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3 years ago

If x and y are positive integers and x+y+xy=54, then x+y equals what

Mathematics

1 answer:

OLga [1]3 years ago

6 0

Answer:

x+y = 14

Step-by-step explanation:

x+y+xy = 54

1+x+y+xy = 55

(1+x)(1+y) = 55

(1+x)(1+y) = 5*11

If x and y are integers,

1+x = 5 => x = 4

1+y = 11 => y = 10

1+x = 11 => x = 10

1+y = 5 => y = 4

In either case, x+y = 14

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A sphere and a cylinder have the same radius and height. The volume of the cylinder is 27 pi feet cubed.

LenaWriter [7]

Answer:

C. V = two-thirds (27)

Step-by-step explanation:

Given

Solid Shapes: Cylinder and Sphere

Volume of Cylinder = 27π ft³

Required

Volume of the sphere.

From the question,

1. The volume of the sphere is the same as the volume of the cylinder

2. The height of the sphere is the same as the height of the cylinder.

From (2) above;

This means that the height of the cylinder equals the diameter of the sphere.

Let h represent the height of the sphere and d represent the diameter of sphere.

Mathematical, d = h

Recall that radius, r = $r = \frac{d}{2}$

Substitute h for d in the above expression

$r = \frac{h}{2}$ . ----- (take note of this)

Calculating the volume of a cylinder.

V = πr²h

Recall that V = 27; This gives us

27 = πr²h

Divide both sides by h

$\pi r^2 = \frac{27}{h}$

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

Calculating the volume of a sphere

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

Expand the above expression

$V = \frac{4}{3}\pi r^2 * r$

Substitute $\pi r^2 = \frac{27}{h}$

$V = \frac{4}{3} * \frac{27}{h} * r$

Recall that $r = \frac{h}{2}$

So,

$V = \frac{4}{3} * \frac{27}{h} * \frac{h}{2}$

$V = \frac{4}{3} * \frac{27}{2}$

$V = \frac{2}{3} * 27$

$V = \frac{2}{3} (27)$

V = two-third (27)

4 0

3 years ago

Which of the following is a way in which statistics are made to be misleading?

hodyreva [135]

The statistics are made to be misleading in such a way that the scale is altered on the graph. So, option C is correct.

<h3>What are statistics?</h3>

Statistics is the study of the discipline that concerns the organization, collection, analysis, and presentation of data.

A hasty generalization is fallacy in which a conclusion is reached before sufficient or unbiased evidence is gathered.

The statistics are made to be misleading in such a way that the scale is altered on the graph. So, option C is correct.

Learn more about statistics ;

brainly.com/question/4352866

#SPJ1

6 0

1 year ago

The scheduled arrival time for a daily flight from Boston to New York is 9:35 am. Historical data show that the arrival time fol

Lady_Fox [76]

Answer:

The mean is 11.5 minutes and the standard deviation is of 6.64 minutes

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The mean is:

$M = \frac{a+b}{2}$

The standard deviation is:

$S = \sqrt{\frac{(b-a)^{2}}{12}}$

Arrival time of 9:18 am and a late arrival time of 9:41 am.

9:41 is 23 minutes from 9:18. So the time is uniformily distributed between 0 and 23 minutes, so a = 0, b = 23.

Mean:

$M = \frac{a+b}{2} = \frac{0+23}{2} = 11.5$

Standard deviation:

$S = \sqrt{\frac{(b-a)^{2}}{12}} = \sqrt{\frac{(23 - 0)^{2}}{12}} = 6.64$

The mean is 11.5 minutes and the standard deviation is of 6.64 minutes

8 0

2 years ago

A man is 32 years older than his son. Ten years ago he was three times as old as his son. find the present age of each?

nekit [7.7K]

The answer to this equation is 17

7 0

3 years ago

Simplify 4x^2 / 3 X 6/ 8x

Leokris [45]

Answer:

Step-by-step explanation:

The answer to

$\frac{4 {x}^{2} }{3} \times \frac{6}{8x}$

= x

3 0

2 years ago

Read 2 more answers