1km goes to 1000 m and 5000 mm goes to 5 m so the answer is 1105
Answer:
[-5, 4) ∪ (4, ∞)
Step-by-step explanation:
Given functions:
Composite function:
![\begin{aligned}(f\:o\:g)(x)&=f[g(x)]\\ & =\dfrac{1}{\sqrt{x+5}-3} \end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%28f%5C%3Ao%5C%3Ag%29%28x%29%26%3Df%5Bg%28x%29%5D%5C%5C%20%26%20%3D%5Cdfrac%7B1%7D%7B%5Csqrt%7Bx%2B5%7D-3%7D%20%5Cend%7Baligned%7D)
Domain: input values (x-values)
For 
to be defined:
Therefore, 
and 
⇒ [-5, 4) ∪ (4, ∞)
X + y is the number of students who were surveyed.
x is the number who own a bike.
y is the number who don't.
the ratio of the ones who own a bike and the ones who were surveyed is x / (x + y)
that ratio is 7/8.
you get x / (x + y) = 7/8
multiply both sides of this equation by (x + y) to get x = (x + y) * 7/8
simplify to get x = 7/8 * x + 7/8 * y
subtract 7/8 * x from both sides of this equation to get:
1/8 * x = 7/8 * y
solve for x to get x = 7 * y
this means that the number of students who own a bike is 7 times the number of students who don't.
divide both sides of that equation by y to get x/y = 7/1.
that means that the ratio of students who own a bike to the number of students who don't is equal to 7/1.
the problem states that the difference between the number who own a bike and the number who don't is 72.
this means that x - y = 72
from the equation of x = 7 * y, replace x with 7 * y in the equation of x - y = 72 to get:
7 * y - y = 72
simplify to get 6 * y = 72
divide both sides of that equation by 6 to get y = 72/6 = 12
this means that the number of students who do not own a bike is 12.
since x = 7 * y, then x = 7 * 12 = 84.
this means that the number of students who own a bike is 84.
since the number of students is x + y, this means that the number of students who were surveyed is 84 + 12 = 96.
let's see if this is right.
96 students were surveyed.
84 own a bike and 12 don't.
the difference between the ones who own a bike and the ones who don't is 84 - 12 = 72.
the ratio of the ones who own a bike and the number surveyed is 84/96 = 7/8.
solution is 96 students were surveyed.
