The coordinates of point A are (−3, 5). What are the coordinates of point B, which is a reflection of point A across the x‑axis?
1 answer:
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Answer:
Triangle DEF is a right, scalene triangle. It is not isosceles, obtuse, acute, or equilateral
Step-by-step explanation:
All we know about m and n are that they are not equal to each other and they are positive. This was given in the problem. See image. Once it is graphed you can see on the graph the lengths of DE and EF. Use Pythagorean theorem to calculate DF. see image.
DE is horizontal and EF is vertical, so you can see their slopes or calculate using a formula. Calculate the slope of DF. Slope is y-y on top of a fraction and x-x on the bottom of the fraction.
Lastly, use midpoint formula to find the midpoints. Average the x's and average the y's to find the x- and y-coordinates of the midpoints. See image.
Finally, DEF is a right triangle. The graph as well as the slopes show us that DE and EF form a right angle. So DEF must be a right triangle (and not obtuse nor acute) We were told that m doesNOT equal n, so the triangle cannot have two equal sides, so it cannot be isosceles (2 equal sides) nor equilateral (3 equal sides) It has 3 different lengths of sides; that is called scalene.
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
represent the probability that the psychic correctly identifies the symbol on the card in a random trial
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
represent the critical value for the margin of error
The population proportion have the following distribution
Numerical estimate for p
In order to estimate a proportion we use this formula:
where X represent the cases successful
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:
For the 95% confidence interval the value of and
, with that value we can find the quantile required for the interval in the normal standard distribution.
And replacing into the confidence interval formula we got:
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.