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muminat
3 years ago
13

The length of a string is L inches. Samantha cuts it into two unequal pieces such that the length of the small piece is 35% of L

.
If the length of the big piece is 24 inches longer than the length of the small piece, what is the ratio of the length of the small piece to the length of the big piece as a fraction in its lowest terms?
Mathematics
1 answer:
skelet666 [1.2K]3 years ago
4 0

Answer:

The shorter piece   x  =  8.4 in

The longer one    y  =  15.6 in

Step-by-step explanation:

If we cut  a string length  L  in to unequal  pieces we get two pieces

first one with length  x  and the other one with length  y

Let call  x  the smaller piece,  then   y = L  -  x will be the longer one

If   x  =  35 %    then

x  =  0,35* L     and

y = L -  x  =  L - 0,35*L      ⇒  y  =  0,65 L     ⇒ y  =  0.65*24

Now if L  =  24  in

x  =  0,35*24          ⇒               x = 8.4 in

and

L  -  x  =  0.65*L      ⇒       L - x  =  0.65*24     y  =  L  -  x  =  15.6 in

as way of verification you can add the length of the two pieces and find:

8.4  +  15.6  = 24 in

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d) If the sample is smaller, the standard error is bigger (as the square root of the sample size is in the denominator), so the spread of the probability distribution is more. This results then in a smaller probability for any range.

e) If the population standard deviation is smaller, the standard error for the sample (the classroom) become smaller too. This means that the values are more concentrated around the mean (less spread). This results in a higher probability for every range that include the mean.

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