Let's assume that there are a total of 𝑥 cars in the used-car lot.
Given that 2/5 of the cars are gray, the number of gray cars on the lot is (2/5)𝑥.
And among the gray cars, 1/3 of them are electrically powered vehicles. So, the number of gray and electrically powered cars is (1/3)(2/5)𝑥 = (2/15)𝑥.
Hence, the fraction of cars on the lot that are both gray and electrically powered is (2/15)𝑥 / 𝑥 = 2/15.
Therefore, the simplified fraction is 2/15.
Bot of the cars in a used-car lot, 2/5 are the color gray. 1/3 of the gray cars are electrically powered vehicles. What fraction of the cars on the lot are both gray and electrically powered? Leave your answer in simplified fraction form.
29 answers
Bot Lake Profondo has a depth of 84 feet. Lake Segundo is 5/6 deep. What is the elevation at the bottom of Lake Segundo? (Remember, the elevation is below sea level. Account for this in your answer.)
To find the elevation at the bottom of Lake Segundo, we need to calculate the difference in depth between the two lakes and account for the fact that the elevation is below sea level.
Given that Lake Profondo has a depth of 84 feet, the depth of Lake Segundo is 5/6 of that.
Depth of Lake Segundo = (5/6) * 84 = 70 feet.
Since the elevation is below sea level, we consider it as a negative value. Therefore, the elevation at the bottom of Lake Segundo is -70 feet.
Given that Lake Profondo has a depth of 84 feet, the depth of Lake Segundo is 5/6 of that.
Depth of Lake Segundo = (5/6) * 84 = 70 feet.
Since the elevation is below sea level, we consider it as a negative value. Therefore, the elevation at the bottom of Lake Segundo is -70 feet.
Bot Divide -72 by -4. then divide the quotient by -9. What is the final quotient?
To find the final quotient, we need to divide -72 by -4, and then divide the resulting quotient by -9.
When we divide -72 by -4, we get a quotient of 18.
Now, we need to divide 18 by -9 to find the final quotient.
18 divided by -9 is equal to -2.
Hence, the final quotient is -2.
When we divide -72 by -4, we get a quotient of 18.
Now, we need to divide 18 by -9 to find the final quotient.
18 divided by -9 is equal to -2.
Hence, the final quotient is -2.
Bot what is the quotient of 100 divided by (-10) divided by 5?
To find the quotient of 100 divided by (-10) divided by 5, we need to divide 100 by -10 and then divide the resulting quotient by 5.
When we divide 100 by -10, we get a quotient of -10.
Now, we need to divide -10 by 5 to find the final quotient.
-10 divided by 5 is equal to -2.
Hence, the quotient of 100 divided by (-10) divided by 5 is -2.
When we divide 100 by -10, we get a quotient of -10.
Now, we need to divide -10 by 5 to find the final quotient.
-10 divided by 5 is equal to -2.
Hence, the quotient of 100 divided by (-10) divided by 5 is -2.
Bot Sophia babysat for 5.75 hours and earned $46. What was Sophia's hourly rate?
To find Sophia's hourly rate, we need to divide the amount she earned ($46) by the number of hours she babysat (5.75).
Hourly rate = Earnings / Hours
Hourly rate = $46 / 5.75
Hourly rate ≈ $8
Therefore, Sophia's hourly rate was approximately $8.
Hourly rate = Earnings / Hours
Hourly rate = $46 / 5.75
Hourly rate ≈ $8
Therefore, Sophia's hourly rate was approximately $8.
Bot what is 4.65 converted to a fraction? The answer should be given in simplest form.
To convert 4.65 to a fraction in simplest form, we can follow these steps:
Step 1: Identify the place value of the decimal point. In this case, the decimal point is after the hundredths place.
Step 2: Write the given number without the decimal point as the numerator. So, the numerator is 465.
Step 3: Write the denominator as 1 followed by the same number of zeros as the number of digits after the decimal point. Since there are two digits after the decimal point, the denominator is 100.
Step 4: Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 465 and 100 is 5.
Dividing the numerator and denominator by 5, we get:
Numerator = 465 ÷ 5 = 93
Denominator = 100 ÷ 5 = 20
Therefore, 4.65 is equivalent to the fraction 93/20 in simplest form.
Step 1: Identify the place value of the decimal point. In this case, the decimal point is after the hundredths place.
Step 2: Write the given number without the decimal point as the numerator. So, the numerator is 465.
Step 3: Write the denominator as 1 followed by the same number of zeros as the number of digits after the decimal point. Since there are two digits after the decimal point, the denominator is 100.
Step 4: Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 465 and 100 is 5.
Dividing the numerator and denominator by 5, we get:
Numerator = 465 ÷ 5 = 93
Denominator = 100 ÷ 5 = 20
Therefore, 4.65 is equivalent to the fraction 93/20 in simplest form.
Bot what is 4.65 converted to a fraction? The answer should be given in simplest form. Pick one of these answers. 4 6/5 4 65/100 4 13/20 4/65
To convert 4.65 to a fraction in simplest form, we have:
4.65 = 4 + 0.65
To convert 0.65 to a fraction, we can write it as 65/100 since there are 2 decimal places.
Thus, 4.65 is equal to 4 + 65/100, and in mixed number form, it is 4 65/100.
However, to express it in simplest form, we can simplify the fraction 65/100 by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 5.
Dividing 65 by 5 gives 13, and dividing 100 by 5 gives 20.
So, in simplest form, 4.65 is equal to 4 13/20.
Therefore, the correct answer is 4 13/20.
4.65 = 4 + 0.65
To convert 0.65 to a fraction, we can write it as 65/100 since there are 2 decimal places.
Thus, 4.65 is equal to 4 + 65/100, and in mixed number form, it is 4 65/100.
However, to express it in simplest form, we can simplify the fraction 65/100 by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 5.
Dividing 65 by 5 gives 13, and dividing 100 by 5 gives 20.
So, in simplest form, 4.65 is equal to 4 13/20.
Therefore, the correct answer is 4 13/20.
Bot use long division to convert 2 7/16 to a decimal.
To convert the mixed number 2 7/16 to a decimal using long division, we can follow these steps:
Step 1: Rewrite the mixed number as an improper fraction.
2 7/16 = (2 * 16 + 7) / 16 = 39/16
Step 2: Perform long division by dividing the numerator (39) by the denominator (16).
39
__________
16 | 39
Step 3: Divide 39 by 16. The quotient is 2 and the remainder is 7.
Step 4: Add a decimal point to the quotient. Since we are converting to a decimal, the decimal point goes right after the whole number part.
Quotient: 2.
Step 5: Bring down a zero after the remainder (7) to continue dividing.
39
_________
16 | 39.0
Step 6: Divide 70 (remainder 70 becomes 700 when multiplied by 10) by 16.
39.0
__________
16 | 39.00
32
__________
700
Step 7: Divide 70 (remainder) by 16. The quotient is 4 and the remainder is 6. Add it to the decimal portion.
39.04
__________
16 | 39.00
32
__________
70
64
__________
60
Step 8: Divide 60 (remainder) by 16. The quotient is 3 and the remainder is 12. Add it to the decimal portion.
39.043
__________
16 | 39.000
32
__________
70
64
__________
60
48
__________
120
Step 9: Divide 120 (remainder) by 16. The quotient is 7 and the remainder is 8. Add it to the decimal portion.
39.0437
__________
16 | 39.0000
32
__________
70
64
__________
60
48
__________
120
112
__________
80
Step 10: Divide 80 (remainder) by 16. The quotient is 5 and the remainder is 0.
39.04375
__________
16 | 39.00000
32
__________
70
64
__________
60
48
__________
120
112
__________
80
80
__________
00
Step 11: The remainder is now 0, indicating that the division is complete.
Hence, 2 7/16, when converted to a decimal using long division, is equal to 2.04375.
Therefore, 2 7/16 as a decimal is approximately 2.04375.
Step 1: Rewrite the mixed number as an improper fraction.
2 7/16 = (2 * 16 + 7) / 16 = 39/16
Step 2: Perform long division by dividing the numerator (39) by the denominator (16).
39
__________
16 | 39
Step 3: Divide 39 by 16. The quotient is 2 and the remainder is 7.
Step 4: Add a decimal point to the quotient. Since we are converting to a decimal, the decimal point goes right after the whole number part.
Quotient: 2.
Step 5: Bring down a zero after the remainder (7) to continue dividing.
39
_________
16 | 39.0
Step 6: Divide 70 (remainder 70 becomes 700 when multiplied by 10) by 16.
39.0
__________
16 | 39.00
32
__________
700
Step 7: Divide 70 (remainder) by 16. The quotient is 4 and the remainder is 6. Add it to the decimal portion.
39.04
__________
16 | 39.00
32
__________
70
64
__________
60
Step 8: Divide 60 (remainder) by 16. The quotient is 3 and the remainder is 12. Add it to the decimal portion.
39.043
__________
16 | 39.000
32
__________
70
64
__________
60
48
__________
120
Step 9: Divide 120 (remainder) by 16. The quotient is 7 and the remainder is 8. Add it to the decimal portion.
39.0437
__________
16 | 39.0000
32
__________
70
64
__________
60
48
__________
120
112
__________
80
Step 10: Divide 80 (remainder) by 16. The quotient is 5 and the remainder is 0.
39.04375
__________
16 | 39.00000
32
__________
70
64
__________
60
48
__________
120
112
__________
80
80
__________
00
Step 11: The remainder is now 0, indicating that the division is complete.
Hence, 2 7/16, when converted to a decimal using long division, is equal to 2.04375.
Therefore, 2 7/16 as a decimal is approximately 2.04375.
Bot use long division to convert 6 7/15 to a decimal.
To convert the mixed number 6 7/15 to a decimal using long division, we can follow these steps:
Step 1: Rewrite the mixed number as an improper fraction.
6 7/15 = (6 * 15 + 7) / 15 = 97/15
Step 2: Perform long division by dividing the numerator (97) by the denominator (15).
97
__________
15 | 97
Step 3: Divide 97 by 15. The quotient is 6 and the remainder is 7.
Step 4: Add a decimal point to the quotient. Since we are converting to a decimal, the decimal point goes right after the whole number part.
Quotient: 6.
Step 5: Bring down a zero after the remainder (7) to continue dividing.
97
________
15 | 6.00
Step 6: Divide 70 (remainder 70 becomes 700 when multiplied by 10) by 15.
97.0
_________
15 | 97.00
90
_________
70
Step 7: Divide 70 (remainder) by 15. The quotient is 4 and the remainder is 10 (which is equivalent to 1/10). Add it to the decimal portion.
97.06
_________
15 | 97.00
90
_________
70
- 60
_________
100
Step 8: Divide 100 (remainder) by 15. The quotient is 6 and the remainder is 10 (which is equivalent to 1/10). Add it to the decimal portion.
97.066
_________
15 | 97.000
90
_________
70
- 60
_________
100
- 90
_________
100
Step 9: Divide 100 (remainder) by 15. The quotient is 6 and the remainder is 10 (which is equivalent to 1/10). Add it to the decimal portion.
97.0666...
_________
15 | 97.0000
90
_________
70
- 60
_________
100
- 90
_________
100
- 90
_________
100
Step 10: The remainder is now 0, indicating that the division is complete.
Hence, 6 7/15, when converted to a decimal using long division, is equal to 6.0666... or approximately 6.067.
Therefore, 6 7/15 as a decimal is approximately 6.067.
Step 1: Rewrite the mixed number as an improper fraction.
6 7/15 = (6 * 15 + 7) / 15 = 97/15
Step 2: Perform long division by dividing the numerator (97) by the denominator (15).
97
__________
15 | 97
Step 3: Divide 97 by 15. The quotient is 6 and the remainder is 7.
Step 4: Add a decimal point to the quotient. Since we are converting to a decimal, the decimal point goes right after the whole number part.
Quotient: 6.
Step 5: Bring down a zero after the remainder (7) to continue dividing.
97
________
15 | 6.00
Step 6: Divide 70 (remainder 70 becomes 700 when multiplied by 10) by 15.
97.0
_________
15 | 97.00
90
_________
70
Step 7: Divide 70 (remainder) by 15. The quotient is 4 and the remainder is 10 (which is equivalent to 1/10). Add it to the decimal portion.
97.06
_________
15 | 97.00
90
_________
70
- 60
_________
100
Step 8: Divide 100 (remainder) by 15. The quotient is 6 and the remainder is 10 (which is equivalent to 1/10). Add it to the decimal portion.
97.066
_________
15 | 97.000
90
_________
70
- 60
_________
100
- 90
_________
100
Step 9: Divide 100 (remainder) by 15. The quotient is 6 and the remainder is 10 (which is equivalent to 1/10). Add it to the decimal portion.
97.0666...
_________
15 | 97.0000
90
_________
70
- 60
_________
100
- 90
_________
100
- 90
_________
100
Step 10: The remainder is now 0, indicating that the division is complete.
Hence, 6 7/15, when converted to a decimal using long division, is equal to 6.0666... or approximately 6.067.
Therefore, 6 7/15 as a decimal is approximately 6.067.
Bot use long division to convert 6 7/15 to a decimal. Pick one of these answers. 6.715 0.46 6.47 6.14285
To convert the mixed number 6 7/15 to a decimal using long division, the correct answer is 6.47.
Bot a pilot is flying an airplane. Due to strong winds, the pilot decides to fly 4,000 feet lower to avoid excessive turbulence. It takes the pilot 3.5 minutes to make this adjustment. Interpret the quotient to describe the rate of change in the plane's altitude. give your answer to the nearest hundredth, and remember the plane is descending. The quotient that best represents the rate of change in the plane's altitude is how many feet/minute.
To find the rate of change in the plane's altitude, we need to divide the change in altitude (4,000 feet) by the time it takes to make this adjustment (3.5 minutes).
Rate of change in altitude = Change in altitude / Time taken
Rate of change in altitude = 4000 feet / 3.5 minutes
Calculating this, we get:
Rate of change in altitude ≈ 1142.86 feet/minute (rounded to the nearest hundredth).
Therefore, the rate of change in the plane's altitude is approximately 1142.86 feet/minute.
Rate of change in altitude = Change in altitude / Time taken
Rate of change in altitude = 4000 feet / 3.5 minutes
Calculating this, we get:
Rate of change in altitude ≈ 1142.86 feet/minute (rounded to the nearest hundredth).
Therefore, the rate of change in the plane's altitude is approximately 1142.86 feet/minute.
Bot a fire engine's water tank holds750 gallons of water. If the pump removes 250 gallons of water in 5 minutes, what is the change in the amount of water in gallons in 1 minute? Pick one of these answers. -50 15 -15 50
To find the change in the amount of water in the fire engine's tank in 1 minute, we can divide the change in water (250 gallons) by the time taken (5 minutes).
Change in water per minute = Change in water / Time taken
Change in water per minute = 250 gallons / 5 minutes
Calculating this, we get:
Change in water per minute = 50 gallons/minute
Hence, the change in the amount of water in the fire engine's tank in 1 minute is 50 gallons. Therefore, the correct answer is 50.
Change in water per minute = Change in water / Time taken
Change in water per minute = 250 gallons / 5 minutes
Calculating this, we get:
Change in water per minute = 50 gallons/minute
Hence, the change in the amount of water in the fire engine's tank in 1 minute is 50 gallons. Therefore, the correct answer is 50.
Bot use the properties of operations and rules for multiplying and dividing to solve the following problem: 3/8 x (-32) divided by (-3) x1/8 Pick one of these answers. 9/2 1/2 96/192 9/2,048
To solve the problem 3/8 x (-32) ÷ (-3) x 1/8, we can follow the order of operations (PEMDAS/BODMAS) and rules for multiplying and dividing:
Step 1: Multiply 3/8 by -32:
(3/8) x (-32) = -96/8 = -12
Step 2: Divide -12 by -3:
-12 ÷ (-3) = 4
Step 3: Multiply 4 by 1/8:
4 x (1/8) = 4/8 = 1/2
Therefore, the solution to 3/8 x (-32) ÷ (-3) x 1/8 is 1/2.
Step 1: Multiply 3/8 by -32:
(3/8) x (-32) = -96/8 = -12
Step 2: Divide -12 by -3:
-12 ÷ (-3) = 4
Step 3: Multiply 4 by 1/8:
4 x (1/8) = 4/8 = 1/2
Therefore, the solution to 3/8 x (-32) ÷ (-3) x 1/8 is 1/2.
Bot a recipe calls for 2 1/3 cups oatmeal. You double the recipe and then divide it evenly into 14 servings. How much oatmeal is in each serving?
To calculate how much oatmeal is in each serving, let's first calculate the amount of oatmeal when doubling the recipe.
The original recipe calls for 2 1/3 cups of oatmeal. Doubling the recipe would be: (2 1/3) x 2.
Rewriting the mixed number as an improper fraction, we have: (7/3) x 2 = 14/3 cups of oatmeal.
Now, we divide this amount evenly into 14 servings.
To divide the oatmeal equally into 14 servings, we perform (14/3) ÷ 14:
(14/3) ÷ 14 = 14/3 ÷ 14/1 (dividing by a fraction is equivalent to multiplying by its reciprocal)
= 14/3 x 1/14 (reciprocal of 14/1)
= 14/42.
Simplifying this fraction by dividing both numerator and denominator by their greatest common divisor (GCD), which is 14, we get:
(14/42) ÷ 14/14 = 1/3.
Therefore, each serving would contain 1/3 cup of oatmeal.
The original recipe calls for 2 1/3 cups of oatmeal. Doubling the recipe would be: (2 1/3) x 2.
Rewriting the mixed number as an improper fraction, we have: (7/3) x 2 = 14/3 cups of oatmeal.
Now, we divide this amount evenly into 14 servings.
To divide the oatmeal equally into 14 servings, we perform (14/3) ÷ 14:
(14/3) ÷ 14 = 14/3 ÷ 14/1 (dividing by a fraction is equivalent to multiplying by its reciprocal)
= 14/3 x 1/14 (reciprocal of 14/1)
= 14/42.
Simplifying this fraction by dividing both numerator and denominator by their greatest common divisor (GCD), which is 14, we get:
(14/42) ÷ 14/14 = 1/3.
Therefore, each serving would contain 1/3 cup of oatmeal.
Bot solve the following word problem. A fish is swimming at -10.8 meters, or 10.8 meters below sea level. Every 2 minutes it descends another 1.5 meters. How long will it take for the fish to reach a depth of -37.8 meters? Show your work and write a sentence to explain what your answer means.
To find out how long it will take for the fish to reach a depth of -37.8 meters, we can set up an equation based on the given information.
Let's denote the time it takes for the fish to descend by "t" minutes.
The initial depth of the fish is -10.8 meters, and it descends by 1.5 meters every 2 minutes. Therefore, after t minutes, the total depth will be:
-10.8 + (1.5/2)t = -37.8
To solve this equation, we can isolate the "t" term:
-10.8 + 0.75t = -37.8
Adding 10.8 to both sides:
0.75t = -37.8 + 10.8
0.75t = -27
Now, divide both sides by 0.75:
t = -27 / 0.75
t = -36
We have found that the time it will take for the fish to reach a depth of -37.8 meters is -36 minutes.
The negative sign in the answer indicates that the fish is reaching a depth below sea level. Therefore, the fish will take 36 minutes to descend to a depth of -37.8 meters below sea level.
Let's denote the time it takes for the fish to descend by "t" minutes.
The initial depth of the fish is -10.8 meters, and it descends by 1.5 meters every 2 minutes. Therefore, after t minutes, the total depth will be:
-10.8 + (1.5/2)t = -37.8
To solve this equation, we can isolate the "t" term:
-10.8 + 0.75t = -37.8
Adding 10.8 to both sides:
0.75t = -37.8 + 10.8
0.75t = -27
Now, divide both sides by 0.75:
t = -27 / 0.75
t = -36
We have found that the time it will take for the fish to reach a depth of -37.8 meters is -36 minutes.
The negative sign in the answer indicates that the fish is reaching a depth below sea level. Therefore, the fish will take 36 minutes to descend to a depth of -37.8 meters below sea level.
30 answers