Vlad spent 20 minutes on his history homework and then completely solved x math problems that each took 2 minutes to
1 answer:
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a) 75 percent of the regular price is the price for senior citizens.
b) $6.712 is the price for senior citizens.
<u>Step-by-step explanation</u>:
- The regular price is the 100% = $8.95
- The offer price for senior citizen = 15% discount from 100%
∴ Percent of the regular price for senior citizens = 100% - 15% = 75%
The price for the senior citizens = 75% of $8.95
⇒ (75/100)8.95
⇒ 0.758.95
⇒ 6.712 dollars.
∴ The price for senior citizens = $6.712
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.
Answer:
a) Table and graph showed
b) The distance will be 231 miles
c) Yes
Step-by-step explanation:
We know the van gets 22 mi/gal, so the distance D in miles traveled by the van can be expressed as
D(g)=22g, being g the number of gallons of gas used
a) The graph of the function D and its corresponding table of values is shown below.
b) If the van used g=10.5 gallons of gas, the distance would be:
D(10.5)=22 x 10.5 = 231 miles
c) The values of g are real in nature because they represent the amount of gas consumed by the van and it can be any real positive number. Being D a linear function of g, it also happens to take positive real values. Then it makes sense to connect the points with lines.
