(A) Before the authority increases tolls on any of the area bridges, it is required by law to hold public hearings at which objections to the proposed increase can be raised.
(B) Whenever bridge tolls are increased, the authority must pay a private contractor to adjust the automated toll-collecting machines.
(C) Between the time a proposed toll increase is announced and the time the increase is actually put into effect, many commuters buy more tokens than usual to postpone the effects of the increase.
(D) When tolls were last increased on the two bridges in question, almost 20 percent of the regular commuter traffic switched to a slightly longer alternative route that has since been improved.
(E) The chairman of the authority is a member of the Tristate Automobile Club that has registered strong opposition to the proposed toll increase.
Answer:
Options A and B are true
(A) Before the authority increases tolls on any of the area bridges, it is required by law to hold public hearings at which objections to the proposed increase can be raised.
B. (B) Whenever bridge tolls are increased, the authority must pay a private contractor to adjust the automated toll-collecting machines.
Step-by-step explanation:
A. In a developed society, it's imperative for the authority to hold public hearings with stake holders to air their views before the tolls are increased, this would enable the authority to carry out proper assessment to know both the positive and negative impact of increasing the toll.
B. Increasing the tolls implies that there must be adjustment in the automated tolling machines and this would incur cost on the authority, this contract would be executed by private contractors.
of the remaining children get off, leaving the bus only half full.
How many children were on the bus at the start?
Answer:
12
Step-by-step explanation:
If there are x children on the bus at the start, after the first stop, there are (x-3) remaining. After two stops, the number on the bus is ...
x/2 = x -3 -(1/3)(x -3)
Multiplying by 6, we have ...
3x = 6x -18 -2(x -3)
3x = 4x -12 . . . . simplify
12 = x . . . . . . . . add 12-3x
There were 12 children on the bus at the start.
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Check
After 3 got off at the first stop, there were 12-3 = 9 remaining. 1/3 of those, or 9/3=3 got off at the second stop, so 9 -3 = 6 remained. This is half the original number, as required.
Let X represent the number of children on the bus originally. The equation formed is 2/3*(X - 3) = X/2, and when we solve it, we find that X equals 12 which indicates that there were 12 children on the bus at the start.
Let's denote the number of children on the bus at the start as X. After the first stop, the number of children on the bus became X - 3, because 3 children got off. After the second stop, a third of the remaining children got off, so the number of children on the bus became 2/3*(X - 3). According to the problem, after all the stops, the bus was half full. Therefore, we can set up an equation: 2/3*(X - 3) = X/2.
To solve the equation, we can multiply all terms by 6 to clear out the fractions and obtain the equation: 4*(X - 3) = 3X. This simplifies to 4X - 12 = 3X which simplifies further to X = 12, meaning there were initially 12 children on the bus.
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A.22 – 14x
B.22 – 6x
C.22 + 6x
D.11x – 5x