This the concept of circumference of circle. The arc length will be given by:
C=theta/360*pi*diameter
theta=62
diameter=d
thus the arc length will be:
C=62/360*π*d
C=0.54d
The correct answer here would be D. -1(3x+1)(x+5). You can find this answer by redistributing the problem.
-1(3x+1)(x+5)
-1(3x²+15x+1x+5)
-1(3x²+16x+5)
-3x²-16x-5
Using the math above, we can see that when we redistribute we get the original equation. That makes Choice D correct.
Answer: the incubation time that separates the bottom 2.5% from the rest of the incubation times is 24.96 days.
Step-by-step explanation:
Suppose the incubation times are approximately normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = incubation times.
µ = mean time
σ = standard deviation
From the information given,
µ = 23 days
σ = 1 day
The probability value for the incubation time that separates the bottom 2.5% from the rest of the incubation times would be (1 - 2.5/100) = (1 - 0.025) = 0.975
Looking at the normal distribution table, the z score corresponding to the probability value is 1.96
Therefore,
1.96 = (x - 23)/1
x = 1.96 + 23
x = 24.96
Answer: Choice B) The expression (10-2x)(30-2x)x represents the volume of the box
----------------------------------------------------
----------------------------------------------------
The original width is 10 inches. The width reduces to 10-2x inches after we cut off the top two corners of the rectangle. We can think of it as taking 10 and subtracting off two copies of x like so: 10-x-x = 10-2x
Similarly, the length goes from 30 inches to 30-2x inches. This time we're taking off the top and bottom corners (focus on either side it doesn't matter).
The height of the box is x inches due to this portion being folded up.
Volume of box = (width)*(length)*(height)
Volume of box = (10-2x)(30-2x)x
Note: the units for the answer are in cubic inches which can be written as "in^3" (inches cubed).
