MATHEMATICS HIGH SCHOOL

The converse of a conditional statement is "If the sum of the exterior angles of a figure is 360°, then the figure is a polygon.” What is the inverse of the original conditional statement?

A. If a figure is a polygon, then the sum of the exterior angles is 360°.

B. If the sum of the exterior angles of a figure is not 360°, then the figure is not a polygon.

C. If the sum of the exterior angles of a figure is 360°, then the figure is not a polygon.

D. If a figure is not a polygon, then the sum of the exterior angles is not 360°.

Answers

Answer 1

Answer:

Answer:

The correct option is D.

Step-by-step explanation:

Converse statement : If the sum of the exterior angles of a figure is 360°, then the figure is a polygon.

Now, to form a converse statement, the conclusion becomes the hypothesis and the hypothesis becomes the conclusion.

So, to form the original statement of the given converse statement : Hypothesis will become conclusion and the conclusion becomes our hypothesis.

⇒ Original Statement : The figure is a polygon if the sum of the exterior angles of a figure is 360°.

Now to form the inverse we need the negation of both hypothesis and the conclusion.

Hence, The inverse of the original statement is : If a figure is not a polygon, then the sum of the exterior angles is not 360°.

Therefore, The correct option is D.

Answer 2

Answer: The answer is D because the statement is saying it's not a polygon if the sum of the exterior angles is not 360 which is the opposite of the statement

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Answers

x - 1st number
y - 2nd number
z - 3rd number

$x=3y\n y=2z\n (x+y+z)/(3)=18\n\n x=3y\n z=(y)/(2)\n x+y+z=54\n\n 3y+y+(y)/(2)=54\n 6y+2y+y=108\n 9y=108\n y=12\n\n z=(12)/(2)\n z=6\n\n x=3\cdot12\n x=36\n\n \boxed{36,12,6}$

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Answers

Answer:

$r= \sqrt[3]{(3V)/(4\pi)}$

Step-by-step explanation:

$V = (4)/(3) \pi r^3 \n\n3V = 4\pi r^3 \n\nr^3 = (3V)/(4\pi)\n\n\huge \purple {r= \sqrt[3]{(3V)/(4\pi)}}$

Recent research suggests that depression significantly increases the risk of developing dementia later in life (BBC News, July 6, 2010). In a study involving 949 elderly persons, it was reported that 22% of those who had depression went on to develop dementia, compared to only 17% of those who did not have depression.a. Choose the relevant population and the sample. (You may select more than one answer. Bold the answer(s) that are correct.)1. The sample consists of all elderly people.2. The sample consists of 949 elderly people.3. The population is all younger and elderly people.4. The population is all elderly people.b. Do the numbers 22% and 17% represent the population parameters or the sample statistics? Bold the answer that is correct.Population parametersSample Statistics

Answers

Answer:

2. The sample consists of 949 elderly people

4. The population is all elderly people

B. The numbers 22% and 17% represents the sample statistics

Step-by-step explanation:

The study was based on a recent research that suggest that depression significantly increases risk of dementia later in life, so for every result gotten from this study, it is tied to only the samples chosen for the aim of the study which are the 949 elderly people.

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Answers

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Answers

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Answers

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