3 Questions
1. Explain what "any multiple of 9 returns to 9" means. The ancient Chinese found the number 9 magical because of this.
2. The dry cleaners raised the price of a sports coat from $ 4 to $5. The same percent increase was applied to cleaning a jacket. The old cost for cleaning a ajacket was $10. What is the new cost? Show your work.
3. If 2(exponent is n)=8 and 3 (exponent is m)=9 what is the value of n+m?
If 2 (exponent is x) =0.0625, then whatis the value of x?
Thanks, i just don't get these put I got the other 7 on the page.
1. When you add the digits in multiples of 9, the answer is 9.
9, 18, 27, 36, 45, 54, 63, 72, 81, 90, (99), 108, 117, etc.
2. The price of cleaning the sport coat was raised 25%. To find how much cleaning a jacket costs now, multiply .25 by $10.
how was it raised 25%???
1/4 = .25 = 25%
25% of $4.00 = $1.00.
The cleaners raised the price $1.00 from $4.00 to $5.00.
1. "Any multiple of 9 returns to 9" means that if you add the digits of any multiple of 9 and keep summing them until you have a single-digit number, it will always be 9. This is considered magical by the ancient Chinese because it is a unique property of the number 9. To understand this, let's take an example:
Let's say we have a multiple of 9, such as 36. If we add the digits together (3 + 6), we get 9. Similarly, let's take another multiple, such as 63. Adding the digits (6 + 3) also gives us 9.
This property holds true for any multiple of 9. For instance, if we take 99, the sum of its digits (9 + 9) is 18, and if we sum the digits again (1 + 8), we get 9. The same is true for larger multiples of 9, such as 999, 9999, and so on.
2. To find the new cost of cleaning a jacket after the price increase, we need to calculate the percent increase. Here's how you can do this step-by-step:
First, find the dollar amount increase:
Price increase = New price - Old price
Price increase = $5 - $4
Price increase = $1
Next, calculate the percent increase:
Percent increase = (Price increase / Old price) * 100
Percent increase = ($1 / $4) * 100
Percent increase = 25%
Finally, calculate the new cost by applying the same percent increase to the old cost of cleaning a jacket:
New cost = Old cost + (Old cost * Percent increase)
New cost = $10 + ($10 * 25%)
New cost = $10 + ($10 * 0.25)
New cost = $10 + $2.50
New cost = $12.50
Therefore, the new cost for cleaning a jacket is $12.50.
3. Let's solve the equations one by one:
Equation 1: 2^(n) = 8
To find the value of n, we rewrite both sides of the equation using the same base:
2^(n) = 2^(3)
Since the bases are equal, we can equate the exponents:
n = 3
Equation 2: 3^(m) = 9
Again, we rewrite both sides using the same base:
3^(m) = 3^(2)
m = 2
Finally, to find the value of n + m, we simply add the values of n and m:
n + m = 3 + 2
n + m = 5
So, the value of n + m is 5.
For the second part of the question:
2^(x) = 0.0625
To find x, we can rewrite 0.0625 as a fraction with a power of 2 as the denominator:
2^(x) = 2^(-4)
Since the bases are equal, the exponents must be equal:
x = -4
Therefore, the value of x is -4.