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xeze [42]
3 years ago
15

The area of the shaded triangles in the fractal shown form a geometric sequence. The area of the largest triangle (not shaded) i

s 1 square unit. Find the areas of these shaded triangles.
Orange: 1/4 square units

Blue: _____ square units

Green: _____ square units


If the pattern continues indefinitely, does the sum of the areas converge? ______
Mathematics
1 answer:
guajiro [1.7K]3 years ago
8 0

Answer:

The correct answers are Blue: \frac{1}{16} square units ; Green:  \frac{1}{64} square units; and Yes the sum converges.

Step-by-step explanation:

Area of the largest triangle is 1 square unit.

The area of the triangle which are colored and follow a geometric sequence with the common ratio being \frac{1}{4}.

Area of the not shaded triangle is given by 1 square unit.

Area of the orange triangle is given by 1 × \frac{1}{4} = \frac{1}{4} square units.

Area of the blue triangle is given by \frac{1}{4} × \frac{1}{4} = \frac{1}{16} square units.

Area of the green triangle is given by \frac{1}{16} × \frac{1}{4} = \frac{1}{64} square units.

If the pattern continues definitely then it becomes an infinite geometric progression series with common ratio \frac{1}{4}. And thus the sum of area coverges as the ratio lies between -1 and 1.

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Juli2301 [7.4K]

Answer:

a) P(X =16 ) = 0.1853

b) P(X \leq 12) = 0.0684

Step-by-step explanation:

GIVEN DATA:

n = 16

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from relation given probabllity can be solve

P(X) = ^nC_x * p^x * ( 1 - p)^{n-x}

a)

P(X =16 ) = ^{16}C_{16} * 0.90^x * ( 1 - 0.90)^{16-16}

P(X =16 ) = 0.1853

b) P(X \leq 12) = 1 - P(X \geq 13)

= 1 - [ P(X = 13) +P(X = 14) +P(X = 15) +P(X = 16) ]

= 1 - [ ^{16}C_{13} * 0.90^{13} * (1 - 0.90)^3 +^{16}C_{14} * 0.90^{14} * (1 - 0.90)^2 +^{16}C_{15} * 0.90^{15} * (1 - 0.90)^1 +^{16}C_{16} * 0.90^{16} * (1 - 0.90)^0 ]

= 0.0684

4 0
3 years ago
Solve for k.<br> 6k - 8 = 4K + 15
Brut [27]

Hi,

Answer:

k = \frac{23}{2}

Step-by-step explanation:

Subtract 4k from both sides

6k - 4k = 2k

2k - 8 = 15

Add 8 on both sides (you want to get rid of the 8 in order to leave the k alone)

2k = 23

k = 23/2

Have a good day!

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