Answer:
55
Step-by-step explanation:
there are two ways to answer : since angle 1 and the 125 degree angle are a linear pair, you can do 180-125 = 55, or, since the three angles in the triangle always add up to 180, you can do 180-37-88 = 55.
Answer:
3⁷
Step-by-step explanation:
it's kinda messy but my step by step is in the picture. practically when you "multiply" an exponent (as long as they have the same base number) with another like 3⁴×3⁵ or (3⁴)⁵ you add the exponents together so you'd get 3⁴×3⁵=3⁹
when dividing an exponent by another exponent (with again, the same base number) you subtract the exponents like this: 3⁶÷3² or 3⁶/3² would equal 3⁴
Answer:
$163.54
Step-by-step explanation:
Volume of rectangular container = 10m^3
Length = 2(width)
Material for the base cost $10 per square meter
Material for the side cost $6 per square meter
Volume = L*B*H
L= 2W
V = (2W).W. H
10 = 2W^2.H
H = 10 /2W^2
H = 5/W^2
Let C(w) = cost function
C(w) = 10(L.W) + 6(2.L.H + 2.W.H)
= 10(2W.W) + 6(2.2W.H + 2.W.H)
= 10(2W^2) + 6(4W.H + 2.W.H)
= 10(2W^2) + 6(4W*5/W^2 + 2.W*5/W^2)
= 20W^2 + 6(20/W + 10/W)
= 20W^2 + 6((10+20)/W)
= 20W^2 + 6(30/W)
C(w) = 20W^2 + 180/W
To find the minimum value, differentiate C with respect to w
C'(w) = 40W - 180/W^2
Put C'(w) = 0
0 = 40W - 180/W^2
40W = 180/W^2
40W^3 = 180
W^3 = 180/40
W^3 = 4.5
W = cube rt(4.5)
W = 1.65m
C = 20(1.65)^2 + 180/1.65
C = 54.45 + 109.09
C= $163.54
Minimum cost = $163.54
Position in the sequence triangular number relation
1 1 1 = 1*(1+1)/2
2 3 3 = 2(2+1)/2
3 6 6 = 3(3+1)/2
4 10 10 = 4(4+1)/2
5 15 15= 5(5+1)/2
Call n the position in the sequence, then the triangular number is: n(n+1)/2
Answer:
Step-by-step explanation:
If k is the number of classes and n is the number of observations, then for number of classes we should select the smallest k such that 2^k > n.
<u>We have n = 50 and:</u>
- 2^5 = 32 < 50
- 2^6 = 64 > 50
As per above described 2 to k rule, we are taking k = 6.
So 6 classes should be used.
