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3 years ago

10

Please help me solve this problem!

1 answer:

Novay_Z [31]3 years ago

5 0

Answer:

20300m^2

Step-by-step explanation:

first try to imagine the shape bisected into a rectangle and a triangle

to find the missing part of the triangle or the bottom side you need to subtract 70m from 140 m

140m-70m=70m this will be the base of your triangle

now you need the side

230m-60m=170

triangle formula base x height/ 2

70m x 170m=a

11900m=a

now the rectangle

base x height=a

60m x140m=a

8400m=a

finally add the two quantities together

8400m+11900m=a

20300m^2=a

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Answer:

(a) $Selection = 6724520$

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Step-by-step explanation:

Given

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$Balloons = 28$ --- at least

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From the question, we understand that; a combination of 28 is to be selected. Because the order is not important, we make use of combination.

Also, because repetition is allowed; different balloons of the same kind can be selected over and over again.

So:

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$Selection = ^{35}^C_{28$

$Selection = \frac{35!}{(35 - 28)!28!}$

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$Selection = \frac{35*34*33*32*31*30*29}{7!}$

$Selection = \frac{35*34*33*32*31*30*29}{7*6*5*4*3*2*1}$

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Solving (b): At most 12 red balloons

First, we calculate the ways of selecting at least 13 balloons

Out of the 28 balloons, there are 15 balloons remaining (i.e. 28 - 13)

So:

$n => 15 + 8 -1 = 22$

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$At\ least\ 13 = ^{22}C_{15}$

$At\ least\ 13 = \frac{22!}{(22-15)!15!}$

$At\ least\ 13 = \frac{22!}{7!15!}$

$At\ least\ 13 = 170544$

Ways of selecting at most 12 =

$At\ most\ 12 = Total - At\ least\ 13$ --- Complement rule

$At\ most\ 12 = 6724520- 170544$

$At\ most\ 12 = 6553976$

Solving (c): At most 8 blue balloons

First, we calculate the ways of selecting at least 9 balloons

Out of the 28 balloons, there are 19 balloons remaining (i.e. 28 - 9)

So:

$n => 19+ 8 -1 = 26$

$r = 19$

Selection of at least 9 =

$At\ least\ 9 = ^{26}C_{19}$

$At\ least\ 9 = \frac{26!}{(26-19)!19!}$

$At\ least\ 9 = \frac{26!}{7!19!}$

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Ways of selecting at most 8 =

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$At\ most\ 8 = 6724520- 657800$

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First, we calculate the ways for selecting 13 red balloons and 9 blue balloons

Out of the 28 balloons, there are 6 balloons remaining (i.e. 28 - 13 - 9)

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$^{11}C_6 = \frac{11!}{(11-6)!6!}$

$^{11}C_6 = \frac{11!}{5!6!}$

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$Selection = At\ most\ 12 + At\ most\ 8 - (12\ red\ and\ 8\ blue)$

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$Only\ 12\ red\ and\ only\ 8\ blue\ = 827882$

$At\ most\ 12\ red\ and\ at\ most\ 8\ blue = Total - Only\ 12\ red\ and\ only\ 8\ blue$

$At\ most\ 12\ red\ and\ at\ most\ 8\ blue = 6724520 - 827882$

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