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N76
13 days ago
9

Triangle E F G is shown. Which statements regarding Triangle E F G are true? Select three options. E F + F G greater-than E G E

G + F G greater-than E F E G minus F G less-than E F E F minus F G greater-than E G E G + E F less-than F G
Mathematics
2 answers:
Zina [3.9K]13 days ago
8 0

Answer:

1) E F + F G is greater than E G

2) E G + F G is greater than E F

3) E G minus F G is less than E F

Step-by-step explanation:

I answered this correctly on Edg

zzz [4K]13 days ago
4 0

Answer:

The correct statements are options 1 (E F + F G > E G), 2 (E G + F G > E F), and 5 (E G + E F < F G).

Step-by-step explanation:

We have triangle EFG.

For any triangle with sides a, b, and c, these inequalities hold:

a+b>c\\ \\a+c>b\\ \\b+c>a

Specifically for triangle EFG:

  • EF+FG>EG;
  • EG+GF>EF;
  • FE+EG>FG.

Thus, the true statements are options 1, 2, and 5.

Statements 3 and 4 are incorrect.

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a) Null hypothesis:\mu \geq 10

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Given that the p-value is lower than the significance threshold in this situation, we have sufficient grounds to reject the null hypothesis.

c) p_v =P(t_{17}

In this case, since the p-value exceeds the significance threshold, we have adequate evidence to FAIL to reject the null hypothesis.

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Step-by-step explanation:

1) Provided data and references

\bar X represents the average of the samples

s denotes the standard deviation of the samples

n=18 indicates the number of samples

\mu_o =10 is the value we are examining

\alpha defines the significance level for the test.

t represents the specific statistic of interest

p_v indicates the p-value relevant to the test (the variable of concern)

Define the null and alternative hypotheses.

To assess if the true mean is at least 10 hours, we must set up a hypothesis:

Part a

Null hypothesis:\mu \geq 10

Alternative hypothesis:\mu < 10

If we consider the sample size being less than 30 and the population deviation unknown, it’s more appropriate to use a t-test to compare the actual mean with the reference value, calculated as:

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

Part b

In this scenario t=-2.3, \alpha=0.05

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Since this is a left-tailed test, the p-value is determined by:

p_v =P(t_{17}

In this instance, with the p-value being less than the significance level, we have sufficient evidence to reject the null hypothesis.

Part c

For this situation t=-1.8, \alpha=0.01

We need to find the degrees of freedom df=n-1=18-1=17

For the left-tailed test, the p-value is given by:

p_v =P(t_{17}

In this case, since the p-value is above the significance level, we have enough grounds to FAIL to reject the null hypothesis.

Part d

For this case t=-3.6, \alpha=0.05

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Since we are conducting a left-tailed test, the p-value is calculated as:

p_v =P(t_{17}

Here, with the p-value being lower than the significance threshold, we can reject the null hypothesis.

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