Please help! thanks!

The volumes of two cylindrical cans of the same shape vary directly as the cubes of their radii. If a can with a six-inch radius

Cerrena [4.2K]

Answer:

The second similar can with a radius of 24-inch radius will hold 12 gallons

Step-by-step explanation:

The given parameters are;

The volumes of the cylindrical can ∝ (The radius of the cans)³

The volume of first can, V₁ = 1¹/₂ pints

The radius of the first can, r₁ = 6-inch

The radius of the second can, r₂ = 24-inch

Therefore, we have;

V ∝ r³

V = k × r³

∴ 1¹/₂ pints ∝ (6 in.)³

1¹/₂ pints = 43.3125 in³

∴ 43.3125 in³ = k × 216 in.³

The constant of proportionality, k = 43.3125/216 = 0.2005208333

Therefore, we have for the second can, we have;

V₂ = k × r₂³ = 43.3125/216 × (24 in.)³ = 2772 in.³

The volume of the second can = 2772 in.³

1 in.³ = 0.004329 gallons

∴ 2772 in.³ = 2772 × 0.004329 gallons = 12 gallons

Therefore, the volume the second similar can with a 24-inch radius will hold = 12 gallons.

8 0

3 years ago

What is 65.079 rounded to the nearest tenth?

Mariana [72]

65.000

Hope I helped:P

6 0

3 years ago

Suppose 10000 people are given a medical test for a disease. About1% of all people have this condition. The test results have a

Alina [70]

Answer:

The percent of the people who tested positive actually have the disease is 38.64%.

Step-by-step explanation:

Denote the events as follows:

X = a person has the disease

P = the test result is positive

N = the test result is negative

Given:

$P(X)=0.01\\P(P|X^{c})=0.15\\P(N|X)=0.10$

Compute the value of P (P|X) as follows:

$P(P|X)=1-P(P|X^{c})=1-0.15=0.85$

Compute the probability of a positive test result as follows:

$P(P)=P(P|X)P(X)+P(P|X^{c})P(X^{c})\\=(0.85\times0.10)+(0.15\times0.90)\\=0.22$

Compute the probability of a person having the disease given that he/she was tested positive as follows:

$P(X|P)=\frac{P(P|X)P(X)}{P(P)}=\frac{0.85\times0.10}{0.22} =0.3864$

The percentage of people having the disease given that he/she was tested positive is, 0.3864 × 100 = 38.64%.

3 0

3 years ago

The sales of a certain product after an initial release can be found by the equation s=10√5t+15 where s represents the total sal

pogonyaev

No it’s not because maybe there’s not good

5 0

3 years ago

A chemical company makes two brands of antifreeze. The first brand is 20% pure antifreeze, and the second brand is 70% pure anti

andre [41]

Answer:

First brand of antifreeze: 21 gallons

Second brand of antifreeze: 9 gallons

Step-by-step explanation:

Let's call A the amount of first brand of antifreeze. 20% pure antifreeze

Let's call B the amount of second brand of antifreeze. 70% pure antifreeze

The resulting mixture should have 35% pure antifreeze, and 30 gallons.

Then we know that the total amount of mixture will be:

$A + B = 30$

Then the total amount of pure antifreeze in the mixture will be:

$0.2A + 0.7B = 0.35 * 30$

$0.2A + 0.7B = 10.5$

Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -0.7 and add it to the second equation:

$-0.7A -0.7B = -0.7*30$

$-0.7A -0.7B = -21$

+

$0.2A + 0.7B = 10.5$

--------------------------------------

$-0.5A = -10.5$

$A = \frac{-10.5}{-0.5}$

$A = 21\ gallons$

We substitute the value of A into one of the two equations and solve for B.

$21 + B = 30$

$B = 9\ gallons$

3 0

3 years ago