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horrorfan
12 days ago
9

Milton is floating in an inner tube in a wave pool. He is 1.5 m from the bottom of the pool when he is at the trough of a wave.

A stopwatch starts timing at this point. In 1.25 s, he is on the crest of the wave, 2.1 m from the bottom of the pool. a) Determine the equation of the function that expresses Milton's distance from the bottom of the pool in terms of time.
Mathematics
1 answer:
lawyer [12.5K]12 days ago
3 0
To tackle this sinusoidal question, we begin with the following: Using the formula; g(t)=offset+A*sin[(2πt)/T+Delay] According to sinusoidal theory, the duration from trough to crest is typically half of the wave's period. Here, T=2.5 The peak magnitude is calculated as: Trough-Crest=2.1-1.5=0.6 m amplitude=1/2(Trough-Crest)=1/2*0.6=0.3 The offset from the center of the circle becomes 0.3+1.5=1.8 As the delay is at -π/2, the wave will commence at the trough at [time,t=0]. Plugging these values into the formula gives: g(t)=1.8+(0.3)sin[(2*π*t)/2.5]-π/2] g(t)=1.8+0.3sin[(0.8πt)/T-π/2]
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76% is between which of the following two numbers?
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Hi there!

While there are no answer choices provided, here's how you can solve a problem like this.

To find the average of two numbers, you simply sum them up and divide by two!

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Using a profit P1 of $5,000, a profit P2 of $4,500, and a profit P3 of $4,000, calculate a 95% confidence interval for the mean
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Answer:

Confidence Interval

Lower Limit = $4,233.3

Upper Limit = $4,766.7

With 95% certainty, SoftBus can anticipate that the average profit per customer will fall within the range of $4,233.30 to $4,766.7, based on the provided sample data.

Step-by-step explanation:

The z-score corresponding to 95% is 1.96

             Profit         Mean      Square Root

                           Difference    of MD

P1        $5,000       $500        $250,000

P2         4,500          0              0

P3         4,000       -500         $250,000

Total $13,500                        $500,000

Mean $4,500 ($13,500/3)    $166,667 ($500,000/3)

Standard Deviation = Square root of $166,667 = 408.2

Margin of error = (z-score * standard deviation)/n

= (1.96 * 408.2)/3

= 266.7

= $266.7

Confidence Interval = Sample mean +/- Margin of error

= $4,500 +/- 266.7

Lower Limit = $4,233.3 ($4,500 - $266.7)

Upper Limit = $4,766.7 ($4,500 + $266.7)

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