Answer:
Thus, every integer is a rational number. Clearly, 3/2,-5/3, etc. are rational numbers but they are not integers. Hence, every integer is a rational number but a rational number need not be an integer.
Step-by-step explanation:
Answer:
170 children
74 students
85 adults
Step-by-step explanation:
Given
Let:
![C = Children; S = Students; A = Adults](https://tex.z-dn.net/?f=C%20%3D%20Children%3B%20S%20%3D%20Students%3B%20A%20%3D%20Adults)
For the capacity, we have:
![C + S + A = 329](https://tex.z-dn.net/?f=C%20%2B%20S%20%2B%20A%20%3D%20329)
For the tickets sold, we have:
![5C + 7S + 12A = 2388](https://tex.z-dn.net/?f=5C%20%2B%207S%20%2B%2012A%20%3D%202388)
Half as many as adults are children implies that:
![A = \frac{C}{2}](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7BC%7D%7B2%7D)
Required
Solve for A, C and S
The equations to solve are:
-- (1)
-- (2)
-- (3)
Make C the subject in (3)
![C = 2A](https://tex.z-dn.net/?f=C%20%3D%202A)
Substitute
in (1) and (2)
-- (1)
![2A + S + A = 329](https://tex.z-dn.net/?f=2A%20%2B%20S%20%2B%20A%20%3D%20329)
![3A + S = 329](https://tex.z-dn.net/?f=3A%20%2B%20S%20%3D%20329)
Make S the subject
![S = 329 - 3A](https://tex.z-dn.net/?f=S%20%3D%20329%20-%203A)
-- (2)
![5*2A + 7S + 12A = 2388](https://tex.z-dn.net/?f=5%2A2A%20%2B%207S%20%2B%2012A%20%3D%202388)
![10A + 7S + 12A = 2388](https://tex.z-dn.net/?f=10A%20%2B%207S%20%2B%2012A%20%3D%202388)
![7S + 22A = 2388](https://tex.z-dn.net/?f=7S%20%2B%2022A%20%3D%202388)
Substitute ![S = 329 - 3A](https://tex.z-dn.net/?f=S%20%3D%20329%20-%203A)
![7(329 - 3A) + 22A = 2388](https://tex.z-dn.net/?f=7%28329%20-%203A%29%20%2B%2022A%20%3D%202388)
![2303 - 21A + 22A = 2388](https://tex.z-dn.net/?f=2303%20-%2021A%20%2B%2022A%20%3D%202388)
![2303 +A = 2388](https://tex.z-dn.net/?f=2303%20%2BA%20%3D%202388)
Solve for A
![A = 2388 - 2303](https://tex.z-dn.net/?f=A%20%3D%202388%20-%202303)
![A = 85](https://tex.z-dn.net/?f=A%20%3D%2085)
Recall that: ![C = 2A](https://tex.z-dn.net/?f=C%20%3D%202A)
![C = 2 * 85](https://tex.z-dn.net/?f=C%20%3D%202%20%2A%2085)
![C = 170](https://tex.z-dn.net/?f=C%20%3D%20170)
Recall that: ![S = 329 - 3A](https://tex.z-dn.net/?f=S%20%3D%20329%20-%203A)
![S = 329 - 3 * 85](https://tex.z-dn.net/?f=S%20%3D%20329%20-%203%20%2A%2085)
![S = 329 - 255](https://tex.z-dn.net/?f=S%20%3D%20329%20-%20255)
![S = 74](https://tex.z-dn.net/?f=S%20%3D%2074)
Hence, the result is:
![C = 170](https://tex.z-dn.net/?f=C%20%3D%20170)
![S = 74](https://tex.z-dn.net/?f=S%20%3D%2074)
![A = 85](https://tex.z-dn.net/?f=A%20%3D%2085)
Answer:
A 270° rotation about point B'
Step-by-step explanation:
Rotation is clockwise so you can see that the final transformation is a rotation 270° clockwise
Answer:
<em>n</em> - <em>k</em> + 1
Step-by-step explanation:
This is assuming (because you did not say) that <em>n</em> and <em>k</em> are integers and <em>n</em> is greater than <em>k</em>.
Example: from 2 to 5 {2, 3, 4, 5} includes 5 - 2 + 1 = 4 numbers.
Example: from -6 to 4 includes 4 - (-6) + 1 = 11 numbers, namely {-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4}
Each member had to have received 14 and two thirds ounces. When you divide 176 by 12 you get 14.66666 which equals 14 and two thirds