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Virty [35]
3 years ago
7

The following data are for 30 observations involving two categorical variables, x and y. The categories for x are A, B, and C; t

he categories for y are 1 and 2.
Observation x y
1 A 1
2 B 1
3 B 1
4 C 2
5 B 1
6 C 2
7 B 1
8 C 2
9 A 1
10 B 1
11 A 1
12 B 1
13 C 2
14 C 2
15 C 2
Observation x y
16 B 2
17 C 1
18 B 1
19 C 1
20 B 1
21 C 2
22 B 1
23 C 2
24 A 1
25 B 1
26 C 2
27 C 2
28 A 1
29 B 1
30 B 2
a. Develop a crosstabulation for the data, with x as the row variable and y as the column
variable.
b. Compute the row percentages.
c. Compute the column percentages.
d. What is the relationship, if any, between x and y?
Mathematics
2 answers:
mr Goodwill [35]3 years ago
7 0
The correct answer is
Answer a

Explanation
Galina-37 [17]3 years ago
6 0
The correct answer would be A
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3 years ago
Express the function graphed on the axes below as a piecewise function.
adoni [48]

Answer:

  f(x) = {x-3 for x ≤ -1; -3x+14 for x > 5}

Step-by-step explanation:

To write the piecewise function, we can consider the pieces one at a time. For each, we need to define the domain, and the functional relation.

__

<h3>Left Piece</h3>

The domain is the horizontal extent. It is shown as -∞ to -1, with -1 included.

The relation has a slope (rise/run) of +1, and would intersect the y-axis at -3 if it were extended.

The first piece can be written ...

  f(x) = x-3 for x ≤ -1

__

<h3>Right Piece</h3>

The domain is shown as 5 to ∞, with 5<em> not included</em>.

The relation is shown as having a slope (rise/run) of (-3)/(1) = -3. If extended, it would intersect the point (5, -1), so we can write the point-slope equation as ...

  y -(-1) = -3(x -5)

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The second piece can be written ...

  f(x) = -3x +14 for x > 5

__

<h3>Whole function</h3>

Putting these pieces together, we have ...

  \boxed{f(x)=\begin{cases}x-3&\text{for }x\le-1\\-3x+14&\text{for }5 < x\end{cases}}

_____

<em>Additional comment</em>

Sometimes it is convenient to write inequalities in number-line order (using < or ≤ symbols). This gives a visual indication of where the variable stands in relation to the limit(s). Perhaps a more conventional way to write the domain for the second piece is, <em>x > 5</em>.

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