Bryce is testing whether school is more enjoyable when students are making high grades. he asked 100 students if they enjoyed school and whether their gpa was above or below 3.0. he found that 33 of the 40 students with a gpa above 3.0 reported that they enjoyed school, and 5 of the 60 students with a gpa below 3.0 reported that they enjoyed school. what is the probability that a student with a gpa below 3.0 does not enjoy school?

The probability is: or

Step-by-step explanation:

We know that probability of an event is given by:

here we are asked to find the probability that a student with GPA<3.0 does not enjoy the school.

we are given that the total number of students with GPA<3.0=60

out of these 60 students 5 enjoy the school so the remaining that do not enjoy school is 55.

hence, here number of favourable outcome=55

total number of possible outcome=60

hence,

Hence, the probability that a student with GPA<3.0 does not enjoy school is   or .

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

4

step-by-step explanation: