When rolling two standard six-sided number cubes, each cube has 6 faces, resulting in a total of 6 × 6 = 36 different possible number pairs. Each pair consists of one number from the first cube and one from the second cube. Therefore, the total combinations range from (1,1) to (6,6).
A number that cannot be expressed as the sum of two cubes is 4. This is because when you analyze all possible pairs of cubes (such as (0^3, 1^3, 2^3, -1^3, -2^3), etc.), you find that no combination of these cubes will yield a total of 4. Other numbers, like 1, 2, and 3, can also be shown not to be expressible as sums of two cubes.
2268 possibl3
First player can be any one of 6. For each of them . . .Second player can be any one of 9.Total number of possible different pairs = 6 x 9 = 54 pairs.
To determine how many rectangles can be made with 24 cubes, we first need to consider how the cubes can be arranged. A rectangle can be formed by choosing two distinct dimensions, which can be represented as factors of the total number of cubes. The pairs of factors of 24 are (1, 24), (2, 12), (3, 8), (4, 6), and their reverses. Therefore, there are a total of 10 unique rectangles that can be formed using 24 cubes.
To calculate the total number of different outfits Don can wear, multiply the number of shoes, pants, and shirts. He has 4 pairs of shoes, 7 pairs of pants, and 7 shirts. Therefore, the total number of outfits is 4 x 7 x 7 = 196 different outfits.
A number that cannot be expressed as the sum of two cubes is 4. This is because when you analyze all possible pairs of cubes (such as (0^3, 1^3, 2^3, -1^3, -2^3), etc.), you find that no combination of these cubes will yield a total of 4. Other numbers, like 1, 2, and 3, can also be shown not to be expressible as sums of two cubes.
32
16 (apex)
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An organism with six pairs of chromosomes (12 total) will produce 2^12 (4096) different genetically unique gametes.
How many different outfits are possible from six shirts, four pairs of pants, and five pairs of socks?
An organism with 6 pairs of chromosomes can produce a variety of gametes through independent assortment during meiosis. The number of different gametes can be calculated using the formula (2^n), where (n) is the number of chromosome pairs. For 6 pairs, this results in (2^6 = 64) different possible gametes. Thus, the organism can produce 64 distinct gametes.
There are (10 x 9)/2 = 45 different possible pairs of 2 teachers. For each of these . . .There are (30 x 29)/2 = 435 different possible pairs of students.The total number of different committees that can be formed is (45 x 435) = 19,575 .
Four: two pairs.
2268 possibl3
10 and 9, 12 and 1
First player can be any one of 6. For each of them . . .Second player can be any one of 9.Total number of possible different pairs = 6 x 9 = 54 pairs.