Use the properties of operations and rules for multiplying and dividing to solve:
(−2)×(15)÷(23)×(−56)÷(34)
(1 point)
Responses
−23
negative Start Fraction 2 over 3 End Fraction
−16
negative Start Fraction 1 over 6 End Fraction
23
Start Fraction 2 over 3 End Fraction
16
To solve the expression (-2) × (15) ÷ (23) × (-56) ÷ (34), we can apply the rules for multiplying and dividing numbers.
First, we can simplify the multiplication part: (-2) × (15) × (-56) equals 1680.
Next, we can simplify the division part by dividing 1680 by 23: 1680 ÷ 23 equals 73.043478260869565 (approximately).
Finally, we can divide 73.043478260869565 by 34: 73.043478260869565 ÷ 34 equals approximately 2.1470588235294117.
Therefore, the solution is approximately 2.1470588235294117.
Solve this multi-step problem. A runner completes 14 of a 5-mile race every 8 minutes. At the same pace, how far can the runner go in 16 minutes?(1 point)
Responses
18 mile
Start Fraction 1 over 8 End Fraction mile
110 mile
Start Fraction 1 over 10 End Fraction mile
212 miles
2 Start Fraction 1 over 2 End Fraction miles
160 miles
To solve this problem, we can find the runner's speed by dividing the distance traveled (14 miles) by the time taken (8 minutes).
The runner's speed is 14 miles / 8 minutes = 1.75 miles per minute.
To find how far the runner can go in 16 minutes, we can multiply the speed by the time:
1.75 miles per minute * 16 minutes = 28 miles.
Therefore, the runner can go 28 miles in 16 minutes.
Solve this multi-step problem. A runner completes 14 of a 5-mile race every 8 minutes. At the same pace, how far can the runner go in 16 minutes?(1 point)
Responses
1.18 mile
Start Fraction 1 over 8 End Fraction mile
2.110 mile
Start Fraction 1 over 10 End Fraction mile
3.212 miles
2 Start Fraction 1 over 2 End Fraction miles
4.160 miles
To solve this problem, we can find the rate at which the runner completes the race, and then multiply that rate by the time given.
The runner completes 14 miles of a 5-mile race in 8 minutes. To find the rate, we divide the distance by the time: 14 miles / 8 minutes = 1.75 miles per minute.
Now, we need to find how far the runner can go in 16 minutes, using the rate we found. We multiply the rate by the time: 1.75 miles per minute x 16 minutes = 28 miles.
Therefore, the runner can go 28 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
−480 gallons
negative 480 gallons
−80 gallons
negative 80 gallons
80 gallons
80 gallons
480 gallons
480 gallons
To find the total change in the amount of water in the tank after 6 days, we need to calculate the change per day and then multiply it by the number of days.
The water tank decreases by 10 gallons every 3 hours. Since there are 24 hours in a day, this means the tank decreases by 10 gallons every (24/3 =) 8 cycles.
The tank decreases by 10 gallons every 8 cycles, which is equivalent to a decrease of 10 gallons every 8 * 3 = 24 hours.
Therefore, the tank decreases by 10 gallons every 24 hours or per day.
After 6 days, the total change in the amount of water in the tank is 10 gallons/day * 6 days = 60 gallons.
Therefore, the total change in the amount of water in the tank after 6 days is 60 gallons.
A recipe calls for 13 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
13×150÷4
Start Fraction 1 over 3 End Fraction times 150 divided by 4
13÷150÷4
Start Fraction 1 over 3 End Fraction divided by 150 divided by 4
13×150×4
Start Fraction 1 over 3 End Fraction times 150 times 4
13×150÷14
To find the correct number of calories per serving, we need to divide the total number of calories by the number of servings.
The recipe calls for 13 of a container of yogurt, and each container has 150 calories. This means the total number of calories used in the recipe is 13 * 150 = 1950 calories.
The recipe makes 4 servings. To find the calories per serving, we divide the total number of calories by the number of servings: 1950 calories / 4 servings = 487.5 calories per serving.
Therefore, the correct set of calculations to find the number of calories per serving is 13 × 150 ÷ 4.
To solve the expression (−2)×(15)÷(23)×(−56)÷(34), we will follow the order of operations, which tells us to perform multiplication and division from left to right.
Step 1: Multiply (-2) and 15: (-2)×(15) = -30.
Step 2: Divide -30 by 23: -30 ÷ 23 = -1.30434783 (approximately, rounded to 8 decimal places).
Step 3: Multiply -1.30434783 by -56: -1.30434783 × -56 = 73.04347848 (approximately, rounded to 8 decimal places).
Step 4: Finally, divide 73.04347848 by 34: 73.04347848 ÷ 34 = 2.14772794 (approximately, rounded to 8 decimal places).
Therefore, the solution to the expression is 2.14772794 (approximately, rounded to 8 decimal places).