Answer:
x=5
Step-by-step explanation:
Simplifying 5x + -7 = 2x + 8 Reorder the terms: -7 + 5x = 2x + 8 Reorder the terms: -7 + 5x = 8 + 2x Solving -7 + 5x = 8 + 2x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2x' to each side of the equation. -7 + 5x + -2x = 8 + 2x + -2x Combine like terms: 5x + -2x = 3x -7 + 3x = 8 + 2x + -2x Combine like terms: 2x + -2x = 0 -7 + 3x = 8 + 0 -7 + 3x = 8 Add '7' to each side of the equation. -7 + 7 + 3x = 8 + 7 Combine like terms: -7 + 7 = 0 0 + 3x = 8 + 7 3x = 8 + 7 Combine like terms: 8 + 7 = 15 3x = 15 Divide each side by '3'. x = 5 Simplifying x = 5
To determine the equation of the best fit line, the graphical approach can be done. A line is used in between the given points. Then, the slope and the y-intercept of the line is determined to give us the equation. The equations of two scatter plots are
y = 0.22 x + 0.46
y = 8x + 8.25<span />
A = event the person got the class they wanted
B = event the person is on the honor roll
P(A) = (number who got the class they wanted)/(number total)
P(A) = 379/500
P(A) = 0.758
There's a 75.8% chance someone will get the class they want
Let's see if being on the honor roll changes the probability we just found
So we want to compute P(A | B). If it is equal to P(A), then being on the honor roll does not change P(A).
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A and B = someone got the class they want and they're on the honor roll
P(A and B) = 64/500
P(A and B) = 0.128
P(B) = 144/500
P(B) = 0.288
P(A | B) = P(A and B)/P(B)
P(A | B) = 0.128/0.288
P(A | B) = 0.44 approximately
This is what you have shown in your steps. This means if we know the person is on the honor roll, then they have a 44% chance of getting the class they want.
Those on the honor roll are at a disadvantage to getting their requested class. Perhaps the thinking is that the honor roll students can handle harder or less popular teachers.
Regardless of motivations, being on the honor roll changes the probability of getting the class you want. So Alex is correct in thinking the honor roll students have a disadvantage. Everything would be fair if P(A | B) = P(A) showing that events A and B are independent. That is not the case here so the events are linked somehow.
The parent function is y = x^2
There is a compression of 3:
y = 3x^2
There is a shift by 1 unit to the left:
y = 3(x + 1)^2
The numbers are 6 and 5 because 6-5=1 and 6^2=36 or 6*6=36,5^2=25 or 5*5=25. 36+25=61
