<span>You can probably just work it out.
You need non-negative integer solutions to p+5n+10d+25q = 82.
If p = leftovers, then you simply need 5n + 10d + 25q ≤ 80.
So this is the same as n + 2d + 5q ≤ 16
So now you simply have to "crank out" the cases.
Case q=0 [ n + 2d ≤ 16 ]
Case (q=0,d=0) → n = 0 through 16 [17 possibilities]
Case (q=0,d=1) → n = 0 through 14 [15 possibilities]
...
Case (q=0,d=7) → n = 0 through 2 [3 possibilities]
Case (q=0,d=8) → n = 0 [1 possibility]
Total from q=0 case: 1 + 3 + ... + 15 + 17 = 81
Case q=1 [ n + 2d ≤ 11 ]
Case (q=1,d=0) → n = 0 through 11 [12]
Case (q=1,d=1) → n = 0 through 9 [10]
...
Case (q=1,d=5) → n = 0 through 1 [2]
Total from q=1 case: 2 + 4 + ... + 10 + 12 = 42
Case q=2 [ n + 2 ≤ 6 ]
Case (q=2,d=0) → n = 0 through 6 [7]
Case (q=2,d=1) → n = 0 through 4 [5]
Case (q=2,d=2) → n = 0 through 2 [3]
Case (q=2,d=3) → n = 0 [1]
Total from case q=2: 1 + 3 + 5 + 7 = 16
Case q=3 [ n + 2d ≤ 1 ]
Here d must be 0, so there is only the case:
Case (q=3,d=0) → n = 0 through 1 [2]
So the case q=3 only has 2.
Grand total: 2 + 16 + 42 + 81 = 141 </span>
The answer is true. We know this because 9^2 - 6^2 is 45.
The answer is 4/9
Have a great day!!
A deck of cards contains red cards numbered 1,2,3, Blue cards numbered 1,2,3,4,5,6, and green cards numbered 1,2. If a single ca
serg [7]
Answer:
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
We have:
3 red cards
6 blue cards
2 green cards.
What is the probability that the card is not green?
3 + 6 + 2 = 11 cards, of which 3 + 6 = 9 are not green. So
probability that the card is not green
Using translation concepts, the correct statements are given as follows:
- Ava's graph is vertical translation of x².
- Ava's graph has a y-intercept of 4.
- Victor's graph moves 4 units from f(x) = x² in a positive direction.
<h3>What is a translation?</h3>
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
Ava's graph is given by:
h(x) = x² + 4.
It is a vertical translation of 4 units of f(x) = x², as the change was in the range of the function. Hence, it has a y-intercept of f(0) = 0² + 4 = 4.
Victor's graph is given by:
g(x) = (x + 4)²
Which means that it moves 4 units from f(x) = x² in a positive direction.
More can be learned about translation concepts at brainly.com/question/4521517
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