Answer:
1, 2, 3, 4, 6, 8, 9, 11, 13, 16, 18 and 23 cents cant be made with 5-cents and 7-cent postage.
Step-by-step explanation:
You can make any multiple of 5 with those stamps. Also, you can make any number x with stamps proven that that number is big enough. If you start with a number that is a multiple of 5, then you can increase that number by 2 each time you replace a 5 with a 7 (in each example, we are starting in a postage of value 5j made by 5-cent stamps):
- If x = 5j + 1, for an integer j, (j ≥ 4), then you can replace 4 five cent stamps with 3 7 cent stamps, to obtain x.
- If x = 5j + 2, you can replace 1 five cent stamp with one seven cent stamp to obtain x (j≥1)
- If x = 5j+3, you can replace 5 five cent stamps with 4 seven cent stamps to obtain x (j ≥5).
- If z = 5j+4, you can replace 2 five-cent stamps with 2 seven-cent stamos to obtain x (j≥2)
Note therefore, that if j is at least 5, then we can obtain a postage with value x. This means that any postage of value at least 25 can be made witg five-cent of seven-cent stamps. Lets see for smaller values
- 1, 2, 3 and 4 cent postage are impossible to make
- 5 cent package is possible, so is 7
- 6,7, 8 and 9 are impossible to make (any package with at least 2 stamp has a value at least 10)
- 10 is possible (5+5)
- 11 is not possible (5+5 = 10, 5+7 = 12)
- 12 is possible (5+7)
- 13 is impossible (5+7 = 12, but 7+7 = 14. Also any combination of 3 stamps has a value at least 15)
- 14 is possible (7+7)
- 15 is possible (5+5+5)
- 16 is not possible (5+5+5 = 15, 5+5+7 = 17)
- 17 = 5+5+7 is possible
- 18 is not possible (5+7+7 = 19, and any postage with 4 stamps has a value of 20 or higher)
- 19 = 5+7+7 is possible
- 20 = 5+5+5+5 is possible
- 21 = 7+7+7 is possible
- 22 = 5+5+5+7 is possible
- 23 is not possible (you cant reach 23 with 3 stamps, and you will get a value at least 25 with 5. If you use 4 stamps, you can obtain only even values)
- 24 = 5+5+7+7 is possible
So we conclude that the amounts of postage that are impossible to make are: 1, 2, 3, 4, 6, 8, 9, 11, 13, 16, 18 and 23 cents.
Answer:
-0.135= -27/200 and -4.06= - 4 3/50
Step-by-step explanation:
The sum of the interior angles of a triangle is 180 degrees.
1.) Translating the problem into equation:
7:11:12 = 180 degrees
7x+11x+12x = 180 degrees; Where x = missing number
30x = 180
30x/30 = 180/30 divide both sides by 30
x = 6
2.) Substitute the values:
7x+11x+12x = 180
7(6)+11(6)+12(6) = 180
42+66+72 = 180
180 = 180
3.) Therefore, the angles should be 42 degrees, 66 degrees and 72 degrees.
4.) See attached drawing of triangle
So one hour is 60 minutes,
5/6 of an hour would be, 50 minutes. Basically 60/6=10 and 10*5=50
so if the robot does 8 tasks in 50 minutes and each tasks takes the same amount, the equation would be 50/8
50/8= 6.25
Each task is 6 minutes and 25 seconds.