Directions: Draw a picture to represent the situation. Then, ssolve the problem. You must show all of your work! An observer at the top of a skyscraper sights a tour bus at an angle of depression of 61 degrees. The skyscraper is 910 feet tall. What is the horizontal distance from the base of the skyscraper to the tour bus? (Round to the nearest foot.)
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Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
Trigonometric Ratios
Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
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- Cholesterol Cholesterol in human blood is necessary, but too much can lead to health problems. There are three main types of cholesterol: HDL (high-density lipoproteins), LDL (low-density lipoproteins), and VLDL (very low-density lipoproteins). HDL is considered “good” cholesterol; LDL and VLDL are considered “bad” cholesterol. A standard fasting cholesterol blood test measures total cholesterol, HDL cholesterol, and triglycerides. These numbers are used to estimate LDL and VLDL, which are difficult to measure directly. Your doctor recommends that your combined LDL/VLDL cholesterol level be less than 130 milligrams per deciliter, your HDL cholesterol level be at least 60 milligrams per deciliter, and your total cholesterol level be no more than 200 milligrams per deciliter. (a) Write a system of linear inequalities for the recommended cholesterol levels. Let x represent the HDL cholesterol level, and let y represent the combined LDL VLDL cholesterol level. (b) Graph the system of inequalities from part (a). Label any vertices of the solution region. (c) Is the following set of cholesterol levels within the recommendations? Explain. LDL/VLDL: 120 milligrams per deciliter HDL: 90 milligrams per deciliter Total: 210 milligrams per deciliter (d) Give an example of cholesterol levels in which the LDL/VLDL cholesterol level is too high but the HDL cholesterol level is acceptable. (e) Another recommendation is that the ratio of total cholesterol to HDL cholesterol be less than 4 (that is, less than 4 to 1). Identify a point in the solution region from part (b) that meets this recommendation, and explain why it meets the recommendation.Based on Angel et al. (2003). A fertilizer companyis trying to determine the cheapest fertilizer mix thatprovides desired amounts of nutrients. The mix ismade by combining the following fertilizers: SSA,SPO, GUR, TSP, KCI, FERT, and SPF. The mix cannot contain both GUR and TSP. The percentage ofpotassium (K), sulfur (S), calcium (Ca), sodium (Na)and phosphorus (P) in each fertilizer is listed in the fileP06_88.xlsx. For example, a pound of SSA is 16% Kand 26% Na. The mix must contain at least 600 poundsof K, 550 pounds of S, 750 pounds of Ca, 900 poundsof Na, and 750 pounds of P. The mix cannot containboth GUR and TSP, because if both are present in themix, the affect of other fertilizers is nullified. The costper pound (in cents) of each fertilizer is listed in thesame file. Develop a linear integer model to find theminimum-cost fertilizer mixture that meets the statedchemical requirements.The Porsche Club of America sponsors driver education events that provide highperformance driving instruction on actual racetracks. Because safety is a primary consideration at such events, many owners elect to install roll bars in their cars. DeeganIndustries manufactures two types of roll bars for Porsches. Model DRB is bolted to thecar using existing holes in the car’s frame. Model DRW is a heavier roll bar that must bewelded to the car’s frame. Model DRB requires 20 pounds of a special high-alloy steel, 40minutes of manufacturing time, and 60 minutes of assembly time. Model DRW requires25 pounds of the special high-alloy steel, 100 minutes of manufacturing time, and 40minutes of assembly time. Deegan’s steel supplier indicated that at most 40,000 poundsof the high-alloy steel will be available next quarter. In addition, Deegan estimates that2000 hours of manufacturing time and 1600 hours of assembly time will be available nextquarter. The profit contributions are $200 per unit for…
- It has been suggested that daily production of a subassembly would be increased if better lighting were installed and background music and free coffee and doughnuts were provided during the day. Management agreed to try the scheme for a limited time. A listing of the number of subassemblies produced per week before and after the new work environment for each employee follows. Employee Past Production Record Production after Installing, Lighting, Music, etc. JD 23 33 SB 26 26 MD 24 30 RCF 17 25 MF 20 19 UHH 24 22 IB 30 29 WWJ 21 25 OP 25 22 CD 21 23 PA 16 17 RRT 20 15 AT 17 9 QQ 23 Show your work, please. Thanks!It has been suggested that daily production of a subassembly would be increased if better lighting were installed and background music and free coffee and doughnuts were provided during the day. Management agreed to try the scheme for a limited time. A listing of the number of subassemblies produced per week before and after the new work environment for each employee follows. Employee Past Production Record Production after Installing, Lighting, Music, etc. JD 23 33 SB 26 26 MD 24 30 RCF 17 25 MF 20 19 UHH 24 22 IB 30 29 WWJ 21 25 OP 25 22 CD 21 23 PA 16 17 RRT 20 15 AT 17 9 QQ 23 30 FIND: State the decision rule and show your work: Reject H0 if T ≤ : Compute T and arrive at a decision (Show your work). T = ____________ , do not reject H0.Pigmented makeup products like mascara and eye shadow may contain metal (e.g., nickel) allergens. Is a nickel allergy more likely to occur in women who report cosmetic dermatitis from using eye shadow or mascara? In a sample of 126 women with cosmetic dermatitis from using eye shadow, 11 were diagnosed with a nickel allergy. In a sample of 266 women with cosmetic dermatitis from using mascara, 26 were diagnosed with a nickel allergy. Use this information to complete parts a through c below. Question content area bottom Part 1 a. Compute a 95% confidence interval for the proportion of women with cosmetic dermatitis from using eye shadow who have a nickel allergy. The 95% confidence interval for eye shadow is enter your response here,enter your response here.
- Pigmented makeup products like mascara and eye shadow may contain metal (e.g., nickel) allergens. Is a nickel allergy more likely to occur in women who report cosmetic dermatitis from using eye shadow or mascara? In a sample of 123 women with cosmetic dermatitis from using eye shadow, 12 were diagnosed with a nickel allergy. In a sample of 261 women with cosmetic dermatitis from using mascara, 27 were diagnosed with a nickel allergy. Use this information to complete parts a through c below. a. Compute a 95% confidence interval for the proportion of women with cosmetic dermatitis from using eye shadow who have a nickel allergy. b. Compute a 95% confidence interval for the proportion of women with cosmetic dermatitis from using mascara who have a nickel allergy. c. Suppose you are informed that the true proportion with a nickel allergy for one of the two groups (eye shadow ormascara) is 0.15. Can you determine which group isreferenced?Pigmented makeup products like mascara and eye shadow may contain metal (e.g., nickel) allergens. Is a nickel allergy more likely to occur in women who report cosmetic dermatitis from using eye shadow or mascara? In a sample of 125 women with cosmetic dermatitis from using eye shadow, 11 were diagnosed with a nickel allergy. In a sample of 267 women with cosmetic dermatitis from using mascara, 25 were diagnosed with a nickel allergy. Use this information to complete parts a through c below. a. Compute a 95% confidence interval for the proportion of women with cosmetic dermatitis from using eye shadow who have a nickel allergy. b. compute a 95% confidence interval for the proportion of women with cosmetic cermatitis from using mascara who have a nickel allergyAn existing mall (Circuit Mall) is located near the residential area and has the following characteristics: Shopping Center Distance from residential area of Zone A (miles) Commercial Floor Space (thousand ft2) Circuit Mall 2.1 220 Three malls are to be built to rival the existing mall and there are currently three proposals. A total of 5000 shopping trips are generated from the residential area. Use n=1.5 Shopping Center Distance from residential area of Zone A (miles) Commercial Floor Space (thousand ft2) SM City 1 3.25 150 SM City 2 5.68 300 SM City 3 6.75 600 How many trips would Circuit Mall make compared to the new competitors?
- A school Psychologist is interested in the effect of violent television programs on a child's agression depending on if the show is a cartoon or not. Eighty children were recruited and were divided into equal groups. Half of the children watched a violent television program while the other half watched a non- violent program. Half of the children watched a cartoon while the other half watched a show that was not a cartoon. The children were then placed in a small group and the researcher measured the level of agressiveness of each child. A) z- test B) t - test C) test independent samples D) T - TEST RELATED SAMPLES E) ANOVA F) FACTORIAL ANOVA G) repeated measures ANOVA H) pearson correlation i) chi squareA dietician prepares a diet specifying the amounts a patient should eat of four basic food groups: group I, meats; group II, fruits and vegetables; group III, breads and starches; group IV, milk products. Amounts are given in “exchanges” that represent 1 oz (meat), 1/2 cup (fruits and vegetables), 1 slice (bread), 8 oz (milk), or other suitable measurements. (a) The number of “exchanges” for breakfast for each of the four food groups, respectively, are 2, 1, 2, and 1; for lunch, 3, 2, 2, and 1; and for dinner, 4, 3, 2, and 1. Write a 3*4matrix using this information.(b) The amounts of fat, carbohydrates, and protein (in appro-priate units) per exchange in each food group, respectively, are as follows.Fat: 5, 0, 0, 10Carbohydrates: 0, 10, 15, 12Protein: 7, 1, 2, 8Use this information to write a 4*3 matrix.(c) There are 8 calories per exchange of fat, 4 calories per ex-change of carbohydrates, and 5 calories per exchange of protein. Summarize these data in a 3*1 matrix.