A horticulturist is studying the relationship between tomato plant height and fertilizer amount. Thirty tomato plants grown in similar conditions were subjected to various amounts of fertilizer (in ounces) over a four-month period, and then their heights (in inches) were measured. Height Fertilizer 20.4 1.9 49.2 5.0 ⋮ ⋮ 46.4 3.1 Click here for the Excel Data File a. Estimate the model: Height = β0 + β1Fertilizer + ε. (Round your answers to 2 decimal places.) Heightˆ = + Fertilizer b-1. Interpret the coefficient of Fertilizer. (Round your answer to 2 decimal places.) b-2. Does the y-intercept make practical sense? multiple choice Yes, since the y-intercept is positive. No, since the y-intercept is positive. Yes, since some farmers may not use any fertilizer. No, since some farmers may not use any fertilizer. c. Use the estimated model to predict, after four months, the height of a tomato plant which received 3.0 ounces of fertilizer. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

 The correct answer is:  " 6 " .

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         { that is;  the simplified expression given is:  " 6" [positive 6].

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Step-by-step explanation:

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Given the expression;  which is intended to be:

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    Simplify:     " 1 + √ [ - (-5²)( - 1³) ] " ?

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Note:

Refer to "comments below" typed directly under 'where the question itself is asked' —for clarification.

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First, solve and simplify the value under the square root sign:

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- (-5²) (-1 ³) =  ?

   → (- 1)( - 5²) (- 1³)  = ?

    ↔  (- 5²)(- 1)( - 1³ )  = ?

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    - 5²  =  -5 * -5  = 25 ;  {Note:  A negative * a negative = a positive ).  

     →  Now, multiply this value by:  "(-1)" ;  

     (-1) * (25) =  -25 ;  

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Now,   (-25) * (-1³)  = ?

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Let us simplify:  " ( - 1 ³ ) " ;  

             " ( - 1³ )  =  (-1 * -1 * -1)  =  

                          ( -1 * -1) * -1  = ?  ;  

Note:  " (-1 * -1) =  1 (positive one) ;  

                   →  {since:  " a negative * a negative = a positive " .}.

               Then,  1 * (-1) =   -1  (negative one);  

      →  {since:  a "positive times a negative =  a negative"} ;  

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So:   " ( - 1³)   =  - 1  " ;

So:  (-25) * (-1³)  =  (-25) * (-1) = 25 (positive 25) ;  

→  {since:  a "negative times a negative = a positive" ; and since:

" any value, multiplied by "1" ; results in that same original value."}.  

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So, back to our problem:  

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Simplify:     " 1  +  √ [ - ( - 5² ) ( - 1 ³ ) " ?

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                               =    1   +  √25 ;  _______________________________________________

{Note that:  "√25 = 5 " ;   25 is a "perfect square";  

  since:  5² = 5 * 5 = 25 ;  and "25" is known as a "perfect square" ; since the square root of the non-zero positive integer  [in this case:  " 25 ") ;   results in a non-zero positive integer [in this case:  " 5 " .].

If not known by trial and error; or by common known knowledge, one may use a  calculator to find:  " √25 " ;  to get:  " 5 " .

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 So:   We can write our original expression:

            "  1  +   " ;

                     =  1   +  5  ;

                     =   6 .

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The correct answer is:  " 6 " {positive 6}.

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Hope this answer — and explanation — is helpful to you!

      Wishing you the best in your academic endeavors

                    — and within the "" community!

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