The half-life of a radioactive substance is 200 years. There are 8000 grams of the substance initially. How many grams of the substance are left after 300 years?

Answer:

a) 97.37%

b) 1.31%

Step-by-step explanation:

a)  

Here we want to calculate the area under the Normal curve with mean 0.52 and standard deviation 0.009 between 0.5 and 0.54

This can be easily done with a spreadsheet and we get

P (0.5くV < 0.54) = 0.9737 or 97.37%

(See picture 1)

b)

Here we want the area under the Normal curve with mean 0.52 and standard deviation 0.009 to the left of 0.5.

P(V ≤ 0.5) = 0.0131 or 1.31%

(See picture 2)

Answer:

23  1/10

Step-by-step explanation:

Final answer:

To find the sum in simplest form of 4 1/2 and 1 3/5, you convert each to an improper fraction, adding the fractions and convert back to a mixed number. The sum is 6 1/10.

Explanation:

The sum in simplest form of the two numbers 4 1/2 and 1 3/5 can be calculated as follows:

1. Change each mixed number into an improper fraction. 4 1/2 becomes 9/2 and 1 3/5 becomes 8/5.
2. Then add the two fractions: 9/2 + 8/5 equals 45/10 + 16/10 (after finding a common denominator), which equals 61/10.
3. Finally, convert back to a mixed number to get 6 1/10.

So, the sum in the simplest form of 4 1/2 and 1 3/5 is 6 1/10.

Learn more about Fraction Addition here:

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Using the concept of binomial probability, the distribution of X which is the number of winning is ;

• X ______ 0 ____1 _____ 2___ 3______ 4

• P(X):_0.0767_0.2762_0.3729_0.2238_0.0503

Given the parmaters :

• Total Number of slots = 38
• Number of reds = 18

The probability of winning,p on a single play :

• p = (red slots / total slots) = 18/38 = 9/19

Number of plays = 4

Number of winnings = X

Using the binomial probability relation :

• P(x = x) = nCx * p^x * q^(n-x)
• q = 1 - 9/19 = 10/19
• n = 4

ForX=0:

P(x = 0) = 4C0 × (9/19)^0 × (10/19)⁴ = 0.0767

ForX=1:

P(x = 0) = 4C1 × (9/19)¹ × (10/19)³ = 0.2762

ForX=2:

P(x = 2) = 4C2 × (9/19)² × (10/19)² = 0.3729

ForX=3:

P(x = 3) = 4C3 × (9/19)³ × (10/19)¹ = 0.2238

For X = 4 :

P(x = 4) = 4C4 × (9/19)⁴ × (10/19)^0 = 0.0503

Therefore, the distribution of X in the roulette spin is :

X ____ 0 ____ 1 _____ 2 ______ 3 ______ 4

P(X):_0.0767_0.2762_0.3729_0.2238 _0.0503

Learn more :brainly.com/question/12474772

Answer:

Step-by-step explanation:

100 gallons/5hours = 20 gallons/hour