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3 years ago

How does the volume of a cone compare to the volume of a cylinder with the same radius and height?

Mathematics

1 answer:

PilotLPTM [1.2K]3 years ago

6 0

Answer:

<h2>one-third of the volume </h2>

Step-by-step explanation:

$\text{The formula of volumes of:}\\\\a\ cone:\ V_{cone}=\dfrac{1}{3}\pi r_1^2H_1\\\\a\ cylinder:\ V_{cylinder}=\pi r_2^2H_2\\\\\text{If cone and cylinder are with the same radius and height, then:}\\\\r_1=r_2=r\ \text{and}\ H_1=H_2=H\\\\V_{cone}=\dfrac{1}{3}\pi r^2H,\ V_{cylinder}=\pi r^2H\to V_{cone}=\dfrac{1}{3}V_{cylinder}$

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The National Health Interview Survey conducted of 33,326 adults by the U.S. National Center for Health Statistics in 2003 indica

ra1l [238]

Answer:

Step-by-step explanation:

Hello!

You have the data of two The National Health Interview Survey conducted in 1991 and 2003 by the U.S. National Center for Health Statistics.

Let

X₁: The number of adults that were smokers in 1991

n₁= 42000

p'₁= 0.256

X₂: The number of adults that were smokers in 2003

n₂= 33326

p'₂= 0.214

The parameter of interest is the difference between the population proportion of adult smokers in 1991 and the population proportion of adult smokers in 2003, symbolically: "p₁ - p₂"

a) The point estimate of "p₁ - p₂" ios the difference between the sample proportions:

p'₁ - p'₂= 0.256-0.214= 0.042

b) and c)

To estimate the difference of proportions using a CI, you have to apply the central limit theorem and approximate the distribution of the sample proportions to normal. for this approximation to be valid, the sample size for both populations should be high enough (n≥30) and the populations should be at least 20 times bigger than the sample taken. Both samples should be random and independent. Each sample must have at least 10 successes and at least 10 failures. If all conditions are met you can calculate the 99% CI as:

(p'₁-p'₂)± $Z_{1-\alpha /2}$ * $\sqrt{\frac{p'_1(1-p'_1){n_1} +\frac{p'_2(1-p'_2)}{n_2} }$

$Z_{1-\alpha /2}= Z_{0.995}= 2.586$

(0.042) ± 2.586* $\sqrt{\frac{0.256*0.744}{42000} +\frac{0.214*0.786}{33326} }$

[0.034; 0.050]

Using a 99% confidence level you'd expect that the interval [0.034; 0.050] will include the true value of the difference between the proportion of adult smokers in 1991 and the proportion of adult smokers in 2003.

I hope this helps!

7 0

3 years ago

What is the answer to this jajabaited snack

marin [14]

Use a Calculator friend

7 0

3 years ago

What is 160,656 rounded to the nearest ten thousandth?

Deffense [45]

It would be 160,000.

The nearest two ten thousands would be 160,000 and 170,000

160,656 is 656 away from 160,000, and 9,344 away from 170,000.

It is much closer to 160,000 than 170,000.

6 0

3 years ago

Read 2 more answers

Identify the initial amount a and the decay factor b in the exponential function. y equals 5 times 0.5 superscript x

Ber [7]

$\bf \qquad \textit{Amount for Exponential Decay}
\\\\
A=a(b)^x\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
a=\textit{initial amount}\\
b=\textit{decay factor}\\
x=\textit{elapsed time}\\
\end{cases}
\\\\\\
y=\stackrel{a}{5}(\stackrel{b}{0.5})^x$

7 0

3 years ago

I need to Match each equation that represents each situation.

almond37 [142]

Step-by-step explanation:

this is quite easy, when you use just common sense and identify the right numbers and variable names.

they is nothing special needed, you don't even need to create the equations yourself.

$4.99 per pound. buys b pounds and pays $14.95.

14.95 = 4.99 × b

$4.99 per pound. buys b pounds and pays c.

this is exactly the same as before, just that this time the total amount is not given as a constant but as a variable.

c = 4.99 × b

d dollars per pound. buys b pounds and pays t.

the same as the 2 cases before, just now everything is a variable. no more constants, but otherwise the completely same structure and method.

t = d × b

earned $275, which is $45 more than Noah ("n").

$275 = n + $45

earned m dollars, which is $45 more than Noah ("n").

m = n + $45

earned m dollars, which is y dollars more than Noah (we are asked that Noah's earnings are now called "v").

here your teacher made a mistake.

sure, the only remaining answer is

v = m + y

but it is not correct. given the names of the prime and associated variables the correct answer would be

m = v + y or v = m - y

7 0

2 years ago