Answer:
The lamp would cost $39.36
<h3>
Answer is 1.5 square meters</h3>
=================================================
Work Shown:
The portion of the fabric that is laying across the ground is 2 meters. The portion of the fabric from the ground to the highest point (along the fabric's edge) is 1.5 meters, half of that is 0.75 meters and this is the length of the shadow. We can see this by forming a 30-60-90 triangle. The hypotenuse is 1.5 meters, the short leg is 0.75 meters. The short leg is always half of the hypotenuse of any 30-60-90 triangle, and the short leg is opposite the 30 degree angle.
So this shadow has length of 2 meters and 0.75 meters, making its area be 0.75*2 = 1.5 square meters when the sun is directly overhead at 12 noon
We have been given an equation
. We are asked to solve the equation for t.
First of all, we will divide both sides of equation by a.


Now we will take natural log on both sides.

Using natural log property
, we will get:

We know that
, so we will get:


Now we will divide both sides by c as:


Therefore, our solution would be
.
The food service gave out 80 samples, which is 4 fewer than 70% of the total number of samples they prepared. Lets make x the total number of samples they prepared.
So lets write it as an equation
80 = (70% of x) -4
70% converts to a decimal by moving the decimal point 2 spaces up, so it is 0.7
80 = 0.7x-4
Add 4 to both sides of the equation
84 = 0.7x
Divide both sides by 0.7 to isolate the x
x = 120
The food service prepared 120 samples.