$larger\ rectangles:3l\ \times\ w\\\\smaller\ rectangles:l\ \times\ w\\\\A_{larger}=kA=3lw\\\\A_{smaller}=A=lw\\\\\frac{A_{larger}}{A_{smaller}}=\frac{kA}{A}=k\\\\k=\frac{3lw}{lw}=3\\\\Answer:J.$

4 0

3 years ago

Four streets enter a traffic circle at points A B C and D name six arcs formed by the streets.

lilavasa [31]

Arcs are just sections of the circle
so lets say you had a pizza

and you put some points on the crust, the legnth of the crust from point to point is that arc

example
if you put poins A and B, then arc AB is the crust between points A and B

arcs can include other points as well
and arc AB=arc BA

so
I wil name easy arcs first
arc AB
arc BC
arc CD
ard DA

now ones that include others
arc AC
arc BD

so the arcs you might want to list are

arc AB
arc BC
arc CD
ard DA
arc AC
arc DB

5 0

3 years ago

A source of information randomly generates symbols from a four letter alphabet {w, x, y, z }. The probability of each symbol is

koban [17]

The expected length of code for one encoded symbol is

$\displaystyle\sum_{\alpha\in\{w,x,y,z\}}p_\alpha\ell_\alpha$

where $p_\alpha$ is the probability of picking the letter $\alpha$ , and $\ell_\alpha$ is the length of code needed to encode $\alpha$ . $p_\alpha$ is given to us, and we have

$\begin{cases}\ell_w=1\\\ell_x=2\\\ell_y=\ell_z=3\end{cases}$

so that we expect a contribution of

$\dfrac12+\dfrac24+\dfrac{2\cdot3}8=\dfrac{11}8=1.375$

bits to the code per encoded letter. For a string of length $n$ , we would then expect $E[L]=1.375n$ .

By definition of variance, we have

$\mathrm{Var}[L]=E\left[(L-E[L])^2\right]=E[L^2]-E[L]^2$

For a string consisting of one letter, we have

$\displaystyle\sum_{\alpha\in\{w,x,y,z\}}p_\alpha{\ell_\alpha}^2=\dfrac12+\dfrac{2^2}4+\dfrac{2\cdot3^2}8=\dfrac{15}4$

so that the variance for the length such a string is

$\dfrac{15}4-\left(\dfrac{11}8\right)^2=\dfrac{119}{64}\approx1.859$

"squared" bits per encoded letter. For a string of length $n$ , we would get $\mathrm{Var}[L]=1.859n$ .

5 0

2 years ago

1. Renting a bicycle at a local Bike shop costs $30 for the first day and $10 for each additional day.

Elza [17]

(a) Create a chart of values and write an equation to find the total cost, C in terms of the number of days d.

C = 10d + 20

(b) Use the equation you created in Part (a) to find the cost of renting a bike for 5 days.

C = 10d + 20
C = 10(5) + 20= 50 + 20 = 70

$70 for 5 days

7 0

3 years ago