Step-by-step explanation:
y = 7 + 3x
y = 3x + 7
y = mx + b, therefore the y-intercept is 7.
3y = 6x + 12
y = 2x + 4
y = mx + b, therefore the y-intercept is 4.
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Answer:
Step-by-step explanation:
If two variables are directly proportional, it means that an increase in the value of one variable would cause a corresponding increase in the other variable.
Given that y varies directly with x, if we introduce a constant of proportionality, k, the expression becomes
y = kx
If y = 8 when x = 3, then
8 = 3k
k = 3/8
Therefore, the direct variation equation that relates x and y is
y = 3x/8
When x = 12, then
y = 3 × 12/8
y = 4.5
Z- score is a statistical tool that is used to determine the probability of finding a number or a value under a normal distribution plot. A normal distribution assumes that the mean is equal to zero and that the standard deviation is equal to 1. Using the z-score table, we can find the probability either on the right side or the left side. Using the table hence, we find the probability to the left of the value. The probability that is equivalent to the unknown z should be equal to 0.5 + (0.27/2) = 0.635. 0.5 comes from the assumption that the area under the curve on each side is 50% of the total. The equivalent z score is equal to z = 0.345.