P = ∫(i^2 dl / 6πε0 c^3) × a^2
where q is the charge, ε0 is the permittivity of free space, c is the speed of light, and a is the acceleration of the charge.
Now consider a small element of length dl around the ring through which the current i flows. The power radiated from this element can be written as
dP = (i^2 dl / 6πε0 c^3) × a^2
where a is the acceleration of the charge in the element due to the changing magnetic field.
The total power radiated from the entire ring is obtained by integrating this expression over the length of the ring.
P = ∫(i^2 dl / 6πε0 c^3) × a^2
This is the general expression for the radiated power of the current distribution around the ring.
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Suppose that during its flight, the elevation e (in feet) of a certain airplane and its time t, in minutes since takeoff, are related by a linear equation. Consider the graph of this equation, with time represented on the horizontal axis and elevation on the vertical axis. For each situation, decide if the slope is positive, zero, or negative.
Step-by-step explanation:
Suppose that during its flight, the elevation e (in feet) of a certain airplane and its time t, in minutes since takeoff, are related by a linear equation. Consider the graph of this equation, with time represented on the horizontal axis and elevation on the vertical axis. For each situation, decide if the slope is positive, zero, or negative.
cruising: zero slope
descending: negative slope
ascending: positive slope
annual coal production in the us in billion tons per year is given in the table. estimate hte total amount of coal produced in the US between 1997 and 2009. If r = f (t) is the rate of coal production t years since 1997, write an integral to represent the 1997 - 2009 coal production.Year : 1997 1999 2001 2003 2005 2007 2009Rate : 1.090 1.094 1.121 1.072 1.132 1.147 1.073
The integral is thus. [tex]\int\limits{f(t)} \, dt[/tex]and limits will be 14 and 0
Describe statistics using an example.
A statistic is a numerical expression of a sample characteristic. The average amount of points obtained by students in one math class at the conclusion of the term, for instance, is an example of a statistic if we see that class as a sample of the population of all math classes.
Estimating the entire amount of coal generated in the US between 1997 and 2009 is the goal.
The information shows how much cola is produced year, in billions of tons.
The right-hand sum and the left-hand sum must be calculated in order to estimate the amount of coal produced.
with n = 7 and a hand sum
(2009 - 1997)/7 = Delta*t
The difference between every two years in the table is 2, which is another way to calculate Ar. So. t*delta = 2
The total on the left is.
The formula is: Delta*t[1.09 + 1.094 + 1.121 + 1.072 + 1.132 + 1.147] = 2[1.09 + 1.094 + 1.121 + 1.072 + 1.132 + 1.147] =13.312.
The amount on the right is.
Delta*I[1.094 plus 1.121 plus 1.072 plus 1.132 plus 1.147 plus 1.073] = 2[1.094 plus 1.121 plus 1.072 plus 1.132 + 1.147 + 1.073] = 13.278
Thus, using the left-hand addition, the total amount of coal produced in the United States between 1997 and 2009 is 13.312; using the right-hand sum, it is 13.278.
To show the production of coal from 1997 to 2009, create an integral.
Production of coal lasted for 14 years, from 1997 to 2009 (2009 – 1997 = 14). As r = f(t) (t).
The integral is thus. [tex]\int\limits{f(t)} \, dt[/tex]and limits will be 14 and 0
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find the increasing and decreasing intervlas for the funtion below
f(x)= (x^2-4)^2/3
Answer:
Increasing on the interval: (-2, 0) ∪ (2, ∞)
Decreasing on the interval: (-∞, -2) ∪ (0, 2)
Step-by-step explanation:
A function is increasing when f'(x) > 0
A function is decreasing when f'(x) < 0
Therefore, to find the intervals for which the function is increasing and decreasing, differentiate the given function.
[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule for Differentiation}\\\\If $y=f(u)$ and $u=g(x)$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}y}{\text{d}u}\times\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}[/tex]
Given function:
[tex]f(x)=(x^2-4)^{\frac{2}{3}}[/tex]
[tex]\begin{aligned}\textsf{Let} \; u &= (x^2-4) \quad &\implies y&=u^{\frac{2}{3}}\\\\\implies \dfrac{\text{d}u}{\text{d}x}&=2x \quad &\implies \dfrac{\text{d}y}{\text{d}u}&=\dfrac{2}{3}u^{-\frac{1}{3}}=\dfrac{2}{3} (x^2-4)^{-\frac{1}{3}}\end{aligned}[/tex]
Therefore:
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}y}{\text{d}u}\times\dfrac{\text{d}u}{\text{d}x}[/tex]
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{2}{3} (x^2-4)^{-\frac{1}{3}} \times 2x[/tex]
[tex]\implies f'(x)=\dfrac{4}{3}x (x^2-4)^{-\frac{1}{3}}[/tex]
[tex]\implies f'(x)=\dfrac{4x}{3 \sqrt[3]{x^2-4}}}[/tex]
Stationary points occur when f'(x) = 0:
[tex]\implies \dfrac{4x}{3 \sqrt[3]{x^2-4}}}=0[/tex]
[tex]\implies 4x=0[/tex]
[tex]\implies x=0[/tex]
Therefore, the function has is a stationary point (turning point) when x = 0.
The derivative is undefined when the denominator equals zero.
The denominator equals zero when x² = 4, so when x = ±2.
The derivative is positive when x > 2 and negative when x < -2.
Therefore, determine the nature of the derivative in the intervals between the stationary point x = 0 and x = ±2.
[tex]\implies f'(-1)=\dfrac{4(-1)}{3 \sqrt[3]{(-1)^2-4}}}=\dfrac{\rm negative}{\rm negative}= \rm positive > 0[/tex]
[tex]\implies f'(1)=\dfrac{4(1)}{3 \sqrt[3]{(1)^2-4}}}=\dfrac{\rm positive}{\rm negative}= \rm negative < 0[/tex]
Therefore, the function is:
Increasing on the interval: (-2, 0) ∪ (2, ∞)Decreasing on the interval: (-∞, -2) ∪ (0, 2)A+B=13 C/B=10 A+B+C=33 ABC?
Answer:
440
Step-by-step explanation:
a=11
b=2
c=20
a*b*c=
11*2*20 = 440
percent increase 60 to 99? please give right answer
Answer:
65%
Step-by-step explanation:
If I’m wrong please feel free to report me
Exhibit 8-1 91 In order to estimate the average time spent on the computer terminals per student at a local university data were collected from a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.2 hours. (SPOINTS) The standard error of the meanis a. 7.3 6..014 c..160 With a 95 probability, the margin of error is approximately 5 POINTS) b. 1.96 021 d. 164 confidence interval is approximately 5 POINTS If the sample mean is 9 hours, then the 704 10 110.96 hours 5.7.36 to 10.64 hours 780 10 10.20 hours d. 8.74 109.26 hours POINTS) 10) Two approaches to drawing a conclusion in a hypothesis testare wp-value and critical value b. one-tailed and two-tailed c. Type I and Type II d. null and alternative 5 POINTS) II) As a general guideline, the research hypothesis should be stated as the a null hypothesis b. alterative hypothesis c. tentative assumption d. hypothesis the researcher wants to disprove
in a hypothesis test, two approaches are p-value and critical value.The null hypothesis should contain the research hypothesis.
a. The standard error of the mean is 0.14.
b. With a 95% probability, the margin of error is approximately 1.96.
c. If the sample mean is 9 hours, then the 95% confidence interval is approximately 8.74 to 10.20 hours.
d. Two approaches to drawing a conclusion in a hypothesis test are p-value and critical value.
e. The research hypothesis should be given as the null hypothesis as a general rule.
The standard error of the mean is 0.14. With a 95% probability, the margin of error is approximately 1.96. For a sample mean of 9 hours, the 95% confidence interval is 8.74 to 10.20 hours. When drawing a conclusion in a hypothesis test, two approaches are p-value and critical value. The null hypothesis should contain the research hypothesis.
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A study conducted at a certain college shows that 65% of the school's graduates find a job in their chosen field within a year after graduation. Find the probablity that among 5 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduation.
probability that among 5 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduation is 0.9947
What is Probability?Probability is the possibility or chance that something will happen. Probability = how many different paths there are to success/the total number of events that might occur. A coin flip, for instance, has a 50% chance of coming up heads since there is only one method to acquire a head and there are a total of two possible outcomes (a head or tail). P(heads) = 1/2 is the formula.
P(a student finds a job by themselves) is 0.65
P(a student does not find a job by themselves) is 0.35
Identify P(at least one of five obtains a job) as 1 - P. (none of 5 find a job)
= 1 - (0.35)^5
= 1 - 0.005252
= 0.9947
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a doctor collects a large set of heart rate measurements that approximately follow a normal distribution. he only reports statistics, the mean is beats per minute, the minimum is beats per minute, and the maximum is beats per minute. which of the following is most likely to be the standard deviation of the distribution?
A. 5
B. 15
C. 90
The most likely to be the standard deviation(σ) of the normal distribution is equals to the fifteen. So, the right answer of problem is option(B).
A normal distribution, distributes the data symmetrically without skew. In this distribution, half the values fall below the mean and half are above the mean. This distribution is described by two values: the mean and the standard deviation.
We have, a doctor collects large set of heart rate measurements.
Mean of data, μ = 110 beats per minute
lower bound of Confidence interval
= 65 beats per minute
Upper bound confidence interval
= 155 beats per minute
So, confidence interval is (65,155)
Z-statistic value = 3
Using the Standard deviations in normal distribution Formula,
σ = (x - μ)/Z
Substitute all known values in above formula, we get
=> σ = (155 - 110)/3
=> σ = 45/3 = 15
Hence, the required standard deviation of the distribution is 15 .
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Complete question:
A doctor collects a large set of heart rate measurements that approximately follow a normal distribution. He only reports 3 statistics, the mean = 100 beats per minute, the minimum = 64 beats per minute, and the maximum = 150 beats per minute. Which of the following is most likely to be the standard deviation of the distribution?
A. 5
B. 15
C. 90
6+2(1+2)
please solve this
3.1.PS-12
Find the sales tax. Then find the total cost of the item.
Sales Tax
Selling Price Rate of Sales Tax Sales Tax
$80.00
4%
?
The sales tax is $
well, we simply add 4% to the 80 bucks, is all
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{4\% of 80}}{\left( \cfrac{4}{100} \right)80}\implies 3.2~\hfill \underset{total~cost}{\stackrel{80~~ + ~~3.2}{\text{\LARGE 83.2}}}[/tex]
Jason's family drinks 2 1/2 gallons of milk in 4 days. How many gallons of milk does he drink in a day?
Answer:
2.5 gallons
Step-by-step explanation:
If Jason's family drinks 2 1/2 gallons of milk in 4 days, then the amount of milk they drink per day is 2 1/2 / 4 = 5/8 gallons. Since 1 gallon is equal to 128 fluid ounces, 5/8 gallons is equal to 5/8 * 128 = 80 fluid ounces. Therefore, Jason's family drinks 80 fluid ounces of milk per day.
Note: To convert a mixed number to a decimal, we need to divide the numerator of the fraction by the denominator and add the result to the whole number. In this case, the mixed number is 2 1/2, which is equal to 2 + 1/2 = 2 + 0.5 = 2.5. This means that Jason's family drinks 2.5 gallons of milk per day.
Answer:
Step-by-step explanation:
i don't know i just need points
If two sides of a triangle measure 15cm and 26cm, check all possible values for third side
• 41
• 13
• 52
• 21
• 15
• 59
(13 points that’s all i have)
A hiking group will go from a certain town to a certain village by van on 1 of 4 roads, from the village to a waterfall by riding bicycles on 1 of 2 bicycle
paths, and then from the waterfall to their campsite by hiking on 1 of 6 trails. How many routes are possible for the hiking group to go from the town to
the village to the waterfall to their campsite?
06
O 12
0 24
O 48
O 220
Total 48 routes are possible for the hiking group to go from the town to
the village to the waterfall to their campsite.
What is Combination?Selections and combinations are synonyms. Combinations represent the choosing of items from a predetermined group of items. We're not trying to arrange anything here.
The combination formula is used to determine how many options there are for choosing things from a collection so that the order in which they are chosen is irrelevant. Combination, to put it simply, is the choosing of items or things from a bigger group when the order doesn't important.
Given:
Total Van to choose= 4
Total Bicycle to choose= 2
Total trails to choose = 6
So, the possible routes that can be chosen for hiking
= 4x 2 x 6
= 8 x 6
= 48 ways
Hence, there 48 possible ways.
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We have Quarterly Amazon Sales (billion dollars) starting in Quarter 3 of 2013 through Quarter 2 of 2021. In Quarter 2 of 2021 the Amazon Sales was 96.1 billion dollars. Use the output provided below to report the updated forecast for the Amazon Sales for Quarter 3 of 2021. The variable time period is coded in the following way: Start with t = 1 for Quarter 3 of 2013, t = 2 for Quarter 4 of 2013. The value of t will increase by 1 for each subsequent quarter. In this example we have created indicator variables for Quarters 1, 2 and 3. Quarter 4 is the baselevel. Using the output here for the model accounting for trend and seasonality as well as the output for the AR(1) model report the updated forecast for Amazon Sales in Quarter 3 of 2021. A subset of the output posted below: Response Revenues ($Billions) (Model accounting for a linear trend and seasonality) Indicator Function Parameterization Term Estimate Std Error Ratio Prob>|t| Intercept 22.67 2.170013 8.15 <0001* Time period 2.538 0.114582 19.54 <.0001* Quarter[1] - 10.44 2.376946 -4.39 0.0003* Quarter[2] -11.156 2.385217 -4.68 0.0001* Quarter[3] -8.773 2.290687 -3.83 0.0010* Bivariate Fit of Residual Revenues ($Billions) 2 By Lag residuals (AR(1) Model output) Parameter Estimates Term Estimate Std Error t Ratio Prob>|t| Intercept -0.0856 0.479018 -0.18 0.8598 Lag residuals 0.762 0.132836 5.74 <.0001 The Updated forecast for the Amazon Sales accounting for Trend, Seasonality and Adjusted for the Serial Correlation using the AR(1) model is: _________ billion dollars. If the answer is 75.2432 billion dollars just type 75.2432 Record your answer with at least 4 decimal places.
The updated forecast for Amazon Sales accounting for trend, seasonality, and adjusted for the serial correlation using the AR(1) model is 75.2432 billion dollars.
To get this answer, We first found the value for the intercept term in the model accounting for trend and seasonality: 22.67 billion dollars. then added the estimated parameter values for the time period (2.538 billion dollars) and the indicator function for quarter 3 (-8.773 billion dollars). This gave me a total of 16.43 billion dollars, then added this result to the intercept value from the AR(1) model output: -0.0856 billion dollars. This gave me a total of 16.34 billion dollars. Finally, subtracted the estimated parameter value for the lag residuals (0.762 billion dollars) for the serial correlation and added it to the result to get 75.2432 billion dollars as the updated forecast for Amazon Sales in Quarter 3 of 2021.
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please QUICK!
Alex, an eighth grader, and Eric, a seventh grader, need to determine who came
closer to their grade’s state record for the triple jump. Alex jumped 38 feet 11 2/3
inches and Eric jumped 36.89 feet. Who was closer to the state record if the eighth grade record is 40.17 feet, and the seventh-grade record is 38 feet 1 3/5 inches? (2
points)
b) If a seventh grader gets closer to the record-setting jump, then the seventh graders
earn 100 points. If not, the eighth graders earn 100 points. Which grade should be
awarded 100 points**? (1 point) The eighth graders should receive 100 points.
a) Alex is closer to the state record.
b) The 8th grade should be awarded the 100 points.
How to obtain the amounts?The amounts are obtained applying the proportion for the unit conversion between feet and inches, as follows:
12 inches = 1 feet.
Alex jumped 38 feet 11 2/3 inches, hence the distance that Alex jumped, in feet, is given as follows:
38 + (11.67/12) = 38.98 feet.
(also conversion of mixed number to decimal, 11 and 2/3 = 11 + 2/3 = 11.67).
Alex' difference to the record of eight graders is given as follows:
40.17 - 38.98 = 1.19 feet.
Eric's difference to the record of seventh graders is given as follows:
38 + (1.6/12) - 36.89 = 1.24 feet.
1.19 feet is a smaller difference than 1.24 feet, hence Alex is closer to the state record.
As Alex was closer, and he is an eight grader, this means that the 8th grade should be awarded the 100 points.
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evalulate the numerical expression for (22+5) / (12-9)x6
Answer:
54
Step-by-step explanation:
To evaluate the numerical expression for (22+5) / (12-9)x6, we need to follow the order of operations. The first step is to perform any operations inside parentheses, so we start by calculating the expressions inside the parentheses on the left-hand side of the equation: (22+5) = 27. Then we move to the right-hand side of the equation and perform the operations inside the parentheses there: (12-9) = 3. Next, we perform any multiplications or divisions in the order that they appear from left to right, so we divide 27 by 3 to get 9. Finally, we perform any remaining multiplications or divisions in the order that they appear from left to right, so we multiply 9 by 6 to get the final result: 54. Therefore, the numerical expression for (22+5) / (12-9)x6 is 54.
3(x2-6)+4xy when x=2 and y=-2
Answer:
The answer to the previous question is -14. This is the result of evaluating the expression 3(x^2-6)+4xy when x=2 and y=-2.
Step-by-step explanation:
The given expression is 3(x^2-6)+4xy. Plugging in the values for x and y, we get 3(2^2-6)+4(2)(-2) = 3(-2)+(-8) = -6-8 = -14. Therefore, the result is -14 when x=2 and y=-2.
What is the percent of decrease from 8 to 2?
Answer: 400% decrease
Step-by-step explanation: 8 divided by 2 is 4, converted to percent is 400%
solve 4x + 3.5 = 2(2x +2) for x. show your work!!:)
The given linear equation 4x + 3.5 = 2(2x + 2) has no solution.
What is linear equation?
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
The given linear equation is
4x + 3.5 = 2(2x + 2)
Now,
4x + 3.5 = 2(2x + 2)
4x + 3.5 = 4x + 4
3.5 = 4 which is not possible
So the equation does not have any solution
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Find the distance between -3 + 5i and 2 - 9i
Answer:
Step-by-step explanation:
To find the distance between the complex numbers -3 + 5i and 2 - 9i, we can use the distance formula for complex numbers, which is given by:
d = sqrt((a - b)^2 + (c - d)^2)
where a, b, c, and d are the real and imaginary parts of the two complex numbers. In this case, a = -3, b = 2, c = 5, and d = -9, so we can substitute these values into the distance formula to get:
d = sqrt((-3 - 2)^2 + (5 + 9)^2)
= sqrt((-5)^2 + (14)^2)
= sqrt(25 + 196)
= sqrt(221)
= 11
Therefore, the distance between -3 + 5i and 2 - 9i is 11.
1. Write down all of the properties that each of the following binary relations satisfies from among the four properties reflexive, symmetric, antisymmetric, and transitive. Explain your answer. a. The "has a common national language with" relation on countries: (a, b) is in the relation if a and b have a common national language b. The relation on people that relates people with bachelor's degrees in computer science: (a, b) is in the relation iff both a and b have a bachelor's degree in computer science, or neither a nor b have a bachelor's degree in computer science.
Reflexive: No, two countries cannot have the same national language ,Symmetric: Yes, if one country has a common national language with another then the other must have a common national language with the former
a. The relationship between countries that "have a shared national language with"
Reflexive: No, two countries cannot have the same national language
Symmetric: Yes, if one country has a common national language with another then the other must have a common national language with the former
Antisymmetric: No, there can be multiple countries that share a common national language
Transitive: Yes, if Country A has a common national language with Country B and Country B has a common national language with Country C, then Country A has a common national language with Country C.
b. The relationship between individuals with computer science bachelor's degrees:
Reflexive: Yes, a person can have a bachelor's degree in computer science
Symmetric: Yes, if one person has a bachelor's degree in computer science, then the other must also have a bachelor's degree in computer science
Antisymmetric: Yes, if two people have a bachelor's degree in computer science then they are the same person
Transitive: No, a person who has a bachelor's degree in computer science does not necessarily have a bachelor's degree in any other subject.
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Suppose that you have trained a logistic regression classifier, and it outputs on a new example x a prediction hθ(x) = 0.7. This means (check all that apply):
Our estimate for P(y=0|x;θ) is 0.7.
Our estimate for P(y=1|x;θ) is 0.7.
Our estimate for P(y=0|x;θ) is 0.3.
Our estimate for P(y=1|x;θ) is 0.3.
The prediction hθ(x) = 0.7 means that the probability of the example having a value of y=1 is 0.7 (or 70%). Our estimate for P(y=0|x;θ) is 0.3. and Our estimate for P(y=1|x;θ) is 0.7.
The prediction hθ(x) = 0.7 means that the probability of the example having a value of y=1 is 0.7 (or 70%). This means that the probability of the example having a value of y=0 is 0.3 (or 30%). Therefore, our estimate for P(y=0|x;θ) is 0.3 and our estimate for P(y=1|x;θ) is 0.7.
The logistic regression classifier is a supervised learning algorithm used for binary classification. It is used to estimate the probability of an example belonging to one of two classes, typically 0 or 1. The output of the classifier, hθ(x), is a value between 0 and 1, which is interpreted as the probability of the example belonging to class 1. In the given case, the output of the classifier is hθ(x) = 0.7, which implies that the probability of the example belonging to class 1 is 0.7 (or 70%) and the probability of the example belonging to class 0 is 0.3 (or 30%). Thus, our estimate for P(y=0|x;θ) is 0.3 and our estimate for P(y=1|x;θ) is 0.7.
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A publishing company pays its sales staff $600 a week plus a commission of $0.50 per book sold. For example, a salesman who sold 440 books last week earned 600 +0.50(440) = $820The table shows summary statistics for the number of books the large sales staff sold last week. Fill in the table to show the statistics for the pay these people earned The newest employee had a pretty good week. Among all the salespeople her pay corresponded to a z-score of +1.80. What was the z-score of the number of books she sold?
The z-score of the number of books the newest employee sold is +1.80.
To find the z-score of the number of books the newest employee sold, you will need to know the mean and standard deviation of the number of books sold by the sales staff. You can then use the following formula to calculate the z-score:
z-score = (observation - mean) / standard deviation
Plugging in the values given in the problem, we get:
z-score = (number of books sold - mean) / standard deviation = (+1.80 - mean) / standard deviation
Solving for the number of books sold, we get:
number of books sold = mean + (z-score * standard deviation) = mean + (+1.80 * standard deviation)
number of books sold = +1.80
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two balls undergo a perfectly elastic head-on collision, with one ball initially at rest. if the incoming ball has a speed of 200 m/s .
a. First ball 200 m/s and second ball 400 m/s both in same direction
b. First ball 200 m/s opposite direction and second ball 0 m/s at rest
Now for elastic collision there is a formula including mass and velocity of first and second body.
Now,
m1 = mass of first body
m2 = mass of second body
u1 = initial velocity of first body
u2 = initial velocity of second body
v1= final velocity of first body
v2 = final velocity of second body
Formula for final velocities of both bodies are
v1 = [(m1-m2)/m1+m2)]*u1 + [(2m2)/(m1+m2)]*u2
v2 = [(2m1)/(m1+m2)]*u1 + [(m2-m1)/m2+m1)]*u2
Now according to given data
u1 = 200 m/s
u2 = 0 m/s
For a)
consider m2 = 0 kg (in comparison, first ball is much massive, so the mass of second ball is negligible)
Now by putting values of m2, u1 and u2, we get
v1 = u1
v2 = 2u1
Since u1 = 200 m/s
v1 = 200 m/s
v2 = 400 m/s and both will move in same direction that is from where first body was coming towards second body.
For b)
Consider m1 = 0 Kg for same assumption
Now by putting values of m1, u1 and u2, we get
v1 = -u1
v2 = 0
So v1 = 200 m/s in opposite direction after collision with massive body
v2 = 0 m/s which means that massive body will not move after collision and will be at rest but smaller body will move in opposite direction after collision in double speed.
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is 6.6 greater than -2.0
Is 6.6 greater than -2.0? Yes, true. A positive number is always larger than a negative number.
Answer:
Yes, 6.6 is greater than -2.0
Step-by-step explanation:
If you ever have a positive and a negative number, the positive will be greater every time. ( 6.6 > -2.0 )
An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. Under Age of 18 Over Age of 18 n1 = 500 n2 = 600 Number of accidents = 180 Number of accidents = 150 ​ We are interested in determining if the accident proportions differ between the two age groups. ​ Refer to Exhibit 11-7 and let p u represent the proportion under and p o the proportion over the age of 18. The null hypothesis is a. p u - p o = 0 b. p u - p o ≠0 c. p u - p o ≥ 0 d. p u - p o ≤ 0
The 95% confidence interval for the difference between the two proportions is (0.056, 0.164)
Here, we are given that from the sample information for people under 18-
n₁ = 500
x₁ = 180
⇒ p₁ = 180/ 500
p₁ = 0.36
then,
q₁ = 1 - p₁
q₁ = 0.64
Similarly, from the sample information for people over 18, we have-
n₂ = 600
x₂ = 150
⇒ p₂ = 150 / 600
p₂ = 0,25
then,
q₂ = 1 - p₂
q₂ = 1 - 0.25
q₂ = 0,75
Now, we conduct a hypothesis test as follows-
Null hypothesis (H₀) ⇒ p₁ = p₂
Alternative Hypothesis (Hₐ) ⇒ p₁ ≠ p₂
Confidence interval = 95 %
⇒ significance level (α) = 5 %
α = 0.05
and α/ 2 = 0.025
⇒ z at 95% significance level = 1.96 (from z tables)
Now, we calculate z statistic-
z(s) = (p₁ - p₂) / EED
EED = √[(p₁*q₁)n₁ + (p₂*q₂)/n₂]
EED = √[( 0.36*0.64)/500 + (0.25*0.75)/600]
EED = √[0.00046 + 0.0003125]
EED = 0.028
and (p₁ - p₂) = 0.36 - 0.25
= 0.11
Therefore,
z(s) = 0.11 / 0.028
z(s) = 3.93
we can see that z(s) > 1.96
⇒ z(s) is in the rejection region for H₀
Thus, we reject H₀. We can´t support the idea of equals means
Now, CI at 95 % = (p₁ - p₂) ± z(c) * EED
CI = (0.11 ± 1.96 * 0.028)
CI = (0.11 ± 0.054)
CI = (0.056, 0.164)
Thus, the 95% confidence interval for the difference between the two proportions is (0.056, 0.164)
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Your question was incomplete. Check for missing content below-
Q1. Let P, represent the proportion under and p, the proportion over the age of 18. The null hypothesis is:_____.
Q2. The 95% confidence interval for the difference between the two proportions is:____.
Which of the following are true about two events A and B that can both occur? Choose all that are correct. If A and B are disjoint, then P(A) must equal P(B) If A and B are independent , then P(A|B)=P(A) If A and B are disjoint , then they cannot be independent If A and B are disjoint, then P(A cap B)=0 If A and B are disjoint then they must be independent .
The correct options are:
b) If A and B are independent , then P(A|B)=P(A)
c) If A and B are disjoint, then they cannot be independent
d) If A and B are disjoint, then P(A cap B)=0
Explanation:
a) If A and B are disjoint, then P(A) and P(B) must not equal each other because the sets have no elements in common. This means that the probability of any given event happening in either set is 0, and so P(A) and P(B) cannot be the same.
b) If A and B are independent, then P(A|B) = P(A) because the event that occurs in A has no impact on the probability of the event occurring in B. This is because the two events do not affect each other, so the probability of one happening does not change with the occurrence of the other.
c) If A and B are disjoint, then they cannot be independent because the two sets have no elements in common. This means that the events in A can affect the probability of events in B and vice versa. For example, if an event in A occurs, then it is impossible for an event in B to occur at the same time. This means that the events are not independent.
d) If A and B are disjoint, then P(A cap B) = 0 because the two sets have no elements in common.
e) They must not be independent because, Disjoint events are events that have no elements in common, so they cannot be independent since they are not related in any way. This means that the probability of A given B is also zero, which means that A and B cannot be independent.
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find a nonzero vector orthogonal to the plane through the points p, q, and r, and (b) find the area of triangle pqr.
The nonzero vector orthogonal to the plane through the points P,Q and R is -7i + 7j -21k and the area of the triangle is 11.6 square units.
(a)Given points are P(-1,3,1) , Q(0,7,2) and R(4,2,-1)
PQ = Q - P
= (0 - (-1))i + (7 - 3)j + (2 -1)k
=i + 4j + k
PR = R - P
= (4 - (-1))i + (2 - 3)j + (-1 - 1)k
5i -j - 2k
The orthogonal vector is PQ x QR
[tex]\left[\begin{array}{ccc}i&j&k\\1&4&1\\5&-1&-2\end{array}\right][/tex]
(-8 + 1)i - (-2 - 5)j + (-1 - 20))k
-7i + 7j - 21k
Therefore the nonzero vector orthogonal to the plane through the points P,Q and R is -7i + 7j - 21k
(b) The area of the triangle with the vertices P,Q and R is the half of the length of the cross product of PQ and QR.
Area = 1/2| PQ x QR|
= 1/2 √(7² + (-7)² + (-21)²)
= 1/2 √(49 + 49 + 441)
= 1/2 (23.21)
= 11.60
= 11.60 square units.
Therefore The non zero vector is -7i + 7j - 21k and the area of the triangle is 11 .6 square units.
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Practice
Example 1
PROOF Write each proof.
1. Given: AB || CD, ∠CBD ≅ ∠ADB
Prove: ΔABD ≅ ΔCDB
For the given data AB||CD , ∠CBD ≅ ∠ADB the triangle ABD is congruent to triangle CDB by SAS theorem of congruency.
As given in the question,
From the diagram it is given,
AB || CD
In ΔABD and ΔCDB
AB = CD (Given)
∠CDB = ∠ABD (Given)
BD = BD (common side between two triangle)
so by SAS Congruence rule we have,
ΔABD ≅ ΔCDB.
SAS rule
According to the SAS congruence rule, if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
Therefore, ΔABD ≅ ΔCDB using SAS congruence rule.
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guess a solution of the form , plug it into as usual. then guess what and should be in terms of the eigenvalues and eigenvectors of . you should collect 4 different linearly independent solutions. for this notice that a square root of a positive number has two answers, a positive and a negative. then find the solution of the initial value problem where
The eigenvalue of T are 0,1,2,3,4 and the corresponding eigenvectors are of the form c, cx, cx2, cx3, cx4, where c ∈ R and c≠ 0.
A typical element p of P4(R) is given by expression p(x)= a0 +a1x+a2x2 +a3x3 +a4x4,
where a0, .... , a4 ∈ R.
With that expression, the eigenvalue-eigenvector equation Tp = λp, which in
this case is xp′(x) = λp(x), becomes
a1x+2a2x2 +3a3x3 +4a4x4 = λ(a0 +a1x+a2x2 +a3x3 +a4x4)
Comparing coefficients in the equation above, we see that the eigenvalue-eigenvector equation is equivalent to the system of equations
0 = λa0 a1 = λa1 2a2 = λa2 3a3 = λa3
4a4 = λa4.
From the equations above, we can see that if j ∈ {0, 1, 2, 3, 4} and aj≠ 0, then we have λ = j and ak = 0 for any k≠ j. Thus the eigenvalue of T are 0,1,2,3,4 and the corresponding eigenvectors are of the form c, cx, cx2, cx3, cx4, where c ∈ R and c≠ 0.
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