1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
krok68 [10]
3 years ago
8

Statements that are true for a cylinder with radius r and height h.

Mathematics
1 answer:
vampirchik [111]3 years ago
7 0

Answer:

Only the second and third statements are correct:

Doubling <em>r</em> quadruples the volume.

Doubling <em>h</em> doubles the volume.

Step-by-step explanation:

The volume of a cylinder is given by:

\displaystyle V=\pi r^2h

We can go through each statement and examine its validity.

Statement 1)

If the radius is doubled, our new radius is now 2<em>r</em>. Hence, our volume is:

\displaystyle V=\pi (2r)^2h=4\pi r^2h

So, compared to the old volume, the new volume is quadrupled the original volume.

Statement 1 is not correct.

Statement 2)

Using the previous reasonsing, Statement 2 is correct.

Statement 3)

If the height is doubled, our new height is now 2<em>h</em>. Hence, our volume is:

V=\pi r^2(2h)=2\pi r^2h

So, compared to the old volume, the new volume has been doubled.

Statement 3 is correct.

Statement 4)

Statement 4 is not correct using the previous reasonsing.

Statement 5)

Doubling the radius results in 2<em>r</em> and doubling the height results in 2<em>h</em>. Hence, the new volume is:

V=\pi (2r)^2(2h)=\pi (4r^2)(2h)=8\pi r^2h

So, compared to the old volume, the new volume is increased by eight-fold.

Statement 5 is not correct.

You might be interested in
150% of 22$ Please help
Volgvan
$22* (150/100)= $33.

150% of $22 is $33~
4 0
3 years ago
A geologist has collected 5 specimens of basaltic rock and 7 specimens of granite. The geologist instructs a laboratory assistan
MaRussiya [10]

The rocks are chosen without replacement, which means that the hypergeometric distribution is used to solve this question. First we get the parameters, and then we answer the questions. From this, we get that:

  • E(X) = 5.25, Var(X) = 0.5966
  • P(X < 6) = 0.9545
  • P(all specimens of one of the two types of rock are selected for analysis) = 0.2046.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

The mean and the variance are:

\mu = \frac{nk}{N}

\sigma^2 = \frac{nk(N-k)(N-n)}{N^2(N-1)}

We have that:

5 + 7 = 12 rocks, which means that N = 12

9 are chosen, which means that n = 9

7 are granite, which means that k = 7

Question a:

E(X) = \mu = \frac{9\times7}{12} = 5.25

Var(X) = \sigma^2 = \frac{9\times7(12-7)(12-9)}{12^2(12-1)} = 0.5966

Thus:

E(X) = 5.25, Var(X) = 0.5966

Question b:

Since there are only 5 specimens of basaltic rock, at least 9 - 5 = 4 specimens of granite are needed, which means that:

P(X < 6) = P(X = 4) + P(X = 5) + P(X = 6)

In which

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

P(X = 4) = h(4,12,9,7) = \frac{C_{7,4}*C_{5,5}}{C_{12,9}} = 0.1591

P(X = 5) = h(5,12,9,7) = \frac{C_{7,5}*C_{5,4}}{C_{12,9}} = 0.4773

P(X = 6) = h(6,12,9,7) = \frac{C_{7,6}*C_{5,3}}{C_{12,9}} = 0.3181

Thus

P(X < 6) = P(X = 4) + P(X = 5) + P(X = 6) = 0.1591 + 0.4773 + 0.3181 = 0.9545

So P(X < 6) = 0.9545.

Question c:

5 of basaltic and 4 of granite: 0.1591 probability.

7 of granite is P(X = 7), in which

P(X = 7) = h(7,12,9,7) = \frac{C_{7,7}*C_{5,2}}{C_{12,9}} = 0.0455

0.1591 + 0.0455 = 0.2046, thus:

P(all specimens of one of the two types of rock are selected for analysis) = 0.2046.

A similar question is found at brainly.com/question/24008577

5 0
3 years ago
Todos los numeros negativos son enteros verdadero o falsom.​
Romashka-Z-Leto [24]

Answer:

False

Step-by-step explanation:

numbers are integers, the integers are negative, zero and positive, 

while natural numbers are only positive, 

therefore the statement is false

 . False. Integers comprise negative and positive numbers (...- 3, -2, -1, 0, 1, 2, 3 ...) and natural numbers only comprise positive integers (0, 1, 2, 3 ...)  

5 0
3 years ago
Ten women sit in 10 seats in a line. All of the 10 get up and then reseat themselves using all 10 seats, each sitting in the sea
Alik [6]

Women can be seated in 89 ways.

Let Sn be the number of possible seating arrangements with n women. Consider n≥3 and focus on the rightmost woman. If she goes back to her seat, then there are Sn−1 ways to seat the remaining n−1 women. If he is sitting in the penultimate seat, then the woman who was sitting there before must now sit in the rightmost seat.

This gives us Sn−2 ways to seat another n−2 woman, so we get the recursion Sn=Sn−1+Sn−2. Starting with S1=1 and S2=2 we can calculate S10=89.

For more information about permutation, visit brainly.com/question/11732255

#SPJ4

5 0
1 year ago
What is the easiest way to find the answer?
amid [387]

multiply the number of ounces by the price per ounce

Blue jelly beans cost 0.28 per ounce and there are 4 ounces

 4 * 0.28 = 1.12

red jelly beans cost 0.55 per ounce and there is 3 ounces

3 *0.55 = 1.65

now add the totals: 1.12 +1.65 = 2.77

 this is more than the total they want of 2.20

 so it is not reasonable.

3 0
3 years ago
Other questions:
  • What is the surface area of the box if it is scaled up by a factor of 10? The surface area is: 736 cm. Lenght: 12 cm. Width: 4 c
    10·1 answer
  • The price s of pair of shoes plus 2% sales tax . the algebraic expression is ?
    9·1 answer
  • How do I solve for -31 -8r = -3(5r -6)
    11·1 answer
  • Write the equation that is the translation of y= |x| right 7 units and down 9 units.
    15·2 answers
  • Cathy volunteered to collect cans for a school project. cathy collected 125 cans in 5 days. there were 6 volunteers including ca
    6·2 answers
  • What is 408 divided 11.35?​
    13·2 answers
  • A farm had 480 acres more wheat than corn. After the farmers collected 80% of the wheat and 25% of the corn, the area of the whe
    15·2 answers
  • Fill in the blanks 3/4 (12x-16) = 1/3 (?x-?)
    6·1 answer
  • Can somebody help me please
    9·2 answers
  • Countries that do not have enough resources to meet the needs of their population are said to be suffering from what?
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!