Roger is planning a party. He needs these ingredients in the following quantities to %0D%0Amake punch:%0D%0A• 2 quarts orange juice%0D%0A• 3 cups cranberry juice%0D%0A• 1 gallon ginger ale%0D%0A• 1 pint pineapple juice%0D%0ARoger knows he will need a relatively large container to mix the punch. %0D%0AUnfortunately, all he can find is a bowl that holds 8 liters of liquid. He is not sure %0D%0Awhether he can fit all of the ingredients in the bowl at the same time.%0D%0AUse the following measurement equivalents to determine if Roger can use the 8-%0D%0Aliter bowl to mix all the ingredients for the punch. Show your work. %0D%0AIf he can use the bowl, he needs to determine how many liters of liquid could still %0D%0Afit into the bowl. If he cannot use the bowl, he needs to determine how many extra %0D%0Aliters of liquid there are. Round your answers to the nearest tenth of a liter.%0D%0A1 liter is about 4.23 cups, 2.11 pints, 1.06 quarts, and 0.26 gallons
To determine if Roger can use the 8-liter bowl to mix all the ingredients for the punch, we need to convert the quantities of the ingredients to liters.
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2 quarts of orange juice:
2 quarts * 1.06 liters/quart = 2.12 liters
3 cups of cranberry juice:
3 cups * 0.24 liters/cup = 0.72 liters
1 gallon of ginger ale:
1 gallon * 3.79 liters/gallon = 3.79 liters
1 pint of pineapple juice:
1 pint * 0.47 liters/pint = 0.47 liters
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Now we can add up the quantities of each ingredient:
2.12 liters + 0.72 liters + 3.79 liters + 0.47 liters = 7.10 liters
Roger needs a total of 7.10 liters of liquid for the punch. Since the 8-liter bowl can hold more than that, he can use it to mix all the ingredients.
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To determine how many liters of liquid could still fit into the bowl, we subtract the total quantity of the ingredients from the capacity of the bowl:
8 liters - 7.10 liters = 0.90 liters
Therefore, if Roger uses the 8-liter bowl to mix all the ingredients, there would be approximately 0.90 liters of free space left in the bowl.
To determine if Roger purchased more turkey or more cheese, we need to convert the quantities of turkey and cheese to the same unit of measurement, either kilograms or pounds.
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1.5 kilograms of turkey * 2.2 pounds/kilogram = 3.3 pounds of turkey
2.25 pounds of cheese * (1 kilogram/2.2 pounds) = 1.02 kilograms of cheese
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Therefore, Roger purchased 3.3 pounds of turkey and 1.02 kilograms of cheese.
Since 1.02 kilograms is less than 3.3 pounds, we can conclude that Roger purchased more turkey than cheese.
To determine the amount in pounds that the chicken could weigh, we need to find a weight that is greater than the weight of beef but less than the weight of turkey.
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1.25 kilograms of beef * 2.2 pounds/kilogram = 2.75 pounds
1.5 kilograms of turkey * 2.2 pounds/kilogram = 3.3 pounds
Therefore, the weight of the chicken must be greater than 2.75 pounds and less than 3.3 pounds.
To round to the nearest hundredth of a pound, we have a range of 2.76 to 3.29 pounds for the weight of the chicken.
Roger also wants to make sandwiches for his guests. He buys the following
sandwich fillings:
• 1.5 kilograms of turkey
• 1.25 kilograms of beef
• 2.25 pounds of cheese
Roger wants to know if he purchased more turkey or more cheese. Use the
conversion ratio 1 kilogram = about 2.2 pounds to determine the correct answer.
Show your work
Roger discovers that he needs to buy some chicken as well. He buys an amount of
chicken that weighs more than the beef he bought and less than the turkey he
bought. Give an amount in pounds that the chicken could weigh, rounded to the
nearest hundredth of a pound.
Roger is curious to know the total weight of all four sandwich fillings he bought. He
weighs it twice, once using ounces and once using grams. If 16 ounces = 1 pound
and 1,000 grams = 1 kilogram, will the total weight of the sandwich fillings be a
greater number of ounces or a greater number of kilograms? Explain your answer.
To determine whether the total weight of the sandwich fillings will be a greater number of ounces or a greater number of kilograms, we need to compare the conversion ratios.
1. When converting from pounds to ounces, 16 ounces = 1 pound.
2. When converting from kilograms to grams, 1,000 grams = 1 kilogram.
Since the total weight of the sandwich fillings is given in both ounces and grams, we need to convert the weights to the same unit of measurement in order to make a comparison.
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First, let's convert the weight to ounces:
- 2.75 pounds of beef * 16 ounces/pound = 44 ounces of beef
- 3.3 pounds of turkey * 16 ounces/pound = 52.8 ounces of turkey
- 2.25 pounds of cheese * 16 ounces/pound = 36 ounces of cheese
Now let's convert the weight to grams:
- 1.25 kilograms of beef * 1,000 grams/kilogram = 1,250 grams of beef
- 1.5 kilograms of turkey * 1,000 grams/kilogram = 1,500 grams of turkey
- 2.25 pounds of cheese * 453.592 grams/pound = 1,020 grams of cheese
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Comparing the total weight in ounces (44 + 52.8 + 36 = 132.8 ounces) and the total weight in grams (1,250 + 1,500 + 1,020 = 3,770 grams).
Since there are more grams than ounces (3,770 grams > 132.8 ounces), the total weight of the sandwich fillings will be a greater number of kilograms when converted.
You are visiting one of the following states: Tennessee, Vermont, Wisconsin, or
Wyoming. Each has a state sales tax on most items that are for sale in stores.
While you are visiting, you decide to buy a board game to play with your hosts. The
cost of the game is between $10 and $20, and it is not a whole dollar amount.
Decide the cost of the board game. Write it here: ______
Now choose one of the four states listed above. Write it here: __________________
Use the internet to find the state’s general sales tax. Note that some counties, towns,
or cities may add more to the general sales tax, but you only need the general sales
tax. Write the tax rate here: ________
What is the total cost of the board game, including sales tax? Show your work
Unfortunately, I don't have the capability to browse the internet and provide real-time information. However, I can guide you on how to find the state's general sales tax and calculate the total cost of the board game including sales tax.
1. Look up the general sales tax rate for the chosen state (Tennessee, Vermont, Wisconsin, or Wyoming) on a reliable source such as the state's government website or the Department of Revenue website.
2. Once you have the sales tax rate, calculate the amount of sales tax for the chosen board game price range. Since the cost of the game is between $10 and $20, assume a specific price within that range.
3. To calculate the sales tax, multiply the price of the board game by the sales tax rate in decimal form. For example, if the sales tax rate is 6%, multiply the price by 0.06.
4. Finally, add the sales tax to the price of the board game to find the total cost.
Please let me know the state and the specific sales tax rate, and I will be happy to assist you in calculating the total cost of the board game including sales tax.
To determine if Roger can use the 8-liter bowl to mix all the ingredients for the punch, we need to calculate the total volume of the ingredients and compare it to the capacity of the bowl.
First, let's convert the quantities of each ingredient to liters using the given measurement equivalents:
- 2 quarts orange juice = 2.11 quarts * 1.06 liters/quart ≈ 2.23 liters
- 3 cups cranberry juice = 3 cups * 0.24 liters/cup ≈ 0.72 liters
- 1 gallon ginger ale = 1 gallon * 3.8 liters/gallon = 3.8 liters
- 1 pint pineapple juice = 1 pint * 0.47 liters/pint ≈ 0.47 liters
Now, let's calculate the total volume of the ingredients:
2.23 liters (orange juice) + 0.72 liters (cranberry juice) + 3.8 liters (ginger ale) + 0.47 liters (pineapple juice) ≈ 7.22 liters
The total volume of the ingredients is approximately 7.22 liters.
Comparing this to the capacity of the 8-liter bowl, we can determine if Roger can use the bowl or not.
- If 7.22 liters ≤ 8 liters: Roger can use the 8-liter bowl to mix all the ingredients for the punch.
- If 7.22 liters > 8 liters: Roger cannot use the 8-liter bowl to mix all the ingredients, and we need to calculate how many extra liters of liquid there are.
(Extra liters = Total volume of ingredients - Capacity of the bowl)
If Roger can use the bowl, we need to determine how many liters of liquid could still fit into the bowl.
(Extra liters = Capacity of the bowl - Total volume of ingredients)
Since the question asks to round the answers to the nearest tenth of a liter, make sure to round the final answers accordingly.