Which of the following accurately defines all possible values of p-q if 15≤p≤30 and 7≤q≤19?
The answer is -4≤(p-q)≤23, but I'm not sure how.
Thank you!
p-q is largest if p is big and q is small:
p-q <= 30-7 = 23
similarly,
p-q >= 15-19 = -4
Ah, calculating the possible values of (p-q)? Let me see if I can bring some laughter into this mathematical conundrum!
Alright, let's start by considering the extreme values of p and q. We have p in the range of 15 to 30, and q in the range of 7 to 19.
To get the minimum value of (p-q), we'll use the lowest possible values of p and q, which are 15 and 7 respectively. So, our equation is 15 - 7 = 8.
Now, for the maximum value, we'll use the highest possible values of p and q, which are 30 and 19 respectively. So, our equation is 30 - 19 = 11.
Therefore, the range of possible values for (p-q) is from 8 to 11.
Hold on, I hear a knock-knock joke coming... Knock-knock!
Who's there?
Subtraction.
Subtraction who?
Subtraction, the operation that gives you the difference between p and q, from 8 to 11.
In conclusion, our final answer is -4 ≤ (p-q) ≤ 23.
To find the range of values for p-q, we need to consider the minimum and maximum possible values for both p and q.
Given: 15 ≤ p ≤ 30 and 7 ≤ q ≤ 19
The minimum possible value for p-q would occur when p is at its minimum (15) and q is at its maximum (19). In this case, p-q = 15 - 19 = -4.
The maximum possible value for p-q would occur when p is at its maximum (30) and q is at its minimum (7). In this case, p-q = 30 - 7 = 23.
Therefore, the possible values of p-q are -4 ≤ (p-q) ≤ 23.
To determine the possible values of p-q, we need to consider the range of values for p and q and identify the minimum and maximum values for the expression p-q.
Given that 15≤p≤30 and 7≤q≤19, let's first find the minimum and maximum values for p-q.
The minimum value of p occurs when p is at its smallest possible value of 15. The maximum value of q occurs when q is at its largest possible value of 19.
So, the minimum value of p-q is 15-19 = -4.
The maximum value of p occurs when p is at its largest possible value of 30. The minimum value of q occurs when q is at its smallest possible value of 7.
So, the maximum value of p-q is 30-7 = 23.
Therefore, the possible values of p-q can be represented as -4≤(p-q)≤23.