Answer:
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".
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
Solution to the problem
For this case we select a sample of n =100
From the central limit theorem we know that the distribution for the sample mean 
is given by:
So then the sample mean would be:
And the standard deviation would be:
Answer:
here's the solution :-
Step-by-step explanation:
i hope it helped...
You haven't provided the choices, therefore, I cannot provide an exact answer. However, I will help you with the concept.
For an order pair to be a solution to a system of equations, it has to satisfy <u>BOTH</u> equations. If it satisfies only one equation of the system or satisfy neither of the equations, the, it is not a solutions
<u><em>Examples:</em></u>
<u>System 1:</u>
x = y + 1
2x + 3y = 7
Let's check (2,1)
2 = 1 + 1 ........> equation 1 is satisfied
2(2) + 3(1) = 7 ......> equation 2 is satisfied
<u>(2,1) is a solution to this system</u>
<u>System 2:</u>
y = x + 3
y = x - 1
Let's check (2,1):
1 ≠ 2 + 3 ........> equation 1 isn't satisfied
1 = 2 - 1 ..........> equation 2 is satisfied
<u>(2,1) isn't a solution to this system</u>
<u>System 3:</u>
2y = 9 - 3x
3x + 2y = 9
Let's ceck (2,1):
2(1) ≠ 9 - 3(2) ..........> equation 1 isn't satisfied
3(2) + 2(1) ≠ 9 .........> equation 2 isn't satisfied
<u>(2,1) isn't a solution to this system
</u>
<u><em>Based on the above,</em></u> all you have to do is substitute with (2,1) in the system you have and pick the one where both equations are satisfied
Hope this helps :)
Answer:
8.5 square mm per minute
Step-by-step explanation:
A = 1/2bh
A' = (1/2)(b'h +bh') . . . . differentiating with respect to time
A' = (1/2)((-13)(1) +(5)(6)) = (1/2)(17) = 8.5 . . . . mm²/min
The area is increasing at the rate of 8.5 mm²/min.
_____
<em>Numerical solution</em>
Consider the triangle dimensions .01 minutes before and after the time of interest.
before: base = 5 + 0.13 = 5.13 mm; height = 1 - 0.06 = 0.94 mm. area = 2.4111 mm²
after: base = 5 -0.13 = 4.87 mm; height = 1 +.06 = 1.06 mm. area = 2.5811 mm²
Average rate of change in that period is
(2.5811 -2.4111)/0.02 = .17/.02 = 8.5 . . . . mm²/min
_____
<em>Comment on the numbers</em>
Note that we have assumed the base is decreasing at 13 mm/min. Quite often, division bars get lost on Brainly, so we're not sure this isn't 1/3 mm/min. At the assumed rate, the triangle will disappear in 5/13 minutes, about 23.08 seconds, when the base becomes zero. Of course, it only came into existence 1/6 minute (10 seconds) ago, when the height became non-zero.
