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4 years ago

What is the value of x? 6 8 010 O 12

Mathematics

2 answers:

Morgarella [4.7K]4 years ago

3 0

Answer:

Step-by-step explanation:

The sum of the internal angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 5, hence

sum = 180° × 3 = 540°

Each exterior angle plus interior angle = 180°

Subtract each exterior angle from 180 for corresponding interior angle.

180 - 59 = 121, 180 - 77 = 103, 180 - 66 = 114, 180 - 62 = 118

Sum the 4 interior angles and subtract from 540 for 5 th interior angle

5 th = 540° - (121 + 103 + 114 + 118)° = 540° - 456° = 84°

The 5 th interior angle and 12x sum to 180 ( same reason as above )

Hence

12x + 84 = 180 ( subtract 84 from both sides )

12x = 96 ( divide both sides by 12 )

x = 8

please mark me brainliest :)

nadezda [96]4 years ago

3 0

The answer is eight.

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Of the 32 students in a class, 18 play the violin, 16 play the piano, and 7 play neither.

german

Answer:

(a)9

(b)I. 0.28125

II. 0.46875

III. 0.25

Step-by-step explanation:

There are a total of 32 students, therefore the number of elements in the Universal set, n(U)=32

$1$8 play the violin, n(V)=18\\16 play the piano, n(P)=16\\ 7 play neither, n(P \cup V)' =7$

(a)The Venn diagram is attached below.

$n(U)=n(V)+n(P)-n(V \cap P)+ n(P \cup V)'\\32=18+16+7-n(V \cap P)\\32=41-n(V \cap P)\\n(V \cap P)=41-32\\n(V \cap P)=9\\$

Therefore, 9 students play both the violin and piano.

(b)

I. Probability that the student plays the violin but not the piano

Number of Students who play violin only =18-x=18-9=9

$P(V \cap P') = \dfrac{n(V \cap P')}{n(U)}\\= \dfrac{9}{32}\\=0.28125$

ii.Probability that the student does not play the violin

Number of Students who does not play violin only =17-x+7=17-9+7=15

P(does not play violin only)

$= \dfrac{15}{32}\\=0.46875$

iii.Probability that the student plays the piano but not the violin

Number of Students who play piano only =17-x=17-9=8

$P(V' \cap P) = \dfrac{n(V' \cap P)}{n(U)}\\= \dfrac{8}{32}\\\\=0.25$

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After 3.5 hours Kim had traveled 217 miles If she traveled at a constant speed how far will she have traveled after 4 hours

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Step-by-step explanation:

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