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3 years ago

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A train leaves Los Angeles at 2 p.m. heading north at 50 mph. If the next train leaves three hours later and also heads north at

60 mph, at what time will the second train catch up with the first?

2 answers:

Svetach [21]3 years ago

7 0

Answer:

8:00 AM

Step-by-step explanation:

alphabetsam had a good step by step explaination but they got the timing wrong.

They put 8 PM instead of AM. The correct answer is 8:00 AM.

Mamont248 [21]3 years ago

5 0

Since the first train has been travelling for 3 hours, we have the following equations:
$d=50t+3*50=50t+150$
$d=60t$

We want to know when they will be equal, so set these equal to eachother:
$60t=50t+150$
$10t=150$
$t=15$

So 15 hours after the second train leaves, they will be at the same distance. This is at 8AM since the second train leaves at 5PM.

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One letter is selected from the word "statistics." What is the probability that an "s" or "t" is chosen?

Pavel [41]

Answer:

3/5

Step-by-step explanation:

There are 10 letters in the word "statistics".

Out of which, there are 3 s's and 3 t's.

So, the question asks what's the probability to get a S or a T out of 10 letters.

Since the number of S's (3) and the number of T's equal 6, that means you have 6 chances out of 10 to pick an S or a T.

6/10 or if we simplify/reduce it... we get 3/5.

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2 years ago

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.â Suppose a small group of 11 Allen's humming

alexira [117]

Answer:

$3.15-1.28\frac{0.38}{\sqrt{11}}=3.003$

$3.15+ 1.28\frac{0.38}{\sqrt{11}}=3.297$

So on this case the 80% confidence interval would be given by (3.003;3.297)

And the margin of error is given by:

$ME = 1.28\frac{0.38}{\sqrt{11}}= 0.147$

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".

$\bar X=3.15$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=0.38$ represent the population standard deviation

n=11 represent the sample size

Solution to the problem

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

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.80 or 80%, the value of $\alpha=0.2$ and $\alpha/2 =0.1$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NOR.INV(0.1,0,1)".And we see that $z_{\alpha/2}=1.28$

Now we have everything in order to replace into formula (1):

$3.15-1.28\frac{0.38}{\sqrt{11}}=3.003$

$3.15+ 1.28\frac{0.38}{\sqrt{11}}=3.297$

So on this case the 80% confidence interval would be given by (3.003;3.297)

And the margin of error is given by:

$ME = 1.28\frac{0.38}{\sqrt{11}}= 0.147$

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Virty [35]

Answer:

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Step-by-step explanation:

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Please do #4 It’s it the one on the bottom

spin [16.1K]

We need to graph this equation:

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