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Evaluate two-variable equations: word problems

FCS\newline(4343) Youtube\newlineGulzes 22\newlineGrade Eool\newlineQuitek chec:\newlineDettalath\newlineslopeinter:\newlineth instructure com\newlinecourses\newline104464104464 exteinal\newlinealtools/retrieverdispiayafu?\newlineReturn\newlineNex\newline1010 points\newlineA city manager made a scatter plot of the number of retail stores in the city over the years. The scatter plot had a trend line with an equation of y y =11x+12 =11 x+12 , where y y is the total number of retail stores and x x is the number of years since 19901990 .\newlineWhen Daryl and his family moved to the city there were 133133 retail stores. Use the equation to determine the year that Daryl and his family moved to the city.\newlineDaryl and his family moved to the city in the year type your answer.
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Name:\newlineqquad\newlineqquad\newlineDate:\newlineqquad\newlineVARIABLES RELATED BY RATES N-GEN MATH \newline262^6 HOMEWORK\newlineUSING YOUR MATH\newlineMarcell is buying flour for his bakery. He can buy it for \newline$0.80\$0.80 per pound. If \newlinecc represents the total cost of the flour and \newlineww represents the weight of flour he buys, in pounds, answer the following questions.\newline(a) How much will Marcell pay for 55 pounds of flour?\newline(b) Using your answer from (a) fill out the table below and plot the relationship on the grid.\newline\newline\newlinew (pounds)\newline00\newline55\newline1010\newline1515\newline2020\newline\newlinec, (dollars)\newline00\newline\newline\newline\newline(d) Write an equation for the cost, \newlinecc, in\newline(c) List which variable is dependent and terms of the weight, \newlineww. which is independent below.\newlineDependent: \newlineqquad\newlineIndependent: \newlineqquad (e) If Marcell wants to buy 1313 pounds and has only \newline$10\$10, will he have enough money? Justify using your graph.\newline22. Jasmine is going to put \newline$20\$20 worth of gasoline in her car. She goes to the gas station where she pays a price of \newline$0.80\$0.8000-dollars per gallon for gas and gets \newline$0.80\$0.8011-gallons for it. Which of these two variables, the price or the gallons, is the dependent variable? Explain.
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Name:\newline \qquad \newline \qquad \newlineDate:\newline \qquad \newlineVARIABLES RELATED BY RATES N-GEN MATH ∗6 { }^{*} 6 HOMEWORK 2 ^{2} \newlineUSING YOUR MATH\newline11. Marcell is buying flour for his bakery. He can buy it for $0.80 \$ 0.80 per pound. If c c represents the total cost of the flour and w w represents the weight of flour he buys, in pounds, answer the following questions.\newline(a) How much will Marcell pay for 55 pounds of flour?\newline(b) Using your answer from (a) fill out the table below and plot the relationship on the grid.\newline\begin{tabular}{|l|l|l|l|l|l|}\newline\hlinew w (pounds) & 00 & 55 & 1010 & 1515 & 2020 \\\newline\hlinec c , (dollars) & 00 & & & & \\\newline\hline\newline\end{tabular}\newline(d) Write an equation for the cost, c c , in\newline(c) List which variable is dependent and terms of the weight, w w . which is independent below.\newline(e) If Marcell wants to buy 1313 pounds and\newlineDependent: \qquad \newlineIndependent: \qquad has only \qquad 44, will he have enough money? Justify using your graph.\newline22. Jasmine is going to put \qquad 55 worth of gasoline in her car. She goes to the gas station where she pays a price of \qquad 66-dollars per gallon for gas and gets \qquad 77-gallons for it. Which of these two variables, the price or the gallons, is the dependent variable? Explain.
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Import favorites\newlineMVNU Students Ho...\newlineA\newlineALEKS - Jameson C...\newlineTrigonometric Graphs\newlineWord problem involving a sine or cosine function: Problem type 11\newline1/5 1 / 5 \newlineJameson\newlineEspañol\newlineA buoy floating in the ocean is bobbing in simple harmonic motion with period 88 seconds and amplitude 4ft 4 \mathrm{ft} . Its displacement d d from sea level at time t=0 t=0 seconds is 0ft 0 \mathrm{ft} , and initially it moves downward. (Note that downward is the negative direction.)\newlineGive the equation modeling the displacement d d as a function of time t t .\newlined= d= \newline□ \square \newline□ \square \newlineExplanation\newlineCheck\newline(C) 20242024 McGraw Hill LLC. All Rights Reserved.\newlineTerms of Use\newlinePrivacy Center\newlineAccessibility\newlineType here to search
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Name:\newlineGaridor\newlinecostin\newlineFind the rate of change and y y -intereept for each representation. Then tell what it means in the context and write an equation in slope-interespt form.\newlineseremy borrowed money from his dad for a car repair. The graph represents the amount of money Jeremy owes his dad (y) and the number of weeks (x) (x) after he started paying it back.\newlinea) What is the y y -intercept of the graph and what does it mean in this context?\newlineb) What is the slope of the graph and what does it mean in this context?\newlinec) Write an equation to represent this scenario.\newlineTrish is ordering t t -shirts from a website that charges a certain amount per t t -shirt plus a flat rate for shipping.\newlineThe cost for a given number of t-shirts ( y y ) and the number of shirts ordered (x) (x) is shown in the table.\newline\begin{tabular}{|c|c|c|c|c|}\newline\hline T-SHIRTS & 00 & 33 & 66 & 99 \\\newline\hline TOTAL COST & $5.99 \$ 5.99 & $32.24 \$ 32.24 & $58.49 \$ 58.49 & (x) (x) 00 \\\newline\hline\newline\end{tabular}\newlinea) What is the initial value and what does it mean in this context?
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\begin{tabular}{|c|c|c|c|c|c|}\newline\hlinet t (minutes) & 00 & 44 & 99 & 1515 & 2020 \\\newline\hlineW(t) W(t) (degrees Fahrenheit) & 5555.00 & 5757.11 & 6161.88 & 6767.99 & 7171.00 \\\newline\hline\newline\end{tabular}\newlineThe temperature of water in a tub at time t t is modeled by a strictly increasing, twice-differentiable function W W , where W(t) W(t) is measured in degrees Fahrenheit and t t is measured in minutes. At time t=0 t=0 , the temperature of the water is 55∘F 55^{\circ} \mathrm{F} . The water is heated for 3030 minutes, beginning at time t=0 t=0 . Values of W(t) W(t) at selected times t t for the first 2020 minutes are given in the table above.\newline(a) Use the data in the table to estimate W(t) W(t) 11. Show the computations that lead to your answer. Using correct units, interpret the meaning of your answer in the context of this problem.
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ame\newlineBox-and-Whisker Graphs\newlineFor Exercises 11−3-3, use the box-and-whisker graph below.\newline11. What is the median? \qquad \newline \qquad \newline22. What are the lower and upper quartiles? \qquad \newline \qquad \newline33. What are the lower and upper extremes and the range? \qquad 1818 and 3030\newlineFor Exercises 44−8-8, use the data in the chart below.\newline\begin{tabular}{|llllllllll|}\newline\hline \multicolumn{1010}{c|}{ Lengths of Phone Calls (in min) } \\\newline\hline 1717 & 2121 & 1616 & 2222 & 2424 & 2626 & 1818 & 2828 & 2525 & 2929 \\\newline2121 & 1818 & 1414 & 2323 & 2525 & 1818 & 2626 & 2424 & 2222 & 2323 \\\newline\hline\newline\end{tabular}\newline44. What is the median? \qquad \newline55. What are the lower and upper quartiles? \qquad \newline66. What are the lower and upper extremes and the range? \qquad \newline77. Make a box-and-whisker graph.\newline88. What fractional part of the data is less than 2525 minutes?\newlineQuartive11\newlineMixed Review\newlineFor 99−10-10, use the data in the chart above for 44−8-8.\newline99. Complete the cumulative frequency\newline1010. Make a line plot for the data. table below for the data.\newline\begin{tabular}{|l|l|l|}\newline\hline \multicolumn{33}{|c|}{ Lengths of Phone Calls } \\\newline\hline Minutes & Frequency & \begin{tabular}{l} \newlineCumulative \\\newlineFrequency\newline\end{tabular} \\\newline\hline 11−15 11-15 & & \\\newline16−20 16-20 & & \\\newline \qquad 00 & & \\\newline\hline \qquad 11 & & \\\newline\hline\newline\end{tabular}
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Write an equation from verbal descriptions\newlinePage 11 of 22\newlinescribble space\newline11\newlineThe water level in a well during a stretch of hot, dry weather decreases at a rate of 0.25 \mathbf{0 . 2 5} feet per week. The level before the hot weather started was 62 \mathbf{6 2} feet below the surface.\newlineWrite an equation in slope-intercept from to determine the water level in the well (l) (l) based on the number of weeks (w) (w) .\newlineAnswer:\newline22\newlineJake and Izzy invest $200 \$ \mathbf{2 0 0} in tools for a summer lawn care business. They charge $20 \$ 20 per hour for their services.\newlineWrite an equation in slope-intercept form to show their profit (p) (p) in terms of the number of hours they work (h) (h) .\newlineAnswer:\newline33\newlineA scuba diver has just entered the water from the boat and is 3 \mathbf{3} feet below the surface. The diver descends at a rate of 2 \mathbf{2} feet per minute. Write an equation in slope-intercept form to show the diver's depth 62 \mathbf{6 2} 00 based on the number of minutes 62 \mathbf{6 2} 11.\newlineAnswer:\newline44\newlineTed buys a 62 \mathbf{6 2} 22-pound bag of birdseed. Each of his birdfeeders holds 2 \mathbf{2} pounds of seed.\newlineWrite an equation in slope-intercept form to determine how many pounds of seed are remaining 62 \mathbf{6 2} 44 in terms of the number of feeders that have been filled 62 \mathbf{6 2} 55.\newlineAnswer:\newlinebyte\newlineFind more\newlinelearn\newlineresources at\newlinebyytelearn.com
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The following table lists the de-seasonalised number of sales of a particular costume in a fancy-dress store for each quarter in 20222022−2023-2023 and the seasonal indices. Quarter 11 De-seasonalised number of sales in 20222022 De-seasonalised number of sales in 20232023 Seasonal index 3333 22 3333 33 44 2525 2222 2022202200 2022202211 2022202222 2022202233 2022202244 2022202255 2022202266 2022202277 a Find the equation of the least squares trend line for the de-seasonalised time series data for 2022202288. Round the slope and intercept to two significant figures. b Plot the time series and draw the trend line for the de-seasonalised data on the same axes. Comment on the trend by interpreting the slope of the trend line equation. c Use the trend line equation to forecast the de-seasonalised number of sales for Quarter 11 2023202300. d Use the trend line equation to forecast the actual number of sales for Quarter 11 2023202300.
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A gym teacher was going to hold a free throw competition during his afternoon gym classes. He decided to let the students shoot 1010 free throws each from the same spot on the free throw line.\newlineAt the end of the afternoon, the student who has made the most free throws will win a prize.\newlineSuppose a player on the basketball team knows his free throw percentage (probability of making a free throw) to be 75% 75 \% . Let the random variable X X equal the number of free throws made by the basketball player.\newlineDescribe the distribution of the random variable, X X .\newlineElimination Tool\newlineSelect one answer\newlineA Binomial, with n=10 n=10 and p=0.5 p=0.5 \newlineB Binomial, with n=10 n=10 and p=0.75 p=0.75 \newlineC Geometric, with n=10 n=10 and p=0.5 p=0.5 \newlineD Geometric, with n=10 n=10 and p=0.75 p=0.75 \newlineE Normal, with n=10 n=10 and p=0.75 p=0.75
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Cim...\newline44. In 20022002,11 had an mp3 \mathrm{mp3} player. Cutting edge, and a whopping 16MB 16 \mathrm{MB} . In 20222022, an IPhone 1414 can have up to 1000 GB 1000 \mathrm{~GB} (or 11TB) of storage!\newlinea. Find the growth rate for memory of mp3 \mathrm{mp3} players.\newline16mb 16 \mathrm{mb} \newlineb. Write an equation for the memory capacity of an mp3 \mathrm{mp3} player as a function of the year.\newlinec. What should the memory capacity be in 20252025?\newlined. When will phones be smarter than people ( 22.55 petabytes or 2.5×109MB) \left.2.5 \times 10^{9} \mathrm{MB}\right) ? Guess।\newline55. In the game Pokemon, there is a move called Super Fang, It takes away half of your health (or HP), regardless of where it starts. Suppose my Pokemon has been hit by 55 Super Fangs and is left with 11HP 11 \mathrm{HP} .\newlinea. How many HP did my Pokemon start with?\newlineb. What will my HP be if I take another 33 Super Fangs?\newlinec. Will I ever get KO'd by this move? Why or why not?\newline66. Viral videos tend to model exponent video to get to 11 billion views on YouT of months tool On July 18th ,2012 18^{\text {th }}, 2012 , the December 21nt,2012 21^{n t}, 2012 , or 162162 days later,\newlinea. What is the growth rate per c c \newlineb. Use this to write a model for\newlinec. It has now been 16MB 16 \mathrm{MB} 00 days sit what would be the viewership\newline77. Carbon dating is a technique used to basically works like this: Carbon has 16MB 16 \mathrm{MB} 11 have 22 extra neutrons, so they are sligh extra neutrons so eventually, they lose using exponential decay models, we car it.\newlineBecause scientists are obnoxious, they many numbers. Instead, they deal with to become 16MB 16 \mathrm{MB} 22. And the half-life for 16MB 16 \mathrm{MB} 33
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Pबा[-ा\newlineJsing the paper provided, writing/odloring utensils, and drawing directions, you are to ofgate a new map of Parallel ctty.\newlineDir ECCtions:\newlineJraw the buildings on the appropriate comers on the Parallel City 22 sheet provided (you may want to practice on the rack of this sheet FIRSTI). Make it neat, label it, and be creative.\newlineConstruction:\newline) 11 The Bank and Wal-Mart are altomate interior angles.\newline11) 22 A Gas Station and the Post Office are vertical angles.\newline11) 33 Your house and the Post Office are consecutive interior angles.\newlinei) 44 Your house and the Park are altemate in terior angles.\newlinei) 55 A Gas Station and the Hespital are a par of supplementary angles. ✓ \checkmark \newlinei) 66 The Church and the Hospitalure alternate exterior angles.
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Maria and Jose have a large tomato garden. On day 11 when the tomatoes first ripened, they picked 33 tomatoes. Each day thereafter, as more tomatoes ripened, they doubled the number of tomatoes they picked. Let T T be the number of tomatoes picked on day d d . Which of the following best explains the relationship between d d and T T ?\newlineChoose 11 answer:\newline(A) The relationship is exponential because T T increases by 66 as d d changes from d=1 d=1 to d=2 d=2 .\newline(B) The relationship is linear because T T increases by a factor of 22 each time d d increases by 11 .\newline(C) The relationship is linear because T T increases by 33 as d d changes from d=0 d=0 to d=1 d=1 .\newline(D) The relationship is exponential because T T increases by a factor of 22 each time d d increases by 11 .
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A block of ice weighing 100100 kilograms begins to melt. Each hour the block of ice loses 5% 5 \% of its weight. Let W W be the weight, in kilograms, of the block of ice after melting for t t hours. Which of the following best explains the relationship between t t and W W ?\newlineChoose 11 answer:\newline(A) The relationship is exponential because W W is multiplied by a factor of 00.9595 each time t t increases by 11 .\newline(B) The relationship is linear because W W is multiplied by a factor of 5% 5 \% each time t t increases by 11 .\newline(C) The relationship is linear because W W decreases by 55 as t t increases from t=0 t=0 to t=1 t=1 .\newline(D) The relationship is exponential because W W decreases by 99.7575 as t t increases from t=0 t=0 to t=2 t=2 .
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Carbon−14-14 is a radioactive isotope used to determine the age of samples of organic matter. The amount of carbon−14-14 in a sample decreases once the organism is no longer alive. The half-life of carbon−14-14 is approximately 57305730 years. This means that every 57305730 years, the amount of carbon−14-14 in an organism that is no longer living will be halved. Which of the following functions, C C , models the fraction of carbon−14-14 remaining in a sample after t t years?\newlineChoose 11 answer:\newline(A) C(t)=2t5730 C(t)=2^{\frac{t}{5730}} \newline(B) C(t)=(12)t5730 C(t)=\left(\frac{1}{2}\right)^{\frac{t}{5730}} \newline(C) C(t)=(12)5730t C(t)=\left(\frac{1}{2}\right)^{5730 t} \newline(D) C(t)=25730t C(t)=2^{5730 t}
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