What is the probability that a point chosen at random in the given figure will be inside the larger square and outside the smaller square? enter your answer, as a fraction in simplest form, in the box. p(inside larger square and outside smaller square) = $\text{basic}$ $x$$y$$x^2$$\sqrt{ }$$\frac{x}{ }$ $x\frac{ }{ }$ $x^{ }$$x_{ }$$\degree$$\left(\right)$$\abs{ }$$\pi$$\infty$ a square with a side length of 7 centimeters is within a larger square with a side length of 10 centimeters. the sides of the inner square do not touch the sides of the outer square.

Step-by-step explanation:

The probability that a point chosen at random in the given figure will be inside the larger square and outside the smaller square is equal to the ratio of the area of interest to the total area:

P(inside larger square and outside smaller square) = area of interest / total area

P(inside larger square and outside smaller square) = area inside the larger square and outside the smaller square / area of the larger square

Calculations:

1. Area inside the larger square: side² = (10 cm)² = 100 cm²

2. Area inside the smaller square = side² = (7cm)² = 49 cm²

3. Area inside the larger square and outside the smaller square

4. P (inside larger square and outside smaller squere)

the fist one is not equalvalent but i think th second one isand the third isnt definetly or the last one is i think. hope this !

step-by-step explanation:

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12