The magnitude spectrum of Fourier coefficients a[n] = 4 sin(nπ/3) is: |C[k]| = 0 so the phase spectrum is undefined. Fourier coefficients of x[n] = cos(2nπ/3) + sin(2nπ/5) for all other values of k, C[k] = 0, so the magnitude and phase spectra are zero. The Fourier coefficient for cos(x) sin(y) = 1/2 (sin(x + y) – sin(x – y)) C[k] is zero when k is not equal to ±2/3 and ±2/5.
To compute the Fourier coefficients of a[n] = 4 sin(nπ/3), we use the formula:
C[k] = (1/N) * Σ[n=0 to N-1] a[n] e^(-j2πkn/N)
where N is the period of the signal (in this case, N = 6 since sin(nπ/3) has a period of 6), and k is the frequency index.
For k = 0, we have:
C[0] = (1/6) * Σ[n=0 to 5] 4 sin(nπ/3) = (4/6) * (sin(0) + sin(π/3) + sin(2π/3) + sin(π) + sin(4π/3) + sin(5π/3))
C[0] = (4/6) * (0 + √3/2 + √3/2 + 0 - √3/2 - √3/2) = 0
For k = ±1, we have:
C[1] = (1/6) * Σ[n=0 to 5] 4 sin(nπ/3) e^(-j2πn/6) = (4/6) * (sin(0) - sin(π/3) - sin(2π/3) + sin(π) + sin(4π/3) - sin(5π/3))
C[1] = (4/6) * (0 - √3/2 + √3/2 + 0 + √3/2 - (-√3/2)) = 0
C[-1] = (1/6) * Σ[n=0 to 5] 4 sin(nπ/3) e^(j2πn/6) = (4/6) * (sin(0) - sin(π/3) - sin(2π/3) + sin(π) + sin(4π/3) - sin(5π/3))
C[-1] = (4/6) * (0 - √3/2 + √3/2 + 0 + √3/2 - (-√3/2)) = 0
For all other values of k, we have C[k] = 0. Therefore, the Fourier series of a[n] is:
a[n] = 0
The magnitude spectrum is:
|C[k]| = 0
The phase spectrum is undefined.
To compute the Fourier coefficients of x[n] = cos(2nπ/3) + sin(2nπ/5), we use the formula:
C[k] = (1/N) * Σ[n=0 to N-1] x[n] e^(-j2πkn/N)
where N is the period of the signal (in this case, N = lcm(3, 5) = 15 since both cos(2nπ/3) and sin(2nπ/5) have periods of 3 and 5, respectively), and k is the frequency index.
For k = 0, we have:
C[0] = (1/15) * Σ[n=0 to 14] (cos(2nπ/3) + sin(2nπ/5)) = (1/15) * (5 + 0 - 5 + 0 + 5 + 0 - 5 + 0 + 5 + 0 - 5 + 0 + 5 + 0 - 5 + 0 + 5) = 5/3
To compute C[k] for k ≠ 0 and k ≠ 5, we can use the trigonometric identity:
cos(x) sin(y) = 1/2 (sin(x + y) – sin(x – y))
Let x = 2kπ/3 and y = 2nπ/5, then:
cos(2kπ/3) sin(2nπ/5) = 1/2 (sin(2kπ/3 + 2nπ/5) – sin(2kπ/3 – 2nπ/5))
= 1/2 (sin(10knπ/15 + 6kπ/15) – sin(10knπ/15 - 2kπ/15))
= 1/2 (sin((2k + 3n)π/3) – sin((2k - n)π/3))
The first term is zero when (2k + 3n) is an odd multiple of 3, and the second term is zero when (2k - n) is an odd multiple of 3. Therefore, C[k] = 0 when k + 3n is odd or k - n is odd.
For k = 3n, we have:
C[3n] = (1/15) * Σ[m=0 to 14] (cos(2mπ/3) sin(2nπ/5))
= (1/30) * Σ[m=0 to 14] (sin((2m + 3n)π/3) – sin((2m - n)π/3))
= (1/30) * (sin(5nπ/3) – sin(nπ/3) + sin(7nπ/3) – sin(5nπ/3) + sin(9nπ/3) – sin(7nπ/3) + sin(11nπ/3) – sin(9nπ/3) + sin(13nπ/3) – sin(11nπ/3) + sin(15nπ/3) – sin(13nπ/3) + sin(17nπ/3) – sin(15nπ/3) + sin(19nπ/3) – sin(17nπ/3))
= (1/30) * (sin(nπ/3) – sin(19nπ/3)) = 0
Therefore, the only non-zero coefficients are C[0] = 5/3 and C[5] = -5/3. The magnitude and phase spectra are:
|C[0]| = 5/3, arg(C[0]) = 0
|C[5]| = 5/3, arg(C[5]) = π
For all other values of k, C[k] = 0, so the magnitude and phase spectra are zero.
To compute the Fourier coefficients of cos(x) sin(y) = 1/2 (sin(x + y) – sin(x – y))
x[n] = 1/2 (sin(2nπ/3 + π/2) - sin(2nπ/3 - π/2)) * 1/2 (sin(2nπ/5) - sin(-2nπ/5))
Using the formula for the Fourier coefficients of a sinusoidal signal:
C[k] = (1/N) Σ[n=0 to N-1] x[n] e^(-j2πnk/N)
we can compute the Fourier coefficients for x[n]:
C[k] = (1/N) Σ[n=0 to N-1] x[n] e^(-j2πnk/N)
= (1/N) [Σ[n=0 to N-1] 1/2 sin(2nπ/3 + π/2) e^(-j2πnk/N) - Σ[n=0 to N-1] 1/2 sin(2nπ/3 - π/2) e^(-j2πnk/N)] [Σ[n=0 to N-1] 1/2 sin(2nπ/5) e^(-j2πnk/N) - Σ[n=0 to N-1] 1/2 sin(-2nπ/5) e^(-j2πnk/N)]
= 1/4 [C1(k-2/3) - C1(k+2/3)] [C1(k-2/5) - C1(k+2/5)]
where C1(k) is the Fourier coefficient of the signal cos(2nπ/3), which is given by:
C1(k) = (1/N) Σ[n=0 to N-1] cos(2nπ/3) e^(-j2πnk/N)
= (1/N) Σ[n=0 to N-1] 1/2 [e^(-j2πnk/3) + e^(j2πnk/3)]
= 1/2 [δ(k-1/3) + δ(k+1/3)]
Therefore, the Fourier coefficient C[k] is zero when k is not equal to ±2/3 and ±2/5.
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Sampling frame Ideally, the sampling frame in a sample survey should list every individual in the population, but in practice, this is often difficult.
Suppose that a sample of households in a community is selected at random from the telephone directory. Explain how this sampling method results in under coverage that could lead to bias.
Using a telephone directory as the sampling frame can lead to under-coverage and bias, and it is generally not considered a representative sampling method.
Other more representative sampling methods, such as random digit dialing, address-based sampling, or a combination of methods, may be used to obtain a more accurate representation of the population.
Selecting a sample of households from the telephone directory can result in under-coverage and bias for several reasons.
Concept: When random sampling is not used, bias or regular flaws in the way the sample mean the population can occur.
Voluntary reply to samples, in which respondents choose their own respondents, and benefit samples, in which people who live nearby are included in the sample, are particularly biased.
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when estimating the population average using the sample mean, adding observations to a sample will always decrease the standard error of your estimate.
When estimating the population average using the sample mean, adding observations to a sample will always decrease the standard error of your estimate is random sampling variability.
In statistical analysis, estimating the population average is a common task. One way to estimate this is by using the sample mean. However, as more observations are added to the sample, the standard error of the estimate decreases. Let's explore why this is the case.
The standard error of the mean (SEM) is a measure of the amount of variability in a sample mean from one sample to another. It can be calculated using the formula:
SEM = standard deviation / square root of sample size
As we can see, the SEM is inversely proportional to the square root of the sample size. This means that as we increase the sample size by adding more observations, the denominator of the SEM formula increases, causing the SEM to decrease.
Now, let's consider how this affects our estimate of the population average. The sample mean is an unbiased estimate of the population mean. This means that on average, the sample mean will equal the population mean. However, due to random sampling variability, the sample mean can differ from the population mean.
The standard error of the mean gives us an idea of how much the sample mean can vary from one sample to another.
Therefore, adding more observations to a sample decreases the SEM, making our estimate of the population average more precise. This is because the average of a larger sample is more representative of the population average, as it is less affected by random sampling variability.
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An online wholesaler sells novelty hats in bulk. The purple and leopard print hat sells for $3.50 each
when you buy less than 25 hats. For orders of 25 or more, the price is $2.97 per hat. Express the total
cost of the order as a function of the number of hats ordered, and graph this function in an appropriate
window on your paper. If your group has a budget of $80 for hats, how many hats can you purchase?
we can purchase a maximum of 23 hats if we buy them for $3.50 each, or a maximum of 27 hats if we buy them for $2.97 each.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Function to represent the total cost of the order in terms of the number of hats ordered:
C(n) = {3.50n, if n < 25;
2.97n, if n >= 25}
where n is the number of hats ordered, and C(n) is the cost of the order.
If the budget for hats is $80, we can set C(n) equal to 80 and solve for n:
3.50n = 80, if n < 25;
2.97n = 80, if n >= 25
For n < 25, we get:
n = 80/3.50 ≈ 22.86 =23
if the budget is $80 and the hats cost $3.50 each, we can buy a maximum of 23 hats.
For n >= 25, we get:
n = 80/2.97 ≈ 26.96
So if the budget is $80 and the hats cost $2.97 each, we can buy a maximum of 27 hats.
Therefore, we can purchase a maximum of 23 hats if we buy them for $3.50 each, or a maximum of 27 hats if we buy them for $2.97 each.
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Find the probability that at most 4 students will attend. (Round your answer to four decimal places.)
Find the probability that more than 3 students will attend. (Round your answer to four decimal places.)
A school newspaper reporter decides to randomly survey 13 students to see if they will attend Tet (Vietnamese New Year) festivities this year. Based on past years, she knows that 24% of students attend Tet festivities. We are interested in the number of students who will attend the festivities.
The school newspaper reporter wants to find out how many students will attend Tet festivities. She randomly surveys 13 students and knows that 24% of students typically attend the festivities. We are interested in the probability of the number of students who will attend.
The probability that at most 4 students will attend is 0.4936 and the probability that more than 3 students will attend is 0.5064. Calculating these probabilities can be done using the binomial probability formula. First, calculate the probability of exactly 4 students attending. This probability is [tex]0.24^4 * 0.76^9 = 0.0038[/tex]. Then, calculate the probability of 3 students or fewer attending by adding the probabilities of 0, 1, 2, and 3 students attending, which is 0.0013 + 0.0358 + 0.1045 + 0.2696 = 0.4113. Finally, subtract 0.4113 from 1 to get 0.4936. We are interested in the probability of the number of students who will attend. To calculate the probability of more than 3 students attending, subtract 0.4113 from 1 to get 0.5064.
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The heights of men (in inches) in the United States follow approximately N(69, 2.25). The heights of women (in inches) in the United States follow approximately N(64,2). A female volleyball player at your college is 6 feet 2 inches tall, and a male college soccer player is also 6 feet 2 inches tall. Based on the distribution above, who is taller in relation to the distribution of heights based on gender?
The female volleyball player is taller in relation to the distribution of heights based on gender.
How to relate distribution of heights based on gender?The mean height of a man is 69 inches and the standard deviation is 2.25 inches. The mean height of a woman is 64 inches and the standard deviation is 2 inches.
To compare the heights of the female volleyball player and the male soccer player, we need to convert their heights to inches.
6 feet 2 inches is equal to 74 inches.
The female volleyball player is 10 inches taller than the mean height for women in the United States, while the male soccer player is 5 inches taller than the mean height for men in the United States.
To determine who is taller in relation to the distribution of heights based on gender, we need to compare the difference between their heights and the mean height for their respective gender in terms of the standard deviation.
For the female volleyball player, the difference is 10 inches - 64 inches (the mean height for women) = 6 standard deviations (since the standard deviation for women is 2 inches).
For the male soccer player, the difference is 10 inches - 69 inches (the mean height for men) = 4.4 standard deviations (since the standard deviation for men is 2.25 inches).
Therefore, the female volleyball player is taller in relation to the distribution of heights based on gender.
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A person invested $3, 700 in an account growing at a rate allowing the money to
double every 6 years. How much money would be in the account after 14 years, to the
nearest dollar?
Answer:
Step-by-step explanation:10299
The function m is given in three equivalent forms. Which form most quickly reveals the y-intercept? Choose 1 answer: m(c) = 2 + 6)(x + 2) m(c) = 2x2 + 16r + 24 m(z) = 2(2 + 42 _ 8 What is the y-intercept? y-intercept (0 Show Calculator
The form of the function that most quickly reveals the y-intercept is m(c) = 2 + 6(x + 2), and the y-intercept is 14.
The form of the function that most quickly reveals the y-intercept is m(c) = 2 + 6(x + 2), because it is in slope-intercept form, y = mx + b, where the y-intercept is given directly by the constant term, b.
To find the y-intercept of this function, we can substitute x = 0, since the y-intercept occurs when x = 0:
m(0) = 2 + 6(0 + 2) = 2 + 12 = 14
Therefore, the y-intercept of the function is 14.
Note that the other two forms of the function, m(c) = 2x^2 + 16x + 24 and m(z) = 2(2 + 4z) - 8, do not reveal the y-intercept as directly as the first form, since they are not in slope-intercept form. However, we could still find the y-intercept by substituting x = 0 or z = 0, respectively, and solving for the corresponding value of y.
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The graph represents the volume of a cylinder with a height equal to its radius. When the diameter is 2 cm, what is the radius of the cylinder? Express the volume of a cube of side length as an equation. Make a table for volume of the cube at 0 cm, 1 cm, 2 cm, and 3 cm. Which volume is greater: the volume of the cube when 3 cm, or the volume of the cylinder when its diameter is 3 cm?
Answer:
Comparing this to the volume of the cube when the side length is 3 cm, which is 27 cm^3, we can see that the volume of the cube is greater than the volume of the cylinder.
Step-by-step explanation:
I'm sorry, but I cannot see the graph you are referring to. However, I can still answer some of your questions based on the information provided.
When the diameter of the cylinder is 2 cm, the radius is equal to half the diameter, which is 1 cm.
To express the volume of a cube of side length s as an equation, we use the formula for the volume of a cube:
Volume of cube = s^3
Making a table for the volume of the cube at different side lengths, we get:
Side Length (cm) Volume (cm^3)
0 0
1 1
2 8
3 27
To compare the volume of the cube when the side length is 3 cm and the volume of the cylinder when the diameter is 3 cm, we need to find the radius of the cylinder first.
When the diameter is 3 cm, the radius is half the diameter, which is 1.5 cm. The height of the cylinder is also equal to the radius, so the volume of the cylinder can be found using the formula:
Volume of cylinder = πr^2h
Substituting r = 1.5 cm and h = 1.5 cm, we get:
Volume of cylinder = π(1.5)^2(1.5) ≈ 10.602 cm^3
Comparing this to the volume of the cube when the side length is 3 cm, which is 27 cm^3, we can see that the volume of the cube is greater than the volume of the cylinder.
Jane’s class gave examples of absolute value in distances traveled. Which example demonstrates the greatest distance traveled? Responses Jim jumped on a trampoline to a height of 8.67 feet. Jim jumped on a trampoline to a height of 8.67 feet. Teresa rode an elevator to a depth of −10 feet. Teresa rode an elevator to a depth of - 10 feet. Brenan dove to a depth of −12.76 feet. Brenan dove to a depth of − 12.76 feet. Kailey hopped a length of 7.612 feet. Kailey hopped a length of 7.612 feet.
Answer:
The example that demonstrates the greatest distance traveled is Brenan diving to a depth of -12.76 feet, as it has the highest absolute value.
The following is the average daily temperature for Frederick, Maryland for the month of June: 94 82 83 86 91 72 88 92 82 75 82 72 | 77 93 71 | 78 | 74 | 81 91 85 90 79 82 72 83 86 85 89 90 94 (a) Complete the frequency distribution for the data. Age Frequency Relative Frequency 70-74 75-79 80-84 85-89 90-94 (b) Which of the following is the correct histogram for this data? Frequency 7080 Temperature Frequency 70 75 80 85 Temperature 90 o Frequency 70 90 80 Temperature 0 Frequency 70 90 75 80 85 Temperature
The data is analyzed and frequency table is created. The correct option for the histogram is the second option.
Here 30 individual samples are given. We are first categorizing the values in a frequency distribution table. It is shown as an image below.
Temperature frequency Relative frequency
70-74 5 5/30 = .166 = 16.6%
75-79 4 4/30 = .133 = 13.3%
80-84 7 7/30 = 0.233 =23.3%
85-89 6 6/30 = 0.2 = 20%
90-94 8 8/30 = 0.266 = 2.66%
From the given histogram the second one represents the data given in the frequency table. It is marked in the image.
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The complete question is included as image
An ancient egyptian stone tablet is found .it is correctly detucted that it is a sum with each symbol representing a different number .suprisingly there are 2 ways of doing it .what are they?
one possible explanation for why there are two different ways of adding up the symbols on the tablet is given below.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
The ancient Egyptian number system was based on hieroglyphs, and it used a decimal system with hieroglyphs representing the powers of 10. However, without seeing the specific symbols on the tablet, it is difficult to provide an accurate answer.
Assuming that the tablet is using a basic arithmetic operation such as addition, and each symbol represents a different number,
it is possible that there are two different ways to add up the numbers represented by the symbols on the tablet.
One way to approach this problem is to try to find two different sets of numbers that when added, produce the same result.
For example, if the symbols represent the numbers 2, 3, and 5, then one way to add them up would be:
2 + 3 + 5 = 10
Another way to add them up would be:
3 + 7 = 10
In this case, the symbol for 2 would represent the number 7, and the symbol for 5 would represent the number 3. This would be one possible explanation for why there are two different ways of adding up the symbols on the tablet.
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sorry but without seeing the actual tablet then we cant work it out to get a correct answer
a) Work out the value of 3² +2³
b) Work out the value of 2¹ - 3²
Answer:
3² +2³= 9+8=17
2¹ - 3²= 2-9=8
Step-by-step explanation:
Answer:
1-7
Step-by-step explanation:
[tex]3^{2}[/tex] + [tex]2^{2}[/tex] (3x3) + (2x2x2) = 9 + 8 = 17
[tex]2^{1}[/tex] - [tex]3^{2}[/tex] = 2 - (3x3) = 2 - 9 = -7
DIG DEEPER A fitness club with 100 members offers one free training session per member in either running, swimming, or weightlifting. Thirty of the fitness center members sign up for the free session. The running and swimming sessions are each twice as popular as the weightlifting session. What is the probability that a randomly chosen fitness club member signs up for a free running session?
The probability that a randomly chosen fitness club member signs up for a free running session is 0.12 or 12%.
What is probability ?
Probability is a measure of the likelihood or chance of an event occurring. It is usually expressed as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to occur. For example, if the probability of an event is 0.5, it means that there is a 50% chance that the event will occur.
Given by the question:
There are a total of 100 members in the fitness club, and 30 members have signed up for the free session. Let's call the number of members who signed up for the weightlifting session "x", so the number of members who signed up for the running session and the swimming session each is "2x".
The total number of members who signed up for the free session is:
x + 2x + 2x = 5x
We know that 30 members signed up for the free session, so we can set up the following equation:
5x = 30
Solving for x, we get:
x = 6
Therefore, 6 members signed up for the weightlifting session, and 12 members signed up for each of the running and swimming sessions.
The probability of a randomly chosen member signing up for a free running session is the number of members who signed up for the running session divided by the total number of members:
P(Running) = 12/100
P(Running) = 0.12
Therefore, the probability that a randomly chosen fitness club member signs up for a free running session is 0.12 or 12%.
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Can you please help with this problem
Answer:
x = 30, -40
Step-by-step explanation:
This a right triangle, so you can use the Pythagorean Theorem.
[tex]a^{2}+ b^{2}=c^{2}[/tex], now in place of the a, b and c use x, x +10 and 50.
so a = x, b =x+10 and c = 50
[tex]x^{2} + (x+10)^{2} =50^{2}[/tex]
[tex]x^{2} +x^{2} +20x +100 = 2500[/tex]
the x-intercept of the graph of f(x)=3log(x+5)+2 is:
10^-2/3 - 5 is the x-intercept of the given equation.
Determine the x-intercept of a functionThe x-intercept of a function is the point where the function f(x) is equivalent to zero.
Given the function below;
f(x)=3log(x+5)+2
3log(x+5)+2 = 0
Make x the subject of the formula:
3log(x+5) = -2
log(x+5) = -2/3
x + 5 = 10^-2/3
x = 10^-2/3 - 5
Hence the x-intercept of the graph of f(x)=3log(x+5)+2 is 10^-2/3 - 5
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Suppose that a population of fish P(t) grows according to the differential equation P' = 4P - 4P^2 - h representing logistic growth with a constant rate of harvesting h. What is the maximum sustainable harvest rate: the largest value of h for which there is still an equilibrium.
The maximum sustainable rate of harvest which is possible for the growth of fish P(t) according to the differential equation " P' = 4P - 4P^2 - h " will be at the harvest rate of h=3.
In order to calculate the maximum sustainable harvest rate possible, we are required to find the equilibrium solutions of the differential equation firstly. Equilibrium solutions occur when P' = 0, so we can set the right-hand side of the differential equation at 0.
4P - 4P² - h = 0
Now a quadratic equation is formed in terms of P, which can be used to obtain P.
P = (1 ± √(1 + h))/2
There are two equilibrium solutions, obtained by these two values of P.
Now, in order to obtain a maximum sustainable harvest rate, we are required to have both equilibrium solutions to as positive ( as negative populations don't make any sense in this context).
Therefore, we have to find the largest value of h for which both of these equations have positive solutions:
(1 + √(1 + h))/2 > 0
(1 - √(1 + h))/2 > 0
On camparing both the inequalities, it can be concluded that the first inequality is always true, since the square root of a positive number is always positive. The second inequality is true when h < 3.
Hence, the maximum sustainable harvest rate is is found to be at h = 3. If the harvesting rate is greater than 3, then there will be no positive equilibrium solutions and the population will eventually be perished.
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FILL IN THE BLANK Quantitative data that measure how many are ________; quantitative data that measure how much are ________.
Answer:
Caca
Step-by-step explanation:
Caca
10. Suppose that you are checking your work on a test, and see that you have computed the cross product of
v=i+2j−3k
and
w=2i−j+2k
. You got
v×w=i+8j−5k
. Without actually redoing
v×w
, how can you spot a mistake in your work?
We clearly seen that a little sign mistake here in 'j'.
In the given question you have computed the cross product of v=i+2j−3k and w=2i−j+2k. You got v×w=i+8j−5k Without actually redoing v×w and we have to tell how can we spot a mistake in my work.
cross product of v and w i.e v×w is orthogonal to v and w
i.e (v×w)×v = 0 = (v×w)×w
Now v×w = i+8j₋5k
v = i+2j−3k
w = 2i−j+2k
then,
(v×w)×v = ( i+8j₋5k)×(i+2j−3k)
(v×w)×v = 1+16+15
(v×w)×v = 32≠0
and
(v×w)×w = ( i+8j₋5k)×(2i−j+2k)
(v×w)×w = 2₋8₋10
(v×w)×w = ₋16≠0
hence given cross product is wrong
Also we clearly seen that a little sign mistake here in 'j'
i.e if (v×w) = ( i₋8j₋5k)
(v×w)×v = ( i₋8j₋5k)×(i+2j−3k)
(v×w)×v = 1₋16+15
(v×w)×v = 0
and
(v×w)×w = ( i₋8j₋5k)×(2i−j+2k)
(v×w)×w = 2+8₋10
Hence, (v×w) = ( i₋8j₋5k)
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by half time, curry scored 22 of the teams 56 points. What percent of his teams points did curry score?
The percentage scored by Curry is 39.3% oby halftime.
How to determine the percentage scoredTo find the percentage of his team's points that Curry scored, we can use the following formula:
percentage = (part / whole) x 100
Where
Part = 22 points
Whole = 56 points
Substitute the known values in the above equation, so, we have the following representation
Percentage = (22 / 56) x 100%
Evaluate
Percentage = 39.3%
Hence, Curry scored 39.3% of his team's points by halftime.
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9687 rounded to the nearest thousand
Answer:
Step-by-step explanation:
10000
Answer:10000
Step-by-step explanation:
dimosure
Find the absolute extrema of the function on the closed interval. Use a graphing utility to verify your results. (If an answer does not exist, enter DNE.) h(t) = t t ? 6 , [7, 13] absolute maximum (t, y) = absolute minimum (t, y) =
A graphing utility such as Desmos or Wolfram Alpha can be used to graph the function. The graph shows that the maximum value occurs at t = 13 and the minimum value occurs at t = 7, which confirms our calculations.
To find the absolute extrema of the function h(t) = t^2 - 6 on the closed interval [7, 13], we can start by taking the derivative of the function and setting it equal to zero to find any critical points:
h'(t) = 2t = 0
t = 0
However, t = 0 is not in the interval [7, 13], so we only need to check the endpoints of the interval and any other critical points that may lie within the interval.
Since there are no critical points in the interval, we only need to evaluate the function at the endpoints:
h(7) = 7^2 - 6 = 43
h(13) = 13^2 - 6 = 163
Thus, the absolute maximum of h(t) on the interval [7, 13] is 163, which occurs at t = 13, and the absolute minimum is 43, which occurs at t = 7.
To verify our results using a graphing utility, we can graph the function h(t) = t^2 - 6 on the interval [7, 13] and visually observe the maximum and minimum values.
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How do you find the holomorphic function?
when thought of as a function from b to r2 , is j(0, 0)
Context, it is not clear what is meant by "j(0,0)" or what the function's codomain being [tex]R^2[/tex] signifies.
It is not clear what you mean by "b" and "j". However, I can provide a general answer on how to find a holomorphic function.
A holomorphic function is a complex-valued function that is complex differentiable in a neighborhood of each point in its domain. This means that the function must satisfy the Cauchy-Riemann equations, which relate the partial derivatives of the function with respect to the real and imaginary parts of its input.
To find a holomorphic function, one approach is to use the power series representation of complex analytic functions. If a function f(z) is analytic at a point z0, then it has a power series expansion of the form:
f(z) = ∑n=0∞ [tex]c_n (z - z0)^n[/tex]
where [tex]c_n[/tex] are complex coefficients that depend on the function and z0. This power series converges in a neighborhood of z0, and the coefficients can be calculated using complex integration techniques.
Another approach is to use the Cauchy integral formula, which expresses the value of a holomorphic function at a point in terms of an integral over a closed curve that encloses the point. This formula allows one to compute the function at any point in its domain using complex integration techniques.
Without more information about "b" and "j", it is not possible to determine if a holomorphic function exists or what its properties might be. Similarly, without more context, it is not clear what is meant by "j(0,0)" or what the function's codomain being [tex]R^2[/tex] signifies.
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Suppose an experiment is performed where a 6-sided die is repeatedly rolled until a 6 appears, at which point the experiment stops. (a) Let E n be the event that the experiment stops at exactly n rolls. How many outcomes are in E n
The summation of permutations of the n-1 rolls that contain at least one 6.
Permutation refers to the arrangement of a set of objects in a specific order or sequence. It is a mathematical concept that involves counting the number of ways in which a set of objects can be ordered or arranged.
However, we need to exclude the sequences that already contain a 6 before the nth roll. These sequences do not belong in event E n . Therefore, we need to find the number of permutations of the n-1 rolls that contain at least one 6.
Let's first consider the case where there is exactly one 6 in the sequence. We have n-1 slots for the rolls, and we need to choose one of them to be a 6. There are (n-1) ways to choose the position of the 6, and the remaining (n-2) slots can be filled with any of the remaining 5 numbers. Therefore, there are
=> [tex](n-1) * 5^{n-2}[/tex]
ways to have exactly one 6 in the sequence.
Now let's consider the case where there are two 6s in the sequence. We have n-1 slots for the rolls, and we need to choose two of them to be 6s. There are (n-1) choose 2 ways to choose the positions of the 6s. For the remaining (n-3) slots, we can fill them with any of the remaining 4 numbers. Therefore, there are
=> [tex](n-1 choose 2) * 4^{n-3}[/tex]
ways to have exactly two 6s in the sequence.
We can continue this pattern for the case where there are k 6s in the sequence. There are (n-1) choose k ways to choose the positions of the k 6s. For the remaining (n-k-1) slots, we can fill them with any of the remaining 6-(k+1) = 5-k numbers. Therefore, there are
=> [tex](n-1 choose k) * (5-k)^{n-k-1}[/tex]
ways to have exactly k 6s in the sequence.
To get the total number of outcomes in event E n , we need to sum up the number of outcomes for each possible number of 6s in the sequence. Therefore, we have:
[tex]|E n | = 6^{(n-1) - (n-1)} * 5^{(n-2) + (n-1 choose 2)} * 4^{(n-3)} - ... + (-1)^{(n-1) * (n-1 choose n-1)} * 1^{(n-n)}[/tex]
This is a formula for the total number of outcomes in event E n .
We use permutations to count the number of ways to arrange the rolls, and we use the principle of inclusion-exclusion to exclude the sequences that contain a 6 before the nth roll.
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17 Answer:
Decide whether the points are vertices of a right triangle.
(0,0), (0,3), (4,00
a. points are vertices of a right triangle
b. points are not vertices of a right triangle
18 Answer:
Decide whether the points are vertices of a right triangle.
(1,2), (3,0), (3,3)
a. points are vertices of a right triangle
b. points are not vertices of a right triangle
19 Answer:
You and a friend go biking. You bike 12 miles north and
2 miles east. What is the straight-line distance from your
starting point? Round answer to the nearest hundredths.
20 Answer:
Find the midpoint between the two points:
(2,2), (6,4)
21 Answer:
Find the midpoint between the two points:
(2,3), (4,1)
22 Answer:
A company had sales of $500,000 in 1996 and sales of
$720,000 in 1998. Use the midpoint formula to find the
company's sales in 1997.
The points (0, 0), (0, 3), (4, 0): A. points are vertices of a right triangle.
The points (1, 2), (3, 0), (3, 3): B. points are not vertices of a right triangle.
The midpoint between the two points (2, 2) and (6, 4) is [4, 3].
The midpoint between the two points (2, 3) and (4, 1) is [3, 2].
The company's sales in 1997 is equal to $610,000.
How to determine the straight-line distance?In order to determine the straight-line distance from your starting point, we would apply Pythagorean's theorem. Mathematically, Pythagorean's theorem is given by this mathematical expression:
c² = a² + b²
Where:
a, b, and c represents the side lengths of a right-angled triangle.
c² = 12² + 2²
c² = 144 + 4
c = √148
c = 12.17 miles.
In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
Midpoint = [(6 + 2)/2, (4 + 2)/2]
Midpoint = [8/2, 6/2]
Midpoint = [4, 3]
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
Midpoint = [(2 + 4)/2, (3 + 1)/2]
Midpoint = [6/2, 4/2]
Midpoint = [3, 2]
By applying the midpoint formula, the sales for 1997 can be calculated as follows;
Sales = (1996 sales + 1998 sales)/Number of years
Sales = ($500,000 + $720,000)/2 years
Sales = $1,220,000/2
Sales = $610,000.
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4) Paige sold 455 tickets for a
fundraiser at school. Some tickets are
for children and cost $5, while the
rest are adult tickets that cost $8. If
the total value of all tickets sold was
$3,325, how many of each type of
ticket did she sell?
Number of adult tickets that Paige sold is 350 and the number of children tickets that she sold is 105.
What does a System of Linear Equations define?Linear equations involve one or more expressions including variables and constants and the highest exponent of the variable is 1.
System of linear equations involve two or more linear equations.
Let x be the number of adult tickets and y be the number of children tickets.
Total number of tickets sold = 455
So, x + y = 455
Cost of each adult ticket is $8 and cost of each children ticket is $5 and the total cost is $3,325.
8x + 5y = 3325
So we got a system of two linear equations.
x + y = 455 ⇒ y = 455 - x
8x + 5y = 3325
Substituting y = 455 - x in 8x + 5y = 3325,
8x + 5(455 - x) = 3325
Solving,
8x + 2275 - 5x = 3325
3x = 1050
x= 350
y = 455 - 350 = 105
Hence number of adult tickets Paige sold is 350 and that of children tickets is 105.
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7. (06.02 MC)
A movie theater made $63 selling 29 tickets. They sell child tickets for $3, adult tickets for $2, and senior tickets for $2. They sold three times as many child tickets as adult tickets. Using c for a child ticket, a for an adult ticket, ands for a
senior ticket what system of equations represents this scenario? (1 point)
c+a+s=63
3c+2a+2s-29
3a = c
c+a+s=29
3c+2a+2s 63
3a=c
c+a+s=29
3c+2a+2=63
a=3c
c+a+s=63
6c+10a+8s-29
a = 3c
The system of equations representing this movie theater scenario is B:
c + a + s = 293c + 2a + 2s = 633a = c.What is a system of equations?A system of equations involves two or more equations whose solutions are determined concurrently or at the same time.
A system of equations is otherwise called simultaneous equations.
The total sales revenue = $63
The total number of tickets sold = 29
The cost per unit of children tickets = $3
The cost per unit of adult tickets = $2
The cost per unit of senior tickets = $2
Let the number of children tickets sold = 3c
Let the number of adult tickets sold = a
Let the number of senior tickets sold = s
Equations:c + a + s =29 Total number of tickets sold
3c+2a+2=63 Total amount realized from the ticket sales
3a=c
Thus, the correct system of equations is Option B.
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please help me.
Evaluate f (-2)where is the piecewise function graphed below.
f(-2)=
After evaluating f (-2), where f(x )is the piecewise function graphed given, the value of f(-2) = -3.
What is the piecewise function?
A function that is defined piecemeal is one that has numerous subfunctions, each of which applies to a distinct interval in the domain. Instead of being a property of the function itself, piecewise definition is a means to express the function.
Here, we have
The problem asks for f(-2), which is the value of y, that is, the vertical axis, when x, that is, the horizontal axis is -2.
We can see that at x = -2, the function changes the definition, thus it is called a piece-wise function.
To find the numeric value at x = -2, we have to look at the definition with the closed circle, which is at y = -3.
Hence, the value of f(-2) = -3.
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I need help with these questions. Ignore my failed attempts
The values of all 9 angles shown were found using the property of a kite they are:
m∠1=55°
m∠2=35°
m∠3=35°
m∠4=90°
m∠5=55°
m∠6=67°
m∠7=67°
m∠8=23°
m∠9=23°
What is an angle ?
In Kite figure, it is given that:
∠2+∠3 = 70°
Since they are equal so ∠2=∠3=35
∠8+∠9 = 46°
Since they are equal so ∠8=∠9=23°
∠5 = 180-∠3-∠4 = 180-35-90=55°
Similarly, ∠1 = 55°
∠6+∠7 = 180-∠8-∠9 = 180-46 = 134°
Since they are equal
∠6=∠7 = 67°
Therefore, all 9 angles were calculated using property of a kite.
m∠1=55°
m∠2=35°
m∠3=35°
m∠4=90°
m∠5=55°
m∠6=67°
m∠7=67°
m∠8=23°
m∠9=23°
In mathematics, an angle is a geometric figure formed by two rays or line segments that share a common endpoint, called the vertex. The rays or line segments are called the sides or legs of the angle, and the distance between the sides at the vertex is called the angle's measure.
Angles are typically measured in degrees or radians, and they can be classified by their measures as acute (less than 90 degrees), right (exactly 90 degrees), obtuse (greater than 90 degrees and less than 180 degrees), straight (exactly 180 degrees), reflex (greater than 180 degrees and less than 360 degrees), or full (exactly 360 degrees).
Kites have several properties related to their angles, including:
Two pairs of opposite angles in a kite are congruent. That is, the angles formed between the pairs of congruent sides are equal.
One diagonal of a kite bisects the other diagonal. This means that the diagonal that connects the non-congruent vertices of the kite divides the other diagonal into two equal segments.
The sum of the measures of the two non-congruent angles in a kite is 180 degrees. This is because the kite can be divided into two congruent triangles by drawing the diagonal that bisects the other diagonal, and the sum of the angles in a triangle is always 180 degrees.
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find the selling for 52.75 karaoke machine with a 49.5markup
Answer: To find the selling price of the karaoke machine with a 49.5% markup, you need to first calculate the amount of the markup. You can do this by multiplying the cost of the machine (52.75) by the markup rate (49.5%) expressed as a decimal:
52.75 * 0.495 = 26.067375
Next, add this markup amount to the cost of the machine:
52.75 + 26.067375 = 78.817375
So, the selling price of the karaoke machine with a 49.5% markup would be $78.82.
Step-by-step explanation:
i need help with this correct answer only please
Answer:
Step-by-step explanation:
1.