Answer: (12, 5)
Step-by-step explanation:
3x + 2y = 46 x + y = 17
Subtract y from both sides of the equation.
x = 17 − y 3x + 2y = 46
Replace all occurrences of x with 17 − y in each equation.
51 − y = 46
x = 17 − y
Solve for y in the first equation.
Move all terms not containing y to the right side of the equation.
Subtract 51 from both sides of the equation.
−y = 46 − 51
x = 17 − y
Subtract 51 from 46.
−y = −5
x = 17 − y
Multiply each term in −y = −5 by −1
Multiply each term in −y = −5 by −1. (−y) ⋅ −1 = (−5) ⋅ −1
x = 17 − y
Multiply (−y) ⋅ −1.
y = (−5) ⋅ −1
x = 17 − y
Multiply −5 by −1.
y = 5
x = 17 − y
Replace all occurrences of y with 5 in each equation.
Replace all occurrences of y in x = 17 − y with 5. x = 17 − (5)
y = 5
Simplify 17 − (5).
Multiply −1 by 5.
x = 17 − 5
y = 5
Subtract 5 from 17.
x = 12
y = 5
The solution to the system is the complete set of ordered pairs that are valid solutions.
(12, 5)
The result can be shown in multiple forms.
Point Form: (12, 5)
Equation Form: x = 12, y = 5
Divided 75000 by 10000 so it would be 7.5 square cm
Part (a)
<h3>
Answer: No, it's not a statistical question</h3>
Why not? Because we can locate the tallest building without having to gather a sample and computing any statistical values based on the sample data. Note how we have one single building and we're focused on just that building only. We aren't asking anything about a population of buildings. Statistics is the science of trying to measure a population in some way, often through the use of a sample statistic. For example, if we asked "what is the average building height in Chicago, Illinois?", then we would be asking a statistical question. Ideally, we would measure every single building in the city. Of course, that's very time consuming and impractical. So the next best thing is to randomly select a sample of buildings and try to estimate the average height like that.
Once again, we're only focused on one single building and not several. So we don't do the operations of gathering a sample and we aren't doing any statistics here. We're simply measuring the building, or looking up the building height in some records database.
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Part (b)
<h3>Answer: Yes, it is a statistical question</h3>
The population is the set of teenagers. This could be narrowed to just the teens in one specific town, county, or regional area. It doesn't make much sense to extend the population out too far because teens too far away would likely not visit this particular mall in question. Let's say the population is every teen in a certain county. We have a lot of people in this population, so we'll have to gather a sample. Doing a census is too time consuming and expensive. This process of gathering a sample points to this question being a statistical one. We don't know which store is the most popular, but we can get a fairly good idea through the sampling process. It won't be a 100% guarantee that we got the right one considering that again the sample isn't the exact population, but we should get close if we did the sampling right.
Note how the variable in question is a qualitative one. The store names are the categories or names that the teens select in the survey. This data type is nominal and not ordinal, since stores do not have an inherent rank (other than alphabetical but that's not of much importance). Also note that the responses for this random variable are, more or less, random in nature. We simply don't know how the teens will respond assuming we go into this completely blind. It's a good idea to do so to avoid bias. This random nature helps add evidence we have a statistical question here. The random variable value is not set in stone like the tallest building is. Keep in mind that the question for part (a) is asked to refer to a very specific narrow window of time. The same can be said for part (b) as well. Be sure to carefully set up the question and avoid any ambiguity.
To summarize, to answer such a question given to us we would need to gather a sample and compute sample statistics. This is why we have a statistical question here.
Answer:
the maximum height of the water is 7 ft
Step-by-step explanation:
Using " ^ " to indicate exponentiation, we have −4x^2 + 24x − 29.
Rewrite -4x^2 + 24x as -4(x^2 - 6x) and then complete the square of (x^2 - 6x). We get:
(x^2 - 6x + 9 - 9), which is exactly equivalent to (x^2 - 6x).
Going back to the original equation: −4x^2 + 24x − 29, or
−4(x^2 - 6x) − 29.
Now replace (x^2 - 6x) with (x^2 - 6x + 9 - 9):
-4(x^2 - 6x + 9 - 9) - 29, which simplifies to:
-4(x - 3)^2 + 36 - 29, or
-4(x - 3)^2 + 7, whose vertex is (3, 7). Thus, the maximum height of the water is 7 ft.
