The combinations of batches that Rebecca can use are the solutions of:
120 ≤ 15*x + 12*y ≤ 360
One example is x = 10 and y = 0.
<h3>What combination of batches of each could Rebecca make?</h3>
Let's define the variables:
- x = number of batches of cookies.
- y = number of batches of cupcakes.
We know that she makes batches of 15 cookies and batches of 12 cupcakes, then the total number of baked goods that she makes is:
15*x + 12*y
And we know that she wants to make at least 120 and no more than 360, then we can write the inequality:
120 ≤ 15*x + 12*y ≤ 360
So any pair of values of x and y that make the inequality true, is a combination of batches that Rebecca could use.
An example is x = 10 and y = 0.
120 ≤ 15*10 + 12*0 ≤ 360
120 ≤ 150 ≤ 360
If you want to learn more about inequalities:
brainly.com/question/24372553
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Answer: The given logical equivalence is proved below.
Step-by-step explanation: We are given to use truth tables to show the following logical equivalence :
P ⇔ Q ≡ (∼P ∨ Q)∧(∼Q ∨ P)
We know that
two compound propositions are said to be logically equivalent if they have same corresponding truth values in the truth table.
The truth table is as follows :
P Q ∼P ∼Q P⇔ Q ∼P ∨ Q ∼Q ∨ P (∼P ∨ Q)∧(∼Q ∨ P)
T T F F T T T T
T F F T F F T F
F T T F F T F F
F F T T T T T T
Since the corresponding truth vales for P ⇔ Q and (∼P ∨ Q)∧(∼Q ∨ P) are same, so the given propositions are logically equivalent.
Thus, P ⇔ Q ≡ (∼P ∨ Q)∧(∼Q ∨ P).
The distance is 20
Have a great day!
Answer:
16.8
Step-by-step explanation: