The average time customers spent on the American Greetings Web site has been 11.85 minutes (Top Web Properties, USA Today, April 27, 2000). You want to show that the average time spent on that web site has now changed. Assume that the population of site visit times is normally distributed with a population standard deviation of 4.0 minutes. In order to test the hypothesis at 0.05 level of significance, the critical value(s) is(are):

± 1.96

Step-by-step explanation:

Given the following :

Mean (m) time spent = 11.85

Standard deviation = 4 minutes

Since the population of site visits is Normally distributed, Hence, the test statistic will follow a normal distribution :

The test the hypothesis that mean time has changed at 0.05 confidence interval

Normal distributions have a mean value of 0 and standard deviation of 1

Using a two tailed test At 0.05 confidence interval ;

Using the critical value calculator, which in general under normal distributions :

0.05% confidence interval for a two tailed test is

± 1.96

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be