Answer:
![\left[\begin{array}{ccc}3&-1&\\-1&1/2\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%26-1%26%5C%5C-1%261%2F2%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
The matrix system for the linear equations: x + 2y = 8, 2x + 6y = 9
![\left[\begin{array}{ccc}1&2&\\2&6\\\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}8\\9\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%262%26%5C%5C2%266%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%5C%5C9%5Cend%7Barray%7D%5Cright%5D)
To get the coefficient of x and y, the inverse of the first matrix (let the first matrix be A) must be known.
= (1 / determinant of A) x Adjoint of A
the determinant of A = (1 x 6) - (2 x 2) = 6 - 4 = 2
Adjoint of A = ![\left[\begin{array}{ccc}6&-2&\\-2&1\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D6%26-2%26%5C%5C-2%261%5C%5C%5Cend%7Barray%7D%5Cright%5D)
= ![\frac{1}{2} \left[\begin{array}{ccc}6&-2\\-2&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D6%26-2%5C%5C-2%261%5Cend%7Barray%7D%5Cright%5D)
=
Answer:
Choice A
1/17; no, they are dependent events
============================================
Explanation:
There are 13 spades and 52 cards total. So 13/52 = 1/4 is the probability of drawing one spade
If we do not replace the card we pull out, then the probability of another spade is 12/51 since there are 12 spades left out of 51 total.
Multiply the fractions 1/4 and 12/51 to get
(1/4)*(12/51) = (1*12)/(4*51) = 12/204 = 1/17
The two events are not independent because the second event (pulling out a second spade) depends entirely on what happens in the first event (pulling out a first spade). The fact that the probability is altered indicates we have dependent events.
Answer:
a = 4
Step-by-step explanation:
a+8 = 12
a= 12-8
a=4
Not 100% sure but I think it’s b. hope this helps!
To determine the Earnings of Shelley last week, we need to make relations with the values that are given. We let x as the total amount she earned last week by x and y as the additional amount she earned this week We do as follows:
20% additional amount she earned this week = y / 72 - y
y = $ 12
x = 72 - 12 = $60 total earnings last week
