Answer:
The remainder theorem
Step-by-step explanation:
The remainder theorem states that given a polynomial f(x) and a linear factor x - k as in the question, then if f(x) is divided by x - k, then remainder is obtained at the value of x - k = 0 ⇒ x = k. That is, the remainder is f(k) when x = k.
For example, if we have a polynomial f(x) = x³ + 3x² -2x + 1 and a linear factor x - 1. The remainder theorem states that the remainder when f(x) is divided by x - 1 is obtained by equating the factor to zero and finding the value of x.
So, x - 1 = 0 ⇒ x = 1
Substituting x = 1 into f(x), we have
f(x) = x³ + 3x² -2x + 1
f(1) = 1³ + 3(1)² -2(1) + 1
= 1 + 3 - 2 + 1
= 3.
So, the remainder is 3.
Using the exponential growth principle, the population of the country in the next 50 years would be 8074764.08722
<u>The</u><u> </u><u>exponential</u><u> </u><u>growth</u><u> </u><u>can</u><u> </u><u>be</u><u> </u><u>modeled</u><u> </u><u>using</u><u> </u><u>the</u><u> </u><u>relation</u><u> </u><u>:</u>
- <em>A</em><em> </em><em>=</em><em> </em><em>initial</em><em> </em><em>population</em><em> </em><em>value</em><em> </em><em>=</em><em> </em><em>3,000,000</em>
- <em>r</em><em> </em><em>=</em><em> </em><em>growth</em><em> </em><em>rate</em><em> </em><em>=</em><em> </em><em>0.02</em><em> </em>
- <em>t</em><em> </em><em>=</em><em> </em><em>time</em><em> </em><em>=</em><em> </em><em>50</em><em> </em><em>years</em><em> </em>
<u>Substituting</u><u> </u><u>the</u><u> </u><u>values</u><u> </u><u>into</u><u> </u><u>the</u><u> </u><u>equation</u><u>,</u><u> </u><u>we'll</u><u> </u><u>have</u><u> </u><u>:</u><u> </u>
= 8074764.08722
Therefore, the population in the next 50 years would be 8074764.08722
Learn more : brainly.com/question/18796573
Answer:
0.61
Step-by-step explanation:
Pr (female) = total number of females(n')/Total number of students(n)
Where P(female) = probability of selectinga female
Pr(female) = n'/n................. Equation 1
Given: n = 44 students, n' = 15+12 = 27 females
Substitute into equation 1
Pr(female) = 27/44
Pr(female) = 0.61.
Hence the probability of selecting a female is 0.61
The answer is $4,307. If he is paying 159 a month for 39 months, then you take 159 and muliply it by 12 for the year. That gives you 1908. You then add the 2399 that you paid when he signed the lease and it gives you the 4307.