When you multiply 2/3 by a fraction less than one, how does the product compare to the factor

1 answer:

3 0

The product is less than either of the factors. Multiplying a number < 1 with 2/3 another number < 1, will give a fraction of a fraction, and part of a fraction is an even smaller fraction. Another way of looking at it: Fractions less than one have numerators smaller than their denominators. When multiplying fractions, you multiply across, so multiplying two fractions that are both less than one will always give a numerator much smaller than the denominator, and a larger denominator makes for a smaller number. I hope this helps, but if you have questions, ask.

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What is the slope of the line that passes through the points (0, –7) and (–4, 3)?

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Step-by-step explanation:

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One line passes through the point (-8,1) and (4,4). Another line passes through points (-9,-7) and (9,-3). Are the lines paralle

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The correct answer is neither.

Step-by-step explanation:

To find the relationship between the lines, find the slope of each. You can do this by using the slope formula.

m(slope) = (y2 - y1)/(x2 - x1)

m = (4 - 1)/(4 - -8)

m = 3/12

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Now do so for the second line.

m(slope) = (y2 - y1)/(x2 - x1)

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Suppose a certain type of fertilizer has an expected yield per acre of mu 1 with variance sigma 2, whereas the expected yield fo

mart [117]

Answer:

See the proof below.

Step-by-step explanation:

For this case we just need to apply properties of expected value. We know that the estimator is given by:

$S^2_p= \frac{(n_1 -1) S^2_1 +(n_2 -1) S^2_2}{n_1 +n_2 -2}$

And we want to proof that $E(S^2_p)= \sigma^2$

So we can begin with this:

$E(S^2_p)= E(\frac{(n_1 -1) S^2_1 +(n_2 -1) S^2_2}{n_1 +n_2 -2})$

And we can distribute the expected value into the temrs like this:

$E(S^2_p)= \frac{(n_1 -1) E(S^2_1) +(n_2 -1) E(S^2_2)}{n_1 +n_2 -2}$

And we know that the expected value for the estimator of the variance s is $\sigma$ , or in other way $E(s) = \sigma$ so if we apply this property here we have: