1) A *the first option*
2)B *the second option*
Step-by-step explanation:
the area of a full circle (360°) is
pi×r²
r = 15 ft in our case
the area of a segment of a circle is the corresponding fraction of the whole circle area.
the angle of the shaded area is
360 - 332 = 28°
therefore, the area of the shaded area is
pi×15²×28/360 = pi×225×28/360 = pi×225×7/90 =
= pi×5×7/2 = 54.97787144... ft²
≈ 54.98 ft²
the area of the "ice rink" is the sum of a rectangle and a circle (which is split into 2 halves that are attached to both sides of the rectangle).
the radius of the circle is 7/2 = 3.5 meters.
the length of the rectangle in the middle is
18 - 2×3.5 = 18 - 7 = 11 meters.
so, the area of the rectangle is 11×7 = 77 m²
the area of the circle is
pi×r² = pi×3.5² = pi×12.25 = 38.48451001... m²
that means the total area is
77 + 38.48451001... = 115.48451... m² ≈ 115.48 m²
I don't know what the "six-step method" is supposed to be, so I'll just demonstrate the typical method for this problem.
Let <em>x</em> be the amount (in gal) of the 50% antifreeze solution that is required. The new solution will then have a total volume of (<em>x</em> + 60) gal.
Each gal of the 50% solution used contributes 0.5 gal of antifreeze. Similarly, each gal of the 30% solution contributes 0.3 gal of antifreeze. So the new solution will contain (0.5 <em>x</em> + 0.3 * 60) gal = (0.5 <em>x</em> + 18) gal of antifreeze.
We want the concentration of antifreeze to be 40% in the new solution, so we need to have
(0.5 <em>x</em> + 18) / (<em>x</em> + 60) = 0.4
Solve for <em>x</em> :
0.5 <em>x</em> + 18 = 0.4 (<em>x</em> + 60)
0.5 <em>x</em> + 18 = 0.4 <em>x</em> + 24
0.5 <em>x</em> - 0.4 <em>x</em> = 24 - 18
0.1 <em>x</em> = 6
<em>x</em> = 6/0.1 = 60 gal
If Lily chooses account A, the balance of her account would increase by a rate of 2.4% on a quarterly basis
<h3>The Equation</h3>
The equation of the function is given as:
<h3>Exponential function</h3>
An exponential function is represented as:
Where:
- a represents the initial value
- r represents the rate
So. by comparison:
Subtract 1 from both sides
Express as percentage
From the function, the exponent of the rate is 4t.
This means that, the balance increases four times in a year.
So, her balance would increase quarterly
Read more about exponential functions at:
brainly.com/question/11464095