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3 years ago

Prove that given any 17 integers, there exist nine of them whose sum is divisible by 9.

Mathematics

2 answers:

vaieri [72.5K]3 years ago

7 0

This is a simple consequence of the Zero-sum problem: https://en.wikipedia.org/wiki/Zero-sum_problem

yaroslaw [1]3 years ago

7 0

Answer:

Step-by-step explanation:

let x,x+1,x+2,x+3,x+4,x+5,x+6,x+7,x+8

be 9 integers

x+x+1+x+2+x+3+x+4+x+5+x+6+x+7+x+8=9x+36=9(x+4)

which is divisible by 9

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Oliga [24]

Answer:

The rate of return is 14%

Step-by-step explanation:

The rate of return can be determined by,

RR = $\frac{A_{f} - A_{i} }{A_{i} }$ x 100%

where:

RR is the rate of return

$A_f}$ is the final amount = $690 - $6 = $684

$A_{i}$ is the initial amount = $15 x 40 = $ 600

So that,

RR = $\frac{684 - 600}{600}$ x 100%

= 0.14 x 100%

= 14%

Therefore, the rate of return is 14%.

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3 years ago

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Gelneren [198K]

Step-by-step explanation:

This isn't. a true identity.

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2 years ago

Determine the relationship between the two triangles and whether or not they

Ira Lisetskai [31]

Answer: These ARE congruent to each other.

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2 years ago

Which statement below compares the decimals correctly?

nata0808 [166]

A. 0.65 < 0.77 0.77 is greater than 0.65

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3 years ago

Read 2 more answers

Cylinders A and B are similar solids. The base of cylinder A has a circumference of 47 units. The base of cylinder B has an

fiasKO [112]

<h3><u>Question:</u></h3>

Cylinders A and B are similar solids. The base of cylinder A has a circumference of 4π units. The base of cylinder B has an area of 9π units.

The dimensions of cylinder A are multiplied by what factor to produce the corresponding dimensions of cylinder B?

<h3><u>Answer:</u></h3>

Dimensions of cylinder A are multiplied by $\frac{3}{2}$ to produce the corresponding dimensions of cylinder B

<h3><u>Solution:</u></h3>

Cylinders A and B are similar solids.

The base of cylinder A has a circumference of $4 \pi$ units

The base of cylinder B has an area of $9 \pi$ units

Let "x" be the required factor

From given question,

Dimensions of cylinder A are multiplied by what factor to produce the corresponding dimensions of cylinder B

Therefore, we can say,

$\text{Dimensions of cylinder A} \times x = \text{Dimensions of cylinder B }$

<h3><u>Cylinder A:</u></h3>

The circumference of base of cylinder (circle ) is given as:

$C = 2 \pi r$

Where "r" is the radius of circle

Given that base of cylinder A has a circumference of $4 \pi$ units

Therefore,

$4 \pi = 2 \pi r\\\\r = 2$

Thus the dimension of cylinder A is radius = 2 units

<h3><u>Cylinder B:</u></h3>

The area of base of cylinder (circle) is given as:

$A = \pi r^2$

Given that, the base of cylinder B has an area of $9 \pi$ units

Therefore,

$\pi r^2 = 9 \pi\\\\r^2 = 9\\\\r = 3$

Thus the dimension of cylinder B is radius = 3 units

$\text{Dimensions of cylinder A} \times x = \text{Dimensions of cylinder B }\\\\2 \times x = 3\\\\x = \frac{3}{2}$

Thus dimensions of cylinder A are multiplied by $\frac{3}{2}$ to produce the corresponding dimensions of cylinder B

5 0

3 years ago