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3 years ago

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the ages of three men are in the ratio 3:4:5.if the difference between the age of the oldest and the youngest is 18years, fine d

the sum of the age of the three men

1 answer:

hram777 [196]3 years ago

3 0

Answer:

108

Step-by-step explanation:

Givens

let the oldest one = 5x
Let the youngest one = 3x
Let the middle one = 4x

Equation

3x + 18 = 5x

Solution

3x + 18 = 5x Subtract 3x from both sides
3x - 3x + 18 = 5x - 3x Combine
18 = 2x Divide by 2
18/2 = 2x/2 Divide
x = 9

Answer

3x = 3*9 = 27
5x = 5*9 = 45
4x = 4*9 = 36
The sum is 108

Comment

This is a very tricky problem. It is not the usual way that 3 part ratios are handled. Thanks for posting.

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A metal cylinder can with an open top and closed bottom is to have volume 4 cubic feet. Approximate the dimensions that require

Aleksandr-060686 [28]

Answer:

$r\approx 1.084\ feet$

$h\approx 1.084\ feet$

$\displaystyle A=11.07\ ft^2$

Step-by-step explanation:

<u>Optimizing With Derivatives </u>

The procedure to optimize a function (find its maximum or minimum) consists in :

Produce a function which depends on only one variable
Compute the first derivative and set it equal to 0
Find the values for the variable, called critical points
Compute the second derivative
Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum

We know a cylinder has a volume of 4 $ft^3$ . The volume of a cylinder is given by

$\displaystyle V=\pi r^2h$

Equating it to 4

$\displaystyle \pi r^2h=4$

Let's solve for h

$\displaystyle h=\frac{4}{\pi r^2}$

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

$\displaystyle A=\pi r^2+2\pi rh$

Replacing the formula of h

$\displaystyle A=\pi r^2+2\pi r \left (\frac{4}{\pi r^2}\right )$

Simplifying

$\displaystyle A=\pi r^2+\frac{8}{r}$

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

$\displaystyle A'=2\pi r-\frac{8}{r^2}=0$

Rearranging

$\displaystyle 2\pi r=\frac{8}{r^2}$

Solving for r

$\displaystyle r^3=\frac{4}{\pi }$

$\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet$

Computing h

$\displaystyle h=\frac{4}{\pi \ r^2}\approx 1.084\ feet$

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

$\displaystyle A''=2\pi+\frac{16}{r^3}$

We can see it will be always positive regardless of the value of r (assumed positive too), so the critical point is a minimum.

The minimum area is

$\displaystyle A=\pi(1.084)^2+\frac{8}{1.084}$

$\boxed{ A=11.07\ ft^2}$

8 0

3 years ago

Suppose that you are conducting a survey on how many students have blue eyes in each first period classroom at Garfield Middle s

rusak2 [61]

Answer:

<u>The correct statement is the first one: </u><u><em>The number of blue-eyed students in Mr. Garcia's class is 2 standard deviations to the right of the mean</em></u><em> </em>

<em />

Explanation:

To calculate how many<em> standard deviations</em> a particular value in a group is from the mean, you can use the z-score:

$z-score=(x-\mu )/\sigma$

Where:

$z-score$ is the number of standard deviations the value of x is from the mean

$\mu$ is the mean

$\sigma$ is the standard deviation

Substitute in the formula:

$z-score=(10-6)/2=4/2=2$

Which means that <em>the number of blue-eyed students in Mr. Garcia's class is 2 standard deviations</em> above the mean.

Above the mean is the same that to the right of the mean, because the in the normal standard probability graph the central value is Z = 0 (the z-score of the mean value is 0), the positive values are to the right of the central value, and the negative values are to the left of the central value.

Therefore, the correct statement is the first one: <em>The number of blue-eyed students in Mr. Garcia's class is 2 standard deviations to the right of the mean, </em>

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I NEED HELP ASAP!!!!!!!!

exis [7]

Answer:

Bruh what is this

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Answer:

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Intelligent Muslim,

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Answer:i

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