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3. Inside a cubic box with edge 35 cm, a ball has been introduced that is tangent to the faces of the cube as shown in the following figure. Calculate the volume included by the free space in the cube-shaped box.

What is the mathematical relationship between F and D²?

1. Administer 10 mg of Morphine every 4 hours in 100 ml of physiological solution. Presentations: 2.5mg vial in 2.5ml. 50mg vial in 2ml and 10mg vial in 10ml How many ml of physiological solution will there be and how many ml of Morphine using the presentation of 2.5mg in 2.5ml? How many vials should you use with the presentation of 2.5mg in 2.5ml? How many ml of physiological solution will there be and how many ml of Morphine using the presentation of 50mg in 2ml? How many ml of physiological solution will there be and how many ml of Morphine using the presentation of 10mg in 10ml?

Given the function f (x, y) = e−x · sin(x + y) b) Study its homogeneity and calculate the degree of homogeneity, if applicable . c) Calculate f(t) when t = 1 if x(t) = t2 + 1, y(t) = ln(t)

FUS After takeoff, an aircraft enters a straight-line flight path with constant speed at point P(1.5|9|0.5). speed. In one minute it travels a distance vector v=(-1 5 0.2) back. Information in km. a) (1) Determine the speed of the aircraft in km/h. (2) After 4 minutes the plane reaches a big city. Calculate the altitude at this time. b) At an altitude of 2500 m the pilot switches to autopilot. Calculate the coordinates of the point where the aircraft is at this moment and state how much time has passed since the aircraft was at point P. c) Between the points A(-5|38|0.1), B(-4|40|0.11) and C (-7|39|0.1) there is a small natural protected area in the shape of a triangle. (1) Examine triangle ABC for special features. (2) Check whether the aircraft is flying over route AB and, if so, at what distance

A poor, underpaid math teacher gets a credit for 3000e to buy a motorcycle. The credit goes over 2 years, the payments are monthly due, and the nominal interest rate is 2% payable monthly of course. (a) How much is the monthly annuity?

A clinic offers an experimental treatment to patients with a certain disease. It is known that the 30% of patients who receive treatment experience significant improvement. However, It is also observed that 20% of patients who do not receive treatment improve. Yes in the end From the study it is observed that 60% of the patients who improved received the treatment, what is the probability that a patient who received the treatment will experience improvement significant?

When solving a problem, two students fell back on a 2nd degree equation, however, when solving it, they both made a mistake. The 1st student only got the independent term of the equation wrong, finding the roots -10 and -2. The 2nd student only got the coefficient of the 1st degree term wrong, finding roots 4 and 8. Were the correct roots of the equation?

He took out a personal law motorized loan for 23,000 at an interest rate of 7.45% with monthly payments for a term of two years find ones monthly payment rounded to the nearest cent.

If 2p-1 ; p+1 ; p-1 form a geometric sequence and p≠0 . What are the first three terms