Lesson 1 Data Problem:

John has to complete a research project on the ape population in Spain. He is trying to estimate the size and population of apes. He randomly catches 37 apes and marks them with paint. He releases the apes Into jungle. The following year he observes 250 apes and he found that 10 were marked with the paint that he used.

Find out the best estimate for the size of the ape population?​

Which geometric principle is used to justify the construction below?

Of f(x) is byof f(x)=-3|x| x-.f(x)? a )f(x)=3|x| b) f(x)=|x+3| c) f(x)= -3|x| d) f(x)= -|x+3|

Evaluate 8x2 + 9x − 1 2x3 + 3x2 − 2x dx. solution since the degree of the numerator is less than the degree of the denominator, we don't need to divide. we factor the denominator as 2x3 + 3x2 − 2x = x(2x2 + 3x − 2) = x(2x − 1)(x + 2). since the denominator has three distinct linear factors, the partial fraction decomposition of the integrand has the form† 8x2 + 9x − 1 x(2x − 1)(x + 2) = correct: your answer is correct. to determine the values of a, b, and c, we multiply both sides of this equation by the product of the denominators, x(2x − 1)(x + 2), obtaining 8x2 + 9x − 1 = a correct: your answer is correct. (x + 2) + bx(x + 2) + cx(2x − 1).