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maxonik [38]
2 years ago
10

How many 4-digit odd numbers can you make using the digits 1 to 7 if the numbers must be less than 6000? No digits are repeated.

Mathematics
1 answer:
bixtya [17]2 years ago
6 0

Answer:

Step-by-step explanation:he first digit must be a 6, 7, or 8, because the number has to be bigger than 6,000.

The last digit must be a 1, 3, 5, or 7, because the number has to be odd.

So if the first digit is 6 or 8, there are 4 odd-number options for the last digit. If the first digit is a 7, then there are only 3 options for the last digit, as 7 can’t be used twice.

The other two digits can be anything that’s not already used. So for each first-and-last combination of digits mentioned above, there will be six options available for one of the middle digits, and then for each of those 3-digit combinations, five options will be available for the final remaining digit.

At this point, we have everything we need to express this as an equation:

x = (2 x 4 + 1 x 3) x 6 x 5

And then we can simplify and solve:

x = (8 + 3) x 30

x = 11 x 30

x = 330

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In this question we should fill the blanks based all information related to Euclidean geometry, especially concepts related to angles, triangles, parallelism and quadrilaterals.

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<em>Since </em><u><em>AD</em></u><em> is parallel to </em><u><em>BC</em></u><em>, alternate interior angles. </em>

<u><em>AD</em></u><em> and </em><u><em>BC</em></u><em> are congruent. </em>

<em>AC is congruent to </em><u><em>AC</em></u><em> since segments are congruent to themselves.</em>

<em>Along with the given information that AD is congruent to BC, triangle ADC is congruent to triangle </em><u><em>CBA</em></u><em> by the Side-Angle-Side Triangle Congruence. </em>

<em>Since the triangles are congruent, all pairs of corresponding angles are congruent, so angle DCA is congruent to </em><u><em>angle BAC</em></u><em>.</em>

<em>Since those alternate interior angles are congruent. AB must be parallel to </em><u><em>CD</em></u><em>. </em>

<em>Since we define a parallelogram as a quadrilateral with both pairs of opposite sides parallel, ABCD is a parallelogram.</em>

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