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2 years ago

Find the volume of this cylinder.

Mathematics

1 answer:

const2013 [10]2 years ago

5 0

Volume of a Right circular cylinder=πr²h

Using "Cavaliers principle" or Just pire logic... it can be understood that...

if we were to cut of the base and top of the cylinder such that it will make up to be a right circular cylinder and join the other two pieces on top; We would obtain a Right circular cylinder With The same radius and height as the Given cylinder.

So;

Given. Base area B=81πcm²

also Base area =πr²

=>πr²=81π cm²

=>r=√81=9cm

Also Given;

Height h=3r

=>Height,h=3×9=27cm

So;Volume of cylinder V=πr²h ;(r²=81,h=27)

=>V=(81×27×22)/7

=>V=6867.18cm³ (approx.)

So,Required Volume =6867.18cm³(approx.)

Hope it helps...

Regards,

Leukonov/Olegion.

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"A consultant compiled the following data set that shows" the number of visits made to the National Museum of American History f

aalyn [17]

Answer:

Step-by-step explanation:

The best option is for the consultant to remove these data points because they are outliers. Unusual data points which are located far from rest of the data points are known as outliers.

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2 years ago

Find the surface area of the regular pyramid shown in the accompanying diagram. If necessary, express your answer in simplest ra

Oksana_A [137]

Answer:

The area of the pyramid is 360 unit²

Step-by-step explanation:

Given

Base Edge, a = 10

Height, h = 12

Required

Determine the surface area

The surface area of a regular pyramid is calculated as thus;

$A = a^2 + 2a\sqrt{\frac{a^2}{4} + h^2}$

Substitute values for a and h

$A = 10^2 + 2 * 10 * \sqrt{\frac{10^2}{4} + 12^2}$

Evaluate all squares

$A = 100 + 2 * 10 * \sqrt{\frac{100}{4} + 144}$

$A = 100 + 2 * 10 * \sqrt{25 + 144}$

$A = 100 + 2 * 10 * \sqrt{169}$

Take positive square root of 169

$A = 100 + 2 * 10 * 13$

$A = 100 + 260$

$A = 360$

<em>Hence, the area of the pyramid is 360 unit²</em>

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1 year ago

Use the geometric probability distribution to solve the following problem. On the leeward side of the island of Oahu, in a small

Greeley [361]

Answer:

(a) $\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1} ; \text{ n} = 1, 2, 3,....$

(b) P(1) = 0.740, P(2) = 0.192, and P(3) = 0.050.

(c) The probability that n ≥ 4 is 0.018.

(d) The expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry is 3.

Step-by-step explanation:

We are given that on the leeward side of the island of Oahu, in a small village, about 74% of the residents are of Hawaiian ancestry.

Let n = 1, 2, 3, … represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village.

(a) We can observe that the above situation can be represented through the geometric distribution because the geometric distribution states that we will keep on going with the trials until we achieve our first success,

Here also, n represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village.

So, the probability distribution of the geometric distribution is given by;

$\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1} ; \text{ n} = 1, 2, 3,....$

where, p = probability that the residents are of Hawaiian ancestry = 74%

(b) The probabilities that n = 1, n = 2, and n = 3 is given by;

$\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1}$

P(1) = $\text{0.74} \times \text{(1 - 0.74)}^{1-1}$ = 0.74

P(2) = $\text{0.74} \times \text{(1 - 0.74)}^{2-1}$ = 0.192

P(3) = $\text{0.74} \times \text{(1 - 0.74)}^{3-1}$ = 0.050

(c) The probability that n ≥ 4 is given by = P(n ≥ 4)

P(n ≥ 4) = 1 - P(n = 1) - P(n = 2) - P(n = 3)

= 1 - 0.74 - 0.192 - 0.050

= 0.018

(d) The expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry is given by = E(n)

We know that the mean of the geometric distribution is given by;

Mean = $\dfrac{p}{1-p}$ = $\dfrac{0.74}{1-0.74}$

= $\dfrac{0.74}{0.26}$ = 2.85 or 3 (approx).

4 0

2 years ago

Paco's cell phone carrier charges him $0.20 for each text message he sends or receives, $0.15 per minute for calls, and a $15 mo

Katarina [22]

Given:

Paco's cell phone carrier charges him $0.20 for each text message he sends or receives, $0.15 per minute for calls, and a $15 monthly service fee. Paco is trying to keep his bill for the month below $30.

To Find:

The number of texts 't' Paco can send/receive in a month.

Answer:

$0\leq t$

best describes the number of texts he can send or receive to keep his bill less than $30 in a month.

Step-by-step explanation:

Paco wants to keep is monthly bill below $30.

We see that he has to pay a foxed monthly service fee of $15. This means he is only left with a limit of $30 - $15 = $15 for his monthly calls and texts.

That is, the amount he has to pay for texting and calling has to be less than $15.

For texts, the cell phone carrier charges $0.20 for sending/receiving texts.

For calls, he is charged $0.15 per minute.

Let the number of text messages Paco can send or receive in a month be denoted by 't'.

Let the number of minutes Paco can call in a month be denoted by 'c'.

Then, the total cost of text messages he can send or receive per month would be 0.20t and the total cost of the minutes he spends on calls would be 0.15c. Together, the sum of these has to be less than $15 if his monthly bill has to be kept less than $30 (accounting for the monthly service fee).

So,

$0.20t+0.15c$

The number of texts he can send will dpend on the number of minutes he spends on his calls. For Paco to spend maximum number of texts, he has to spend 0 minutes on calls.

So, putting c = 0, the aboce equation can be written as

$0.20t+0$

That is, Paco has to send and receive less than 75 texts.

So,

$0\leq t$

best describes the number of texts he can send or receive to keep his bill less than $30 in a month.

3 0

2 years ago

Read 2 more answers

Moises is determining the solution to the system of equations that is show below. Equation representing line A: mc018-1.jpg Poin

dimulka [17.4K]

Answer:
equation of line is:
y = -2x - 6

Explanation:
The general form of the line is:
y = mx + c
where:
m is the slope of the line
c is the y-intercept

(a) getting the slope of the line:
slope of the line is calculated using the following rule:
slope of line (m) = (y2-y1) / (x2-x1) = (-24--12) / (9-3) = -2
The equation now becomes:
y = -2x + c

(b) getting the y-intercept:
The two given points belong to the line. Therefore, to get the y-intercept, we will use one of the points and substitute in the equation and solve for c.
I will use the point (3,-12)
y = mx + c
-12 = -2(3) + c
-12 = -6 + c
c = -12 + 6
c = -6

Based on the above, the equation of the line is:
y = -2x - 6

Hope this helps :)

6 0

2 years ago