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julia-pushkina [17]
1 year ago
14

What is the volume of the following cone? What is the capacity?

Mathematics
1 answer:
timurjin [86]1 year ago
7 0

ANSWER

Volume of Cone = 37.7cm^3

EXPLANATION

\begin{gathered} V\text{ = }\Pi\ast r^2\frac{h}{3}^{} \\ \text{ = 3.142}\ast3^2\ast\frac{4}{3}=37.699cm^3 \end{gathered}

Hence, the Volume of Cone = 37.7cm^3

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Answer:

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Step-by-step explanation:

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An instructor in a college class recently gave an exam that was worth a total of 100 points. The instructor inadvertently made t
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Answer:

B) Method 2 will increase the standard deviation of the students' scores.

Step-by-step explanation:

Given that an instructor in a college class recently gave an exam that was worth a total of 100 points.

The average score for his students was 43 and the standard deviation of the scores was 5 points.

And now he is considering two different strategies for rescaling the exam results of which:

Method 1 = Add 17 points to everyone's score.

Method 2 = Multiply everyone's score by 1.7 .

And we have to check what will be the impact of these methods on the standard deviation of the students' scores.

For this let us consider a simple example to understand this:

Firstly, Formula for calculating Standard Deviation =  \sqrt{\frac{\sum (X-Xbar)^{2}}{n-1}}

Suppose,

     X             X - Xbar       (X - Xbar)^{2}

     3              3 - 6 = -3         -3 * -3 = 9

     5              5 - 6 = -1          -1 * -1 = 1

     10            10 - 6 = 4          4 * 4 = 16

<em>Mean of above data, Xbar</em> = \frac{3+ 5+10}{3} = 6

<em>Standard Deviation of data </em>= \sqrt{\frac{26}{3-1} } = 3.6055

Now let us suppose that we multiply each value of above data with 2 so the new data will be:

     X                X - Xbar           (X - Xbar)^{2}

 3*2 = 6        6 - 12 = -6         -6 * -6 = 36

 5*2 = 10       10 - 12 = -2       -2 * -2 = 4

10*2 =20      20 - 12 = 8         8 * 8 = 64

<em>Mean of new data, Xbar </em>= \frac{6+ 10+20}{3} = 12

<em>Standard Deviation of new data</em> = \sqrt{\frac{104}{3-1} } = 7.2111

<em>Hence, we see that when we multiply any value to the data the standard deviation will increase and in other words it will multiplied by that value which value we multiplied with each data value i.e. when we multiply each data value with 2 the standard deviation also get multiplied by as </em>

  3.6055 * 2 = 7.2111

Therefore option B is correct that Method 2 will increase the standard deviation of the students' scores.

<em>And on the other hand Similarly by adding any constant to the data the Standard Deviation will remain same. Therefore Method 1 will have no impact on standard deviation of the students' scores.</em>

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Last month, Ebony had 72 dollars in a checking account. The current balance is 126 dollars. What is the percent change in the ac
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Answer:

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Step-by-step explanation:

Last month, 72.

This month, 126.

Last month, ebony had 72/126 in her account to what she has this month. 72/126 as a percentage.

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Answer:

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Step-by-step explanation:

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A and B are independent events. P(A) = 0.30. P(B) = 0.60 What is P(A/B)?
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