Shown in the picture below are three concentric (having the same center) circles. Let's name them small, larger and largest. You are
blindfolded and throwing a dart at the target. What is the probability
that the dart will hit the white area inside the circles? The white area
is formed by the small circle and by the area between the larger and
largest circles that looks like a ring. Assume that the dart you throw,
will hit somewhere inside the largest circle,
Enter your answer as a decimal.

The probability that the dart will hit the white area is 16/25

Step-by-step explanation:

The given circle is composed of three concentric circles as follows;

Small circle with radius, r₁ = 1

Larger circle with radius, r₂ = 3

Largest circle with radius, r₃ = 5

The area of the small circle = π × r₁² = π

The area of the larger circle = π × r₂² = π × 3² = 9·π

The area of the largest circle = π × r₃² = π × 5² = 25·π = The total target area

The total white area = The total target area - The area of the larger circle

The total white area = 25·π - 9·π = 16·π

The probability of hitting the white area = 16·π/25·π = 16/25

Therefore, the probability that the dart will hit the white area = 16/25.

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.