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1 answer:
1. Okay, we're looking at this list, and we need to find the mathematical mean, median, and modes of this list.
Median = The value closest to the middle of the set.
17, 18, 18, 19, 20, 21, 21, 21, 22, 22, 22, 22, 23, 25, 26
If we count, there are 15 values, so we just have to find the middle one, which is 21
The median of the first problem is 21.
Mode = The number that occurs most frequently in the set. In this set, we can see that the number 22 appears 4 times, which is more than any other number in the set.
22 is the mode for the first problem.
Range = The distance in numeric value between the highest number of the set and the lowest number.
26 is the highest number and 17 is the lowest.
26 - 17 = 9
The range of the first problem is 9.
2. We solve for average by adding all values together and then dividing by the amount of values there are.
(17 + (18 * 2) + 19 + 20 + (21 * 3) + (22 * 4) + 23 + 25 + 26) / 15 = 21.13... =
<span>The average amount of grain needed is
3. For this one, we just have to solve it the same way, and then compare the central measures.
Median = 21 (For this one, there was an even amount of numbers, so we just took the average of the two closest to the middle, both of which were 21. The average of two numbers of the same value is that same number)
Mode = 22
Range = 9
The three values have not changed from the original values, so there is no change.
Hope that helped =)</span>
Median = The value closest to the middle of the set.
17, 18, 18, 19, 20, 21, 21, 21, 22, 22, 22, 22, 23, 25, 26
If we count, there are 15 values, so we just have to find the middle one, which is 21
The median of the first problem is 21.
Mode = The number that occurs most frequently in the set. In this set, we can see that the number 22 appears 4 times, which is more than any other number in the set.
22 is the mode for the first problem.
Range = The distance in numeric value between the highest number of the set and the lowest number.
26 is the highest number and 17 is the lowest.
26 - 17 = 9
The range of the first problem is 9.
2. We solve for average by adding all values together and then dividing by the amount of values there are.
(17 + (18 * 2) + 19 + 20 + (21 * 3) + (22 * 4) + 23 + 25 + 26) / 15 = 21.13... =
<span>The average amount of grain needed is
3. For this one, we just have to solve it the same way, and then compare the central measures.
Median = 21 (For this one, there was an even amount of numbers, so we just took the average of the two closest to the middle, both of which were 21. The average of two numbers of the same value is that same number)
Mode = 22
Range = 9
The three values have not changed from the original values, so there is no change.
Hope that helped =)</span>
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9514 1404 393
Answer:
±√58 ≈ ±7.616
Step-by-step explanation:
The linear combination of sine and cosine functions will have an amplitude that is the root of the sum of the squares of the individual amplitudes.
|x| = √(3² +7²) = √58
The motion is bounded between positions ±√58.
_____
Here's a way to get to the relation used above.
The sine of the sum of angles is given by ...
sin(θ+c) = sin(θ)cos(c) +cos(θ)sin(c)
If this is multiplied by some amplitude A, then we have ...
A·sin(θ+c) = A·sin(θ)cos(c) +A·cos(θ)sin(c)
Comparing this to the given expression, we find ...
A·cos(c) = 3 and A·sin(c) = -7
We know that sin²+cos² = 1, so the sum of the squares of these values is ...
(A·cos(c))² +(A·sin(c))² = A²(cos(c)² +sin(c)²) = A²(1) = A²
That is, A² = (3)² +(-7)² = 9+49 = 58. This tells us the position function can be written as ...
x = A·sin(θ +c) . . . . for some angle c
x = (√58)sin(θ +c)
This has the bounds ±√58.
