Use the properties of operations and rules for multiplying and dividing to solve:
(−2)×(15)÷(23)×(−56)÷(34)
(1 point)
Responses
1/6
2/3
−2/3
−1/6
To solve the expression (−2)×(15)÷(23)×(−56)÷(34), we will use the properties of operations and rules for multiplying and dividing.
First, we multiply -2 by 15:
(-2) × (15) = -30
Next, we divide -30 by 23:
-30 ÷ 23 ≈ -1.3043 (rounded to four decimal places)
Then, we multiply -1.3043 by -56:
-1.3043 × -56 ≈ 73.0068 (rounded to four decimal places)
Finally, we divide 73.0068 by 34:
73.0068 ÷ 34 ≈ 2.1479 (rounded to four decimal places)
Therefore, the simplified value of (-2)×(15)÷(23)×(−56)÷(34) is approximately 2.1479.
Use the properties of operations and rules for multiplying and dividing to solve:
(−2)×(1/5)÷(2/3)×(−5/6)÷(3/4)
(1 point)
Responses
1/6
2/3
−2/3
−1/6
To solve the expression (−2)×(1/5)÷(2/3)×(−5/6)÷(3/4), we will use the properties of operations and rules for multiplying and dividing.
First, we multiply -2 by 1/5:
(-2) × (1/5) = -2/5
Next, we divide -2/5 by 2/3:
(-2/5) ÷ (2/3) = (-2/5) * (3/2) = -6/10 = -3/5
Then, we multiply -3/5 by -5/6:
(-3/5) × (-5/6) = (3/5) * (5/6) = 15/30 = 1/2
Finally, we divide 1/2 by 3/4:
(1/2) ÷ (3/4) = (1/2) * (4/3) = 4/6 = 2/3
Therefore, the simplified value of (−2)×(1/5)÷(2/3)×(−5/6)÷(3/4) is 2/3.
Use the properties of operations and rules for multiplying and dividing to solve:
(9)÷(5/4)×(7/9)×(−5)÷(7/2)
(1 point)
Responses
1,225/8
−8
−1,225/8
8
To solve the expression (9)÷(5/4)×(7/9)×(−5)÷(7/2), we will use the properties of operations and rules for multiplying and dividing.
First, we divide 9 by 5/4:
9 ÷ (5/4) = 9 * (4/5) = 36/5
Next, we multiply 36/5 by 7/9:
(36/5) × (7/9) = (36 * 7) / (5 * 9) = 252/45 = 28/5
Then, we multiply 28/5 by -5:
(28/5) × (-5) = (28 * -5) / 5 = -140/5 = -28
Finally, we divide -28 by 7/2:
(-28) ÷ (7/2) = (-28) * (2/7) = -56/7 = -8
Therefore, the simplified value of (9)÷(5/4)×(7/9)×(−5)÷(7/2) is -8.
Solve this multi-step problem. A runner completes 1/4 of a 5-mile race every 8 minutes. At the same pace, how far can the runner go in 16 minutes?(1 point)
Responses
2 1/2 miles
1/8 mile
160 miles
1/10 mile
To solve this problem, we need to find how many 1/4 segments of the race the runner can complete in 16 minutes.
Since the runner completes 1/4 of the race every 8 minutes, in 16 minutes, the runner would complete 2 segments (16 minutes ÷ 8 minutes/segment = 2 segments).
Therefore, the runner can complete 2 segments, which is equal to 2/4 or 1/2 of the 5-mile race.
Thus, the runner can go 1/2 of 5 miles in 16 minutes.
The simplified value of 1/2 of 5 miles is 2 1/2 miles.
Therefore, the runner can go 2 1/2 miles in 16 minutes.
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?(1 point)
Responses
−80 gallons
−480 gallons
480 gallons
80 gallons
To find 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 multiply it by the number of days.
The water tank decreases by 10 gallons every 3 hours, which means it decreases by 10 gallons every 3 hours * 8 hours/day = 24 gallons every day.
Therefore, the change in water for each day is -24 gallons.
To find the total change in the amount of water in the tank after 6 days, we multiply the change in water per day (-24 gallons) by the number of days (6 days):
-24 gallons/day * 6 days = -144 gallons.
Therefore, the total change in the amount of water in the tank after 6 days is -144 gallons.
Thus, the correct response is -144 gallons, which is not listed among the given options.
U SURE
Apologies for the mistake in my response. Let's recalculate the total change in the amount of water in the tank after 6 days.
The water tank decreases by 10 gallons every 3 hours, which means it decreases by 10 gallons every 3 hours * 8 hours/day = 80 gallons every day.
Therefore, the change in water for each day is -80 gallons.
To find the total change in the amount of water in the tank after 6 days, we multiply the change in water per day (-80 gallons) by the number of days (6 days):
-80 gallons/day * 6 days = -480 gallons.
Therefore, the correct response is −480 gallons.
Apologies for the confusion in my previous response. The corrected answer is −480 gallons.
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?(1 point)
Responses
1/3÷150÷4
1/3×150÷4
1/3×150×4
1/3×150÷1/4
To find the correct number of calories per serving in the recipe, we need to multiply the amount of yogurt used per serving by the number of calories in each container.
The recipe calls for 1/3 of a container of yogurt, which is equivalent to 1/3 × 150 = 50 calories per container.
The recipe makes 4 servings, so to find the number of calories per serving, we divide the total number of calories by the number of servings.
Therefore, the correct set of calculations to find the number of calories per serving is:
1/3 × 150 ÷ 4
This simplifies to 50 ÷ 4 = 12.5 calories per serving.
Thus, the correct response is 1/3 × 150 ÷ 4.