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oksian1 [2.3K]
3 years ago
6

The variance can never bea.zerob.larger than the standard deviationc.negatived.smaller than the standard deviation

Mathematics
1 answer:
MrRa [10]3 years ago
7 0

Answer:

c.negative

True, by definition since the variance take in count the differences around the mean squared, then we can't have a negative value for a sum of square values.

Step-by-step explanation:

We need to remember that the variance is a measure of dispersion for a dataset respect to a measure of central tendency called the mean. The mean is defined as:

\bar x = \frac{\sum_{i=1}^n X_i}{n}

And the population mean is given by:

\mu= \frac{\sum_{i=1}^n X_i}{N}

The population variance is defined by:

\sigma^2 = \frac{\sum_{i=1}^n (X_i -\mu)^2}{N}

And the sample variance is defined as:

s^2= \frac{\sum_{i=1}^n (X_i -\bar x)}{n-1}

Now if we analyze the options we have this:

a.zero

False, if all the values are the same then the mean would be the same to the values and the difference between each value and the mean would 0 and indeed the variance would be 0.

b.larger than the standard deviation

False, if the population standard deviation is \sigma=2 then the variance would be \sigma^2 = 4 and as we can see is higher than the standard deviation

c.negative

True, by definition since the variance take in count the differences around the mean squared, then we can't have a negative value for a sum of square values.

d.smaller than the standard deviation

False, if the population standard deviation is \sigma=0.1 then the variance would be \sigma^2 = 0.01 and as we can see is lower than the standard deviation

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SVETLANKA909090 [29]

We are given, cost of the robot for 0 number of year = $16,000.

0 represents initial time of the robot.

After 10 year cost of the robot is = $0

The problem is about the number of the years and cost of the robot over different number of years.

So, we could take x coordinate by number of hours and y coordinate for y number of hours.

So, from the problem, we could make two coordinates for the given situation.

(x1,y1) = (0, 16000) and (x2,y2) = (10, 0).

In order to find the function of time, we need to find the rate at which robot rate depreciates each year.

Slope is the rate of change.

So, we need to find the slope of the two coordinates we wrote above.

We know, slope formula

Slope (m) = \frac{y2-y1}{x2-x1}

Plugging values in formula, we get

m=\frac{0-16000}{10-0} = \frac{-16000}{-10} = -1600.

Brecasue of depreciation we got a negative number for slope or rate of change.

Therefore, rate of depreciation is $1600 per year.

We already given inital cost, that is $16,000.

So, we can setup an a function

f(x) = -1600x + 16000.

But the problem is asked to take the variable t for time.

Replacing x by t, we get

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3 years ago
Two angles are said to be congruent if:
IRISSAK [1]
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1/y - 1/x = 1/60<br> 3y - 2x = 6 <br> (Simultaneous question)
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1y - 1/x = 1/60 = x*y =60 = x=60/y

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y^2-40-2y=0

y = 7.4


3(7.4)-2x=6

22.2-2x = 6

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6 0
3 years ago
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ankoles [38]
ANSWER-

B

EXPLANATION-

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