Answer:
Step-by-step explanation:
Assuming a mean of $204 per night and a deviation of $55.
a. What is the probability that a hotel room costs $225 or more per night (to 4 decimals)?
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"
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Let X the random variable that represent the cost per night at the hotel, and for this case we know the distribution for X is given by:
Where 
and 
And let 
represent the sample mean, the distribution for the sample mean is given by:
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability on this way:
Give a counterexample to disprove the statement all squares are congruent
Answer:
f(x) = 3^x increases steadily on the interval [4,5].
Step-by-step explanation:
This exponential function f(x) = 3^x has a positive base (3) which is larger than 1. Thus, this function continues to increase as x increases, including the case where x increases from 4 to 5.
Answer:
12 m²
Step-by-step explanation:
Area of the floor:
area = length * width
area = 4 m * 5 m
area = 20 m²
area of carpet = 60% of area of the floor
area of carpet = 0.6 * 20 m²
area of carpet = 12 m²
Let's assume that the statement "if n^2 is odd, then is odd" is false. That would mean "n^2 is odd" leads to "n is even"
Suppose n is even. That means n = 2k where k is any integer.
Square both sides
n = 2k
n^2 = (2k)^2
n^2 = 4k^2
n^2 = 2*(2k^2)
The expression 2(2k^2) is in the form 2m where m is an integer (m = 2k^2) which shows us that n^2 is also even.
So this contradicts the initial statement which forces n to be odd.
