Answer:
and 
expressed in interval notation.
Step-by-step explanation:
A compound inequality 
has been provided. Our task is to determine the solution for this inequality.
Initially, we will address each inequality independently, followed by merging the findings by combining the overlapping intervals.
By dividing with a negative number, it is necessary to reverse the inequality sign:
Again, dividing by a negative requires flipping the inequality sign:
In combining both intervals, we will arrive at:
Thus, the solution for the inequality provided is and in interval notation.
Answer:
Step-by-step explanation:
If you compare numbers based on the hundreds digit, the digits to the left (thousands and ten-thousands) remain the same, while the hundreds digit differs.
This applies for any five-digit numbers structured like:
(3)(5)(not 7)(any digit)(any digit).
Digits to the right of the decimal point, as well as those in the tens and ones places, don't impact this comparison.
To solve this problem, you'll need to create two equations:
x + y = 155 (total packages)
3x + 8y = 815 (total weight)
Next, multiply the first equation by 3: 3x + 3y = 465.
Then, subtract the first equation from the second to find that 5y = 350, which means y = 70. Thus, there are 70 packages that weigh 8 pounds.
To tackle this problem, we first need to ascertain the commission taken by the pizza shop and how much money belongs to Mindy. We know that Mindy sells her artwork for $15, and the pizza shop retains a 15% commission. Therefore, the commission is calculated as (15/100) * 15, which equals 2.25 dollars. This means the pizza shop deducts $2.25 from each art sale made by Mindy. Consequently, the amount Mindy receives is (15 - 2.25), resulting in $12.75. Since Mindy opts not for cash but instead chooses a pizza valued at $12, including a 5% sales tax, it seems she benefits by $0.75 plus the pizza worth $12. Therefore, this arrangement appears fair for Mindy. Meanwhile, the pizza shop also makes an additional $2.25 from this transaction, making it equitable for both Mindy and the shop owner.
Answer:
Yes, the cost 
in dollars and the quantity of yogurt 
are indeed proportional.
The relationship can be expressed as: 
Step-by-step explanation:
1. If varies directly with , it can be represented as:
Here, 
represents the constant of proportionality.
2. We'll calculate the proportionality constant. Given that 
and 
, we have:
3. Thus, the equation becomes:
4. Now, we need to verify proportionality. Substituting 
, which is the quantity of yogurt purchased by Jonah, we should arrive at $0.48:
5. They are indeed directly proportional.
