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beks73 [17]
3 years ago
14

Find the largest three-digit number that can be written in the form 3^m + 2^n, where m and n are positive integers.

Mathematics
1 answer:
joja [24]3 years ago
8 0

Answer:

985

Step-by-step explanation:

let\ m=6

3^{6}=729999-729=270

2^{8}=256 and 2^{9}=512 which would be to big of a number.

3^{6}+2^{8}=729+256=985

Therefore the largest three-digit integer in this system is 985

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I'm not sure how to simplify this expression with the exponents rules of multiplication
Vedmedyk [2.9K]
The rule of exponential multiplication is (a^x)*(a^y)=a^(x+y)
using this with your expression, we can do
(10^1)*(10^3)*(10^2)=10^(1+3+2)=10^6
Final answer:
10^6 or 1 million
Hope I helped :)
3 0
3 years ago
1. Chris takes 25 minutes to replace one car tyre.
vekshin1

Chris and Jim must replace a <em>total</em> quantity of 17 tyres.

<h3>What is the minimum number of tyres to be replaced?</h3>

In this problem we must use an inequality of the form f(x) ≥ a, where f(x) is the difference between the number of tyres replaced by Jim and the number of tyres replaced by Chris:

(25/20) · x - x ≥ 3

(5/20) · x ≥ 3

x ≥ 12

Then, the <em>minimum</em> number of tyres to be replaced is n = 15 + 12 = 17 tyres.  

To learn more on inequalities: brainly.com/question/20383699

#SPJ1

3 0
2 years ago
Graph the data below and then answer the questions that follow. year 1=$20,000, year 2=$21,750, year 3=$23,500, year 4=$25,250,
Mariana [72]

Answer:

Since the difference between the value for each year is constant, this is an arithmetic sequence.

Step-by-step explanation:

Year 2 - Year 1 = 21,750 - 20,000 = 1,750

Year 3 - Year 2 = 23,500 - 21,750 = 1,750

Year 4 - Year 3 = Year 5 - Year 4 = 1,750

3 0
3 years ago
You borrow $3750 to buy new fitness equipment.The simple interest rate is 2%. You pay the loan off after 4 years. What is the to
Alinara [238K]
Provided the 2% interest rate. The interest itself over a period of 4 years, compounds to $300. Thus, the total interest plus the cost of the fitness equipment would be a total of, $4,050.
6 0
3 years ago
Ryan buys a bag of cookies that contains 8 chocolate chip cookies, 4 peanut butter cookies, 4 sugar
Pavlova-9 [17]

Answer:

4/69 to be exact. Slightly greater than 1/18

Step-by-step explanation:

The chance of selecting the PB cookie on the first try is 4 out of 24 or 1 out of 6. There are now 23 coolies left; 8 are chocolate, so 8/23 chance. (Slightly greater than 1/3) The chance of both events happening is the product if the individual events' chances. So multiply 1/6 times 8/23 to get 8/138. That reduces to 4/ 69. If he had put that first cookie back, the multiplication would have been 1/6×1/3. A lot easier.

4 0
3 years ago
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