Two thirds of the employees at an office stated that they preferred soft cookies over crispy cookies. More than 36 employees stated their preference. Ren was asked to write, solve, and graph an inequality to find the number of employees working at the office. His work is shown below.

Step
Ren’s work

Step 1

Two-thirds x less-than 36

Step 2

x less-than 54

Step 3
A number line going from 51 to 57. An open circle is at 54. Everything to the left of the circle is shaded.

Where, if any, did Ren first make a mistake in his work?

Consider the reaction 2x2y2+z2⇌2x2y2z which has a rate law of rate= k[x2y2][z2] select a possible mechanism for the reaction.

Apositive number a or the same number a increased by 50% and then decreased by 50% of the result?

For this option, you will work individually. the pythagorean theorem can be used in many real-world scenarios. part 1 write your own real-world scenario where the pythagorean theorem can be applied to find a missing piece. you may choose to write a problem that is two- or three-dimensional in nature. be sure that you will be able to draw a diagram of your scenario. write out your problem and submit it for part 1. be sure to end your scenario with a question. part 2 draw a diagram of the scenario you created in part 1. you may draw by hand and scan and upload your drawing or create a computer-generated drawing for submission. be sure to label all parts and dimensions of the drawing. part 3 solve the question that you posed in part 1. show all of your steps in answering the question. for this option, you will need to submit all three parts for full credit—your real-world problem and question, the diagram that you created, and your work solving the problem, showing all steps. * note that your instructor is looking for your own original idea. while it is acceptable to use the internet for research and inspiration, academic integrity policies apply.