MATHEMATICS HIGH SCHOOL

If the half-life of a unstable isotope is 10,00 years and only 1/8 of the radioactive parent remains how old is the sample? A.10,000 B. 20,000 C. 30,000 D. 40,000

Answers

Answer 1

Answer:

Answer:

C. 30,000

Step-by-step explanation:

We know that, the exponential function for decay is,

$y=ae^(rt)$

where,

y = the amount after time t,

a = initial amount,

r = rate of decay.

The half-life of a unstable isotope is 10,000 years, so

$\Rightarrow (1)/(2)=1\cdot e^(r\cdot 10000)$

$\Rightarrow (1)/(2)=e^(r\cdot 10000)$

$\Rightarrow \ln (1)/(2)=\ln e^(r\cdot 10000)$

$\Rightarrow -\ln 2={r\cdot 10000}\cdot \ln e$

$\Rightarrow -\ln 2={r\cdot 10000}\cdot 1$

$\Rightarrow r=(-\ln 2)/(10000)$

Now the function becomes,

$y=ae^{(-\ln 2)/(10000)\cdot t}$

Now, only 1/8 of the radioactive parent remains, so

$\Rightarrow (1)/(8)=1\cdot e^{(-\ln 2)/(10000)\cdot t}$

$\Rightarrow (1)/(8)=e^{(-\ln 2)/(10000)\cdot t}$

$\Rightarrow \ln (1)/(8)=\ln e^{(-\ln 2)/(10000)\cdot t}$

$\Rightarrow -\ln 8={(-\ln 2)/(10000)\cdot t}\cdot \ln e$

$\Rightarrow -\ln 8={(-\ln 2)/(10000)\cdot t}$

$\Rightarrow t=(-\ln 8\cdot 10000)/(-\ln 2)$

$\Rightarrow t=30,000$

Answer 2

Answer: IF the half-life of an unstable isotope is 10,000 years and only 1/8 of the radioactive parent remains, the sample is 30,000 years old.

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Fill in the blank. A _______ probability of an event is a probability obtained with knowledge that some other event has already occurred.

Answers

Answer:

A conditional probability of an event is a probability obtained with knowledge that some other event has already occurred.

Step-by-step explanation:

Conditional probability of an event (A) is a probability obtained with knowledge that some other event (B) has already occurred and is denoted as P(A|B).

It satisfies the following equation:

P(A|B)=P(A and B) / P(B)

where P(A and B) is the probability of A and B occurring together.

Conditional probability is applied in many areas of Bayesian statistics and machine learning.

Final answer:

The blank space should be filled with 'conditional'. A conditional probability of an event is a probability calculated with the knowledge that another event has already happened.

Explanation:

The blank space should be filled with 'conditional'. A conditional probability of an event is a probability obtained with knowledge that some other event has already occurred. Suppose you have events A and B from the same sample space. The conditional probability of event A given that event B has occurred, denoted as P(A|B), is computed as P(A and B) divided by P(B), where P(A and B) represents the probability that both events happen, and P(B) is the probability of B happening. This quantity is meaningful as long as P(B) is not zero.

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A row of plaques covers 120 square feet of space along a wall. If the plaques are 3 feet tall, what length of the wall do they cover?

Answers

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A person earns $25,100 one year and gets a 5% raise in salary. what is the new salary?

Answers

Answer:

A 5% raise can be written as 1.05 so the new salary is 25100 * 1.05 = $26355.

Who is SohCahToa Joe? on Csi geometry:trigonometry I need the answers.

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SohCahToa is an acronym for the basic trigonometric functions which are sine, cosine, and tangent. Sine's value comes from the quotient of the opposite side and the hypotenuse. Cosine's value comes from the quotient of the adjacent side and the hypotenuse. Lastly, Tangent is the quotient of the opposite side and the adjacent side.

Solve for x
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Answers

$\log{x} + \log{(x-4)} = 2 \log{5}\n\n\log{\big(x(x-4)\big)} = \log{5^2}\n\n\log{(x^2-4x)} = \log{25} \n\nx^2-4x = 25\n\nx^2-4x-25=0 \n\nx = (4 \pm√(16+100))/(2) \n\nx = (4\pm2√(29))/(2) \n\nx = 2 \pm √(29) \n\n\text{But } x > 0 \implies x = 2 + √(29)$

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Solve the triangle.A = 33°, a = 19, b = 14
Select one:
a. B = 23.7°, C = 143.3°, c ≈ 23.3
b. B = 23.7°, C = 123.3°, c ≈ 17.5
c. Cannot be solved
d. B = 23.7°, C = 123.3°, c ≈ 29.2

Answers

Using the sine law to find the value of angle B:

a / sin A = b / sin B
19 / sin 33 = 14 / sin B

B = arcsin (14 * sin 33 / 19 )
B = 23.66° = 23.7°

Since the sum of all interior angles of a triangle is 180°, we can solve for angle C like so:

C = 180° - 23.7° - 33°
C = 123.3°

Using sine law to solve for side c:

a / sin A = c / sin C
c = (a*sin C)/sin A
c = 29.157 = 29.2

Therefore, among the choices, the correct answer is D.

Answer:

Took the test

B=23.7 degrees

C=123.3 degrees

c=29.2

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