Center of the circle: ABC

    => AB = BC = AC = 2R = 4

    => ABC is a equilateral triangle

    The area for the shaded region: S

    The area for a sector definition by A and 2 tangential points: SA

    S = SABC - 3SA

    SABC = 12

.4.4.√32 = 4√3

SA = 60360
Scircles = 16π22 = 2π3

=> S = 4√3
 - 32π3 = 4√3 - 2π

The fraction is: \(\left(\dfrac{5}{5}-\dfrac{2}{5}\right):2=\dfrac{3}{10}\)

Answer:

There are: \(\dfrac{103-3}{4}+1=26\) in this series:

So their sum is:

\(\dfrac{26}{2}\left(3+103\right)=1378\)

Ans:...

We have:

100 = 10²

999 = \(3\sqrt{111}\) > 31

=> The numbers from 10 to 31 i the ssquare root of three-digit positive intergers.

So there are:

31 - 10 + 1 = 22 numbers

Ans:

We have: The perimeter = 62 cm

=> \(\dfrac{1}{2}\) perimeter = 62 : 2 = 31 cm

The area of the each increased is:

2 . 2 = 4 cm

So square centimeters does area increase is:

4 . 31 = 124 cm²

Ans: 124 cm²

N/t: But I don't certain

tth Coordinator

2 .We can't fine the smallest value of the expression.

We have:

25 do not divide to 10

So 25 can't be true about number N of doors .

Note: I'm not certain

In P.1 , we have:

_ in P.1 , we have three squares.

Ans:

So she it took more:  17.36 = 9.78 $

But $9.78 is the sum money must cost of Puzzle and Wallet.

So she didn't bought Puzzle and Wallet

So the positive difference of their is:

3.49 = 2.8$

We have:\(2^{45}=\left(2^5\right)^9=32^9\)

\(32^n\) with n ∈ N divide 7 then we have remainder is 1

So 245 divide for 7  then we have remainder is 1

We have: 

Sum of 10 + 10 + 10 = 30

=> Average of the sum is: 30 : 3 = 10

Ans: 10

Apply the same ratio. We have:

\(\dfrac{a}{6}=\dfrac{b}{3}=\dfrac{c}{12}=\dfrac{a-b+c}{6-3+12}=30\)

<=> \(\dfrac{a-b+c}{15}=30\)

But 30 : 15 = 2

=>\(a=6.2=12\)

=> b = 3 . 2 = 6

=> c = 12 . 2 = 24

The meters cloth clothes is:

1 m  5dm + 1 m 8 dm = 3 m 2 dm

Ans: 3 m 2 dm