Benford’s law states that the probability that a number in a set has a given leading digit, d, isP(d) = log(d + 1) - log(d).

State which property you would use to rewrite the expression as a single logarithm, and rewrite the logarithm. What is the probability that the number 1 is the leading digit? Explain.

Answers

Answer 1

Answer: Benford’s law states that the probability that a number in a set has a given leading digit, d, is
P(d) = log(d + 1) - log(d)
The division property of logarithm should be use to make it as a single logarithm
P(d) = log ( (d + 1)/ d)
So the probability that the number 1 is the leading digit is
P(1) = log ( ( 1+1)/ 1)
P(1) = log ( 2)
P(1) = 0.301

Answer 2

Answer:

The probability that the number 1 is the leading digit is $0.301$ .

Given information:

Benford’s law states that the probability that a number in a set has a given leading digit $d$ , is $P(d) =\log(d+1)-\log(d)$

As mentioned in question,

Probability of a number in a set is given by $P(d) =\log(d+1)-\log(d)$ .

The division property of logarithm should be use to make it as a single logarithm $P(d)=\log((d+1)/(d))\;\;\;\{\log(a)-\log(b)=\log(a)/(b)\}$ .

So, the probability that the number 1 is the leading digit is,

$P(1) = \log ( ( 1+1)/ 1)\nP(1) = \log ( 2)\nP(1) = 0.301\n$

Hence, The probability that the number $1$ is the leading digit is $0.301$ .

Learn more about Probability here:

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$108.59

Step-by-step explanation:

The dime which is worth 0.10 U.S. dollar, is a ten-cent coin, one-tenth of a United States dollar

the value is 0.1

Now in rounding up of numbers the dime is located one decimal place away i.e 0.5 in the number given in the problem statement

to round up to the nearest dime we have to consider the next number to the dime if this number is greater than 5 we will round up if it is less than five we can not perform any rounding up operation

hence the greatest amount of money is

since the number next to 5 is 9 and 9 is greater than 5 we will round up from 5 to 6

This makes 108.59 the greatest amount of money that rounds to $108.60

Final answer:

The least amount of money that rounds to $108.60 is $108.60. The greatest amount that rounds to $108.60 is $108.64.

Explanation:

When rounding to the nearest dime, there is a range of values that can round to $108.60. The least amount of money that rounds to $108.60 is exactly $108.60 because when you are at the target, you don't need to round up or down. The greatest amount that rounds down to $108.60 would be any amount that is less than halfway to the next dime, which is $108.65. So, anything less than $108.65, but more than $108.60, would round to $108.60. As such, the greatest amount that would round to $108.60 when rounded to the nearest dime would be $108.64.

Learn more about Rounding Numbers here:

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Anyone know this? Help pls!

Answers

Answer:

Step-by-step explanation:

r = 4.9 miles

Area of circle = πr²

= 3.14 * 4.9 * 4.9

= 75.39 square miles

[3.5x10^6]-[1.5x10^5] in scientific notation

Answers

Answer:

3.35 × 10^6

Step-by-step explanation:

If 4x - 3 = 5, then x=

Answers

Answer:

x=2

Step-by-step explanation:

4x-3=5

4x-3 plus 3 and 5 plus 3

4x=8

Divide both sides by 4

x=2

Answer:

X = 2

Step-by-step explanation:

This is how I got the answer:

Move constant to the right-hand + change signs

4x = 5 + 3

add

4x =5 + 3

4x = 8

Divide by both sides to get the answer of;

X = 2

Simplify 8(R + 6) - 2R.

Answers

So the first thing you do is distrubute.

8(R+6) - 2R = 8R+48-2R = 6R + 48

Answer is 6R + 48.

okay first lets distribute the 8 to the R and the 6
Now we have (8R+48)-2R
then we need to combined like terms
8r-2r=6R
So we are left with 6R+48
I hope this helped

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