Answer:
Step-by-step explanation:
Given that two fair dice are rolled 3 times and the sum of the numbers that come up is recorded.
a) The sum is 4 on each of the three rolls.
(1,3) (2,2) (3,1) HEnce for one throw prob = 3/36 =1/12
Prob for getting same sum 4 in 3 rolls = 
(since each trial is independent)
b) Prob sum =4 in exactly 2 rolls
= 
=
<em>Answer:</em>
<em>7/78 - 35/78i</em>
<em>Step-by-step explanation:</em>
<em>A complex number is a real number, an imaginary number or a number with both real and imaginary number. Its standard form is:
</em>
<em>a + bi
</em>
<em>
</em>
<em>For the expression, 7/ 3-15i
</em>
<em>
</em>
<em>(7/ 3-15i) (3+15i)
</em>
<em>21 - 105i / (234)
</em>
<em>7/78 - 35/78i
</em>
Answer:
t = (C - 3*A)/B + 3
Step-by-step explanation:
Given in the question that,
the speed with which canoe travelled for first 3 hours = A
the speed with which he travelled for any and all time thereafter = B
As we do not know the values of A, B, or C, so the answer will be an expression for C in terms of A and B.
<h3>Formula to use</h3>
distance = speed x time
C = A*3 + B*(t-3)
Rearranging and solving for t
C - (A*3) = B*(t-3)
C - (A*3) = Bt - B3
C - (A*3) + B3 = Bt
t = C - (A*3) + B3 / B
or
t = (C - 3*A)/B + 3
Answer:
Step-by-step explanation:
Let the side of the square base be x
h be the height of the box
Volume V = x²h
13500 = x²h
h = 13500/x² ..... 1
Surface area = x² + 2xh + 2xh
Surface area S = x² + 4xh ...... 2
Substitute 1 into 2;
From 2; S = x² + 4xh
S = x² + 4x(13500/x²)
S = x² + 54000/x
To minimize the amount of material used; dS/dx = 0
dS/dx = 2x - 54000/x²
0 = 2x - 54000/x²
0 = 2x³ - 54000
2x³ = 54000
x³ = 27000
x = ∛27000
x = 30cm
Since V = x²h
13500 = 30²h
h = 13500/900
h = 15cm
Hence the dimensions of the box that minimize the amount of material used is 30cm by 30cm by 15cm
