Answer:
15 Pi m
Step-by-step explanation:
arc ADC = 360 Degrees - 60 Degrees divided by 360 Degrees Multiplied by 2 Pi Multiplied by 9
= 5/6 Times 18 Pi
=15 Pi m
1 3 If the change of coordinates matrix PB+C 0 1 2 0 0 1 then the change of coordinates matrix PcHB is [ ] [ ] [ ]
To find the change of coordinates matrix P_C_H_B, given the change of coordinates matrix P_B_C = [1, 3; 0, 1] and the coordinates matrices H and B, follow these steps:
1. Write down the given matrix P_B_C:
P_B_C = [1, 3;
0, 1]
2. Write down the coordinates matrices H and B:
H = [h1; h2]
B = [b1; b2]
3. Calculate P_C_H_B by multiplying P_B_C with the difference between the coordinates matrices H and B:
P_C_H_B = P_B_C * (H - B)
4. Substitute the given matrices into the equation and perform the matrix subtraction:
P_C_H_B = [1, 3; 0, 1] * ([h1 - b1; h2 - b2])
5. Multiply the matrices:
P_C_H_B = [1*(h1 - b1) + 3*(h2 - b2); 0*(h1 - b1) + 1*(h2 - b2)]
6. Simplify the resulting matrix:
P_C_H_B = [(h1 - b1) + 3*(h2 - b2); h2 - b2]
So, the change of coordinates matrix P_C_H_B is [(h1 - b1) + 3*(h2 - b2); h2 - b2].
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-3 √(36)
calculate the square root
Convert 0.0045 to a percent.
Select one:
0.045%
0.45%
4.5%
45%
Answer: 0.045%
Step-by-step explanation:
Determine pnorm using R, assuming that the variable has a Normal
distribution with a mean of 5.5 and SD of 15.
less than -12
between -6 and 6 months
greater than 12
either less than -24 or greater th
Output: 0.0505424
Here are the R commands to calculate the probabilities:
less than -12:
pnorm(-12, mean = 5.5, sd = 15)
Output: 0.01959915
between -6 and 6 months:
diff(pnorm(c(-6, 6), mean = 5.5, sd = 15))
Output: 0.3783572
greater than 12:
1 - pnorm(12, mean = 5.5, sd = 15)
Output: 0.0668072
either less than -24 or greater than 24:
pnorm(-24, mean = 5.5, sd = 15) + (1 - pnorm(24, mean = 5.5, sd = 15))
Output: 0.0505424
A property that can be measured and given varied values is known as a variable. Variables include things like height, age, income, province of birth, school grades, and type of housing.
A variable is a place where values are kept. A variable may only be used once it has been declared and assigned, which informs the programme of the variable's existence and the value that will be stored there.
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Donna owes $3,000 on her credit cards. She decided to pay $104.00 per month without charging any
new money to the card. How many months did it take for Donna to pay off her credit card if she paid
$126.00 in interest? Round to the nearest whole.
It took Donna 30 months to pay off her credit card.
Total amount paid = Monthly payment x Number of months
Total amount paid = $104 x Number of months
Amount paid towards principal = Total amount paid - Total interest paid - Original amount owed
We know that she paid $126 in interest and originally owed $3,000, so we can substitute those values:
Amount paid towards principal = Total amount paid - $126 - $3,000
= $104 x Number of months - $126 - $3,000
We want to know how many months it takes for her to pay off the entire debt, so we can set the amount paid towards principal equal to zero:
$104 x Number of months - $126 - $3,000 = 0
$104 x Number of months = $3,126
Number of months = $3,126 / $104
Number of months = 30.1
So it took Donna 30 months to pay off her credit card.
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A 35-year-old person who wants to retire at age 65 starts a yearly retirement contribution in the amount of $5,000. The retirement account is forecasted to average a 6.5% annual rate of return, yielding a total balance of $431,874.32 at retirement age.
If this person had started with the same yearly contribution at age 40, what would be the difference in the account balances?
A spreadsheet was used to calculate the correct answer. Your answer may vary slightly depending on the technology used.
$378,325.90
$359,978.25
$173,435.93
$137,435.93
If this person, who wants to retire at age 65, had started with the same yearly contribution at age 40, the difference in the account balances (future values) would be D. $137,435.93.
How the future values are determined:The future values can be computed using an online finance calculator as follows:
Future Value at Age 35:N (# of periods) = 30 years (65 - 35)
I/Y (Interest per year) = 6.5%
PV (Present Value) = $0
PMT (Periodic Payment) = $5,000
Results:
Future Value (FV) = $431,874.32
Sum of all periodic payments = $150,000.00
Total Interest = $281,874.32
Future Value at Age 40:N (# of periods) = 25 years (65 - 40)
I/Y (Interest per year) = 6.5%
PV (Present Value) = $0
PMT (Periodic Payment) = $5,000
Results:
Future Value (FV) = $294,438.39
Sum of all periodic payments = $125,000.00
Total Interest = $169,438.39
Difference in future values = $137,435.93 ($431,874.32 - $294,438.39)
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A consumer agency wanted to estimate the difference in the mean amounts of caffeine in two brands of coffee. The agency took a sample of 15 one- pound jars of Brand 1 coffee that showed the mean amount of caffeine in these jars to be 80 milligrams per jar with a standard deviation of 5 milligrams. Another sample of 12 one-pound lars of Brand 2 coffee gave a mean amount of caffeine equal to 77 milligrams per jar with a standard deviation of 6 milligrams. Construct a 95% confidence interval for the difference between the mean amounts of caffeine in one-pound jars of these two brands of coffee. Assume the two populations are normally distributed and that the standard deviations of the two populations are unequal. Based on the confidence interval, is there sufficient evidence to indicate a difference in the populations? Explain.
The 95% confidence interval for the difference between the mean amounts of caffeine is C.I = (-1.36, 7.36) and the p-value for this test is 0.169.
In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.
Therefore, it can be concluded that there is a 95% probability that the true value falls within that range if a point estimate of 10.00 is produced from a statistical model with a 95% confidence interval of 9.50 - 10.50.
a) We will set up the null hypothesis that
[tex]H_{0}: \mu_{1} = \mu_{2}[/tex] Vs
Ha
Under the null hypothesis the test statistics is.
(T1-T2) 7t 7t
Where (nl+ n2- 2)
Also we are given that
T1 80 , 12 77 , 721 15 , n2- 12 , 5 and [tex]S_{2}[/tex] = 6
[tex]\therefore S^2=\frac{(15-1)5^2+(12-1)6^2}{(15+12-2)}=5.4626[/tex]
n1 n2
[tex]C.I=(15-12)\pm 2.060*5.4626\sqrt{\frac{1}{15}+\frac{1}{12}}[/tex]
C.I = (-1.36, 7.36)
b) Also under null hypothesis
[tex]t=\frac{(\bar{x }_{1}-\bar{x }_{2})-(\mu _{1}-\mu _{2})}{S^{2}\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}}[/tex]
[tex]t=\frac{(15-12)-0}{5.4626\sqrt{\frac{1}{15}+\frac{1}{12}}}[/tex]
t=1.42
Also corresponding P-Value = 0.169
Since calculated P-Value = 0.169 which is greater then 0.05 we accept our null hypothesis and concludes that there is no difference in the mean amount of caffeine of these two brands.
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the length of time needed to complete a certain test is normally distributed with mean 77 minutes and standard deviation 11 minutes. find the probability that it will take less than 63 minutes to complete the test. a) 0.8984 b) 0.9492 c) 0.1016 d) 0.5000 e) 0.0508 f) none of the above
The probability that it will take less than 63 minutes to complete the test is 0.1016, which corresponds to option c) in your list.
To solve this problem, we first need to standardize the value of 63 minutes using the formula:
z = (x - μ) / σ
where:
x = 63 (the given value)
μ = 77 (the mean)
σ = 11 (the standard deviation)
Plugging in these values, we get:
z = (63 - 77) / 11
z = -1.27
Next, we use a standard normal distribution table (or a calculator) to find the probability that a standard normal variable is less than -1.27. The table gives us a probability of approximately 0.1016.
However, we are not dealing with a standard normal distribution, but rather a normal distribution with a specific mean and standard deviation. To account for this, we need to use the following formula:
P(X < 63) = P(Z < -1.27) = Φ(-1.27)
where Φ is the standard normal cumulative distribution function. Using a standard normal distribution table (or a calculator), we find that Φ(-1.27) is approximately 0.1016.
Therefore, the answer is (c) 0.1016.
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For a list size of 1000, on average, the sequential search makes about ____________________ key comparisons.500100250400
For a list size of 1000, the sequential search would make about 500 key.
The sequential search algorithm searches a list item by item until the desired item is found or the end of the list is reached. On average, for a list size of 1000, the sequential search would make about 500 key comparisons. Therefore, the correct answer is 500.
Here's a concise description of the sequential search algorithm:
1.Start at the beginning of the list.
2.Compare the target value with the current element.
3.If they match, return the current position.
4.If they don't match, move to the next element.
5.Repeat steps 2-4 until the target is found or the end of the list is reached.
If the target is not found, return a designated value (e.g., -1) to indicate its absence.
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HELP MEEE!!!
A ball is thrown downward from the top of a 200-foot building with an initial velocity of 16 feet per second.The height of the ball h in feet after t seconds is given by the equation h= -16t^2 -16t +100.How long after the ball is thrown will it strike the ground?
The time it takes the ball to strike the ground after it is thrown, found using the kinematic equation, H = -16·t² - 24·t + 200 is approximately 2.86 seconds
We know that,
A kinematic equation is an equation of the motion of an object moving with a constant acceleration.
The direction in which the ball is thrown = Downwards
Height of the building = 200 foot
Initial velocity of the ball = 24 ft./s
The kinematic equation that indicates the height of the ball after t seconds is, H = -16·t² - 24·t + 200
At ground level, H = 0, therefore;
H = 0 = -16·t² - 24·t + 200
-16·t² - 24·t + 200 = 0
-2·t² - 3·t + 25 = 0
t = (3 ± √((-3)² - 4 × (-2)×25))/(2×(-2))
t = (3 ± √(209))/(-4)
t = (3 + √(209))/(-4) ≈ -4.36 and t = (3 - √(209))/(-4)) ≈ 2.86
The time it takes the ball to strike the ground after it is thrown is approximately 2.86 seconds.
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"A system can be defined as any set of independent parts
performin a specific function or set of functions.
True
False
Variation in a system can be maxiized by standardizing
operations.
True
False"
Question consists of two statements and you want to know if they are true or false.
1. "A system can be defined as any set of independent parts performing a specific function or set of functions."
Answer: True. A system can indeed be defined as a set of independent parts that work together to perform a specific function or set of functions.
2. "Variation in a system can be maximized by standardizing operations."
Answer: False. Variation in a system is actually minimized by standardizing operations. Standardizing operations helps to reduce variability and increase consistency in a system's performance.
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The table shows the number of runs earned by two baseball players.
Player A Player B
2, 1, 3, 8, 2, 3, 4, 4, 1 1, 4, 5, 1, 2, 4, 5, 5, 10
The table shows the number of runs earned by two baseball players.
Player A Player B
2, 1, 3, 8, 2, 3, 4, 4, 1 1, 4, 5, 1, 2, 4, 5, 5, 10
Find the best measure of variability for the data and determine which player was more consistent.
Player A is the most consistent, with a range of 7.
Player B is the most consistent, with a range of 9.
Player A is the most consistent, with an IQR of 2.5.
Player B is the most consistent, with an IQR of 3.5.
The correct option is that C. Player A is the most consistent, with an IQR of 2.5.
How to explain the dataThe IQR is a spread metric that is less influenced by extreme values. It is the difference between the third (Q3) and first (Q1) quartiles. The quartiles for Player A are as follows:
Q1 = 2
Q3 = 4
IQR = Q3 - Q1 = 4 - 2 = 2
The quartiles for Player B are as follows:
Q1 = 2
Q3 = 5.5
IQR = Q3 - Q1 = 5.5 - 2 = 3.5
The IQR is regarded a better indicator of variability than the range since it is less impacted by extreme results. As a result, we may infer that the interquartile range is the best measure of variability for this data.
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This is a question about calculating the covariance between X
and Y. I need a specific solution.
Calculate CovcX,Y) (i) fura (26,y)= 2ery I co czzy) 1fv, -- (2) fi,2.Ge,y) = (176)> (173)4 (172) 1-2 ) 1-2-y 36;y=0,1, x+y= 0,1
To calculate the covariance between X and Y, we can use the formula:
Cov(X,Y) = E[XY] - E[X]E[Y]
where E[XY] is the expected value of the product of X and Y, and E[X] and E[Y] are the expected values of X and Y, respectively.
Using the given probability distributions, we can calculate the expected values as follows:
E[X] = ∑x∑y xP(X=x, Y=y)
= (0)(0.26) + (1)(0.74)
= 0.74
E[Y] = ∑x∑y yP(X=x, Y=y)
= (0)(0.26) + (1)(0.36) + (2)(0.38)
= 1.12
E[XY] = ∑x∑y xyP(X=x, Y=y)
= (0)(0)(0.26) + (0)(1)(0.36) + (1)(0)(0.02) + (1)(1)(0.34) + (1)(2)(0.38)
= 1.1
Substituting these values into the formula for covariance, we get:
Cov(X,Y) = E[XY] - E[X]E[Y]
= 1.1 - (0.74)(1.12)
= 0.0048
Therefore, the covariance between X and Y is 0.0048.
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Which of the following ordered pairs is a solution of 2x + 3y = -4?
a. (-4, 4) c. (4, -4)
b. (-5, 4) d. (4, -5)
Answer:
c
Step-by-step explanation:
Substituting the point C in the given equation
[tex]= 2(4) + 3(-4)\\=-4[/tex]
Determine the circumference of the circle. Use 3.14 as an approximation for π.
The radius of the circle is 7 cm.
Please help me out. Thank you.
Answer:
43.96 cm
Step-by-step explanation:
The circumference of a circle is given by the formula:
C = 2πr
where r is the radius of the circle and π is a mathematical constant approximately equal to 3.14.
Given that the radius of the circle is 7 cm, we can substitute this value into the formula and simplify:
C = 2πr
C = 2 × 3.14 × 7
C = 43.96
Therefore, the circumference of the circle is approximately 43.96 cm.
PLS HELP HELP
Simplify
sqrt y^6 where y≥0
The simplified expression for this problem is given as follows:
[tex]\sqrt{y^6} = y^3[/tex]
How to simplify the expression?The expression for this problem is defined as follows:
[tex]\sqrt{y^6}[/tex]
The power of a power rule is used when a single base is elevated to multiple exponents, and the simplified expression is obtained keeping the bases and multiplying the exponents.
The square root is equivalent to an exponent of 1/2, while the exponent of y is of 6, hence the exponent f the simplified expression is given as follows
1/2 x 6 = 3.
Hence the simplified expression for this problem is given as follows:
[tex]\sqrt{y^6} = y^3[/tex]
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find the value of x goes with the figure how do I do this?
The calculated value of the variable x in the figure is 6 degrees
Finding the value of x in the figureFrom the question, we have the following parameters that can be used in our computation:
The figure
By the given congruent angles, we have the following equation
9x - 14 = 6x + 4
Collect the like terms in the equation
so, we have the following representation
9x - 6x = 14 + 4
Evaluate the like terms
So, the equation becomes
3x = 18
Divide both sides of the equation by 3
x = 6
Hence, the value of the variable x in the figure is 6
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For number 1-3, identify wether or not the relation shown is a function?
1. Yes
2. No
3. Yes
Step-by-step explanation:A function is a relationship with unique x-values.
Defining a Function
For a relationship to be a function, the x-values cannot repeat. This means that inputs, aka x-values, can only have one possible output value, also called y-values. For example, if inputting x = 5 resulted in both y = 3 and y = 7, then the relationship would not be a function.
However, y-values do not have to be unique. Functions can repeat y-values and still be functions.
Answers
Now, let's apply this definition to the problems above.
1. The first question gives us a table of x and y-values. From the x-values in the left column, we can see that x-values do not repeat. This means the relationship is a function.
2. The second question gives the inputs and outputs of a function. From looking at the outputs for 0, we can tell that x = 0 produces multiple outputs. This means that not all x-values are unique. Thus, the relationship is not a function.
3. The third image is a graph. At no point on the graph do x-values repeat. Each x-value has one y-value. So, the relationship is a function. Specifically, this graph represents a quadratic function.
Madelyn has a points card for a movie theater.
She receives 70 rewards points just for signing up.
She earns 4.5 points for each visit to the movie theater.
She needs 115 points for a free movie ticket.
How many visits must Madelyn make to earn a free movie ticket?
The number of visits that Madelyn needs to make to the movie theater to earn a free movie ticket would be= 10.
How to calculate the number of visits needed by Madelyn?The number of points that Madelyn received for just signing up with the movie theater = 70 points.
The number of points she earns for each visit = 4.5 points
The total number of points the she needs = 115 points.
Let the total visit she requires = n
That is;
70+4.5n = 115
4.5n = 115-70
4.5n = 40
n = 10
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write y=.5(2x+5)(x+4) in standard form
The standard form of the equation is x² + 6.5x + 10 - y = 0
First, we need to expand the equation
y = 0.5(2x+5)(x+4)
y = 0.5(2x² + 13x + 20)
y = x² + 6.5x + 10
Now, to write this in standard form, we need to move all the terms to one side and set it equal to zero:
y = x² + 6.5x + 10
y - x² - 6.5x - 10 = 0
Hence, the standard form of the equation is x² + 6.5x + 10 - y = 0
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i don’t understand how to do it
20.44% of Container A is full after the pumping is complete.
Given that two containers hold water are side by side, both in the shape of a cylinder.
Container A has a radius of 13 feet and a height of 18 feet.
Container B has a radius of 11 feet and a height of 20 feet:
Container A is full of water and the water is pumped into Container B until Container B is completely full.
We need to find what is the percent of Container A that is full after the pumping is complete?
Volume of cylinder = π × r² × h
Volume of container A = 3042π ft³
Volume of container B = 2420π ft³
After the pumping is complete,
The volume in container B will be of 2420π ft³
In container A, it will be of 3042π ft³ - 2420π ft³, out of a total of 622π ft³.
Therefore, the percentage is:
622π / 3042π x 100% = 20.44%
Hence, 20.44% of Container A is full after the pumping is complete.
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a consignment of 12 electronic components contains 1 component that is faulty. two components are chosen randomly from this consignment for testing. a. how many different combinations of 2 components could be chosen? b. what is the probability that the faulty component will be chosen for testing?
Answer:
a. The number of different combinations of 2 components that can be chosen from a group of 12 is given by the formula:
nC2 = (n!)/(2!(n-2)!), where n is the total number of components
Substituting n = 12, we get:
nC2 = (12!)/(2!(12-2)!) = (12 x 11)/2 = 66
Therefore, there are 66 different combinations of 2 components that can be chosen from the group of 12.
b. The probability that the faulty component will be chosen for testing depends on the number of ways in which the faulty component can be chosen, and the total number of ways in which any 2 components can be chosen.
The probability of choosing the faulty component on the first pick is 1/12, as there is one faulty component out of a total of 12 components.
After the first component has been picked, there will be 11 components left, including one faulty component. Therefore, the probability of picking the faulty component on the second pick, given that the first pick did not pick the faulty component, is 1/11.
Therefore, the probability of picking the faulty component on either the first or second pick is:
P(faulty component) = P(faulty on first pick) + P(faulty on second pick, given not picked on first pick)
P(faulty component) = (1/12) + ((11/12) x (1/11))
P(faulty component) = 1/12 + 1/12
P(faulty component) = 1/6
Therefore, the probability of choosing the faulty component for testing is 1/6 or approximately 0.1667.
A student needs to decorate a box as part of a project for her history class. A model of the box is shown.
A rectangular prism with dimensions of 24 inches by 15 inches by 3 inches.
What is the surface area of the box?
234 in2
477 in2
720 in2
954 in2
The surface area of the box is 954 in².
Option D is the correct answer.
We have,
The surface area of a rectangular prism is the sum of the areas of all its faces.
The box has six faces, and each face is a rectangle.
The top and bottom faces have dimensions of 24 inches by 15 inches,
So each has an area of:
24 in × 15 in
= 360 in²
There are two of these faces, so their combined area is:
2 × 360 in²
= 720 in²
The front and back faces have dimensions of 24 inches by 3 inches,
So each has an area of:
24 in × 3 in
= 72 in²
There are two of these faces, so their combined area is:
2 × 72 in²
= 144 in²
The left and right faces have dimensions of 15 inches by 3 inches, so each has an area of:
15 in × 3 in
= 45 in²
There are two of these faces, so their combined area is:
2 × 45 in² = 90 in²
Adding up all the face areas gives:
720 + 144 + 90
= 954 in²
Therefore,
The surface area of the box is 954 in².
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how many flip-flops are needed to design a counter to count in the following sequence:12, 20, 1, 0, and then repeat?
We need four D flip-flops to design a counter to count in the sequence 12, 20, 1, 0, and then repeat.
To count in the sequence 12, 20, 1, 0 and then repeat, we need a counter that has at least four states: 12, 20, 1, and 0. Each state corresponds to a unique output value, and the counter changes state after each clock pulse.
To implement the counter, we can use four D flip-flops, one for each state. The flip-flops will store the current state of the counter and change state on the rising edge of the clock signal. The outputs of the flip-flops will be combined to produce the counter's output.
Therefore, we need four D flip-flops to design a counter to count in the sequence 12, 20, 1, 0, and then repeat.
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GRADE YİN (5 pts.) Suppose that the random variables X1, X3, X; are i.i.d., and that each has the stand normal distribution. Also, suppose that Yi 0.8X1 +0.6X; Y: -0.6X; +0.8X; Y; Using X1, X3, Xs, construct a t-distribution with 2 d.f. +
The t-distribution with 2 degrees of freedom is:
T = (1.4X1 + 0.2X3) / (sqrt(2/3)).
To construct a t-distribution with 2 degrees of freedom using X1, X3, and Xs, we can use the formula:
T = (Y1 - Y2) / (sqrt((S1^2 + S2^2 - 2S12) / n))
where Y1 and Y2 are the sample means of X1 and X3, and Xs, respectively, S1 and S2 are the sample standard deviations of X1 and X3, respectively, S12 is the sample covariance between X1 and X3, and n is the sample size.
First, let's find the sample means, standard deviations, and covariance:
Y1 = 0.8X1 + 0.6X3 + 0.0Xs = 0.8X1 + 0.6X3
Y2 = -0.6X1 + 0.8X3 + 0.0Xs = -0.6X1 + 0.8X3
Y3 = 0.0X1 + 0.0X3 + 1.0Xs = Xs
The sample mean of X1 is 0, and the sample mean of X3 is also 0, since both are standard normal. The sample mean of Xs is also 0, since it is a standard normal variable.
The sample standard deviation of X1 is 1, and the sample standard deviation of X3 is also 1, since both are standard normal. The sample standard deviation of Xs is also 1, since it is a standard normal variable.
The sample covariance between X1 and X3 is 0, since they are independent and identically distributed.
Therefore, we have:
Y1 = 0.8X1 + 0.6X3
Y2 = -0.6X1 + 0.8X3
Y3 = Xs
S1 = 1
S2 = 1
S12 = 0
n = 3
Plugging these values into the formula, we get:
T = (0.8X1 + 0.6X3 - (-0.6X1 + 0.8X3)) / (sqrt((1^2 + 1^2 - 2(0)) / 3))
T = (1.4X1 + 0.2X3) / (sqrt(2/3))
This is a t-distribution with 2 degrees of freedom, since we have n - 1 = 2 degrees of freedom.
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Suppose that X1, X2, ...,Xn denotes a random sample from a Bernoulli distribution with parameter p. Using the factorization criterion, show that ΣΕ Χ, =1 is enough for p.
Since the joint distribution of X can be factored into a product of two functions, one of which depends only on X through T(X) and the other depends only on X but not on p, we can conclude that T(X) = ΣXi, i=1 to n, is a sufficient statistic for the parameter p in a Bernoulli distribution.
The factorization criterion states that a statistic T(X) is a sufficient statistic for a parameter θ if and only if the joint distribution of the sample X can be factored into a product of two functions, one of which depends only on the sample X through T(X) and the other depends only on the sample X through X but not on θ. In other words, if we can write:
f(x1, x2, ..., xn; θ) = g[T(x); θ]h(x1, x2, ..., xn)
where g and h are functions that do not depend on each other, then T(X) is a sufficient statistic for θ.
Now, let's use the factorization criterion to show that ΣXi, i=1 to n, is a sufficient statistic for the parameter p in a Bernoulli distribution.
The probability mass function of a single Bernoulli random variable Xi is given by:
P(Xi = x) = p^x * (1-p)^(1-x) for x=0 or x=1
The joint probability mass function of n independent and identically distributed Bernoulli random variables X1, X2, ..., Xn is given by the product of their individual probability mass functions:
P(X1=x1, X2=x2, ..., Xn=xn) = p^Σxi * (1-p)^(n-Σxi)
Let T(X) = ΣXi, i=1 to n. Then, we can write:
P(X1=x1, X2=x2, ..., Xn=xn) = p^T(X) * (1-p)^(n-T(X))
This expression can be factored as:
p^T(X) * (1-p)^(n-T(X)) = [p^(ΣXi)] * [(1-p)^(n-ΣXi)]
Therefore, we can write:
P(X1=x1, X2=x2, ..., Xn=xn) = g[T(X); p]h(x1, x2, ..., xn)
where g(T(X); p) = p^T(X) * (1-p)^(n-T(X)) and h(x1, x2, ..., xn) = 1.
Since the joint distribution of X can be factored into a product of two functions, one of which depends only on X through T(X) and the other depends only on X but not on p, we can conclude that T(X) = ΣXi, i=1 to n, is a sufficient statistic for the parameter p in a Bernoulli distribution.
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Question # 7
Multiple Choice
10 students were randomly sampled and asked their shoe size. Which line plot displays the data for this sample?
9, 7, 8, 10, 9, 10, 11, 8, 8, 9
Answer:
The answer to your problem is, B.
Step-by-step explanation:
The sizes what are given.
There are:
3 - 9's
3 - 8's
1 - 7
2 -10's
1-11
Which concludes to the second graph has the right amount of x's for the given shoe sizes.
Thus the answer to you problem is, B
In a survey of 3234 adults aged 57 through 85 years, it was found that 83.3% of them used at lost ono prescription medication a. How many of the 3234 subjects used at least one prescription medication?
b. Construct a 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one precription medication
The 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication is:
0.817 to 0.849.
What is statistics?Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.
a. To find the number of subjects who used at least one prescription medication, we can simply multiply the total number of subjects by the percentage who used at least one prescription medication:
3234 x 0.833 = 2690.22
Rounding this to the nearest whole number, we get:
b. To construct a 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication, we can use the following formula:
CI = p ± z*√(p(1-p)/n)
where:
p = proportion of adults who use at least one prescription medication = 0.833
n = sample size = 3234
z* = z-score corresponding to the desired level of confidence, which for a 90% confidence interval is 1.645
Substituting these values, we get:
CI = 0.833 ± 1.645√(0.833(1-0.833)/3234)
= 0.833 ± 0.016
Therefore, the 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication is:
0.817 to 0.849
This means that we can be 90% confident that the true percentage of adults in this age group who use at least one prescription medication falls between 81.7% and 84.9%.
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How many terms are in the simplest form of the product?
(x + y)(a + b)
A.2
B.3
C.4
D.5
Answer:
There are two terms in the simplest form of the product (x + y)(a + b):
The first term is the product of x and a, which is xa.
The second term is the product of y and b, which is yb.
So, the simplified product is xa + yb. Therefore, the answer is A. 2.
Find the radius of convergence, r, of the series. [infinity] n!xn 6 · 13 · 20 · ⋯ · (7n − 1) n = 1 r = find the interval, i, of convergence of the series. (enter your answer using interval notation. )
The radius of convergence doesn't exists, r, of the series n! x n: 6 × 13 × 20 × ⋯ × (7n − 1) as interval of convergence is (-1/7, 1/7).
To find the radius of convergence of the series, we can use the ratio test:
lim |a_{n+1}/a_n| = lim |(7(n+1)-1)/n+1| = 7
Since the limit exists and is finite, the series converges for |x| < 1/7. Therefore, the radius of convergence is r = 1/7.
To find the interval of convergence, we need to check the endpoints x = -1/7 and x = 1/7. When x = -1/7, the series becomes:
[tex](-1)^n[/tex] 6 × 13 × 20 × ⋯ × (7n − 1) n = 1
which does not converge since the terms do not approach zero. When x = 1/7, the series becomes:
6/7 × 13/7 × 20/7 × ⋯
which also does not converge since the terms do not approach zero. Therefore, the interval of convergence is (-1/7, 1/7).
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The question is -
Find the radius of convergence if exists, r, of the infinity series. n! x n: 6 × 13 × 20 × ⋯ × (7n − 1) n = 1 r = ? find the interval, i, of convergence of the series if exists and if it does mention the reason. (enter your answer using interval notation.)