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Questions in mathematics

[Jawaban] Solve $\frac{z-1}{10}=\frac{z+1}{12}$.

[Jawaban] What is the approximate volume of a tree trunk if the trunk is 13 feet tall with a circumference of 4.5 feet? Recall that the circumference of a circle is equal to pi times its diameter. A. $33.09 ft ^3$ B. $27.14 ft ^3$ C. $20.95 ft ^3$ D. $17.16 ft ^3$

[Jawaban] Which of the following expressions accurately describes the relationship $5x + 7y = 17$ as a function $y = f(x)$? A. $y = f(x) = \frac{7}{17} - \frac{5}{7}x$ B. $y = f(x) = \frac{7}{17} - \frac{7}{5}x$ C. $y = f(x) = \frac{17}{7} - \frac{7}{5}x$ D. $y = f(x) = \frac{17}{7} - \frac{5}{7}x

[Jawaban] $41 \frac{1}{2}+4 \frac{1}{6}$

[Jawaban] 2.(a) Define systematic sampling. Discuss sample selection procedures in this sampling. Suggest an unbiased estimator of the population mean. Show that the systematic sample mean \(\bar{y}_{sys}\) is more efficient than the simple random sample mean \(\bar{y}\) if the variance within the systematic samples is more than the total variation in the population, i.e., \(S_w^2 > S^2\).

[Jawaban] 1. Estimate each difference to the nearest ten. Also, find the actual difference. a) 92 - 47 b) 72 - 21 2. Estimate each difference to the nearest hundred. Also, find the actual difference. a) 439 - 302 b) 710 - 592

[Jawaban] An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?

[Jawaban] Given the equation $3 x^2-7 x-1=0$, find $\alpha-\beta$.

[Jawaban] What is the solution of the equation [tex]x^2-2 x+4=0[/tex]?

[Jawaban] Select the correct answer. Exponential function [tex]$f$[/tex] is represented by the table. Function [tex]$g$[/tex] is an exponential function passing through the points [tex]$(0,15)$[/tex] and [tex]$(2,0)$[/tex]. Which statement correctly compares the behavior of the two functions on the interval [tex]$(0,2)$[/tex]? A. Both functions are positive on the interval, but one function is increasing while the other is decreasing. B. Both functions are positive and decreasing on the interval. C. Both functions are positive and increasing on the interval. D. One function is positive on the interval, while the other is negative.