Answer: 13 whole pieces of wire can be cut from that spool and 
of wire is left over.
Step-by-step explanation:
Convert from mixed number to improper fraction. To do it you must multiply the whole numbe part by the denominator of the fraction and then add the product to the numerator. The denominator does not change. Then:
Since the spool contains 100 inches of wire, you must divide this lenght by 
:
Convert from improper fraction to mixed number:
- When you divide the numerator 800 by the denominator 59, the quotient is 13 (this is the whole number part)
- The remainder is 33 (This is the numerator of the fraction).
- The denominator does not change.
Then:
Therefore 13 whole pieces can be cut from that spool.
The amount of wire left over is:
Answer:
.0039
Step-by-step explanation:
Answer:
A 404 mi
Step-by-step explanation:
If we designate the points of the triangle A, B, and C for the locations of the western station, eastern station, and balloon, respectively, we have the following:
∠CAB = 90° - 41° = 49°
∠CBA = 90° + 21° = 111°
∠ACB = 41° -21° = 20°
side "c" (opposite ∠ACB) is 148 miles
The distance we're asked to find is AC = b, the longest side of the triangle. The law of sines tells us ...
b/sin(B) = c/sin(C)
b = c·sin(B)/sin(C) = (148 mi)·sin(111°)/sin(20°) ≈ 403.98 mi ≈ 404 mi
Answer: False, there are actually 900 different three-digit numbers
========================================================
Explanation:
The three digit numbers span from 100 to 999, including both endpoints.
This means we have 999-100+1 = 900 different three-digit numbers.
You subtract the endpoints (large-small) and add 1 to include the lower endpoint.
Here's a smaller example of why this works: say you had the set {1,2,3,4} and we wanted to count the number of items in this set. Clearly there are 4 items. Note how subtracting the endpoints 4-1 gets us 3 instead, so we add on 1 to include that left endpoint.
