Numerade

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Patients patient with anemia may have an elevated heart rate and respiration due to competence, compensatory mechanisms, true or orf

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Stephen Jay Gould The theory proposes that most evolution is characterized by long periods of evolutionary stability, infrequently punctuated by swift periods of branching

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Body temperature increases. Increase in the production of sweat. Body temperature decreases. This is an example of Blank______ feedback.

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(4) Consider a continuous Markov chain with two states S = {0, 1}. Suppose the waiting time parameters are given by $v_0 = v_1 = \lambda > 0$. Hence, the time that the process spends in each state before going to the other state has an exponential($\lambda$) distribution. Find the transition matrix $P(t)$, i.e., find $\begin{aligned} P(t) = \begin{bmatrix} P_{00}(t) & P_{01}(t) \\ P_{10}(t) & P_{11}(t) \end{bmatrix} \end{aligned}$ (Hint: Use the following identities: $\sum_{n=0}^{\infty} \frac{x^{2n+1}}{(2n+1)!} = \frac{e^x - e^{-x}}{2}$ and $\sum_{n=0}^{\infty} \frac{x^{2n}}{(2n)!} = \frac{e^x + e^{-x}}{2}$.)

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Complete the reaction below, and indicate whether the equilibrium will favor the products or reactants, and provide a brief explanation for your answer. On the reactant side, the pKa of hypobromous acid is 8.55 and the pKb of pyridine is 8.77. $C_5H_5N(aq) + HBrO(aq) \rightleftharpoons$

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Let $f$ be a function that has derivatives of all orders on the interval $(5, 7)$. Use the values in the table below and the formula for Taylor polynomials to give the $4^{th}$ degree Taylor polynomial for $f$ centered at $x = 6$. $\begin{array}{|c|c|c|c|c|} \hline f(6) & f'(6) & f''(6) & f'''(6) & f^{(4)}(6) \\ \hline -2 & 4 & 8 & -4 & -2 \\ \hline \end{array}$ $-2 + 4(x + 6) + 8(x + 6)^2 - 4(x + 6)^3 - 2(x + 6)^4$ $-2 + 4(x - 6) + 4(x - 6)^2 - \frac{2}{3}(x - 6)^3 - \frac{1}{12}(x - 6)^4$ $-2 + 4(x - 6) + 8(x - 6)^2 - 4(x - 6)^3 - 2(x - 6)^4$ $-\frac{1}{12}x^4 - \frac{2}{3}x^3 + 4x^2 + 4x - 2$

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x 2 3. Given the functions f(x)= andax= x + 3 x-5 a. find(f:g)(x) and simplify (3 marks) b.state the domain of(f : g)() 4. A bike manufacturer determines that the revenue (in dollars) from producing and selling x bikes is given by R(x)= -0.4x2 + 340x -2000 and the cost of producing and selling x bikes is given by C(x) = 1000 + 20x. (3 marks) a Determine the profit function where P(x)= R(x)-C(x) b) Determine the number of bikes that must be produced and sold to maximize profit c) Determine the maximum profit. 5. Write the given expressions as a single logarithm. Simplify if possible. (6 marks) a. log5x2-4-2 log5x-2+3log5 x b. 4[x2 6.Express log in terms of sums or differences of logarithms.There should be no y radicals or powers remaining. Simplify if possible. (3 marks) 7. Solve. Give an exact answer and an approximation if possible,rounded to 3 decimal places. (16 marks) a. 3=g2x+6 b. 53x=70 C. 23x-1 = 3x d. log4 (x2 -5x + 10= 1 e. logs(x - 3= 1 -logs(x - 5) f. log3 (3x -8-logs(x + 5= logs 2 8. How much must be invested at an interest rate of 3.6% compounded semiannually over 4 years in order to end up with $18,000? (2 marks 9.A $100.000 lottery windfall is used to open an account earning 4.4% interest compounded quarterly. How many years (to the nearest hundredth of a year) will the money have to remain in the account before accumulating to $140, 000? Assume no additional withdrawals or deposits and a fixed interest rate.(3 marks) 10.The population of a colony of insects obeys the law of uninhibited growth. (6 marks) a) If there are 20 insects present initially and there are 45 after l hour, determine the growth rate (to the nearest 4 decimal places). b) How many insects (rounded to the nearest whole number) will there be after 8 hours? c) In how many hours (to the nearest tenth of an hour) will there be 200,000 insects?

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Show that \begin{equation*} \vec{y}(t) = \begin{bmatrix} e^{4t} \\ e^{4t} \\ e^t \end{bmatrix} \end{equation*} is a solution to the system of linear homogeneous differential equations \begin{align*} y_1' &= 2y_1 + y_2 + y_3, \\ y_2' &= y_1 + y_2 + 2y_3, \\ y_3' &= y_1 + 2y_2 + y_3. \end{align*}a. Find the value of each term in the equation $y_1' = 2y_1 + y_2 + y_3$ in terms of the variable $t$. (Enter the terms in the order given.) b. Find the value of each term in the equation $y_2' = y_1 + y_2 + 2y_3$ in terms of the variable $t$. (Enter the terms in the order given.) c. Find the value of each term in the equation $y_3' = y_1 + 2y_2 + y_3$ in terms of the variable $t$. (Enter the terms in the order given.)

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A Fourbar Grashof - Crank Rocker mechanism that have a quick return to give a 65° angle in the rocker has a time ratio back and forward of 1:1.2, from a constant speed motor input. Find the angle: $\delta$

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The formula N = p + 0.05p models the new population, N, of a town with a current population p if the town is expecting population growth of 5% next year. Find the new population of a town whose current population is 7300 persons.

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hector j.