(This is what I think) First, we minus 720 from her 1000. Now she has $280 left. 280 divided by 28 (the trainer cost) is 10. So, she can spend 10 hours with the personal trainer.
Answer:
12
Step-by-step explanation:
The correct answer is: [C]: " $4290.00 " .
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Explanation:
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Given: principal, "P": equals: $14,300 ;
rate, "r" : equals: 7.5 % = 7.5 / 100 = 0.075 ;
time, "t" (in years): equals: 4 ;
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What is the interest, "i" ?
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Note: The formula: i = P * r * t .
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So, we plug in our given values for "P", "r", and "t", and solve for "i" (interest).
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i = ($14,300) *(0.075) * (4) ;
i = $1,490 ; which is answer choice: [C]: " $4290.00 " .
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<span>12.3
Volume function: v(x) = ((18-x)(x-1)^2)/(4pi)
Since the perimeter of the piece of sheet metal is 36, the height of the tube created will be 36/2 - x = 18-x.
The volume of the tube will be the area of the cross section multiplied by the height. The area of the cross section will be pi r^2 and r will be (x-1)/(2pi). So the volume of the tube is
v(x) = (18-x)pi((x-1)/(2pi))^2
v(x) = (18-x)pi((x-1)^2/(4pi^2))
v(x) = ((18-x)(x-1)^2)/(4pi)
The maximum volume will happen when the value of the first derivative is zero. So calculate the first derivative:
v'(x) = (x-1)(3x - 37) / (4pi)
Convert to quadratic equation.
(3x^2 - 40x + 37)/(4pi) = 0
3/(4pi)x^2 - (10/pi)x + 37/(4pi) = 0
Now calculate the roots using the quadratic formula with a = 3/(4pi), b = -10/pi, and c = 37/(4pi)
The roots occur at x = 1 and x = 12 1/3. There are the points where the slope of the volume equation is zero. The root of 1 happens just as the volume of the tube is 0. So the root of 12 1/3 is the value you want where the volume of the tube is maximized. So the answer to the nearest tenth is 12.3</span>