Answer:
All points between z = 0 and z = 7 along the z-azis in R3 x-y-z plane
Step-by-step explanation:
The inequality 1 z
7 represents all sets of points on the z-axis in the R3 plane that lies bewteen z = 0 and z= 7.
It is represents a line segment joining two point z= 0 and z=7 along z- axis in the R3 plane, while x=0 and y=0 on the x-y plane.
Answer:
Step-by-step explanation:
f(x) = 70 + 11x
To find the value of x when f(x) =158 , equate f(x) to 158
We have
Divide both sides by 11
We have the final answer as
<h3>x = 8</h3>Hope this helps you
Answer:
Point E is given by
Step-by-step explanation:
Let points C and D be and let point E divides it in ratio
.
Then coordinates of point E are given by
Put
Point E is given by
Now plot point E.
Answer:
(a) The variance decreases.
(b) The variance increases.
Step-by-step explanation:
According to the Central Limit Theorem if we have a population with mean <em>μ</em> and standard deviation <em>σ</em> and we take appropriately huge random samples (<em>n</em> ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.
Then, the mean of the sample mean is given by,
And the standard deviation of the sample mean is given by,
The standard deviation of sample mean is inversely proportional to the sample size, <em>n</em>.
So, if <em>n</em> increases then the standard deviation will decrease and vice-versa.
(a)
The sample size is increased from 64 to 196.
As mentioned above, if the sample size is increased then the standard deviation will decrease.
So, on increasing the value of <em>n</em> from 64 to 196, the standard deviation of the sample mean will decrease.
The standard deviation of the sample mean for <em>n</em> = 64 is:
The standard deviation of the sample mean for <em>n</em> = 196 is:
The standard deviation of the sample mean decreased from 0.7 to 0.4 when <em>n</em> is increased from 64 to 196.
Hence, the variance also decreases.
(b)
If the sample size is decreased then the standard deviation will increase.
So, on decreasing the value of <em>n</em> from 784 to 49, the standard deviation of the sample mean will increase.
The standard deviation of the sample mean for <em>n</em> = 784 is:
The standard deviation of the sample mean for <em>n</em> = 49 is:
The standard deviation of the sample mean increased from 0.2 to 0.8 when <em>n</em> is decreased from 784 to 49.
Hence, the variance also increases.