A processing machine crushes 3 1/4 kilograms of dried fruit(s) in 3/4 minute.
What is the unit rate at which the machine crushes dried fruits?
A. 3/13
B. 16/39
C. 2 7/16
D. 4 1/3
To calculate the unit rate, we need to divide the amount of dried fruit crushed by the time it took to crush it.
Step 1: Convert 3 1/4 kilograms to an improper fraction.
3 1/4 = (4*3) + 1 = 13/4
Step 2: Calculate the unit rate.
Unit rate = (3 1/4) / (3/4) = (13/4) / (3/4)
Unit rate = 13/3 = 4 1/3
Therefore, the unit rate at which the machine crushes dried fruits is D. 4 1/3.
The average of hair growth is 2.5 centimeters every 2 months.
At that rate how many months will it take to grow 22.5 centimeters of hair?
To find out how many months it will take to grow 22.5 centimeters of hair at a rate of 2.5 centimeters every 2 months, we need to set up a proportion.
Let x be the number of months it will take to grow 22.5 centimeters.
Using the information given:
2.5 centimeters in 2 months
x centimeters in x months
We can set up the proportion:
2.5 / 2 = 22.5 / x
To solve for x, cross multiply:
2.5 * x = 2 * 22.5
2.5x = 45
x = 45 / 2.5
x = 18
Therefore, it will take 18 months to grow 22.5 centimeters of hair at a rate of 2.5 centimeters every 2 months.
During cooking a chicken loses 10% of its weight due to water loss. In order to obtain 1,170 grams of cooked chicken how many grams of uncooked chicken must be used?
Since a chicken loses 10% of its weight during cooking, it means you will end up with 90% of the original weight after cooking.
Let x be the weight of the uncooked chicken.
After cooking, the weight of the cooked chicken is 90% of the weight of the uncooked chicken:
0.9x = 1170
To solve for x:
x = 1170 / 0.9
x = 1300
Therefore, 1,300 grams of uncooked chicken must be used in order to obtain 1,170 grams of cooked chicken after accounting for the 10% weight loss during cooking.
A satellite is 18 centimeters wide. A model of it was built with a scale of 1 centimeter : 3 meters. How wide is the model?
To find the width of the model, you need to use the scale factor provided in the problem.
The scale given is 1 centimeter : 3 meters. This means that every 1 centimeter on the model represents 3 meters in real life.
Since the satellite is 18 centimeters wide, you need to multiply this width by the scale factor to find the width in meters:
Width of model = 18 centimeters * 3 meters/centimeter
Width of model = 54 meters
Therefore, the model of the satellite is 54 meters wide.
Find the constant (k) of proportionality in the table.
x: 2, 3, 8, 10
y: 8, 12, 32, 40
What equation represents the table?
To find the constant of proportionality (k) in the table, we can select two corresponding values for x and y and set up a proportion.
Let's choose the first pair (2, 8) and the second pair (3, 12) to find k.
For the first pair:
x = 2, y = 8
8 = k * 2
k = 8 / 2
k = 4
For the second pair:
x = 3, y = 12
12 = 4 * 3
Since the value of k is 4, the equation representing the table in the form of y = kx is:
y = 4x