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FrozenT [24]
2 years ago
6

A father's age is thrice the sum of the ages of his two children. After five years, his age will be

Mathematics
1 answer:
jenyasd209 [6]2 years ago
4 0

Answer: 45 years old

Step-by-step explanation:

<u>Given:</u>

- Father's age is thrice the sum of ages of his two children

- After five years, his age will be twice the sum of their ages

Let x be the two children's current age and 3x be the father's current age

<u>Solve:</u>

Set equation

3x + 5 = 2 ( x + 10 )

Expand parenthesis

3x + 5 = 2x + 20

Subtract 5 on both sides

3x + 5 - 5 = 2x + 20 - 5

3x = 2x + 15

Subtract 2x on both sides

3x - 2x = 15

x = 15

15 × 3 = 45 years old

Hope this helps!! :)

Please let me know if you have any questions

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( for graph , see attachment ) .

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Answer:

a=200 +0.253*50=212.65

So the value of height that separates the bottom 60% of data from the top 40% is 212.65. And rounded would be 212.7.  

Step-by-step explanation:

1) Previous concepts

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".  

2) Solution to the problem

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z=\frac{x-\mu}{\sigma}

For this part we want to find a value a, such that we satisfy this condition:

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P(X   (b)

Both conditions are equivalent on this case.

As we can see on the figure attached the z value that satisfy the condition with 0.60 of the area on the left and 0.40 of the area on the right it's z=0.253. On this case P(Z<0.253)=0.60 and P(z>0.253)=0.4

If we use condition (b) from previous we have this:

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P(Z

But we know which value of z satisfy the previous equation so then we can do this:

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And if we solve for a we got

a=200 +0.253*50=212.65

So the value of height that separates the bottom 60% of data from the top 40% is 212.65. And rounded would be 212.7.  

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3 years ago
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