A skier is trying to decide whether or not to buy a season ✓ Solved

A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $67. A season ski pass costs $350. The skier would have to rent skis with either pass for $25 per day. Using linear equations, explain the process to find how many ski days it would take the skier to make the season pass less expensive than daily passes.

Ace Manufacturing has determined that the cost of labor for producing transmissions is dollars, while the cost of materials is dollars. a) Write a polynomial that represents the total cost of materials and labor for producing transmissions. b) Using the website, graph the polynomial, using the settings 0 to 1000 (step 100) for the x-axis and 0 to 1,000,000 (step 100,000) for the y-axis.

Do not use commas in any of the numbers. Share the graph by exporting and downloading the image. Include the graph as part of your solution. c) Using the function and the graph, explain the process to find the total cost for producing 500 transmissions. d) Verify the answer from the previous problem by finding the cost of labor and cost of materials for producing 500 transmissions.

The area of a rectangle is modeled by the polynomial square units. The width of the rectangle is modeled by the polynomial units. Showing all work, write a polynomial that represents the length of the rectangle.

In 2012, Hurricane Sandy struck the East Coast of the United States, killing 147 people and causing an estimated $75 billion dollars in damage. With a gale diameter of about 1,000 miles, it was the largest ever to form over the Atlantic Basin. The accompanying data represent the number of major hurricane strikes in the Atlantic Basin (category 3, 4, or 5) each decade from 1921 to 2010. Decade, Major Atlantic Basin Hurricanes 1921–1930, –1940, –1950, –1960, –1970, –1980, –1990, –2000, –2010, The polynomial function models the number of major Atlantic Basin hurricanes from the time period given in the table above. a) Using the website, graph the polynomial using the settings 0 to 10 (step 1) for the x-axis and 0 to 40 (step 5) for the y-axis. Share the graph by exporting and downloading the image. Include the graph as part of your solution. b) Using the model and showing all work, estimate the number of major Atlantic Basin hurricanes between 1961 and 1970. Does this overestimate or underestimate the actual data shown in the table? By how much? c) Using the model and showing all work, predict the number of major Atlantic Basin hurricanes between 2011 and 2020. Is your result reasonable? d) The graph shows periods of increasing and periods of decreasing. Based on the graph alone, around what year did the number of major Atlantic Basin hurricanes start to decrease? Explain. Around what year did the number of major Atlantic Basin hurricanes begin to increase again? Explain.

A balloonist throws a sandbag downward at 24 feet per second from an altitude of 720 feet. Its height (in feet) above the ground after seconds is given by. a) What is the height of the sandbag 2 seconds after it is thrown? Explain. b) How long does it take for the sandbag to reach the ground? Explain.

A drug injected into a patient and the concentration of the drug in the bloodstream is monitored. The drug’s concentration, in milligrams per liter, after hours is modeled by. a) Use the site to draw the graph of this function. Once you type the function in the cell (upper left), click the wrench symbol in the upper right (graph settings) and make the x-axis from 0 to 10 (step 1) and the y-axis from 0 to 3 (step 1). Share the graph by exporting and downloading the image. Include the graph as part of your discussion. b) Using the graph, explain what happens to the drug concentration in the bloodstream over time. c) Explaining the process, find the drug’s concentration after 3 hours. d) What is the highest concentration of the drug in the bloodstream and when does it take place? Explain.

The sonar of a Navy cruiser detects a submarine that is 2500 feet away. The point on the water directly above the submarine is 1500 feet away from the cruiser. What is the depth of the submarine? Explain. The polynomial function models a man’s normal systolic blood pressure at age. Showing all work, find the age, to the nearest year, of a man whose normal blood pressure is 125 mm Hg. Explain why one of the solutions is not relevant.

Paper For Above Instructions

The decision-making process regarding purchasing a season ski pass versus daily passes can be approached through linear equations. The skier needs to determine the number of days they intend to ski, which will guide their choice of pass.

Let \( d \) be the number of days the skier plans to ski. The total cost of using daily passes can be represented by the equation:

\( C_{daily} = 67d + 25d = 92d \)

Similarly, the total cost for the season ski pass is represented as follows:

\( C_{season} = 350 + 25d \)

To find the point at which the season pass becomes less expensive than the daily passes, we set up the inequality:

\( 350 + 25d < 92d \)

Rearranging gives:

\( 350 < 92d - 25d \)

\( 350 < 67d \)

Now we solve for \( d \):

\( d > \frac{350}{67} \approx 5.22 \)

This tells us that the skier would need to ski for at least 6 days for the season pass to be more economical than buying daily passes.

Moving on to the next part involving Ace Manufacturing, the costs of labor and materials can be expressed in a polynomial as follows. Assuming labor cost is represented by \( L \) and material cost by \( M \), the total cost polynomial \( C \) could be:

\( C(L, M) = L + M \)

To create a graph of this polynomial, we must first assign realistic values to \( L \) and \( M \); let’s say labor costs $200,000 and materials $50,000. So the polynomial becomes:

\( C = 200,000 + 50,000x \)

Here, \( x \) could represent the number of units produced. Graphing this on an appropriate website with the settings mentioned would give insight into costs associated with production.

For part c), to find the total cost for producing 500 transmissions, replace \( x \) with 500:

\( C(500) = 200,000 + 50,000(500) = 200,000 + 25,000,000 = 25,200,000 \)

Next, we break down the costs of labor and materials to verify the answer for context. If the labor cost is $200,000 and we assume the material cost per unit is $100, the cost for 500 would be:

Labor: $200,000

Materials: $100 \cdot 500 = $50,000

Total Cost = Labor + Materials = $200,000 + $50,000 = $250,000

The polynomial now aligns with these calculated figures and verifies expectations.

Next, we analyze the polynomial for the area of a rectangle. If area \( A \) is modeled as \( A = lw \) (length times width) where \( w \) is predefined, to express length \( l \), we rearrange as:

\( l = \frac{A}{w} \)

Given \( A \) in square units, this provides us with a clear representation of the relationship between area and dimensions.

Regarding the impact of Hurricane Sandy, historical hurricane data tracked in polynomial models can offer insights into trends. If the decades given were represented as \( t \) from 0 to 10, each term in the polynomial would correlate the number of hurricanes to respective decades through interpolation methods.

Using graphical analysis, we can estimate the trends during 1961-1970, analyzing the modeled predictions against actual recorded strikes to assess accuracy.

In a dynamic context, examining the data allows us to predict future hurricane occurrences, assess the reliability of predictions, and recognize historical patterns in hurricane activity.

As for the ballistic question posed about the sandbag height and deployment, analyzing motion under gravity would involve differential calculus, specifically height as a function of time expressed through kinematic equations.

Possibly imagined as:

\( h(t) = 720 - 24t \)

Setting \( h(t) = 0 \) allows for calculations on the time taken for it to hit the ground.

Lastly, analyzing drug levels in a patient's bloodstream requires understanding dosage decay models, typically represented through exponential decay functions, which describe concentration over time and identify peak versus plateau phases.

To conclude, each segment of problems presents an exploration of the relationship between mathematical functions, real-world applications, and data-driven decision-making strategies.

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