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3 years ago

4. Given: a + m = n, n= 4a; Prove: m = 3a

Mathematics

1 answer:

IrinaVladis [17]3 years ago

4 0

Answer:

<em>Proof below</em>

Step-by-step explanation:

<u>Algebraic Manipulation</u>

It refers to the process of modifying algebraic expressions, often into a simpler form or more easily handled and dealt with.

It also helps us to prove some identities.

We are given the relations:

a + m = n

n = 4a

Substituting the last equation in the first, we have:

a + m = 4a

Subtracting a on both sides of the equation:

m = 4a - a

Simplifying:

m = 3a

Hence proved

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Georgianna claims that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons.

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Answer:

The condition are

The Null hypothesis is $H_o : \mu = 5$

The Alternative hypothesis is $H_a : \mu < 5$

The check revealed that

There is sufficient evidence to support the claim that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 5 \ year$

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The sample mean is $\= x = 4.6 \ years$

The standard deviation is $\sigma = 2.2 \ years$

The Null hypothesis is $H_o : \mu = 5$

The Alternative hypothesis is $H_a : \mu < 5$

So i will be making use of $\alpha = 0.05$ level of significance to test this claim

The critical value of $\alpha$ from the normal distribution table is $Z_\alpha = 1.645$

Generally the test statistics is mathematically evaluated as

$t = \frac{\= x - \mu}{ \frac{\sigma }{\sqrt{n} } }$

substituting values

$t = \frac{ 4.6 - 5}{ \frac{2.2}{\sqrt{20} } }$

$t = -0.8131$

Looking at the value of t and $Z_{\alpha }$ we see that $t < Z_{\alpha }$ so we fail to reject the null hypothesis

This implies that there is sufficient evidence to support the claim that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons.

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