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.