write each ratio in simplest form..1) 2 yards to 15 feet.2) in a survey,9 out of 10 doctors recommended a certain medicine.if 80 doctors were surveyed,how many doctors recommended the medicine? 3)find each unit rate.travel 804 miles in 16 hours.4) the mass of a diamond is 1.76 g. the volume is 0.5 cm what is the density of the diamond?
2yd:15ft = 2yd:5yd = 2:5
80 * 9/10 = 72
804mi/16hr = 50.25 mi/hr
1.76g/.5cm^3 = 3.52 g/cm^3
1) Sure, let's dive into it:
For the first ratio, we have 2 yards to 15 feet. Now, we need to convert the units so that we are comparing the same thing. Since 1 yard equals 3 feet, we can write the ratio as 2 yards to (15 feet/3) yards. Simplifying further, we get 2/5 as the simplest form of the ratio.
2) Ah, a survey question! So, if 9 out of 10 doctors recommended the medicine, it means that if we surveyed 10 doctors, 9 of them would recommend it. Now we are told that we surveyed 80 doctors, so we can calculate how many recommended it by setting up a proportion: 9/10 = x/80. Cross multiplying, we get x = (9/10) × 80. Simplifying, that gives us x = 72 doctors.
3) Time to calculate a unit rate! To find the unit rate for traveling 804 miles in 16 hours, we simply divide the two quantities. So, 804 miles ÷ 16 hours equals 50 miles per hour.
4) Density, a classic topic! Density is defined as the mass divided by the volume. In this case, the mass of the diamond is given as 1.76 grams, and the volume is 0.5 cubic centimeters. So, dividing mass (1.76 g) by volume (0.5 cm³) gives us a density of 3.52 grams per cubic centimeter. Voila!
1) To find the simplest form of the ratio between 2 yards and 15 feet, we need to convert both measurements to the same unit. Since there are 3 feet in 1 yard, we can convert the 2 yards to feet by multiplying it by 3:
2 yards * 3 feet/yard = 6 feet.
Now we have 6 feet to 15 feet, and we can simplify the ratio by dividing both numbers by their greatest common divisor, which is 3:
6 feet ÷ 3 = 2 feet.
15 feet ÷ 3 = 5 feet.
Therefore, the simplest form of the ratio is 2 feet to 5 feet.
2) If 9 out of 10 doctors recommended a certain medicine, we can use that proportion to find the number of doctors who recommended the medicine when 80 doctors were surveyed.
First, we set up a proportion:
9 doctors recommended / 10 doctors surveyed = x doctors recommended / 80 doctors surveyed.
To solve for x, we cross-multiply:
9 * 80 = 10 * x.
720 = 10x.
Divide both sides by 10:
720 / 10 = x,
72 = x.
Therefore, out of 80 surveyed doctors, 72 doctors would have recommended the medicine.
3) To find the unit rate of traveling 804 miles in 16 hours, we divide the total distance by the total time:
804 miles / 16 hours = 50.25 miles/hour.
Therefore, the unit rate of travel is 50.25 miles per hour.
4) Density is defined as mass divided by volume. In this case, the mass of the diamond is given as 1.76 g, and the volume is given as 0.5 cm³.
To find the density, we divide the mass by the volume:
Density = mass / volume.
Density = 1.76 g / 0.5 cm³.
To simplify the density, we divide the numerator and denominator by their greatest common divisor, which is 0.02:
1.76 g ÷ 0.02 = 88 g.
0.5 cm³ ÷ 0.02 = 25 cm³.
Therefore, the density of the diamond is 88 g/cm³.
1) To find the simplest form of a ratio, divide both numbers by their greatest common factor (GCF).
To simplify the ratio of 2 yards to 15 feet, convert either yards to feet or feet to yards so that both quantities are in the same units.
Since there are 3 feet in 1 yard, we can convert 2 yards to feet by multiplying 2 by 3, which gives us 6 feet.
Now we have the ratio of 6 feet to 15 feet. To simplify it, find the GCF of 6 and 15, which is 3.
Divide both numbers by 3:
6 ÷ 3 = 2
15 ÷ 3 = 5
Therefore, the simplest form of the ratio is 2:5.
2) The ratio given states that 9 out of 10 doctors recommended the medicine.
To find how many doctors recommended the medicine out of 80 surveyed doctors, we can set up a proportion:
9/10 = x/80
Here, x represents the number of doctors who recommended the medicine.
Cross-multiplying, we get:
10x = 9 * 80
10x = 720
Dividing both sides by 10, we find:
x = 720/10
x = 72
Therefore, out of the 80 doctors surveyed, 72 doctors recommended the medicine.
3) A unit rate is a ratio that compares a quantity to one unit of another quantity. To find the unit rate, divide the total quantity by the corresponding unit.
In this case, the ratio is 804 miles to 16 hours.
To find the unit rate of miles per hour, divide the total miles by the total hours:
804 miles ÷ 16 hours = 50 miles per hour
Therefore, the unit rate is 50 miles per hour.
4) Density is calculated by dividing the mass of an object by its volume.
Given the mass of the diamond as 1.76 g and the volume as 0.5 cm³, we can calculate the density.
Density = mass/volume
Density = 1.76 g / 0.5 cm³
To simplify the density, divide both the numerator and denominator by their greatest common factor, if possible.
In this case, we cannot simplify the ratio further, so the density of the diamond is 3.52 g/cm³.