Answer:
Lets say that P(n) is true if n is a prime or a product of prime numbers. We want to show that P(n) is true for all n > 1.
The base case is n=2. P(2) is true because 2 is prime.
Now lets use the inductive hypothesis. Lets take a number n > 2, and we will assume that P(k) is true for any integer k such that 1 < k < n. We want to show that P(n) is true. We may assume that n is not prime, otherwise, P(n) would be trivially true. Since n is not prime, there exist positive integers a,b greater than 1 such that a*b = n. Note that 1 < a < n and 1 < b < n, thus P(a) and P(b) are true. Therefore there exists primes p1, ...., pj and pj+1, ..., pl such that
p1*p2*...*pj = a
pj+1*pj+2*...*pl = b
As a result
n = a*b = (p1*......*pj)*(pj+1*....*pl) = p1*....*pj*....pl
Since we could write n as a product of primes, then P(n) is also true. For strong induction, we conclude than P(n) is true for all integers greater than 1.
Answer:
mean life = 8264.5 s
Step-by-step explanation:
k = - 0.000121
The relation is given by
Now, the mean life is the life time for which the sample retains.
The mean life is the reciprocal of the decay constant.
The relation between the mean life and the decay constant is
Answer:
Trapezoid
Step-by-step explanation:
We have been given that Marcus drew a quadrilateral with only 1 pair of parallel sides. We are asked to determine the quadrilateral that Marcus drew.
We know that a parallelogram has two pair of parallel sides.
We also know that rhombus is a parallelogram whose 4 sides are equal is measure and rectangle is a parallelogram with opposite sides equal.
Since parallelogram, rhombus and rectangle has two pair of parallel sides, therefore, Marcus didn't draw any of these.
We know that trapezoid has only one pair of parallel sides, therefore, Marcus drew a trapezoid.
An equation is formed of two equal expressions. The number of weeks for which Jamison needs to deliver papers to earn enough money for a bike is 24.
<h3>What is an equation?</h3>
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that Jamison needs a total of $395 to buy a new bike but he has only $35 saved. Also, He earns $15 each week delivering newspapers.
Now, the equation that can represent the situation can be written as,
Cost of the bike = Amount Saved + Earning by delivering newspapers
Substituting the values,
$395 = $35 + $15x
where x is the number of weeks for Which Jamison needs to work in order to purchase the new bike. Therefore, solving the equation for x,
395 = 35 + 15x
395 - 35 = 15x
360 = 15x
x = 360 / 15
x = 24
Hence, the number of weeks for which Jamison needs to deliver papers to earn enough money for a bike is 24.
Learn more about Equation here:
brainly.com/question/10413253
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