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Nataly [62]
3 years ago
12

The average age of three people running for election is 42. A fourth person joins the race and the average drops to 40. What is

the fourth
person's age?
A. 32
B. 34
c. 35
D36
E. 40
Mathematics
1 answer:
Anton [14]3 years ago
7 0

Answer:

B - 34 years old

Step-by-step explanation:

First you have to multiply 42 times 3 to find the total age of the three people. Then multiply 40 times 4 to find the age of the four people in all. Subtract.

42 × 3 = 126

40 × 4 = 160

160 - 126 = 34

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1) \frac{2}{5}

2) 49.225

3) \frac{7}{2}

Step-by-step explanation:

1) To find the expected value of the dice we can use the following equation:

E(x)=x_{1}*P(x_{1})+x_{2}*P(x_{2})+...+x_{n}*P(x_{n})

So in our problem the values x will be: 1/1, 1/2, 1/3, 1/4, 1/5 and 1/6 and the probavility for all values is 1/6 so the expected values will be:E(x)=(\frac{1}{1} *\frac{1}{6}) +(\frac{1}{2} *\frac{1}{6}) +(\frac{1}{3} *\frac{1}{6})+(\frac{1}{4} *\frac{1}{6})+(\frac{1}{5} *\frac{1}{6})+(\frac{1}{6} *\frac{1}{6})

E(x)=0.167+0.083+0.056+0.042+0.033+0.028=0.409\approx \frac{2}{5}

2) To find the variance of the expected values we can use the equation:

Var(x)=\frac{\sum_{i=1}^{n}(x_{i}-\overline{x})^{2} }{n}

So for our problem will be:

Var(x)=\frac{(3-10.5)^2+(4-10.5)^2+(17-10.5)^2+(18-10.5)^2}{4}

Var(x)=\frac{56.25+42.25+42.25+56.25}{4}Var(x)=\frac{196.9}{4}=49.225

3) To find the expected value of the dice we can use the following equation:

E(x)=x_{1}*P(x_{1})+x_{2}*P(x_{2})+...+x_{n}*P(x_{n})

So in our problem the values x will be: 1, 2, 3, 4, 5 and 6 and the probavility for all values is 1/6 so the expected values will be:E(x)=(1*\frac{1}{6}) +(2 *\frac{1}{6}) +(3 *\frac{1}{6})+(4 *\frac{1}{6})+(5 *\frac{1}{6})+(6 *\frac{1}{6})

E(x)=0.17+0.33+0.5+0.67+0.83+1=3.5\approx \frac{7}{2}

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