The first step is to ignore the inequality symbol first and replace it with '=' sign. Then, find the x- and y-intercepts.
15x + 10y = 1,100
x-intercept:
15x + 0 = 1,100
x = 1,100/15 = 73.33
y-intercept:
0 + 10y = 1,100
y = 1,100/10 = 110
Now, plot points (73.33,0) and (0,110). Since the equality symbol is ≥, which has an equal sign to it, connect the points using a solid line.
Next, let's find a point on the graph. Suppose it is the origin at (0,0). Use this points to the equation.
15x + 10y ≥ 1,100
15(0) + 10(0) ? 1,100
0 ? 1,100
0 < 1,100
It makes the symbol ≥ false. Therefore, it means that the other region bounded by the line is the solution. So, you shade this area. The final graph is shown in the picture attached.
There are 13 heart cards
Now 1 heart card can be drawn from a pack of 13 heart cards in 13C1 ways
13C1=13
Also,1 card can be drawn from a pack of 52 cards in 52C1 ways
52C1=52
The probability of drawing a heart card from a pack of 52 cards is
13/52=1/4
there are 26 black cards in total
(13 spades +13 clubs)
Now 1 black card can be drawn from a pack of 26 black cards in 26C1 ways
26C1=26
Also,1 card can be drawn from a pack of 52 cards in 52C1 ways
52C1=52
The probability of drawing a black card from a pack of 52 cards is
26/52=1/2
Now as both the task are performed one after the other and after replacement so the probability of drawing a heart after a black card is
=1/2 * 1/4
=1/8
F(x) − g(x) = 2x^2 − 9x - (<span> -5x^2 + 4x)
</span>f(x) − g(x) = 2x^2 − 9x + 5x^2 - 4x
f(x) − g(x) = 7x^2 - 13x
