MATHEMATICS COLLEGE

2. Suppose the measures of the interior angles of a convex octagon are eightnumbers, each separated by a value of 1 degree from its neighbors. Find
the measure of the second smallest angle.
118°
131°
132.5°
142°
None of these answers are correct.

Answers

Answer 1
Answer:

Answer:  132.5 degrees  (choice C)

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Explanation:

The interior angles are consecutive numbers such as 1,2,3,... or 7,8,9... and so on. The gap between any two adjacent neighbors is 1.

For any polygon with n sides, the interior angles add up to 180(n-2)

We have n = 8 sides so the interior angles sum to 180(n-2) = 180(8-2) = 1080 degrees.

Any octagon has its interior angles add up to 1080 degrees.

-----------------------------

Let x be the smallest angle. The next angle up is x+1. After that is x+2 and so on until we reach x+7 as the 8th angle.

Add up those 8 angles, set the sum equal to 1080 and solve for x

x+(x+1)+(x+2)+(x+3)+(x+4)+(x+5)+(x+6)+(x+7) = 1080

8x+28 = 1080

8x = 1080-28

8x = 1052

x = 1052/8

x = 131.5

This is the smallest angle. The next angle up or the second smallest angle is x+1 = 131.5+1 = 132.5 degrees  (choice C)

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Of the 50 states in the Uinted States, 26 have more than four million people. What fraction of US states states have LESS than four million people?

Answers

Answer:

12 / 25 = fraction. 48% = percent.

Step-by-step explanation:

If 26 states have more than four million people then we would do 50 - 26 = 24 (assuming that a state does not have exactly four million people. That would be 24 / 50 = 12 / 25 if you want to simplify it.

In a poll conducted by the Gallup organization in April 2013, 48% of a random sample of 1022 adults in the U.S. responded that they felt that economic growth is more important than protecting the environment. We can use this information to calculate a 95% confidence interval for the proportion of all U.S. adults in April 2013 who felt that economic growth is more important than protecting the environment. Make sure to include all steps.

Answers

Answer:

The  95% confidence interval is  0.449 < p < 0.48 + 0.511

Step-by-step explanation:

From the question we are told that  

     The sample proportion is \r p = 0.48

      The sample size is n = 1022

Given that the confidence level is 95%  then the level of significance is mathematically evaluated as

       \alpha = 100 - 95

       \alpha = 5 \%

       \alpha = 0.05

Next we obtain the critical value of  (\alpha )/(2) from the z-table , the value is

     Z_{(\alpha )/(2) } =Z_{(0.05 )/(2) }= 1.96

The reason we are obtaining critical value of    (\alpha )/(2) instead of    \alpha is because  

 \alpha represents the area under the normal curve where the confidence level interval (  1-\alpha ) did not cover which include both the left and right tail while    (\alpha )/(2) is just the area of one tail which what we required to calculate the margin of error

NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)

    Generally the margin of error is mathematically represented as

         E = Z_{(\alpha )/(2) } * \sqrt{(\r p (1- \r p ))/(n) }

substituting values

          E = 1.96* \sqrt{(0.48 (1- 0.48 ))/(1022) }

          E = 0.03063

The 95% confidence interval is mathematically represented as

      \r p - E < p < \r p + E

substituting values

       0.48 - 0.03063 < p < 0.48 + 0.03063

       0.449 < p < 0.48 + 0.511

Need answer asap The manager of a video game store found that 35 of the 140 people who preordered the latest baseball game canceled their orders the day before the game was released. He used that data to create a simulation to predict the probability that future customers will cancel their preorders.

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StartFraction 1 over 16 EndFraction
StartFraction 1 over 8 EndFraction
One-fourth
One-half

Answers

Answer:

1/4 will cancel

Step-by-step explanation:

Simplify the fraction

35

-----

140

Divide the top and bottom by 7

5

---

20

divide the top and bottom by 5

1

----

4
I think it from 4 how I know this cause I tried

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1. $140 for 18 ft?

Answers

Answer: 17.5

Step-by-step explanation:

Someone please tell me and also what b is

Answers

18(b+19)=18
(18)(b)+(18)(19)=18
18b+342=18
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18b/18=-324/18
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(I hope i wasn’t too late)
I think it is number two because 19-18=1 but I might be wrong.

What is the slope of line segment E F?
A)1/3
B)3/2
C)2/3
D)-3/2

Answers

Step-by-step explanation:

the picture even tells you the formula.

what ? you cannot do these simple subtractions yourself ? what don't you understand there ? please tell me, so that I can help you with that.

as the formula says, the slope is y difference / x difference between the 2 points.

E = (-2, -4)

F = (2, 2)

for the difference calculation it is just important that you do both in the same direction.

x difference = 2 - -2 = 4

y difference = 2 - -4 = 6

so the slope is 6/4 = 3/2

therefore, B 3/2 is the correct answer

that's it. that is all there was to this.

FYI - the slope indicates how many units y changes, when x changes a certain amount of units when you go from one point on the line to another.

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