Answer: Mean = 7.8
Median = 9
Mode = 2,9
Step-by-step explanation: <u>Mean</u> is the average value of a data set. Mean from a frequency table is calculated as:
E(X) = 7.8
Mean for the given frequency distribtuion is 7.8.
<u>Median</u> is the central term of a set of numbers. Median in a frequency table is calculated as:
1) Find total number, n:
n = 10 + 9 + 10 + 7 + 3 + 4 + 3 = 46
2) Find position, using: 
= 23.5
Median is in the 23.5th position.
3) Find the position by adding frequencies: for this frequency distribution, 23.5th position is 9
Median for this frequency distribution is 9.
<u>Mode</u> is the number or value associated with the highest frequency.
In this frequency distribution, 2 and 9 points happen 10 times. So, mode is 2 and 9.
Mode for this distribution is 2 and 9.
I cannot see it all is their something you could do to help me help you?
Answer:
We have the equation
![c_1\left[\begin{array}{c}0\\0\\0\\1\end{array}\right] +c_2\left[\begin{array}{c}0\\0\\3\\1\end{array}\right] +c_3\left[\begin{array}{c}0\\4\\3\\1\end{array}\right] +c_4\left[\begin{array}{c}8\\4\\3\\1\end{array}\right] =\left[\begin{array}{c}0\\0\\0\\0\end{array}\right]](https://tex.z-dn.net/?f=c_1%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%5C%5C0%5C%5C0%5C%5C1%5Cend%7Barray%7D%5Cright%5D%20%2Bc_2%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%5C%5C0%5C%5C3%5C%5C1%5Cend%7Barray%7D%5Cright%5D%20%2Bc_3%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%5C%5C4%5C%5C3%5C%5C1%5Cend%7Barray%7D%5Cright%5D%20%2Bc_4%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%5C%5C4%5C%5C3%5C%5C1%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%5C%5C0%5C%5C0%5C%5C0%5Cend%7Barray%7D%5Cright%5D)
Then, the augmented matrix of the system is
![\left[\begin{array}{cccc}0&0&0&8\\0&0&4&4\\0&3&3&3\\1&1&1&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D0%260%260%268%5C%5C0%260%264%264%5C%5C0%263%263%263%5C%5C1%261%261%261%5Cend%7Barray%7D%5Cright%5D)
We exchange rows 1 and 4 and rows 2 and 3 and obtain the matrix:
![\left[\begin{array}{cccc}1&1&1&1\\0&3&3&3\\0&0&4&4\\0&0&0&8\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%261%261%261%5C%5C0%263%263%263%5C%5C0%260%264%264%5C%5C0%260%260%268%5Cend%7Barray%7D%5Cright%5D)
This matrix is in echelon form. Then, now we apply backward substitution:
1.
2.
3.
4.
Then the system has unique solution that is 
and this imply that the vectors 
are linear independent.
Answer:
2201.8348 ; 3 ; x / (1 + 0.01)
Step-by-step explanation:
1)
Final amount (A) = 2400 ; rate (r) = 6% = 0.06, time, t = 1.5 years
Sum = principal = p
Using the relation :
A = p(1 + rt)
2400 = p(1 + 0.06(1.5))
2400 = p(1 + 0.09)
2400 = p(1.09)
p = 2400 / 1.09
p = 2201.8348
2.)
12000 amount to 15600 at 10% simple interest
A = p(1 + rt)
15600 = 12000(1 + 0.1t)
15600 = 12000 + 1200t
15600 - 12000 = 1200t
3600 = 1200t
t = 3600 / 1200
t = 3 years
3.)
A = p(1 + rt)
x = p(1 + x/100 * 1/x)
x = p(1 + x /100x)
x = p(1 + 1 / 100)
x = p(1 + 0.01)
x = p(1.01)
x / 1.01 = p
x / (1 + 0.01)
Using the Pythagorean theorem, the diagonal measure is found as
√((18 m)² +(24 m)²) = √(324 +576) m = √900 m
= 30 m
You would be swimming 30 meters.
