Answer: d
Step-by-step explanation:
To get the average, you must add all together and divide by the amount of numbers there are
(-4 - 6 - 3 - 1 + 0 + 2 - 1 - 3)/ 8
(-16)/8 = -2
-2 is your average
hope this helps
Let A = {a, b, c}, B = {b, c, d}, and C = {b, c, e}. (a) Find A ∪ (B ∩ C), (A ∪ B) ∩ C, and (A ∪ B) ∩ (A ∪ C). (Enter your answe
wariber [46]
Answer:
(a)




(b)




(c)


<em>They are not equal</em>
<em></em>
Step-by-step explanation:
Given



Solving (a):




B n C means common elements between B and C;
So:


So:

u means union (without repetition)
So:

Using the illustrations of u and n, we have:


Solve the bracket

Substitute the value of set C

Apply intersection rule


In above:

Solving A u C, we have:

Apply union rule

So:


<u>The equal sets</u>
We have:



So, the equal sets are:
and 
They both equal to 
So:

Solving (b):



So, we have:

Solve the bracket

Apply intersection rule


Solve the bracket

Apply union rule


Solve each bracket

Apply union rule

<u>The equal set</u>
We have:



So, the equal sets are:
and 
They both equal to 
So:

Solving (c):


This illustrates difference.
returns the elements in A and not B
Using that illustration, we have:

Solve the bracket


Similarly:



<em>They are not equal</em>
Answer:
The answer is below
Step-by-step explanation:
Given the system of equations:
x + y + 2z = 9
2x + 4y - 3z = 1
3x + 6y - 5z = 0
This system of equation can be solved using matrix. This done by first representing the equations as matrix and then solving:
The matrix form is:
![\left[\begin{array}{ccc}1&1&2\\2&4&-3\\3&6&-5\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}9\\1\\0\end{array}\right] \\\\\\ \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}1&1&2\\2&4&-3\\3&6&-5\end{array}\right] ^{-1} \left[\begin{array}{c}9\\1\\0\end{array}\right] \\\\\\](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%262%5C%5C2%264%26-3%5C%5C3%266%26-5%5Cend%7Barray%7D%5Cright%5D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D9%5C%5C1%5C%5C0%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%262%5C%5C2%264%26-3%5C%5C3%266%26-5%5Cend%7Barray%7D%5Cright%5D%20%20%5E%7B-1%7D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D9%5C%5C1%5C%5C0%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5C)
![\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}2&-17&11\\-1&11&-7\\0&3&-2\end{array}\right] \left[\begin{array}{c}9\\1\\0\end{array}\right] \\\\\\ \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{c}1\\2\\3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26-17%2611%5C%5C-1%2611%26-7%5C%5C0%263%26-2%5Cend%7Barray%7D%5Cright%5D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D9%5C%5C1%5C%5C0%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D1%5C%5C2%5C%5C3%5Cend%7Barray%7D%5Cright%5D)
Given that initial time for jogging is,

After each week the time is increased by

This gives an arithmetic sequence.
To find n such that,

Therefore,

So,

Therefore, 9 weeks before you are up to jogging 70 minutes.