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natali 33 [55]
3 years ago
11

A plane flies 405 miles with the wind and315 miles against the wind in the same amount of time. If the speed of the wind is 20 m

ph find the speed of the plane in still air
Mathematics
1 answer:
gayaneshka [121]3 years ago
4 0

Answer:

  160 mph

Step-by-step explanation:

The relationship between time, speed, and distance is ...

  time = distance/speed

__

If p represents the plane's speed, then the speed with the wind is p+20 and the time to go 405 miles is ...

  405/(p+20)

The speed against the wind is p-20, and the time to go 315 miles is ...

  315/(p-20)

These two times are equal, so we have ...

  405/(p+20) = 315/(p-20)

  405(p-20) = 315(p+20) . . . . . . cross multiply

  90p = 6300 +8100 = 14400 . . . . add 8100 -315p

  p = 14400/90 = 160

The speed of the plane in still air is 160 mph.

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Sales personnel for Skillings Distributors submit weekly reports listing the customer contacts made during the week.
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Answer:

a) The 90% confidence interval would be given by (18.52;20.49)  

b) The 95% confidence interval would be given by (18.32;20.68)    

Step-by-step explanation:

1) Previous concepts

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".

\bar X=19.5 represent the sample mean for the sample  

\mu population mean (variable of interest)

\sigma=5.2 represent the population standard deviation

n=75 represent the sample size  

2) Confidence interval 90%

The confidence interval for the mean is given by the following formula:

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}   (1)

Since the Confidence is 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.005, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that z_{\alpha/2}=1.64

Now we have everything in order to replace into formula (1):

19.5-1.64\frac{5.2}{\sqrt{75}}=18.515    

19.5+1.64\frac{5.2}{\sqrt{75}}=20.485

So on this case the 90% confidence interval would be given by (18.52;20.49)    

3) Confidence interval 95%

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that z_{\alpha/2}=1.96

Now we have everything in order to replace into formula (1):

19.5-1.96\frac{5.2}{\sqrt{75}}=18.323    

19.5+1.96\frac{5.2}{\sqrt{75}}=20.677

So on this case the 95% confidence interval would be given by (18.32;20.68)    

5 0
3 years ago
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