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3 years ago

Find the length of the hypotenuse

Mathematics

1 answer:

denpristay [2]3 years ago

4 0

Answer: The answer is “10cm”

Step-by-step explanation: To get to this answer we first need to know the formula for find the hypotenuse which is a^2 + b^2 = c^2. A and B are the two sides in this case a and b are 8 cm and 6 cm. Then you plug in the values into the equation, it looks like this 8^2 + 6^ = c^2 once you solve you get 64 + 36 = c. When you add 64 and 36 you get 100 but their is one more step. You must find the square root of 100 which is 10. So your answer for the hypotenuse is “10cm”

Have a nice day!

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Answer:

$t=\frac{435-430}{\frac{29}{\sqrt{23}}}=0.827$

The degrees of freedom are given by:

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And the p value taking in count that we have a bilateral test we got:

$p_v =2*P(t_{(22)}>0.827)=0.417$

Since the p value is higher than the significance level of 0.05 we have enough evidence to conclude that the true mean is not significantly different from 430 the required value

Step-by-step explanation:

Information given

$\bar X=435$ represent the mean for the weight

$s=\sqrt{841}=29$ represent the sample standard deviation

$n=23$ sample size

$\mu_o =430$ represent the value that we want to verify

$\alpha=0.05$ represent the significance level

t would represent the statistic

$p_v$ represent the p value

System of hypothesis

We are trying to proof if the filling machine works correctly at the 430 gram setting, so then the system of hypothesis for this case are:

Null hypothesis: $\mu = 430$

Alternative hypothesis: $\mu \neq 430$

In order to cehck the hypothesis the statistic for a one sample mean test is given by

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

Replacing the info given we have this:

$t=\frac{435-430}{\frac{29}{\sqrt{23}}}=0.827$

The degrees of freedom are given by:

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And the p value taking in count that we have a bilateral test we got:

$p_v =2*P(t_{(22)}>0.827)=0.417$

Since the p value is higher than the significance level of 0.05 we have enough evidence to conclude that the true mean is not significantly different from 430 the required value

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