The table shows the price for different numbers of board games: Number of Board Games Price (in dollars)
2 7
4 14
5 17.50
9 31.50

Does this table of numbers represent a proportional relationship? (5 points)

a
Yes, because 3.5 times the price is the number of board games

b
Yes, because the price is 3.5 times the number of board games

c
No, because the price of 4 board games should be $9 and not $14

d
No, because the price of 9 board games should be $40.50 and not $31.50

We conclude that the price is 3.5 times the number of board games.

Hence, option B is true.

Step-by-step explanation:

We know that when y varies directly with x, the equation is

y ∝ x

y = kx

k = y/x

where 'k' is called the proportionality constant.

From the table,

For the point (2, 7)

k = y/x

  = 7/2

  = 3.5

For the point (4, 14)

k = y/x

   = 14 / 4

   = 7/2

    = 3.5

For the point (5, 17.50)

k  = y/x

   = 17.5 / 5

   = 3.5

For the point (9, 31.50)

k  = y/x

   = 31.50 / 9

   = 3.5

From the above calculations, we computed that the value of the proportionality constant remains the same.

Thus, the table of numbers represents a proportional relationship.

Therefore, the equation becomes

y = kx

The price of 2 board game

y = 3.5 (2)

  = 7

The price of 4 board game

y = 3.5 (4)

  = 14

Therefore, we conclude that the price is 3.5 times the number of board games.

Hence, option B is true.

the population of other specie of birds will decline or other specie of birds will find some alternate source of food to survive.

explanation:

according to the competitive exclusion principle, which is also known as gause's law, two specie living in the same niche and feeding on the same resource cannot co-exist stably.

as we have well studied the theory of natural selection which states that only those organisms survive which have better tendency to compete for food and adapt to the environmental conditions.

coming towards the question, what wi ll happen when one species outcompetes the other for the small fish , the other specie will not get enough food and will start to die or decline in population. eventually either other specie needs to find another alternative food source for itself or migrate at some other location where there is less competition otherwise it will just not exist anymore at that niche.

hope it !

the answer is d

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