A random sample of 50 students from a high school with 900 students is surveyed. Each student is asked what science class he or
she is taking and all students at the school take science. The table shows the responses.
1 answer:
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Answer:
Option C
Step-by-step explanation:
we have
The compound inequality can be divided into two inequality
-----> inequality A
----> inequality B
Solve inequality A
Divide by -3 both sides
when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol
Rewrite
The solution of the inequality A is the interval (-∞,-3]
Solve the inequality B
Divide by -3 both sides
when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol
The solution of the inequality B is the interval [-6,∞)
The solution of the compound inequality is
[-6,∞) ∩ (-∞,-3]=(-6,-3]
The answer is: " 
" .
______________________________
Given: 0.1212121212..... repeating ; write that value as a fraction;
______________________________________________________
In other words; we are given: "0.1212121212..... repeating infinitely" ;
→ that is to say; "0.12 ... ; {the "12" decimal portion repeats infinitely} ;
_______________________________________________________
→ We write this value, as a fraction, as: "12/99" ;
__________________________________________
→Explanation:
__________________________________________
Note: "0.99999999...... repeating infinitely; = "1" .
_________________________________________
→Since:
Let us say that we have:
"x = 0.999999 ; repeating infinitely;
In order words, let us say we have: "x = 0.9.... ; the "9" decimal repeats infinitely;
_____________________________________________________
Then "10x" ; (that is: "10" multlipled by "x"; or "10*x" or "10x" ); is equal to:
"10" * (0.999999.....) = 9.99999999...... (the "9" decimal repeats infinitely);
in other words: 10x = 9.99999999....
Divide each side by "10" ;
to get "x = 0.9999999....." ; the decimal "9" repeats indefinitely...." ;
But if you have: "10x = 10" ; divide each side of the equation by "10" ;
you get: "x = 1" .
____________________
Also, if "x = 0.9999...(repeating infinitely);
then: 10x = 9.99999.
_______________________________________________
10x = 9.999999999999999......
− x = 0.999999999999999.......
_____________________________________
9x = 9.00000000000000000000.....
→ 9x = 9 ;
Divide each side of the equation; to get;
9x /9 = 9/ 9 ; to get: x = 1 ; and we have: x = 0.9999.... ; so
x= 0.99999.... = 1 ;
__________________________________________________
So, if the numbers "12" is repeating, we divie "12" by "99" ;
that is; we divide "12" by "two 9's" ; since "12" is a "TWO-digit number"; a "two-digit number" is being repeated infinitely.
________________________________________
So; 0.12121212.....(the "12" is the decimal that repeats infinitely);
= 12/99 ; which can be simplified;
Divide each side (both the numerator AND the denominator); by "3" ;
_________________________________________
" 12/99 " = "(12÷3) / (99÷3) = 4/33 " .
_________________________________________
The answer is: .
_________________________________________
______________________________
Given: 0.1212121212..... repeating ; write that value as a fraction;
______________________________________________________
In other words; we are given: "0.1212121212..... repeating infinitely" ;
→ that is to say; "0.12 ... ; {the "12" decimal portion repeats infinitely} ;
_______________________________________________________
→ We write this value, as a fraction, as: "12/99" ;
__________________________________________
→Explanation:
__________________________________________
Note: "0.99999999...... repeating infinitely; = "1" .
_________________________________________
→Since:
Let us say that we have:
"x = 0.999999 ; repeating infinitely;
In order words, let us say we have: "x = 0.9.... ; the "9" decimal repeats infinitely;
_____________________________________________________
Then "10x" ; (that is: "10" multlipled by "x"; or "10*x" or "10x" ); is equal to:
"10" * (0.999999.....) = 9.99999999...... (the "9" decimal repeats infinitely);
in other words: 10x = 9.99999999....
Divide each side by "10" ;
to get "x = 0.9999999....." ; the decimal "9" repeats indefinitely...." ;
But if you have: "10x = 10" ; divide each side of the equation by "10" ;
you get: "x = 1" .
____________________
Also, if "x = 0.9999...(repeating infinitely);
then: 10x = 9.99999.
_______________________________________________
10x = 9.999999999999999......
− x = 0.999999999999999.......
_____________________________________
9x = 9.00000000000000000000.....
→ 9x = 9 ;
Divide each side of the equation; to get;
9x /9 = 9/ 9 ; to get: x = 1 ; and we have: x = 0.9999.... ; so
x= 0.99999.... = 1 ;
__________________________________________________
So, if the numbers "12" is repeating, we divie "12" by "99" ;
that is; we divide "12" by "two 9's" ; since "12" is a "TWO-digit number"; a "two-digit number" is being repeated infinitely.
________________________________________
So; 0.12121212.....(the "12" is the decimal that repeats infinitely);
= 12/99 ; which can be simplified;
Divide each side (both the numerator AND the denominator); by "3" ;
_________________________________________
" 12/99 " = "(12÷3) / (99÷3) = 4/33 " .
_________________________________________
The answer is:
_________________________________________