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ruslelena [56]
3 years ago
12

The women’s heptathlon in the Olympics consists of seven track and field events: the 200-m and 800-m runs, 100-m high hurdles, s

hot put, javelin, high jump, and long jump. In the 2000 Olympics, the best 800-m time, run by Gertrud Bacher of Italy, was 8 seconds faster than the mean. The winning long jump by the Russian Yelena Prokhorova was 60 centimeters longer than the mean. Bacher’s winning 800-m time of 129 seconds was 8 seconds faster than the mean qualifying time of 137 seconds (the standard deviation of the qualifying times was 5 seconds). Prokhorova’s winning long jump was 60cm longer than the average 6-m jump (Note: the standard deviation of the long jumps was 30 cm). Which performance is more outstanding (and hence deserves more points when computing their overall score)? Explain.
Mathematics
1 answer:
SpyIntel [72]3 years ago
3 0

Answer: Prokhorova is more outstanding.

Step-by-step explanation: To compare scores from different distributions, first standardize it:

z-score = \frac{x-\mu}{\sigma}

where

x is the individual mean you want to compare

μ is the mean of the population

σ is standard deviation

For <u>Gertrud Bacher</u>:

z-score = \frac{129-137}{5}

z-score = -1.6 (s)

The negative sign indicates Bacher's mean is less than the mean

For <u>Yelena Prokhorova</u>:

z-score = \frac{660-600}{30}

z-score = 2 (cm)

The positive sign indicates Prokhorova's mean is more than the mean.

Using z-score table, you determine the percentiles are:

For Bacher: Percentile = 5.5%

For Prokhorova: Percentile = 97.7%

Bacher's percentile means she is above 5.5% of the participants, while Prokhorova is 97.7% above the other competitors, which means Prokhorova have a better performance and deserves more points.

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4 0
2 years ago
What is the factorise 3m-6
cupoosta [38]

The answer is:      "  3(m − 2)  "  .

__________________________________

  →  The "factorized version" of the binomial expression, " 3m − 6 " ,  is:

__________________________________

                →   "  3(m − 2) " .

__________________________________

Explanation:

To solve:

__________________________________

<u>Note</u>:  We are given the expression:  " 3m − 6 " ;

and we are asked to "factorize" this expression.

Note that this expression is a "binomial expression" — which means there are two (2) terms — in this case:   "3m" and "6" .

Since only one (1) of these 2 (two) terms has a variable, and the remaining terms is a "constant" (non-zero integer), write these 2 (two) terms as:

 1)  the coefficient of the variable given in the term shown with a "coefficient" :

       →   that is:  "3"  ;  and:

 2)  the other term:  "6" .

→  With the numbers:  "3 and 6" , we can factor out a "3" ;  

          →  {since:  " 6 ÷ 3 = 2 "} ;

 →   So;  given:  

               " 3m − 6 " ;  

 →   We can "factor out" a "3" ; as follows:

           →   Take the first term:  " 3m " :

                    " 3m  =  3 * m " ;

__________________________________

           →   Take the second term:  "  6 " :

                    "  6 = 3 * (what value?) ;

                 → divide each of this equation by "3" ;

    to isolate the "missing value" on one side of the equation; & to solve for the "missing value" ; as follows:

        →           "  6 / 3 = [ 3 * (what value?) ] / 3  ;

                    →  to get:  " 2  =  "(the missing value)"  ;

    →   So;    "  6 = 3 * (what value?) ;

           →     " 6 = 3 * 2 " .  

           →   Take the second term:  "  6 " :

           →     " 6 = 3 * 2 " .

__________________________________

So:    " 3m − 6 "  =  (3 * m) − (3 * 2) " .  

Factor out a "3" ;  as follows:

__________________________________

    →  " 3m − 6 "  =  (3 * m) − (3 * 2) " ;

                           =   " 3(m − 2)  "

__________________________________

Let us check our answer:

__________________________________

Note the "distributive property of multiplication"  :

__________________________________

        a(b + c) = ab +  ac ;  

        a(b − c) = ab −  ac ;

__________________________________

So:  Take our answer:  " 3(m − 2) " .

__________________________________

" 3(m − 2)  = ?  (3*m)  −  (3*2)  " ??  ;

__________________________________

Let us substitute "4" for "m" ;  in both sides of the equation;

              →  to see if the equation holds true;  i.e. to see if both sides of the equation are equal when:  " m = 4 " ;

__________________________________

 We have:

__________________________________

     →  " 3(m − 2)  = ?  (3*m)  −  (3*2)  " ??  ;

First let us rewrite this equation;  substitute "4" for "m" ; as follows:

     →   " 3(4 − 2)  = ?  (3*4)  −  (3*2)  " ??  ;

__________________________________

And calculate;  to see if each side of the equation is equal ; i.e. to see if the equation holds true; as follows:

     →   " 3(2)  = ?  (12)  −  (6)  " ??  ;

     →   "  6  = ?  (6)  " ??  ;

     →   "  6 = 6 " !  Yes!  The equation holds true!

__________________________________

Hope this answer was helpful!

Best wishes!

__________________________________

8 0
3 years ago
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