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anyanavicka [17]
1 year ago
5

Find the smallest evan number that contains every digit once

Mathematics
1 answer:
Fynjy0 [20]1 year ago
6 0

Answer:

  • The smallest even number that contains every digit once is 1023456798.

============================

Conditions we need to meet:

  • Use every digit once,
  • Even number,
  • Smallest possible number.

To get the smallest number we'd use all 10 digits in the ascending order:

  • 0123456789

Here we can't have zero in the beginning as the number becomes 9-digit.

So swapping zero with the closest digit, 1.

Our number should be even, so we should swap 9 with one even digit.

Again it should be the closest one to 9, so it is 8.

We get the following number as a result:

  • 1023456798

<em>To test you may swap digits, any number you get will be greater than this number.</em>

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For the first city, the 95% confidence interval would be:

28,900 +/- 2300 x 3 = 28,900 +/-6900$

For the second city, the 95% confidence interval would be:

30,300 +/- 2100 x 3 = 30,300 +/- 6300$

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Triangles 3 and 4 are identical. They are joined in the poster to form a square. Construct a math argument to show why triangles
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Triangles 3 and 4 are isosceles right angles because they have same length.

<h3>How to explain the triangle?</h3>

It should be noted be noted that the square has all right angles equal. The largest angle of the triangle is the right angle m.

Here, the triangles are isosceles right angles as both the legs and the acute angles are congruent.

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2 years ago
Triangle XYZ is shown, where n ≥ 5. Triangle X Y Z is shown. The length of side X Y is n + 4, the length of side Y Z is 2 n, and
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Answer:

The longest side of the triangle is YZ, the shortest side is ZX, the largest angle is ∠X and the smallest angle is ∠Y.

Step-by-step explanation:

The lengths of the sides of the triangle XYZ are as follows:

XY = n + 4

YZ = 2n

ZX = n - 2

According to the triangle inequality theorem, the sum of two sides of a triangle is always greater than the third side.

Then,

XY < YZ + ZX ⇒ n + 4 < 2n + n - 2 ⇒ n + 4 < 3n - 2 ⇒ 2n > 6 ⇒ n > 3

YZ < XY + ZX ⇒ 2n < n + 4 + n - 2 ⇒ 2n < 2n + 2 ⇒ 0 < 2

ZX < XY + YZ ⇒ n - 2 < n + 4 + 2n ⇒ n - 2 < 3n + 4 ⇒ 2n > -6 ⇒ n > -3

It is provided that <em>n</em> ≥ 5.

Then the sides of the triangle are:

XY = n + 4 ≥ 5 + 4 = 9

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ZX = n - 2 ≥ 5 - 2 = 3

So, the longest side of the triangle is YZ. And the shortest side is ZX.

The largest angle of a triangle is opposite to the longest side.

The angle opposite to YZ would be X. So, the largest angle is ∠X.

The smallest angle of a triangle is opposite to the shortest side.

The angle opposite to ZX would be Y. So, the smallest angle is ∠Y.

Thus, the longest side of the triangle is YZ, the shortest side is ZX, the largest angle is ∠X and the smallest angle is ∠Y.

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The formula is:

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The values of the parameters for this problem are:

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