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evablogger [386]
3 years ago
5

The speed of a sparrow is x km/h in still air. When the

Mathematics
1 answer:
Semmy [17]3 years ago
4 0

Answer:

x = 5m/s

Step-by-step explanation:

Distance flying out = 12 km  (headwind)

Distance flying back = 12 km (tailwind)

total distance = 12 + 12 =24 km

wind speed = 1km/h

speed going out (with headwind) = (x - 1) km/h

speed coming back (with tailwind) = (x + 1) km/h

Time taken to go out = distance going out / speed going out

= 12 / (x-1)

Time taken to come back = distance coming back / speed coming back

= 12 / (x+1)

total time = time taken to go out + time taken to come back

5 =[ 12/(x-1) ] + [ 12/(x-1)]

expanding this, we will get

5x² - 24x - 5 = 0

solving quadratic equation, we will get

x = -1/5 (impossible because speed cannot be negative)

or

x = 5 (answer)

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Answer:

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Step-by-step explanation:

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A manufacturer of sprinkler systems designed for fire protection claims that the average activating temperature is at least 135°
nirvana33 [79]

Answer:

z=\frac{133-135}{\frac{3.3}{\sqrt{32}}}=-3.428      

p_v =P(z  

If we compare the p value and the significance level given for example \alpha=0.1 we see that p_v so we can conclude that we reject the null hypothesis, and the true mean is significantly lower than 135 so the claim not makes sense      

Step-by-step explanation:

Data given and notation      

\bar X=133 represent the sample mean

\sigma=3.3 represent the standard deviation for the population      

n=32 sample size      

\mu_o =135 represent the value that we want to test    

\alpha represent the significance level for the hypothesis test.    

z would represent the statistic (variable of interest)      

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.      

We need to conduct a hypothesis in order to determine if the true mena is at least 135, the system of hypothesis would be:      

Null hypothesis:\mu \geq 135      

Alternative hypothesis:\mu < 135      

We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:      

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)      

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic      

We can replace in formula (1) the info given like this:      

z=\frac{133-135}{\frac{3.3}{\sqrt{32}}}=-3.428      

Calculate the P-value      

Since is a one-side lower test the p value would be:      

p_v =P(z  

Conclusion      

If we compare the p value and the significance level given for example \alpha=0.1 we see that p_v so we can conclude that we reject the null hypothesis, and the true mean is significantly lower than 135 so the claim not makes sense      

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Answer:

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Step-by-step explanation:

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3 years ago
Read 2 more answers
An airplane is traveling at a speed of 240 miles/hour with a bearing of 110°. The wind velocity is 56 miles/hour at a bearing of
vodka [1.7K]

Answer:

Actual speed = 288 miles per hour

Actual direction angle = 116.38^\circ

Step-by-step explanation:

"Bearing" is the relative position of an object outside the plane compared to the position of the plane.  

Heading the the direction the nose of the plane is pointing.  

Course is the direction that pilot wants the plane to go.  

Wind direction is always the direction the wind is blowing from.  

The airplane is traveling at a speed of 240 miles/hour with a bearing of 110°.  

If the plane is traveling with a bearing of 110° and the wind is blown at a bearing of 325°.  

 325^{\circ}- 110^{\circ} =225^{\circ}

215^{\circ}- 180^{\circ} =35^{\circ}

The Ground speed will be in excess of the airspeed and true direction will be south if the indicated heading.  

The tailwind component is:

56 cos (35^\circ)

And the cross wind component is:

56 sin (35^\circ)  


And that is,

C^2 = (286)^2 + (32)^2


c = 288

So the actual speed of the plane is 288 miles per hour.

The deviation in the direction is:

Let the direction angle be 'x'.

x = tan ^{-1}\left ( \frac{32}{286} \right )=6.38^\circ

So the actual direction angle is 110^\circ+ 6.38^\circ=116.38^\circ.

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