In a certain pentagon, the interior angles are $a^\circ,$ $b^\circ,$ $c^\circ,$ $d^\circ,$ and $e^\circ,$ where $a,b,c,d,e$ are integers strictly less than $180$. ("strictly less than $180$" means they are "less than and not equal to" $180$.) if the median of the interior angles is $61^\circ$ and there is only one mode, then what are the degree measures of all five angles?

Answers

Answer 1

The degree measures of all of these angles are 60, 61, 61, 179, 179.

How to solve for the angle measures

Given that the 3rd largest angle that we have here is 61 degrees, the three angles are not going to be more than 183.

The sum of all the angles must be 540 degrees. The total of the largest of the numbers is less that 179 x 2 = 358 degrees.

The sum of the smallest three would be

540 - 358 = 182 degrees

Therefore the possible sets of these angles would be  60, 61, 61, 179, 179 degrees

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Answer 2

Answer:

61, 61, 61, 178, 179

Explanation:

The five interior angles of any pentagon add up to 3*180= 540

If the median is 61, then we know the three smallest angles are each no more than 61, and so they add up to at most 3*61= 183 degrees. This means the two largest angles must add up to at least 540-183= 357 degrees. Since 178+179=357, and since the angles are all integers strictly less than 180, the only possibilities for the two largest angles are 178, 179 or 179, 179. 

We consider these possibilities one at a time.

If the two largest angles are 178 and 179, then the three smallest angles add up to exactly 183, so they must each be exactly 61. Thus, one set of angles that satisfy the conditions in the problem is 61, 61, 61, 178, 179.

If the two largest angles are 179 and 179, then the three smallest angles add up to 182. The only way this can happen is for one of them to be 60 and the other two to be 61, but in this case, the set of angles would have more than one mode. So we can rule out this answer.

In conclusion, the five angles must be 61, 61, 61, 178, 179.


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Cyber savvy is the computer and internet knowledgeable person who deals with the cyber system. Cyber savvy can overcome the indifferences by launching awareness campaigns.

What are human rights violations?

Human rights are the fundamental freedom and liberties that every individual have over their life. The violation of these rights can be due to denial or due to genocide, murder, torture, etc.

Campaigns can be used to overcome the indifference that deals with the violation act of the humans. Cyber help can be used to connect to a large number of people to make them aware of the negative impact of human rights violations.

Therefore, awareness campaigns can be launched to aware of violation acts.

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What effect does the modality of this exhibit most likely have on the visitors to the museum?visitors can use the gustatory modality to taste the tomatoes picked by laborers.visitors can use the auditory modality to hear stories about modern enslavement first-hand.visitors can use the tactile modality to feel the weight of the heavy tomato buckets.visitors can use the logic modality to calculate and compare earnings.

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Answer:

Visitors can use the tactile modality to feel the weight of the heavy tomato buckets.

Explanation:

Got it right

Which of these refers to the average distance or difference of a score from the mean of the data set?

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The influential statistics are used to analyze the data sample so that a conclusion about the information is reached. The standard deviation is the average distance and the mean of the data set.

What is the standard deviation?

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This allows the understanding of the data collected by the analyzer and lets the easy comparison of the information that was collected for the analysis of the research topic.

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Which of these pieces of data about an animal at the zoo is considered numerical data?

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Explanation:

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Answer:

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Various poets address the element of death in their poems by referring to it as something dark.

How poets address the element of death

Various poets address the element of death in their poems by mentioning something that relates to dark.

Death is used as a motif when it uses a symbol to represent death.

Thus, poets address the element of death in their poems by referring to it as something dark.

The complete question is below:

A common motif in the poetry of this unit is death. How do the various poets address the element of death?

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Two football players with mass 80 kg and 120 kg run directly toward each other with speeds of 8 m/s and 10 m/s respectively. if they grab each other as they collide, the combined speed of the two players just after the collision would be

Answers

The combined speed after the collision is -2.8 m/s.

How to get the combined speed?

Here we must have conservation of momentum, where momentum is the product between mass and velocity.

At the beginning, one of the players has a mass of 80kg and a velocity of 8m/s, so its momentum is:

P₁ = 80kg*(8m/s) = 640 kg*m/s

The other player has a mass of 120 kg and runs in the opposite direction at a speed of -10m/s (the negative sign is because of the direction). So its momentum is:

P₂ = 120kg*(-10m/s) = -1200 kg*m/s

The initial total momentum is:

P = P₁ + P₂ = 640 kg*m/s + ( -1200 kg*m/s) = -560 kg*m/s

At the end, the move together as a mass of (80kg + 120kg) = 200kg with a velocity V.

Such that the final total momentum is equal to the initial total momentum.

So we must have:

200kg*V =  -560 kg*m/s

V = (-560 kg*m/s)/200kg = -2.8 m/s.

The combined speed after the collision is -2.8 m/s.

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Evidence such as spectra from distant stars suggests that the universe is... what?

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Answer:

jake

Explanation:

Answer:

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Explanation:

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What is complex number?

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a+bi

Here, (a) is the real part while (b) is the imaginary part.

The complex number which need to convert into its polar representation is,

n=-4i

It can be rewritten as,

n=0-4i

The radius r of the polar form is,

r²=0²+(-4)²

r²=0+16

r=4

The value of cos theta is,

tan θ=0/-4

θ=tan⁻¹(0)

θ=π

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z=rcos θ+(r sin θ)i

z=-4(cos π+ isin π)

Thus, the expression which represent the polar form of complex number -4i when converted into the polar form is 4(cos π+ isin π)

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Dr. smithe is designing a study to investigate whether aggressive preschoolers are likely to become aggressive adolescents. dr. smithe should use

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Answers

By definition of probability, the probability that a student surveyed was either a boy or had a bicycle is 62%.

Definition of Probabitity

Probability is the greater or lesser possibility that a certain event will occur.

In other words, the probability is the possibility that a phenomenon or an event will happen, given certain circumstances. It is expressed as a percentage.

Union of events

The union of events, AUB, is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs. AUB is read as "A or B".

The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:

P(A∪B)= P(A) + P(B) -P(A∩B)

The intersection of events, A ∩ B, is the event formed by all the elements that are, at the same time, from A and B. That is, the event A ∩ B is verified when A and B occur simultaneously.

Events and probability in this case

In first place, let's define the following events:

A: The event that a student surveyed was a boy.B: The event that  a student surveyed had a bicycle.

Then you know:

P(A)= [tex]\frac{490}{1000}[/tex]=0.49= 49%P(B)= [tex]\frac{320}{1000}[/tex]= 0.32= 32%P(A and B)= P(A∩B)= [tex]\frac{190}{1000}[/tex]= 0.19= 19% [320 students had bicycles. Of those who had bicycles, 130 were girls. Then, 190 were boys.]

In this case, considering the definition of union of eventes, the probability that a student surveyed was either a boy or had a bicycle is calculated as:

P(A∪B)= P(A) + P(B) -P(A∩B)

P(A∪B)= 0.49 + 0.32 -0.19

P(A∪B)= 0.62= 62%

Then, the probability that a student surveyed was either a boy or had a bicycle is 62%.

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Answer:

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Answer:

Death Note

Explanation:

Now this is how Death Note works in a note book ya wrote someone first and last name and then they die IS THAT GREAT oki death is near but now as close as you think your probaly stillyounge so live you life to the fullest and BE CONFUSSLED

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Answer:

A: anger is an emotion, aggression is a description for behavior

Explanation:

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In ring theory, a commutative ring can be defined as a ring in which the multiplication operation is considered to be commutative in nature.

Let R represent a commutative ring with characteristic K.

Therefore, we have: Kr = 0∀r ∈ R.

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Answers

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The contract really worth today if global enterprises can earn 12 percent on its money will be 2.58 million.

What is a contract signing?

The participants that sign the agreement agree to the statement's provisions as well as their commercial duties.

Global enterprises have just signed a $3 million contract.

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Then the contract really worth today if global enterprises can earn 12 percent on its money will be

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Answer:

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The speaker which begins the poem has the primary transformation sought overall is recapturing of a sense of life's possibilities.

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Here, the primary transformation sought overall is recapturing of a sense of life's possibilities.

The speaker which begins the poem has the primary transformation sought overall is recapturing of a sense of life's possibilities.

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Answer:

Sunnis is the answer on OW.

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Answers

The best description of overall structure of the part of the text is it explains what causes Pasteur to want to find a cure for rabies.

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Louis Pasteur is a famous French chemist and microbiologist. He is known for discovering the cure for rabies.

He is also known for preventing diseases in silk eggs. Pasteurization is the process of preventing microbes that spoil milk or other beverages. The process is in his name.

Thus, the correct option is A, it explains what causes Pasteur to want to find a cure for rabies.

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2. Now, let's turn our attention to memory strategies. (10 points) a. List two of the memory strategies you have learned. b. Provide specific examples of how you could use each memory strategy

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