<u>Step-by-step explanation:</u>
To prove:
Identities used:
......(1)
........(2)
.......(3)
Taking the LHS:
Using identity 1:
Using identities 2 and 3:
As, LHS = RHS
Hence proved
If you add 6% your answer would be $<span>51.41 hope it helps <3</span>
Answer:
So the answer for this case would be n=22547 rounded up to the nearest integer
Step-by-step explanation:
Let's define some notation
represent the sample mean
population mean (variable of interest)
represent the population standard deviation
n represent the sample size
represent the margin of error desire
The margin of error is given by this formula:
(a)
And on this case we have that ME =+1 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
The critical value for 99% of confidence interval now can be founded using the normal distribution. The significance would be 
and the critical value 
, replacing into formula (b) we got:
So the answer for this case would be n=22547 rounded up to the nearest integer
We can create two equations here:
(1) Volume = area of square * height of box
85.75 = s^2 h
(2) Cost = 3 * area of square + 1.5 * area of side box
C = 3 s^2 + 1.5 s h
From (1), we get:
h = 85.75 / s^2
Combining this with (2):
C = 3 s^2 + 1.5 s (85.75 / s^2)
C = 3 s^2 + 128.625 s-
Taking the 1st derivative and equating dC/ds =
0:
dC/ds = 6s – 128.625 / s^2 = 0
Multiply all by s^2:
6s^3 – 128.625 = 0
6s^3 = 128.625
s = 2.78 cm
So h is:
h = 85.75 / s^2 = 85.75 / (2.78)^2
h = 11.10 cm
So the dimensions are 2.78 cm x 2.78 cm x 11.10 cm
The total cost now is:
C = 3 (2.78)^2 + 1.5 (2.78) (11.10)
C = $69.47
Answer:
A) (i) a = 95° (180 - 85), b = 85° (180 - 95), c = 85° (180 - 95), d = 95° (180 - 85)
A) (ii) a = 103° (180 - 77), b = 77° (180 - 103), c = 103° (180 - 77), d = 77° (180 - 103)
B) (i) 95 + 85 + 85 + 95 = 360°
B (ii) 103 + 77 + 103 + 77 = 360°
Tip: Angles on a straight line add to 180°
Hope this helps!
