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lisabon 2012 [21]
3 years ago
6

Lasers can provide highly accurate measurements of small movements. To determine the accuracy of such a laser, it was used to ta

ke 82 measurements of a known quantity. The sample mean error was 20 μm with a standard deviation of 60 μm. The laser is properly calibrated if the mean error is μ = 0. A test is made of H0 : μ = 0 versus H1 : μ ≠ 0. Find the P value?
Mathematics
1 answer:
sp2606 [1]3 years ago
4 0

Answer: p-value \approx 0.01

Step-by-step explanation:

Hypothesis testing

\\\left\{\begin{matrix}H_0 : \mu_0 =0\\ H_1: \mu_0 \neq 0\end{matrix}\right.\\

For this problem, we need to use the t-student distribution to  make inference about the data. We calculate the t-statistics as below:

\bar{X} = 20\:\mu m\\S.E. = 60\:\mu m\\n=82\\t_{stat} = \frac{\bar{X}-\mu_0}{S.E/\sqrt{n}}=\frac{20-0}{60/\sqrt{82}}=3.0185

Using a t-statistics table, or using the function TDIST in Microsoft Excel with t_{stat} = 3.0185,\: df (degree\: of\: freedom) = 14 - 1 = 13 with two-tailed distribution, we obtain p-value \approx 0.01.

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Step-by-step explanation:

This triangle is a 30, 60, 90 so that means it would be - a, 2a, a\sqrt{3} on each side, so add that all together and you get x-15 and y-15\sqrt{3}

5 0
3 years ago
Justify your reasoning
love history [14]

Answer:

Yes

Step-by-step explanation:

You can conclude that ΔGHI is congruent to ΔKJI, because you can see/interpret that there all the angles are congruent with one another, like with vertical angles (∠GIH and ∠KIJ) and alternate interior angles (∠H and ∠J, ∠G and ∠K).

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3 years ago
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vagabundo [1.1K]
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7 0
3 years ago
Please help!
Reika [66]

The greatest number of friends who can receive a necklace is 6. The reason why is because 6 is the greatest common factor of 72 and 42.

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4 0
3 years ago
Tickets to a football game cost $15.00 each including tax and a bag of popcorn cost $2.25 and a soda cost $1.75 Xavier has $350.
adoni [48]

Answer:

18 (full answer: 18.4210526316)

Step-by-step explanation:

<em>I LOST MY ANSWER RIGHT WHEN I WAS ABOUT TO FINISH DUE TO BRAINLY ROBOT DETECTION  </em>

This question seems incomplete. I dont know the tax, and what he wants to do with the $350, so I'll just work without them.

I'm going to assume that he wants to buy extra tickets, popcorn, and soda with the extra money.

1. add $15, $2.25, and $1.75

2. 15.00+2.25+1.75= 19.00

3. divide 350 by 19

350/19= roughly 18.42

So, Xavier can buy 18 tickets with food and drinks.

8 0
3 years ago
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