1. Entomologist Heinz Kaefer has a colony of bongo spiders in his lab. There are 1000 adult spiders in the colony, and their weights are normally distributed with mean 12 grams and standard deviation 2 grams. (a) If a spider weighs 15.6 grams, what is the standard score (z-score)?

(b) What is the standard score of a spider in this colony that weighs 10 grams?

(c) Look at your answers for a and b. When the value is greater than the mean, what is the sign of the standard score? What happens to the sign when the value becomes less than the mean?

(d) About what percent of spiders in the colony weigh between 10 grams and 14 grams?

(e) About how many spiders in the colony weigh more than 13 grams? Remember to calculate the number of spiders, not a %

(f) What percent of the spiders weigh less than 9 grams?
(g) What is the weight of a spider at the 90th percentile?
(h) What is the weight of at the 15th percentile?

The rate of decay of a radioactive substance depends upon the amount present initially. the mass y (mg) of the radioactive substance cobalt-60 present in a sample at time t (years) is represented by the exponential equation y=50e −0.1315 t . answer the following questions in complete sentences. 1. how does the exponential equation above compare to the equation for simple interest that is compounded continuously? explain the similarities. 2. what is the initial amount of cobalt-60 in the sample? 2. how much cobalt-60 is left after 8.4 years? show your work. 3. what would be the y-intercept of the graph? what does it represent? 4. after how many years will the amount of cobalt-60 left be 6.25 mg? explain what happens to the cobalt-60 after 50 years? 5. discuss some “real-world” examples and uses of cobalt-60

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.

Which expression gives the exact value of x?