Answer:
24 
Step-by-step explanation:
volume formula= l x w x h
Box A:
4 x 3 x 4 = 48
Box B: 48/2 = 24
$256.75
Add $178 + $98.25= $276.25
Then $276.25 - $19.50 = $256.75
Answer:
P(x) = x^4 -16x^3 +76x^2 -72x -100
Step-by-step explanation:
The two roots 1-√3 and 1+√3 give rise to the quadratic factor ...
... (x -(1-√3))(x -(1+√3)) = (x-1)^2 -(√3)^2 = x^2 -2x -2
The complex root 7-i has a conjugate that is also a root. These two roots give rise to the quadratic factor ...
... (x -(7 -i))(x -(7 +i)) = (x-7)^2 -(i)^2 = x^2 -14x +50
The product of these two quadratic factors is ...
... P(x) = (x^2 -2x -2)(x^2 -14x +50) = x^4 +x^3(-14 -2) +x^2(50 +28 -2) +x(-100+28) -100
... P(x) = x^4 -16x^3 +76x^2 -72x -100
Triangular sequence = n(n + 1)/2
If 630 is a triangular number, then:
n(n + 1)/2 = 630
Then n should be a positive whole number if 630 is a triangular number.
n(n + 1)/2 = 630
n(n + 1) = 2*630
n(n + 1) = 1260
n² + n = 1260
n² + n - 1260 = 0
By trial an error note that 1260 = 35 * 36
n² + n - 1260 = 0
Replace n with 36n - 35n
n² + 36n - 35n - 1260 = 0
n(n + 36) - 35(n + 36) = 0
(n + 36)(n - 35) = 0
n + 36 = 0 or n - 35 = 0
n = 0 - 36, or n = 0 + 35
n = -36, or 35
n can not be negative.
n = 35 is valid.
Since n is a positive whole number, that means 630 is a triangular number.
So the answer is True.
Answer: A. 85.7
Step-by-step explanation:
Given : Two sections of a class took the same quiz.
Section A had 15 students who had a mean score of 80, and Section B had 20 students who had a mean score of 90.
We know that , 
Then , for section A :
Similarly in Section B, 
Total scores = Sum of scores in sec A+Sum of scores in sec B
=1200+1800=3000
Total students = Students in sec A +Students in sec B
=15+20=35
Now , the mean score for all of the students on the quiz =
Hence, the approximate mean score for all of the students on the quiz = 85.7
Thus , the correct answer is option A. 85.7.
