You throw a dart at the board shown. Your dart is equally likely to hit any point inside the square board

This question is incomplete and the picture of the board is not attached.

Find attached to this answer the picture of the board.

Complete question

You throw a dart at the board shown. Your dart is equally likely to hit any point inside the square. What is the probability your dart lands in the yellow region?

56.32%

Step-by-step explanation:

From the attached diagram, we can see different sections on the board, with different colours as well.

We have the

a. Blue square shape

b. Yellow region circular shape

c. Green region triangular shape

White region = square shape

Red region = circular shape

Step 1

We need to determine the area of the

various shapes.

First, we find the areas of all the shapes in the dartboard.

The Blue Square shape and the Area of a square = Length of the sides ²

Length of the side = 18 inches

The area of the square = 18²= 324 square inches.

The yellow circular in shape

Area of a circle = πr²

Since the circle is found in a square, the diameter of the circle = Length of the square side

So, diameter of the circle = 18 inches.

Radius of a circle = Diameter ÷ 2

Radius of the circle = 18 inches ÷ 2 = 9 inches.

The area of a circle = π × 9² = 254.469 square inches.

The Green triangular shape

We have 2 green triangles and looking at the attached diagram, the base of both = 6 inches and a height of 6 inches as well.

Area of a triangle = 1/2 × base × height

Area of a triangle = 1/2 × 6inches × 6 inches.

= 18 square inches.

For the two triangles , their combined areas = 2 × 18 square inches = 36 square inches.

We have a small inner square painted white with a side length of 6 inches.

Area of the square = s² = (6² inches) = 36 inches² = 36 square inches.

We also have a small inner circle as well which is coloured red

Area of a circle = πr²

Since the circle is found in a square, the diameter of the circle = Length of the square side

So, diameter of the circle = 6 inches.

Radius of a circle = Diameter ÷ 2

Radius of the circle = 6 inches ÷ 2 = 3 inches.

The area of a circle = π × 3² = 28.274 square inches.

Since, the area of the entire board is the same as the outer square area.

The area of the blue region = Area of the outer square - Area of the outer circle =   324 - 254.469 = 69.531 square inches.

The area of the yellow region =

Area of the outer circle - Area of 2 triangles - Area of the inner square

Area of the outer circle = 254.469 square inches

Area of 2 triangles = 36 square inches

Area of the inner square = 36 square inches

= (254.469 - 36 - 36) square inches. = 182.469 square inches.

The final step would be to find the probability.

Formula for probability =

number of favorable outcomes ÷ the total number of outcomes.

The probability of dart landing on yellow region =

182.469 square inches ÷ 324 = 0.5631759259

= 56.32%

answer: learning objective(s)

·         describe the creation and use of systems of equations.

·         graph a system of linear equations on the coordinate plane and identify its solution.

introduction

sometimes graphing a single linear equation is all it takes to solve a mathematical problem. other times, one line just doesn’t do it, and a second equation is needed to model the situation. this is often the case when a problem involves two variables. solving these kinds of problems requires working with a system of equations, which is a set of two or more equations containing the same unknowns.

let’s take a look at systems of equations, and see what the graphs of individual equations within a system reveal about the mathematical relationship of the variables.

systems of equations

a system of equations contains two or more linear equations that share two or more unknowns. to find a solution for a system of equations, we must find a value (or range of values) that is true for all equations in the system.

the graphs of equations within a system can tell us how many solutions exist for that system. look at the images below. each show two lines that make up a system of equations (in the graph on the right the two lines are superimposed and look like a single line). how many points in common does each system of lines reveal?

one solution

no solutions

infinite solutions

if the graphs of the equations intersect, then there is one solution that is true for both equations.

if the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations.

if the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations.

remember, the graph of a line represents every point that is a possible solution for the equation of that line. so when the graphs of two equations cross, the point of intersection lies on both lines, meaning that it is a possible solution for both equations. when the graphs of two equations never touch, there are no shared points and there are no possible solutions for the system. when the graphs of two equations lie on top of one another, they share all their points and every one is a possible solution.

graphing as a solution method

graphing equations in order to identify a specific point of intersection is usually not a precise way to solve systems because it is often difficult to see exactly where two lines intersect (unless you are using a computer-based graphing program that allows you to zoom in on a point). however, the graph of a system of equations can still give a good idea of what type of solution, if any, exists. let’s graph a system, and see how it works.

graph the system y = 3x and x + 2y = 4. how many solutions does this system have?

a graph of the two lines y = 3x and x + 2y = 4 shows us that the lines intersect, meaning that there is a single (x, y) value that satisfies both equations. looking at the graph does not tell us exactly where that point is, but we don’t need to know that information here, because the question only asks for the number of solutions.

so a system made of two intersecting lines has one solution. now let’s look at a different situation:

how many solutions exist for the system y -0.5x = 7 and 2y = x − 3?

plotting both equations, it looks like there is no solution—the lines are parallel. to check this finding, we can compare the slopes of the equations. to make that easy, we’ll rearrange the equations into slope-intercept form, or y = mx + b.   that gives us the equations y = 0.5x + 7 and y = 0.5x − 1.5.   yes, the slope of both lines is 0.5, which means the lines really are parallel. they never intersect, so there is no point that lies on both lines, and no solution to the system.

step-by-step explanation:

plants store their excess carbohydrate in the form of starch so that it could be used as energy source later on. the excess carbohydrate is converted into starch in the plastid i.e. chloroplast & this process occurs in the presence of sunlight. it is an insoluble polymer of glucose which gets stored in cell organelles named as amyloplasts. in some plants, starch is also stored in roots and embryos.