Vivian surveyed bicyclists in her community to see the average number of miles they biked per day. Her results are shown below.

A rational number refers to any number that can be written as a fraction, such as 2, -3, 2/3, etc.

Essentially, any non-repeating number found between 31.5 and 31.6 would suffice.

Examples include: 31.51, 31.52, 31.568, 31.599

I suggest 31.55 since it’s straightforward and can be expressed as the fraction: 361/20

Answer:

• Yes; refer to the question's clarification and the detailed answer below for more information.

Explanation:

Sets are in bijection if there is a bijective function connecting them.

This implies that the question can be interpreted as: can sets A and B be related via a bijective function?

A bijective function must be both injective and surjective, which means it is reversible.

Injective indicates that each element in the domain corresponds uniquely to an element in the codomain.

Surjective denotes that every element in the codomain relates to exactly one element in the domain.

This ensures there are no unmatched elements.

If we consider set A as the function's domain and set B as the codomain.

The core question then becomes: can the set {17, 34, 51, 68, 85,...} be in bijection with the set {11, 22, 33, 44, 55,...}?

Notice that the two sets share no common elements, as 17 and 34 are coprime.

A bijective function can only be established between sets A and B or B and A if both sets possess the same cardinality (number of elements).

Indeed, the cardinality of sets A and B is identical: both sets are of equal size, affirming that a bijective relationship exists between them.

The correct answers are 0, 5, and 8. Clearly, having negative bags isn't feasible. Additionally, 10 is not possible since the balloon has a weight limit.

The blue line depicted in the attached image illustrates the reflection of f(x) across the x-axis. To elucidate, the function f(x) is an exponential function displaying the characteristics: the y-intercept calculates as f(0) = 6(0.5)⁰ = 6; the multiplicative rate of change is 0.5, signifying a decay function (decreasing); and the horizontal asymptote exists at y = 0, defining the limit of f(x) as x approaches positive infinity. The reflection across the x-axis for f(x) results in a function denoted as g(x) = -f(x), leading to g(x) reflecting the features discussed including growth into the third quadrant while never intersecting the x-axis. Therefore, using these insights, it is feasible to sketch the corresponding graph across the x-axis.

Answer:

A. Cone

D. Rectangular Prism

E. Cylinder

F. Sphere

Step-by-step explanation:

A rectangular prism is defined as a three-dimensional solid shape with six rectangular faces. It is commonly known as a cuboid. It cannot be formed from two-dimensional figures. A sphere is an example of a three-dimensional circular object. The circumference gives it its distinct shape, which also cannot be constructed using two-dimensional forms.