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Irina-Kira [14]
3 years ago
14

The longest frontier between countries is between the u.s and Canada a distance of 3,987 miles how many weeks would it take some

one jogging at an average speed of 10 minutes per mile for 8 hours a day to jog the length of this frontier
Mathematics
1 answer:
Step2247 [10]3 years ago
8 0
10 mins = 1 miles
1 hour = 1 x 6 = 6 miles
8 hours = 6 x 8 = 48miles

The jogger could cover 48 miles a day.

3987 ÷ 48 = 83.06 days

It takes 83.06 days to jog the length of this frontier.

83.06 days ÷ 7 = 11.87 weeks = 12 weeks (round to the nearest whole number)

It takes 12 weeks to jog the length of this frontier.
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Answer:

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

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

And the confidence interval is given by:

(0.123, 0.177)

And for this case the interval contains the value 0.16, so then we can conclude at 5% of significance that the true proportion is not different from 0.16

Step-by-step explanation:

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".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value would be given by:

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

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

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

And the confidence interval is given by:

(0.123, 0.177)

And for this case the interval contains the value 0.16, so then we can conclude at 5% of significance that the true proportion is not different from 0.16

3 0
3 years ago
Find the surface area of a right cone with diameter 30 in. and slant height 8 in.Your answerEXTRA CREDIT: Find the surface area
Anon25 [30]

<u>Answer:</u>

Surface area = 1084 in²

<u>Step-by-step explanation:</u>

To find the surface area of a right cone, we can use the following formula:

\boxed{{Area = \pi r^2 + \pi rl}},

where:

• r = radius

• l = slant height.

In the question, we are told that the diameter of the cone is 30 in. Therefore its radius is (30 ÷ 2 = ) 15 in. We are also told that its height is 8 in.

Using this information and the formula above, we can calculate the surface area of the cone:

Surface area = \pi \times (15)^2 + \pi \times 15 \times 8

                     = 345 \pi

                     \approx 1084 in²

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Answer:

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