My answer is : C

Call Alice's age is a

        Betty's age is b

 and  Clara is c 

Follow the threads , we have :

a + b + c = 29  (1)

b = a + 4  (2)

c = b + 6   (3)

Change (3) , (2) to (1)

a + b + c = a + (a + 4) + (b + 6)

<=> a + (a + 4) + (a + 10) = 29

=> 3a + 14 = 29

=> 3a = 15

=> a = 5

So , Alice's age is 5

Call Alice's age: a

        Betty's age: b

        Clara's age: c

    (a,b,cN*)

According to the theme we have:
(1)

(2)

(3)

Change (2)(3) to (1) we have:

(satisfy)

Alice's age: 5 years old

Call Alice's age: a

        Betty's age: b

        Clara's age: c

    (a,b,c\(\in\)N*)

According to the theme we have:
\(a+b+c=29\)(1)

\(b-a=4\Rightarrow b=a+4\)(2)

\(c-b=6\Rightarrow c=b+6\Rightarrow c=a+4+6=a+10\)(3)

Change (2)(3) to (1) we have:
\(\left(1\right)\Leftrightarrow a+b+c=29\)

\(a+a+4+a+10=29\)

\(3a+14=29\)

\(3a=29-14=15\)

\(a=5\)(satisfy)

Alice's age: 5 years old

We have : 2³ . x² = 32

=> 8.x² = 32

=> x² = 4

=> x = -2;2

\(2^3.x^2=32\)

<=> \(8.x^2=32\)

<=> \(x^2=32:8=4\)

We see: \(2^2=4\) => \(x=2\)

So the value of \(x\) is: \(2\)

2³ . x² = 32

=> 2³.x² = 2⁵

=> x² = 2²

=> x² = 4

=> x = \(\pm2\)

NP is tangent to circle center O at N,so \(NP\perp ON\) at N

Assume that the circle center O and the circle center P touch each other at M, then O,M,P are collinear.

=> OP = OM + MP = 16 + 4 = 20 (cm)

Applying the Pythagoras theorem to the right \(\Delta ONP\),we have :

\(NP=\sqrt{OP^2-ON^2}=\sqrt{20^2-16^2}=\sqrt{144}=12\left(cm\right)\)

So,the answer is 12 cm

There are 3 possible values of Ash's secret number : 1 ; 4 ; 8

Their sum is : 1 + 4 + 8 = 13

Ta has: abcabc = abc000 + abc 

                      = Abc x 1000 + abc 

                      = Abc. (1000 +1)

                      = Abc. 1001

                      = Abc. 7. 11. 13

The abcabc of the abc with 7; 11; 13 => abcabc divide by 7; 11 and 13

The sum of books : 6 + 3 + 7 = 16 (books)

The number of math books is : \(3+7=10\left(books\right)\)

The probability is : \(\dfrac{10}{16}=\dfrac{5}{8}\)

Answer : \(\dfrac{5}{8}\)

a - b = 8 => a = 8 + b

=> ab = (b + 8)b = 48

By replacing b by 1, 2, 3, 4, ... respectively, we have b = 4

=> a = 12 => a + b = 12 + 4 = 16