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Hitman42 [59]
3 years ago
7

A bird leaves its nest and travels 20 miles per hour downwind for x hours. On the return trip, the bird travels 4 miles per hour

slower and has 6 miles left after x hours. What is the distance of the entire trip? How long does the entire trip take?
Mathematics
1 answer:
natali 33 [55]3 years ago
5 0
We need to calculate a total TIME.  
Let the time required to cover distance d at 20 mph be x.  d is the ONE WAY distance, not the total distance traveled (which would be 2d).

Remember the formula d=rt:  the distance traveled equals the rate times the time.  Here, d = rx, and thus x = d/r  = d/(20mph)

Let's begin by recognizing  that       d(going) = d(returning)
Then                                            (20 mph)x   = 6 + (16 mph)x

                                                      (20 mph)x - (16 mph)x = 6 miles
Then:                                                    (4 mph)x = 6 miles
or:                                                             x = 1.5 hours

It takes the bird 1.5 hours at 20 mph to cover distance d, which is 30 miles.
Thus, the total time spent flying is 1.5 hours (going) and [1.5 hours + (6 miles)/(16 mph) returning:

                            1.5 hours + 1.5 hours + 0.375 hours = 3.375 hours total.

The total distance covered is 2d, or 2(30 miles) = 60 miles.

It took me a while and a lot of experimentation to arrive at these results.  Please, if my arguments here are not clear, ask questions.
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Answer:

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Step-by-step explanation:

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2 years ago
The coordinates of the image of line segment RT are R'(-2,-4) and T'(4.4). The image was produced by a dilation with a scale fac
Daniel [21]

Given the coordinates of the image of line segment RT to be R'(-2,-4) and T'(4.4), if the image produced was dilated by a scale factor of 12 centered at the origin, to get the coordinate of the end point, we will simply multiply the x and y coordinates of by the factor of 12 as shown:

For R' with coordinate R'(-2,-4), the coordinates of endpoint of the pre-image will be:

R = 12R'

R = 12(-2, -4)

R = (-24, -48)

For T' with coordinate T'(4,4), the coordinates of endpoint of the pre-imagee will be:

T = 12T'

T = 12(4, 4)

T = (48, 48)

Hence the coordinate of the endpoint of the preimage will be at R(-24, -48) and T(48, 48)

6 0
1 year ago
the weekly salaries for 7 employees of a small business are given below 632, 750, 829, 839, 841, 881, 954 suppose the 632 salary
PolarNik [594]
I don't understand your question.. Is this multiple choice or something else?
7 0
3 years ago
A random sample of 25 glass sheets is obtained and their thicknesses are measured. The sample mean is x= 3.54 mm and sample stan
lisabon 2012 [21]

Answer: (3.46, 3.62)

Step-by-step explanation:

The formula to find the confidence interval for population mean is given :-

\overline{x}\ \pm\ t_{\alpha/2}\dfrac{s}{\sqrt{n}}

, where n = sample size.

t_{\alpha/2} = Two-tailed t-value for significance level of (\alpha) and degree of freedom df= n-1.

s = sample standard deviation.

As per given , we have

\overline{x}= 3.54 mm

s= 0.20 mm

n= 25

Significance level =\alpha=1-0.95=0.05

Since population standard deviation is not given , it means the given problem has t- distribution.

Two-tailed t-value for significance level of (0.05) and degree of freedom df= 24:

t_{\alpha/2\ ,df}=t_{0.025,\ 24}=2.0639

95% Confidence interval for population mean:

3.54\ \pm\ (2.0639)\dfrac{0.20}{\sqrt{25}}

=3.54\ \pm\ (2.0639)\dfrac{0.20}{5}

=3.54\ \pm\ (2.0639)(0.04)

=3.54\ \pm\ 0.082556

=(3.54- 0.082556,\ 3.54+ 0.082556 )=(3.457444,\ 3.622556)\approx(3.46,\ 3.62)

Hence, the 95% two-sided confidence interval for the mean glass thickness = (3.46, 3.62)

7 0
3 years ago
A giraffe can run speed of 15 miles per hour. which equation represents the total number of miles, m, a giraffe can h hours.
Elena-2011 [213]
<h3>Answer:  A.  m = 15h</h3>

Explanation:

This is because

distance = speed*time

7 0
3 years ago
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