In a manufacturing plant, a work center is a specific production facility that consists of one or more people and or machines and is treated as one unit for the purposes of capacity requirements planning and job scheduling. If the jobs arriveat a particular work center at a faster rate than they depart, the work center impedes the overall production process and is referred to as a bottleneck. This sample was collected by an operations manager for use in investigating a potential bottleneck work center. There are 315 hours in the work week when items can come into the work center. The manager selects every 15th hour and counts how many items come into the work center during that hour. What type of sample is this?

Systematic sampling

Step-by-step explanation:

Systematic sampling is a sampling technique in which the first sample selection is a random selection but other subsequent selection of samples occurs within a fixed sampling interval. The determination of this interval is based on the division of the population size by sample size.

Let assume that, our first random selection is unit, then the other fixed selection occurs at a fixed sampling interval of k.

Therefore, using systematic sampling method, the sampling unit will be every unit after the unit.

From  the question given:

We notice that the manager selects a sampling unit every 15th  hour. This tells us that he is taking the sampling unit by the usage of a fixed time interval.

Hence, this appears to be a systematic sample.

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

step-by-step explanation:

assume that you have 3 different side lengths.   apply the pythagorean theorem here:   square each of the two shortest sides; call them a and b, so that their squares are a² and b².   also square the longest side, calling the result c².

now, if a² + b² = c² is true, the triangle is a right triangle; otherwise it is not a right triangle.