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mezya [45]
3 years ago
15

A bottle of cranberry juice contains 32 fluid ounces and costs $2.56. What is the unit rate?

Mathematics
2 answers:
Triss [41]3 years ago
8 0
So,

32 fl. oz. costs $2.56.  To find the unit rate, we need to divide 2.56 by 32.

This is a special case, because we notice that 256 and 32 are perfect powers of 2.

\frac{256}{32} = \frac{2^8}{2^5} =2^3=8

The cranberry juice costs 8 cents per fluid ounce.
Tamiku [17]3 years ago
6 0
Unit rate is (cost) per 1 unit
the unit is fluid oz
'per' is fraction
cost/1unit
so we do
2.56/32
divide completely
2.56/32=0.08/1
the unit rate is $0.08 per oz
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The slope of two lines are 5/6 and 2/p. determine the value of p that will make the lines
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Parallel:  the lines have = slopes.  We thus need 5/6 to equal 2/p.  then 5p must equal 12, and p = 12/5.   (answer)

Check:  Is 5/6 = 2 / (12/5)?  YES

Perp.:  The lines have slopes that are negative reciprocals of one another.

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A steamer travels 36 km upstream and 32 km downstream in 6.5 hours. The same steamer travels 4 km upstream and 40 km downstream
rewona [7]

Answer:

The streamer's speed in still water is 90.23 km/h while the stream's speed is 33.33 km/h

Step-by-step explanation:

Let v = streamer's speed in still water and v' = stream's speed. His speed upstream is V = v + v' and his speed downstream is V' = v - v'.

Since he travels 36 km upstream, the time taken is t = 36/V = 36/(v + v').

he travels 32 km downstream, the time taken is t' = 32/V' = 32/(v - v')

The total time is thus t + t' = 36/(v + v') + 32/(v - v')

Since the whole trip takes 6,5 hours,

36/(v + v') + 32/(v - v') = 6.5  (1)

Multiplying each term by (v + v')(v - v'), we have

(v + v')(v - v')36/(v + v') + (v + v')(v - v')32/(v - v') = 6.5(v + v')(v - v')  (1)

(v - v')36 + (v + v')32 = 6.5(v + v')(v - v')  (1)

36v - 36v' + 32v + 32v' = 6.5(v² + v'²)

68v - 4v' = 6.5(v² + v'²)        (2)

Also he travels 4 km upstream, the time taken is t" = 4/V = 4/(v + v').

he travels 40 km downstream, the time taken is t'" = 40/V' = 40/(v - v')

The total time is thus t" + t'" = 4/(v + v') + 40/(v - v')

Since the whole trip takes 180 minutes = 3 hours,

4/(v + v') + 40/(v - v') = 3  (3)

Multiplying each term by (v + v')(v - v'), we have

(v + v')(v - v')4/(v + v') + (v + v')(v - v')40/(v - v') = 3(v + v')(v - v')  (1)

(v - v')4 + (v + v')40 = 3(v + v')(v - v')  (1)

4v - 4v' + 40v + 40v' = 3(v² + v'²)

44v - 36v' = 3(v² + v'²)      (4)

Dividing (2) by (4), we have

(68v - 4v')/(44v - 36v') = 6.5(v² + v'²)/3(v² + v'²)      

(68v - 4v')/(44v - 36v') = 6.5/3

3(68v - 4v') = 6.5(44v - 36v')

204v - 12v' = 286v - 234v'

204v - 286v = 12v' - 234v'

-82v = -222v'

v = -222v'/82

v = 111v'/41

Substituting v into (2), we have

68v - 4v' = 6.5(v² + v'²)      

68(111v'/41) - 4v' = 6.5[(111v'/41)² + v'²]        

[68(111/41) - 4]v' = 6.5[(111/41)² + 1]v'²    

[68(111/41) - 4]v' = 6.5[(111/41)² + 1]v'²

[7548/41 - 4]v' = 6.5[12321/1681 + 1]v'²

[(7548 - 164)/41]v' = 6.5[(12321 + 1681)/1681]v'²

[7384/41]v' = 6.5[14002/1681]v'²

[7384/41]v' = [91013/1681]v'²

[91013/1681]v'² - [7384/41]v' = 0

([91013/1681]v' - [7384/41])v' = 0

⇒ v' = 0 or ([91013/1681]v' - 7384/41) = 0

⇒ v' = 0 or [91013/1681]v' - 7384/41) = 0

⇒ v' = 0 or v' =  7384/41 × 16841/91013

⇒ v' = 0 or v' =  180.097 × 0.185

⇒ v' = 0 or v' =  33.33 km/h

Since v' ≠ 0, v' = 33.33 km/h

Substituting v' into v = 111v'/41 = 111(33.33 km/h)/41 = 3699.63 km/h ÷ 41 = 90.23 km/h

So, the streamer's speed in still water is 90.23 km/h while the stream's speed is 33.33 km/h

5 0
3 years ago
To determine the number of squirrels in a conservation area a researcher cashers tags and releases 114 squirrels you later catch
Ede4ka [16]

Answer:

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Step-by-step explanation:

-This is a Mark-Recapture method.

-The population is estimated using the formula:

N=\frac{MC}{R}

where:

  • N-is the estimated population size.
  • M-is the number of individuals tagged
  • C- is the total number captured the second time(both tagged and untagged)
  • R-is the total number of tagged individuals recaptured.

#We substitute our values as follows to estimate N:

N=\frac{MC}{R}\\\\=\frac{114\times 97}{33}\\\\=335.0909\approx336

Hence, there are approximately 336 squirrels in the conservation area.

*population is always rounded up to the next whole number.

5 0
3 years ago
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