Based on the given variation, y does not vary directly with x and the constant of variation are 8, 3.2 and 1.25 respectively.
<h3>Variation</h3>
y = k × x
where,
k = constant of proportionality
y = -40
x = -5
y = k × x
-40 = k × -5
-40 = -5k
k = -40/-5
k = 8
when,
y = 8 and x = 2.5
y = k × x
8 = k × 2.5
8 = 2.5k
k = 8/2.5
k = 3.2
when,
y = 5 and x = 4
y = k × x
5 = k × 4
5 = 4k
k = 5/4
k = 1.25
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Answer:
unreadable score = 35
Step-by-step explanation:
We are trying to find the score of one exam that is no longer readable, let's give that score the name "x". we can also give the addition of the rest of 9 readable s scores the letter "R".
There are two things we know, and for which we are going to create equations containing the unknowns "x", and "R":
1) The mean score of ALL exams (including the unreadable one) is 80
so the equation to represent this statement is:
mean of ALL exams = 80
By writing the mean of ALL scores (as the total of all scores added including "x") we can re-write the equation as:
since the mean is the addition of all values divided the total number of exams.
in a similar way we can write what the mean of just the readable exams is:
(notice that this time we don't include the grade x in the addition, and we divide by 9 instead of 10 because only 9 exams are being considered for this mean.
Based on the equation above, we can find what "R" is by multiplying both sides by 9:
Therefore we can now use this value of R in the very first equation we created, and solve for "x":
.9 because the tenth place is 9 and the tenth place for the other one is 8 so its gonna be
.89 < .90 = .9
Answer:
C = 8 + 3x
The rate of change in the above equation is 3 dollars per game and it interpret the cost per game.
The initial value in the above equation is 8 dollars, which interpret the entry fee that every one person has to pay to enter the fair.
Step-by-step explanation:
Let the admission cost of the fair is $x and each game is $3.
Now, Steven went to the state fair, played 4 games and spent a total of $20 on admission and games.
So, we can write 20 = x + 4 × 3 {As the relation is linear}
⇒ x = $8
Therefore, the admission cost in the fair is $8.
Therefore, the equation that models the situation is
C = 8 + 3x ............ (1)
Where C is the total cost and x is the number of games played.
So, the rate of change in equation (1) is 3 dollars per game and it interprets the cost per game.
Again, the initial value in equation (1) is 8 dollars, which interprets the entry fee that each person has to pay to enter the fair. (Answer)
