Your answer is L = 11 cm.
If the volumes of both shapes are the same, then we can set them equal to each other and solve for L to find the answer.
The volume of a rectangular prism is base × height × depth, which comes to 5 × 6 × L = 30L
The volume of the trapezoid prism (the shape on the left) would be the area of the trapezoid on the front, multiplied by the depth. This gives you:
× 6 × 10 = 5.5 × 6 × 10 = 330
So now we get:
330 = 30L
÷ 30
L = 11
I hope this helps!
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.
Answer:
Step-by-step explanation:
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