A movie producer conducted a survey after the screening of his movie to find out how the film would be received by viewers from different age groups. The columns in the two-way table indicate the numbers of viewers who rated the film on a four-point scale: excellent, good, average, and poor. Viewer's Age Totals
16-255242127113
26-3533505997
36-4558122834132
46-552517221276
56 and Above1253828
Marginal Totals1801267070446
3
Select the correct answer.
Which of these observations is supported by the data in the table?

Note: A rating of good or excellent means the audience liked the movie, while a rating of poor means the audience disliked the movie.

A.
The majority of the audience in the 26-35 age group disliked the movie.
B.
Among those who liked the movie, the majority were in the oldest age group.
C.
Among those who disliked the movie, the majority were in the 26-35 age group.
D.
The majority of the audience in the 16-25 age group liked the movie.
E.
The majority of the audience from all the age groups disliked the movie.

78.59 is the mean

step-by-step explanation:

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq

yx = 36

step-by-step explanation:

cos f = opposite side/ hypotenuse

cos f = yw / yx

we know cos f = 4/9 and yw =16

4/9 = 16/yx

multiply each side by yx

4/9 yx = 16/ yx * yx

4/9 yx = 16

multiply each side by 9/4

9/4 * 4/9 yx = 16 *9/4

yx = 36