Translate each sentence into symbolic form: symbols let r="it is raining" f(x) = "x is a frog" use for all g(x) = "x is green" h(x) = "x hops" . 7 there exists let the domain for f, g, and h be all animals. (a) some frogs are not green. 1 = and ve or = then (b) all green frogs hop. ~= negation (c) if nothing is green, then green frogs do not exist. (d) green frogs hop if and only if it isn't raining. (e) if exactly two green frogs hop, then it is raining. (f) some animals are green and some are not green. (g) find the negation of the answer in part (f) and write it in english.

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.

Zoey made 5 1/2 cups of trail mix for a camping trip. she wants to divide the trail mix into 3/4 cup servings. a. ten people are going on the trip. can zoey make enough 3/4 cup servings so that each person gets one serving? b. what size would the servings need to be for everyone to have a serving?

Which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression (-1+i)+(21+5i)+0