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Related Questions
Place each function below in the appropriate cell to show the transformation from f to g. (Desmos)
Answers
Answer:
First row: 2,1
Second row: 3,4
according to a survey taken at an amusement park about visitors favorite rides. 15 of the (15/50) visitors surveyed like the roller coasters the best. What percent of people chose the roller coasters their favorite ride
Answers
Answer:
30%
Step-by-step explanation:
A recent Gallup poll asked American adults if they had COVID-19 symptoms, would they avoid seeking treatment due to the high costs of healthcare? The poll contained a sample of 1,017 American adults and 143 of them said they would avoid seeking treatment due to the high costs of healthcare. Construct the 95% confidence interval for the proportion of the American adult population who would avoid seeking treatment for COVID-19 due to the high costs of healthcare.
What is N in this study? _____
What is P in this study? _____
Answers
The solution to the given problem is as follows:N in this study = 1017P in this study = 143/1017 = 0.1407 (rounded to 4 decimal places)
Given, the sample size n = 1017, and the sample proportion of people who would avoid seeking treatment due to high healthcare costs = 143/1017 = 0.1407
Since we need to calculate the 95% confidence interval for the proportion of the American adult population who would avoid seeking treatment for COVID-19 due to the high costs of healthcare, we need to calculate the standard error of the proportion.
The formula to calculate the standard error of the proportion is:
Standard error of the proportion = sqrt [ p * (1 - p) / n ]
Substituting the values, we get:
Standard error of the proportion = sqrt [ 0.1407 * (1 - 0.1407) / 1017 ]= 0.0141 (rounded to 4 decimal places)
To calculate the 95% confidence interval, we use the following formula:
95% confidence interval = sample proportion ± margin of error
Margin of error = Z * (standard error of the proportion)
where Z is the Z-score corresponding to the confidence level.
For 95% confidence level, Z = 1.96.
Substituting the values, we get:
Margin of error = 1.96 * 0.0141= 0.0276 (rounded to 4 decimal places)
Therefore, the 95% confidence interval for the proportion of the American adult population who would avoid seeking treatment for COVID-19 due to the high costs of healthcare is given by:
0.1407 ± 0.0276= (0.1131, 0.1683) (rounded to 4 decimal places)
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fx=x-2, state the domain and range for the function and its inverse. Write each step.
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The function f(x) = x - 2 has a domain of all real numbers and a range of all real numbers. Its inverse function, f^(-1)(x), also has a domain and range of all real numbers.
The domain of a function represents the set of all possible input values for the function. In the case of f(x) = x - 2, since there are no restrictions or limitations on the input variable x, the domain is all real numbers.
To find the range of the function, we consider the possible output values. The function f(x) = x - 2 is a linear function with a slope of 1. It means that for any input value of x, the output value will be that input value minus 2. Therefore, the range is also all real numbers.
To find the inverse function, we swap the roles of the input and output variables and solve for the new output variable. For the given function, we have f(x) = x - 2. Replacing f(x) with y, we get the equation y = x - 2. To find the inverse, we isolate x:
x = y + 2
Now, we replace x with the inverse function notation f^(-1)(x) and y with x:
f^(-1)(x) = x + 2
The inverse function has the same domain and range as the original function, which is all real numbers.
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Intuitively, a larger sample should lead to a smaller confidence interval (fixing the level of confidence). Which of the following most accurately gives a reason for this in the mathematics we use to make the confidence interval? And the t'-value associated to the t-distribution goes down because t_n have "smaller tails" as n gets large. (And other aspects remain the same.)r The standard error goes down because of the greater sample size in the denominator. (And other aspects remain the same.) The standard error goes down because the standard deviation of the sample will go down. And the t*-value associated to the t-distribution goes down because t_n have "smaller tails" as n gets large. O The standard error goes down because the standard deviation of the sample will go down. (And other aspects remain the same.) The mean will be more accurate with a larger sample size. The standard error goes down because of the greater sample size in the denominator. And the t-value associated to the t-distribution goes down because t_n have "smaller tails" as n gets large.
Answers
Intuitively, a larger sample should lead to a smaller confidence interval (fixing the level of confidence). The following most accurately gives a reason for this in the mathematics we use to make the confidence interval:
The standard error goes down because of the greater sample size in the denominator. (And other aspects remain the same.) And the t'-value associated to the t-distribution goes down because t_n have "smaller tails" as n gets large. This is true.
The standard error goes down because of the greater sample size in the denominator. This is because the formula for the standard error involves taking the square root of the sample size in the denominator. Therefore, as the sample size increases, the denominator of the standard error formula increases, causing the standard error to decrease. And the t'-value associated to the t-distribution goes down because t_n have "smaller tails" as n gets large. This is because the t-distribution is symmetrical and bell-shaped, with fatter tails than the normal distribution. As the sample size n increases, the t-distribution approaches the normal distribution, with thinner tails, which means that the t-values become smaller as n increases.
Hence, the correct option is (O) The standard error goes down because the standard deviation of the sample will go down. (And other aspects remain the same.) The mean will be more accurate with a larger sample size. The standard error goes down because of the greater sample size in the denominator. And the t-value associated with the t-distribution goes down because t_n has "smaller tails" as n gets large.
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Three of these fractions are equivalent: B. 12 C . 21 D. 74 30 A. . 70 Which one is the odd one out?
Answers
Answer:
12/30
Step-by-step explanation:
Here is the complete question
Three of these fractions are equivalent A.30/70 B.12/30 C.9/21 D.6/14 which one is the odd one out
to determine the equivalent fractions, convert the fractions to percentage
[tex]\frac{30}{70}[/tex] × 100 = 42.86%
[tex]\frac{12}{30}[/tex] × 100 = 40%
[tex]\frac{9}{21}[/tex] × 100 = 42.86%
[tex]\frac{6}{14}[/tex] x 100 = 42.86%
Another method is to convert the fraction to its simplest form
30/70
To transform to the simplest form. divide both the numerator and the denominator by 10 = 3/7
12/30
To transform to the simplest form. divide both the numerator and the denominator by 6 = 2/5
9/21
To transform to the simplest form. divide both the numerator and the denominator by 3 = 3/7
6/14
To transform to the simplest form. divide both the numerator and the denominator by 2 = 3/7
Using either methods, 12/30 is the odd one out
can someone please help me find the slope on khan academy? and please provide an explanation if possible
Answers
Answer: 7/4
Step-by-step explanation: To find the slope of a line, pick any two integer points, in this scenario the only two are (3,4) and (-1,-3). The slope is the rise over run, so think about it. To get from (-1,-3) to )3,4) you need to rise 7 units (difference in y coordinates) and from there you need to run 4 units, so it is 7/4. Keep in mind that rising up is positive for y and running to the right is positive for x.
Answer:
[tex]\frac{7}{4}x[/tex]
Step-by-step explanation:
How do you find slope on a graph? The slope is "rise/run" where "rise" is how much y spaces are moved to the next point and "run" is the how much spaces are moved to the next x point.
Step One: In this case, the point moves up 7 spaces to the next point, so that's the "rise" and then it moves 4 spaces to the right to the next point, so that's the "run"
Step Two: When we put it together, it is 7/4x. The x is just an indication that this is slope, and you don't have to worry about it until you learn how to plug it in.
31. Which equation can be used to describe the relationship between x and y shown in the graph below?
Study the graph below...
A. y = 45x − 1
B. y = −45x − 1
C. y = 54x − 1
D. y = −54x − 1
Answers
Please explain steps
= If two events A and B are collectively exhaustive with P(A) = P(B). Given, P(AUB) = 0.60, find P(AB). =
Answers
The question asks us to find P(AB) given that A and B are collectively exhaustive events with P(A) = P(B) and P(AUB) = 0.60.
This means that A and B are mutually exclusive, and they together represent the entire sample space. Therefore, we can write the following equations: P(A) + P(B) = 1 (Collectively exhaustive events)
P(A) = P(B) (Given)P(AUB) = P(A) + P(B) - P(AB) (Addition rule of probability)
We know that P(AUB) = 0.60 and P(A) = P(B).
Substituting these values in the above equations, we get:
0.60 = 2P(A) - P(AB) ...(1)P(A) + P(B) = 1P(A) + P(A) = 1 (P(A) = P(B))2P(A) = 1P(A) = 1/2
Substituting P(A) in equation (1), we get:0.60 = 2(1/2) - P(AB)P(AB) = 1 - 0.60P(AB) = 0.40
Therefore, P(AB) = 0.40.
Hence, this is the required answer.
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A cat is stuck in the tree and the fire department needs a ladder to rescue the cat. The fire truck available has a 95-foot ladder, which starts 8 feet above ground. Unfortunately, the fire truck must park 75 feet away from the tree. If the cat is 60 feet up the tree, does the cat get rescued? If not, what ladder length is need to allow the cat to be rescued?
Group of answer choices
A. No because an 117-foot ladder is needed but the truck has only a 95-foot ladder.
B. No because an 96-foot ladder is needed but the truck has only a 95-foot ladder.
C. Yes because only a 75-foot ladder is needed and the truck has a 95-foot ladder.
D. Yes because only a 91-foot ladder is needed and the truck has a 95-foot ladder.
Answers
Answer:
I guess the ans d is correct because using pythagoras theorem we get 91.26 ft .
which of the following are least likely to be primary means of investigating normality in a distribution X?
a. graphically you data in a histogram and use eyeball to test to see if there in any asymmetry or skew
b. observe a computerized output for the Q-Q plot of the distribution
c. calculate the observed and expected z score values and determine any major deviations
d. start with a normal approximation as most variables are normal
Answers
d. "Start with a normal approximation as most variables are normal" is least likely to be primary means of investigating normality in a distribution X.
How to analyze all the options?
a. Graphically plot the data in a histogram and use the eyeball test to check for asymmetry or skew. This method involves visually examining the shape of the distribution by creating a histogram. Any noticeable asymmetry or skewness can indicate non-normality.
b. Observe a computerized output for the Q-Q plot of the distribution. A Q-Q plot compares the quantiles of the observed data with the quantiles of a theoretical distribution, such as the normal distribution. If the points on the Q-Q plot closely follow a straight line, it suggests the data is normally distributed.
c. Calculate the observed and expected z-score values and determine any major deviations. By transforming the data into z-scores and comparing them to the expected values under a normal distribution, deviations from normality can be identified. Significant deviations indicate departures from normality.
d. Start with a normal approximation as most variables are normal. This option suggests assuming normality without conducting specific tests or employing appropriate techniques to assess normality. While this approach may be reasonable in certain cases based on prior knowledge or theoretical considerations, it lacks a direct means of investigating normality.
d. "Start with a normal approximation as most variables are normal" is least likely to be primary means of investigating normality in a distribution X.
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Hybrid and electric cars have gained in popularity in the last decade as a consequence of high gas prices. But their great gas mileages often come with higher car prices. There may be savings, but how much and how long before those savings are realized? Suppose you are considering buying a Honda Accord Hybrid, which starts around $31,665 and gets 48 mpg. A similarly equipped Honda Accord will run closer to $26,100 but will get 31 mpg. How long would it take for the Prius to recoup the price difference with its lower fuel costs, assuming you drive 800 miles per month? First, use the following formula for gas savings, where GM stands for gas mileage, to determine how far you will need to drive to recoup the cost difference in the vehicles. Use the known values and the average price of gas in your area to write a specific equation. $Gas is $4.35 Determine the type of equation that results, and then solve it algebraically. $Saved = $Gas x (distance driven) x ( GM now GM improved) Choose a Tesla (electric car) that has NO gas cost and compare it in a similar way to a gas-powered cari, the Honda Accord. How long will it take to recoup the price difference for the miles you drive per month? Assume you still drive 800 miles a month. Be sure to consider TOTAL COST of each car. Explain what you thought TOTAL COST meant in the previous question.
Answers
The Honda Accord Hybrid would recoup the price difference with its lower fuel costs in approximately 6.8 years when driving 800 miles per month.
How long does it take for the Honda Accord Hybrid to recover the price difference with its lower fuel costs, assuming a monthly mileage of 800 miles?The Honda Accord Hybrid, priced at $31,665, has a fuel efficiency of 48 mpg, while the gas-powered Honda Accord, priced at $26,100, has a fuel efficiency of 31 mpg. To determine the distance that needs to be driven to recoup the cost difference, we can use the formula: $Saved = $Gas x (distance driven) x (GM now / GM improved). Considering the average gas price of $4.35, we can substitute the values into the formula and solve for the distance driven.
Using algebraic calculations, we find that the distance needed to recoup the price difference is approximately 50,472 miles. With a monthly mileage of 800 miles, it would take approximately 63 months or 6.8 years to recover the cost difference between the two vehicles.
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You are to create a password using 8 letters from the alphabet (repetition allowed). What is the probability that no letter is repeated if the letters were randomly chosen to be in the password?
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The probability that no letter is repeated in the password is approximately 0.0000194293, or about 0.0019%.
To calculate the probability that no letter is repeated in a password created using 8 letters from the alphabet (repetition allowed), we need to consider the total number of possible passwords and the number of passwords without repeated letters.
The number of possible passwords can be calculated by considering that each letter in the password can be chosen independently from the 26 letters in the alphabet. Therefore, there are 26 choices for each of the 8 positions, resulting in a total of 26^8 possible passwords.
To calculate the number of passwords without repeated letters, we can consider the choices for each position. For the first position, we have 26 options. For the second position, we have 25 options (since we cannot repeat the letter chosen for the first position). Similarly, for the third position, we have 24 options, and so on.
Using the multiplication principle, the number of passwords without repeated letters is given by 26 * 25 * 24 * 23 * 22 * 21 * 20 * 19.
Therefore, the probability that no letter is repeated in the password can be calculated as:
Probability = (Number of passwords without repeated letters) / (Total number of possible passwords)
= (26 * 25 * 24 * 23 * 22 * 21 * 20 * 19) / (26^8)
Calculating this probability:
Probability ≈ 0.0000194293
So, the probability that no letter is repeated in the password is approximately 0.0000194293, or about 0.0019%.
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What is the area of this triangle in the coordinate plane? 5 units 6 units 7 units 12 units?
Answers
Answer:
6 units
Step-by-step explanation:
Using readings taken from the coordinate upon which the triangle is drawn :
The area of triangle is given as :
Area of triangle = 0.5 * base * height
The base of the triangle = 4 units
The height of the triangle = 3 units
The Area of the triangle is thus :
0.5 * 4 * 3
0.5 * 12
= 6 units
Answer:
The area of the given triangle is 6 units²
the sixth term is 22 and the common difference is 6 what is the 15th term?
Answers
Answer:
76
Step-by-step explanation:
I made a chart to simplify it
1 | -8
2| -2
3| 4
4| 10
5| 16
6| 22
7| 28
8| 34
9| 40
10| 46
11| 52
12| 58
13| 64
14| 70
15| 76
If a hotel has 33 king-size beds, 24 queen-size beds, 25 double beds, and 24 twin beds, what is the probability that you will be given a queen-size or a twin-bed when you register, if the beds are chosen randomly?
Answers
The probability of being given a queen-size or a twin bed when registering is approximately 0.453 or 45.3%.
To calculate the probability of being given a queen-size or a twin bed, we need to determine the total number of queen-size and twin beds available, as well as the total number of beds overall.
Total number of queen-size beds = 24
Total number of twin beds = 24
Total number of beds = 33 (king-size) + 24 (queen-size) + 25 (double) + 24 (twin) = 106
To calculate the probability, we divide the number of favorable outcomes (queen-size or twin bed) by the number of possible outcomes (total number of beds).
Number of favorable outcomes = Number of queen-size beds + Number of twin beds = 24 + 24 = 48
Probability = Number of favorable outcomes / Total number of beds
Probability = 48 / 106 ≈ 0.453
Therefore, the probability of being given a queen-size or a twin bed when registering is approximately 0.453 or 45.3%.
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The atmospheric pressure on an object decreases as altitude increases. If a is the height (in km) above sea level,
then the pressure P(a) (in mmHg) is approximated by P(a) = 760e-0.13a. Determine the atmospheric pressure at
8.47 km. Round to the nearest whole unit.
Answers
Answer:
253 mmHg
Step-by-step explanation:
Since the atmospheric pressure, [tex]P(a) = 760e^{-0.13a}[/tex]
when a = height (in km) = 8.47 km, then the atmospheric pressure P(a) is
[tex]P(a) = 760e^{-0.13a}\\P(8.47) = 760e^{-0.13X8.47}\\P(8.47) = 760e^{-1.1011} \\P(8.47 )= 760 X 0.33251 \\P(8.47)= 252.7 mmHg\\[/tex]
P(8.47) ≅ 253 mmHg
What is the value of A when we rewrite 3^x as A^5x
Answers
The value of A when we rewrite 3^x as A^5x is 3^⅕
We have given that,
The value of A when we rewrite 3^x as A^5x.
What is power?The power (or exponent) of a number says how many times to use the number in a multiplication. It is written as a small number to the right and above the base number.
3^x
(3^⅕)^(5x)
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Answer:
3^1/5
Step-by-step explanation:
3yd 4yd what is the length of the hypotenuse
Answers
Answer:
5 yd
Step-by-step explanation:
Use Pythagorean theorem,
Hypotenuse² = base² + altitude²
= 3² + 4²
= 9 + 16
= 25
Hypotenuse = √25 = √5*5 = 5 yd
The sequence an = 5, an+1 = an + 8, a > 1 is an example of which of the following? a. a recursively-defined geometric sequence. b. none of these. c. a variation of the recursively-defined Factorial sequence. d. a recursively-defined arithmetic sequence. e. a recursively-defined Fibonacci-like sequence.
Answers
The sequence an = 5, an+1 = an + 8, a > 1 is an example of a recursively-defined arithmetic sequence. It does not fit the definitions of a geometric sequence, factorial sequence, or Fibonacci-like sequence. The correct option is (d) a recursively-defined arithmetic sequence.
An arithmetic sequence is characterized by a common difference between consecutive terms. In this case, each term (an+1) is obtained by adding a constant value of 8 to the previous term (an).
This satisfies the definition of an arithmetic sequence.
While the sequence does not fit the definition of a geometric sequence, factorial sequence, or Fibonacci-like sequence, it does follow the pattern of an arithmetic sequence.
The terms increase by a constant value of 8 with each step, making it a recursively-defined arithmetic sequence.
Therefore, the correct option is (d) a recursively-defined arithmetic sequence.
Note: A geometric sequence would have a common ratio between consecutive terms, which is not the case here. The factorial sequence involves multiplying terms by consecutive positive integers, and a Fibonacci-like sequence follows the pattern of adding the previous two terms to obtain the next term.
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What is the IQR of the data set below?
15, 13, 25, 18, 15, 12, 10, 35, 30, 52,
Answers
Answer:
17
Step-by-step explanation:
IQR = Q3 - Q1
1st Quartile: 13
3rd Quartile: 30
IQR = 30 - 13 = 17
3 Write down the gradient of each line segment.
Answers
Answer:
One on the left = -1
One on the right = 1/3
Step-by-step explanation:
[tex]slope=\frac{rise}{run}[/tex]
One on the left = [tex]\frac{-3}{3} =-1[/tex]
One on the right = [tex]\frac{1}{3} =\frac{1}{3}[/tex]
The gradient of the first line and the second line will be 1 and 1/3, respectively.
What is the slope?The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.
The slope of the line is given as,
m = (y₂ - y₁) / (x₂ - x₁)
The gradient of the first line is given as,
m = 3 / 3
m = 1
The gradient of the second line is given as,
m = 1 / 3
The gradient of the first line and the second line will be 1 and 1/3, respectively.
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Landon is going to invest in an account paying an interest rate of 4.3%
compounded continuously. How much would Landon need to invest, to the
nearest hundred dollars, for the value of the account to reach $11,300 in 14
years?
Answers
Answer:
$6,100
Step-by-step explanation:
So to solve this problem, let's give the amount of money the variable "x". We just need to do x - 0.043 × x. Then we replace x with our answer and repeat the process 13 more times.
Answer:
$6200
Step-by-step explanation:
Suppose you are interested in learning about how much time seventh grade students at your school spend outdoors on a typical school day. Select all the samples that are a part of the population you are interested in. a. The 20 students in a seventh grade math class. b. The first 20 students to arrive at school on a particular day. c. The seventh grade students participating in a science fair put on by the four middle schools in a school district. d. The 10 seventh graders on the school soccer team. e. The students on the school debate team.
Answers
Answer:
1. The 20 students in a seventh grade math class.
4. The 10 seventh graders on the school soccer team.
Step-by-step explanation:
I just submitted the form and these are the right answers :)
It might be not on time but still lol.
I AM SURE THOSE ARE RIGHT ANSWERS !!! :)))
The 20 students in a seventh grade math class, the seventh grade students participating in a science fair put on by the four middle schools in a school district and the 10 seventh graders on the school soccer team are the samples.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
The samples that are a part of the population of interest, which is seventh grade students at your school, are:
The 20 students in a seventh grade math class.
The seventh grade students participating in a science fair put on by the four middle schools in a school district (if the students are from your school).
The 10 seventh graders on the school soccer team (if they are from your school).
The samples that are not a part of the population of interest are:
The first 20 students to arrive at school on a particular day (as this may include students from different grades or schools).
The students on the school debate team (as this may include students from different grades or schools).
Hence, the 20 students in a seventh grade math class, the seventh grade students participating in a science fair put on by the four middle schools in a school district and the 10 seventh graders on the school soccer team are the samples
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( Need help !!!!!!!!!! Pls )
Answers
Gavyn was thinking of a number. Gavyn doubles it, then adds 14 to get an answer of 17.2. What was the original number?
Answers
Answer:
Original number we'll call "x".
2x + 14 = 17.2
x = 1.6
Step-by-step explanation:
Answer:
Original number we'll call "x".
2x + 14 = 17.2
x = 1.6
Step-by-step explanation:
Learn
1. A psychologist was interested in the effect of Vitamin A deficiency on maze learning rats. A group of nine rats learned a simple maze. Next, these same rats were deprived of Vitamin A for six weeks and were then tested again on their ability to learn a second maze equal in difficulty to the first. The scores represent the number of maze errors made under the two treatment conditions. Perform an appropriate two-tailed test of the significance of the mean difference.
Answers
Answer: hello your question has some missing information attached below is the missing information
we fail to reject H0 hence μ1 = μ2mean difference ( d ) = -2.444Step-by-step explanation:
H0 : μ1 = μ2
Ha : μ1 ≠ μ2
where : μ1 = mean number of errors made in pretest
μ2 = mean number of errors made in post test
n = 9
attached below is the detailed solution
ill give brainliest
Your options are:
A. 115
B. 42
C. 159
D. 21
Answers
Answer:
the answer is D
Step-by-step explanation:
3x-21=x+7
2x-21=7
2x=28
x=14
substitute x for 14
14+7=21
2X14-21+21
Write down the formula for calculating an unbiased estimate, Sry, of the covariance coefficient of variables x and y of a large (but finite) population, based on a random sample of n items. Define any symbols you use.
Answers
The formula for calculating an unbiased estimate
of the covariance coefficient of variables x and y of a large (but finite) population, based on a random sample of n items is:
(1/n-1) * ∑(Xi - X bar) * (Yi - Y bar)`,
where Xi and Yi are the values of the it h observation of x and y, X bar and Y bar are the means of x and y, respectively, and n is the sample size.
If we have to get an unbiased estimate of the covariance coefficient of variables x and y of a large (but finite) population, based on a random sample of n items, then we can use the formula:
(1/n-1) * ∑(Xi - X bar) * (Yi - Y bar)
where, the unbiased estimate of the covariance coefficient of x and y
Xi = the value of the it h observation of x
Yi = the value of the it h observation of y
X bar = the mean of x
Y bar = the mean of y
n = the sample size of the population
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Which of the following is the Laplace transformation L {f(t)} if f(t)=(sin(-4t) 2 ? 32 33 +645 O None of them s2 $4 + 3252 +256 $+32 S + 64s ) 16 54 + 3252 +256
Answers
The Laplace transform of f(t) = (sin(-4t))^2 is not among the given options.
The Laplace transform of f(t) = (sin(-4t))^2 is none of the given options. Let's find the correct Laplace transform for the given function.
The Laplace transform of a function f(t) is denoted as L{f(t)} and is defined as:
L{f(t)} = ∫[0 to ∞] f(t) * e^(-st) dt,
where s is the complex variable.
In this case, f(t) = (sin(-4t))^2. To find its Laplace transform, we need to apply the definition of the Laplace transform and evaluate the integral:
L{f(t)} = ∫[0 to ∞] (sin(-4t))^2 * e^(-st) dt.
However, before proceeding with the integration, we can simplify the function using trigonometric identities:
(sin(-4t))^2 = (-sin(4t))^2 = sin^2(4t).
Now, we can rewrite the Laplace transform as:
L{f(t)} = ∫[0 to ∞] sin^2(4t) * e^(-st) dt.
At this point, we can utilize a well-known trigonometric identity that relates the square of the sine function to a combination of 1 and cosine functions:
sin^2(θ) = (1 - cos(2θ))/2.
Applying this identity to our expression:
L{f(t)} = ∫[0 to ∞] (1 - cos(8t))/2 * e^(-st) dt.
Now, we can split this integral into two parts and simplify further:
L{f(t)} = (1/2) ∫[0 to ∞] e^(-st) dt - (1/2) ∫[0 to ∞] cos(8t) * e^(-st) dt.
The first integral represents the Laplace transform of 1, which is 1/s:
L{f(t)} = (1/2) * (1/s) - (1/2) ∫[0 to ∞] cos(8t) * e^(-st) dt.
The second integral can be evaluated using standard Laplace transform formulas. However, without additional information or constraints on the Laplace transform variable 's', we cannot simplify it further.
To know more about the Laplace transform, click here;
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