Given:
The equation is
To find:
The value of x.
Solution:
We have,
Isolating the variable, we get
Therefore, the value of x is 44.2.
What is the distance between the points (4, 7) and (4, -5)
2 answers:
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By definition, the span of two vectors is the set of all possible linear combinations of said vectors. So, any element in W is obtaining by choosing two numbers a,b and building
(a)
So, you can show a nonzero polynomial in W by choosing any values of a and b, as long as they're not both zero. To keep it as simple as possible, we can choose for example a=1, b=0 and we obtain one of the base vectors of W:
(b)
Factoring the powers of x, we see that a generic polynomial in W looks like
So, we must build a polynomial
such that it is not possible that
For example, let's try the polynomial
We should solve the system
And you can check that it has no solutions. So, the polynomial does not belong to W. On the other hand, it surely belongs to V, because it is a polynomial with degree less than 3. So, the polynomial
belongs to V/W.
For Felix's books, Mean = 11.30769... , Median = 9, Mode = none and Range = 26
For Tyler's books, Mean = 56.56521... , Median = 68, Mode = none and Range = 92
Explanation:
Felix Price
3 4 5 6 7 8 9 11 13 15 18 19 29
Mean is just the average of all numbers. As there is total 13 numbers, so for finding the average, we will divide the Sum of all numbers by 13.
So, Mean =
Median is the middle value in the data set. For finding the median, first we need to rearrange the data set in numerical order, but here the data set is already in numerical order. As there is total 13 numbers, so the middle value will be the (13+1)÷2 = 7th number
3 4 5 6 7 8 9 11 13 15 18 19 29
So, the median is 9
The mode is the number that is repeated more often than any other in the data set, but here all the numbers in this set appear only once.
So, there is no mode.
Range is the difference between the largest and smallest values in the set. The largest is 29 and the smallest is 3.
So, the range = 29 - 3 = 26
Tyler Price
7 8 9 13 16 18 32 36 38 64 66 68 69 75 76 78 79 82 86 89 96 97 99
There are total 23 numbers.
So, the Mean =
The middle value will be the (23 + 1)÷ 2 = 12th number.
7 8 9 13 16 18 32 36 38 64 66 68 69 75 76 78 79 82 86 89 96 97 99
So, the median = 68
Here also all the numbers in this data set appear only once. So, there is no mode.
Largest value is 99 and smallest value is 7.
So, the range = 99 - 7 = 92