A taste test asks people from Texas and California which pasta they preferred brand a or brand b this table shows the results. A

Response:

Detailed breakdown:

Considering a rectangle measuring 3cm by 4cm with a circle of 1 cm diameter within it:

The area of the shaded section equals Area of Rectangle minus Area of Circle

The area of a rectangle is calculated as Length multiplied by Width

The area of the circle is

Area of shaded region = 12 - 3.142

Answer:

The union of sets A and B is represented as A U B = {1,2,3,4,5,6,8}

Detailed explanation:

We begin by defining our sets.

Let ¢ signify the universal set (which includes every element in the given sets)

¢ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A= {2, 4, 6, 8}

B= {1,2,3,4,5,6}

Consequently: A U B (the union of A and B):

A U B = {1, 2, 3, 4, 5, 6, 8}

Comment
Let's first tackle the simplest approach to finding the area of a triangle.

Formula for area is
A = 1/2 b * h

Substituting values
Area = 60 in^2
where b = x
and h = 2x - 1 
Thus, 60 = 1/2 * x * (2x - 1)

Now, we solve
60 = 1/2 * x (2x - 1) Multiply by 2
60 * 2 = x(2x - 1)
120 = x (2x - 1) Expand the brackets.
120 = 2x^2 - x  Subtract 120 from both sides.
2x^2 -  x - 120 = 0 which factors out to
(2x + 15)(x - 8) = 0

Now, solving for x
2x + 15 = 0
2x = - 15
thus, x = -15/2
which yields a negative value, hence discard this solution.

x - 8 = 0
gives us x = 8 

Area verification
base = 8
height = 16 - 1 = 15

thus Area = 1/2 * 8 * 15 = 60 confirming the calculation

Response
Utilize Area = 1/2 * b * h to determine both the base and height.