Answer:
k = 4
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
 - Parenthesis
 - Exponents
 - Multiplication
 - Division
 - Addition
 - Subtraction
 
Equality Properties
- Multiplication Property of Equality
 - Division Property of Equality
 - Addition Property of Equality
 - Subtract Property of Equality
 
Step-by-step explanation:
<u>Step 1: Define</u>
5k + (-7) = 13
<u>Step 2: Solve for </u><em><u>k</u></em>
- Simplify equation:                             5k - 7 = 13
 - Addition Property of Equality:          5k - 7 + 7 = 13 + 7
 - Simplify equation:                             5k = 20
 - Division Property of Equality:           5k/5 = 20/5
 - Simplify equation:                             k = 4
 
<u>Step 3: Check</u>
<em>Plug in k into the original equation to verify it's a solution.</em>
- Substitute in <em>k</em>:                    5(4) + (-7) = 13
 - Multiply:                               20 + (-7) = 13
 - Add:                                     13 = 13
 
Here we see that 13 does indeed equal 13.
∴ k = 4 is the solution to the equation.
 
        
                    
             
        
        
        
Answer:
3 + 9x = 11x - 7
simplify
9x + 3 = 11x - 7
subtract 11x from both sides
-11x             -11x
-2x + 3 = -7
get rid of constants first by subtracting by 3 from both sides
-3            -3
-2x = -10
divide both sides by -2 since that is the inverse operation of multiplication
/-2    /-2
X = 5
 
        
                    
             
        
        
        
Answer:
The first option is correct.
Step-by-step explanation:
We have been told that a chef knows that ground beef used for hamburger is safe to eat once it reaches 160 degrees Fahrenheit. For optimized taste and safety, he will not allow a hamburger cooked to a temperature under 160 degrees or over 170 degrees to be served. 
Let us see our graphs one by one.
Upon looking at first graph we can see it shows that hamburger should be cooked under 160 degrees and over 170 degrees. It is the case which chef will not allow. So this is our graph that represents the conditions under which the chef will not allow the hamburger to be served.
Second graph represents that hamburger should be cooked at and under 160 degrees and at and over 170 degrees. This can't be our choice as it includes 160 and 170 degrees.
Third graph represents the temperature at which chef will allow hamburgers to be served that is temperature between 160 to 170 degrees Fahrenheit including 160 and 170 degrees Fahrenheit. So this can't be our choice either.
Fourth graph represents the temperature between 160 to 170 degrees Fahrenheit excluding 160 and 170 degrees Fahrenheit.
Therefore, option 1 is the correct choice. 
 
        
                    
             
        
        
        
1.68 mm per year for 1.5 years could be rewritten as 
(2.00-0.32) mm per year for 1.5 yrs.
Multiply:  (1.5 yrs)(2.00-0.32)(mm/yr) = 3 mm + 0.48 mm = 3.48 mm
This approach makes use of the distributive property of multiplication.
        
             
        
        
        
Answer:
 The standard deviation is 10.38
Step-by-step explanation:
Given;
Variance, v = 107.76
mean, x = 34.2
The standard deviation is given by;
standard deviation = √variance
standard deviation = √107.76
standard deviation =  10.381
standard deviation = 10.38 (two decimal places)
Therefore, the standard deviation is 10.38