- 58593750 + 15728640 - 1180980 + 15360 - 6 = \boxed{2941680}
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- $ k = 4 $: $ \binom{6}{4} \cdot 2^{10} = 15 \cdot 1024 = 15360 $
- $ k = 5 $: $ -\binom{6}{5} \cdot 1^{10} = -6 \cdot 1 = -6 $
- $ k = 6 $: $ \binom{6}{6} \cdot 0^{10} = 1 \cdot 0 = 0 $
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In 4 hours, the train will travel \( 80 \text{ km/h} \times 4 \text{ hours} = 320 \text{ km} \).
#### 320
A rectangular garden has a length that is 3 times its width. If the perimeter is 64 meters, what is the area of the garden?
The perimeter is \( 2(x + 3x) = 8x = 64 \).
Solving for \( x \), we get \( x = 8 \).
The width is 8 meters, and the length is \( 3 \times 8 = 24 \) meters.
The area is \( 8 \times 24 = 192 \text{ square meters} \).
The sum of three consecutive even numbers is 54. What is the largest of these numbers?
Let the numbers be \( x, x+2, x+4 \).
Their sum is \( x + (x+2) + (x+4) = 3x + 6 = 54 \).