The answer is a. a circle is inscribed in a regular hexagon with side length 10 feet. what is the area of the shaded region? recall that in a 30 – 60 – 90 triangle, if the shortest leg measures x units, then the longer leg measures x√3 units and the hypotenuse measures 2x units.(150√3 - 75π) ft^2(300 – 75π) ft^2(150√3 – 25π) ft^2(300 – 25π) ft^2

Option A. (150√3- 75π) ft².

Step-by-step explanation:

In the given picture a circle is inscribed in a regular hexagon with a side length = 10 feet.

Formula of the area of a regular hexagon

                                                              =

                                                             = 3√3×50 = 150×√3 feet²

Now we will calculate the area of circle inscribed.

Already given in the question that In a 30-60-90 triangle

Longer leg of triangle r = x√3 = = 5√3 feet

Now area of circle = π r² = π(5√3)² = 75π feet²

Area of shaded part = Area of Hexagon-Area of circle inscribed.

                                 = (150√3 - 75π) ft²

75 tickets have been sold so far.

step-by-step explanation:

in this question it is clearly mentioned that 45 children's tickets have been sold and this number is 60% of the total tickets sold.

now let's assume the total number of tickets sold be x.

then 60% of x = 45

⇒

⇒ x(.6) = 45

by dividing with .6 on both the sides of the equation

⇒ x = 75

therefore 75 tickets have been sold so far.

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)