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Katarina [22]
3 years ago
10

Over a 24-hour period, the tide in a harbor can be modeled by one period of a sinusoidal function. The tide measures 4.35 ft at

midnight, rises to a high of 8.3 ft, falls to a low of 0.4 ft, and then rises to 4.35 ft by the next midnight.
What is the equation for the sine function f(x), where x represents time in hours since the beginning of the 24-hour period, that models the situation?

f(x)=
Mathematics
1 answer:
netineya [11]3 years ago
8 0

Answer:

  f(x) = 4.35 +3.95·sin(πx/12)

Step-by-step explanation:

For problems of this sort, a sine function is used that is of the form ...

  f(x) = A + Bsin(2πx/P)

where A is the average or middle value of the oscillation, B is the one-sided amplitude, P is the period in the same units as x.

It is rare that a tide function has a period (P) of 24 hours, but we'll use that value since the problem statement requires it. The value of A is the middle value of the oscillation, 4.35 ft in this problem. The value of B is the amplitude, given as 8.3 ft -4.35 ft = 3.95 ft. Putting these values into the form gives ...

  f(x) = 4.35 + 3.95·sin(2πx/24)

The argument of the sine function can be simplified to πx/12, as in the Answer, above.

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Mrs. Walters has 30 Markers. she gives each student 10 markers. how many students received the markers?​
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Answer:

3 students would get 10 markers

Step-by-step explanation:

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Two consecutive integers have a product of 132.Find the integers
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The difference between consecutive integers is 1.
Let x = smaller integer.
Then x + 1 is the next greater consecutive integer.

x(x + 1) = 132

x^2 + x - 132 = 0

(x + 12)(x - 11) = 0

x + 12 = 0   or   x + 11 = 0

x = -12   or   x = -11

Since x is the smaller of the two integers, the answers are:
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Apply the distributive property and the greatest common factor to write an equivalent expression.
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4 0
3 years ago
Refrigerators in a random sample of 60 refrigerators, the mean repair cost was $150.00 and the standard deviation was $15.50. Co
worty [1.4K]

Answer:

The 99% confidence interval is given by ($144.677;$155.323)  

We are confidenct at 99% that the true mean for the reapir cost of refrigerators is between 144.677 and 155.323.

Step-by-step explanation:

1) Notation and definitions  

n=60 represent the sample size  

\bar X= 150 represent the sample mean  

s=15.5 represent the sample standard deviation  

m represent the margin of error  

Confidence =99% or 0.99

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

2) Calculate the critical value tc  

In order to find the critical value is important to mention that we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 99% of confidence, our significance level would be given by \alpha=1-0.99=0.01 and \alpha/2 =0.005. The degrees of freedom are given by:  

df=n-1=60-1=59  

We can find the critical values in excel using the following formulas:  

"=T.INV(0.005,59)" for t_{\alpha/2}=-2.66  

"=T.INV(1-0.005,59)" for t_{1-\alpha/2}=2.66  

The critical value tc=\pm 2.66  

3) Calculate the margin of error (m)  

The margin of error for the sample mean is given by this formula:  

m=t_c \frac{s}{\sqrt{n}}  

m=2.66 \frac{15.5}{\sqrt{60}}=5.323  

4) Calculate the confidence interval  

The interval for the mean is given by this formula:  

\bar X \pm t_{c} \frac{s}{\sqrt{n}}  

And calculating the limits we got:  

150 - 2.66 \frac{15.5}{\sqrt{60}}=144.677  

150 + 2.66 \frac{15.5}{\sqrt{60}}=155.323  

The 99% confidence interval is given by ($144.677;$155.323)  

We are confidenct at 99% that the true mean for the reapir cost of refrigerators is between 144.677 and 155.323.

7 0
3 years ago
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