The Fourier series of one period a(x) on [tex]-\pi[/tex] to [tex]\pi[/tex] is 23.096.
What is Fourier series ?
A fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier Series makes use of the orthogonality relationships of the sine and cosine functions. Expand the function f(x) = ex in the interval [ – π , π ] using Fourier series formula.
Have given,
a(x) on domain ([tex]-\pi ,\pi[/tex])
Let ,
I = ∫[tex]\pi[/tex] [tex]e^{x}[/tex] dx
on integration
I = [tex][e^{x}]^{\pi }_{-\pi }[/tex]
I = [tex]e^{\pi } - e^{-\pi }[/tex]
I = 23.14 - 0.043
Thus, I = 23.096
The Fourier series of one period a(x) on [tex]-\pi[/tex] to [tex]\pi[/tex] is 23.096.
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What do you mean by 3 more than 7?
The statement 3 more than 7 means, a number is 3 more than a given number. Since here the number is 7 so the required number will be 7+3= 10
In numerical more than simply refers to adding and less than refers to subtracting. If it is given that a number let's say Z is Y more than X then the value will be Z= X+Y
If a given number let's say Z is Y less than X then the value of Z will be
Z=X-Y
More than means add which gives us a bigger value. Less than means subtract which gives us a smaller value
So, 3 more than 7 means 7+3 = 10
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What are the properties of the circumcenter of a triangle quizlet?
For different types of triangle, The circumcenter has different properties. The properties varies for acute, obtuse and right angle triangles.
What do you mean by a triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.
What do you mean by circumcenter of triangle?The spot where the three perpendicular bisectors of a triangle's sides meet and which is equally spaced from the triangle's three vertices.
Properties of circumcenter of triangle are:
In an acute-angled triangle, circumcenter lies inside the triangle. In an obtuse-angled triangle, it lies outside of the triangle. Circumcenter lies at the midpoint of the hypotenuse side of a right-angled triangle.To learn more about circumcenter visit:
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60% of all the students passed an exam. if a random sample of 10 students is selected, what is the mean and standard deviation ? write every rule you are going to use.
If a random sample of 10 students is selected from 60% passed students,with mean 6 and standard deviation 1.5492.
The mean and standard deviation of a random sample of 10 students can be calculated in order to determine the probability that a given student has passed an exam. This requires knowledge of some basic principles of statistics and probability.
Probability , p = 0.6 (60%=60/100)
Number of trial,n = 10(selected)
Mean = number of trial ✕ probability
= 10 ✕ 0.6
= 6.0
Mean is 6.0
Standard deviation :
σ = np(1-p)
= 10 ✕ 0.6 ✕(1- 0.6 )
= 2.4
Standard deviation = 1.5492
If a random sample of 10 students is selected from 60% passed students,with mean 6 and standard deviation 1.5492.
Rules of Probability : The first rule of probability used in this essay is the definition of a random sample. A random sample is a set of data taken from a larger population that is chosen by a method that gives each element of the population an equal chance.
The mean and standard deviation of a random sample of 10 students can be calculated in order to determine the probability that a given student has passed an exam. This requires knowledge of some basic principles of statistics and probability.
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Which coordinates BEST represent the y-intercept of the line graphed below? (0, 2) (6, 0) (2, 0) (0, 6)
How do you sum a column in Excel on a Mac?
To see the steps of sum a column in Excel on a Mac.
Now, According to the question:
1. Click the first empty cell below a column of numbers.
2. Do one of the following: Excel 2016 for Mac: : On the Home tab, click AutoSum. Excel for Mac 2011: On the Standard toolbar, click AutoSum. ...
3. Press RETURN .
How do you sum cells on a Mac?
Once the cells are selected, press the Command key and the = (equal sign) key at the same time. This will automatically sum the selected cells. If you want to sum a specific range of cells, you can do so by selecting the first cell in the range, pressing the Shift key, and then selecting the last cell in the range.
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what is the value of y if the slope of the line is 3 and two points on the line is (0,y) and (2,4)
The value of y is -2.
What is coordinate of point?
The coordinates are a pair of numbers that, using the horizontal and vertical lines, precisely pinpoint a point's location on a cartesian plane. typically represented by (x, y), the point's x and y values on a graph. There are two coordinates in every point or ordered pair.
Given points are (0,y) and (2,4).
The formula of slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).
The slope of the given line is (4 - y)/(2 - 0) = (4 - y)/2.
Again given that the slope of the line is 3.
Therefore,
(4 - y)/2 = 3
Multiply both sides by 2
4 - y = 6
Subtract 4 from both sides:
-y = 2
Multiply both sides by -1:
y = -2
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Discuss the difference between r and p. Choose the correct answers below. r represents the p represents the sample correlation coefficient thing critical value for the correlation coefficient. population correlation coefficient. Click to select your answer(s) 1 - 35 of 35 Type here to search o te Discuss the difference between r and p. Choose the correct answers below. r represents the p represents the critical value for the correlation coefficient. population correlation coefficient. sample correlation coefficient. Click to select your answers) 1.35 of 35
The difference between r and p. is that r represents the sample correlation coefficient while p represents the p-value
What is the sample correlation coefficient?Generally, r represents the sample correlation coefficient, which is a measure of the strength and direction of the linear relationship between two variables in a sample of data. It ranges from -1 to 1, where -1 represents a perfect negative correlation, 0 represents no correlation, and 1 represents a perfect positive correlation.
p represents the p-value, which is a measure of the statistical significance of the sample correlation coefficient. It represents the probability that the observed correlation occurred by chance, assuming that there is no true correlation in the population.
A p-value of less than 0.05 is often used as a threshold for determining statistical significance, meaning that the observed correlation is unlikely to have occurred by chance and is likely to reflect a true correlation in the population.
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Is the mean of the following data is 18.75 then find the value of p?
The value of p is 20
Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Mean = (Sum of all the observations/Total number of observations)
Is the mean of the following data is 18.75 then find the value of p?
Xi 10 15 p 25 30
Fi 5 10 7 8 2
We may prepare th frequency table as given below:
mean=(∑Fi *Xi) / ∑Fi
= (5*10 + 10*15 + 7*p + 8*25 + 2* 30)/ (5 + 10 +7 +8 +2)
= (460+7p)/ 32
=18.75
460+7p=(18.75×32)
⇒(460+7p)=600
⇒7p=140
⇒p=20
The value of p is 20
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over the past several years, a random sample of 40 women athletes at the school showed that 23 eventually graduated. does this indicate that the population proportion of women athletes who graduate from the university is now less than 67%? use a 1% level of significance.
The population proportion of women athletes who graduated from the university is more than 67%.
A random sample of 40 women athletes at the school showed that 23 eventually graduated.
n=40 , X=23 , p0 =67% = 0.67 , alpha = 1% = 0.01
H0: : p0 = 0.67 Vs H1 : p0 < 0.67
Test statistics = (p-p0) / (square root ((p0(1-p0) / n))
p=X/n
H0::p0=0.67 Vs H1:p0<0.67
Test statistics = z = (p-p0) / ( square root ((p0(1-p0)/n))
p=X/n=23/40
z = (0.575-0.67) / (square root (0.67(1-0.67)/40))=-1.278
P - value = P(z < -1.278) = 0.1007
Since the p-value is 0.1007 that is less than the level of significance the decision is to reject the null hypothesis. In conclusion, there is a sufficient evidence to support that the population proportion of women athletes who graduated is now more than 67%.
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the names of 5 students from section a, 6 students from section b and 7 students from section c were selected. the age of all the 18 students was different. again, one name was selected from them and it was found that it was of section b. what was the probability that it was the youngest student of the section b?
The probability that the selected student was the youngest student from Section B is 2/6.
The total number of students is 18 which include
Section A: 5 students
Section B: 6 students
Section C: 7 students
Given that the selected student was from Section B
Calculate the probability of selecting a student from Section B
P(Section B) = 6/18 = 1/3
Calculate the probability of selecting the youngest student from Section B
Since there are 6 students in Section B, the probability of selecting the youngest student is 1/6.
Calculate the probability of selecting the youngest student from Section B given that the selected student was from Section B
P(Youngest student from Section B|Section B) = P(Youngest student from Section B ∩ Section B) / P(Section B)
= (1/6) / (1/3)
= 2/6
Therefore, the probability that the selected student was the youngest student from Section B is 2/6.
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3) Part of the population of 4,500 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 8 of them are infected. How many elk are likely to be infected?
Using percentage on the population size, the number of infected is 720
Probability SamplingProbability sampling is a technique in which the researcher chooses samples from a larger population using a method based on probability theory. For a participant to be considered as a probability sample, he/she must be selected using a random selection.
In this question, we can find the percentage of infected in a sample size of 50.
Percentage of infected = (8 / 50) * 100
Percentage of infected = 0.16 * 100
Percentage of infected = 16%
Using this value, we can further calculate the total number of infected in the population.
16 % of 4500 = ?
16 / 100 = x / 4500
0.16 = x / 4500
x = 4500 * 0.16
x = 720
The number of infected are 720
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What are the 10 expressions?
The 10 expressions in Math are:
1. Sum 2. Difference 3. Product 4. Quotient 5. Exponent 6. Root 7. Absolute Value 8. Factor 9. Power 10. FractionUnderstanding the Basics of Math Through the 10 ExpressionsMath is a subject that can be intimidating to many, but it is a fundamental part of life that is necessary to understand. It is important to have a basic grasp of different expressions in order to be successful in math. This essay will explore the ten expressions of math and provide insight into their importance.
The first expression is the sum. This is the answer you get when adding two or more numbers together. For example, if you have the numbers 5, 7, and 8, the sum would be 20. Sums can also be used to find the total amount of a group of objects.
The second expression is the difference. This is the answer you get when subtracting two or more numbers. For example, if you have the numbers 8 and 5, the difference would be 3. Differences can also be used to find the difference between two amounts.
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help it is an assignment
Answer:
13. Given below is a graph showing the number of Hindi movies released in the first six months of 2005. Which of the following questions can be answered from this graph?
D. How many movies were released during the period 1st Match to 31st May 2005?14. The table below gives the dimensions of some rectangles.
D. rectangles that are equal in perimeter could have different areas.Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Answer + Explanation:
13. A. can be answered - add all the monthly figures using the bar height.
B. cannot be answered - the graph shows May has the least movies but the graph doesn't tell you WHY it has the least movies, it does not give any reason.
C. can be answered - look at the highest bar height (it's February)
D. can be answered - calculate March, April and May figures together.
As such, circle A , C and D.
14.
A. Wrong - perimeter does not change in the table despite increase in area (all the perimeters in the table are the same).
B. Wrong - none have equal areas that have equal perimeters.
C. Wrong - none of the rectangles with equal perimeters have equal areas.
D. Correct - All the rectangles with the equal perimeter do not have equal areas (areas can be different).
So circle only D.
Gavin has a deck that measures 6 feet by
3 feet. He wants to increase each
dimension by equal lengths so that its
area is tripled. By how much should he
increase each dimension?
Answer:
feet
Each dimension should be increased by four times so that the area is tripled and each dimension is equal in length.
What is a quadratic equation?
Any equation of the form where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
In mathematics, a dimension is the length or width of an area, region, or space in one direction.
area = length × width
a = l × w
But, we want to triple than area;
3A = 3 (l × w)
3A = (k × l) (k × w)
k² = 3
k = √3
The new dimensions will be: 6√3 and 3√3
Increased Dimension: 6√3 - 6 and 3√3 - 3
let x is the amount of increase in each side:
(x + 6) (x + 3) = 3(18)
x² + 3x + 6x + 18 = 54
x² + 9x + 18 = 54
x² + 9x - 36 = 0
∵ x = 4
Hence, each dimension should be increased by four times so that the area is tripled and each dimension is equal in length.
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Answer:3
Step-by-step explanation:
(Laws of Exponents with Integer Exponents LC)
Create an equivalent expression for 17−7 • 175.
one over seventeen raised to the second power
one over seventeen raised to the power of negative two
172
−172
One over seventeen raised to the second power is (1/17)².One over seventeen raised to the power of negative two is (1/17)⁻².
Define power and exponents.In mathematics, a base number raised to an exponent is referred to as a power. The base number is the factor that is multiplied by itself, and the exponent indicates how many times the base number has been multiplied. Let's learn more about power and exponent. A power is a phrase that depicts the same component being multiplied repeatedly. For instance, in the number 52, the base is the number 5, and the exponent is the number 2. The base is multiplied by the exponent, which is 2, to get the total number of factors.
Given,
one over seventeen raised to the second power
(1/17)²
one over seventeen raised to the power of negative two
(1/17)⁻²
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What are the roots of the quadratic equation 2x² 5x 3?
The roots of the quadratic equation 2x^2 + 5x + 3 are the two values of x that make the equation equal to 0. These two values are x = -3 and x = -1/2.
The roots of a quadratic equation are the two values of x that make the equation equal to 0. To find the roots of the equation 2x^2 + 5x + 3, we need to set the equation equal to 0 and solve for x. We can do this by using the Quadratic Formula, which states that the two roots of a quadratic equation ax^2 + bx + c = 0 are x = [-b +/- sqrt(b^2 - 4ac)] / 2a. In this equation, a = 2, b = 5, and c = 3. We can plug these values into the formula to get x = [-5 +/- sqrt(25 - 24)] / 4. Simplifying this expression gives us x = -3 and x = -1/2, which are the two roots of the equation 2x^2 + 5x + 3.
x = [-5 +/- sqrt(25 - 24)] / 4
x = [-5 +/- sqrt(1)] / 4
x = [-5 +/- 1] / 4
x = -3 and x = -1/2
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8. Solve the Right Triangle.
The length of the perpendicular of the right-angle triangle will be 20.4 meters.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
The hypotenuse is 30 m and the base is 22 m. Then the length of the perpendicular is given as,
30² = P² + 22²
900 = P² + 484
P² = 900 - 484
P² = 416
P = 20.4 m
The length of the perpendicular of the right-angle triangle will be 20.4 meters.
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Finding angle measures of a triangle given two angles of a similar triangle
ok
Answer:
the answer would be this 5,8,3
If dx-2=h, then x is equal to?
Answer:
x=h+2 divided by d x = h+2/d
Step-by-step explanation:
Please Help ASAP, end of term is the 15th and I’m super behind!!
What is the rate of change of the line in the graph below?
(Picture below)
The rate of change is 1 and the y-intercept is 1/2.
How do you find the rate of change on a line graph?
To get the slope of a graphed function, use the average rate of change formula. Divide the change in y-values by the change in x-values to determine the average rate of change.
The slope, rise over run, or change in over the change in of a line determines its rate of change. A graph's slope triangle or two points in a table can be used to compute the slope.
It is frequently referred to as rate of change when determining the slope of real-world scenarios. "Rate of change" and "slope" have the same meaning. Use the slope formula or create a slope triangle if you are asked to determine the rate of change.
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statistical significance: a. indicates a high likelihood that your results are due to your treatment versus due to chance. b. is more likely to be reliable if you have a small sample size versus a large sample size. c. is a requirement of the data from a scientific experiment. d. indicates that the hypothesis should be rejected. e. depends on large data sets.
Answer:
Step-by-step explanation:
sean
What are 3 odd consecutive numbers of 75?
The three consecutive odd numbers of the number 75 are:
77, 79 and 81
What are consecutive numbers?Consecutive numbers are those numerical values that are found just after a specific number or value, for example consecutive numbers from 5 will be 6 onwards.
In our case we have a specific value and this is the number 75, if we want to know the consecutive numbers immediately we add +1, +2 and so on.
But as we only want the odd numbers we will add +2, +4 and +6, having as a result the following numbers:
75 + 2 = 7775 + 4 = 7975 + 6 = 81The consecutive and odd numbers will be 77, 79, 81.
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What are the 4 theorems that can be used in proving congruence in right triangles?
Answer: The leg-leg theorem, the hypotenuse-leg theorem, the hypotenuse-angle theorem, and the leg-angle theorem.
Step-by-step explanation: Search it up.
How do you find the inverses?
To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.
Inverse function
An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by 'f' or 'F', then the inverse function is denoted by f^-1 or F^-1.
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need your help please
Answer:
Hi ! the answer is .38!
Step-by-step explanation:
i need help i dont understand how to solve
By using the concept of depreciation, it can be calculated that
Value of x is 3.6%
What is depreciation?
Depreciation is the exponential decrease in the value of an asset or population or cost of an article at a certain rate over a certain period of time.
Now opposite of depreciation is growth.
Growth is the exponential increase in the value of an asset or population or cost of an article at a certain rate over a certain period of time.
Here concept of depreciation has been used
Number of deer in 2005 = 1480
Rate = x%
Time = 7 years
Number of deer after 7 years = 1141
[tex]1141 = 1480(1-\frac{x}{100})^7\\(1 - \frac{x}{100})^7 = \frac{1141}{1480}\\(1-\frac{x}{100}) = (\frac{1141}{1480})^{\frac{1}{7}}\\1 - \frac{x}{100} = 0.964\\\frac{x}{100} = 1 - 0.964\\\frac{x}{100} = 0.036\\x = 0.036 \times 100\\[/tex]
x = 3.6 %
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Which number of simulation trials would be likely to produce results that are closest to those predicted by probability theory?.
The number of simulation trials that would be likely to produce results that are closest to the actual probability is 25. The correct option is C).
The following steps can be used in order to determine the number of simulations:
Step 1 - Remember the maximum number of trials gives the maximum chance to produce results that are closest to the actual probability.
Step 2 - Now, check all the options given in the question and choose the largest one.
From the above steps, it can be concluded that the correct option is C) 25.
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Full question :
Which number of simulation trials would be likely to produce results that are closest to those predicted by probability theory?.
A. 10
B. 15
C. 25
D. 20
Does someone mind helping me with this problem? Thank you!
Answer:
y = - [tex]\frac{1}{4}[/tex] x - 10
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 4x - 2 ← is in slope- intercept form
with slope m = 4
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{4}[/tex] , then
y = - [tex]\frac{1}{4}[/tex] x + c ← is the partial equation
to find c substitute (4, - 11 ) into the partial equation
- 11 = - [tex]\frac{1}{4}[/tex] (4) + c = - 1 + c ( add 1 to both sides )
- 10 = c
y = - [tex]\frac{1}{4}[/tex] x + (- 10) , that is
y = - [tex]\frac{1}{4}[/tex] x - 10 ← equation of line
If f(x) is a third degree polynomial function and g(x) = f(2x) + 2, which of the following MUST be true?
F f(x) and g(x) have the same x-intercepts.
G f(x) and g(x) have the same y-intercepts.
H f(x) and g(x) have the same number of zeros.
J f(0)=g(0)−2
Philip wants to enclose his garden using 32 meters of fence. What is the largest interger value area, in square meteres, that he can enclose? what are the dimensions of the rectangular enclosure for his garden?.
The dimensions of the rectangular enclosure for his garden is length of 8.0 m and width of 8.0 m.
Given :
Let x represent the length of the garden and y represent the width of the garden.
Perimeter = 2(x + y)
32 = 2(x + y)
x + y = 16
y = 16 - x
Area (A) = length * width
A = xy
A = x(16 - x)
A = 16x - x²
Maximum area is at dA/dx = 0:
dA/dx = 16 - 2x
0 = 16 - 2x
2x = 16
x = 8.0 m
y = 16 - x = 15 - 7.5 = 8.0 m
The dimensions of the rectangular enclosure for his garden is length of 8.0 m and width of 8.0 m.
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