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HACTEHA [7]
3 years ago
13

QUESTION 6 OF 17 A Lyft driver has received 160 reviews with an average rating of 4.4 out of 5 stars. If the driver wanted to ra

ise his average star rating to 4.7, how many consecutive 5-star reviews does he need?
Mathematics
1 answer:
dexar [7]3 years ago
4 0
He needs 160 5-star reviews in a role. We can write a function to solve this problem. His current total stars is 4.4*160=704. Suppose he needs x more 5-star reviews, then his total stars will be 704+5x. 160+x is the new number of reviews, and the new average will be 4.7, so 4.7*(160+x)=704+5x. The solution is 160. Besides, if you want to get the answer really fast, you can see that 4.7 is right in the middle of 4.4 and 5, so you can immediately guess that the number of new 5-star reviews should be equal to the number of current reviews.
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Answer:

<u><em>y = -190 cos(π t / 120) + 195</em></u>

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<em>General form of a sinusoidal function: y = A cos(Bt - C) + D </em>

<em> </em>

<em>Now generally a cosine function starts at the maximum value, so to start at the minimum value, flip the cosine function by making it negative. </em>

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<em>A is the amplitude of the curve and will be the radius of the ferris wheel. Therefore, A = 380 / 2 = 190 feet. </em>

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<em> 2π / B is the period of the curve and will be the time to complete one full rotation. The time to complete one full rotation is given as 4 minutes. Convert this into seconds to get period = 4 minutes * (60 seconds / minute) = 240 seconds. Therefore, B = 2π / period = 2π / 240 seconds = π / 120. </em>

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<em> C/B is the phase shift, or horizontal shift of the graph. Since the negative cosine function already starts at the minimum value, there is no phase shift so C/B = 0, meaning C = 0. </em>

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<em> D is the vertical shift and will be the height of the center of the ferris wheel. Therefore, D = 195 feet. </em>

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<em> Your final function will be:</em>

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