4. A representative sample of 50 students from a high school is surveyed. Each student is asked what science class he or she is taking. This table show the responses. Select all the statements that are valid based on the results of
the survey.
Science Class
Physics
Chemistry
Biology
Earth Science
Health Science
Number of
Students
6
10
18
A. About 20% of students at the high school are taking
Chemistry.
B. About twice as many students are taking Health Science
than are taking Physics.
C. For every 150 students we could predict that at least 18
of the students are taking Physics.
D. For every 25 students we could predict that at least 4 of
the students are taking Earth Science.
4
12

A, B, C

Step-by-step explanation:

The total number of students is the sum of the students taken each course. Hence the total number of students is:

Total number = 6 + 10 + 18 + 4 + 12 = 50 students

A) The percentage of students offering chemistry = (number of students offering chemistry / total number of students) * 100%

percentage of students offering chemistry = (10 / 50) * 100% = 20%

Option A is correct

B) number of students taking health science = 12, while number of students taking physics = 6. Hence About twice as many students are taking Health Science  than are taking Physics.

Option B is correct.

C) The percentage of students taking physic = (6 / 50) * 100% = 12%

Therefore for 150 students, the number of students taking Physics = 12% * 150 = 0.12 * 150 = 18

Option C is correct

D) The percentage of students taking earth science = (4 / 50) * 100% = 8%

Therefore for 25 students, the number of students taking earth science = 8% * 25 = 0.08 * 25 = 2

For every 150 students we could predict that 18  of the students are taking Physics.

Option D is correct

14.3

step-by-step explanation:

add all the numbers together.

9 + 12 + 15 + 16 + 17 + 17 = 86

now, divide 86 by how many numbers we have: 6.

86 / 6 = 14.3

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.