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jolli1 [7]
3 years ago
14

A particular dress requires 4 1/4 yards of fabric for manufacturing. If the matching jacket requires 1/6 yards less fabric, how

much fabric is needed for both pieces? Need answer now!
Mathematics
2 answers:
ASHA 777 [7]3 years ago
6 0

Answer:

4  5/12 + 4 1/4  

Step-by-step explanation:

4  1/4 - 1/6 - you have to turn the mixed # into improper fraction  -  17/4,

17/4 - 1/6 = 4 5/12

4 5/12 + 4 1/4  8 2/3

8 2/3 is the answer i hope this helps lol, :)

sveta [45]3 years ago
5 0

Answer: A total of 8 1/3 yards of fabric is needed for both pieces.

Step-by-step explanation: First, you must subtract 1/6 from 4 1/4 to figure out how many yards of fabric is needed for the matching jacket. To do this, you have to find common denominators for each fraction. Since the fractions have a least common denominator of 12, change each fraction to satisfy this new denominator: 1/6 changes to 2/12 and 4 1/4 changes to 4 3/12. Now, you must subtract: 4 3/12 - 2/12 = 4 1/12. Therefore, the matching jacket requires 4 1/12 yards of fabric. Next, add the amount of fabric for the dress (4 3/12) to the amount of fabric for the matching jacket (4 1/12): 4 3/12 + 4 1/12 = 8 4/12. Simplify 8 4/12 to get a final answer of 8 1/3 yards of fabric in total.

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<span>The mathematical theory of probability assumes that we have a well defined repeatable (in principle) experiment, which has as its outcome a set of well defined, mutually exclusive, events.</span>


If we assume that each individual coin is equally likely to come up heads or tails, then each of the above 16 outcomes to 4 flips is equally likely. Each occurs a fraction one out of 16 times, or each has a probability of 1/16.

Alternatively, we could argue that the 1st coin has probability 1/2 to come up heads or tails, the 2nd coin has probability 1/2 to come up heads or tails, and so on for the 3rd and 4th coins, so that the probability for any one particular sequence of heads and tails is just (1/2)x(1/2)x(1/2)x(1/2)=(1/16).

Now lets ask: what is the probability that in 4 flips, one gets N heads, where N=0, 1, 2, 3, or 4. We can get this just by counting the number of outcomes above which have the desired number of heads, and dividing by the total number of possible outcomes, 16. 
  
 

<span>N     # outcomes with N heads     probability to get N heads</span>

0                1                                       1/16 = 0.0625

1                4                                       4/16 = 1/4 = 0.25

2                6                                      6/16 = 3/8 = 0.375

3                4                                      4/16 = 1/4 = 0.25

4                1                                      1/16 = 0.0625

We can plot these results on a graph as shown below.

 
The dashed line is shown just as a guide to the eye. Notice that the curve has a "bell" shape. The most likely outcome is for N=2 heads, where the curve reaches its maximum value. This is just what you would expect: if each coin is equally likely to land heads as tails, in four flips, half should come up heads, that is N = 4x(1/2) = 2 is the most likely outcome. Note however that an occurrence of N = 1 or N = 3 is not so unlikely - they occur 1/4 or 25% of the time. To have an occurrence of only N = 0, or N = 4 (no heads, or all heads) is much less likely - they occur only 1/16 or 6.25% of the time.

The above procedure is in principle the way to solve all problems in probability. Define the experiment, enumerate all possible mutually exclusive outcomes (which are usually assumed to be each equally likely), and then count the number of these outcomes which have the particular property being tested for (here for example, the number of heads). Dividing this number by the total number of possible outcomes then gives the probability of the system to have that particular property.

Often, however, the number of possible outcomes may be so large that an explicit enumeration would become very tedious. In such cases, one can resort to more subtle thinking to arrive at the desired probabilities. For example, we can deduce the probabilities to get N heads in 4 flips as follows:

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N=3: To get 3 heads, means that one gets only one tail. This tail can be either the 1st coin, the 2nd coin, the 3rd, or the 4th coin. Thus there are only 4 outcomes which have three heads. The probability is 4/16 = 1/4.

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