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soldi70 [24.7K]
3 years ago
8

Physicists estimate that there are between 1078 and 1082 atoms in the universe. How do these two numbers compare with one anothe

r? If the larger number is right, how many universes with the smaller number of atoms would fit inside the larger universe?
Mathematics
1 answer:
S_A_V [24]3 years ago
4 0

Answer:

10,000 universes with the smaller number of atoms would fit inside the larger universe

Step-by-step explanation:

The correct question is as follows;

Physicists estimate that there are between 10^78 and 10^82 atoms in the universe. How do these two numbers compare with one another? If the larger number is right, how many universes with the smaller number of atoms would fit inside the larger universe?

Solution

To find the amount of the smaller number of atoms that will fit into the larger, we simply divide

Thus, we have;

10^82/10^78 = 10^4 = 10,000

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Divide:<br> 10mm2-30m<br> 5mn<br> O 2mºn - 6<br> O2mn3 - 6mn?<br> O2mn – 30mn<br> O 5m4n - 25
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The phenomenon of bottle flipping has hit the nation. You design a machine that can randomly flip a bottle. You observe 2180 ran
krek1111 [17]

Answer:

The variable of interest is the proportion of flips that land the correct way when flipped randomly.

The necessary conditions n\pi \geq 10 and n(1-\pi) \geq 10 are present.

The 98% confidence interval for the overall proportion of bottles that land correctly when flipped randomly is (0.131, 0.167).

Step-by-step explanation:

Variable of Interest:

Proportion of flips that land the correct way when flipped randomly.

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 zscore that has a pvalue of 1 - \frac{\alpha}{2}.

Necessary conditions:

The necessary conditions are:

n\pi \geq 10

n(1-\pi) \geq 10

You observe 2180 random, independent flips, and 325 land the correct way.

This means that n = 2180, \pi = \frac{325}{2180} = 0.149

Necessary conditions

n\pi = 2180*0.149 = 325 \geq 10

n(1-\pi) = 2180*0.851 = 1855 \geq 10

The necessary conditions n\pi \geq 10 and n(1-\pi) \geq 10 are present.

98% confidence level

So \alpha = 0.02, z is the value of Z that has a pvalue of 1 - \frac{0.02}{2} = 0.99, so Z = 2.33.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.149 - 2.33\sqrt{\frac{0.149*0.851}{2180}} = 0.131

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.149 + 2.33\sqrt{\frac{0.149*0.851}{2180}} = 0.167

The 98% confidence interval for the overall proportion of bottles that land correctly when flipped randomly is (0.131, 0.167).

8 0
3 years ago
Simplify (8j3 + 3j2 + 7) – (3j3 – 7j2 – 7j – 12)
ehidna [41]
8j³+3j²+7-(3j³-7j²-7j-12)
8j³+3j²+7-3j³+7j²+7j+12
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3 years ago
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Choose the expression that mathematically represents the difference between ‘3 times a number’ and the quantity ‘5 times another
Trava [24]

Answer:

b. 3x - (5y -7)

Step-by-step explanation:

Let x represent "a number". Let y represent "another number."

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And "5 times another number less 7" is represented by 5y -7.

The difference between these quantities is the second subtracted from the first:

... 3x - (5y -7) . . . . matches selection b.

4 0
4 years ago
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