Bot use the properties of operations and rules for multiplying and dividing to solve the following problem: (17/6) divided by (4/17) x (7/34) x (-1) x (6/17). Pick one of these answers. -14/289 -2856/58956 -7/8 -7/578
To solve the problem, let's start by simplifying the expression step by step:
1. Divide (17/6) by (4/17):
(17/6) ÷ (4/17) = (17/6) x (17/4)
Now, we can simplify this by multiplying the numerators and denominators:
(17 x 17) / (6 x 4) = 289/24
2. Next, multiply (289/24) by (7/34):
(289/24) x (7/34)
Multiply the numerators: 289 x 7 = 2023
Multiply the denominators: 24 x 34 = 816
Therefore, (289/24) x (7/34) = 2023/816
3. Now, multiply (2023/816) by (-1):
(2023/816) x (-1) = -2023/816
4. Lastly, multiply (-2023/816) by (6/17):
(-2023/816) x (6/17)
Multiply the numerators: -2023 x 6 = -12138
Multiply the denominators: 816 x 17 = 13872
Thus, (-2023/816) x (6/17) = -12138/13872
From the provided answer choices, the simplified expression evaluates to -12138/13872, which is equivalent to -7/8.
Therefore, the correct answer is -7/8.
Bot a water tank decreases by 10 gallons every 3 hours every day. What is the total change in the amount of water in the tank after 6 days? Pick one of these answers. 80 gallons. -480 gallons. -80 gallons. 480 gallons.
To determine the total change in the amount of water in the tank after 6 days, we need to find the change in water for each day and then sum them up.
In one day, the water tank decreases by 10 gallons every 3 hours. Since there are 24 hours in a day, this means there are 8 sets of 3 hours in a day. Therefore, for each day, the water tank decreases by 10 gallons/3 hours x 8 sets = 80 gallons.
Now, to find the total change in the amount of water after 6 days, we multiply the daily change by the number of days:
Total change = 80 gallons/day x 6 days = 480 gallons.
Hence, the correct answer is 480 gallons.
Bot a recipe calls for 1/3 of a container of yogurt. Each container of yogurt has 150 calories. The recipe makes 4 servings. Which set of calculations would give the correct number of calories per serving? Pick one of these answers. (1/3 x 150 divided by 4) (1/3 x 150 x 4) (1/3 divided by 150 divided by 4) (1/3 x 150 divided by 1/4)
To determine the correct number of calories per serving in the recipe, we can divide the total amount of calories in the yogurt container by the number of servings.
Given that each container of yogurt has 150 calories and the recipe calls for 1/3 of a container, we need to calculate:
(1/3) of 150 calories divided by 4 servings.
The correct set of calculations would be:
(1/3 x 150) divided by 4.
Let's calculate this:
(1/3) x 150 = 50
50 divided by 4 = 12.5
Therefore, the correct set of calculations is (1/3 x 150) divided by 4, which gives us 12.5 calories per serving.
Hence, the correct answer is (1/3 x 150) divided by 4.
Bot solve this multi-step problem. A household uses 1/4 of a 15-pound bag of rice every 3 weeks. What is the change in the number of pounds of rice in the bag of rice after 8 weeks? Pick one of these answers. -90 -10 -2/3 10
To determine the change in the number of pounds of rice in the bag after 8 weeks, we need to find the amount of rice used in 8 weeks and subtract it from the initial amount of rice.
The household uses 1/4 of a 15-pound bag of rice every 3 weeks.
So, in 1 week, they will use 1/3 of that amount (since 8 weeks is 8/3 = 2 and 2 times 1/4 equals 1/2).
1/4 x 15 pounds = 15/4 pounds of rice used every 3 weeks.
1/3 x (15/4 pounds) = 15/12 pounds of rice used every week.
Now, to find the total amount of rice used in 8 weeks, we need to multiply the amount used in one week by 8:
(15/12 pounds/week) x 8 weeks = 15/12 x 8/1 = 30/3 = 10 pounds.
Finally, to find the change in the number of pounds of rice in the bag after 8 weeks, we subtract the amount used from the initial amount:
15 pounds - 10 pounds = 5 pounds.
Therefore, the correct answer is 5 pounds.
Bot please pick one of the answers that i have given you
The correct answer from the options you provided is 10.
To solve this problem using the properties of operations and rules for multiplying and dividing, follow these steps:
1. Start by simplifying each fraction individually, if possible:
- (17/6) divided by (4/17) simplifies to (17/6) x (17/4).
- (17/4) simplifies further as there are no common factors to cancel.
2. Multiply all the simplified fractions together:
- (17/6) x (17/4) x (7/34) x (-1) x (6/17).
3. Cancel any common factors between the numerators and denominators of different fractions:
- The denominator 6 in (17/6) cancels out with the numerator 6 in (6/17).
- The numerator 17 in (17/4) cancels out with the numerator 17 in (17/17).
4. Multiply all the remaining numerators together and multiply all the remaining denominators together:
- Numerator: 17 x 7 x (-1) = -119.
- Denominator: 1 x 17 x 34 x 4 = 2312.
5. Simplify the resulting fraction if possible:
- The fraction -119/2312 is already simplified as there are no common factors to cancel.
Therefore, the answer is -119/2312. None of the provided options (-14/289, -2856/58956, -7/8, -7/578) matches the result of the calculation.