Based on the information marked in the diagram, ABC and DEF must be congruent.True Or False?
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Applying the HL congruence theorem, the information marked in the diagram cannot be congruent, so it is FALSE.
What is the HL Congruence Theorem?
The HL congruence theorem states that if the corresponding legs of two right traingles are congruent, and the their hypotenuse are also congruent, then the triangles are congruent.
From the information given, we are not told if the hypotenuse of the right triangles are congruent, so we can't apply the HL congruence theorem to prove they are congruent. The answer is FALSE.
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Related Questions
Which product is positive?
Evaluate: 8x6 + (12-4) divided by 2
The difference of a number h and 8 is greater than 12 and less than 22
A sample of 16 items from population 1 has a sample variance 5.8 and a sample of 21 items from population 2 has a sample variance 2.4. Test the following hypotheses at the .05 level of significance. H0: Population 1 Variance < Population 2 Variance Ha: Population 1 Variance > Population 2 Variance a. What is the p-value
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Answer:
D=[0, 64]
Step-by-step explanation:
The domain of a function is the interval of all possible values of the independent variable. In this situation, the independent variable is the number of people on the ferris wheel 'p'. Since the capacity is 64 people, the possible interval for 'p' is from 0 to 64 people. Therefore, the domain is;
D=[0, 64]
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Answer:
We conclude that the mean is greater than 25.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 25
Sample mean, = 27
Sample size, n = 100
Alpha, α = 0.05
Sample standard deviation, s = 6.5
First, we design the null and the alternate hypothesis
We use One-tailed(right) z test to perform this hypothesis.
Formula:
Putting all the values, we have
Now,
Since,
We reject the null hypothesis and accept the alternate hypothesis.
Thus, the mean is greater than 25.
Final answer:
The null hypothesis is the mean is equal to 25 and the alternative is that the mean is greater than 25. Using a one-sample t-test and 0.05 significance level, the calculated statistic results in rejection of the null hypothesis. Thus, there is sufficient evidence to suggest that the mean daily census in pediatrics is greater than 25.
Explanation:
1. The hypotheses for this scenario are that the null hypothesis (H0): the mean daily census in the pediatrics service is equal to 25, and the alternative hypothesis (H1): the mean daily census in the pediatrics service is greater than 25.
2. The appropriate test for this scenario would be a one-sample t-test, given that we have a sample mean, a population mean, a standard deviation, and we're examining a single group of hospitals.
3. The decision rule would be: if the p-value of our t-test is less than the significance level (α=.05), we reject H0 and accept H1.
4. The test statistic is calculated as follows: t = (Sample Mean-Population Mean)/(Sample Standard Deviation/ √number of observations), this would give us (27-25)/(6.5/√100) = 3.08.
5. Since 3.08 is greater than the critical value for a 0.05 significance level, we reject the null hypothesis. Therefore, there is sufficient evidence to conclude that the mean daily census in the pediatrics service is greater than 25.
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Hope this helps!
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B-The purpose of (1) inferential (2) descriptive statistics is to use the limited data from a sample as the basis for making general conclusions about the population.
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Answer:
A-The purpose of (2)descriptive statistics is to simplify the organization and presentation of data.
B-The purpose of (1) inferential statistics is to use the limited data from a sample as the basis for making general conclusions about the population.
Step-by-step explanation:
The descriptive statistics is used to make large data presentable into usable short forms, without which it would look impossible to solve. We draw a sample from the population and find its mean or draw histograms for the frequency distributions. This is descriptive statistics.
The inferential statistics is used to make inferences and conclusions from limited data given from a population. We do the hypothesis testing for the random samples obtained from larger populations. The hypothesis tests or the confidence intervals help us decide whether the rseults are accepted or not.
Final answer:
Descriptive statistics is used to summarize and organize data from a sample, such as providing the average or frequency of a variable. Inferential statistics, on the other hand, uses this sample data to make broad generalizations about the population.
Explanation:
The two major categories of statistical techniques are inferential statistics and descriptive statistics. The general purpose of descriptive statistics is to simplify the organization and presentation of data. They provide simple summaries about the sample and the measures. For example, we may want to know the average, maximum, minimum, or frequency of some variable.
On the other hand, inferential statistics involve using the limited data from a sample as the basis for making general conclusions about the population. They also include the theory of hypothesis testing, which is a method for testing statistical results. For example, inferential statistics would be used to determine if a difference observed between groups is a real one or if it might have happened by chance in this study.
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