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Illusion [34]
3 years ago
8

The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass

. Starting with 125 grams of a radioactive isotope, how much will be left after 5 half-lives? Use the calculator provided and round your answer to the nearest gram.
Mathematics
1 answer:
krok68 [10]3 years ago
7 0
So, 0.5^5 is 0.03125
multiply that by 125 and get your answer.
*3.90625* (4)
just saying, I got the 0.5^5 thing because 5 is the number of half-lives (x) and 0.5 is the rate of loss (or whatever its called).
If it were to gain, you would put 1.5

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In the image below, 10 is the long leg of the 30-60-90 triangle.<br><br><br> True or false?
never [62]

The measure of the angle between the hypotenuse and the <em>short</em> leg is 60° and we can conclude that the side with length 10 is not the <em>long</em> leg of the 30 - 60 - 90 <em>right</em> triangle. (Right choice: False)

<h3>Is the length of a known arm in a 30 - 60 - 90 right triangle the long arm?</h3>

In accordance with geometry, the length of the <em>long</em> arm of a 30 - 60 - 90 <em>right</em> triangle is √3 / 2 times the length of the hypotenuse, the length of the <em>short</em> arm is 1 / 2 times the length of the hypotenuse and the length of the <em>long</em> arm is √3 times the length of the arm.

Thus, the measure of the angle between the hypotenuse and the <em>short</em> leg is 60° and we can conclude that the side with length 10 is not the <em>long</em> leg of the 30 - 60 - 90 <em>right</em> triangle. (Right choice: False)

To learn more on right triangles: brainly.com/question/6322314

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3 0
2 years ago
Magda is playing a game with colored cards. Each card has a number on it. Magda chooses one card at random. All possible outcome
9966 [12]

Answer: It is 1/12

Step-by-step explanation:

There are a total of 12 cards. If you look at the table, there is only one yellow card that is even. So it is 1/12.

5 0
3 years ago
In a random sample of students who took the SAT test, 427 had paid for coaching courses and the remaining 2733 had not. Calculat
Dvinal [7]

Answer:

The 95% confidence interval for the proportion of students who get coaching on the SAT is (0.1232, 0.147).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the z-score that has a p-value of 1 - \frac{\alpha}{2}.

427 had paid for coaching courses and the remaining 2733 had not.

This means that n = 427 + 2733 = 3160, \pi = \frac{427}{3160} = 0.1351

95% confidence level

So \alpha = 0.05, z is the value of Z that has a p-value of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1351 - 1.96\sqrt{\frac{0.1351*0.8649}{3160}} = 0.1232

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1351 + 1.96\sqrt{\frac{0.1351*0.8649}{3160}} = 0.147

The 95% confidence interval for the proportion of students who get coaching on the SAT is (0.1232, 0.147).

8 0
3 years ago
A gym instructor has a total of 60 hand weights in her studio.Some of the hand weights are 3 pound weights and the rest are 5 po
Masja [62]

Answer:

35 5-lb weights and 25 3-lb weights

Step-by-step explanation:


6 0
3 years ago
How many 1/ 4-inch cubes does it take to fill a box with width 2 1/ 4 inches, length 2 1/ 2 inches, and height 1 3/ 4 inches?
lys-0071 [83]

Answer:

630.

Step-by-step explanation:

<u>Given the following data;</u>

Dimensions for cube = ¼ inches

Volume \; of \; cube = \frac {1}{4} * \frac {1}{4} * \frac {1}{4}

Volume = 1/64 cubic inches.

For rectangular box;

Length = 2½ = 5/2 inches.

Width = 2¼ = 9/4 inches.

Height = 1¾ = 7/4 inches.

Volume \; of \; cube = \frac {5}{2} * \frac {9}{4} * \frac {7}{4}  

Volume = 315/32 inches

Therefore, to find the amount of cubes;

Number \; of \; cubes = \frac {Volume \; of \; box}{Volume \; of \; cube}

Substituting into the equation, we have;

Number \; of \; cubes = \frac {\frac {315}{32}} {\frac {1}{64}}

Number \; of \; cubes = \frac {315}{32} * 64

Number \; of \; cubes = 315 * 2

Number of cubes = 630

6 0
3 years ago
Read 2 more answers
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