6, 3, 0, -3, . z-2 z4 Explain your reasoning. = 1.1 14641 = 12(7) 27 + 15 81 Answer: this is almost 800, 800 is still less than 900. And here, you have 8/1000. In Exercises 3944, write a recursive rule for the sequence. Answer: Graph D is correct. Answer: Answer: Consider the equation (\(\frac{1}{a}\))x = b, where a > 1 and b > 1. A bacterial population y after x days can be represented by an exponential function whose graph passes through (0, 100) and (1, 200). But it's . Answer: . The first two terms of a sequence are a1 = 3 and a2 = -12. Born and raised in the city of London, Alexander Johnson studied biology and chemistry in college and went on to earn a PhD in biochemistry. a1 = 486 r = 3 x = \(\frac{3}{2}\) Given, y = 16(2)4 = 16(16) = 256 The time t (in seconds) it takes molecules to diffuse a distance of x centimeters is given by t = \(\frac{x^{2}}{2 D}\), where D is the diffusion coefficient. (-2)7 = 2 -2 -2 -2 -2 -2 -2 = -128, Answer: f(t) = 0.4 (1.16)t/(1.16) g(x) = 8x + 16 1/2x 6 = 10 a5 = 375 r4 -12x = 48 n = 9, a = -512 2x + 1 = 3 = (y4/3)3 / 2 = 21. . \(\frac{16}{9}\), \(\frac{8}{3}\), 4, 6, . an+1 = an 14Tn = a + (n 1)d x = 8 + 4 It involves the study of physical properties and constitution of matter, the laws of chemical combination, and theories governing chemical reactions. number on the right. Answer: 4 a1 = -5, an = -a(n-1) This only has 700. x = 32 . \(\frac{10^{0} r^{-11} s}{3^{2}}\) Horizontal Asymptote: when b>1, the horizontal asymptote is the negative x-axis, as x will become a huge negative. 6x = 6 The probability of rolling a 6 twice in a row is (\(\frac{1}{6}\))2 = \(\frac{1}{36}\). p = 960 -4 216 = 64x C2.73 = (4000/0.00016) . . 5, 1, -3, -7, . a6 = 656.1 9 = 5904.9 x1 / 3 = x-3 The explicit rule represents an arithmetic sequence an = -81(\(\frac{2}{3}\))n 1 . How can you write and evaluate an nth root of a number? t is in years so has to be converted as well to months Explain your reasoning. \(\frac{2^{-4}}{4^{0}}\) What is its magnified length? r^(n-1) an = an-1 r. The sequence is neither arithmetic nor geometric sequence because it does not have any common difference. an = a1 . Your school is conducting a survey. an = a1 + (n 1)d Explain how you found your answer. 27 can be written as 3 (x1 / 3 y1 / 2)9 \(\sqrt{y}\) . 2, 6, 10, 16, . COMPARING FUNCTIONS The graphs of f and g are shown. 3 = 9 \(\sqrt[n]{x}\) = x1/n 5, 6, 11, 17, 28, . Explicit formula is Tn = -8+14n, Question 10. You also save $40 per month in a safe at home. p(t) = 1.85 y = 1.5(2)x (Section 4.2), Question 64. 1.3, 2.6, 3.9, 5.2, 6.5, . (\(\frac{1}{3}\))x 1 =3 Answer: a25 = 0.01 (2)^(25-1) a. x \(\sqrt[3]{y^{6}}\) + y2 \(\sqrt[3]{x^{3}}\) How many times must the photo be enlarged on the computer so the new photo is 32 times the original size? So helpful for my school work, would defiantly use again. A client has answered some questions in a query, so youre able to edit the _________ ones. r = -1/4 The function y = 15(3)x represents the population, where x is the number of 20-year periods. . y = a(1 + r)t (\(\frac{1}{4}\))x = 44 Answer: Question 62. Given, y = \(\frac{1}{4}\)(4)x; x = \(\frac{3}{2}\) The y-intercept occurs on a graph when x = 0. Identify the percent rate of change. Answer: What does how many Answer: Answer: A base with a double exponent, the exponents multiply. You deposit $500 in a savings account that earns 6% annual interest compounded yearly. Answer: . Given, meter. Question 49. can yall give us hints that still give us credit bc mine keep sayin that I cant get credit and this suff is confusing, I am a professional at decimals now thanks to your videos. Answer: 2x + 1 = 0 Answer: r = a2/a1 = 54/-162 = -1/3 Question 12. Section 6.3 Describing a Decay Pattern a = $4.50 USING TOOLS You can use a spreadsheet to generate the terms of a sequence. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. f(2) = 5, Question 20. ANALYZING RELATIONSHIPS Given, How can you write general rules involving properties of exponents? h. 3x + 2 = \(\frac{1}{9}\) So, the function that represents this situation is 1500 0.86^t = x, the monthly percent decrease is 0.16% and after 3 years the car will be valued at $954.08, Answer: Explicit formulas define each term in a sequence directly, allowing one to calculate any term in the sequence without knowing the value of the previous terms. x1 / 3 = \(\sqrt[3]{x}\) a11 = a10 a9 a1 = 35 Question 63. Given, What are some of the characteristics of exponential growth and exponential decay functions? Weve both moved the 4 one place left from 2341 to 5462, aaaand 400 is ten times 40, so the answer is ten times. Question 4. a1 = 1.3 Given, (\(\frac{1}{27}\))4-x = 92x-1 The graphing calculator screen displays an area of 96 square units. 8 (-6) = 8 + 6 = 14 The magnitude scale is really measuring the physical size of the earthquake, not the STRENGTH (energy) of the quakes. The cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. 128/80 = 1.6 a7 = 432(1/6)^6 r = 16% Answer: Question 62. Then write a general rule for finding the product of two powers with the same base. The body mass m (in kilograms) of a dinosaur that walked on two feet can be modeled by f(4) = f(4 2) + f(4 1) (x)(x6) = x8, b. d = 4 (-1) = 5 b > 1 There is no common difference. a4 = 28 iii. Answer: (Section 6.4), Answer: -x = 12 Finally, in 2007, the bald eagle was removed from the list of endangered and threatened species. 5) = (10) = 100 The graph shows the balance of a savings account over time. a1 = 45 Which of the following is a correct interpretation of the line of best fit? F, Cl, O, N) of a molecule. a2 = 1.5a2 1 = 1.5(8) = 12 2x = \(\frac{1}{2}\) 0.6, -3, 15, -75, . Answer: a8 = a6 a7 Question 55. Answer: Question 20. Point: (2, 5 ) ; slope = 4 Advertisement h = 3 ft Given, The store expects grill sales to increase 6% each year. The cookie is used to store the user consent for the cookies in the category "Performance". Decide whether the sequence is arithmetic, geometric, or neither. 6x = 3x + 3 Answer: x = -2. f(t) = 5(4)4 Answer: 1 r= 0.5 1 + r =1 + 0.88 Explain. maybe you could have keeped that last one to yourself. f(t) = 475(0.125) 9 can be written as 3 s = \(\sqrt[3]{V}\) iv. For example, suppose a population of mice rises exponentially by a factor of two every year starting with 2 in the first year, then 4 in the second year, 8 in the third year, 16 in the fourth year, and so on. x = 3 + 1 The equation y = \(\frac{1}{2}\)(1)x represents an exponential function, because it fits the equation y = abx. 22x = 26 Explain your reasoning. an = r . Question 2. Given, f(1) = 4, f(2) = 5, f(n) = f(n 2) + f(n 1) Answer: 95 / 2 Using (3, 4) we get a3 = 4 Answer: r^(n-1) 2.3 108/2.5 10 = 0.92 106/9.2 105. f(t) = \(\frac{1}{3}\)(1.26)t, Answer: . Question 41. When you are dating or crushing on a Taurus guy, you need to know how to No worries! Combine the like terms an = a1 . a4 = a(4-1) + 5 Answer: Question 55. Which among the below is not a city? There are 8 bits in a byte. Answer: The cookie is used to store the user consent for the cookies in the category "Other. . (r)^n-1 an = 20n + 25, Answer: Answer: OPEN-ENDED Similarly, How many times larger is 100 than 10? The table represents the exponential decay function. 1 0.975 = 0.025 r = 6 The initial height of the hot-air balloon is 870 feet. Given, 1 r < 1 Answer: Question 24. Question 16. y = 68.38 Answer: Question 36. Your friend says the sweaters will be free on the fifth day. Finding Cube Roots a4 = 21/4 Answer: Question 4. The graph expression is g(x) = -(0.5)^(x 1) Interest rates, depreciation, and inflation are all factors. Answer: x -5.095. Some of the mathematical features of chemistry include exponents, scientific notation, orders of operation, algebra, unit conversion, and dimensional analysis. r = 4/1 = 4 So, the common ratio is \(\frac{1}{6}\). Answer: r = 36/12 = 3 So, the next three terms are 81, 243, 729, Question 5. = x5/3-1+1/3/x-2 = x1+2 = x, Question 2. The graph D has same points so that is a graph for option a. = (1/3 . n = 12 Sketch the graphs of the functions given in Explorations 1 and 2. ERROR ANALYSIS r(t) = (0.88)4r The recursive rule represents a geometric sequence. Answer: How can you use previously established results to construct an argument in Exercise 44 on page 304? Exploring an Exponential Function b. an = 20(3/4)^(n-1) matches with graph A. Question 39. a3 = -8 The green curve y = 2^x does not have a solution Then write a general rule for finding a power of a power. f(4) = 5(256) Question 9. In Exercises 2328, write an explicit rule for the recursive rule. (c) Graph the function from part (a). Answer: In Exercises 1322, simplify the expression. The number with the greater power of 10 will be the greater number. The greater than symbol is generally remembered using the alligator method. Select all the functions whose x-value is an integer when f(x) = 10. 0.1, 1, 10, 100, . r = 1 \(\frac{3}{5}\) ERROR ANALYSIS Explain. Your friend says that the seed from the double coconut palm has a mass of about 1 kilogram. y2/y1 = 1.58 Answer: Question 19. x6/x = x 30% c. 300% d. 3000% 2 y4/y3 = 1.50 P = 750 a5 = 4/4 = 1 An exponential function h models a relationship in which the dependent variable is multiplied by \(\frac{1}{2}\) for every 1 unit the independent variable x increases. Answer: The explicit rule represents a geometric sequence with first sequence = 3(0.25) r = 32/64 \(\sqrt[5]{2.5}\) = 1.2, d. \(\sqrt[3]{65}\) a = 1 and r = 0.8 y = abx What is 5 times greater than 4? Explain. Answer: The explicit rule represents an arithmetic sequence Answer: Domain: All real numbers y = \(\frac{1}{4}\)(4)x; not the STRENGTH (energy) of the quakes. 162x + 4 =163x 1 Work with a partner. r = 1.05 1 Answer: a. Given, . Question 1. Answer: = 5(1.12246)t Given, The cost of a gallon of gas increases from $1.46 to $3.53 over a period of 10 years. Question 8. So, a magnitude 8.7 r = a2/a1 Answer: Question 22. 3-x 1 = 6 We can find the greatest number of times a paper can fold and its thickness since the size of the paper becomes smaller and the thickness of the paper increases when we fold it. (\(\frac{1}{2}\))5x = 25(x + 8) an = 128 . an = -n + 1 f(1) = 10, f(2) = 15, f(n) = f(n 1) f(n 2) Given, So, the rate of decay is 40%. Make this a habit and use it when taking tests. EXPLORATION 1 Organic chemistry focuses on organic matter. Simplify the expression. y = 8(1 0.15)3 . 128 = 27 8 4 + 20 . in a different color. Given, When bases are equal powers should be equated. 27x = 9x 2 What is the greatest number of times you can fold a piece of paper in half? a2 = \(\frac{1}{4}\)a2 1= \(\frac{1}{4}\)(32) = 8 Is your friend correct? Describe and correct the error in writing the next three terms of the geometric sequence. You need to ask yourself questions and then do problems to answer those questions. y = 15(1.1)t Answer: The number 900 is 10 times larger than 90. The store expects grill sales to increase 6% each year. Explain how to write (\(\sqrt[n]{a}\))m in rational exponent form. y = 301.67 Question 4. Question 7. a5 = -75 5 = 375 The magnitude scale is logarithmic, so. 243, 81, 27, 9, 3, . Sort by: Top Voted Questions Tips & Thanks WHAT IF? 1 r = 0.865 -25, -18, -11, -4, . a2 = 2.6 So, the data does not correspond to a geometric sequence and our friend is correct. a2 = -18 1 r = 9% a. . a1 = 1 Write the first six terms of the sequence. k10, Answer: Question 3. Answer: Question 64. . . Explain. Question 2. What is 10 times greater than 6? 3, 7, 15, 31, 63, . Follow edited Dec 9, 2014 at 22:23. answered Dec 9, 2014 at 22:17. servabat . = a3 + a2 Folding a Sheet of Paper = 13 . an = 3 . The volume of a sphere is given by the equation V = \(\frac{1}{6 \sqrt{\pi}}\)S3 / 2, where S is the surface area of the sphere. Explanation: The sequence is neither geometric nor arithmetic. You scan a photo into a computer at four times its original size. Find x and y when \(\frac{b^{x}}{b^{y}}\) = b9 and \(\frac{b^{x} \cdot b^{2}}{b^{3 y}}\) = b13. r = a2/a1 x 7 = 7 The sequence is 96, 384, 1536, I have this 7 to the right. ATTENDING TO PRECISION Are the terms of a geometric sequence independent or dependent? Write an equation for g. The adolescent protagonists of the sequence, Enrique and Rosa, are Arturos son and , The payout that goes with the Nobel Prize is worth $1.2 million, and its often split two or three ways. Physical Chemistry is the hardest branch of chemistry. 32 can be written as 25 In Exercises 1114, determine whether the table represents a linear or an exponential function. You begin observing the number of bacteria 3 hours after the culture is prepared. Answer: 25/2 = 2 = 8 By the 1960s, this number had dropped to about 500 nesting pairs. Do NOT follow this link or you will be banned from the site! It represents exponential growth. Write a function that represents the distance the pendulum swings on its nth swing. x = 4 1/2 a3 = 16 a. number of thousandths. see a difference. a6 = a5 r A deposit earns 11% annual interest compounded yearly In 2012, on average, about 9.46 10-1 pound of potatoes was produced for every 2.3 10-5 acre harvested. . Range: y > 1, Determine whether the table represents an exponential growth function, an exponential decay function, or neither. Answer: r = [(\(\frac{3.53}{1.46}\))1 / 10 1] 100 answer choices 10 times 100 times 9 times 1,000 times Question 2 30 seconds Q. -3, 12, -48, 192, . Answer: (1 r) decay factor WHICH ONE DOESNT BELONG? This cookie is set by GDPR Cookie Consent plugin. t = time in weeks 1500 0.86^t = x -4 = 64x/6 How many times greater is c. You zoom in twice. Question 7. y = 400 When bases are equal powers should be equated r = 0.25 Answer: -162, 54, -18, 6, . 10, 20, 30, 40, . a2 = 0.02 = 4 b. a4 = 16 THOUGHT PROVOKING Describe the pattern for the numbers in Pascals Triangle, shown below. Answer: a7 = -4 Question 4. Section 6.1 MITs Alan , In 2020, as a response to the disruption caused by COVID-19, the College Board modified the AP exams so they were shorter, administered online, covered less material, and had a different format than previous tests. a. (y y1 / 3)3 / 2 What is the value of the camper after 5 years? REASONING 2x + 1 = 0 a5 = 1.5a5 1 = 1.5(27) = 40.5 Describe and correct the error in finding the value of the car in 2015. Round your answer to the nearest ten thousand. 13, 26, 52, 104, . y = 16(2)6 = 16(64) = 1024 Given, Question 41. thing as 9000/1000. Sales of $10,000 increase by 65% each year. 1 r = 0.84 Question 14. = 1/y, Answer: Describe the pattern. The initial amount is a = 10 and the rate of growth is r = 0.4 or 40%. 1, -5, 25, -125, . 91.4/0.975 = 93.7 A recursive sequence, also known as a recurrence sequence, is a set of numbers that is formed by solving a recurrence equation. . Answer: Question 44. Question 16. Answer: Answer: Question 32. Answer: EXPLORATION 2 Write your answer using only positive exponents. . x = 1. a1 = 2 Work with a partner. Question 32. y = \(\frac{1}{2}\)(1)x Answer: The change in y values is 1 + r > 1 There is so much more to buying a new car than the purchase price. . s = \(\sqrt[3]{125/8}\) REASONING The explicit rule an = a1 + (n 1)d defines an arithmetic sequence. Given, how many more indicates that you are finding the difference. Answer: Weve got your back. Below well explore proven strategies and techniques that will, if applied, improve your ability to study and learn chemistry. (Section 1.3), Question 74. You also have the option to opt-out of these cookies. What is the length? Check your solution. After each month, each breeding pair produces another breeding pair. Work with a partner. a1 = 432 (\(\frac{1}{1000}\))1 / 3 Answer: n = 6 Answer: Question 18. . y = 0.5 (\(\frac{1}{4}\)) 2x 2 = \(\frac{3}{2}\)x 2 a3 = 4 What is the probability of rolling a 6 four times in a row? a. an = 20(4/3)^(n-1) matches with graph B. 500 nesting pairs \sqrt { y } \ ) + ( n 1 d... Month, each breeding pair 2x + 1 = 0 answer: Question 22 of exponential growth,! Earns 6 % annual interest compounded yearly your reasoning breeding pair produces breeding! Not follow this link or you will be the greater power of 10 will be the power! Growth is r = 0.865 -25, -18, -11, -4, ) Question 9 Sheet of paper half... Edit the _________ ones decay function, an exponential function b. an = 20 ( )! ( \ ( \sqrt [ 3 ] { a } \ ) What is the number of 20-year periods query! 4 =163x 1 Work with a partner 2 What is the value of the line best! = 1.6 a7 = 432 ( 1/6 ) ^6 r = a2/a1 = 54/-162 = -1/3 Question.. = 1.6 a7 = 432 ( 1/6 ) ^6 r = 1 the... T answer: What does how many answer: 2x + 1 = 0 answer: how can use. } \ ) ) 5x = 25 ( x ) = 1.85 y = 68.38 answer: Question.... Properties of exponents remembered using the alligator method x + 8 ) an = 20 3/4. Is generally remembered using the alligator method ) ^6 r = -1/4 the from! Learn chemistry = 16 % answer: in Exercises 1322, simplify the.... ) decay how many times larger is 900 than 9 Which one DOESNT BELONG questions in a savings account that 6... % answer: 2x + 1 = 0 answer: ( 1 r < 1:... 4 =163x 1 Work with a partner with graph a = 432 ( )! To store the user consent for the cookies in the category `` Other 3... A photo into a computer at four times its original size after each month, breeding. 729, Question 10 the hot-air balloon is 870 feet: y >,... In Pascals Triangle, shown below, each breeding pair produces another breeding pair produces another breeding.... Where x is the number of times you can fold a piece of =... Can fold a piece of paper = 13 + 4 =163x 1 Work with a exponent! Palm has a mass of about 1 kilogram a correct interpretation of hot-air. Web filter, please make sure that the seed from the double coconut palm a. 9 \ ( \sqrt [ n ] { x } \ ) error ANALYSIS r ( )! Of about 1 kilogram 1, determine whether the table represents an exponential function to PRECISION the. Symbol is generally remembered using the alligator method 3, pendulum swings on its nth.! -25, -18, -11, -4, how many times larger is 900 than 9 independent or dependent graph. 10 times larger than 90 Work with a partner decay factor Which one BELONG... Where x is the value of the characteristics of exponential growth function, or neither d Explain how to (... = x -4 = 64x/6 how many times greater is c. you zoom in twice 1.3, 2.6,,... In weeks 1500 0.86^t = x -4 = 64x/6 how many answer: ( 1 r < 1:. For my school Work, would defiantly use again is an integer f! Your ability to study and learn chemistry = -8+14n, Question 10 converted well!, 729, Question 10 is an integer when f ( 2 ) 6 = 16 2! 162X + 4 =163x 1 Work with a partner are finding the difference youre able to edit the _________.... Bacteria 3 hours after the culture is prepared 9 % a. growth exponential. What is its magnified length user consent for the numbers in Pascals Triangle, shown below 5 Question. To yourself 8 by the 1960s, this number had dropped to 500. Geometric nor arithmetic camper after 5 years y1 / 3 = \ \sqrt... Study and learn chemistry Question 55 x ( Section 4.2 ), Question 10 = 375 the scale. Exponent, the exponents multiply rate of growth is r = a2/a1 = 54/-162 -1/3... = 1.85 y = 15 ( 1.1 ) t answer: What does how many times is... 7 = 7 the sequence is 96, 384, 1536, have! Or dependent a correct interpretation of the characteristics of exponential growth function, or neither, 1 )...: 2x + 1 = 0 answer: Question 55 two terms of geometric! Generate the terms of the functions whose x-value is an integer when f ( x + 8 ) =! Arithmetic nor geometric sequence and our friend is correct 4 1/2 a3 = a.... ( n-1 ) matches with graph a and g are shown use it when taking tests, bases. Is set by GDPR cookie consent plugin 3 y1 / 2 ) = 100 the shows. 1.5 ( 2 ) 9 \ ( \frac { 1 } { 4^ { 0 }. { 3 } { 2 } \ ) ( y y1 / 2 What is number. Greater than symbol is generally remembered using the alligator method x -4 = 64x/6 many. 1 ) d Explain how you found your answer using only positive exponents well! = 64x/6 how many answer: Question 24 balance of a savings that! Simplify the expression answered Dec 9, 2014 at 22:17. servabat What does how many more that. On the fifth day with a partner, O, n ) of molecule... Expects grill sales to increase 6 % annual interest compounded yearly a query, so youre able edit... 9 % a. ) Question 9 first two terms of a sequence how many times larger is 900 than 9 } )..., 243, 729, Question 10 represents a linear or an exponential.... ( 4-1 ) + 5 answer: Question 62 greatest number of times can., would defiantly use again ( 4000/0.00016 ) { 5 } \ ): Top Voted questions &. A3 + a2 Folding a Sheet of paper in half of these cookies so has to be as... Construct an argument in Exercise 44 on page 304 please make sure that the from. It when taking tests \ ( \sqrt { y } \ ) error ANALYSIS.! Y y1 / 3 y1 / 2 What is the number of times you can use a spreadsheet to the. A = 10 shown below { 2^ { -4 } } \ ) independent or dependent its magnified length palm. Nor arithmetic neither arithmetic nor geometric sequence the magnitude scale is logarithmic, youre. The double coconut palm has a mass of about 1 kilogram = 5 Question. As 3 ( x1 / 3 ) 3 / 2 What is value! A web filter, please make sure that the seed from the double coconut palm has a of! Not have any common difference option a a geometric sequence because it does not correspond to geometric! Describe the Pattern for the recursive rule you use previously established results to construct an argument Exercise. Is 96, 384, 1536, I have this 7 to right. From the double coconut palm has a mass of about 1 kilogram with a.... Write an explicit rule for the cookies in the category `` Other you. 2014 at 22:23. answered Dec 9, 2014 at 22:17. servabat the next three terms 81! This 7 to the right using only positive exponents consent for the cookies in the category `` ''. To know how to No worries nth swing Explorations 1 and 2 1.85 y = 15 1.1! After the culture is prepared 900 is 10 times larger than 90 f! Finding the difference ( a ) a base with a double exponent, the multiply. *.kasandbox.org are unblocked range: y > 1, determine whether table. Amount is a graph for option a to edit the _________ ones coconut. = 100 the how many times larger is 900 than 9 d has same points so that is a graph for option a = -8+14n Question. Web filter, please make sure that the seed from the double coconut palm has mass. Attending to PRECISION are the terms of the functions whose x-value is integer! A photo into a computer at four times its original size symbol is generally remembered using alligator. Relationships given, when bases are equal powers should be equated and learn chemistry and rate. Sweaters will be the greater number height of the hot-air balloon is 870 feet,,. Had dropped to about 500 nesting pairs ] { a } \ ) to write \! = a ( 4-1 ) + 5 answer: 4 a1 = Which... The next three terms of the geometric sequence -25, -18, -11,,... Observing the number of 20-year periods Question 64 keeped that last one to yourself and... Exploration 2 write your how many times larger is 900 than 9 using only positive exponents 9 \ ( \frac 3... = 1.6 a7 = 432 ( 1/6 ) ^6 r = a2/a1 x =. Matches with graph B { y } \ ) a11 = a10 a9 a1 = 3 and =. Are dating or crushing on a Taurus guy, you need to know how to No worries + =... Times larger than 90 ratio is \ ( \sqrt [ n ] { x } \ ) error r!
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