Answer:
- a) 3
- b) 6
- c) 9
- d) the outputs are 3 times as far apart as the inputs
Step-by-step explanation:
(a) "x" in considered to be the input to the function f(x). The variable(s) in parentheses as part of the function name are the inputs. The function value itself is the output.
That is, for an input (x-value) of 0, the output (f(0)) is 5. For an input of 1, the output (f(1)) is 8. These input values (0 and 1) are 1 unit apart: 1 - 0 = 1. The corresponding output values are 3 units apart: 8 - 5 = 3.
(b) Inputs -1 and 1 are 2 units apart (1-(-1)=2). The corresponding output values, 2 and 8, are 6 units apart. (8-2=6)
(c) Inputs 0 and 3 are 3 units apart. The corresponding output values, 5 and 14, are 9 units apart.
(d) The ratio of output differences to input differences can be seen to be ...
... 3/1 = 6/2 = 9/3 = 3
Output differences are 3 times input differences.
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<em>Comment on the problem</em>
These ratios are constant everywhere, so the function is considered to be "linear." The ratio is the "slope" of the line you see when the function is graphed.
Answer:
b
Step-by-step explanation:
Answer:
Scale of the new blueprint: 2 inches = 2.5 feet (or 4 inches = 5 feet)
Width of the new blueprint: 14.4 inches
Step-by-step explanation:
To solve this problem we can use rules of three to find each of the questions: blueprint's new scale and new width.
To find the new scale, we can find the real length of the patio first:
2 inches -> 3 feet
14 inches -> X feet
2/14 = 3/X
X = 21 feet
Now we can use this value to create the new scale:
16.8 inches -> 21 feet
2 inches -> X feet
16.8/2 = 21/X
X = 2*21/16.8 = 2.5 feet
So the new scale is 2 inches = 2.5 feet, or 4 inches = 5 feet
Now, to find the new width of the blueprint, we can do the following rule of three:
14 inches of length -> 16.8 inches of length
12 inches of width -> X inches of width
14/12 = 16.8/X
X = 12*16.8/14 = 14.4 inches
Answer: 5.37
Step-by-step explanation:
Let x = ACT scores.
Given: ACT scores have a mean of 20.8 and 9 percent of the scores are above 28. The scores have a distribution that is approximately normal.
i.e. P(X>28)=0.09 (i)
Now,
(ii)
One -tailed z value for p-value of 0.09 =1.3408 [By z-table]
From (i) and (ii)
Hence, the standard deviation = 5.37