Answer: (-2, -1)
Step-by-step explanation: Since these lines are already graphed, we are looking for their point of intersection. This point where the two lines intersect will represent the <em>x</em> and <em>y</em> that is the solution to this system of equations.
The two lines intersect in quadrant III
where <em>x</em> and <em>y</em> are both negative.
When finding the coordinates of a given point,
be very careful with your signs.
Let's just do a quick review on the coordinate system. On the x-axis, left means negative and right means positive and on the y-axis, down means negative and up means positive.
So to find the coordinates for this point, we start at the origin.
Then we move to the left 2 and down 1 so that's (-2, -1).
So the solution to this system is (-2, -1).
Answer:
The probability that components #1 and #2 fail, and at least one of components #3 and #4 fails is 0.031875
Step-by-step explanation:
Let's define the following events,
F1: Component #1 fails
F2: Component #2 fails
F3: Component #3 fails
F4: Component #4 fails
We are looking for the following probability
P[(F1∩F2)∩(F3∪F4)]
using distributive laws we have
P[(F1∩F2)∩(F3∪F4)] = P[(F1∩F2∩F3)∪(F1∩F2∩F4)] = P(F1∩F2∩F3) + P(F1∩F2∩F4) - P(F1∩F2∩F3∩F4) = P(F1)P(F2)P(F3) + P(F1)P(F2)P(F4) - P(F1)P(F2)P(F3)P(F4) = (0.25)(0.25)(0.3) + (0.25)(0.25)(0.3) - (0.25)(0.25)(0.3)(0.3)=0.031875
by the assumption of independence (the components fail independently) and because P(F1) = P(F2) = 0.25, P(F3) = P(F4) = 0.3
While a credit card is usually better for short-term debt, a personal loan is often ideal for people who need more time to repay. Then again, which option is best for you may boil down to how much interest you'll pay, too.
Answer: Let x represent the cost of one of Tanya's items.
Then the cost of one of Tony's items =x - 2.25. But we have:
3x =4(x - 2.25)
3x =4x - 9 subtract 3x from both sides
0 =x - 9 add 9 to both sides
x=$9 The cost of one of Tanya's items
27 Total cost of Tanya's 3 items
2.25 =$6.75 cost of one of Tony's items.
27 Total cost of Tony's 4 items.
3 x 6.75 =$27. This shows that both Tony and Tanya spent the same amount of money.
Step-by-step explanation:
