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Arte-miy333 [17]
4 years ago
10

1. Simplify -7 + {12 - 3[50 - 4(2+3)] }

Mathematics
1 answer:
Komok [63]4 years ago
6 0

1. Simplify -7 + (12 - 3[50 - 4(2+3)]) this expression step by step:

  • 2+3=5;
  • 4\cdot (2+3)=4\cdot 5=20;
  • 50-4\cdot (2+3)=50-20=30;
  • 3\cdot [50-4(2+3)]=3\cdot 30=90;
  • 12-3\cdot[50-4(2+3)]=12-90=-78;
  • -7 + (12 - 3[50 - 4(2+3)])=-7+(-78)=-7-78=-85.

2. Simplify the expression \dfrac{1}{3} + 6\left(\dfrac{2}{3} - \dfrac{1}{6}\right)^2 in the same way:

  • \dfrac{2}{3}-\dfrac{1}{6}=\dfrac{2\cdot 2-1}{6}=\dfrac{3}{6}=\dfrac{1}{2}
  • \left(\dfrac{2}{3} - \dfrac{1}{6}\right)^2=\left(\dfrac{1}{2} \right)^2=\dfrac{1}{4}
  • \dfrac{1}{3} + 6\left(\dfrac{2}{3} - \dfrac{1}{6}\right)^2=\dfrac{1}{3} + 6\cdot \dfrac{1}{4}=\dfrac{1}{3}+\dfrac{3}{2}=\dfrac{1\cdot 2+3\cdot 3}{6}=\dfrac{11}{6}
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Step-by-step explanation:

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Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the pulse rates of a population, and for this case we know the distribution for X is given by:

X \sim N(77.5,11.6)  

Where \mu=77.5 and \sigma=11.6

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