Advanced Placement (AP), 11.02.2021 03:00 kaitlynpaigge

In 2018 China had the world’s largest population and India had the second largest population. A. Identify the TWO types of data shown in the table that are used to calculate the rate of natural increase.

B. Describe what the total fertility rate represents.

C. Using India's rate of natural increase shown in the table, describe how to calculate the doubling time of India's population.

D. Using the data shown in the table, describe the ability of China's population to replace itself over time.

E. Explain how China's population statistics are unusual for a country with an economy that is still in the process of industrializing.

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Answer from: Quest

answer: the net deposit amount (option c)

in order to fill in the deposit slip, michael needs to fill in the amount that he wants to deposit in the bank. without the net deposit amount, he will not be able to deposit the money because it is mandatory for him to mention it, as the bank needs to maintain a record to avoid any inconveniences for the bank and michael in the future.

the bank officer checks and verifies the amount received against the amount written on the deposit slip to process the slip.

Answer from: Quest

This metaphor uses symbolism when describing the “arch” of ulysses life. he is trapped in a time of life where adventure is moving as he tries to proceed to it. he will never reach it and will learn to accept it. ulysses symbolizes that arch in life, that no one can reach every goal, or every sight in life. even though this personality of curiosity and purposefulness exist in all mankind, the purpose of showing his strive to succeed symbolizes great leaders today. his curiosity represents the curiosity of humans that everyone desires to find answers and wont give up without a fight. ulysses is a symbol of the human race.

Answer from: Quest

Answer: the interval on which the curve is concave up is (-∞, -1/2)====== $\displaystyle y = \int_{0}^x \frac{1}{1 + t + t^2} \; dt$ we find the interval where this curve is concave up by finding the interval in which the 2nd derivative is positive.differentiate the curve equation with respect to x $\begin{aligned} \frac{dy}{dx} & = \frac{d}{dx} \int_{0}^x \frac{1}{1 + t + t^2} \; dt \end{aligned}$ let the function f denote be the anti-derivative of the inside expression, i.e. a function such that $(d/dx)f(x) = 1/(1 + t + t^2)$ .then use the fundamental theorem of calculus: $\begin{aligned} \frac{dy}{dx} & = \frac{d}{dx} \int_{0}^x \frac{1}{1 + t + t^2} \; dt \\& = \frac{d}{dx} \big[ f(x) - f(0) \big] & & \text{\footnotesize apply ftc} \\ & = \frac{d}{dx}f(x) - 0 \\ & = \frac{1}{x + x + x^2} & & \text{\footnotesize since $\frac{d}{dx}f(x) = \frac{1}{1 + x + x^2}$ } \end{aligned}$ differentiate again to get second derivative. we can use chain rule with 1/x as the outside function and 1 + x + x² as the inside function $\begin{aligned} \frac{d}{dx} \left( \frac{dy}{dx} \right) & = \frac{d}{dx}\left(\frac{1}{1 + x + x^2} \right) \\ \frac{d^2y}{dx^2} & = \frac{-1}{\left(1 + x + x^2\right)^2} \cdot \tfrac{d}{dx}(1 + x + x^2) \\ & = \frac{-1}{\left(1 + x + x^2\right)^2} \cdot (1 + 2x) \\ & = \frac{-(1 + 2x)}{\left(1 + x + x^2\right)^2} \end{aligned}$ find critical numbers of the second derivative. these numbers are where the 2nd deriv. is undefined or zero.where the 2nd derivative is zero: set (d²y/dx²) to equal 0 and solve for x $\begin{aligned} 0 & = \frac{-(1 + 2x)}{\left(1 + x + x^2\right)^2} \\ 0 & = -(1+2x) \\ -1 & = 2x \\ x & = -1/2 \end{aligned}$ where the 2nd derivative is undefined: if the denominator is equal to zero, the derivative will be undefeined. attempting to solve the equation 1 + x + x² = 0results in a discriminant of $b^2 - 4ac = 1^2 - 4(1)(1) = -3$ meaning that the equal 1 + x + x² = 0 has no real solutions and therefore will never equal zero.======our only critical number is x = -1/2.this forms two intervals to test the sign for: (-∞, -1/2) and (-1/2, ∞)test values into the 2nd derivative for (-∞, -1/2)if we try x = -1, we get $\begin{aligned} \left.\frac{d^2y}{dx^2}\right|_{x = -1} & = \frac{-(1+2(-1))}{\left(1+(-1)+(-1)^2\right)^2} \\ & = \frac{-(1-2)}{1} \\ & = 1 \end{aligned}$ so the since the 2nd derivative of the curve is positive on the interval (-∞, -1/2), the curve is concave up on (-∞, -1/2)test values into the 2nd derivative for (-1/2, ∞)if we try x = 0, we get $\begin{aligned} \left.\frac{d^2y}{dx^2}\right|_{x = 0} & = \frac{-(1+2(0))}{\left(1+(0)+(0)^2\right)^2} \\ & = \frac{-(1)}{1} \\ & = -1 \end{aligned}$ so the since the 2nd derivative of the curve is positive on the interval (-∞, -1/2), the curve is concave down on (-∞, -1/2).the interval on which the curve is concave up is (-∞, -1/2)

Answer from: Quest

answer: all of the above

identity theft, is stealing other person's identity to commit fraud or other crimes. identities, are stolen through hi tech and low tech methods and all these can result in the consequences mentioned above. because a criminal when has stolen your identity, can get a loan under your name which will increase a debt burden on the victim, it will also make it harder for the victim to get a loan in the future due to poor credit history and as a result may face loss of a job. there will be a loss of money since the criminal can even rent or buy an apartment under your name.

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