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Phoenix [80]
3 years ago
14

A two-person relay race consists of eight times around a football field. Juan runs four and one-sixth times and Antonio runs thr

ee and two-thirds times around the field. What are the distances they ran as improper fractions? A. Juan: 25⁄6 ; Antonio: 11⁄3 B. Juan: 32⁄3 ; Antonio: 41⁄6 C. Juan: 41⁄6 ; Antonio: 32⁄3 D. Juan: 11⁄3 ; Antonio: 25⁄6
Mathematics
1 answer:
Serga [27]3 years ago
5 0

Answer:

A


Step-by-step explanation:


To convert mixed number as improper fractions, use this rule:

A\frac{B}C}=\frac{(A*C)+B}{C}


<u>For Juan:</u>  (4\frac{1}{6})

4\frac{1}{6}=\frac{(4*6)+1}{6}=\frac{25}{6}


<u>For Antonio:</u>  (3\frac{2}{3})

3\frac{2}{3}=\frac{(3*3)+2}{3}=\frac{11}{3}


Answer choice A is correct.


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slamgirl [31]

9514 1404 393

Answer:

  • 5290 units
  • $57.10 per unit
  • $279,591 profit

Step-by-step explanation:

For price p, the quantity q of units sold is said to be ...

  q = 3000 +10(80-p)/0.10 . . . . for price in dollars

Then the revenue will be ...

  r(p) = p·q = p(3000 +100(80-p)) = 100p(110 -p)

The cost is said to be ...

  c(q) = 250 +4.20q

  c(p) = 250 +4.20(100(110 -p)) = 250 +420(110 -p)

Then the profit function is ...

  P(p) = r(p) -c(p)

  P(p) = 100p(110 -p) -(250 +420(110 -p)) = (110 -p)(100p -420) -250

__

Ignoring the vertical offset of -250, the quadratic has zeros at 110 and 4.2. So, its line of symmetry (and vertex) will be found at ...

  p = (110 +4.2)/2 = 57.1 . . . . dollars per unit

The quantity that should be produced at that price is ...

  q(57.1) = 100(110 -57.1) = 5290 . . . . units produced

The profit at that price is ...

  P(57.1) = (110 -57.1)(100·57.1 -420) -250 = 52.9(5290) -250

  = $279,591 . . . . best profit

_____

<em>Additional comment</em>

After you have seen a few of these, you can write down the revenue function based on the rate of change of units sold.

If p is the price of a unit, then 80-p is the number of dollars of decrease in price for a price of p. Then (80 -p)/0.10 is the number of 10¢ decreases in price. The increase in units sold is 10 times this, or 10(80 -p)/0.10 = 100(80 -p). When that is added to 3000 units sold, the total is ...

  3000 +100(80 -p) = 3000 +8000 -100p

  = 11000 -100p = 100(110 -p) . . . . . quantity sold at price p

Revenue is the product of price times the number of units sold at that price.

Profit is the difference between revenue and cost.

6 0
2 years ago
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EastWind [94]

Answer:

B, C, E

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the dependent variable <em>depends </em>on the independent variable

thus, p is dependent on t, p is the dependent variable, and t is the independent variable (B)

every month, Gloria paints 2 pieces

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7 0
1 year ago
A pilot can travel 450 miles with the wind in the same amount of time as 360 miles against the wind. Find the speed of the wind
Lunna [17]

Given:

A pilot can travel 450 miles with the wind in the same amount of time as 360 miles against the wind.

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5(315)-5x=4(315)+4x

5(315)-4(315)=4x+5x

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\dfrac{(1)315}{9}=x

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What is the simplified value of the exponential expression 16^1\4
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If you observe that 16 = 2^4, you can rewrite the expression as

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Now, if you use the exponent rule (a^b)^c = a^{bc}, you may rewrite the expression again:

(2^4)^{\frac{1}{4}} = 2^{4\cdot\frac{1}{4}} = 2^1 = 2

6 0
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