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Ilia_Sergeevich [38]
2 years ago
15

The speed limit on a road drops down to 15 miles per hour around a curve. Mr. Gerard slows down by 10 miles per hour as he drive

s around the curve. He never drives above the speed limit. What speed was Mr. Gerard driving before the curve The speed limit on a road drops down to 15 miles per hour around a curve. Mr. Gerard slows down by 10 miles per hour as he drives around the curve. He never drives above the speed limit. What speed was Mr. Gerard driving before the curve? Graph the solution.? Graph the solution.
Mathematics
1 answer:
emmasim [6.3K]2 years ago
8 0

Answer:

Mr. Gerard speed was at most 25 miles per hour before the curve

Step-by-step explanation:

<u>How to solve the speed Mr. Gerard was driving before the curve</u>

Let’s just assume that Gerard went <em>exactly</em> the speed limit 15 miles per hour (mph) <em>after</em> when he slowed down by 10 miles per hour and drove around the curve. The reason why I’m using exactly 15mph is because it’s the max speed he can go. He can go 15 miles per hour and still be safe, but it’s just that he can’t go any faster than that.

Now, you can do 15 + 10 to find the speed he went <em>before</em> he drove around the curve. So, that would be 25mph <em>before</em> he drove around the curve.

<u>You might be asking:</u> What if he went slower than 25mph before he drove around the curve, and what if he went faster than 25mph?

-When he drives exactly 25mph and slows down by 10mph when he makes the turn around the curve, he’s going exactly 15mph which it safe for him because it’s not faster than 15mph.

-It could be possible that he went slower than 25mph before he drove around the curve, but he still will be safe because when he makes the turn around the curve and slows down by 10 miles per hour, now he’ll reach below 15 miles per hour which is even safer for him. Here’s an example for you to understand: Let’s say he drove 23mph <em>before</em> the curve (which is less than 25mph). As soon as he makes the turn around the curve, he slows down by 10mph. So after he goes around the curve, he’s going 13mph, which is less than the speed limit 15mph. You can take any number less than 25mph and he’ll still be safe because it will be less than 15mph.

-Now, if he went faster than 25mph, he wouldn’t be safe anymore because after when he slows down by 10mph and goes around the curve, he’ll be <em>above</em> the speed limit of 15mph. Here’s an example for you to understand: Let’s say he drove 27mph <em>before</em> the curve (which is faster than 25mph). As soon as he makes the turn around the curve, he slows down by 10mph. So after he goes around the curve, he’s going 17mph, which is faster than the speed limit 15mph.

<u>Answer:</u> Mr. Gerard speed was at most 25 miles per hour before the curve

<u>Graphing it</u>

A way to graph this is to write out a compound inequality. You can write it as:

0 < y ≤ 25  ⇒ Where any speed has to be <em>less than or equal to</em> 25 miles per hour, because 25 miles per hour is the most/biggest speed Mr. Gerard can drive. But it has to be <em>greater than</em> 0 because you can’t go negative miles per hour, or 0 miles per hour

<u>The graph is shown below ↓</u>

I don’t know what graph you want, or how your teacher wants you to graph it. So I put two options for you :)

I hope you understand and that this helps with your question! :)

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Answer:

We conclude that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%.

Step-by-step explanation:

We are given that a survey of 2,254 American adults indicates that 17% of cell phone owners browse the internet exclusively on their phone rather than a computer or other device. According to an online article, a report from a mobile research company indicates that 38 percent of Chinese mobile web users only access the internet through their cell phones.

We have to conduct a hypothesis test to determine if these data provide strong evidence that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%.

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Alternate Hypothesis, H_a : p \neq 38%  {means that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%}

The test statistics that will be used here is <u>One-sample z proportion statistics</u>;

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where, \hat p = proportion of cell phone owners who browse the internet

                 exclusively on their phone in a survey of 2,254 adults = 17%

          n  = sample of adults = 2,254

So, <em><u>test statistics</u></em> = \frac{0.17-0.38}{\sqrt{\frac{0.17(1- 0.17)}{2,254} } }

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<em>Since in the question we are not given with the significance level so we assume it to be 5%. So, at 0.05 level of significance, the z table gives critical values between -1.96 and 1.96 for two-tailed test. Since our test statistics does not lie in between the critical values of z so we have sufficient evidence to reject null hypothesis as it will fall in the rejection region.</em>

Therefore, we conclude that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%.

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