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evablogger [386]
3 years ago
10

a long-distance runner passes the 23 km mark of a race in 2 hr 30 min and passes the 44 mark 3 hours later. Assuming a constant

rate, find the speed of the long-distance runner in km/h
Mathematics
1 answer:
Vikentia [17]3 years ago
8 0

Answer:

The speed of the long distance runner is 8km/h

Step-by-step explanation:

In this question, we have a long-distance runner, running at a constant rate and we want to find his speed.

Mathematically,

speed = distance/ Time

From the question, we are told that he passes the 44km mark 3 hours after passing the 23km mark in 2 hours and 30 minutes

what this means is that the total distance he ran was just 44km

Now to the total time, that would be 2 hours 30 minutes + 3 hours = 5hrs 30 minutes or 5.5 hours

The speed is thus = 44km/5.5 hours =

8km/h

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Answer:

7/22

Step-by-step explanation:

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5 0
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The data given to the right includes data from ​candies, and of them are red. The company that makes the candy claims that ​% of
Dafna1 [17]

Using the z-distribution, the 95% confidence interval for the percentage of red candies is of (7.84%, 33.18%). Since 33% is part of the interval, there is not enough evidence to conclude that the claim is wrong.

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions is given by:

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which:

  • \pi is the sample proportion.
  • z is the critical value.
  • n is the sample size.

In this problem, we have a 95% confidence level, hence\alpha = 0.95, z is the value of Z that has a p-value of \frac{1+0.95}{2} = 0.975, so the critical value is z = 1.96.

Researching this problem on the internet, 8 out of 39 candies are red, hence the sample size and the estimate are given by:

n = 39, \pi = \frac{8}{39} = 0.2051

Hence the bounds of the interval are:

  • \pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2051 - 1.96\sqrt{\frac{0.2051(0.7949)}{39}} = 0.0784
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As a percentage, the 95% confidence interval for the percentage of red candies is of (7.84%, 33.18%). Since 33% is part of the interval, there is not enough evidence to conclude that the claim is wrong.

More can be learned about the z-distribution at brainly.com/question/25890103

#SPJ1

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Combine any like terms in the expression. If there are no like terms, rewrite the expression.
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Step-by-step explanation:

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