Translate "The sum of nine and a number is four" into an equation and solve.
2 answers:
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Answer:
(a)
(b)
(c)
(d)
Step-by-step explanation:
Given
--- at least
Solving (a): 28 combinations
From the question, we understand that; a combination of 28 is to be selected. Because the order is not important, we make use of combination.
Also, because repetition is allowed; different balloons of the same kind can be selected over and over again.
So:
Solving (b): At most 12 red balloons
First, we calculate the ways of selecting at least 13 balloons
Out of the 28 balloons, there are 15 balloons remaining (i.e. 28 - 13)
So:
Selection of at least 13 =
Ways of selecting at most 12 =
--- Complement rule
Solving (c): At most 8 blue balloons
First, we calculate the ways of selecting at least 9 balloons
Out of the 28 balloons, there are 19 balloons remaining (i.e. 28 - 9)
So:
Selection of at least 9 =
Ways of selecting at most 8 =
--- Complement rule
Solving (d): 12 red and 8 blue balloons
First, we calculate the ways for selecting 13 red balloons and 9 blue balloons
Out of the 28 balloons, there are 6 balloons remaining (i.e. 28 - 13 - 9)
So:
Selection =
Using inclusion/exclusion rule of two sets:
Answer:
The graph that best fits this model of profit and price per unit is attached to this solution.
Step-by-step explanation:
A couple of graphs are missing from the question. According to the full question as obtained online, there are a number of graph options, and we are expected to pick the best option. I would not add all the other graphs to limit the chances of deletion due to violating community guidelines.
The function is to model the profits of a new pet-monitoring system, so, if the profits are y and x is the price per unit, y = f(x)
The profits vary as the price per unit varies, there is no profit made until the price reaches
$95 per unit, a maximum profit at a price of $140 per unit, and no profit at a price over $185 per unit.
This description of the curve shows that y is negative at values of x less than $95, then the profits increase when x varies between $95 and $140. The profits reach a maximum at $140 and then the profits start to decline as x increases again, the profits go to 0 at x = $185.
This description shows that the function is a quadratic function with a graph that is n-shaped, peaking at x=185 and the graph crosses the x-axis at x=95 and x=185.
The most fitting graph for this model is attached to this solution provided.
From the graph, all the descriptions above are evident.
Hope this Helps!!!
