Solve (using change of base formula) 9^(x-5)=10

Select the correct answer. The radius of a nitrogen atom is 5. 6 × 10-11 meters, and the radius of a beryllium atom is 1. 12 × 1

Grace [21]

A negative exponent means the number of the exponent divide by the number. The the radius of beryllium atom is larger than the radius of a nitrogen atom by two times.

Given information-

The radius of a nitrogen atom is $5.6\times10^{-11}$ meters.

The radius of a beryllium atom is $1.12 \times10^{-10}$ meters

<h3>Negative exponents</h3>

A negative exponent means the number of the exponent divide by the number.

As the radius of the nitrogen atom is $5.6\times10^{-11}$ meters. Convert it in the power of negative exponent of 10.

Let the radius of the nitrogen is $r$ mm. Thus,

$r=5.6\times 10^{-11}\\
r=5.6\times 10^{-10-1}\\
r=5.6\times 10^{-10}\times10^{-1}\\
r=\dfrac{5.6\times 10^{-10}}{10} \\
r=0.56\times 10^{-10}$

Now the base of the exponents of both the atoms are same. As the radius of the nitrogen atom is $0.56\times 10^{-10}$ meters and the radius of the beryllium atom is $1.12 \times10^{-10}$ . Thus the radius of beryllium atom is larger.

To calculate how many times, the radius of beryllium atom should be divided by the radius of a nitrogen atom. Thus,

$=\dfrac{1.12\times10^{-10}}{0.56\times10^{-10}} \\
=2$

Thus the the radius of beryllium atom is larger than the radius of a nitrogen atom by two times.

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Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Positive reading

Event B: Contains raritanium

Probability of a positive reading:

98% of 13%(positive when there is raritanium).

0.5% of 100-13 = 87%(false positive, positive when there is no raritanium). So

$P(A) = 0.98*0.13 + 0.005*0.87 = 0.13175$

Positive when there is raritanium:

98% of 13%

$P(A) = 0.98*0.13 = 0.1274$

What is the probability the rock sample actually contains raritanium?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.1274}{0.13175} = 0.967$

0.967 = 96.7% probability the rock sample actually contains raritanium

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