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2 years ago

In a polygon with 100 sides, 99 of the angles add up to 17,595°. What is the measure of the last angle?

Mathematics

1 answer:

dalvyx [7]2 years ago

7 0

Answer:

45 degrees

Step-by-step explanation:

The formula to find the sum of all the interior angles in an "n-gon" (n is a variable that stands for the numbers of sides, ex) 20-gon --> 20 sided polygon) is $180(n-2)$ .

Let's plug in 100 to find the sum of all the interior angles in a 100-gon.

$180(100-2)$

I would rather distribute than simplify the parentheses and have to multiply 180 by 98.

So:

$18000-360$

= $17640$ degrees

[REMEMBER, IT WAS NOT GIVEN THAT THIS POLYGON IS REGULAR, SO DO NOT DIVIDE 17640 BY 100]

Now to find the last angle, we can just subtract since we are given the value of 99 of the 100 angles (17595 degrees).

So the last angle is $17640-17595=45$ degrees

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Luden [163]

The problem statement gives a relation between the amount removed from one bag and the amount removed from the other. It asks for the amount remaining in each bag. Thus, there are several choices for variables in this problem, some choices resulting in more complicated equations than others.

Let's do it this way: let x represent the amount remaining in bag 1. Then the amount removed from bag 1 is (100-x). The amount remaining in bag 2 is 2x, so the amount removed from that bag is (100-2x). The problem statement tells us the relationship between amounts removed:

... (100 -x) = 3(100 -2x)

... 100 -x -3(100 -2x) = 0 . . . . . . subtract the right side

... 5x -200 = 0 . . . . . . . . . . . . . . eliminate parentheses and collect terms

... x -40 = 0 . . . . . . . . . . . . . . . . .divide by 5

... x = 40 . . . . . . . . . . . . . . . . . . . add 40

40 kg is left in the first bag
80 kg is left in the second bag

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Check

The amount removed from the first bag is 60 kg. The amount removed from the second is 20 kg. The amount removed from the first bag is 3 times the amount removed from the second bag, as described.

4 0

3 years ago

Solve for n 10n+0.3=0.1+0.3

galina1969 [7]

Answer:

0.01 is the awnser can you put me as the brainlest awnser

Step-by-step explanation:

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3 years ago

The average human gestation period is 270 days with a standard deviation of 9 days. The period is normally distributed. What is

Anna35 [415]

Answer:

Probability that a randomly selected woman's gestation period will be between 261 and 279 days is 0.68.

Step-by-step explanation:

We are given that the average human gestation period is 270 days with a standard deviation of 9 days. The period is normally distributed.

Firstly, Let X = women's gestation period

The z score probability distribution for is given by;

Z = $\frac{ X - \mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = average gestation period = 270 days

$\sigma$ = standard deviation = 9 days

Probability that a randomly selected woman's gestation period will be between 261 and 279 days is given by = P(261 < X < 279) = P(X < 279) - P(X $\leq$ 261)

P(X < 279) = P( $\frac{ X - \mu}{\sigma}$ < $\frac{279-270}{9}$ ) = P(Z < 1) = 0.84134

P(X $\leq$ 261) = P( $\frac{ X - \mu}{\sigma}$ $\leq$ $\frac{261-270}{9}$ ) = P(Z $\leq$ -1) = 1 - P(Z < 1)

= 1 - 0.84134 = 0.15866

Therefore, P(261 < X < 279) = 0.84134 - 0.15866 = 0.68

Hence, probability that a randomly selected woman's gestation period will be between 261 and 279 days is 0.68.

3 0

3 years ago

A motel rents double rooms at $34 per day and single rooms at $26 per day. If 26 rooms were rented one day for a total of $804,

lubasha [3.4K]

Answer: 16 double rooms and 10 single rooms were rented.

Step-by-step explanation:

Let x represent the number of double rooms that were rented.

Let y represent the number of single rooms that were rented.

The total number of rooms rented in a day is 26. It means that

x + y = 26

A motel rents double rooms at $34 per day and single rooms at $26 per day. If all the rooms that were rented for one day cost a total of $804, it means that

34x + 26y = 804 - - - - - - - - - - -1

Substituting x = 26 - y into equation 1, it becomes

34(26 - y) + 26y = 804

884 - 34y + 26y = 804

- 34y + 26y = 804 - 884

- 8y = - 80

y = - 80/ - 8 = 10

x = 26 - y = 26 - 10

x = 16

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3 years ago

In B E C, F is the centroid, and AC = 12. Find A F and F C

klemol [59]

bearing in mind that the centroid in a triangle cuts each of the three medians in a 2:1 ratio.

since we know that A C = 12, let's split it in a 2:1 ratio then, cleary from the picture the larger is F C, so F C : A F is on a 2:1 ratio.

$\bf A C=A F+F C\qquad \qquad \cfrac{F C}{A F}=\cfrac{2}{1}\qquad \qquad \cfrac{2\cdot \frac{12}{2+1}}{1\cdot \frac{12}{2+1}}\implies \cfrac{2\cdot 4}{1\cdot 4}\implies \cfrac{8}{4}$

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3 years ago