Answer:
See below
Step-by-step explanation:
I think it’s four less than the quotient of a number cubed and seven, increased by three
I hope you get this right!
Answer:
The answer should be "No Solution" as these lines never meet each other
There are five different pasta choices. The probability for you to pick one of them is: 1/5
There are four different flavors. The probability for you to pick one of them is: 1/4
The probability for you to pick both bow ties and cheese sauce is the same as picking ravioli and olive oil, or spaghetti and meat sauce.
The probability is: 1/5 x 1/4 = 0.05
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Answer:
- to interest: $532.97
- to principal: $54.23
- new balance: $79,891.90
Step-by-step explanation:
The interest is found by multiplying the monthly rate by the balance on the loan. For the first month, the balance is the loan amount.
$79,946.13 × 0.08 ×(1/12) . . . . . one month = 1/12 year
= $532.97
The interest amount in the first payment is $532.97.
__
The amount of the first payment that goes to principal is what is left after the interest is paid:
$587.20 -532.97 = $54.23 . . . amount to principal
__
The new balance is the previous balance less the amount to principal:
$79,946.13 -54.23 = $79,891.90 . . . new balance
Answer:
See proof below
Step-by-step explanation:
We will use properties of inequalities during the proof.
Let 
. then we have that 
. Hence, it makes sense to define the positive number delta as 
(the inequality guarantees that these numbers are positive).
Intuitively, delta is the shortest distance from y to the endpoints of the interval. Now, we claim that 
, and if we prove this, we are done. To prove it, let 
, then 
. First, 
then 
hence 
On the other hand, 
then 
hence 
. Combining the inequalities, we have that 
, therefore as required.
