X/0.5 = 24
X/0.5(0.5) = 24(0.5)
X = 12
A bag contains four red marbles, two Yellow Marbles and five blue marbles.
Two marbles are drawn at random without replacement.
Total number of marbles are,

There are 11 ways to select first marble and 10 ways to select second marble.
The total number of possible outcomes are calculated as,

Thus the total number of possible outcomes are 110.
Answer:
x=-2, y=-6
Step-by-step explanation:
Simple substitution.
Since y is isolated in one of the equations already, you can plug it into the second equation.
x - 2(3x) = 10
x - 6x = 10
-5x = 10
x = -2
Sub. x = -2 into 3x = y:
3(-2) = y
y = -6
Answer:
Option b is correct (8,13).
Step-by-step explanation:
7x - 4y = 4
10x - 6y =2
it can be represented in matrix form as![\left[\begin{array}{cc}7&-4\\10&-6\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}4\\2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D7%26-4%5C%5C10%26-6%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D4%5C%5C2%5Cend%7Barray%7D%5Cright%5D)
A=
X= ![\left[\begin{array}{c}x\\y\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D)
B= ![\left[\begin{array}{c}4\\2\end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D4%5C%5C2%5Cend%7Barray%7D%5Cright%5D)
i.e, AX=B
or X= A⁻¹ B
A⁻¹ = 1/|A| * Adj A
determinant of A = |A|= (7*-6) - (-4*10)
= (-42)-(-40)
= (-42) + 40 = -2
so, |A| = -2
Adj A=
A⁻¹ =
/ -2
A⁻¹ = ![\left[\begin{array}{cc}3&-2\\5&-7/2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%26-2%5C%5C5%26-7%2F2%5Cend%7Barray%7D%5Cright%5D%20)
X= A⁻¹ B
X= ![\left[\begin{array}{cc}3&-2\\5&-7/2\end{array}\right] *\left[\begin{array}{c}4\\2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%26-2%5C%5C5%26-7%2F2%5Cend%7Barray%7D%5Cright%5D%20%2A%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D4%5C%5C2%5Cend%7Barray%7D%5Cright%5D)
X= ![\left[\begin{array}{c}(3*4) + (-2*2)\\(5*4) + (-7/2*2)\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%283%2A4%29%20%2B%20%28-2%2A2%29%5C%5C%285%2A4%29%20%2B%20%28-7%2F2%2A2%29%5Cend%7Barray%7D%5Cright%5D)
X= ![\left[\begin{array}{c}12-4\\20-7\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D12-4%5C%5C20-7%5Cend%7Barray%7D%5Cright%5D)
X= ![\left[\begin{array}{c}8\\13\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%5C%5C13%5Cend%7Barray%7D%5Cright%5D)
x= 8, y= 13
solution set= (8,13).
Option b is correct.
Answer:
4.56
Step-by-step explanation:
"Ordinary" interest will be more than "exact" interest because the number of days in a year is a smaller value. The difference will be ...
Io = Prt = 5000(0.12)(200/360) = 333.33
Ie = Prt = 5000(0.12)(200/365) = 328.77
The difference is ...
333.33 -328.77 = 4.56 . . . the difference in interest values
_____
<em>Additional comment</em>
The question asks for the difference between exact and ordinary interest, so the result is technically negative:
328.77 -333.33 = -4.56