Answer:
Tomatoes = 11.5
Onions = 2
Step-by-step explanation:
Andre wants to purchase some onions and tomatoes to make tomato soup. The recipe states that four times the number of tomatoes, , plus five times the number of onions, x, should produce 56 bowls of tomato soup. A different recipe states that two times the number of tomatoes used minus the number of onions used should produce 21 bowls of tomato soup. What is the resulting recipe for the number or tomatoes and onions used in the soup when Andre adds the two recipes together?
Let
Tomatoes = x
Onions = y
Recipe 1:
4x + 5y = 56
Recipe 2:
2x - y = 21
4x + 5y = 56 (1)
2x - y = 21 (2)
Multiply (2) by 5
4x + 5y = 56 (1)
10x - 5y = 105 (3)
Add
10x + 4x = 105 + 56
14x = 161
x = 161 / 14
= 11.5
Substitute x =11.5 into
2x - y = 21
2(11.5) - y = 21
23 - y = 21
-y = 21 - 23
-y = -2
y = 2
Tomatoes = 11.5
Onions = 2
You take all the like terms and put the together so you take 2t+2t and that's 4t then you take -8+3 and get -5 then 5k to the second power and then you put all that together and get 4t-5+5k to the second power
To solve the inequality 3/10 is greater than or equal to k - 3/5, we must first set it up. Since 3/10 is greater than or equal to something, we will have a greater than or equal to symbol, with the 'mouth' pointing towards 3/10. Setting this up we get:
3/10 ≥ k - 3/5
Now we want to get k by itself on one side. We can do this by adding 3/5 to each side.
3/10 + 3/5 ≥ k
Simplify
9/10 ≥ k
sqrt(-49) / [ (7-2i) - (4+9i) ]
= 7i / (3 - 11i)
= 7i (3+11i) / [ (3 - 11i) (3 + 11i) ]
= (21 i - 77) / (9 + 121) = choice (d), (-77 + 21i) / 130
Set up the two events
A = first card is a 9
B = second card is a 9
The probability for event A is
P(A) = 4/52
because there are four "9" cards out of 52 total
If event A happens first, and B follows, then the probability is
P(B|A) = 3/51
because there are 3 nines left over out of 52-1 = 51 total left over
No replacement has been made
The notation P(B|A) means "probability of event B given that event A has happened"
Multiply the probabilities
P(A and B) = P(A)*P(B|A)
P(A and B) = (4/52)*(3/51)
P(A and B) = (4*3)/(52*51)
P(A and B) = 12/2652
P(A and B) = 1/221
P(A and B) = 0.00452488687782
Rounded to 4 decimal places, the approximate answer is 0.0045
The exact answer as a fraction is 1/221
