Answer: 2.5
Step-by-step explanation:
Let 
be the population mean .
Then, Null hypothesis : 
Alternative hypothesis : 
We assume that this is a normal distribution.
Given : Sample size : n=25 , since the sample is small (n<30) so we cannot apply z-test . Thus the test is t-test.
Sample mean : 
Population standard deviation : 
The test statistic for population mean is given by :-
i.e. 
Hence, the observed critical value = 2.5
Percent increase = (new number - original number) / original number...* 100
= (39.99 - 29.62) / 29.62....* 100
= 10.37 / 29.62....* 100
= 0.35 * 100
= 35% markup <===
Let <em>x</em> be the smallest of the three integers. Then the next two are <em>x</em> + 2 and <em>x</em> + 4.
• "The ratio of the smallest number to 1 less than twice the smallest number..."
This translates to
<em>x</em> / (2<em>x</em> - 1)
• "... the ratio of 3 more than the middle number to twice the largest number."
This translates to
((<em>x</em> + 2) + 3) / (2 (<em>x</em> + 4))
or, simplifying a bit,
(<em>x</em> + 5) / (2<em>x</em> + 8)
The ratioes are said to be equivalent, so
<em>x</em> / (2<em>x</em> - 1) = (<em>x</em> + 5) / (2<em>x</em> + 8)
Solve for <em>x</em> :
<em>x</em> (2<em>x</em> + 8) = (<em>x</em> + 5) (2<em>x</em> - 1)
2<em>x</em>² + 8<em>x</em> = 2<em>x</em>² + 9<em>x</em> - 5
8<em>x</em> = 9<em>x</em> - 5
-<em>x</em> = -5
<em>x</em> = 5
So the three integers are 5, 7, and 9.
B! cosine is adjacent over hypotenuse
