Astudent at a junior college conducted a survey of 20 randomly selected? full-time students to determine the relation between the number of hours of video game playing each? week, x, and? grade-point average, y. she found that a linear relation exists between the two variables. the? least-squares regression line that describes this relation is modifyingabove y with caret equals negative 0.0537 x plus 2.9453y=? 0.0537x+2.9453.

This question is incomplete. Assuming that the question is similar to the reference I found, we will look for the grade-point average, y, of a student who plays video games 8 hours per week. To calculate for this, just plug in x = 8 in the equation given.

y = - 0.0537x + 2.9453

y = - 0.0537 * 8 + 2.9453

y = 2.5157 = 2.52

The grade-point average is about 2.52.

Note: if the given x is not 8, just plug in that value into the equation then calculate.

The y-intercept of the equation 2.9452 indicates the grade-point average of the student who does not play video games (x = 0).

The slope -0.0537 indicates that for every hour the student plays, the grade-point average decreases by 0.0537 points.

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752

246

step-by-step explanation: