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3 years ago

Which is the most logical order of statements and justifications I, II, III, and IV to complete the proof?

Mathematics

2 answers:

Tamiku [17]3 years ago

6 0

I think its B IV,III, I, II

Verdich [7]3 years ago

5 0

Answer:

IV,III,I,II

Step-by-step explanation:

We are given that a triangle ABC in which three medians are given .

We are given a proof of three medians of a triangle which intersect at common point.

We have to find which is the most logical order of statement and justifications I,II,III and IV to complete the proof.

Statement:Point F is the mid- point of segment AB and point E is the mid-point of segment AC.

Draw segment BE and draw segment FC.

Justification: By construction

Statement: Point G is the point of intersection of segment BC and segment FC.

Justification: Intersecting lines postulate

Statement:Draw segment AG.

Justification: By construction

Statement:Point D is the mid- point of intersection between segment AG and segment BC.

Justification: Intersecting lines postulate

Statement:Point H lies on segment AG such that $AG\cong GH$

Justification: By construction

Step:IV $FG\parallel BH,GE\parallel CH$

Justification: Midpoint segment theorem

Step III. $GC\parallel BH,BG\parallel CH$

Justification: Substitution

Step I.BGCH is parallelogram

Justification: By property of parallelogram (Opposite sides are parallel)

StepII: $BD\cong DC$

Justification: Property of parallelogram (diagonals of parallelogram bisect each other)

Statement: AD is median

Justification: Definition of median

Answer:IV,III,I,II

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Sheldon picked 4 4/10 kg but 15 kg were rotten and had to be thrown away. How many kilograms of tomatoes were not rotten?

nataly862011 [7]

Answer:

10.6 kg

Step-by-step explanation:

first convert 4 4/10 to kg

4/10 is equal to .4

so 4.4kg were rotten

subtract from total

15-4.4=10.6 kg

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3 years ago

Fernando makes 1/6 cup of apple juice with 1/3 cup of grape juice which shows a correct comparison of these two fractions

Alenkasestr [34]

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3 years ago

Historically, a certain region has experienced 92 thunder days annually. (A "thunder day" is day on which at least one instance

DiKsa [7]

Answer:

We conclude that the mean number of thunder days is less than 92.

Step-by-step explanation:

We are given that Historically, a certain region has experienced 92 thunder days annually.

Over the past fifteen years, the mean number of thunder days is 72 with a standard deviation of 38.

Let $\mu$ = mean number of thunder days.

So, Null Hypothesis, $H_0$ : $\mu \geq$ 92 days {means that the mean number of thunder days is more than or equal to 92}

Alternate Hypothesis, $H_A$ : $\mu$ < 92 days {means that the mean number of thunder days is less than 92}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean number of thunder days = 72

s = sample standard deviation = 38

n = sample of years = 15

So, test statistics = $\frac{72-92}{\frac{38}{\sqrt{15} } }$ ~ $t_1_4$

= -2.038

The value of z test statistics is -2.038.

Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% significance level the t table gives critical value of -1.761 at 14 degree of freedom for left-tailed test.

Since our test statistics is less than the critical value of t as -2.038 < -1.761, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean number of thunder days is less than 92.

7 0

3 years ago

If the two triangles shown below are similar based on the giveninformation, complete the similarity statement, otherwise choose

SVETLANKA909090 [29]

1) Two triangles are similar if they have congruent angles and proportional sides (for each corresponding leg).

2) So let's check whether there are similar triangles by setting a proportion: