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zhannawk [14.2K]

3 years ago

11

Given the lengths of two sides of a triangle, find the range for the length of the third side. (Range means find between which t

wo numbers the length of the third side must fall.) Write an inequality. a 11.5 and 23.6

1 answer:

Dahasolnce [82]3 years ago

4 0

Answer:

$12.1 < Y < 35.1$

Step-by-step explanation:

Given

Sides: 11.5 and 23.6

Required

Determine the range of the third side

Let the third side with Y

<em>Two of the following conditions must be satisfied to calculate the range of the third side</em>

<em></em> $11.5 + Y > 23.6$

$23.6+ Y > 11.5$

$11.5 + 23.6 > Y$

We'll solve one after other

1. $11.5 + Y > 23.6$

$Y > 23.6 - 11.5$

$Y > 12.1$

2. $23.6+ Y > 11.5$

$Y > 11.5- 23.6$

$Y > -12.1$

3. $11.5 + 23.6 > Y$

$35.1 > Y$

$Y < 35.1$

Inequalities with negative can't be used' So, we have

$Y > 12.1$ and $Y < 35.1$

Rewrite inequality

$12.1 < Y$ and $Y < 35.1$

Combine inequality

$12.1 < Y < 35.1$

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Answer:

$z=\frac{1.02-1}{\frac{0.04}{\sqrt{40}}}=3.162$

$p_v =2*P(z>3.162)=0.0016$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to to reject the null hypothesis, so we can conclude that the true mean is different from 1 pound at 5% of signficance.

Step-by-step explanation:

Data given and notation

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$\sigma=0.04$ represent the population standard deviation

$n=40$ sample size

$\mu_o =1$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

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

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We need to conduct a hypothesis in order to check if the true mean is equal to 1 pound or no :

Null hypothesis: $\mu =1$

Alternative hypothesis: $\mu \neq 1$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

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z-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".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{1.02-1}{\frac{0.04}{\sqrt{40}}}=3.162$

P-value

Since is a two-sided test the p value would be:

$p_v =2*P(z>3.162)=0.0016$

Conclusion

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