No, the velocity vector v(t) of a curve r(t) is not always perpendicular to the acceleration vector a(t). To understand this concept, we first need to understand what these vectors are.
The velocity vector v(t) of a curve r(t) represents the rate of change of position of an object with respect to time. In other words, it tells us how fast an object is moving and in what direction. It is a tangent vector to the curve r(t) at any given point on the curve.
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twelve bronchial cancer patients who received a certain treatment had an average survival time of 111.3 days with standard deviation 62.9 days. can we conclude from this that the average survival time for all bronchial cancer patients who receive that treatment will be different from 90 days? we will use a 5% significance level.
The one-sample t-test with a significance level of 5% fails to reject the null hypothesis that the mean survival time for all bronchial cancer patients who receive that treatment is equal to 90 days, and the P-value is 0.0974.
To determine whether the average survival time for all bronchial cancer patients who receive that treatment is different from 90 days, we can perform a one-sample t-test. The null hypothesis is that the mean survival time is equal to 90 days, and the alternative hypothesis is that the mean survival time is different from 90 days.
We can use the following formula to calculate the t-statistic:
[tex]$t = \frac{\bar{x} - \mu}{s/\sqrt{n}}$[/tex]
Substituting the given values, we get:
t = (111.3 - 90) / (62.9 / √12) = 1.83
Using a t-distribution table with 11 degrees of freedom, and a significance level of 5%, we find the critical values to be ±2.201.
Since the calculated t-value of 1.83 falls within the range of -2.201 to +2.201, we fail to reject the null hypothesis. This means that we do not have sufficient evidence to conclude that the average survival time for all bronchial cancer patients who receive that treatment is different from 90 days.
To find the P-value using a calculator, we can use the t-distribution with 11 degrees of freedom and calculate the probability of getting a t-value greater than 1.83 or less than -1.83 (since it is a two-tailed test). The P-value turns out to be 0.0974. Rounded to the nearest 4th decimal digit, the P-value is 0.0974.
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Complete question:
Twelve bronchial cancer patients who received a certain treatment had an average survival time of 111.3 days with a standard deviation of 62.9 days. Can we conclude from this that the average survival time for all bronchial cancer patients who receive that treatment will be different from 90 days? We will use a 5% significance level. Do the T-test on your calculator and enter the P-value below. Enter it as a decimal (not a percentage), and round it to the nearest 4th decimal digit.
A certain breed of mouse was introduced onto a small island with an initial population of 240 mice, and scientists estimate that the mouse population is doubling every year.
(a) Find a function N that models the number of mice after t years.
N(t) =
(b) Estimate the mouse population after 5 years.
mice
The estimated mouse population after 5 years is 7,680 mice. (a) The mouse population is doubling every year,
which means that the population at any time t will be double the population at time t-1. We can use this information to write the function N(t) that models the number of mice after t years as follows: N(t) = 240 * 2^t
(b) To estimate the mouse population after 5 years, we can simply substitute t=5 into the function we found in part (a): N(5) = 240 * 2^5 = 7,680
Therefore, the estimated mouse population after 5 years is 7,680 mice. However, it is important to note that this is only an estimate based on the assumption that the population is doubling every year.
In reality, there may be factors such as limited resources and predation that could affect the growth rate of the population.
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a tukey multiple comparison is performed to compare the means of 5 populations. how many confidence intervals will be obtained?
There will be 10 confidence intervals obtained in a Tukey multiple comparison of 5 populations.
In a Tukey multiple comparison, the confidence intervals are constructed to compare the means of all pairs of groups. To calculate the number of confidence intervals, we use the following formula:
C = n(n-1)/2
Where C is the number of confidence intervals, and n is the number of groups. In this case, there are five populations being compared, so n=5. Plugging this into the formula, we get:
C = 5(5-1)/2 = 10
Each confidence interval will provide information about the difference between the means of two groups, with a certain level of confidence. These confidence intervals can be used to identify which pairs of groups have significantly different means.
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If there is no variability (all the scores of the variable have the same value), measures of dispersion will equal ___________ A) 0 B) 1 C) -1 D) 2
If there is no variability (all the scores of the variable have the same value), measures of dispersion will equal 0. Option A) 0 is the correct answer.
When there is no variability, it means all the scores of the variable have the same value. Therefore, there is no difference between the scores, and the deviation of each score from the mean is zero. As a result, all measures of dispersion such as the range, variance, and standard deviation will be zero because they are all based on the deviation of scores from the mean.
Therefore, option A) 0 is the correct answer.
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a team of medical researchers sample 30 subjects from a population with replacement, and find that 8 of them have high bone mineral density (bmd). unbeknownst to the researchers, the population consists of 622 patients, of whom 147 have high bmd. what is the researchers' estimate for the proportion of patients with high bmd?
The researchers estimate for the proportion of patients with high BMD in the population is equal to the sample proportion since they used a random sampling method with replacement. Therefore, their estimate for the proportion of patients with high BMD in the population is 0.267 or 26.7%.
In statistics, a population refers to the entire group of individuals, objects, or events that meet certain criteria. A sample, on the other hand, is a smaller subset of the population that is selected to represent the larger group.
In this case, the population is comprised of 622 patients, of whom 147 have high bone mineral density (BMD). The researchers selected a sample of 30 subjects from this population with replacement. This means that after selecting a subject, they put it back in the population before selecting the next subject.
Of the 30 subjects in the sample, 8 have high BMD. To estimate the proportion of patients with high BMD in the population, the researchers use the sample proportion.
The sample proportion is calculated by dividing the number of subjects with high BMD in the sample (8) by the total number of subjects in the sample (30).
Sample proportion = 8/30 = 0.267
It's important to note that the larger the sample size, the more accurate the estimate will be. However, in this case, the sample size is relatively small, so there may be some error in the estimate. Nonetheless, the researchers estimate provides a good indication of the proportion of patients with high BMD in the population.
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in how many ways 7 people be seated at a round table if they can sit anywhere and two particular people must not sit next to each other
There are 360 ways to seat 7 people at a round table if they can sit anywhere and no restrictions are imposed. However, if two particular people must not sit next to each other, the number of possible seating arrangements decreases to 240.
To see why there are 360 ways to seat 7 people without restrictions, we can fix one person's position and then arrange the remaining 6 people in a line, giving us 6! ways to arrange the remaining people. However, since it is a round table, each arrangement can be rotated in 7 ways, so we divide by 7 to avoid overcounting, giving us a total of 6! / 7 = 360 ways.
To find the number of ways to seat 7 people if two particular people must not sit next to each other, we can first fix one of the two people in a seat. The other person cannot sit in either of the two adjacent seats, so there are 4 remaining seats where they can sit. Once we have placed the two people, there are 5 people remaining to seat. We can arrange them in a line in 5! ways, and then rotate the line in 5 ways to get all the possible arrangements at the round table. Therefore, the total number of ways to seat the 7 people with the restriction is 4 x 5! x 5 = 240.
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one card is drawn from a deck of 16 cards numbered 1 through 16. find the probability of each scenario. (enter your probabilities as fractions.)(a) the card drawn is odd and divisible by 4.
The probability of drawing a card that is both odd and divisible by 4 from a deck of 16 cards numbered 1 through 16 is 0.
To see why, note that a number that is both odd and divisible by 4 does not exist in the given set of numbers. Every even number in the set is divisible by 2 but not 4, while every multiple of 4 in the set is even and not odd. Therefore, the intersection of the sets of odd and multiples of 4 is the empty set, and the probability of drawing a card that belongs to this set is 0.
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find the points (x,y) at which the curve x(t)=4cos(t),y(t)=4sin(2t) has a horizontal tangent.
The curve has horizontal tangents at the points (0,0) for all values of t. To find the points at which the curve has a horizontal tangent, we need to find the values of t that make the derivative of y(t) equal to zero.
First, we need to find the derivative of y(t):
y'(t) = 8cos(t)
Next, we set y'(t) equal to zero and solve for t:
8cos(t) = 0
cos(t) = 0
This occurs when t = π/2 or 3π/2.
Now, we can plug these values of t back into the original equations to find the corresponding points:
When t = π/2,
x(π/2) = 4cos(π/2) = 0
y(π/2) = 4sin(2(π/2)) = 0
So the point is (0,0).
When t = 3π/2,
x(3π/2) = 4cos(3π/2) = 0
y(3π/2) = 4sin(2(3π/2)) = 0
So the point is also (0,0).
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What multimedia element would enhance a speech about the problems of coastal erosion?
A tree on a floating globe that is crumbling.
A road that has collapsed next to a beach.
A graph drawn in sand.
Starfish on a beach.
The multimedia element that would enhance a speech is multimedia element would enhance a speech about the problems of coastal erosion, the correct option is B.
We are given that;
The four options
Now,
A multimedia element is a visual or auditory aid that can enhance a speech by making it more engaging, informative or persuasive. A multimedia element should be relevant to the topic, clear and accurate, and appropriate for the audience and occasion. Here are some criteria to evaluate the multimedia elements:
A road that has collapsed next to a beach. This element is relevant to the topic of coastal erosion, as it shows one of the consequences of losing land and infrastructure due to erosion. It is also clear and accurate, as it depicts a realistic scenario that might happen in some areas. It might engage and persuade the audience by appealing to their emotions or interests.
Therefore, by the unitary method answer will be A road that has collapsed next to a beach.
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Classify each pair of angles as alternate interior, alternate exterior, or corresponding.
∠4 and ∠5
The pair of angles ∠4 and ∠5 should be classified as corresponding angles.
What are corresponding angles?In Mathematics, corresponding angles can be defined as a postulate (theorem) which states that corresponding angles are always congruent when the transversal intersects two (2) parallel lines.
This ultimately implies that, the corresponding angles will be always equal (congruent) when a transversal intersects two (2) parallel lines.
By applying corresponding angles theorem to parallel lines h and k, we have the following:
∠1 ≅ ∠8
∠3 ≅ ∠6
∠4 ≅ ∠5
∠7 ≅ ∠2
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the Dimensions of this figure are changed so that the new surface area is Exactly 1/4 What it was Originally. What is the New Surface Area? enter your Answer as a Decimal in the box.
The new surface area of the figure is given as follows:
S = 164.61 ft².
What is the surface area of a rectangular prism?The surface area of a rectangular prism of height h, width w and length l is given by:
S = 2(hw + lw + lh).
This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.
The prism in this problem is composed as follows:
6.5 ft, 9.8 - 4.3 = 5.5 ft and 10.6 ft.4.3 ft, 10.6 ft and 8.1 ft.Hence the surface area of the original prism is given as follows:
S = 2 x (6.5 x 5.5 + 5.5 x 10.6 + 6.5 x 10.6) + 2 x (4.3 x 10.6 + 4.3 x 8.1 + 10.6 x 8.1)
S = 658.44 ft².
The new surface area is one fourth of the original surface area, hence it is given as follows:
S = 0.25 x 658.44
S = 164.61 ft².
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The perimeter of a semicircle is 30.84 meters. What is the semicircle's radius?
Answer:
radius is 6 meters
Step-by-step explanation:
perimeter of semicircle = πr + 2r
πr + 2r = 30.84
3.14r + 2r = 30.84
5.14r = 30.84
r = 30.84 ÷ 5.14
r = 6
In a study done on the life expectancy of 500 people in a certain geographic region, the mean age at death was 72 years and the standard deviation was 5.3 years.If a sample of 50 people from this region is selected, and the probability that the mean life expectancy will be less than 70 years, which of the following will you use?
a.Normal Distribution
b.Central Limit Theorem
c.Discrete Probability Distribution
d.Binomial Distribution
b. Central Limit Theorem. in this scenario, we would use the Central Limit Theorem to determine the probability that the mean life expectancy will be less than 70 years.
The Central Limit Theorem states that for a large enough sample size, the sampling distribution of the sample mean will approach a normal distribution, regardless of the shape of the population distribution. In this case, a sample of 50 people is selected, which is reasonably large.
Since the mean and standard deviation of the population are known, we can calculate the z-score for a sample mean of 70 years. The z-score is calculated as:
z = (sample mean - population mean) / (population standard deviation / sqrt(sample size))
= (70 - 72) / (5.3 / sqrt(50))
≈ -1.19
By referring to a standard normal distribution table or using a calculator, we can find the probability of a z-score less than -1.19. This probability corresponds to the probability that the sample mean will be less than 70 years.
Using the Central Limit Theorem, we can approximate the distribution of the sample mean as a normal distribution and calculate the desired probability.
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PLSS HELP!!!!!!!!!!
A computer generates 80 integers from 1 to 8 at random. The results are recorded in this table.
Outcome 1 2 3 4 5 6 7 8
Number of times outcome occurred 14 16 10 12 4 7 6 11
What is the experimental probability of the computer generating a 2 or a 5?
Responses
9%
15%
20%
25%
Answer:
25%
Step-by-step explanation:
To find the experimental probability of the computer generating a 2 or a 5, we need to calculate the total number of times the outcomes 2 and 5 occurred and divide it by the total number of trials (which is 80 in this case).
Looking at the table, the outcome 2 occurred 16 times and the outcome 5 occurred 4 times.
Total number of times 2 or 5 occurred = 16 + 4 = 20
Experimental probability = (Number of times 2 or 5 occurred) / (Total number of trials) = 20 / 80 = 0.25
To express this as a percentage, we multiply the decimal value by 100:
Experimental probability = 0.25 * 100 = 25%
Therefore, the correct answer is 25%.[tex][/tex]
A scientist has a sample of 125 bacteria cells. The number of cells doubles each week. After how many weeks will there be 16,000 bacteria cells?
It will take 7 weeks for the number of bacteria cells to double enough times and reach 16,000 cells
Now, By using an exponential growth model to find the time it would take for the number of bacteria cells to reach 16,000:
N(t) = N₀ * 2^(t/k)
where N₀ is the initial number of bacteria cells, N(t) is the number of bacteria cells at time t, k is the doubling time (in weeks), and t is the time (in weeks).
We know that;
N₀ = 125,
And, For the value of t when N(t) = 16,000.
So we can set up an equation:
16,000 = 125 x 2^(t/k)
Next, we can simplify this equation by dividing both sides by 125:
128 = 2^(t/k)
Then we can take the logarithm of both sides (with base 2) to solve for t/k:
log2(128) = t/k
7 = t/k
Therefore, it will take 7 weeks for the number of bacteria cells to double enough times and reach 16,000 cells.
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Mike saves $2000 at a year simple interest rate of 2%. He earns $280 in interest for how many years does he save this money
Mike saved his money for 7 years to earn $280 in interest at a simple interest rate of 2%.
The simple interest formula:
I = P × r × t
Where:
I is the interest earned
P is the principal (the initial amount of money saved)
r is the interest rate
t is the time (in years)
We know that Mike saves $2000 at a simple interest rate of 2% and he earns $280 in interest.
So we can plug in these values and solve for "t":
280 = 2000 × 0.02 × t
Dividing both sides by (2000 × 0.02):
280 / (2000 × 0.02) = t
t = 7
I = P r t is the formula for calculating interest.
P stands for principle, which is the original sum of money saved and r stands for interest rate.
The date is (in years).
We are aware that Mike gets $280 in interest on his savings of $2000 at a basic interest rate of 2%.
Thus, we may enter these numbers and find the value of "t":
280 = 2000 × 0.02 × t
by (2000 0.02), divide both sides:
280 / (2000 × 0.02)= 7
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Give the slope and the y-intercept of the line y=-6x-2 Make sure the y-intercept is written as a coordinate. This means the y-intercept must be in the form (0,b)
In summary, the slope of the line is -6, and the y-intercept is (0, -2).
To find the slope and y-intercept of the line y = -6x - 2, we can compare it to the slope-intercept form of a linear equation, which is y = mx + b. In this form, "m" represents the slope, and "b" represents the y-intercept.
For the given equation y = -6x - 2:
1. Identify the slope (m): The coefficient of the x term, which is -6, represents the slope. Therefore, the slope (m) is -6.
2. Identify the y-intercept (b): The constant term, which is -2, represents the y-intercept. To express the y-intercept as a coordinate (0, b), substitute 0 for the x value. So the y-intercept coordinate is (0, -2).
In summary, the slope of the line is -6, and the y-intercept is (0, -2).
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what other equation
equals m - 3 > -2
Any values of m that satisfy this equation will also satisfy the inequality m - 3 > -2. However, this equation has infinitely many solutions, since we can choose any value for k and get a corresponding value for m.
The inequality m - 3 > -2 can be solved as follows:
Add 3 to both sides of the inequality to isolate the variable m:
m - 3 + 3 > -2 + 3
m > 1
So the equivalent inequality is: m > 1.
Alternatively, we could also write the inequality in the form of an equation by adding a variable k on both sides of the inequality:
m - 3 + k = -2 + k
Simplifying this equation, we get:
m = k - 1
So any values of m that satisfy this equation will also satisfy the inequality m - 3 > -2. However, this equation has infinitely many solutions, since we can choose any value for k and get a corresponding value for m.
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We need to find the hidden box whith using the formulae pls help
The complete table:
Number of paces per minute Pace length (metres)
63 0.45
70 0.5
77 0.55
84 0.6
To fill in the missing numbers in the table, we can use the relationship given as:
n / P = 140
Where n is the number of paces per minute, and P is the pace length in meters.
For the second row, we are given the number of paces per minute, n = 70, and we need to find the pace length, P. We can rearrange the formula as:
P = n / 140
Substituting the values, we get:
P = 70 / 140 = 0.5 meters
So the missing pace length in the table is 0.5 meters.
For the fourth row, we are given the pace length, P = 0.6 meters, and we need to find the number of paces per minute, n. We can rearrange the formula as
n = P x 140
Substituting the values, we get:
n = 0.6 x 140 = 84
So the missing number of paces per minute in the table is 84.
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b= 4a-5 when a=10 what are the values of b and c
Answer:
b=35
Step-by-step explanation:
We are given that:
b=4a-5
and are asked to find b when a=10
So, we can first substitute in 10 for a:
b=4(10)-5
simplify
b=40-5
b=35
So, b=35.
Hope this helps! :)
Edit: There is not a c variable? I'm confused so I left this out.
The graphs of the functions f(x) and g(x) are shown below.
The numeric value for each expression is given as follows:
a) (f x g)(1) = 9.
b) (f - g)(0) = -3.
How to obtain the numeric value for each expression?Tracing a vertical line through x = 1, we have that:
The graph crosses the red function f(x) at y = 3, hence f(1) = 3.The graph crosses the blue function g(x) at y = 3, hence g(1) = 3.Then the product of f and g at x = 1 is given as follows:
(f x g)(1) = f(1) x g(1) = 3 x 3 = 9.
Tracing a vertical line through x = 0, we have that:
The graph crosses the red function f(x) at y = 1, hence f(0) = 1.The graph crosses the blue function g(x) at y = 4, hence g(0) = 4.Then the subtraction of the functions f(x) and g(x) at x = 0 is given as follows:
f(0) - g(0) = 1 - 4 = -3.
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Find f(t). ℒ−1 {1/ (s^2 − 4s + 5)} f(t) = ____________
Step-by-step explanation:
To find f(t), we need to take the inverse Laplace transform of 1/(s^2 - 4s + 5).
We can start by factoring the denominator of the Laplace transform:
1/(s^2 - 4s + 5) = 1/[(s - 2)^2 + 1^2]
We can recognize this as the Laplace transform of the function f(t) = e^2t * sin(t). Therefore,
ℒ^{-1} {1/(s^2 - 4s + 5)} = e^{2t} sin(t)
Thus, f(t) = e^{2t} sin(t).
A number cube with the numbers 1 through 6 is rolled. Find the given probability.
1. P(number < 2) (1 point)
A. 1/6 <--- i think this one
B. 2/6
C. 4/6
D. 3/6
Answer:
P(less than 2) = P(1) = 1/6
A is correct.
If you roll a 6-sided die 6 times, what is the best prediction possible for the number of times you will roll a three?
Answer: The best prediction possible for the number of times you roll a three is 1/6 of a roll.
Step-by-step explanation:
When you find the statistics of something like rolling a die, you will need to divide how many times you roll the die by how many sides are on the die.
6 - how many times you roll the die
6 - how many sides are on the die
When you divide 6 by 6, you will get one. Since both of the statistical numbers are the same, you will get an 1/6 chance of rolling a 1, 2, 3, 4, 5, and 6. So 1/6 is the answer! Hope this helps!!!
P.S (I learned this in 5th grade :))
c) at a certain event, 45 people attend, and 5 will be chosen at random to receive door prizes. the prizes are all the same, so the order in which people are chosen does not matter. [3 marks] how many different groups of five people can be chosen?
The different groups of five people chosen from 45 people by applying combination is equal to 1,221,759.
Total number of people = 45
Number of people chosen at random to receive door prize = 5
The number of different groups of five people that can be chosen out of 45 attendees,
we need to use the combination formula,
ⁿCₓ = n! / (x! × (n-x)!)
where n is the total number of attendees,
x is the number of people to be chosen,
and ! denotes factorial (e.g., 5! = 5 x 4 x 3 x 2 x 1).
Here, we have n = 45 and x = 5, so we can plug these values into the formula,
⁴⁵C₅
= 45! / (5! × (45-5)!)
= (45 x 44 x 43 x 42 x 41) / (5 x 4 x 3 x 2 x 1)
= 1,221,759
Therefore, there are 1,221,759 different groups of five people that can be chosen from a total of 45 attendees using combination.
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I tried 9.90 but that doesn't work, please help
Question 3 Part A (4 points): Use the draw it tools to complete the question below. Be sure to show all work that supports your answer to receive full credit. IS THE BLUE CORRECT?
The area of Mrs. Leger's garden is equal to 6x² + 41x + 70 square inches.
How to calculate the area of a rectangle?In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:
A = LW
Where:
A represent the area of a rectangle.W represent the width of a rectangle.L represent the length of a rectangle.Based on the information provided about this rectangular garden, we have the following:
Area of Mrs. Leger's garden = (2x + 7)(3x + 10)
Area of Mrs. Leger's garden = 6x² + 20x + 21x + 70
Area of Mrs. Leger's garden = 6x² + 41x + 70 square inches.
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Suppose that you're interested in the effect of class attendance on student performance: performance = Bo + Biattendance + B2ACT + B3GPA + u a. Let distance be the distance from the students' living quarters to the lecture hall. Assume distance and u are uncorrelated. What additional assumptions are required for distance to be an IV for attendance?
To determine if distance can be an instrumental variable (IV) for attendance in the model of given performance, we need to ensure that it satisfies the following assumptions: Relevance, Exogeneity and Exclusion restriction.
1. Relevance: Distance must be correlated with attendance, meaning that it has a significant effect on attendance. Intuitively, students living closer to the lecture hall may attend classes more frequently.
2. Exogeneity: Distance must not be directly correlated with the error term (u) in the performance equation, meaning that it should not have any direct effect on student performance apart from its impact on attendance. The assumption given already states that distance and u are uncorrelated, which fulfills this requirement.
3. Exclusion restriction: Distance should not have any direct effect on performance except through its influence on attendance. In other words, after controlling for attendance, ACT scores, and GPA, distance should not be a significant predictor of performance.
Additionally, we must assume that there are no other unobserved variables that could be driving the relationship between distance and performance. If these assumptions are met, we can use distance as an instrumental variable to identify the causal effect of attendance on performance.
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find the coordinate matrix of x in rn relative to the basis b'. b' = {(−7, 8), (4, −3)}, x = (−31, 37)
The coordinate matrix of x in rn relative to the basis b' is [-3, 2] because x can be expressed as -3 times the first vector in b' plus 2 times the second vector in b'.
What is the vector representation of x in the basis b' of rn?To find the coordinate matrix of x in rn relative to the basis b', we need to express x as a linear combination of the basis vectors in b', and then write the coefficients of that linear combination as entries in the coordinate matrix. In this case, we have:
x = (-31, 37)
b' = {(-7, 8), (4, -3)}
We want to find scalars a and b such that:
x = a(-7, 8) + b(4, -3)
Solving this system of equations, we get:
a = -3
b = 2
Therefore, the coordinate matrix of x in rn relative to the basis b' is:
[-3, 2]
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list all the elements of each set. (Note that sometimes you will have to put three dots at the end because the set is infinite.) E={All possible remainders from dividing a natural number by 6}.
PLEASE HELP I GIVE BRAINLIEST :D
[tex]E=\{0,1,2,3,4,5\}[/tex]
The remainders from dividing a natural number by a natural number [tex]n[/tex] are [tex]0,1,2,3,\ldots,n-1[/tex].