At a large university, 68% of the students have a laptop, while only 43% of professors have one. Let p hat Subscript s and P hat Subscript p be the sample proportions of students and professors, respectively, who have a laptop. Suppose 56 students and 31 professors from this university are selected at random and asked if they have a laptop. Which of the following is the correct calculation and interpretation of the standard deviation of the sampling distribution of p hat Subscript s Baseline minus p hat Subscript p ?

The difference (student – professor) in the sample proportions of those who have a laptop typically varies about 0.012 from the true difference in proportions.
The difference (student – professor) in the sample proportions of those who have a laptop typically varies about 0.035 from the true difference in proportions.
The difference (student – professor) in the sample proportions of those who have a laptop typically varies about 0.109 from the true difference in proportions.
The difference (student – professor) in the sample proportions of those who have a laptop typically varies about 0.25 from the true difference in proportions.

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation:

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solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.