Jimthompson5910 is such a great and so important in making a differnce here.

a given line has the equation 2x + 12y = −1.

what is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (0, 9)?

y = ( )x + 9

6

Step-by-step explanation:

find the gradient of the line using the y=mx +c method rearrange 2x+12y=-1 to become 12y=-2x-1...divide both sides by 12 so m=-1/6. To find the slope of a line perpendicular to 2x+12y=-1 when their slopes multiply they give -1. The gradient of the perpendicular line is 6. Using the point it passed through (0,9) use the equation of a line formula which would be y-9/x-0=6

cross multiply and you'll get y=6x+9

if x = 1, then the answer is 3.5

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;