Answer:
width = 1.8 in
length = 3.6 in
height =
Step-by-step explanation:
A designer is making a rectangular prism box with maximum volume, with the sum of its length, width, and height 8 in
Let l , w and h are the length , width and height

Plug it in the first equation

volume the box is length times width times height

To get maximum volume we take derivatived

set the derivative =0 and solve for w

width = 1.8 in
length = 2w= 3.6 in
height =
Answer:
75 degrees.
Step-by-step explanation:
All interior angles of a triangle add up to 180.
So we can set up an equation: 65+40+x=180
105+x=180
x=180-105
x=75
If a random sample of 20 persons weighed 3,460, the sample mean x-bar would be 3460/20 = 173 pounds.
The z-score for 173 pounds is given by:

Referring to a standard normal distribution table, and using z = 0.66, we find:

Therefore

The answer is: 0.2546
Answer:
The common difference (or common ratio) = 0.75
Step-by-step explanation:
i) let the first term be
= 80
ii) let the second term be
=
. r = 80 × r = 60 ∴ r =
= 0.75
iii) let the third term be
=
. r = 60 × r = 45 ∴ r =
= 0.75
iv) let the fourth term be
=
. r = 45 × r = 33.75 ∴ r =
= 0.75
Therefore we can see that the series of numbers are part of a geometric progression and the first term is 80 and the common ratio = 0.75.
Answer:
x = 14.4
Step-by-step explanation:
x is sin(angle 24/30)×24
how do we get the angle at 24/30 ?
by using the extended Pythagoras for baselines opposite other than 90 degrees.
c² = a² + b² - 2ab×cos(angle opposite of c)
in our example the angle 24/30 is opposite of the side 18.
so,
18² = 24² + 30² - 2×24×30×cos(angle 24/30)
324 = 576 + 900 - 1440×cos(angle 24/30)
324 = 1476 - 1440×cos(angle 24/30)
1440×cos(angle 24/30) = 1152
cos(angle 24/30) = 1152/1440 = 576/720 = 288/360 = 144/180 = 72/90 = 36/45 = 12/15 = 4/5
angle 24/30 = 36.9 degrees
x = sin(36.9) × 24 = 14.4