A package designer wants the hexagonal base of a hat box to have an area of about 200 in.2. About how long is each side?

About 9inches long

Step-by-step explanation:

Area of a hexagon = 3√3/2 a²

a is the length of each side

Given

Area of the hexagon = 200in²

Substitute

200 = 3√3/2 a²

200×2 = 3√3 a²

400 = 3√3a²

a² = 400/3√3

a² = 400/5.196

a² = 76.982

a = √76.982

a = 8.774

Hence the length of each side is about 9inches long (to nearest inches)

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

The answer is in the image 

The solution is in the following image

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

The answer is in the image 

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales