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2 years ago

Help! I need to know how to solve this

Mathematics

1 answer:

bagirrra123 [75]2 years ago

7 0

Every triangle measures 180 degrees.
In order to get the answer you need to add every equation and set it equal to 180.

2x+4+2x-9+x=180
Combine like terms.
5x-5=180
Add 5 to the other side.
5x=185
Divide by 5.
x = 37

Now, plug 37 in for every x.
Angle A: 2(37)-9
Angle B: 2(37)+4
Angle C: 37

The measures are:
Angle A = 65
Angle B = 78
Angle C = 37

Hope this helps!

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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 $\mu = 5 \ year$

The sample size is n = 20

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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