Exponentiation - math word problems

If n is a positive integer and x is any real number, then x^n corresponds to repeated multiplication x^n=x×x×⋯×x (n times). We can call this “x raised to the power of n,” “x to the power of n,” or simply “x to the n.” Here, x is the base, and n is the exponent or the power.

Number of problems found: 118

What is 10
What is the 5th term, if the 8th term is 80 and common ratio r =1/2?
If the 3
If the 6th term of a GP is 4 and the 10th is 4/81, find common ratio r.
What is
What is the annual percentage increase in the city when the population has tripled in 20 years?
All use computer
It is reported that 72% of working women use computers at work. Choose 3 women at random, find the probability that all 3 women use a computer in their jobs.
The half life
The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 145 grams of a radioactive isotope, how much will be left after 3 half-lives?
Savings
The depositor regularly wants to invest the same amount of money in the financial institution at the beginning of the year and wants to save 10,000 euros at the end of the tenth year. What amount should he deposit if the annual interest rate for the annua
Five element
The geometric sequence is given by quotient q = 1/2 and the sum of the first six members S₆ = 63. Find the fifth element a₅.
Volume of wood
Every year, at the same time, an increase in the volume of wood in the forest is measured. The increase is regularly p% compared to the previous year. If in 10 years the volume of wood has increased by 10%, what is the number p?
Cube construction
A 2×2×2 cube is to be constructed using 4 white and 4 black unit cube. How many different cubes can be constructed in this way? ( Two cubes are not different if one can be obtained by rotating the other. )
Before yesterday
He merchant adds a sale sign in his shop window to the showed pair of shoes in the morning: "Today by p% cheaper than yesterday. " After a while, however, he decided that the sign saying: "Today 62.5% cheaper than the day before yesterday". Determine the
The tickets
The tickets to the show cost some integer number greater than 1. Also, the sum of the price of the children's and adult tickets, as well as their product, was the power of the prime number. Find all possible ticket prices.
Three members GP
The sum of three numbers in GP (geometric progression) is 21 and the sum of their squares is 189. Find the numbers.
Investment 2
Jack invested $5000 in a 5-month term deposit at 4.7% p. A. . At the end of the 5-months, jack reinvested the maturity value from the first deposit into an 11-month term deposit at 7.3% p. A. What is the maturity value at the end of the second term deposi
Curiosity factor
A blogger starts a new website, initially the number of the traffic is 293 due to their curiosity factor. The business owner estimated that the traffic will increase by 2,6% per week. What will be the number of it in week 5?.
Substitution method
Solve goniometric equation: sin⁴ θ - 1/cos² θ=cos² θ - 2
Precious metals
In 2006-2009, the value of precious metals changed rapidly. The data in the following table represent the total rate of return (in percentage) for platinum, gold, an silver from 2006 through 2009: Year Platinum Gold Silver 2009 62.7 25.0 56.8 2008 -41.3 4
Cube surface and volume
Find the surface of the cube with a volume of 27 dm³.
Boys and girls
There are eight boys and nine girls in the class. There were six children on the trip from this class. What is the probability that left a) only boys b) just two boys
Last digit
What is the last number of 2016 power of 2017
Geometric progression
In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is: sn≤217.

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