Answer:
false: the event will never occur; the event will definitely occur; the event is likely to occur
true: there is a small chance that the event will occur
Step-by-step explanation:
Answer:
y=1/4x-1
Step-by-step explanation:
Answer:
3 1/2 cups
Step-by-step explanation:
Let's start by figuring out how much sugar Karen needs in total.
She needs (1+1/3) cups for her original recipe. To triple that, we need (1+1/3) 3 times. We can calculate this by multiplying it by 3.
(1+1/3) * 3 = 3 + 1 = 4
Karen needs 4 cups in total. She has 1/2 cup. The difference is how much more she needs. Therefore, she needs 4 - 1/2 = 3 1/2 cups
At the bank, Derek made 7 withdrawals, each in the same amount. His brother, John, made 5 withdrawls, each in the same amount.
Let x be the amount of one of Derek's withdrawals
Each of John's withdrawals was $5 more than each withdrawal that Derek made.
x + 5 is t the amount of one of John's withdrawals
Derek made 7 withdrawals
So amount withdraw 7 times = 7x
John made 5 withdrawals
So amount withdraw 5 times = 5(x+5)
Both Derek and John withdrew the same amount of money in the end
(A) 7x = 5(x+5)
(B) Solve for x
7x = 5x + 25
Subtract 5x from both sides
2x = 25
Divide by 2
x = 12.5
(C) check your solution
we plug in 12.5 for x in 7x= 5x + 25
7(12.5) = 5(12.5) + 25
87.5 = 62.5+ 25
87.5 = 87.5
(D) Each brother withdrawal 87.5 dollars
We know that:

is an equation of a circle.
When we substitute x and y (from the pairs we have), we'll get a system of equations:

and all we have to do is solve it for a, b and r.
There will be:

From equations (II) and (III) we have:

and from (I) and (II):

Now we can easly calculate a and b:

Finally we calculate

:

And the equation of the circle is: