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wariber [46]
3 years ago
14

A company's sales in Seattle were $330,000 in 2012, while their sales in Portland were $235,000 for the same year. Complete the

following statements: a. Seattle's sales were % larger than Portland's. b. Portland sales were % smaller than Seattle's. c. Portland sales were % of Seattle's. Give answers accurate to at least one decimal place.
Mathematics
1 answer:
barxatty [35]3 years ago
5 0

Answer:

A) Seattle's sales were 40.42% larger than Portland's.

B) Portland sales were 28.79% smaller than Seattle's.

C)  Portland sales were 71.21% of Seattle's.

Step-by-step explanation:

Since a company's sales in Seattle were $ 330,000 in 2012, while their sales in Portland were $ 235,000 for the same year, the following calculations must be performed to complete the sentences:

A)

235,000 = 100

330,000 = X

330,000 x 100 / 235,000 = X

33,000,000 / 235,000 = X

140.42 = X

Seattle's sales were 40.42% larger than Portland's.

B)

330,000 = 100

235,000 = X

235,000 x 100 / 330,000 = X

23,500,000 / 330,000 = X

71.21 = X

100 - 71.21 = 28.79

Portland sales were 28.79% smaller than Seattle's.

C)

330,000 = 100

235,000 = X

235,000 x 100 / 330,000 = X

23,500,000 / 330,000 = X

71.21 = X

Portland sales were 71.21% of Seattle's.

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Using set notations, we have that:

1. The range of the function is:

  • Inequality: x ≥ -15.
  • Set-builder: {x | x ≥ -15}
  • Interval: [-15, ∞).

2. The function is increasing on:

  • Inequality: x > 3.
  • Set-builder: {x | x > 3}
  • Interval: (3, ∞).

3. The function is decreasing on:

  • Inequality: x < 3
  • Set-builder: {x | x < 3}
  • Interval: (-∞, 3).

4. The function is negative on:

  • Inequality: 0.918 < x < 5.082.
  • Set-builder: {x | 0.918 < x < 5.082}.
  • Interval: (0.918, 5.082).

<h3>What is the standard interval notation?</h3>

The standard interval notation of an interval of lower bound a and upper bound b is given by:

[a,b].

The inequality notation is:

a ≤ x ≤ b

The set builder notation is:

{x | a ≤ x ≤ b}.

<h3>What is the range of the function?</h3>

The range of a function is the set that contains all possible output values for the function. In a graph, it is given by the values of y of the function.

Hence, for this problem, the range is given by these following notations:

  • Inequality: x ≥ -15.
  • Set-builder: {x | x ≥ -15}
  • Interval: [-15, ∞).

<h3>When is a quadratic function increasing and when it is decreasing?</h3>

Considering a concave up quadratic function, as given in this problem, we have that:

  • It decays for the values of x before the vertex.
  • It increases for the values of x after the vertex.

In this problem, the vertex is at x = 3, hence the intervals are given as follows:

2. The function is increasing on:

  • Inequality: x > 3.
  • Set-builder: {x | x > 3}
  • Interval: (3, ∞).

3. The function is decreasing on:

  • Inequality: x < 3
  • Set-builder: {x | x < 3}
  • Interval: (-∞, 3).

<h3>When a function is negative?</h3>

A function is negative when it's graph is below the x-axis. Hence, for this problem, we have that:

4. The function is negative on:

  • Inequality: 0.918 < x < 5.082.
  • Set-builder: {x | 0.918 < x < 5.082}.
  • Interval: (0.918, 5.082).

More can be learned about set notations at brainly.com/question/24462379

#SPJ1

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