Answer:
Wyjaśnienie krok po kroku:
Załóżmy, że prostokąt ma wierzchołki (x,y,z) w dodatnim oktancie. Prostokątny pudełko musi być symetryczne względem wszystkich trzech osi.
Wtedy jego boki to
Objętość = 
Maksymalizuj objętość przy założeniu
tj. 
Użyj mnożników Lagrange'a, mamy
przy maksimum
Dzieląc otrzymujemy
Podobnie 
Zatem otrzymujemy 
Stąd wymiary to
(2x,2y,2z)
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</pzatem>
Answer:
a) 0.00019923%
b) 47.28%
Step-by-step explanation:
a) To determine the likelihood that all sockets in the sample are defective, we can use the following approach:
The first socket is among a group that has 5 defective out of 38, leading to a probability of 5/38.
The second socket is then taken from a group of 4 defective out of 37, following the selection of the first defective socket, resulting in a probability of 4/37.
Extending this logic, the chance of having all 5 defective sockets is computed as: (5/38)*(4/37)*(3/36)*(2/35)*(1/34) = 0.0000019923 = 0.00019923%.
b) Using similar reasoning as in part a, the first socket has a probability of 33/38 of not being defective as it's chosen from a set where 33 sockets are functionally sound. The next socket has a proportion of 32/37, and this continues onward.
The overall probability calculates to (33/38)*(32/37)*(31/36)*(30/35)*(29/34) = 0.4728 = 47.28%.
The triangle's vertex coordinates are (–8, 8), (–8, –4), and (10, –4). QR serves as the base of this triangle, measuring b = 18 units, with a height of h = 12 units. The area of triangle PQR is 108 square units.
Answer: 6000 steps Step-by-step explanation: 1/15 +1/10+1/2=2/30+3/30+15/30=20/30=2/3. Therefore, 2/3 equals 12000 steps, meaning 1/3 is 6000 steps. Overall, she should tally 18000 steps, and she has recorded 12000 steps, hence 18000-12000=6000 steps.
Answer:
The solution yields a number equal to -136.
Step-by-step explanation:
Let x represent the number, leading to the following equation:
x + 2 = 7/8 x - 15
Rearranging gives:
x - 7/8 x = -15 - 2
1/8 x = -17
x = -17 * 8 resulting in -136.
