Answer:
The probability that Albert's sample of 64 will have a mean between 13.5 and 16.5 minutes is 0.9973.
Step-by-step explanation:
Previous concepts
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 interest on this case, and for this case we know the distribution for X is given by:
And let 
represent the sample mean, the distribution for the sample mean is given by:
On this case 
Solution to the problem
We are interested on this probability
If we apply the Z score formula to our probability we got this:
And we can find this probability on this way:
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
The probability that Albert's sample of 64 will have a mean between 13.5 and 16.5 minutes is 0.9973.
Answer:
.
Step-by-step explanation:
Given information:
According to the Pythagoras theorem,
Using Pythagoras theorem, we get
Taking square root on both sides.
Hence, the expression of the hypotenuse is .
<span>65 = number of different arrangements of 2 and 3 card pages such that the total number of card slots equals 18. 416,154,290,872,320,000 = number of different ways of arranging 18 cards on the above 65 different arrangements of page sizes. ===== This is a rather badly worded question in that some assumptions aren't mentioned. The assumptions being: 1. The card's are not interchangeable. So number of possible permutations of the 18 cards is 18!. 2. That all of the pages must be filled. Since the least common multiple of 2 and 3 is 6, that means that 2 pages of 3 cards can only be interchanged with 3 pages of 2 cards. So with that said, we have the following configurations. 6x3 card pages. Only 1 possible configuration. 4x3 cards and 3x2 cards. These pages can be arranged in 7!/4!3! = 35 different ways. 2x3 cards and 6x2 cards. These pages can be arranged in 8!/2!6! = 28 ways 9x2 card pages. These can only be arranged in 1 way. So the total number of possible pages and the orders in which that they can be arranged is 1+35+28+1 = 65 possible combinations. Now for each of those 65 possible ways of placing 2 and 3 card pages such that the total number of card spaces is 18 has to be multiplied by the number of possible ways to arrange 18 cards which is 18! = 6402373705728000. So the total amount of arranging those cards is 6402373705728000 * 65 = 416,154,290,872,320,000</span>
Answer:
I suppose it should be
6b² and (6b²)²
or
6b² and 36
Step-by-step explanation:
(a+b)² = a² + 2ab + b²
therefore
(6b²+2a)² = (6b²)² + 12ab² + 4a²
Answer:
1 Superscript 13 and 1 Superscript 15
Step-by-step explanation:
The process of exponentiation can be mathematically written as:
a^b
where a is called the base, and b is called the exponent.
Basically it means that we have to multiply the base with itself as many times as the value of the exponent.
For example 2^4 is 2•2•2•2
Having this in mind, 1^13 and 1^15 have equivalent values, because no matter how many times we multiply 1 with itself it will always be equal to 1.
