A random sample of 184 students at South High School were surveyed on whether they would prefer going to a movie or a concert. The results are shown in the relative frequency table. A 4-column table with 4 rows. The first column has no label with entries 10th, 11th, 12th, total. The second column is labeled movie with entries 0.18, 0.16, 0.24, 0.58. The third column is labeled concert with entries 0.15, 0.18, 0.09, 0.42. The fourth column is labeled total with entries 0.33, 0.34, 0.33, 1.00. Which statements are correct? Check all that apply. The marginal relative frequency for 10th graders is 0.18. 42% of the students prefer a concert over a movie. A greater ratio of 11th graders prefer a concert to a movie. More 12th graders were surveyed than any other grade level. The difference in the percent of students who prefer a movie over a concert is16%.

42% of the students prefer a concert over a movie.  

A greater ratio of 11th graders prefer a concert to a movie.

The difference in the percent of students who prefer a movie over a concert is16%.  

Step-by-step explanation:

              10th   11th   12th   total

movie       .18    .16     .24    .58

concert     .15     .18     .09   .42

total           .33     .34    .33    1

The marginal relative frequency for 10th graders is 0.18.   This is an incomplete statement

The marginal frequency is a number not a percent

42% of the students prefer a concert over a movie.   42% preferred a convert to the 58% who preferred a movie.  True

A greater ratio of 11th graders prefer a concert to a movie. 18/100 concert to 16/100 for the movie for 11th graders

18:16  This is true

More 12th graders were surveyed than any other grade level.

There were more 11th graders surveyed (34%) to (33%) for 12 graders False

The difference in the percent of students who prefer a movie over a concert is16%.  True

B. 42% of the students prefer a concert over a movie

C. A greater ratio of 11th graders prefer a concert to a movie

E. The difference in the percent of students who prefer a movie over a concert is 16%

Step-by-step explanation:

No. movie concert total

10th - 0.18 - 0.15 - 0.33

11th - 0.16 - 0.18 - 0.34

12th - 0.24 - 0.09 - 0.33

Total - 0.58 - 0.42 - 1.00

0.42 is 42%

(0.58 -0.42) × 100 = 16%

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

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