It takes 28 minutes to manufacture the piece now.
<u>Step-by-step explanation:</u>
It is given that,
- A factory manufactures a metal piece in 32 minutes.
After the new technology,
- the factory cut that time by 8%.
Therefore, the time after the new technology is known by reducing the 8% of total time from the 32 minutes.
⇒ 8% of 32 = (8/100) × 32
⇒ 0.08 × 32
⇒ 2.56 minutes
The time after the new technology allowed = 32 minutes - 2.56 minutes
⇒ 29.44 minutes.
Again,
- the time is cut by 5% after the another improvement.
Therefore, the time after the another improvement is known by reducing the 5% of previous time 29.44 minutes.
⇒ 5% of 29.44 = (5/100) × 29.44
⇒ 0.05 × 29.44
⇒ 1.472 minutes
The time after the another improvement = 29.44 minutes - 1.472 minute
⇒ 27.9 minutes. (Which is approximately 28 minutes)
Answer:
9. -4x+19y-7
10. 7x+20
Step-by-step explanation:
9. To simplify this expression, simply combine like terms. Add all of the terms with the x variable together, then the terms with the y variable, then the constant terms. I will show this step by step, but usually you do not have to show this work. The order of the terms does not matter.
x variable terms: (4x-8x)+7y-2+6y+6y-5= -4x+7y-2+6y+6y-5
y variable terms: (7y+6y+6y)-4x-2-5=19y-4x-2-5
constant terms: (-2-5)-4x+19y=-4x+19y-7
10. To simplify this expression, expand all terms and then combine like terms. The first term can be expanded by multiplying each term in the parentheses by 2.
Expand terms: 2(5+3x)+(x+10)= 10+6x+x+10
Now, you can combine like terms as done on the last problem. Note that I got rid of the parentheses in the second term, as they did not matter (since there was no term in front of them).
x variable terms: (6x+x)+10+10=7x+10+10
constant terms: (10+10)+7x=7x+20
Answer:
x = 45.3°
Step-by-step explanation:
The distant between the first bird and the bird watcher is opposite to the reference angle, x° = 32 ft
The hypotenuse is the distance between the second bird and the bird watcher = 45 ft.
Therefore,
THe area of the whole circle is pi r^2 = 6^2 * pi = 36pi
There are 360 degrees in a crcle so this sectors area i (30/360) *36pi
= 3 pi
