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Based on the properties of similar triangles, the two true statements are:
- ΔAXC ≅ ΔCXB.
- ΔACB ≅ ΔAXC.
In Mathematics, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Based on the properties of similar triangles, we have the following points:
- ∠A in ΔAXC matches ∠A in ΔABC and ∠C in ΔCXB.
- ∠C in ΔAXC matches ∠B in ΔABC and ∠B in ΔCXB.
- ∠X in ΔAXC matches ∠C in ΔABC and ∠X in ΔCXB.
In this scenario, we can can logically deduce that the two true statements are:
- ΔAXC is congruent to ΔCXB (ΔAXC ≅ ΔCXB).
- ΔACB is congruent to ΔAXC (ΔACB ≅ ΔAXC).
Read more on similar triangles here: brainly.com/question/7411945
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Answer:
z = -0.139
The data provide evidence that this particular meets the government regulation
Step-by-step explanation:
To determine if the the data provide evidence that this particular meets the government regulation, we need to define a null and alternative hypothesis as:
H0: m = 0.3
H1: m > 0.3
where m is the population mean NOX emission.
Then, we need to find the appropriate statistic. So, taking into account that the model follows a Normal distribution with standard deviation equal to 0.05, the statistic is equal to:
where x is the mean of the sample, m is 0.3 g/mi, s is the population standard deviation and n is the size of the sample.
Therefore, replacing x by 0.298, m by 0.3, s by 0.05 and n by 12, we get that the test statistic is:
Finally, we need to find the p-value using the normal distribution table as:
p-value = P(z > -0.139 ) = 0.4443
So, taking into account that the p-value is big value, we can conclude that we don't reject H0. It means that the data provide evidence that this particular meets the government regulation.