Sophia worked 5.75 and earned 46$. What was her hourly rate?
To calculate Sophia's hourly rate, we need to divide the total amount earned ($46) by the total hours worked (5.75):
Hourly rate = Total earnings / Total hours worked
Hourly rate = $46 / 5.75 hours
Hourly rate ≈ $8
Therefore, Sophia's hourly rate is approximately $8.
4.65 as a fraction in simplest form
To simplify 4.65 as a fraction in simplest form, we need to express it as a fraction with the numerator and denominator having no common factors other than 1.
Starting with 4.65, we can move the decimal point two places to the right to get rid of the decimal: 465.
Now, the fraction is 465/100. To simplify it further, we can divide both the numerator and denominator by their greatest common divisor. The greatest common divisor of 465 and 100 is 5:
465 ÷ 5 = 93
100 ÷ 5 = 20
Therefore, the simplified form of 4.65 is 93/20.
Simplified fraction as a mixed number
To convert the simplified fraction 93/20 into a mixed number, we need to see how many times the denominator (20) goes into the numerator (93).
20 goes into 93 four times (4 x 20 = 80), with a remainder of 13.
So, the mixed number representation of the simplified fraction 93/20 is 4 and 13/20.
2 7/16 as a decimal
Explain using long division
To convert the mixed number 2 7/16 into a decimal, we can use long division. Here's the step-by-step process:
1. Rewrite the mixed number as an improper fraction: Multiply the whole number (2) by the denominator (16), then add the numerator (7) to get the new numerator. The denominator remains the same.
2 * 16 + 7 = 32 + 7 = 39
The improper fraction is 39/16.
2. Perform long division:
2.4375 → Start by placing the decimal point above the division bar.
───────────────── then divide the numerator (39) by the denominator (16).
16 | 39
-32 → Divide the first digit of the numerator (3) by the denominator (16) to get 0.1875.
70
-64
60
-48
120
-112
80
-80
0
3. Continue dividing and bringing down zeros until the desired level of precision is attained. In this case, the answer terminates without repeating, so we can stop here.
Therefore, the mixed number 2 7/16 expressed as a decimal is approximately 2.4375.
6 7/15 as a decimal using long division
To convert the mixed number 6 7/15 into a decimal using long division, we follow these steps:
1. Rewrite the mixed number as an improper fraction: Multiply the whole number (6) by the denominator (15), then add the numerator (7) to get the new numerator. The denominator remains the same.
6 * 15 + 7 = 90 + 7 = 97
The improper fraction is 97/15.
2. Perform long division:
6.4666... → Start by placing the decimal point above the division bar.
───────────────── then divide the numerator (97) by the denominator (15).
15 | 97
-90 → Divide the first digit of the numerator (9) by the denominator (15) to get 0.6.
70
-60
100
-90
100
-90
100
-90
100
-90
100
-90
100
-90
100
-90
100
-90
100
-90
...
As we can see, the division continues in a repeating pattern of 6 and 4 digits.
Therefore, the mixed number 6 7/15 expressed as a decimal is approximately 6.4666... (which continues to repeat).
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
To interpret the quotient to describe the rate of change in the plane's altitude, we divide the change in altitude (4,000 feet) by the time it takes to make this adjustment (3.5 minutes):
Rate of change = Change in altitude / Time
Rate of change = 4,000 feet / 3.5 minutes
Rate of change ≈ 1142.86 feet per minute
Therefore, the rate of change in the plane's altitude, given the context, is approximately 1142.86 feet per minute.
A fire engine’s water tank holds 750 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?
To find the change in the amount of water in 1 minute, we need to divide the amount of water removed (250 gallons) by the time it takes to remove that amount (5 minutes):
Change in amount of water per minute = Amount of water removed / Time
Change in amount of water per minute = 250 gallons / 5 minutes
Change in amount of water per minute = 50 gallons
Therefore, the change in the amount of water in 1 minute is 50 gallons.