a scientific context, is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon.
What is Null and Alternative Hypotheses?Null and alternative hypotheses are used in statistical hypothesis testing. The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.
Let 'p' be the population proportion.
Given statement : The new brand of seeds advertises that 93% of the seeds germinate, which is higher than the germination rate of the seeds she is currently using.
Since null hypothesis shows that there is no significant difference between the quantities where as alternative hypothesis believes that there is some difference,
Hence, the null and alternative hypotheses for this hypothesis test will be :- H₀ : p = 0.93
Hₐ : p > 0.93
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someone help please!!
Answers
Answer:
Step-by-step explanation:
Misha’s hamster weighed 0.845 kilograms. About how much does it weigh, rounded to the nearest hundredth?
0.85 kilograms
0.8 kilograms
1 kilograms
0.84 kilograms
Answers
Answer: 0.85 kilograms
Step-by-step explanation:
If cosх A/2 =3/5, find the value of cos A
Answers
Answer:
cosA = - \(\frac{7}{25}\)
Step-by-step explanation:
Using the double angle identity
cos2A = 2cos²A - 1 , then
cosA = 2cos²(\(\frac{A}{2}\) ) - 1 , that is
cosA = 2 × (\(\frac{3}{5}\) )² - 1
= 2 × \(\frac{9}{25}\) - 1
= \(\frac{18}{25}\) - \(\frac{25}{25}\)
= - \(\frac{7}{25}\)
Your Assignment: Furry Friends
Choosing a Group of Dogs
Josue and Sara both walk dogs during the week. They each walk 10 dogs in the morning and 10 other dogs in the afternoon. Select one of the groups to see how much the dogs in each group weigh. The heavier dogs usually have more energy and want to take longer walks than the smaller dogs.
Josue's dogs:
Morning:
26, 21, 15, 35, 38, 16, 13, 28, 30, 25
Afternoon:
15, 12, 9, 7, 44, 23, 55, 10, 37, 35
Sara's dogs:
Morning:
39, 21, 12, 27, 23, 19, 19, 31, 36, 25
Afternoon:
15, 51, 8, 16, 43, 34, 27, 11, 8, 39
1. Which dog-walker did you select? Circle one.
JosueSara
Comparing the Morning and Afternoon Groups
2. Create frequency tables to represent the morning and afternoon dogs as two sets of data. Group the weights into classes that range 10 pounds. (4 points: 2 points for appropriate intervals, 2 points for correctly portraying data)
3. What is the median of the morning (AM) group? What is the median of the afternoon (PM) group? (2 points: 1 point for each answer)
4. What is the first quartile (Q1) of the morning (AM) group? What is the first quartile (Q1) of the afternoon (PM) group? (2 points: 1 point for each answer)
5. What is the third quartile (Q3) of the morning (AM) group? What is the third quartile (Q3) of the afternoon (PM) group? (2 points: 1 point for each answer)
6. Create a comparative box plot for the morning and afternoon dogs, and label each with its five-number summary. (6 points: 3 points for the correct form of plot, 3 points for appropriate labels)
7. What is the interquartile range (IQR) of the morning (AM) group? What is the interquartile range (IQR) of the afternoon (PM) group? (2 points: 1 point for each answer)
8. The average weights of the dogs are the same for the morning and afternoon groups. But based on your comparative box plot and the IQRs of the two groups, which group of dogs do you think would be easier to walk as one group? Why? (2 points: 1 point for answer, 1 point for justification)
Answers
I selected Josue as the dog-walker.
Frequency tables:
Morning dogs:
Weight (lbs) Frequency
10-19 2
20-29 5
30-39 2
40-49 1
Afternoon dogs:
Weight (lbs) Frequency
7-16 4
17-26 2
27-36 1
37-46 1
47-56 2
The median of the morning (AM) group is 26.5 lbs. The median of the afternoon (PM) group is 23 lbs.
The first quartile (Q1) of the morning (AM) group is 16.25 lbs. The first quartile (Q1) of the afternoon (PM) group is 9.5 lbs.
The third quartile (Q3) of the morning (AM) group is 34.75 lbs. The third quartile (Q3) of the afternoon (PM) group is 38.5 lbs.
Comparative box plot:
yaml
Copy code
Morning dogs: Afternoon dogs:
13 | 7 |
| |
16 | 9 |
| |
21 | 11 |
| |
25 | 15 |
| |
26 | 27 |
| |
28 | 34 |
| |
30 | 35 |
| |
35 | 39 |
| |
38 | 43 |
| |
| 44 |
+------------------------------+
1 2 3 4 5 6
Group
Morning dogs:
Min: 13
Q1: 16.25
Median: 26.5
Q3: 34.75
Max: 38
Afternoon dogs:
Min: 7
Q1: 9.5
Median: 23
Q3: 38.5
Max: 44
The interquartile range (IQR) of the morning (AM) group is 18.5 lbs. The IQR of the afternoon (PM) group is 29 lbs.
Based on the comparative box plot and the IQRs, the morning group of dogs would be easier to walk as one group. This is because the morning group has a smaller IQR, indicating that the weights of the dogs are more similar to each other. The afternoon group has a larger IQR, indicating that the weights of the dogs are more spread out, which could make it more difficult to walk them as a group.
1. JosueSara
2. Frequency table
3. Median of the Morning Group: 26.5, Median of the Afternoon Group: 18.5
4. Q1 of the Morning Group: 17.5, Q1 of the Afternoon Group: 10.5
5. Q3 of the Morning Group: 32.5, Q3 of the Afternoon Group: 36.5
6. Comparative Boxplot blue is morning dogs and red is afternoon dogs.
7. IQR of the Morning Group: 15, IQR of the Afternoon Group: 26
8. Based on the comparative box plot and the IQRs, the morning group of dogs would be easier to walk as one group.
What is boxplot?
A box plot, also known as a box-and-whisker plot, is a graphical representation of the distribution of a dataset. It displays summary statistics and provides a visual summary of the data's key characteristics.
1. Which dog-walker did you select?
JosueSara
I selected Sara.
2. Create frequency tables to represent the morning and afternoon dogs as two sets of data. Group the weights into classes that range 10 pounds.
Morning Dogs Frequency Table:
Weight Range Frequency
10-19 2
20-29 4
30-39 4
Afternoon Dogs Frequency Table:
Weight Range Frequency
0-9 1
10-19 3
20-29 2
30-39 2
40-49 1
50-59 1
3. What is the median of the morning (AM) group? What is the median of the afternoon (PM) group?
Median of the Morning Group: 26.5
Median of the Afternoon Group: 18.5
4. What is the first quartile (Q1) of the morning (AM) group? What is the first quartile (Q1) of the afternoon (PM) group?
Q1 of the Morning Group: 17.5
Q1 of the Afternoon Group: 10.5
5. What is the third quartile (Q3) of the morning (AM) group? What is the third quartile (Q3) of the afternoon (PM) group?
Q3 of the Morning Group: 32.5
Q3 of the Afternoon Group: 36.5
6. Create a comparative box plot for the morning and afternoon dogs, and label each with its five-number summary.
Morning Dogs:
Min: 13
Q1: 17.5
Med: 26.5
Q3: 32.5
Max: 38
Afternoon Dogs:
Min: 7
Q1: 10.5
Med: 18.5
Q3: 36.5
Max: 55
7. What is the interquartile range (IQR) of the morning (AM) group? What is the interquartile range (IQR) of the afternoon (PM) group?
IQR of the Morning Group: 15
IQR of the Afternoon Group: 26
8. The average weights of the dogs are the same for the morning and afternoon groups. But based on your comparative box plot and the IQRs of the two groups, which group of dogs do you think would be easier to walk as one group? Why?
Based on the comparative box plot and the IQRs, the morning group of dogs would be easier to walk as one group. This is because the morning group has a smaller interquartile range (IQR) of 15 compared to the afternoon group's IQR of 26. A smaller IQR indicates that the weights of the dogs in the morning group are more clustered together.
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Next Londell needs a total of $400 to buy a new bicycle. He has $40 saved. He earns $15 each week delivering newspapers. How many weeks will Londell have to deliver papers to have enough money to buy the bicycle?
Answers
Londell needs to deliver newspapers for 24 weeks to have enough money to buy the bicycle.
Londell currently has $40 saved, and he needs a total of $400 to buy the bicycle. Each week, he earns $15 delivering newspapers.
To calculate the number of weeks Londell needs to work, we can set up an equation:
$40 (current savings) + $15 (weekly earnings) × (number of weeks) = $400 (total cost of the bicycle)
Simplifying the equation:
$40 + $15 = $400
Subtracting $40 from both sides of the equation:
$15 = $400 - $40
$15 = $360
Dividing both sides of the equation by $15:
= $360 / $15
≈ 24
Therefore, Londell will have to deliver newspapers for approximately 24 weeks to have enough money to buy the bicycle.
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a bottle weighs 300gand holds 630ml,how much does it weight if i fill it with water
Answers
If a bottle weighs 300g and can hold 630ml, then it will weigh approximately 930g when filled with water.
As per the question statement, a bottle weighs 300g and can hold 630ml.
We are required to find out the weight of the bottle when it is filled up with water.
To solve this question, we need to know about the concept of density of a substance, i.e.,
\(Density=\frac{Mass}{Volume}\\ or, Mass=[Density*Volume]\).
And density of water is 1gm/ml, i.e., 1gm of water has a mass of 1ml.
Using the above info, we will calculate the mass of 630ml of water and then we will have to add up the mass of water and the mas of the bottle to obtain our desired answer.
Using the unitary method, if 1ml of water has a mass of 1gm, then,
630 ml of water has a mass of \((630*1)=630\\\) gms.
Hence, total weight of the bottle filled with water will be
\((630+300)=930\) gms.
Density: Density is the measure of degree of compactness of a substance, calculated as the ratio of Mass to volume of a substance.Unitary Method: This is a technique for solving a problem where first, we find the value of a single unit, and then find the necessary value by multiplying the single-unit value.To learn more about Unitary Method, click on the link below.
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Biologists have observed that the chirping rate of crickets of a certain species is related to temperature, and the relationship appears to be nearly linear. A cricket produces 120 chirps per minute at 70 degrees F and 168 chirps per minute at 80 degrees F.
A. Find a linear equation that models the temperature T when crickets are chirping at x chirps per minute.
B. If the crickets are chirping at 150 chirps per minute, estimate the temperature.
C. Find the y-intercept of the line. What does it represent?
Answers
Answer:
A. To find a linear equation that models the temperature T when crickets are chirping at x chirps per minute, we need to use two points that are known. In this case, we are given that a cricket produces 120 chirps per minute at 70 degrees F and 168 chirps per minute at 80 degrees F. We can use these two points to find the slope and y-intercept of the line.
The slope of a line can be found using the formula: m = (y2 - y1) / (x2 - x1)
In this case, we can substitute the given values to get:
m = (168 - 120) / (80 - 70) = 48/10 = 4.8
The y-intercept of a line can be found using the formula: b = y - mx
We can use the point (70, 120) and the slope that we found to get:
b = 120 - (4.8 * 70) = -264
So the linear equation that models the temperature T when crickets are chirping at x chirps per minute is:
T = 4.8x - 264
B. If the crickets are chirping at 150 chirps per minute, we can substitute this value for x in the equation we found above to estimate the temperature:
T = 4.8x - 264
T = 4.8(150) - 264 = 720 - 264 = 456
So the estimated temperature is 456 degrees F.
C. The y-intercept of the line is -264, it represents the temperature when x (chirps per minutes) is zero. In this case it represents the temperature when the cricket is not chirping which is impossible, so it doesn't have any physical meaning.
Pleaseeee
Convert the equations form standard form to slope intercept form 8x-10y=20
Answers
Answer:
y=4/5x-2
Step-by-step explanation:
8x-10y=20
-10y=-8x+20 subtract 8x from both sides
x=4/5x-2 divide everything by -10
You have 2 slices of pizza, and I gave you 3 slices of pizza. Can you write the simple expression to find the total number of slices of pizza?
Answers
The expression to find the total number of slices of pizza is 2 + 3
How to determine the expression to find the total number of slices of pizza?From the question, we have the following parameters that can be used in our computation:
Initial slices of pizza = 2
Additional slices of pizza = 3
This means that
The expression to find the total number of slices of pizza is
Total number of slices of pizza = Initial slices of pizza + Additional slices of pizza
Substitute the known values in the above equation, so, we have the following representation
Total number of slices of pizza = 2 + 3
Hence, the expression is 2 + 3
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If DM = 26 and point G lies on the perpendicular bisector of DM¯¯¯¯¯¯¯, what is the value of r? Segment D M with point G between the endpoints. Segment D G has length R plus 3, and segment G M has length 4R minus 28. A. 10 B. 13 C. 30 D. 52
Answers
Applying the segment addition postulate, the value of r is determined as: A. 10.
What is the Perpendicular Bisector?A perpendicular bisector is a line segment which divides another line segment into two equal parts, that is, the segments formed have equal lengths.
Since point G lies on the perpendicular bisector of segment DM, therefore:
DG = GM
Given the following:
DM = 25
GM = 4r - 28
DG = r + 3
Therefore:
DG + GM = DM [segment addition postulate]
Substitute
r + 3 + 4r - 28 = 25
Combine like terms
5r - 25 = 25
5r = 25 + 25
5r = 50
5r/5 = 50/5
r = 10
Thus, applying the segment addition postulate, the value of r is determined as: A. 10.
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what will be the effect of executing the following code segment, given that int num1 is 0 and int num2 is 10? if ((num1 / num2 < 0) || (num1 num2 > 0)) statement1; else statement2;
Answers
The execution of the code segment will result in statement2 being executed. The code segment contains a conditional statement that uses the logical OR operator (||) to combine two conditions.
The first condition checks whether the result of dividing num1 by num2 is less than 0, while the second condition checks whether the product of num1 and num2 is greater than 0.
Given that num1 is 0 and num2 is 10, the first condition will evaluate to false, because 0 divided by any positive number is 0. However, the second condition will evaluate to true, because the product of two non-zero numbers with the same sign is always positive.
Since the logical OR operator requires only one of the conditions to be true for the entire statement to be true, the overall result will be true. As a result, statement1 will not be executed, and statement2 will be executed instead.
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If Y has a binomial distribution with parameters n and p, then p(hat)1 = Y/n is an unbiased estimator of p. Another estimator of p is p(hat)2 = (Y+1)/(n+2).
a. Derive the biase of p(hat)2.
b. Derive MSE(Pphat)1) and MSE(p(hat)2).
c. For what values of p is MSE(p(hat)1) < MSE(p(hat)2)?
Answers
a. To derive the bias of p(hat)2, we need to calculate the expected value (mean) of p(hat)2 and subtract the true value of p.
Bias(p(hat)2) = E(p(hat)2) - p
Now, p(hat)2 = (Y+1)/(n+2), and Y has a binomial distribution with parameters n and p. Therefore, the expected value of Y is E(Y) = np.
E(p(hat)2) = E((Y+1)/(n+2))
= (E(Y) + 1)/(n+2)
= (np + 1)/(n+2)
The bias of p(hat)2 is given by:
Bias(p(hat)2) = (np + 1)/(n+2) - p
b. To derive the mean squared error (MSE) for both p(hat)1 and p(hat)2, we need to calculate the variance and bias components.
For p(hat)1:
Bias(p(hat)1) = E(p(hat)1) - p = E(Y/n) - p = (1/n)E(Y) - p = (1/n)(np) - p = p - p = 0
Variance(p(hat)1) = Var(Y/n) = (1/n^2)Var(Y) = (1/n^2)(np(1-p))
MSE(p(hat)1) = Variance(p(hat)1) + [Bias(p(hat)1)]^2 = (1/n^2)(np(1-p))
For p(hat)2:
Bias(p(hat)2) = (np + 1)/(n+2) - p (as derived in part a)
Variance(p(hat)2) = Var((Y+1)/(n+2)) = Var(Y/(n+2)) = (1/(n+2)^2)Var(Y) = (1/(n+2)^2)(np(1-p))
MSE(p(hat)2) = Variance(p(hat)2) + [Bias(p(hat)2)]^2 = (1/(n+2)^2)(np(1-p)) + [(np + 1)/(n+2) - p]^2
c. To find the values of p where MSE(p(hat)1) < MSE(p(hat)2), we can compare the expressions for the mean squared errors derived in part b.
(1/n^2)(np(1-p)) < (1/(n+2)^2)(np(1-p)) + [(np + 1)/(n+2) - p]^2
Simplifying this inequality requires a specific value for n. Without the value of n, we cannot determine the exact values of p where MSE(p(hat)1) < MSE(p(hat)2). However, we can observe that the inequality will hold true for certain values of p, n, and the difference between n and n+2.
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In the given scenario, we have two estimators for the parameter p of a binomial distribution: p(hat)1 = Y/n and p(hat)2 = (Y+1)/(n+2). The objective is to analyze the bias and mean squared error (MSE) of these estimators.
The bias of p(hat)2 is derived as (n+1)/(n(n+2)), while the MSE of p(hat)1 is p(1-p)/n, and the MSE of p(hat)2 is (n+1)(n+3)p(1-p)/(n+2)^2. For values of p where MSE(p(hat)1) is less than MSE(p(hat)2), we need to compare the expressions of these MSEs.
(a) To derive the bias of p(hat)2, we compute the expected value of p(hat)2 and subtract the true value of p. Taking the expectation:
E(p(hat)2) = E[(Y+1)/(n+2)]
= (1/(n+2)) * E(Y+1)
= (1/(n+2)) * (E(Y) + 1)
= (1/(n+2)) * (np + 1)
= (np + 1)/(n+2)
Subtracting p, the true value of p, we find the bias:
Bias(p(hat)2) = E(p(hat)2) - p
= (np + 1)/(n+2) - p
= (np + 1 - p(n+2))/(n+2)
= (n+1)/(n(n+2))
(b) To derive the MSE of p(hat)1, we use the definition of MSE:
MSE(p(hat)1) = Var(p(hat)1) + [Bias(p(hat)1)]^2
Given that p(hat)1 = Y/n, its variance is:
Var(p(hat)1) = Var(Y/n)
= (1/n^2) * Var(Y)
= (1/n^2) * np(1-p)
= p(1-p)/n
Substituting the bias derived earlier:
MSE(p(hat)1) = p(1-p)/n + [0]^2
= p(1-p)/n
To derive the MSE of p(hat)2, we follow the same process. The variance of p(hat)2 is:
Var(p(hat)2) = Var((Y+1)/(n+2))
= (1/(n+2)^2) * Var(Y)
= (1/(n+2)^2) * np(1-p)
= (np(1-p))/(n+2)^2
Adding the squared bias:
MSE(p(hat)2) = (np(1-p))/(n+2)^2 + [(n+1)/(n(n+2))]^2
= (n+1)(n+3)p(1-p)/(n+2)^2
(c) To compare the MSEs, we need to determine when MSE(p(hat)1) < MSE(p(hat)2). Comparing the expressions:
p(1-p)/n < (n+1)(n+3)p(1-p)/(n+2)^2
Simplifying:
(n+2)^2 < n(n+1)(n+3)
Expanding:
n^2 + 4n + 4 < n^3 + 4n^2 + 3n^2
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validity is :
a. an entity that can take on different values. b. the consistency in measurement. c. the strength of the relationship between two variables. d. the truth of a measurement
Answers
It is not an entity that can take on different values, the consistency in measurement, the strength of the relationship between variables, or the truth of a measurement.
Validity is concerned with the degree to which a measure or conclusion accurately represents the concept or phenomenon it is intended to assess or describe. It focuses on the appropriateness and accuracy of inferences or interpretations based on the measurement or observation. Validity addresses the question of whether a measure or conclusion captures the intended construct or relationship and provides meaningful and reliable information.
Validity is distinct from other concepts mentioned. While an entity can take on different values, it is not synonymous with validity. Consistency in measurement refers to reliability, which is a separate concept related to the consistency and stability of measurements. The strength of the relationship between two variables is typically referred to as the correlation or association, but it is not directly related to validity. Lastly, the truth of a measurement is a broader philosophical concept, but validity specifically relates to the accuracy and appropriateness of a measure within a specific context or purpose.
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PLS EXPLAINIIf y = 16x, which table shows the values of y for different values of x?
x 0 2 4
y 0 18 20
x 0 2 4
y 0 8 4
x 0 2 4
y 0 32 64
x 0 2 4
y 0 16 32
Answers
Answer:
Step-by-step explanation:
I think it's B but I'm not 100% sure
x 0 2 4
y 0 32 64
Explanation
When x = 0
y = 16 • 0 = 0
When x = 2
y = 16 • 2 = 32
When x = 4
y = 16 • 4 = 64
<~>\_/<~> Ho_odini <~>\_/<~>
This equation has one solution. 5(x – 1) 3x = 7(x 1) what is the solution?
Answers
Answer:
send the complete question . there are some missing signs .
How do you prove that lines are similar in triangles if it is parallel? (look at photo)
Answers
Answer:
they are similar cuz it resembles a "z" pattern. The angles are so the same.
please help I need this for a math pre-test.
PETS Each month, Travis spends $20 for premium food, $10 for treats, $18 for grooming, and $3 for toys for his pet. Write an expression that could be used to determine the amount he spends on these items for his pet over a period of 12 months.
Answers
Answer:
612 I think well how this helps
Please help
Identify the proportional relationship
Answers
There is no proportional relationship between the given equations.
What is proportional relationship?
Relationships between two variables where their ratios are equal are known as proportional relationships. The fact that one variable is always a constant value multiplied by the other in a proportionate connection is another way to conceive of them. This parameter is referred to as the "constant of proportionality".
The given equations are,
7x - 2 = y
y = 2x + 4
y = 5x
y + 1 = 3x
These equations can be written as,
y = 7x - 2
y = 2x + 4
y = 5x
y = 3x - 1
Now consider the following table,
x y y/x
7 1 1/7
2 1 1/2
5 1 1/5
3 1 1/3
From above we can see that none of the ratio are equal, all ratios are different.
Hence, none of the given equations having proportional relationship.
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Find the sum.
(-7b + 8C) - (12a + 14) + (5a + 5b)
Answers
Steps to solve:
(-7b + 8C) - (12a + 14) + (5a + 5b)
~Remove parenthesis and combine like terms
(-7b + 5b) + (8c) + (-12a + 5a) + 14
-2b + 8c - 7a + 14
~Put in order
-7a - 2b + 8c + 14
Best of Luck!