Add 0.0025 kg, 1750 mg, 2.25 g, and 825,000 μg, and express the answer in grams.
1 answer:
Answer:
6.75g
Step-by-step explanation:
The initial step is to convert all values to grams using rules of three, followed by summation.
In a rule of three calculation, the first step is identifying the measures and how they interrelate; whether their connection is direct or inverse.
In direct relationships, as one measure increases, so does the other.
In inverse relationships, as one measure increases, the other decreases.
Problems involving unit conversion, like this, illustrate a direct relationship between measures.
First step: convert 0.0025kg to grams
One kilogram equals 1000 grams, so:
1kg - 1000g
0.0025kg - xg
x = 1000*0.0025 = 2.5g
Thus, 0.0025kg is equal to 2.5g
Second step: handle 1750 mg
One gram consists of 1000mg, so:
1g - 1000mg
xg - 1750mg
1000x = 1750
x = 1.75g
Therefore, 1750 mg converts to 1.75g
2.25g is fine
Third step: convert 825,000 μg to grams
One gram consists of 1,000,000 micrograms, so:
1g - 1,000,000 μg
xg - 825,000 μg
1,000,000x = 825,000
x = 0.25g
So, 825,000 μg equals 0.25g
Final step: sum all values
0.25g + 2.25g + 1.75g + 2.50g = 6.75g
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Answer: 0.5507
Step-by-step explanation:
Given: The time between sightings of speeders by a radar system is represented by the continuous random variable X, which follows a cumulative distribution function
If we convert 12 minutes into hours, it equals hours or 0.2 hours.
To find the probability of waiting less than 12 minutes:
Thus, the probability we are looking for is: 0.5507
Answer:
The shaped region accounts for 7/18 of the area of ACIG.
Step-by-step explanation:
Refer to the attached diagram for further clarity on the problem.
Step 1
Determine the length of one side of square ABED.
We know that
AB=BE=ED=AD
The area of a square can be calculated as
where b is the side length.
We have
So we substitute
Thus,
Step 2
Calculate the area of ACIG.
The area of rectangle ACIG is determined by
Substituting the given values yields
Step 3
Determine the area of the shaded rectangle DEHG.
The area of rectangle DEHG is given by
We find
and substitute
Step 4
Calculate the area of shaded rectangle BCFE.
The area of rectangle BCFE equals
We see that
and substitute
Step 5
Add the areas of the shaded regions together.
Step 6
Divide the area of the shaded region by the area of ACIG.
Simplify this fraction by dividing both the numerator and denominator by 5.
Hence, the shaped region represents 7/18 of the area of ACIG.
