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Monica [59]
3 years ago
14

G(x)= 3 - |2x-4| is defined for the domain -1 < x < 6.

Mathematics
1 answer:
vodomira [7]3 years ago
8 0
(a) The range of g is the set of y values that g covers for the given domain. Given the shape of g, you will be interested in the starting point and ending point g(-1)=1, g(6)=-5 and the tip of g, which is where |2x-4|=0, ie., x=2. g(2) =3. 

The highest encountered g is 3 (at x=2). The lowest one is -5 (at x=6). Note that the highest is inclusive, the lowest is exclusive (since x=6 is not part of the domain).

So the range is (-5,3].

(b) Solve g(x) = 2, then find the x values that cause g(x)>2.

g(x)=2 => 3-|2x-4| = 2 => |2x - 4| = 1 => | x-2 | = 1/2

x-2 = 1/2 or 2-x = 1/2 => x=5/2 or x=3/2

From the graph you can see that x has to be in between these values, so the solution is:

3/2 < x < 5/2. 

The values themselves are excluded (ie., no ≤) since g(x) > 2 and not ≥ 2

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Here are the prices of five new pairs of hockey skates, in dollars: 59, 60, 65, 99, 175. The standard deviation is about $49. If
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Answer:

The standard deviation of the new data will be increased as compared to the previous standard deviation of the data.

Step-by-step explanation:

The prices are given to be : 59, 60, 65, 99, 175

Standard deviation = $49

Now, if we add or subtract any constant value to each of the terms then the standard deviation remains unchanged.

But, we add a new price in the given data that is $450

\text{New standard deviation = }\sqrt{\frac{\sum (\bar{x}-x_i)^2}{n}}\\\\\bar{x}\text{ is the mean of data after adding 450 and}\\x_i\text{ are the price values of the sample data}

Hence, Standard deviation is calculated to be 139.5

Therefore, the standard deviation of the new data will be increased as compared to the previous standard deviation of the data.

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3 years ago
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You can solve these two equations by any of several means. The variable p can be eliminated by subtracting 5 times the first from the second.
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which agrees with answer C listed.

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Step-by-step explanation:

Problem 2)

The Domain is the set of real numbers in which the function (given by a graph in this case) is defined. We see from the graph that the line is defined for all x values between 0 and 240. Such set, expressed in "set builder notation" is:

\left \{x\, |\,0\leq x\leq 240\,\right \}

Problem 3)

notice that the function contains information on the end points to specify which end-point should be included and which one should not. The one on the left (for x = -3 is an open dot, indicating that it should not be included in the function's definition, therefor the Domain starts at values of x strictly larger than -3. So we use the "parenthesis" delimiter in the interval notation for this end-point. On the other hand, the end point on the right is a solid dot, indicating that it should be included in the function's definition, then we use the "square bracket notation for that end-point when writing the Domain set in interval notation:

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Range = [-5, 7]

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