What is the average rate of change of the function y = 3 sin(2x) on the interval [0,π4] ?
![What Is The Average Rate Of Change Of The Function Y = 3 Sin(2x) On The Interval [0,4] ?](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/7RqhQU2KqxJCPhqfhK355QsX64xUoJIF.png)
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The average rate of change of the trigonometric function f(x) = 3 · sin 2x on the interval [0, π / 4] is 12 / π. (Correct choice: D)
How to find the average rate of change of a trigonometric function in a given interval
In this question we need to determine the average rate of change of a trigonometric function on the interval [0, π / 4]. Graphically speaking, the average rate of change is represented by a line secant to the curve of the function, whose definition is shown below:
m = [f(π / 4) - f(0)] / (π / 4 - 0)
If we know that f(x) = 3 · sin 2x, then the average rate of change is:
m = [3 · sin (π / 2) - 3 · sin 0] / (π / 4 - 0)
m = (3 - 0) / (π / 4)
m = 12 / π
The average rate of change of the function is 12 / π.
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Related Questions
your sample consists of 87 subjects, with 71 successes. calculate the test statistic, rounded to 2 decimal places
Answers
sample consists of 87 subjects, with 71 successes.the test statistic, rounded to 2 decimal places ,Test statistic = (71/87) = 0.81
To calculate the test statistic, you need to divide the number of successes by the total number of subjects in the sample.
In this case, the number of successes is 71 and the total number of subjects is 87.
Therefore, the test statistic is calculated a
s 71/87 = 0.81
which can be rounded to two decimal places. The result of the calculation is that the test statistic is 0.81.
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f(x)=2x^2
g(x)=x+1
prove fg(x)=gf(x)
Answers
Answer:
here is the answer with proper steps.
During one winter snow storm in Denver, Colorado, Jesse noted that 6 inches of snow fell in 2
1/3 hours. What was the rate of snowfall in one hour?
Answers
Answer:
2 4/7 inches per hour---------------------------------------------
Given:
6 inches of snow fell in 2 1/3 hours.Divide the number of inches by the time to get the rate of snowfall:
6 ÷ 2 1/3 = 6 ÷ 7/3 = 6 × 3/7 = 18/7 = 2 4/7 inchesthanks for helping me!
Answers
Answer:
<E=180-60=120
t=60 degrees
u=8
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T= 60
So U=8
PLEASE HELP!!!!! 90 POINTS!!!!!
Graph the following system of equations.
2x + 4y = 8
2x + 6y = 18
What is the solution to the system?
There is no solution.
There is one unique solution, (−6, 5).
There is one unique solution, (−4, 4).
There are infinitely many solutions.
Answers
Answer:
There is one unique solution, (−6, 5).
Step-by-step explanation:
2x + 4y = 8
2x + 6y = 18
2x + 4y = 8 ==> solve for 2x
2x + 4y - 4y = 8 - 4y
2x = 8 - 4y
2x + 6y = 18 ==> solve for 2x
2x + 6y - 6y = 18 - 6y
2x = 18 - 6y
8 - 4y = 18 - 6y ==> 2x = 8 - 4y and 2x = 18 - 6y
8 - 4y + 6y = 18 - 6y + 6y ==> solve for y by first adding 6y on both sides to
remove negative y
8 + 2y = 18 ==> simplify
8 - 8 + 2y = 18 - 8 ==> isolate y
2y = 10
y = 5
2x + 4(5) = 8 ==> substitute 5 for y in 2x + 4y = 8
2x + 20 = 8
2x - 20 + 20 = 8 - 20 ==> subtract 20 on both sides to isolate 2x
2x = -12
x = -6
x = -6, y = 5 ==> (6, 5)
Answer: There is one unique solution, (−6, 5).
The question asks you to graph and find the solution. I graphed this and attached it.
The solution is where the lines intersect, at (-6, 5)
(3x)°
(6x-12)
(2x+13)° find the value of x
Answers
Answer:
x = 25
Step-by-step explanation:
The two interior angles equal the exterior angle.
6x - 12 = 3x + 2x + 13 Combine like terms
6x - 12 = 5x + 13 Subtract 5x from both sides of the equation
6x -5x - 12= 5x - 5x + 13
x - 12 = 13 Add 12 to both sides of the equation
x - 12 + 12 = 13 + 12
x = 25
. a paper cup has the shape of a cone with height 10 cm and radius 3 cm (at the top). if water is poured into the cup at a rate of 2 cm3 ys, how fast is the water level rising when the water is 5 cm deep?
Answers
The water level is rising at a rate of 0.0764 cm per second.
Using implicit differentiation, it is found that the water level is rising at a rate of 0.0764 cm per second.
The volume of a cone of radius r and height h is given by:
V = πr²h/3
Applying implicit differentiation, the rate of change is given by:
dV/dt = 2πr/3 dr/dt + πr²/3 dh/dt
In this problem:
The radius is constant, thus dr/dt = 0
Height of 5 cm and radius of 3 cm, thus h = 5, r=3.
Water poured at a rate of 2 cm³/s, thus dV/dt = 2
Then
dV/dt = 2πr/3 dr/dt + πr²/3 dh/dt
2 = 25π/3 dh/dt
dh/dt = 6/25π
dh/dt = 0.0764
The water level is rising at a rate of 0.0764 cm per second.
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use the graphs of f and g to graph h(x) = (f + g)(x). (graph segments with closed endpoints.)
Answers
Different x values must be taken into account in order to graph h (x). So the graph of the h(x) is given below.
In the given question, we use the graphs of f and g to graph h(x) = (f + g)(x).
A diagram that compares the fluctuation of one variable to that of one or more other variables, such as a collection of points, lines, line segments, curves, or regions.
The graph is given below:
h (x) = (f + g) (x)
The function h(x) can be written as
h (x) = f (x) + g (x)
Different x values must be taken into account in order to graph h (x).
h (0) = f (0) + g (0) = 2 - 1 = 1
h (1) = f (1) + g (1) = 3 + 0 = 3
h (2) = f (2) + g (2) = 1 + 0.5 = 1.5
h (3) = f (3) + g (3) = 2 + 0 = 2
So the graph of the h(x) is given below:
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Question 1
© Drake - Sticky (Official Audio 41 × +
25 pts
The prices paid for a model of a new car are approximately normally distributed with a mean of $17,000 and a standard deviation of $500.
The price that is 3 standard deviations above the mean is $__
The price that is 2 standard deviations below the mean is $__
The percentage of buyers who paid between $16,500 and $17,500 is __%
The percentage of buyers who paid between $17,000 and $18,000 is __%
The percentage of buyers who paid less than $16,000 is __%
Answers
If new automobile prices are roughly regularly distributed, with a mean of $17,000 and a standard deviation of $500, then it means that the majority of the prices paid for the car will fall within a certain range.
Specifically, approximately 68% of the prices paid will be within one standard deviation of the mean, which in this case would be between $16,500 and $17,500.
Approximately 95% of the prices paid will be within two standard deviations of the mean, which would be between $16,000 and $18,000. And approximately 99.7% of the prices paid will be within three standard deviations of the mean, which would be between $15,500 and $18,500. This demonstrates that the prices paid for the cars are generally consistent, with only a tiny percentage deviating from the mean and standard deviation-defined range.
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Moussa is younger than Sophia. Their ages are consecutive even integers. Find Moussa's age if the product of their ages is 24.
Answers
Moussa's age if the product of their ages is 24 is 4 years.
How to calculate their age?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Moussa is younger than Sophia. Their ages are consecutive even integers.
Let the ages be x and x + 2.
This will be illustrated as:
x(x + 2) = 24
x² + 2x = 24
x² + 2x - 24 = 0
x² + 6x - 4x - 24 = 0
x(x + 6) -4(x + 6) = 0
x - 4 = 0
x = 4
x + 2 = 4 + 2 = 6
The ages are 4 and 6 years.
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If the product of Sophia age and Moussa age is 24, the age of Moussa is 4 years.
How to find the Moussa's age?Moussa is younger than Sophia. Their ages are consecutive even integers.
The product of there ages is 24. Moussa's age can be found as follows:
Even numbers are those numbers that can be divided into two equal groups or pairs and are exactly divisible by 2.
Hence,
Let
x = age of Moussa
x + 2 = age of Sophia
Hence, the product of their age will be as follows:
x(x + 2) = 24
x² + 2x = 24
x² + 2x - 24 = 0
lets factorise the quadratic equation. The numbers one can multiply to get -24 and add to get 2 are -4 and 6. Therefore,
x² - 4x + 6x - 24 = 0
x(x - 4) + 6(x - 4) = 0
(x + 6)(x - 4) = 0
Therefore,
x = - 6 and x = 4
We can only use positive numbers.
Therefore, the age of Moussa is 4 years
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g you would like to obtain a 90% confidence interval with margin of error 0.02, what is the minimum sample size you need?
Answers
I would like to construct a 95% confidence interval with a 4% margin of error. We don't have an estimate for the percentage, so we use a conservative estimate.
This is the minimum sample size, so we need to round up to 601. The larger the sample, the more confident the responses truly represent the population.
This shows that for a given confidence level, the confidence interval gets smaller as the sample size increases. At least 1450 samples from each group are required.
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here is a famous problem: nn guests arrive at a party. each person is wearing a hat. we collect all hats and then randomly redistribute the hats, giving each person one of the nn hats randomly. what is the probability that at least one person receives his/her own hat?hint: use the inclusion-exclusion principle.
Answers
The probability that at least one person receives his/her own hat is 1 - (1/n)^n, using the inclusion-exclusion principle.
The inclusion-exclusion principle states that the probability of event A or B occurring is equal to the probability of event A plus the probability of event B minus the probability of event A and B occurring. In this case, the probability of at least one person receiving his/her own hat is the probability of one person receiving his/her own hat plus the probability of two people receiving their own hats minus the probability of three people receiving their own hats, and so on. This can be expressed mathematically as 1 - (1/n)^n, where n is the number of guests. This formula can be applied to any situation where a random event is being repeated multiple times with the same set of outcomes.1 - (1/10)^10 = 0.99.
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if it is not possible to obtain a list of all elements in a population, this is a; group of answer choices infinte population sample finite population statistic
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if it is not possible to obtain a list of all elements in a population, this is a; group of answer choices finite population statistic
It is also known as the group of the study, that targets the population, which helps to find the survey, which is the sampled population. It is measured by an ideal world, which will be the same, and they're always unique.
Its sampling distribution of the "x bar" should also be naturally independent of the random sample, that is usually distributed.
We consider the population as endless if the sampling size is at least 20 times greater than the sample size.
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PLEASE HELP I AM SO BEHIND ON SCHOOL WORK !!!
Which equation represents the same line as the points in the table?
y=−3x+2y is equal to negative 3 x plus 2
y=−34x+83y is equal to negative 3 fourths x plus 8 thirds
y=2x−34y is equal to 2 x minus 3 fourths
y=−34x+2
Answers
Answer:
Use this site, it will help you in the long run.
FILL IN THE BLANK. the _______ _______ is a statement we are trying to find evidence to support.
Answers
Answer:
Alternative Hypothesis
Help me quickly please! (I will mark brainliest)
Answers
The graphs in this problem that show continuous data are given as follows:
Top right.Bottom left.What are continuous and discrete graphs?Continuous and discrete graphs have different formats to show the data, which are presented as follows:
For a continuous data, the data shown is all the real numbers in an interval, hence a continuous graph is represented by solid lines. This means that the second and third graphs in this problem, that is, the top right and the bottom left graphs represent continuous data.
For discrete data, only certain values are represented in an interval, hence the graph of discrete data is composed only by dots, which is the case for the first and last graphs in this problem, that is, the top left graph and the bottom right graph.
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I don’t know how to do this PLEASE HELP
Answers
3 15/8 = 39/8 = 4 7/8
2 13/6 = 25/6 = 4 1/6
1.shade 3 full 8/8 circles 2. Shade 15 little slices in the rest 3. You done with the first one 1. Shade 2 full 6/6 circles 2. Shade 13 more little slices in the rest 3. TADAAA you done
Step-by-step explanation:
What is the first quartile of the given data set?
Answers
The value of first quartile of the given data set is 2.5
What is first quartile?The lower quartile, or first quartile (Q1), is the value under which 25% of data points are found when they are arranged in increasing order.
Given is a data set,
According to the data,
The lower quartile is between 0 and 2.5, which under 25% of the data.
Hence, The value of first quartile of the given data set is 2.5
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HELP QUICK!!
An item on sale costs 35% of the original price. If the original price was $60, what is the sale price?
Answers
•
•
When dealing with percentages they are numerators (?wc) of 100, so 0.35 = 35/100.
In percentage calculations you want to make the original/starting value equivalent to the 100 denominator
35/100 * 6000/100
This sum is the same as the first line… sorry if this is more confusing ;-;
TL;DR: take the percentage as 0.XX and times by original value if going lower in value. If your going higher do 1.XX
Factorize:
x^4 - (x-z)^4
Answers
=(2x2 −2xz+z ^2 )(2x−z)(z)
Frank drove 567 miles in 9 hours. At the same rate, how long would it take him to drive 441 miles?
Answers
In this case, the distance Frank traveled is 567 miles and the time it took him to travel that distance is 9 hours, so the rate is 567 miles / 9 hours = 63 miles per hour.
To find the time it would take Frank to travel 441 miles at this rate, we can divide the distance by the rate. This would give us 441 miles / 63 miles per hour = <<441/63=7>>7 hours.
Therefore, if Frank were to travel 441 miles at the same rate as his previous trip, it would take him 7 hours.
Each year the value of a car decreases by 12% of its value at the beginning of that year. The original value of the car is $20000. Calculate the value of the car at the end of 3 years
Answers
Answer:
The value of the car at the end of 3 years will be $13707.
Step-by-step explanation:
If the original value of the car is $20000, then after the first year, the value of the car will be $20000 - (12/100)*$20000 = $17600.
After the second year, the value of the car will be $17600 - (12/100)*$17600 = $15552.
After the third year, the value of the car will be $15552 - (12/100)*$15552 = $13707.
Therefore, the value of the car at the end of 3 years will be $13707.
Ma Amati’s bought x number of shirts for the new members of the dance team. The total amount paid for x shirts, including $2.99 shipping, was $118.99. Each shirt cost $14.50. There was no sales tax on this purchase. Which equation could be used to find x, the number of shirts bought
Answers
Answer: y = 14.50x + 2.99
Step-by-step explanation:
The equation is y = mx + b
y is the total cost and x is the number of shirt
We know each shirt is $14.50, and she bought x shirts, so 14.50 is the slope
The 2.99 shipping fee is the y-intercept
So our equation is
y = 14.50x + 2.99
Help asp thank you show your work if you want
Answers
Answer:
[tex]y=-\frac{2}{3}x+1[/tex]
Step-by-step explanation:
Parallel means same slope.
[tex]y=-\frac{2}{3}x+b[/tex]
[tex]5=-\frac{2}{3} (-6)+b[/tex]
5 = 4 + b
b = 1
[tex]y=-\frac{2}{3}x+1[/tex]
Light travel about `180000000` kilometer in `10` minute. How many kilometer per minute i that?
Answers
The distance traveled by light in 1 minute = 18 million kilometers and the distance traveled by light in 1 second = 0.3 million kilometers.
We are given that -
The distance traveled by light in 10 minutes = 180 million km.
Now we have to find the distance traveled by light in 1 minute.
Using the unitary method, we get -
Distance traveled by light in 1 min = 180000000 / 10
Distance traveled by light in 1 min = 18 million kilometers
Now we have to find the distance traveled by light in 1 second.
We know that 1 minute= 60 seconds,
Thus, In 60 seconds light travels a distance of = 18 million kilometers. (from above)
therefore, in 1 second light would travel a distance of = 18 million / 60
= 0.3 million km
Hence, the distance traveled by light in 1 second = 0.3 million kilometers.
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The complete question is -
Light travels about 180 million kilometers in 10 minutes. How far does it travel in one minute? How far does it travel in one second?
Elie built a large rectangular vegetable garden that i 9 meter long and ha an area of 72 quare meter. What i the perimeter of Elie’ vegetable garden
Answers
Answer:
The perimeter of Elie's vegetable garden is 34 meters.
Step-by-step explanation:
The formula for area is: a=w*l.
A = area
W = width
L = length
If the length is 9 meters, then we know two of the values, the area, and the length. Substitute.
72=w*9
You can divide both sides by 9 to get the width, which is 8 meters.
To find perimeter, we add l+w+l+w, or 2l+2w. Substitute for our values:
2(9)+2(8)=34
The perimeter of Elie's vegetable garden is 34 meters.
At a school there are six lessons in a day.
In total, the six lessons last for 4 hours.
a) Assume that each lesson lasts the same amount of time.
How many minutes long is the final lesson?
Optional working
Answers
Answer:
40mins
Step-by-step explanation:
4hrsx60
=240mins
240mins/6 lessons
=40mins per lesson
solve each equation by completing the square
[tex]x^{2} -34x+289=0[/tex]
After completing the square, the equation is ____ and the solution is _________
WHOEVER ANSWERS CORRECTLY WILL BE MARKED BRAINLIEST
Answers
Answer:
x = 17------------------------------------------------
Complete the square as follows:
x² - 34x + 289 = 0x² - 2*17*x + 17² = 0 Identity (a ± b)² = a² ± 2ab + b²(x - 17)² = 0x - 17 = 0 Square root both sidesx = 17What is the equation of the linear function in point-slope form that passes through (6, 5) and has a slope of?
y-5=(x-6)
x-6=1/(x-5)
Answers
Answer:
y – 5 = m(x – 6)
Step-by-step explanation:
using y =mx +c as our guide line
Step 1 : identification of coordinates
(6,5) ;x1= 6,y1 = 5
step 2 : applying the formula
y – y1 = m(x – x1)
y – 5 = m(x – 6)
Store A sells a dozen donuts in packages as a BOGO, with the regular price of dozen at $6.35. Store B offers a dozen donuts without a special for $3.35. Store C offers a dozen and a half at a price of $6.50. Store D gives you a 25% discount if you buy 2 at a price of $3.70 each. Which is the better buy?
Answers
Store D provides the best value, with the lowest price per donut at $0.24.
To determine which store has the best deal, you should compare the price per donut at each store.
At Store A, the BOGO offer means that you can buy one dozen donuts for the regular price of $6.35 and get a second dozen for free. This means that you are paying $6.35 for 2 dozen donuts, or $0.27 per donut.
At Store B, a dozen donuts cost $3.35, or $0.28 per donut.
At Store C, a dozen and a half donuts cost $6.50, or $0.26 per donut.
At Store D, if you buy 2 dozen donuts at $3.70 each and receive a 25% discount, you will pay $3.70 × 2 × (1 - 0.25) = $5.77 for 2 dozen donuts, or $0.24 per donut.
Thus, based on these prices, Store D is the best deal, as it has the lowest price per donut at $0.24.
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