Olivia wants to know the proportion of students at her school who use a certain social media app. She interviews a random sample of students at her school. She finds that 30% of the students in the sample use the app.
What conclusion can she draw from the sample?
We can find the prime factors of 42 by dividing it by the smallest prime number, 2, and then dividing the result by the smallest prime number that goes into it, which is 3. We continue this process until we can no longer divide by any more prime numbers:
42 ÷ 2 = 21
21 ÷ 3 = 7
Since 7 is a prime number and cannot be divided any further, we have found the prime factors of 42: 2, 3, and 7.
Therefore, the prime factors of 42 are 2, 3, and 7.
Olivia can conclude that 30% of the students in her sample use the social media app. However, she cannot necessarily generalize this result to the entire population of students at her school, as her sample may not be representative of the entire population. She would need a larger, more randomized sample to make more accurate conclusions about the entire population.
A new washing machine uses 45% less water than an older model. A family used 1,440 gallons of water per month to run the old washing machine. About how much water will they use each month to run the new washing machine?
If the new washing machine uses 45% less water than the old model, then it uses 100% - 45% = 55% of the old amount of water.
To calculate the amount of water used by the new washing machine:
1. Convert the old amount of water to a percentage: 1,440 gallons / 100% = 14.4 gallons per 1%
2. Multiply this by the percentage of water used by the new machine: 14.4 gallons per 1% * 55% = 7.92 gallons per 1%
3. Convert back to the actual amount of water used by multiplying by the total percentage: 7.92 gallons per 1% * 100% = 792 gallons
Therefore, the family will use about 792 gallons of water per month to run the new washing machine.
What percent of 59 is 44.1? Round the answer to the nearest hundredth of a percent if necessary.
To find the percent, divide the second number (44.1) by the first number (59), then multiply by 100 to convert to a percentage:
percent = (44.1 / 59) x 100
percent = 74.576
Rounding this answer to the nearest hundredth of a percent gives:
percent ≈ 74.58%
Therefore, approximately 74.58% of 59 is 44.1.
Factor the expression using the greatest common factor.
24a3 + 32a? + 40a
The greatest common factor of the terms 24a³, 32a², and 40a is 8a. We can factor it out as follows:
24a³ + 32a² + 40a = 8a(3a² + 4a + 5)
Therefore, 24a³ + 32a² + 40a can be factored as 8a(3a² + 4a + 5) using the greatest common factor.
Convert 35 mL/s to liters per minute (L/min).
To convert from milliliters per second (mL/s) to liters per minute (L/min), we need to multiply by a conversion factor. There are 60 seconds in a minute and 1000 milliliters in a liter, so:
35 mL/s × (60 s/min) ÷ (1000 mL/L) = 2.1 L/min
Therefore, 35 mL/s is equivalent to 2.1 L/min.