1 batch of muffins included 2/3 cups of raisins. We can use this to set a proportion: 1 : 2/3. That means for every 1 batch, she uses 2/3 cups of raisins.
Now, Ina made 2 1/2 batches. To find out how, we need to look at our proportion again: 1 : 2/3. Whatever operation you do to one side, you must do to the other. So, to get 2 1/2 batches, we need to multiply the left side of the proportion, which is 1 batch, by 2 1/2 to get 2 1/2 batches.
BUT, we also need to multiply the other side, 2/3 cups, by 2 1/2. We can start by converting this into an improper fraction, 5/2. (Because 1=2/2, so 2=4/2, and 4/2+1/2=5/2.) When multiplying fractions, you multiply the numerators together to get the new numerator, and the denominators to get the new denominator. 2*5=10, and 3*2=6. Our new fraction is 10/6. Since these are both divisible by 2, we simplify by dividing each side by 2 to get 5/3. Finally, we can convert this into a mixed number: 1 2/3. (Because 1=3/3 and 5/3 - 3/3 = 2/3, and 1 + 2/3 = 1 2/3.) This is the cups of raisins she used.
Answer: She used 1 2/3 cups of raisins.
Answer:
Step-by-step explanation:
We are given that a and b are rational numbers where 
and x is irrational number .
We have to prove a+bx is irrational number by contradiction.
Supposition:let a+bx is a rational number then it can be written in 
form
where 
where p and q are integers.
Proof:
After dividing p and q by common factor except 1 then we get
r and s are coprime therefore, there is no common factor of r and s except 1.
where r and s are integers.
When we subtract one rational from other rational number then we get again a rational number and we divide one rational by other rational number then we get quotient number which is also rational.
Therefore, the number on the right hand of equal to is rational number but x is a irrational number .A rational number is not equal to an irrational number .Therefore, it is contradict by taking a+bx is a rational number .Hence, a+bx is an irrational number.
Conclusion: a+bx is an irrational number.
Answer: Kyle received $0.77
Step-by-step explanation:
B - 3/4 = 7/10
add 3/4 to both sides to isolate the b
b = 7/10 + 3/4
b = 28/40 + 30/40
b = 58/40
b = 1 18/40
b = 1 9/20
