. Use strong induction to show that every positive integer can be written as a sum of distinct powers of two, that is, as a sum of a subset of the integers 20 =1, 21 =2, 22 =4, and so on. [Hint: For the inductive step, separately consider the case where k+1 is even and where it is odd. When it is even, note that (k+1)∕2 is an integer.]

Browning labs is testing a new growth inhibitor for a certain type of bacteria. the bacteria naturally grows exponentially each hour at a rate of 6.2%. the researchers know that the inhibitor will make the growth rate of the bacteria less than or equal to its natural growth rate. the sample currently contains 100 bacteria.the container holding the sample can hold only 300 bacteria, after which the sample will no longer grow. however, the researchers are increasing the size of the container at a constant rate allowing the container to hold 100 more bacteria each hour. they would like to determine the possible number of bacteria in the container over time.create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable.

Write a fraction less than 1, which has a denominator of 6 and is greater than 3/4 plz answer !

Common binomial factor of 6x(3x+7)+5(3x+7)