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3 years ago

A cone of radius 10 cm and height 16 cm is divided into two parts by a plane through the midpoint of its

Mathematics

1 answer:

bazaltina [42]3 years ago

7 0

Answer:

The ratio of their volumes (the top to bottom half) is 1/7

Step-by-step explanation:

The given parameters are;

The radius, r, of the cone = 10 cm

The height of the cone = 16 cm

The point at which the cone is divided = The midpoint of the its axis and parallel to its base

The ratio of the of the volume of the two parts is given as follows;

The volume, V of the entire cone = 1/3 × Base area (π·r²) × Height, h

Therefore;

V = 1/3 × π × 10² × 16 =1600·π/3 = 1675.52 cm³

The height at which the cone is divided = 16/2 = 8 cm

The height, h₁ of the uppermost divided cone = 8 cm

The ratio of the radius to the height of the cone = 10/16 = 5/8

The radius r₁, of the uppermost divided cone = The height of the uppermost divided cone × The ratio of the radius to the height of the cone

∴ r₁ = 8 × 5/8 = 5 cm

The volume, V₁, of the uppermost divided cone = 1/3 × (π·r₁²) × h₁

∴ V₁ = 1/3 × π × 5² × 8 = 200·π/3 = 209.44 cm³

Which gives;

The volume of the lower cone, V₂ = V - V₁

V₂ = 1675.52 cm³ - 209.44 cm³ = 1400·π/3 = 1466.1 cm³

The ratio of their volumes V₁ : V₂ = V₁/V₂ = (200·π/3)/(1400·π/3) = 209.44/1466.1 = 1/7.

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A math textbook is 1 1/4 in. thick. how much shelf space is needed for 30 copies of the book?

inysia [295]

Hello!

You have to multiply 1 1/4 by 30 because each math book is 1 1/4 in. thick, and 30 books is 1 1/4 by 30. First change 30 and 1 1/4 to an improper fraction.

$\frac{30}{1} \times \frac{5}{4} = \frac{150}{4} = 37 \frac{1}{2}$

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3 years ago

If you shift the absolute value parent function, F(x) = |x|, left 4 units, what is the equation of the new function?

san4es73 [151]

Answer:

The equation of new function is: G(x)=|x+4|

Step-by-step explanation:

We are given:

If you shift the absolute value parent function, F(x) = |x|, left 4 units,

We need to find:

the equation of the new function

We know that: If we have parent function f(x) and g(x)=f(x+c) there will be horizontal translation left c units.

We are parent function, F(x) = |x|

So, Our function went translation of 4 units left

So, the new function will be:

G(x)=|x+4|

So, The equation of new function is: G(x)=|x+4|

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3 years ago

Determine the equation of the line in y-intercept form.

bagirrra123 [75]

Answer: 2x -6

Step-by-step explanation:

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3 years ago

What is meant by "bias due to selective survival" in cross-sectional studies? Under what circumstances might there be no selecti

Rudik [331]

Answer:

What is meant by "bias due to selective survival" in cross-sectional studies?

First lets understand what is selective bias in cross-sectional studies. Basically its the bias that occurs when the random sample data for some analysis is selected in improperly. Such a selected sample is not able to represent the population that is to be analyzed. The reason is the improper randomization. So "bias due to selective survival" means that only the survival participants or survivors can be considered in this cross sectional studies. So if there is more probability of exposed cases to survive than unexposed cases or it could also be possible that unexposed cases have more probability to survive than exposed ones, so in either case the conclusion drawn from this cross sectional studies may differ from the proper cohort study. So the selective bias is introduced. Hence we can say that there is bias due to selective survival.

Step-by-step explanation:

Under what circumstances might there be no selective survival bias even if the selection probabilities are not all equal?

If the cross product of selection probabilities equals 1. Then there might be no selective survival bias even if the selection probabilities are not all equal. As we know that the cross product of odd ratio of selection probabilities is 1 means there is no relation between exposure and consequence or outcome and there is no bias in odd ratio.

Suppose that you could assess that the direction of possible selective survival bias in your study was towards the null. If your study data yielded a non-statistically significant odds ratio of 1.04, would it be correct to conclude that there was no exposure-disease association in your source population?

It would not be correct to conclude that there was no exposure-disease association in your source population because if the possible selective survival bias in the study was towards the null then this implies that the true odds ratio would be larger than 1.04. and therefore likely to be large and also differ statistically for the null value.

8 0

3 years ago

An analyst has a limit order outstanding on a stock. He argues that the probability that the order will execute before the close

dalvyx [7]

Answer:

b. One in Five

Step-by-step explanation:

To calculate probability, we need to know the formula: $\frac{Number of Expected outcomes}{Total Number of possible outcomes}$

in this case the probability is given in its decimal form, which is = 0.20

∴ to be able to use our formula easily, we will need to convert the probability to its fraction form.

which is 0.20 = $\frac{20}{100}$ (<em> to do this, just simply put a 1 under the decimal point and replace the remaining values of 20 with zeroes)</em>

reducing $\frac{20}{100}$ to its simplest form gives $\frac{1}{5}$ .

Hence, relating it to our formula, we can see that the number of possible out comes is = 1

and the total number of outcomes = 5.

This means that the probability that the order will execute before the same of closing is the same as 1 in 5

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3 years ago