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goblinko [34]
3 years ago
11

Tom is 4 more than twice Andrews age. Sara is 8 less than 5 times Andrews age. If Tom and Sara are twins, how old is Andrew? Sho

w your work
Mathematics
1 answer:
horsena [70]3 years ago
3 0
T = 4 + 2A
S = 5A - 8
T = S
Since T and S are equal, set them against each other
2A + 4 = 5A - 8
Subtract 2A from each side, and add 8 to each side
12 = 3A
Divide each side by 3
A = 4
So Andrew is 4 years old
If Andrew is 4, then Tom is twice that plus 4, or 12. Sarah is 5 times 4 less 8, or 12. 
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VashaNatasha [74]

Answer:

1. P(940 ≤ Y ≤ 1,060) is equal to: 0.9927.

2. E(X) is equal to: 1.

3. The standard deviation of X is equal to: 0.707.

4. E(Y) is equal to: 1,000.

Step-by-step explanation:

The number of heads (or tails) in a repeated toss of a coin can be modeled as a binomial random variable.

When the number of trials becomes bigger, the calculations for the binomial distribution became more tedious, as we have to calculate it for each individual number of tails or head.

This can be solved with the approximation to the normal distribution, where we treat the variable as continuous and the calculations are easier.

For n=2, the calculations for the binomial distribution are feasible and accurate.

The expected value for the number of heads is:

E(X)=n\cdot p=2\cdot0.5=1

where n is the number of trials and p the probability of heads.

The standard deviation can be calculated as:

\sigma_x=\sqrt{np(1-p)}=\sqrt{2\cdot0.5\cdot0.5}=\sqrt{0.5}\approx0.707

For n=2000 trials, the normal approximation is reasonable.

The mean of the normal distribution can be calculated as:

E(Y)=\mu=n\cdot p=2,000\cdot 0.5=1,000

where n is the number of trials and p the probability of heads.

The standard deviation of the normal approximation can be calculated as:

\sigma_y=\sqrt{np(1-p)}=\sqrt{2,000\cdot0.5\cdot0.5}=\sqrt{500}\approx22.36

To calculate then the probability P(940 ≤ Y ≤ 1,060), we calculate the z-score for each value:

z_1=\dfrac{Y_1-\mu}{\sigma}=\dfrac{940-1000}{22.36}=\dfrac{-60}{22.36}=-2.683\\\\\\z_2=\dfrac{Y_2-\mu}{\sigma}=\dfrac{1060-1000}{22.36}=\dfrac{60}{22.36}=2.683

Now, we can calculate the probability as:

P(940\leqY\leq1060)=P(-2.683

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