Answers
Answer:
1. D.
2. b
Step-by-step explanation:
1.Change to 2.375 to a fraction
2.735=19/8
2. 6^2=36
8^2=64
36+64=10^2
36+64=100
100=100
Question 2:
Choose D.
[tex]\frac{19}{8} = 2\frac{3}{8} =2.375[/tex]
Look at the fraction 19/8.
The numerator (19) is greater than the denominator (8). That means we have a number > 1.
So how many 8's are in 19?
Well, 8 x 2 = 16. So that would be 16/8 = 2.
Then we'd have 3 leftover because 19-16 = 3.
That's how we know that 19/8 = 2 3/8.
Are you allowed to use a calculator? Because if so, 3/8 = 0.375. That's the fastest way to figure it out!
If not, we can do it the old fashioned way (ha). 3/8 is halfway between 2/8 and 4/8.
2/8 = 1/4 = 0.25 (1/4 = one quarter, just like a quarter worth 0.25)
4/8 = 1/2 = 0.50 (1/2 = a half, a half dollar, 0.50)
0.25 + 0.50 = 0.75 >>> Now divide that by 2 to find the halfway between 0.25 and 0.50 = 0.75/2 = 0.375.
^^^^ That's just a workaround way of figuring out 3/8 as a decimal if you can't use a calculator.
Question 3: Use the pythagorean theorem. a^2 + b^2 = c^2.
C is the hypotenuse, aka the LONGEST length of the right triangle.
If the numbers work in that formula, it's a right triangle. If not, it's NOT a right triangle.
Marissa: 5, 12, 13
Does 5^2 + 12^2 = 13^2?
25 + 144 = 169
13^2 = 169
So YES, Marissa can make a right triangle.
Berta: 6, 8, 10
6^2 + 8^2 = 100 = 10^2
So YES, Berta can make a right triangle.
Corrin: 12, 16, 20
12^2 + 16^2 = 400 = 20^2
So YES, Corrin can make a right triangle.
So the answer is D, all 3 can make right triangles.
Related Questions
if a seed is planted, it has a 65% chance of growing into a healthy plant.if 6 seeds are planted, what is the probability that exactly 1 doesn't grow? (exactly 1 failures)incorrect
Answers
The probability of exactly 1 seed not growing is 31.36%. we can use the binomial probability formula, which is:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k). P(X=k) is the probability of getting k successes in n trials n is the number of trials
k is the number of successes p is the probability of success in each trial.
To calculate the probability of exactly 1 failure, we can use the binomial probability formula, which is:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
P(X=k) is the probability of getting k successes in n trials
n is the number of trials
k is the number of successes
p is the probability of success in each trial
(n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items
In this case, n=6, k=1, p=0.65, and (n choose k) = 6. Plugging these values into the formula, we get:
P(X=1) = (6 choose 1) * 0.65^1 * (1-0.65)^(6-1) = 6 * 0.65 * 0.35^5 = 0.3136
Therefore, the probability of exactly 1 seed not growing is 31.36%.
In this case, the probability of getting exactly 1 failure in 6 trials, where the probability of success is 0.65. We use the binomial coefficient to count the number of ways to choose 1 item (the failure) from a set of 6 items (the seeds). We then multiply this by the probability of getting 1 failure and 5 successes, which is given by the formula p^k * (1-p)^(n-k), where p is the probability of success and k and n-k represent the number of successes and failures, respectively. Finally, we calculate the probability of exactly 1 failure by multiplying the binomial coefficient and the probability of getting 1 failure and 5 successes.
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ct the correct answer from each drop-down menu.
Consider the graph of f(x) = (²)*.
Y18
Answers
The correct graph to the exponential function f(x) = (1/2)ˣ is attached accordingly.
What are the key functions of f?Exponential Growth - The function represents exponential growth because the base (1/2) is between 0 and 1. As x increases, the function values get smaller but remain positive.
Y-Intercept - The function intersects the y-axis at y = 1, meaning that when x = 0, the value of f(x) is 1.
Asymptote - The function approaches but never reaches the x-axis (y = 0) as x approaches negative infinity. This is because the base (1/2) is a fraction less than 1.
Decreasing Function - The function is decreasing as x increases. This is because the base (1/2) is less than 1, causing the exponent to be negative, resulting in smaller values for f(x) as x increases.
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find the inflection point of the function. (hint: g''(0) does not exist.) g(x) = 4x|x| (x, g(x)) =
Answers
x = 0 is a point of change in curvature for the function g(x) = 4x|x|.
The given function is g(x) = 4x|x|.
The first derivative of g(x) is:
g'(x) = 4|x| + 4x * d/dx (|x|)
= 4|x| + 4x * sgn(x)
where sgn(x) is the sign function that equals 1 if x > 0, -1 if x < 0, and 0 if x = 0.
The second derivative of g(x) is:
g''(x) = 4 * d/dx (|x|) + 4 * sgn(x) + 4x * d^2/dx^2 (|x|)
= 4 * sgn(x) + 4 * δ(x)
where δ(x) is the Dirac delta function that equals infinity at x = 0 and 0 elsewhere.
Since the second derivative of g(x) does not exist at x = 0, g(x) has no inflection point at x = 0.
However, we can see that g(x) changes from concave down to concave up at x = 0, which is a point of interest. At x < 0, g(x) is a downward-facing parabola, while at x > 0, g(x) is an upward-facing parabola. Therefore, we can say that x = 0 is a point of change in curvature for the function g(x) = 4x|x|.
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determine if the following statement is true or false. to perform a one-way anova, the populations must have the same variance.
Answers
The statement is false. One-way ANOVA is a statistical test used to compare the means of three or more groups that are independent of each other. However, it does not assume that the populations have the same variance.
Instead, one of the assumptions of one-way ANOVA is that the populations being compared have equal variances, which means that the variation within each group is the same. This assumption is called homogeneity of variances or homoscedasticity.
If the populations do not have equal variances, it can lead to biased results and inaccurate conclusions. In such cases, a modified version of one-way ANOVA called Welch's ANOVA can be used, which does not assume equal variances among the groups.
To test for the homogeneity of variances assumption in one-way ANOVA, researchers can use statistical tests such as Levene's test or Bartlett's test. These tests assess whether the variances of the groups are significantly different from each other. If the results of these tests are significant, it indicates that the assumption of equal variances has been violated, and a modified version of ANOVA should be used instead.
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It took 40 minutes for Dale and Tami to paddle 6 Mi Downstream on white river. It took 3 hours for them to return the same distance. They puddled at the same rate, both up and down. What is the speed of the river's current?
Answers
The speed of the river's current is -27/2 or -13.
let's use d to represent the distance between their starting point and the point 6 miles downstream and r to represent the speed of the river's current. since they were able to paddle downstream, they must have been going faster than the speed of the river's current. let's call their downstream speed s1. similarly, their upstream speed would have been slower than the speed of the river's current, so let's call their upstream speed s2. using the formula distance = rate x time, we can write two equations based on the given information:equation 1: d = (s1 + r) x (40/60) (since they paddled downstream for 40 minutes)equation 2: d = (s2 - r) x 3 (since they paddled upstream for 3 hours)
we can solve for s1 and s2 by adding and subtracting equation 1 and equation 2:d = (s1 + r) x (40/60)d = (s2 - r) x 32d = (s1 + r) x (40/60) + (s2 - r) x 3simplifying this equation, we get:
2d = (s1 + r) x (2/3) + (s2 - r) x 32d = (2s1 + 2r + 3s2 - 3r) / 36d = 2s1 + 2r + 3s2 - 3r6d = 2s1 + 3s2 - rnow we can use equation 1 to substitute s1 + r with d x (3/8):
d = (s1 + r) x (40/60)d = (s1 + r) x (2/3)s1 + r = d x (3/4)substituting this expression into the previous equation, we get:6d = 2(d x (3/4)) + 3s2 - r6d = (3d/2) + 3s2 - r
9d/2 = 3s2 - rr = 3s2 - (9d/2)now we need to find s2, which we can do by using equation 2:d = (s2 - r) x 3s2 = (d/3) + r
substituting r with the previous expression, we get:s2 = (d/3) + 3s2 - (9d/2)s2/3 = -3d/2s2 = -9d/2finally, we can substitute this value of s2 into the expression for r:
r = 3s2 - (9d/2)r = -27d/2 5 miles per hour. however, since this answer is negative, it does not make physical sense.
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the proportion of college football players who have had at least one concussion is estimated to be 34% in the united states. we wanted to know if football players at our university were less likely to have suffered a concussion, so we surveyed a random sample of 100 past and present football players at our university. is this survey valid or not valid for testing the hypothesis that the proportion of college football players at our university with at least one concussion is less than the national average?
Answers
All of the criteria's are fulfilled the survey is valid.
We have the information from the question:
The proportion of college football players who have had at least one concussion is estimated to be 34% in the united states.
Then, 34% = 0.34
The sample size of the data is = 100
p: the ‘proportion’ of ‘college’
The required conditions for testing the hypothesis of population proportion are,
(i) The population is larger than the sample
(ii) np > 10
=> 100 × 0.34
=34
(iii) n(1-p) > 10
100 × (1 - 0.34)
=> 100 × 0.66
=66
iv)The ‘sample’ is drawn randomly from the population.
Since all of the above criteria's are fulfilled the survey is valid.
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True or false. A p-value of .4 means we should accept that the null hypothesis is true. If false, please explain why.
True or false. The p-value is the probability that the null hypothesis is true.
A student feels unwell and decides to take a strep test. The student received a negative result, however they still felt very sick so decide to go to the nurse. The nurse gives them additional tests and found that they did have strep. What type of error did the first test make?
Answers
(1) False. A p-value of 4 indicates that there is a high probability of obtaining the observed results by chance alone.
(2) False. The p-value is the probability of obtaining the observed results or more extreme results if the null hypothesis is true.
False. A p-value of .4 means we should not necessarily accept that the null hypothesis is true. The p-value represents the probability of obtaining a result as extreme or more extreme than the one observed, assuming the null hypothesis is true. A common threshold to reject the null hypothesis is a p-value less than 0.05. Since 0.4 is greater than 0.05, we do not have enough evidence to reject the null hypothesis, but it does not mean we should accept it as true.
False. The p-value is not the probability that the null hypothesis is true. It is the probability of observing the given results (or more extreme results) assuming the null hypothesis is true.
In the strep test scenario, the first test made a Type II error. This occurs when the test fails to reject a false null hypothesis, meaning the test showed a negative result (no strep) when the student actually had strep.
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When we assume that the supply of money is a variable that the central bank controls, we 1. must then assume as well that the demand for money is not influenced by the value of money. 2. must then assume as well that the price level is unrelated to the value of money. 3. are ignoring the fact that, in the real world, households are also suppliers of money. 4. are ignoring the complications introduced by the role of the banking system.
Answers
Money is a variable that the central bank controls, we " must then assume as well that the price level is unrelated to the value of money". The correct answer is option 2:
When we assume that the central bank controls the supply of money, we assume that it has the power to adjust the quantity of money in circulation. This assumption, however, implies that the price level is unrelated to the value of money, which is not necessarily true in the real world. Option 1 is incorrect because the demand for money is often influenced by the value of money. Option 3 is incorrect because households, along with banks and other financial institutions, play a role in the creation and supply of money. Option 4 is incorrect because the banking system is a crucial part of the monetary system, and its role cannot be ignored when discussing the supply of money.
Option 2 is answer.
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repeat the census logistic regression model that controlled only for capital gains but using a different random number seed (365 instead of 364) for the 80%/20% split. would you expect big differences in the accuracy using the training data? testing data?
Answers
Changing the seed value during testing and training of models would not have a huge impact on the model accuracy.
RANDOM NUMBER SEED
Seed values are used during model building mainly to ensure reproducibility. Setting a random state value means that output value generated for randomly generated events would be the same.
Features which impact accuracy of models include the amount of training set , number of features used in training , level of cleanliness of the data fed into the model and other factors which could impact how the model learns.
Therefore , random number seed does not determine how the model learns or captures information. Hence, having little to no impact on the accuracy of the model.
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what's the answer I really need it
Answers
Answer:A
Step-by-step explanation:
using the raiload racks
For which sample size (n) and sample proportion (p) can a normal curve be
used to approximate the sampling distribution?
A. n = 24; p = 0.5
B. n = 20; p = 0.6
OC. n = 24; p = 0.4
O D. n = 20; p = 0.3
Answers
The sample size 24 and sample proportion (p) is 0.5 will be a normal curve be used to approximate the sampling distribution
The condition for a normal curve to be used to approximate the sampling distribution is that the sample size should be large enough such that both np and n(1-p) are greater than or equal to 10.
Let's check the options one by one:
n = 24; p = 0.5
Here, np = 24 x 0.5 = 12 and
n(1-p) = 24 x 0.5 = 12
Both of which are greater than or equal to 10.
So, a normal curve can be used to approximate the sampling distribution.
n = 20, p = 0.6
n×p = 12, n×(1-p) = 8, so a normal curve cannot be used.
C. n = 24, p = 0.4: n × p = 9.6, n ×(1-p) = 14.4, so a normal curve cannot be used.
D. n = 20, p = 0.3: n × p = 6, n×(1-p) = 14, so a normal curve cannot be used.
Therefore, the sample size is 24 and sample proportion (p) is 0.5 will be a normal curve be used to approximate the sampling distribution
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how many groups of 3/4 are in 1
Answers
Answer:
4/3
Step-by-step explanation:
Divide 1 by 3/4 to find out how many groups.
1 divided by 3/4 is 4/3
7. consider y 0 = 1 − 2t 3y, y(0) = 0.5. find approximate values of the solution at t = 0.2. use the improved euler’s method with h = 0.1.
Answers
Therefore, the approximate value of the solution at t = 0.2 using the improved Euler's method with h = 0.1 is y ≈ 0.6994.
To approximate the solution of the differential equation y' = 1 - 2t^3y, with the initial condition y(0) = 0.5, at t = 0.2 using the improved Euler's method with h = 0.1, we can follow these steps:
Step 1: Initialize the values
Let t0 = 0 and y0 = 0.5 be the initial values.
Let h = 0.1 be the step size.
Let N = (t - t0) / h = (0.2 - 0) / 0.1 = 2 be the number of iterations.
Step 2: Iterate using the improved Euler's method
For i = 1 to N:
Calculate the slope at the current point using the equation:
k1 = 1 - 2t^3y
Calculate the value of y at the midpoint using the equation:
ymid = y0 + h * k1
Calculate the slope at the midpoint using the equation:
k2 = 1 - 2(t + h/2)^3 * ymid
Update the value of y using the equation:
y1 = y0 + h * k2
Update the value of t:
t = t0 + i * h
Update the value of y0 for the next iteration:
y0 = y1
Step 3: Calculate the approximate value of y at t = 0.2
After N iterations, the value of y at t = 0.2 will be y1.
Let's calculate the values using the above steps:
Iteration 1:
t = 0
y0 = 0.5
k1 = 1 - 2(0)^3 * 0.5 = 1
ymid = 0.5 + 0.1 * 1 = 0.6
k2 = 1 - 2(0.05)^3 * 0.6 = 0.99999375
y1 = 0.5 + 0.1 * 0.99999375 = 0.599999375
Iteration 2:
t = 0.1
y0 = 0.599999375
k1 = 1 - 2(0.1)^3 * 0.599999375 = 0.99800000624
ymid = 0.599999375 + 0.1 * 0.99800000624 = 0.6997994375
k2 = 1 - 2(0.15)^3 * 0.6997994375 = 0.99437500348
y1 = 0.599999375 + 0.1 * 0.99437500348 = 0.699437537823
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f(x)=x^3+3x^2-4x-12=(x+3)(x^2-4)
Hello, if you could quickly solve for the zeroes this showing your work, first person who does will get brainliest
Answers
Answer:
To begin, we set each component to zero:
x + 3 = 0 x^2 - 4 = 0
When we solve for x in the first equation, we get:
x = -3
We may factor the second equation further using the difference of squares formula which is:
(x + 2)(x - 2) = 0
Then, in each factor, we solve for x:
x + 2 = 0 or x - 2 = 0
x = -2 or x = 2
As a result, the function's zeroes are x = -3, x = -2, and x = 2.
Answer:
-3, -2, and 2.
Step-by-step explanation:
Solving for x in the first equation gives:
x+3 = 0
x = -3
Solving for x in the second equation gives:
x^2-4 = 0
(x+2)(x-2) = 0
x+2 = 0 or x-2 = 0
x = -2 or x = 2
Therefore, the zeroes of the function F(x) are -3, -2, and 2.
11. A series of three transformations are performed on AABC, finally resulting in AA"B"C"". Identify each of the
three transfomations:
a. ABC to AA'B'C'
b. ABC to M"B"C
c. ABC to M"'B"C"
d. Write all three of the transformations in composition of tranformation form.
e. Explain why all of the the transformations above are isometries.
f. Which one of the transformations above does not preserve orientation and explain why?
Answers
The answers are explained in the solution below.
Given is map of transformations,
a) ΔABC → ΔA'B'C' = Translation
b) ΔABC → ΔA''B''C'' = Translation → Reflection
c) ΔABC → ΔA'''B'''C''' = Translation → Reflection → Rotation.
d) The composition of the transformation is =
T₂ ⁰ [tex]r_{y-axis[/tex] ⁰ R₉₀
e) An isometric transformation is a shape-preserving transformation in the plane or in space.
The isometric transformations are reflection, rotation and translation and combinations of them such as the glide, which is the combination of a translation and a reflection.
f) Reflection does not preserve orientation because this transformation changes vertices.
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[Need all work] and also need the restriction
Answers
100 Points! PLEASE BE HONEST!!! Have some integrity :(
If f(x) = 9x+5 then what is f(4c+1) ?
Answers
[tex]f(4c+1)=9(4c+1)+5=36c+9+5=36c+14[/tex]
you can choose to add the common factor which is 2(18c+7)
i need help with this
Answers
Answer:
y ≥ 2x +1
Step-by-step explanation:
You want the inequality whose graph is shown.
GraphThe line has a rise of 2 units for each 1 to the right, so its slope is ...
m = rise/run = 2/1 = 2
The line crosses the y-axis at y = 1, so the y-intercept is ...
b = 1
The boundary line is ...
y = mx + b
y = 2x + 1
ShadingThe shading is above the solid line, so the inequality symbol is ≥.
The inequality for the graph is ...
y ≥ 2x +1
<95141404393>
what is the probability of pulling a queen or a black 3 out of a standard deck of cards?
Answers
Answer:
[tex]\frac{3}{26}[/tex] of pulling a queen or a black 3.
Step-by-step explanation:
Since there's 52 cards in an average deck and there's 4 queens, divide 52 with 4 and you'll get 13, so that means it's a [tex]\frac{1}{13}[/tex] chance of getting a queen.
Also because there's 4 "3"s and 50% of those cards are black (clubs and spades), divide 52 with 2 and you'll get a [tex]\frac{1}{26}[/tex] chance of getting a black 3.
Add both quotients to a common denominator of 52 and you will end up with 6/52. Then simplify the sum.
You should end up with [tex]\frac{3}{26}[/tex].
In a competition, 5 marks are given for every correct answer, and (-2)
marks are given for every incorrect answer.
a) Rehan gets 6 correct answers and 5 incorrect answers. What is his
score?
b) Rohan scored 30 marks. If he gets 10 correct answers, how many
questions he answered incorrectly?
Answers
Rehan has 6 correct ones and 5 incorrect ones, and as mentioned correct ones are 5 marks and incorrect ones are -2 marks. Now we can basically say he has (6*5) + (5*-2) marks because we can just multiply the number of questions done with the marks it gives. Simplifying, we get 30-10=20. So he got a total of 20 marks.
For part B:-
Let’s say he got “x” questions incorrect. We know that he got 10 correct answers and 30 marks in total, so it can be written like this
(10*5) + (x*-2) = 30 Similar idea to part A. Now we simplify 50 - 2x = 30
-2x=30-50
-2x=-20
-x=-10
X=10
So Rohan got 10 questions incorrectly. Hope this helps
based on a sample of 30 randomly selected years, a 90% confidence interval for the mean annual precipitation in one city is frm 48.7 inches to 51.3 inches. find the margin of error
Answers
To find the margin of error, we need to first determine the formula for it. The margin of error (ME) is calculated by multiplying the critical value of the confidence level (in this case 90%) with the standard error (SE) of the sample mean.
The critical value for a 90% confidence interval can be found using a t-distribution table with n-1 degrees of freedom (where n is the sample size). For a sample size of 30, the degrees of freedom would be 29. Using the table, the critical value for a 90% confidence interval is approximately 1.697.
Next, we need to calculate the standard error. The formula for the standard error of the sample mean is the standard deviation of the population divided by the square root of the sample size. However, we don't know the standard deviation of the population, so we will use the sample standard deviation as an estimate.
Assuming that the sample is representative of the population, we can assume that the sample standard deviation is an unbiased estimate of the population standard deviation. Therefore, we can use the formula:
SE = s / sqrt(n)
where s is the sample standard deviation and n is the sample size.
Since we are not given the sample standard deviation, we cannot calculate the standard error. However, we can use the range of the confidence interval to estimate it. The range of the confidence interval is equal to the margin of error multiplied by 2. Therefore:
ME = (51.3 - 48.7) / 2 = 1.3
Using the formula for the margin of error, we can solve for the standard error:
ME = t*SE
1.3 = 1.697*SE
SE = 0.767
Therefore, the margin of error is approximately 1.3 inches.
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Homework Grade (x) Test Grade (y)
75
92
86
57
78
78
67
90
76
89
82
70
85
78
82
90
Answers
The linear regression equation is ŷ = 1.47x - 41.67
The projected test grade is 2.43
How to calculate the linear regression equationFrom the question, we have the following parameters that can be used in our computation:
The grade (x) and test grade (y) scores
The linear regression equation can be calculated using a graphing tool, where we have the following summary:
Sum of X = 652Sum of Y = 623Mean X = 81.5Mean Y = 77.875Sum of squares (SSX) = 316Sum of products (SP) = 463.5The regression equation is
ŷ = bx + a
Where
b = SP/SSX = 463.5/316 = 1.46677
a = MY - bMX = 77.88 - (1.47*81.5) = -41.66693
So, we have
ŷ = 1.47x - 41.67
For the test grade 30, we have
ŷ = 1.47 * 30 - 41.67
Evaluate
ŷ = 2.43
Hence, the projected test grade is 2.43
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if y1 and y2 are linearly independent solutions of t2y′′ 3y′ (5 t)y=0 and if w(y1,y2)(1)=2, find w(y1,y2)(4). round your answer to two decimal places.
Answers
If y1 and y2 are linearly independent solutions of the equation t^2y'' + 3ty' + 5y = 0 and the Wronskian w(y1, y2)(1) = 2, you want to find w(y1, y2)(4) rounded to two decimal places.
Using Abel's Identity, we know that the Wronskian is constant for linearly independent solutions of a homogeneous linear differential equation with variable coefficients. So, w(y1, y2)(t) = w(y1, y2)(1) = 2 for all t.
Therefore, w(y1, y2)(4) = 2. In decimal form, the answer is 2.00.
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What is the smallest integer k such that √n = O(n^k)?
Answers
The smallest integer k that satisfies the given condition is k = 1. In Big O notation, this can be expressed as √n = O([tex]n^1[/tex]) or simply √n = O(n).
The smallest integer k such that √n = O([tex]n^k[/tex]) can be determined by comparing the growth rates of the functions. In this case, we want to find the value of k that makes the function √n grow at most as fast as n^k.
The square root function, √n, is less complex than any positive integer power of n. In other words, as n becomes large, any positive integer power of n will grow faster than the square root of n. To satisfy the condition √n = O([tex]n^k[/tex]), we need to find the smallest integer value of k such that[tex]n^k[/tex] grows faster than √n.
Since k must be an integer, the smallest possible value is k = 1. This means we are comparing the growth rates of √n and n^1 (which is simply n). As n becomes large, n will indeed grow faster than √n.
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an urn contains one red and one black ball. each time, a ball is drawn independently at random from the urn, and then returned to the urn along with another ball of the same color. for example, if the first ball drawn is red, the urn will subsequently contain two red balls and one black ball. what is the probability of observing the sequence r,b,b,r,r?
Answers
The probability of observing the sequence r, b, b, r, r in the given scenario is 1/120.
To find the probability of observing the sequence r, b, b, r, r in the given scenario, we can break it down step by step:
Probability of drawing the first ball as red (r):
Since the urn initially contains one red and one black ball, the probability of drawing a red ball is 1/2.
Probability of drawing the second ball as black (b) after the first ball was red:
After drawing the first red ball, it is returned to the urn along with another red ball, so the urn now contains two red balls and one black ball.
The probability of drawing a black ball is 1/3.
Probability of drawing the third ball as black (b) after the previous sequence was r, b:
After drawing the second black ball, it is returned to the urn along with another black ball, so the urn now contains two red balls and two black balls.
The probability of drawing a black ball is now 2/4 = 1/2.
Probability of drawing the fourth ball as red (r) after the previous sequence was r, b, b:
After drawing the third black ball, it is returned to the urn along with another black ball, so the urn still contains two red balls and two black balls.
The probability of drawing a red ball is 2/4 = 1/2.
Probability of drawing the fifth ball as red (r) after the previous sequence was r, b, b, r:
After drawing the fourth red ball, it is returned to the urn along with another red ball, so the urn now contains three red balls and two black balls.
The probability of drawing a red ball is 3/5.
To find the overall probability of observing the sequence r, b, b, r, r, we multiply the probabilities of each individual step:
[tex]P(r, b, b, r, r) = (1/2) \times (1/3) \times (1/2) \times (1/2) \times (3/5)[/tex]
= 1/120.
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What transformation of Figure 1 results in Figure 2?
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A transformation of Figure 1 results in Figure 2 will be rotation.
Picture, after translation, refers to the object's ultimate organization and placement.
Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.
Rotation in math involves rotating a figure around a fixed point by a certain angle. This can be done clockwise or counterclockwise and is typically measured in degrees.
Figure 1 is rotated to form Figure 2.
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find the area of the surface the part of the sphere x^2+y^2+z^2 = b^2 that lies inside the cylinder x^2+y^2 = a^2 where 0
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To find the area of the surface, we will use the formula. Therefore, the area of the surface is $\frac{4\pi}{3}(b^2-a^2)$.
$A=\iint\limits_{S},dS$
where $S$ is the surface of the sphere inside the cylinder.
Since the surface of the sphere and the cylinder are both symmetric about the $z$-axis, we can use cylindrical coordinates.
$x=r\cos\theta, y=r\sin\theta, z=z$
The sphere has the equation $x^2+y^2+z^2=b^2$, so substituting the cylindrical coordinates we get:
$r^2+z^2=b^2$
The cylinder has the equation $x^2+y^2=a^2$, so substituting the cylindrical coordinates we get:
$r^2=a^2$
The limits of integration for $r$ are from $0$ to $a$, and for $\theta$ are from $0$ to $2\pi$. The limits of integration for $z$ are from $-\sqrt{b^2-r^2}$ to $\sqrt{b^2-r^2}$.
$A=\int\limits_{0}^{2\pi}\int\limits_{0}^{a}\sqrt{1+(\frac{\partial z}{\partial r})^2+(\frac{\partial z}{\partial\theta})^2},r,dr,d\theta$
$\frac{\partial z}{\partial r}=\frac{-r}{\sqrt{b^2-r^2}}$, and $\frac{\partial z}{\partial\theta}=0$.
$A=\int\limits_{0}^{2\pi}\int\limits_{0}^{a}\sqrt{1+\frac{r^2}{b^2-r^2}},r,dr,d\theta$
Letting $u=\frac{r^2}{b^2-r^2}$, we have $\frac{du}{dr}=\frac{2b^2}{(b^2-r^2)^2}$, and so $du=\frac{2b^2}{(b^2-r^2)^2},r,dr$. Substituting $u$ and $du$ we get:
$A=\int\limits_{0}^{2\pi}\int\limits_{0}^{\frac{a^2}{b^2-a^2}}\sqrt{1+u},du,d\theta$
Using the substitution $v=1+u$, we get $dv=du$, and so:
$A=\int\limits_{0}^{2\pi}\int\limits_{1}^{1+\frac{a^2}{b^2-a^2}}\sqrt{v},dv,d\theta$
$A=\int\limits_{0}^{2\pi}\frac{2}{3}(1+\frac{a^2}{b^2-a^2})^{\frac{3}{2}},d\theta$
$A=\frac{4\pi}{3}(b^2-a^2)$
Therefore, the area of the surface is $\frac{4\pi}{3}(b^2-a^2)$.
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find the particular solution of the differential equation. dy dx=−9x8e−x9;
Answers
The particular solution is y = (-9/8) * (9x + 81) e^(-x/9) + 85.125.
To solve this differential equation, we can use separation of variables.
dy/dx = -9x/8 e^(-x/9)
dy = (-9/8)x e^(-x/9) dx
Integrating both sides, we get:
y = (-9/8) * (9x + 81) e^(-x/9) + C
where C is the constant of integration.
To find the particular solution, we need to use the initial condition. Let's say that y(0) = 4.
Then, when x = 0, we have:
4 = (-9/8) * (0 + 81) e^(0) + C
C = 4 + (9/8) * 81
C = 85.125
Therefore, the particular solution is:
y = (-9/8) * (9x + 81) e^(-x/9) + 85.125
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if p(e∩f)=0.012, p(e|f)=0.06, and p(f|e)=0.6, thenP(E) P(E U F) Are E and F independent? Why?
Answers
The probability of E is not given, but P(E U F) can be calculated using the formula P(E U F) = P(E) + P(F) - P(E ∩ F).
From the given information, P(E ∩ F) = P(F|E) * P(E) = 0.6 * P(E) and P(E|F) = P(E ∩ F) / P(F) = 0.012 / P(F). Using Bayes' theorem, P(F|E) = P(E|F) * P(F) / P(E) = 0.06 * P(F) / P(E), which can be simplified to P(F) = 0.1 * P(E). Substituting these values into the formula for P(E U F), we get P(E U F) = P(E) + 0.1 * P(E) - 0.012 = 1.1 * P(E) - 0.012. Therefore, we cannot determine if E and F are independent without knowing the probability of E.
Two events E and F are independent if and only if P(E ∩ F) = P(E) * P(F). In this case, we have P(E ∩ F) = 0.012, which is not equal to P(E) * P(F) = P(E) * 0.1 * P(E) = 0.1 * P(E)^2, since P(E) is not given. Therefore, we cannot conclude that E and F are independent.
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for the model yi = β1 β2xi ui, define the fitted value ˆyi and residual ˆui.
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The model yi = β1 + β2xi ui is a linear regression model that describes the relationship between a response variable yi and a predictor variable xi. In this model, β1 and β2 are the intercept and slope coefficients, respectively, while ui represents the error term.
The fitted value ˆyi is the predicted value of yi based on the linear regression model. It is calculated as the sum of the intercept and the product of the slope coefficient and the predictor variable: ˆyi = β1 + β2xi.
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