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alexdok [17]
2 years ago
7

Find the unknown sides of the triangle

Mathematics
1 answer:
DedPeter [7]2 years ago
7 0

Answer:

the unknown side of the triangle is 2\sqrt{21}

Step-by-step explanation:

a^2+b^2=c^2

4^2+b^2=10^2

16+b^2=100

b^2=100-16

b^2=84

b=\sqrt{84} or 2\sqrt{21}

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A self proclaimed psychic was tested for ESP. The psychic was presented with 200 cards face down and asked to determine if the c
swat32

Answer:

The 95% confidence interval would be given (0.172;0.288).  

We are confident at 95% that the true probability that the psychic correctly identifies the symbol on the card in a random trial is between (0.172;0.288).  

We can conclude that her random guessing would have got her correct 20% of the time. Since the confidence interval contains 0.2, she has no psychic powers, rather she just guessed it like normal people. Any person could have got it correct this many times.

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".  

Description in words of the parameter p

p represent the probability that the psychic correctly identifies the symbol on the card in a random trial

\hat p represent the estimated probability that the psychic correctly identifies the symbol on the card in a random trial

n=200 is the sample size required  

z_{\alpha/2} represent the critical value for the margin of error  

The population proportion have the following distribution  

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

Numerical estimate for p

In order to estimate a proportion we use this formula:

\hat p =\frac{X}{n} where X represent the cases successful

\hat p=\frac{46}{200}=0.23 represent the estimated probability that the psychic correctly identifies the symbol on the card in a random trial

Confidence interval

The confidence interval for a proportion is given by this formula:

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

For the 95% confidence interval the value of \alpha=1-0.95=0.05 and \alpha/2=0.025, with that value we can find the quantile required for the interval in the normal standard distribution.  

z_{\alpha/2}=1.96  

And replacing into the confidence interval formula we got:  

0.23 - 1.96 \sqrt{\frac{0.23(1-0.23)}{200}}=0.172  

0.23 + 1.96 \sqrt{\frac{0.23(1-0.23)}{200}}=0.288  

And the 95% confidence interval would be given (0.172;0.288).

We are confident at 95% that the true probability that the psychic correctly identifies the symbol on the card in a random trial is between (0.172;0.288).  

We can conclude that her random guessing would have got her correct 20% of the time. Since the confidence interval contains 0.2, she has no psychic powers, rather she just guessed it like normal people. Any person could have got it correct this many times.

6 0
3 years ago
Y = 3/2x + 3<br> The slope and y-intercept
ra1l [238]

Answer:

Slope=3/2

Y-intercept=3

Step-by-step explanation:

7 0
2 years ago
12(a−4) simplified I am confused with this question
Ksenya-84 [330]

Answer:

-48

Step-by-step explanation:

8 0
3 years ago
Evaluate the expression.<br><br><br><br> 10+83÷16
Korolek [52]
The answer is 15.18
10+83/16= 15.18
7 0
2 years ago
Sam needs a web designer. Designer A is offering her services for an initial $510 in addition to $80 per hour. Designer B is off
lutik1710 [3]

Answer:

The answer is when they work 4 hours  x=4

Step-by-step explanation:

510 + 80x = 650 + 45x

80x - 45x = 650 - 510

35x = 140

x = 140/35

x = 4 hours

3 0
3 years ago
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