answer:The hazard rate function given that a device failed between time t_1 and t_2 is: h_{t_1,t_2}(t) = frac{f(t)}{F(t_2) - F(t_1)}, where f(t) is the probability density function of the exponential distribution, and F(t) is its cumulative distribution function. For the exponential distribution, this simplifies to: h_{t_1,t_2}(t) = frac{lambda}{e^{-lambda t_1} - e^{-lambda t_2}}.

answer:To evaluate the function ( f(x) ) at ( x = 26 ), we substitute ( x ) with 26 in both parts of the function: ( f(26) = arctan(9 - 3 cdot 26^4) + tan(6 - 3 cdot 26) ) First, calculate the terms inside the arctangent and tangent functions: ( 9 - 3 cdot 26^4 = 9 - 3 cdot 456976 = 9 - 1370928 = -1370919 ) ( 6 - 3 cdot 26 = 6 - 78 = -72 ) Now, evaluate the arctangent and tangent: ( arctan(-1370919) ) gives approximately ( -1.308 ) ( tan(-72) ) is negative because it falls in the fourth quadrant, and its value is close to ( -1.308 ) as well. Adding these two values together, we get: ( f(26) = -1.308 - 1.308 approx -2.616 ) So, the evaluation of the function at ( x = 26 ) is approximately ( -2.616 ).

answer:The solution to the system of equations is x = 22, y = 31, and z = -7.

answer:Bacteria do not have mitochondria, but they have respiratory enzymes present in their cell membranes. These enzymes facilitate cellular respiration, allowing bacteria to respire aerobically or anaerobically.