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maw [93]
3 years ago
12

Find the RANGE for the data set: 8, 4, 6, 6, 8, 2, 6,5

Mathematics
2 answers:
saul85 [17]3 years ago
6 0

Answer:

\boxed {\boxed {\sf range= 6}}

Step-by-step explanation:

The range of a data set is the difference between the biggest value and the smallest value.

We are given this data set:

  • 8, 4, 6, 6, 8, 2, 6, 5

If we order it from smallest to largest:

  • 2, 4, 5, 6, 6, 6, 8, 8

We see that the smallest value is 2 and the largest is 8. Now we can find the range.

  • range= largest value - smallest value
  • range= 8-2
  • range= 6

The range for the data set is <u>6.</u>

Ber [7]3 years ago
3 0
Range = highest number - lowest number
Highest number = 8
Lowest number = 2
Range = 8-2 = 6

6 is the range
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Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite.
PolarNik [594]

Answer:

  one point

Step-by-step explanation:

A system of two linear equations will have one point in the solution set if the slopes of the lines are different.

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When the equations are written in the same form, the ratio of x-coefficient to y-coefficient is related to the slope. It will be different if there is one solution.

  • ratio for first equation: 1/1 = 1
  • ratio for second equation: 1/-1 = -1

These lines have <em>different slopes</em>, so there is one solution to the system of equations.

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<em>Additional comment</em>

When the equations are in slope-intercept form with the y-coefficient equal to 1, the x-coefficient is the slope.

  y = mx +b . . . . . slope = m

When the equations are in standard form (as in this problem), the ratio of x- to y-coefficient is the opposite of the slope.

  ax +by = c . . . . . slope = -a/b

As long as the equations are in the same form, the slopes can be compared by comparing the ratios of coefficients.

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If the slopes are the same, the lines may be either parallel (empty solution set) or coincident (infinite solution set). When the equations are in the same form with reduced coefficients, the lines will be coincident if they are the same equation.

8 0
2 years ago
Any suggestions or ideas
kirill115 [55]
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4 0
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What is an equation of the line that passes through the points (0, 3) and (5,−3)?
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Answer:

y = -6/5x + 3

Step-by-step explanation:

y = mx + c (or b, depending on where you're from)

Slope = m = -6/5

y = -6/5x + c

You can sub (0, 3) and (5, -3) into y = -6/5x + c and they both have the same answer where c = 3

Therefore, the equation is y = -6/5x + 3

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2 years ago
Write 55% as a decimal and as a fraction.
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3 years ago
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A company manufactures and sells x television sets per month. The monthly cost and​ price-demand equations are ​C(x)equals72 com
solmaris [256]

Answer:

Part (A)

  • 1. Maximum revenue: $450,000

Part (B)

  • 2. Maximum protit: $192,500
  • 3. Production level: 2,300 television sets
  • 4. Price: $185 per television set

Part (C)

  • 5. Number of sets: 2,260 television sets.
  • 6. Maximum profit: $183,800
  • 7. Price: $187 per television set.

Explanation:

<u>0. Write the monthly cost and​ price-demand equations correctly:</u>

Cost:

      C(x)=72,000+70x

Price-demand:

     

      p(x)=300-\dfrac{x}{20}

Domain:

        0\leq x\leq 6000

<em>1. Part (A) Find the maximum revenue</em>

Revenue = price × quantity

Revenue = R(x)

           R(x)=\bigg(300-\dfrac{x}{20}\bigg)\cdot x

Simplify

      R(x)=300x-\dfrac{x^2}{20}

A local maximum (or minimum) is reached when the first derivative, R'(x), equals 0.

         R'(x)=300-\dfrac{x}{10}

Solve for R'(x)=0

      300-\dfrac{x}{10}=0

       3000-x=0\\\\x=3000

Is this a maximum or a minimum? Since the coefficient of the quadratic term of R(x) is negative, it is a parabola that opens downward, meaning that its vertex is a maximum.

Hence, the maximum revenue is obtained when the production level is 3,000 units.

And it is calculated by subsituting x = 3,000 in the equation for R(x):

  • R(3,000) = 300(3,000) - (3000)² / 20 = $450,000

Hence, the maximum revenue is $450,000

<em>2. Part ​(B) Find the maximum​ profit, the production level that will realize the maximum​ profit, and the price the company should charge for each television set. </em>

i) Profit(x) = Revenue(x) - Cost(x)

  • Profit (x) = R(x) - C(x)

       Profit(x)=300x-\dfrac{x^2}{20}-\big(72,000+70x\big)

       Profit(x)=230x-\dfrac{x^2}{20}-72,000\\\\\\Profit(x)=-\dfrac{x^2}{20}+230x-72,000

ii) Find the first derivative and equal to 0 (it will be a maximum because the quadratic function is a parabola that opens downward)

  • Profit' (x) = -x/10 + 230
  • -x/10 + 230 = 0
  • -x + 2,300 = 0
  • x = 2,300

Thus, the production level that will realize the maximum profit is 2,300 units.

iii) Find the maximum profit.

You must substitute x = 2,300 into the equation for the profit:

  • Profit(2,300) = - (2,300)²/20 + 230(2,300) - 72,000 = 192,500

Hence, the maximum profit is $192,500

iv) Find the price the company should charge for each television set:

Use the price-demand equation:

  • p(x) = 300 - x/20
  • p(2,300) = 300 - 2,300 / 20
  • p(2,300) = 185

Therefore, the company should charge a price os $185 for every television set.

<em>3. ​Part (C) If the government decides to tax the company ​$4 for each set it​ produces, how many sets should the company manufacture each month to maximize its​ profit? What is the maximum​ profit? What should the company charge for each​ set?</em>

i) Now you must subtract the $4  tax for each television set, this is 4x from the profit equation.

The new profit equation will be:

  • Profit(x) = -x² / 20 + 230x - 4x - 72,000

  • Profit(x) = -x² / 20 + 226x - 72,000

ii) Find the first derivative and make it equal to 0:

  • Profit'(x) = -x/10 + 226 = 0
  • -x/10 + 226 = 0
  • -x + 2,260 = 0
  • x = 2,260

Then, the new maximum profit is reached when the production level is 2,260 units.

iii) Find the maximum profit by substituting x = 2,260 into the profit equation:

  • Profit (2,260) = -(2,260)² / 20 + 226(2,260) - 72,000
  • Profit (2,260) = 183,800

Hence, the maximum profit, if the government decides to tax the company $4 for each set it produces would be $183,800

iv) Find the price the company should charge for each set.

Substitute the number of units, 2,260, into the equation for the price:

  • p(2,260) = 300 - 2,260/20
  • p(2,260) = 187.

That is, the company should charge $187 per television set.

7 0
2 years ago
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