Answer:
x=4 Inch
Step-by-step explanation:
Length of the Square = 24 Inches
If a Square of Length x cm is cut out from each corner
Length of the Box = 24-x-x=(24-2x) Inches
Width of the Box =24-x-x=(24-2x) Inches
Height of the box = x inches
Volume of a Cuboid = Length X Width X Height
V(x)= x(24-2x)(24-2x)
Simplifying
V(x)=4x(12-x)(12-x)
To determine the value of x at which V is largest, we take the derivative of V(x) and solve for the critical points.
V(x)=4x(12-x)(12-x)
Set the derivative equal to zero to obtain the critical points
x cannot be equal to 12 as it divides the length of the square cardboard into exactly two equal parts.
When x=4
V(4)=4*4(12-4)(12-4)=16*8*8=1024 Cubic Inches
When x=4 Inch, the volume, V of the open box is largest.
Answer:
$16,000 should be invested in the 4.25% bond
Step-by-step explanation:
Attached is the full solution
Answer:
x = 60°
Step-by-step explanation:
AOB Center: O AB: diameter
arc ADB = 180°
arc DB = 180 - arc AD = 80°
x = 1/2 x ( arc DB + arc AC) = 1/2 x (80 + 40) = 60°
Define three events A,B,C such that
A = first card is a face card
B = second card is a face card (assuming event A happens)
C = third card is a face card (assuming events A & B happen)
No replacements are made
There are 3 face cards (J, K, Q) per suit. There are 4 suits. In total, there are 3*4 = 12 face cards out of 52 total
P(A) = probability that event A happens
P(A) = 12/52
P(A) = 3/13
After event A happens, we have 12-1 = 11 face cards out of 52-1 = 51 total
P(B) = 11/51
After B happens, we have 11-1 = 10 face cards out of 51-1 = 50 left over
P(C) = 10/50
P(C) = 1/5
Based on how the events A,B,C are set up, we can form this equation
P(A and B and C) = P(A)*P(B)*P(C)
P(A and B and C) = (3/13)*(11/51)*(1/5)
P(A and B and C) = 11/1105
P(A and B and C) = 0.00995475113122
Rounded to the nearest tenth, the answer is simply 0.0 which is a lousy answer in my opinion because it implies that the answer is truly 0 instead of something really small. Though to be fair, the result is very close to 0. A much better approach is to round to the nearest hundredth to get 0.01; though I would ask your teacher for clarification and guidance.
note: a probability of 0 means that the event is impossible to happen, yet it is not impossible to pull out three face cards in a row. Is it unlikely? Yes. Because the result is roughly 0.00995 which is a really small decimal close to 0. But it's not 0 itself.
