.Slim-Down Manufacturing makes a line of nutritionally complete, weight-red ction beverages. One of their products is a strawberry shake which is designe to be a complete meal. The strawberry shake consists of several ingredients. ome information about each of these ingredients is given below. Take the ing edient of strawberry flavoring for example, the amount of calories from fat of ach unit (tbsp) of strawberry flavoring is 1, the amount of total calories from ach unit of strawberry flavoring is 50, similarly, the amount of vitamin content nd thickeners is 20mg and 3mg per tbsp. The cost of each tbsp of strawberry avoring is 10 dollars. Thickener Calories from F Total Calorie Vitamin Conte Cost Ingredient at nt (S/tbs (mg/tbs (per/tbsp) (per/tbsp) (mg/tbsp) p) p) Strawberry flavori 1 50 20 3 10 ng Cream 30 90 10 9. itamin suppleme 50 1 25 nt artificial sweetene 90 2 12 Thickening agent 30 60 2 25 he nutritional requirements are as follows. There must be at least 20 milligra s (mg) of vitamin content. For taste reasons, there must be at least 2 tablesp ons (tbsp) of strawberry flavoring for each tablespoon of artificial sweetener. o maintain proper thickness, there must be exactly 24 mg of thickeners in the everage. Finally, the beverage must total between 300 and 400 calories (inclu ve), and no more than 20 percent of the total calories should come from fat. lanagement would like to select the quantity of each ingredient for the bevera e which would minimize cost while meeting the above requirements.

Step 3: Assess the Evidence (Calculate the test statistic for the observed sample mean. Sketch the T-distribution and identify the position of the observed test statistic. Shade the area that represents the P-value. Use the test statistic to find the P-value.)

A survey looked at how long it takes a typical company to recoup an investment in research. The survey determined that 39% of the corporations took six months or less to recoup their investment. The data table below shows a sample of the time, in months, it might have taken 20 corporations to recoup their investment. Complete parts a and b. 9.0 8.0 4.0 4.0 7.0 8.0 7.0 7.0 9.5 5.5 7.5 12.0 8.5 5.5 10.5 10.0 7.5 4.5 7.0 7.5 a. Determine the number of corporations that recovered their investement in research in six months or less. There were 5 corporations that recovered their investment in research in six months or less. b. Calculate the probability of obtaining at most the number of corporations that you determined in part a if the percent of those recovering their investment is as indicated by the survey. The probability (Round to four decimal places as needed.)

5 Imagine that a company sells portable walkie-talkie radios to construction crews. The batteries for these radios last for an average of 55 hours. The purchasing manager for this company receives a brochure in the mail that advertises a new brand of batteries. This new brand of batteries is cheaper than the brand that the company currently uses. However, the purchasing manager is concerned that the cheaper batteries may have a shorter average battery life than the current brand. (Note: The number of hours that batteries last is called their battery life.) The pricing manager installs 40 randomly selected batteries of the cheaper brand in the company's walkie-talkie radios. He finds that the mean battery life for the sample is 52 hours, with a standard deviation of 10 hours. He wants to perform a statistical test at the 1% level of significance to determine whether the cheaper batteries have a shorter average battery life span than the average life span of the brand of batteries the…

An interdepartmental task force is being formed to investigate an increase in violent crimes. 1/5 of the task force will be police officers from the local precinct. 1/4 will be ATF agents, and the remaining 22 will be from the FBI. How many people are participating in the task force?

9. After looking at this list, you are concerned that you may not be able to afford the food that you have chosen to provide enough protein for your diet. So you have decided to get the biggest bang for your buck by comparing the amount of protein for the price that you can buy the food for. The following 4 items were priced at Walmart on 1/2/2014. Also included is the serving per item and the protein for each serving for the product chosen. Make sure to show your work. Price per Protein (g) Food Item Bush Pinto Beans Jif Peanut Butter Bumblebee Canned Chicken Cherrios Cereal Price per item $0.84 $3.98 $2.38 $3.68 Servings per item 3.3 25 4 18 Protein (g) per serving 78 78 13g 3g of protein?