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Name: _________________________ Score: ______ / ______ 1. Find the indicated sum. Show your work. k = 1, (-1)^k (k + 11) = (-1)^(1) (1 + 11)= -1*(12) = -12 k = 2, (-1)^k (k + 11) = (-1)^(2) (2 + 11)= 1*(13) = 13 k = 3, (-1)^k (k + 11) = (-1)^(3) (3 + 11)= -1*(14) = -14 k = 4, (-1)^k (k + 11) = (-1)^(4) (4 + 11)= 1*(15) = 15 (-12)+(13)+(-14)+(15)=2 2. Locate the foci of the ellipse. Show your work. X^2=(x-h)^2, then h=0 Y^2=(x-k)^2, then k=0 The centre is (0,0) X^2/36+y^2/11=1 When x=0 y^2/11=1; y=0 When y=0,x=0 X^2/36=1;x=0 11+c^2=36 C=5 Foci (5,0) and (-5,0) 3. Solve the system by the substitution method. Show your work. 2y - x = 5 x2 + y2 - 25 = 0 x: 2y - x = 5 2y - 5 = x so x = 2y - 5 -Plug this into 2nd equation: (2y - 5)² + y² - 25 = 0 -Use FOIL to solve the (2y - 5)² part: (2y - 5)(2y - 5) 4y² - 10y - 10y + 25 4y² - 20y + 25 So : 4y² - 20y + 25 + y² - 25 = 0 Which can be simplified to: 4y² + y² - 20y = 0 4y² + y² - 20y = 0 y(4y + y - 20) = 0 So, because of the 0 multiplication rule, y=0 x= -5 (plug in y=0 to original equations: 2y - x = 5 2(0) - x = 5, so x= -5) (-5,0) Y(4y+y-20)=0 So, y=0 or 4y+y-20=0 5y-20=0 Y=4 X=2y-5 when y=4 X=8-5=3 (-5,0) (3,4) 4. Graph the function. Then use your graph to find the indicated limit. You do not have to provide the graph f(x) = 5x - 3, f(x) 22 5. Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists. Show your work. 4x - y + 3z = 12 x + 4y + 6z = -32 5x + 3y + 9z = 20 6. Solve the system of equations using matrices. Use Gaussian elimination with back-substitution. x + y + z = -5 x - y + 3z = -1 4x + y + z = -2 X=1/3, y=-(11/3),z=-(5/3) 7. A woman works out by running and swimming. When she runs, she burns 7 calories per minute. When she swims, she burns 8 calories per minute. She wants to burn at least 336 calories in her workout. Write an inequality that describes the situation. Let x represent the number of minutes running and y the number of minutes swimming. Because x and y must be positive, limit the boarders to quadrant I only. 7x+8y>=336 Short Answer Questions: Type your answer below each question. Show your work. 8. A statement S n about the positive integers is given. Write statements S 1 , S 2 , and S 3 , and show that each of these statements is true. Show your work. S n : 1 2 + 4 2 + 7 2 + . . . + (3n - 2) 2 = S1=1(6*1^2-3(1)-1)/2=1 S2=1^2+4^2=17 S31^2+4^2+7^2=66 9. A statement S n about the positive integers is given. Write statements S k and S k+1 , simplifying S k+1 completely. Show your work. S n : 1 ∙ 2 + 2 ∙ 3 + 3 ∙ 4 + . . . + n ( n + 1) = [ n ( n + 1)( n + 2)]/3 10. Joely's Tea Shop, a store that specializes in tea blends, has available 45 pounds of A grade tea and 70 pounds of B grade tea. These will be blended into .
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Pre-Calculus Quarter 4 Exam Name: _________________________ Score: ______ / ______ 1. Find the indicated sum. Show your work. 2. Locate the foci of the ellipse. Show your work. 3. Solve the system by the substitution method. Show your work. 2y - x = 5 x2 + y2 - 25 = 0 4. Graph the function. Then use your graph to find the indicated limit. You do not have to provide the graph f(x) = 5x - 3, f(x) 5. Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists. Show your work. 4x - y + 3z = 12 x + 4y + 6z = -32 5x + 3y + 9z = 20 6. Solve the system of equations using matrices. Use Gaussian elimination with back-substitution. x + y + z = -5 x - y + 3z = -1 4x + y + z = -2 7. A woman works out by running and swimming. When she runs, she burns 7 calories per minute. When she swims, she burns 8 calories per minute. She wants to burn at least 336 calories in her workout. Write an inequality that describes the situation. Let x represent the number of minutes running and y the number of minutes swimming. Because x and y must be positive, limit the boarders to quadrant I only. Short Answer Questions: Type your answer below each question. Show your work. 8. A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. Show your work. Sn: 12 + 42 + 72 + . . . + (3n - 2)2 = 9. A statement Sn about the positive integers is given. Write statements Sk and Sk+1, simplifying Sk+1 completely. Show your work. Sn: 1 ∙ 2 + 2 ∙ 3 + 3 ∙ 4 + . . . + n(n + 1) = [n(n + 1)(n + 2)]/3 10. Joely's Tea Shop, a store that specializes in tea blends, has available 45 pounds of A grade tea and 70 pounds of B grade tea. These will be blended into 1 pound packages as follows: A breakfast blend that contains one third of a pound of A grade tea and two thirds of a pound of B grade tea and an afternoon tea that contains one half pound of A grade tea and one half pound of B grade tea. If Joely makes a profit of $1.50 on each pound of the breakfast blend and $2.00 profit on each pound of the afternoon blend, how many pounds of each blend should she make to maximize profits? What is the maximum profit? 11 Your computer supply store sells two types of laser printers. The first type, A, has a cost of $86 and you make a $45 profit on each one. The second type, B, has a cost of $130 and you make a $35 profit on each one. You expect to sell at least 100 laser printers this month and you need to make at least $3850 profit on them. How many of what type of printer should you order if you want to minimize your cost? 12 A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. Show your work. Sn: 2 + 5 + .
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Pre-Calculus Quarter 4 Exam 1 Name: _________________________ Score: ______ / ______ 1. Find the indicated sum. Show your work. 2. Locate the foci of the ellipse. Show your work. 𝑥2 36 + 𝑦2 11 = 1 Pre-Calculus Quarter 4 Exam 2 3. Solve the system by the substitution method. Show your work. 2y - x = 5 x2 + y2 - 25 = 0 4. Graph the function. Then use your graph to find the indicated limit. You do not have to provide the graph f(x) = 5x - 3, f(x) 5. Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists. Show your work. 4x - y + 3z = 12 x + 4y + 6z = -32 5x + 3y + 9z = 20 Pre-Calculus Quarter 4 Exam 3 6. Solve the system of equations using matrices. Use Gaussian elimination with back- substitution. x + y + z = -5 x - y + 3z = -1 4x + y + z = -2 7. A woman works out by running and swimming. When she runs, she burns 7 calories per minute. When she swims, she burns 8 calories per minute. She wants to burn at least 336 calories in her workout. Write an inequality that describes the situation. Let x represent the number of minutes running and y the number of minutes swimming. Because x and y must be positive, limit the boarders to quadrant I only. Short Answer Questions: Type your answer below each question. Show your work. 8. A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. Show your work. Sn: 1 2 + 4 2 + 7 2 + . . . + (3n - 2) 2 = 𝑛(6𝑛2−3𝑛−1) 2 Pre-Calculus Quarter 4 Exam 4 9. A statement Sn about the positive integers is given. Write statements Sk and Sk+1, simplifying Sk+1 completely. Show your work. Sn: 1 ∙ 2 + 2 ∙ 3 + 3 ∙ 4 + . . . + n(n + 1) = [n(n + 1)(n + 2)]/3 10. Joely's Tea Shop, a store that specializes in tea blends, has available 45 pounds of A grade tea and 70 pounds of B grade tea. These will be blended into 1 pound packages as follows: A breakfast blend that contains one third of a pound of A grade tea and two thirds of a pound of B grade tea and an afternoon tea that contains one half pound of A grade tea and one half pound of B grade tea. If Joely makes a profit of $1.50 on each pound of the breakfast blend and $2.00 profit on each pound of the afternoon blend, how many pounds of each blend should she make to maximize profits? What is the maximum profit? 11 Your computer supply store sells two types of laser printers. The first type, A, has a cost of $86 and you make a $45 profit on each one. The second type, B, has a cost of $130 and you make a $35 profit on each one. You expect to sell at least 100 laser printers this month and you need to make at least $3850 profit on them. How many of what type of p
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Name: _________________________ Score: ______ / ______ 1. Find the indicated sum. Show your work. k = 1, (-1)^k (k + 11) = (-1)^(1) (1 + 11)= -1*(12) = -12 k = 2, (-1)^k (k + 11) = (-1)^(2) (2 + 11)= 1*(13) = 13 k = 3, (-1)^k (k + 11) = (-1)^(3) (3 + 11)= -1*(14) = -14 k = 4, (-1)^k (k + 11) = (-1)^(4) (4 + 11)= 1*(15) = 15 (-12)+(13)+(-14)+(15)=2 2. Locate the foci of the ellipse. Show your work. X^2=(x-h)^2, then h=0 Y^2=(x-k)^2, then k=0 The centre is (0,0) X^2/36+y^2/11=1 When x=0 y^2/11=1; y=0 When y=0,x=0 X^2/36=1;x=0 11+c^2=36 C=5 Foci (5,0) and (-5,0) 3. Solve the system by the substitution method. Show your work. 2y - x = 5 x2 + y2 - 25 = 0 x: 2y - x = 5 2y - 5 = x so x = 2y - 5 -Plug this into 2nd equation: (2y - 5)² + y² - 25 = 0 -Use FOIL to solve the (2y - 5)² part: (2y - 5)(2y - 5) 4y² - 10y - 10y + 25 4y² - 20y + 25 So : 4y² - 20y + 25 + y² - 25 = 0 Which can be simplified to: 4y² + y² - 20y = 0 4y² + y² - 20y = 0 y(4y + y - 20) = 0 So, because of the 0 multiplication rule, y=0 x= -5 (plug in y=0 to original equations: 2y - x = 5 2(0) - x = 5, so x= -5) (-5,0) Y(4y+y-20)=0 So, y=0 or 4y+y-20=0 5y-20=0 Y=4 X=2y-5 when y=4 X=8-5=3 (-5,0) (3,4) 4. Graph the function. Then use your graph to find the indicated limit. You do not have to provide the graph f(x) = 5x - 3, f(x) 22 5. Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists. Show your work. 4x - y + 3z = 12 x + 4y + 6z = -32 5x + 3y + 9z = 20 6. Solve the system of equations using matrices. Use Gaussian elimination with back-substitution. x + y + z = -5 x - y + 3z = -1 4x + y + z = -2 X=1/3, y=-(11/3),z=-(5/3) 7. A woman works out by running and swimming. When she runs, she burns 7 calories per minute. When she swims, she burns 8 calories per minute. She wants to burn at least 336 calories in her workout. Write an inequality that describes the situation. Let x represent the number of minutes running and y the number of minutes swimming. Because x and y must be positive, limit the boarders to quadrant I only. 7x+8y>=336 Short Answer Questions: Type your answer below each question. Show your work. 8. A statement S n about the positive integers is given. Write statements S 1 , S 2 , and S 3 , and show that each of these statements is true. Show your work. S n : 1 2 + 4 2 + 7 2 + . . . + (3n - 2) 2 = S1=1(6*1^2-3(1)-1)/2=1 S2=1^2+4^2=17 S31^2+4^2+7^2=66 9. A statement S n about the positive integers is given. Write statements S k and S k+1 , simplifying S k+1 completely. Show your work. S n : 1 ∙ 2 + 2 ∙ 3 + 3 ∙ 4 + . . . + n ( n + 1) = [ n ( n + 1)( n + 2)]/3 10. Joely's Tea Shop, a store that specializes in tea blends, has available 45 pounds of A grade tea and 70 pounds of B grade tea. These will be blended into .
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Pre-Calculus Quarter 4 Exam Name: _________________________ Score: ______ / ______ 1. Find the indicated sum. Show your work. 2. Locate the foci of the ellipse. Show your work. 3. Solve the system by the substitution method. Show your work. 2y - x = 5 x2 + y2 - 25 = 0 4. Graph the function. Then use your graph to find the indicated limit. You do not have to provide the graph f(x) = 5x - 3, f(x) 5. Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists. Show your work. 4x - y + 3z = 12 x + 4y + 6z = -32 5x + 3y + 9z = 20 6. Solve the system of equations using matrices. Use Gaussian elimination with back-substitution. x + y + z = -5 x - y + 3z = -1 4x + y + z = -2 7. A woman works out by running and swimming. When she runs, she burns 7 calories per minute. When she swims, she burns 8 calories per minute. She wants to burn at least 336 calories in her workout. Write an inequality that describes the situation. Let x represent the number of minutes running and y the number of minutes swimming. Because x and y must be positive, limit the boarders to quadrant I only. Short Answer Questions: Type your answer below each question. Show your work. 8. A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. Show your work. Sn: 12 + 42 + 72 + . . . + (3n - 2)2 = 9. A statement Sn about the positive integers is given. Write statements Sk and Sk+1, simplifying Sk+1 completely. Show your work. Sn: 1 ∙ 2 + 2 ∙ 3 + 3 ∙ 4 + . . . + n(n + 1) = [n(n + 1)(n + 2)]/3 10. Joely's Tea Shop, a store that specializes in tea blends, has available 45 pounds of A grade tea and 70 pounds of B grade tea. These will be blended into 1 pound packages as follows: A breakfast blend that contains one third of a pound of A grade tea and two thirds of a pound of B grade tea and an afternoon tea that contains one half pound of A grade tea and one half pound of B grade tea. If Joely makes a profit of $1.50 on each pound of the breakfast blend and $2.00 profit on each pound of the afternoon blend, how many pounds of each blend should she make to maximize profits? What is the maximum profit? 11 Your computer supply store sells two types of laser printers. The first type, A, has a cost of $86 and you make a $45 profit on each one. The second type, B, has a cost of $130 and you make a $35 profit on each one. You expect to sell at least 100 laser printers this month and you need to make at least $3850 profit on them. How many of what type of printer should you order if you want to minimize your cost? 12 A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. Show your work. Sn: 2 + 5 + .
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Pre-Calculus Quarter 4 Exam 1 Name: _________________________ Score: ______ / ______ 1. Find the indicated sum. Show your work. 2. Locate the foci of the ellipse. Show your work. 𝑥2 36 + 𝑦2 11 = 1 Pre-Calculus Quarter 4 Exam 2 3. Solve the system by the substitution method. Show your work. 2y - x = 5 x2 + y2 - 25 = 0 4. Graph the function. Then use your graph to find the indicated limit. You do not have to provide the graph f(x) = 5x - 3, f(x) 5. Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists. Show your work. 4x - y + 3z = 12 x + 4y + 6z = -32 5x + 3y + 9z = 20 Pre-Calculus Quarter 4 Exam 3 6. Solve the system of equations using matrices. Use Gaussian elimination with back- substitution. x + y + z = -5 x - y + 3z = -1 4x + y + z = -2 7. A woman works out by running and swimming. When she runs, she burns 7 calories per minute. When she swims, she burns 8 calories per minute. She wants to burn at least 336 calories in her workout. Write an inequality that describes the situation. Let x represent the number of minutes running and y the number of minutes swimming. Because x and y must be positive, limit the boarders to quadrant I only. Short Answer Questions: Type your answer below each question. Show your work. 8. A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. Show your work. Sn: 1 2 + 4 2 + 7 2 + . . . + (3n - 2) 2 = 𝑛(6𝑛2−3𝑛−1) 2 Pre-Calculus Quarter 4 Exam 4 9. A statement Sn about the positive integers is given. Write statements Sk and Sk+1, simplifying Sk+1 completely. Show your work. Sn: 1 ∙ 2 + 2 ∙ 3 + 3 ∙ 4 + . . . + n(n + 1) = [n(n + 1)(n + 2)]/3 10. Joely's Tea Shop, a store that specializes in tea blends, has available 45 pounds of A grade tea and 70 pounds of B grade tea. These will be blended into 1 pound packages as follows: A breakfast blend that contains one third of a pound of A grade tea and two thirds of a pound of B grade tea and an afternoon tea that contains one half pound of A grade tea and one half pound of B grade tea. If Joely makes a profit of $1.50 on each pound of the breakfast blend and $2.00 profit on each pound of the afternoon blend, how many pounds of each blend should she make to maximize profits? What is the maximum profit? 11 Your computer supply store sells two types of laser printers. The first type, A, has a cost of $86 and you make a $45 profit on each one. The second type, B, has a cost of $130 and you make a $35 profit on each one. You expect to sell at least 100 laser printers this month and you need to make at least $3850 profit on them. How many of what type of p
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The recently published educational policy document under the title ‘National Education Policy Reform’ (NEPF for short) has been the subject of much criticism. Various parties have expressed their grave concerns about this proposed NEPF on many platforms. This document attempts to cover some angles which the author deems less covered in other criticisms. This critique is by no means complete or exhaustive; rather, the author prefers that it be read in conjunction with other such criticisms.
A Critique of the Proposed National Education Policy Reform
A Critique of the Proposed National Education Policy Reform
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Study smart! The most important topics for your IGNOU exam are in this document. We analyzed the examination pattern for IGNOU’s PGDCFT and MSCCFT courses – taking into account every single question of every exam of every single subject to generate these very useful, high-quality insights. Forget about 10 years papers – study smart using FIHC’s IGNOU Exam Question Pattern!
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Discover the Kisan Call Centre: Your Gateway to Agricultural Assistance KISAN CALL CENTRE In order to harness the potential of ICT in Agriculture, Ministry of Agriculture & Farmers Welfare launched the scheme “Kisan Call Centres” (KCCs) on January 21, 2004. Main aim of the scheme is to answer farmers’ queries on a telephone call in their own language. These call centres are working in 21 different locations in the country covering all the States and UTs. A countrywide common eleven digit Toll Free Number 1800-180-1551 has been allotted for Kisan Call Centre. This number is accessible through mobile phones and landlines of all telecom networks including private service providers. Replies to the farmers’ queries are given in 22 local languages. Kisan Call Centre services are available from 6.00 AM to 10.00 PM on all seven days of the week at each KCC location. Kisan Call Centre agents known as Farm Tele Advisors (FTAs), who are graduate or above (i.e. PG or Doctorate) in Agriculture or allied sectors (Horticulture, Animal Husbandry, Fisheries, Poultry, Bee-Keeping, Sericulture, Aquaculture, Agricultural Engineering, Agricultural Marketing, Bio-Technology, Home Science, etc.) and possess excellent communication skills in respective local language. Queries which cannot be answered by FTAs are transferred to higher level experts. These experts are Subject Matter Specialists (SMSs) of State Departments of Agriculture (SDAs), ICAR Institutes, KVKs and State Agricultural Universities (SAUs). A Kisan Knowledge Management System (KKMS) has been developed to capture all the details of the caller and sending gist of answer given through SMS. KKMS has its independent website : http://dackkms.gov.in. The KCC, FTAs working at various KCC locations throughout the country have access to this website through their specific IDs and password provided to them. Welcome to the Kisan Call Centre - your one-stop destination for agricultural assistance and support. With dedicated team of experts and cutting-edge technology, we're here to revolutionize the way farmers access information and guidance. In this powerpoint, we delve into the world of the Kisan Call Centre, exploring how it functions, the services it offers, and the impact it has on farmers across the nation. From real-time advisory services to multilingual support, we'll uncover the key features that make the Kisan Call Centre an indispensable resource for farmers of all backgrounds. Join us as we showcase the achievements of the Kisan Call Centre, from its enhanced farmer outreach to its empowerment of women farmers. Discover how our feedback mechanism ensures continuous improvement, and learn about our collaborations with agricultural institutions to provide accurate and reliable information. Whether you're a seasoned farmer or just starting out, the Kisan Call Centre is here to support you every step of the way. Subscribe now to stay updated on the latest agricultural insights
Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...
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Russian Escort Service in Delhi 11k Hotel Foreigner Russian Call Girls in Delhi
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In this webinar, nonprofits learned how to delve into the minds of funders, unveiling what they truly seek in qualified grant applicants, and tools for success. Learn more about the Grant Readiness Review service by Remy Consulting at TechSoup to help you gather, organize, and assess the strength of documents required for grant applications.
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This presentation was provided by William Mattingly of the Smithsonian Institution, during the fourth segment of the NISO training series "AI & Prompt Design." Session Four: Structured Data and Assistants, was held on April 25, 2024.
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