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3 years ago

Mother is m years old, and she is four times as old as her daughter. How much older is the mother than her daughter?

Mathematics

1 answer:

yuradex [85]3 years ago

5 0

The mother is older than her daughter by $\frac{3}{4}m$ years

Step-by-step explanation:

Mother is m years old, and she is four times as old as her daughter.

we need to find how much older the mother is than her daughter

Put the age of mother equal 4 times the age of daughter
Find the age of daughter
Subtract the age of daughter from the age of mother to find how much older the mother than her daughter

∵ The mother's age = m

∵ Her age is four times as old as her daughter

∴ m = 4 × daughter's age

- Divide both sides by 4

∴ $\frac{1}{4}m$ = daughter's age

- Subtract the daughter's age from her mother's age

∵ The difference of their ages = m - $\frac{1}{4}m$

- Change 1 m to a fraction of denominator 4, then 1 m = $\frac{4}{4}m$

∴ The difference between their ages = $\frac{4}{4}m$ - $\frac{1}{4}m$ = $\frac{3}{4}m$

∴ The mother is older than her daughter by $\frac{3}{4}m$ years

The mother is older than her daughter by $\frac{3}{4}m$ years

Learn more:

You can learn more about the fractions in brainly.com/question/1648978

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Step-by-step explanation:

1) Data given and notation

$\bar X$ represent the sample mean

$s$ represent the standard deviation for the sample

$n$ sample size

$\mu_o =20$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

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Alternative hypothesis: $\mu > 20$

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$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

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