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Which function below has the largest slope?f(x)x f(x)2 44 126 20g(x)g(x)=10x − 4h(x)Lance gains 1 level each time he plays his favorite video game. He started at level 10.Answers: f(x) g(x) h(x) The functions all have the same slope
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7 months ago
QUESTIONYour Assignment: Coffee Shop PricesChoosing a ModelYou are helping your boss, the owner of a coffee shop, set prices. She has gathered some data by counting the number of cups sold per day at various prices. Your job is to see if there is a relationship between price and sales for one of the two most popular drinks.Coffee sales:Price: 1.50 2.20 2.70 2.50 2.90 2.00 1.60 2.10 3.00 1.80Sales: 96 79 70 73 64 85 94 83 63 91Tea sales:Price: 2.40 1.50 1.10 1.60 2.50 1.30 1.00 1.70 2.20 2.00Sales: 64 85 94 83 63 91 96 79 70 731. Which drink did you select? Circle one.CoffeeTeaFind a line of best fit.2. Enter the data into your calculator and perform a linear regression. Round a and b to the nearest tenth. (2 points: 1 point for slope and 1 point for y-value of y-intercept)What is your linear regression equation?3. What is the meaning of the slope? (2 points)4. Create a scatterplot for your beverage using the data from the table. Then graph the linear regression equation you found in question 2. (4 points)5. Does the line of best fit seem like a good model for the data? Why or why not? (2 points)6. Complete the table. (10 points: 1 point for each row)Identify the actual number of sales at each price.Use your line of best fit to calculate the predicted sales at each price.PROMPTOn-screen text:Coffee Shop PricesA Begin button starts the animation.[Click "Begin."]On-screen text:You are helping your boss, the owner of a coffee shop, set prices. She has gathered some data by counting the number of cups sold per day at various prices. Your job is to see if there is a relationship between price and sales for one of the two most popular drinks. Will you choose coffee or tea?Which will you choose?[Two images of mugs are shown: one filled with coffee and surrounded by coffee beans, and the other filled with tea, with a sprig of mint next to the mug.][Click "Coffee."] Great! You will look at coffee sales. Use the data in the table to find the line of best fit. Then evaluate your model.[A table with two sets of data is shown.]Price: 1.50, 2.20, 2.70, 2.50, 2.90, 2.00, 1.60, 2.10, 3.00, 1.80Sales: 96, 79, 70, 73, 64, 85, 94, 83, 63, 91[Click "Tea."] Great! You will look at tea sales. Use the data in the table to find the line of best fit. Then evaluate your model.[A table with two sets of data is shown.]Price: 2.40, 1.50, 1.10, 1.60, 2.50, 1.30, 1.00, 1.70, 2.20, 2.00Sales: 64, 85, 94, 83, 63, 91, 96, 79, 70, 73
General
7 months ago
QUESTIONYour Assignment: Profit from SalesYou are deciding how much to charge for an item you want to sell. To answer these questions, you will factor a polynomial expression to find the break-even points, or the prices at which your profit from sales will be 0.1. Circle the item that you want to sell.T-shirts Hats Water bottlesMaking Sense of the ProblemMake Sense of the ProblemWhat do you know? What do you want to find out? What kind of answer do you expect? 3. Fill in the blanks. (1 point)The profit expression is __________________.4. Set the profit expression as an equation equal to 0. (1 point)____________________ = 05. Factor out the coefficient of the squared term. (2 points)6. Factor the remaining trinomial. (4 points: 2 points for each factor)7. If a product is equal to 0, then at least one of the factors must be 0. The constant factor cannot be 0. Set each binomial factor equal to 0 and solve for the variable. (2 points: 1 point for each factor)8. Use your answer from question 7 to identify the two break-even points. (1 point)You will make a profit if you sell your item for between $_______ and $_________.9. Check your work. Substitute each value into the equation from question 4 to confirm that it makes the expression equal to 0. (2 points: 1 point for each value)10. Below are the graphs for the profit functions. Write the coordinates of the highest point on the graph for your item. (1 point)(____, ____).11. The x-value of the point from question 10 is the price that will give you the maximum profit. The y-value of the point is the maximum profit that you can make. (3 points)PROMPTTranscript: Modeling: Factoring PolynomialsThis interactive animation shows an image of a basketball game between two teams. The title "Profit from Sales" is shown and a "Begin" button starts the animation. [Click "Begin."]On-screen text and Audio:Profit from Sales: You're setting up a table at a basketball game to sell items to raise money for the Student Association. There are costs associated with buying the items. After you pay these costs, the profit, or money you make, will depend on the price the item sells for. You need to decide how much to charge. First, pick an item that you want to sell. [An image of a grey T-shirt, a water bottle, and a black hat can be seen on the screen. Any of the images can be clicked and a message pops up.]T-shirts: Great! You've decided to sell T-shirts. The expression –2t2 + 60t – 250 represents your profit when the price of a T-shirt is t dollars.The break-even points are the prices at which your profit will be 0. Write an equation by setting the above expression equal to 0. Then factor the expression to find the break-even points for this item.Water bottles: Great! You've decided to sell water bottles. The expression –10w2 + 100w – 90 represents your profit when the price of a water bottle is w dollars.The break-even points are the prices at which your profit will be 0. Write an equation by setting the above expression equal to 0. Then factor the expression to find the break-even points for this item.Hats: Great! You've decided to sell hats. The expression –3h2 + 66h – 120 represents the profit for the hats when the price of a hat is h dollars.The break-even points are the prices at which your profit will be 0. Write an equation by setting the above expression equal to 0. Then factor the expression to find the break-even points for this item.
General
7 months ago
QUESTIONScenario: The StageInstructions:View the video found on page 1 of this Journal activity.Using the information provided in the video, answer the questions below.Show your work for all calculations.Analyze The Students' ConjecturesMalcolm wants to build an outdoor stage with a total area of 350 square feet. The length of the stage should be 3 feet shorter than the width. He calculated the equation to be w2 − 3w = 3501. Complete the table to summarize each student's suggestion for figuring out the equation: (2 points: 1 point for each row of the chart)Student ConjectureMalcolm's bandmate Malcolm 2. Malcolm and his bandmate have different ideas for figuring out the equation. Which one do you think will make it easiest to solve the equation? Why? (2 points)3. Malcom's bandmate starts by making a factor table for w2 – 3w – 350 = 0.He is looking for the factors (w + p)(w + q) = 0, where p • q = –350 and p + q = –3. Fill in the last row of the table with different factors, p and q, so that p • q = –350. (2 points).p q p + q10 –35 –25–10 35 2550 –7 43–50 7 –43_____ _____ _____4. The bandmate’s factor table is not complete. It does not contain all the factors of –350.Does the factoring table contain the factors that can be used to solve w2 – 3w – 350 = 0? Explain your reasoning. (1 point)5. To make a perfect square trinomial, Malcolm said the rule for figuring out the number to add is . Is he correct? If not, what is the rule? (1 point)6. Calculate the number that you need to add to each side of the equation w2 – 3w = 350 to create a perfect square trinomial. Add this number to each side of the equation. Show your work. (3 points)7. Factor the trinomial. (3 points)8. Now that you've factored the equation, find the square root of each side and solve for w. Show your work and both solutions. (2 points)9. Do both of these solutions make sense in terms of the problem? Why or why not? (2 points)10. What are the maximum dimensions of the stage that Malcolm can build? (Round to the nearest foot.) (2 points)w = _____ feet l = _____ feetPROMPTAudio:O.K., everybody, it's "Do-It-Yourself" time! They say all it takes is the right tools, a little determination, and a good plan. Well, I've got the lumber, I've got the power saw — I've even got the elbow grease! The only thing I don't have is a plan. [The images change to show a young man carrying a plank of lumber, then a circle saw, then of an up close shot of a nail with a hammer about to hit it and a person in the background driving the hammer.]Here's the situation: My rock band got permission from the community center to build an outdoor wooden stage so we can perform some concerts this summer. [A park-like area with lots of trees is shown with benches and a small wooden stage.]I used all my powers of charm and persuasion to get a local lumberyard to donate some lumber. [A large red truck is shown filled with lumber.]We have enough materials to build a stage with a total area of 350 square feet. But because of the way our band does our setup, the length of the stage should be three feet shorter than the width. [A grass area is animated with a dashed-line outline of a square with "350 ft2." Wood is then shown inside the square but the right side elongates and "l = w – 3" is shown on the right side of the rectangle and "w" on the bottom of the rectangle.]Based on that info, I want to build the biggest platform I can. I think I can figure out the dimensions using a quadratic equation. (I know what you're thinking: He's musically talented and good at algebra? Wow!)Here's what I've come up with so far:We know that width times length equals total area. ["w • l = area" appears on-screen.] In this case, the length equals the width minus 3. So, width times width minus 3 should equal 350. [The following text appears on-screen: "l = w – 3; w(w – 3) = 350; w2 – 3w = 350"]That means: w squared minus 3w equals 350. I've been arguing with my bandmate about what to do next.[Spoken by a different voice:] Hey, it's not an argument, it's just a lively discussion!Student: So what's your suggestion?[Spoken by a different voice:] I think we need to subtract 350 from both sides, and then factor the equation. [w2 – 3w – 350 = 0 appears on-screen.]Student: I think it would be easier to factor if we change the equation so that it has a perfect square trinomial.[Spoken by a different voice:] That sounds too complicated.Student: We just have to figure out what number will complete the square on the left side of the equation, and then add that number to both sides of the equation. I think the rule for figuring out the number is b divided by 2, squared. ["" is shown on screen.]
General
7 months ago
Four students plan to rent a minivan for a weekend trip and equally share the rental cost of the van. By adding two more people, each persona can save $10 on his or her shre of the cost. How much is the total rental cost of the van?
General
7 months ago
Given a circle with a diameter of 4, which equation expresses π as the ratio of the circumference of a circle to its diameter?
General
7 months ago
You coach a basketball ball team of 12 players; 5 players must be on the floor at all times; Figuring that every player can play every position.. How many teams can you put on the floor? Now consider that you have 2 centers, 5 guards, and 5 forwards; You must place on the floor at all times 1 center; 2 guards; 2 forwards, How many teams can you 'put on the floor' ??
General
7 months ago
If y= 3x + 6, what is the minimum value of (x^3)(y)?
General
7 months ago
Its A, I just need the numbers
General
7 months ago
Simplify:x^1/3[x^1/2 +2x^2]answers: A) x^1/6 + 2x^2/3B) x^2/5 + 2x^7/3C) x^2/5 + 2x^3/4D) x^5/6+ 2x^7/3
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7 months ago
Given two triangles with three corresponding angles that are congruent, why can't the two triangles be proved congruent? A) Given three congruent angles, only the longest side can be congruent. B) Given three congruent angles, only the shortest side can be congruent. Eliminate C) The triangles could have the same shape but not necessarily the same size. D) The triangles could have the same size but not necessarily the same shape.
General
7 months ago
two fair 6 sided dice p(sum<12)p(dice show same value)
General
7 months ago
The vertex angle of an isosceles triangle is 20° less than the sum of the base angles. Which system of equations can be used to find the measure of the vertex and base angles?
General
7 months ago
Let u = PQ be the directed line segment from P(0,0) to Q(9,12), and let c be a scalar such that c < 0. Which statement best describes cu?A) the terminal point of vector cu lies in quadrant IIB) the terminal point of vector cu lies in quadrant IIIC) the terminal point of vector cu lies in quadrant ID) the terminal point of vector cu lies in quadrant IV
General
7 months ago
Consider the equation below.-3(4x-7) = 15 -2xThe equation was solved using the following steps.Step 1: -12x + 21 = 15 - 2xstep 2: -10x + 21 = 15step 3: -10x = -6step 4: x = -6/-10step 5: x = 3/5Complete the statements below with the process used to achieve steps 1-4.Step 1: _______ -3 to 4x and -7step 2:_______ 2xstep 3:_______ 21step 4: _______ -10options: divide, subtract, distribute, add, multiply by,
General
7 months ago
An internet service provider is implementing a new program based on the number of connected devices in each household. Currently, customers are charged a flat rate of $175 per month. The new plan would charge a flat rate of $94 plus an additional $4.50 per device connected to the network. Find and graph the number of devices, x, for which the cost of the new plan is less than the current plan.
General
7 months ago
Refer to the accompanying technology display. the probabilities were obtained by entering the values of n equals 5 and p equals 0.774. in a clinical test of a drug, 77.4% of the subjects treated with 10 mg of the drug experienced headaches. in each case, assume that 5 subjects are randomly selected and treated with 10 mg of the drug. find the probability that at least four of the subjects experience headaches. is it unusual to have fewer than four subjects experience headaches?
General
7 months ago
The length of a rectangle is 16 centimeters, and the diagonal of the rectangle is 20 centimeters long. what is the perimeter of the rectangle
General
7 months ago
The measure of an angle is twenty-nine times the measure of a complementary angle. what is the measure of each angle?
General
7 months ago
The automatic opening device of a military cargo parachute has been designed to open when the parachute is 195 m above the ground. suppose opening altitude actually has a normal distribution with mean value 195 and standard deviation 33 m. equipment damage will occur if the parachute opens at an altitude of less than 100 m. what is the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes? (round your answer to four decimal places.)
General
7 months ago
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