Use the properties of operations and rules for multiplying and dividing to solve: (- 2)(1/5) / (2/3) * (- 5/6) / (3/4)
(1 point)
To solve the expression (- 2)(1/5) / (2/3) * (- 5/6) / (3/4), we can follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) and use the properties of operations and rules for multiplying and dividing.
First, let's simplify the divisions from left to right:
(- 2)(1/5) / (2/3) = (-2) * (1/5) * (3/2) = -3/5
Next, simplify the divisions from left to right:
(- 5/6) / (3/4) = (-5/6) * (4/3) = -20/18 = -10/9
Finally, multiply the simplified divisions:
-3/5 * (-10/9) = 30/45 = 2/3
The simplified result of the expression 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)
To solve the expression (9) / (5/4) * (7/9)(- 5) / (7/2), we can follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) and use the properties of operations and rules for multiplying and dividing.
First, let's simplify the divisions from left to right:
(9) / (5/4) = 9 * (4/5) = 36/5
Next, multiply the fractions from left to right:
(7/9)(- 5) = (7 * -5) / 9 = -35/9
Finally, simplify the divisions from left to right:
-35/9 / (7/2) = (-35/9) * (2/7) = -70/63 = -10/9
Now, multiply the remaining fraction with the simplified expression from the previous step:
(36/5) * (-10/9) = -360/45 = -8
The simplified result of the expression is -8.
Sove this mut-step problem. A runner completes 1/2 of a 5-mile race every 8 minutes. At the same pace, how far can the runner go in 16 minutes? (1 point)
To find out how far the runner can go in 16 minutes, knowing that the runner completes 1/2 of a 5-mile race every 8 minutes, we can use the unit rate that the runner covers.
In 8 minutes, the runner covers 1/2 of a 5-mile race.
So, in 1 minute, the runner covers (1/2) ÷ 8 = 1/16 of a mile.
Therefore, in 16 minutes, the runner can cover (1/16) × 16 = 1 mile.
The runner can go 1 mile in 16 minutes.
Is itA 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)
O 480 gatons
O-480 gallons
80 gatons
80 gatons
To find the total change in the amount of water in the tank after 6 days, knowing that the water tank decreases by 10 gallons every 3 hours every day, we need to calculate the change in the amount of water in 6 days.
Every 3 hours, the water tank decreases by 10 gallons.
Therefore, in 24 hours (1 day), the water tank decreases by 10 × (24 ÷ 3) = 80 gallons.
After 6 days, the total change in the amount of water in the tank would be 80 × 6 = 480 gallons.
So, the correct answer is: 480 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)
To solve the expression (- 2)(1/5) / (2/3) * (- 5/6) / (3/4), we will follow the order of operations and apply the properties and rules of multiplying and dividing.
Step 1: Simplify each multiplication and division operation independently:
Multiply:
(- 2)(1/5) = -2/5
(- 5/6)(3/4) = (-15/24) = -5/8
Divide:
(2/3) / (3/4) = (2/3) * (4/3) = (8/9)
After simplifying, the expression becomes:
(-2/5) / (8/9) * (-5/8)
Step 2: Apply the rule of division by multiplying by the reciprocal:
(-2/5) / (8/9) can be rewritten as multiplying by the reciprocal of (8/9), which is (9/8).
So, the expression becomes:
(-2/5) * (9/8) * (-5/8)
Step 3: Multiply the numerators and denominators separately:
Numerator:
(-2/5) * (9/8) * (-5/8) = (-2 * 9 * -5) = 90
Denominator:
5 * 8 * 8 = 320
Step 4: Simplify the fraction by canceling common factors, if any:
The fraction 90/320 can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 10.
90/320 = 9/32
Therefore, the simplified expression is 9/32.