1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
xxMikexx [17]
2 years ago
11

Element X is a radioactive isotope such that every 30 years, its mass decreases by half. Given that the initial mass of a sample

of Element X is 100 grams, how long would it be until the mass of the sample reached 64 grams, to the nearest tenth of a year?
Mathematics
1 answer:
Lena [83]2 years ago
8 0

Answer:

19.3 years

Step-by-step explanation:

Given that the initial mass of a sample of Element X is 100 grams,

The formula is given as:

N(t) = No × (1/2) ^t/t½

Element X is a radioactive isotope such that every 30 years, its mass decreases by half.

N(t) = Mass after time (t)

No = Initial mass = 100 grams

t½ = Half life = 30 grams

N(t) = 100 × (1/2) ^t/30

How long would it be until the mass of the sample reached 64 grams, to the nearest tenth of a year?

This means we are to find the time

N(t) = 100 × (1/2) ^t/30

N(t) = 64 grams

64 = 100(1/2)^t/30

Divide both sides by 100

64/100 = 100(1/2)^t/30/100

0.64 = (1/2)^t/30

Take the Log of both sides

log 0.64 = log (1/2)^t/30

log 0.64 = t/30(1/2)

t = 19.315685693242 years

Approximately = 19.3 years

You might be interested in
What is36.8+[11.6-(2.5×3)]2
givi [52]

Answer:

Step-by-step explanation:

The answer is 33.4

4 0
3 years ago
A distribution of values is normal with a mean of 220 and a standard deviation of 13. From this distribution, you are drawing sa
Paraphin [41]

Answer:

The interval containing the middle-most 48% of sample means is between 218.59 to 221.41.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributied random variable X, with mean \mu and standard deviation \sigma, the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 220, \sigma = 13, n = 35, s = \frac{13}{\sqrt{35}} = 2.1974

Find the interval containing the middle-most 48% of sample means:

50 - 48/2 = 26th percentile to 50 + 48/2 = 74th percentile. So

74th percentile

value of X when Z has a pvalue of 0.74. So X when Z = 0.643.

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

0.643 = \frac{X - 220}{2.1974}

X - 220 = 0.643*2.1974

X = 221.41

26th percentile

Value of X when Z has a pvalue of 0.26. So X when Z = -0.643

Z = \frac{X - \mu}{s}

-0.643 = \frac{X - 220}{2.1974}

X - 220 = -0.643*2.1974

X = 218.59

The interval containing the middle-most 48% of sample means is between 218.59 to 221.41.

5 0
3 years ago
Sydney needs to earn $35 so she can buy her father a birthday present. her mom said she can make $6 per hour cleaning around the
grin007 [14]
K = 13The smallest zero or root is x = -10
4 0
3 years ago
Stella has a cylindrical pool. She needs 20 cubic meters of water to fill the pool to the top. The pool has a diameter of 3 m. U
Leno4ka [110]
I think if u multiply 20 times 3 it will =60

4 0
3 years ago
What is the voume of depth 1 2/3 inches and length of 2 1/3 inches and width 2 inches
Vlad [161]

Answer:

20/9 or 2 2/9 or 2.2 repeating

Step-by-step explanation:

7 0
2 years ago
Other questions:
  • A basket of fruit contains 4 bananas, 3 apples, and 5 oranges. You intend to draw a piece of fruit from the basket, keep it, dra
    12·1 answer
  • The first term in a Geometric series is 3 and the third term is 27. What is the second term
    8·2 answers
  • In a class of 60 students, 5 recieved a grade of A. What fraction of the class did not recieve a grade of A. Reduce in lowest te
    7·2 answers
  • 1. State if each scenario involves a permutation or a combination. Then find the number of possibilities:(a) Castel and Joe are
    7·1 answer
  • 25% of what number is 30.2? i need help solving.​
    8·2 answers
  • Andre’s apartment is 800 square feet. If he wants to carpet 40% of it, how much carpet will he need?
    13·2 answers
  • PLEASE HELP ME PLEASE I REALLY NEED HELP
    15·1 answer
  • Pls help pls pls hii lol bye hahaha math fractions lol. videostar
    7·1 answer
  • You can read 45 pages of your new book in 2 hours. how much an you read in 3
    10·1 answer
  • G(-4)<br> if g(x)=x^2 - 4x
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!