Answer:
12 minutes
Step-by-step explanation:
Candles can be manually packed at the rate of ...
... (400 candles)/(36 minutes) = 11 1/9 candles/minute
The two systems together pack candles at the rate of ...
... (400 candles)/(9 minutes) = 44 4/9 candles/minute
Then the machine's packing rate is the difference between the total and the manual rates:
... machine rate = (44 4/9 candles/minute) - (11 1/9 candles/minute)
... = 33 1/3 candles/minute.
At this rate, the machine working alone can pack 400 candles in ...
... (400 candles)/(33 1/3 candles/minute) = (400/(100/3)) minutes
... = 400 × 3/100 minutes = 12 minutes
Answer:
Cabin is 567 yards away...
Step-by-step explanation:
The angle 21.2° is also the angle of the upper interior angle of the triangle (near the cabin)
Use the tan function:
opposite = 220 yards
adjacent = x
tan(21.2°) = (opposite / adjacent)
tan(21.2°) = 220 yards/x
x * tan(21.2°) = 220 yards
x = 220 yards/ tan(21.2°)
x= 220/ 0.388
x = 567 yards.
Cabin is 567 yards away...
Answer:
If a box is supposed to contain 18 ounces, and the acceptable error is 1 ounce, then the acceptable range is:
18 oz - 1oz = 17oz to 18oz + 1oz = 19oz
Then the acceptable range is (17oz, 19oz)
if the weight is smaller than 17 oz, the box is not acceptable.
If the weight is bigger than 19 oz, the box is not acceptable.
Then the graph of the boxes that can not be sold as full boxes is:
<---16---------17-------18--------19-------20----------->
where 17oz and 19oz are not included, because are acceptable weigths.
<span>1. The two boats picked for the trip are the steamboat and the tall ship. Let us assume that we will take the steamboat going to the island, and then we will take the tall ship for the return trip. We will then relate the distances travelled by both ships to each other.
2. We know that the steamboat takes five hours to complete the trip. The tall ship takes more time, at ten hours to complete the trip. We do not have the exact speeds of the steamboat or of the tall ship, but we do know that the tall ship is 10 knots slower than the steamboat. We likewise do not know the exact distance travelled by either ship, but we do know that both travel the same distance. We want to find out how fast each boat travels. We expect the answers to be in knots, with a difference of 10.
3. We know that distance is equivalent to the product of speed of a boat multiplied by the time of travel. For the trip going to the island, we will use the steamboat. Let its speed be x knots (equivalent to x nautical miles per hour), and let the distance going to the island be d nautical miles. Given that the time takes is 5 hours, this means that d = 5x.
4. If we let x be the speed of the
boat you are taking to the island (the steamboat), then we know that the speed of the other boat (the tall ship) is 10 knots less than the steamboat's. So the speed of the tall ship (for the return trip) is (x - 10) knots.
5. Similar to part 3: we will multiply speed by time to determine the distance from the island. From part 4, we have determined that the speed of the tall ship to be used in returning is (x - 10) knots. Meanwhile, the given in the problem says that the tall ship will take 10 hours to make the trip. Therefore the distance will be equal to d = 10(x - 10) = 10x - 100 nautical miles.
6. We can assume that the distance travelled going to the island is the same distance travelled coming back. Therefore, we can equate the formula for distance from part 3 for the steamboat, to the distance from part 5 for the tall ship.
5x = 10x - 100
7. Solving for x: 5x = 10x - 100
-5x = -100
x = 20
Since x is the speed of the steamboat, x = 20 means that the steamboat's speed is 20 knots.
8. We determined in part 4 that the speed of the second boat (in our case, the tall ship) is (x - 10) knots. Since we have calculated in part 7 that the steamboat travels at x = 20 knots, then the speed of the tall ship is (x - 10) = 20 - 10 = 10 knots.</span>
X/21 = y/33
xy = 21·33 = 693
The factors of 693 are 1,3,7,9,11,21,33,63,77,99,231,693.
(x,y) = (1,693), (693,1), (3,231), (231,3), (7,99), (99,7), (9,77), (77,9), (11,63), (63,11), (21,33), (33,21)
