Makayla is taking a math course and is working with the perimeter of rectangles. She knows the perimeter and length of her recta

Answer:

The rotation angle measures 2.11 °

Step-by-step explanation:

Stated as follows:

The radius of the circular path = r = 18 feet

The distance rolled by the wheel = l = 38 feet

Let us denote the angle of rotation as Ф

Now, according to the problem:

∵ the length of an arc at the center corresponds to an angle Ф

Thus,

distance rolled by the wheel = π × radius ×

As 180° represents π radians

And π approximates to 3.14

Thus, distance rolled by the wheel = 180 °× radius ×

That is l = r × Ф

So, Ф =

Consequently, Ф =

Therefore, Ф = 2.11 °

Thus, the rotation angle is Ф = 2.11 °

Hence, the rotation angle is 2.11 ° Answer

In the ratio of miles traveled, Mr. Storey and Mrs. Storey's journey is represented as mr: mrs = 3: 1. The total of these ratio units equals 4 (3+1), which means each unit corresponds to 3200 divided by 4, resulting in 800 miles. Mr. Storey drove 3 multiplied by 800, equating to 2400 miles, while Mrs. Storey drove 1 multiplied by 800, totaling 800 miles.

Answer:

We would recommend the Country Route as its travel time is consistently estimated between 15 and 18 minutes.

Step-by-step explanation:

Jean lives approximately 10 miles away from the college where she plans to attend a summer class lasting ten weeks. She has two primary routes available, one that traverses the city and another that goes through the countryside.

Jean has set up a randomized trial in which she flips a coin each day to determine her travel route, collecting data from five days for both.

Country Route - 17, 15, 17, 16, 18 (in minutes)

City Route - 18, 13, 20, 10, 16 (in minutes)

Next, we need to evaluate which route is superior for Jean.

The data indicates that the Country route has timing ranging from 15 to 18 minutes, suggesting she will typically arrive within this timeframe.

Conversely, the City route timings show significant variation with a minimum of 10 minutes and a maximum of 20 minutes, indicating uncertainty regarding her arrival time.

Hence, it is advisable for her to select the Country route.

Response:

The more trials conducted, the stronger the observed theoretical trend becomes

Stepwise explanation:

Firstly, we need to define the probabilities,

-Theoretical probability quantifies success versus total possible outcomes of an experiment.

-Experimental probability calculates the ratio of the desired outcome relative to the total attempts made in the experiment.

Accordingly, the reasoning that best supports this is that as the experiment is repeated, the experimental probability aligns more closely with the theoretical probability, because repetition increases the likelihood of achieving predicted results.

we possess

Step

Eliminate the variable y

Add to each side

Step

Change to function notation

Define

thus

the result is