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Elden [556K]
3 years ago
9

Your parents take your family out to dinner on a Wednesday night when they have a 15% off coupon. Your parents wanted to give th

e waiter a 18% tip for doing a great job. If the total amount of the dinner was $42.00, how much tip money should the waiter get? What is the new total? **Tip is given before the discount**
Mathematics
1 answer:
Rom4ik [11]3 years ago
8 0

Answer:

a. Tip is before the discount so the waiter will get;

= 42 * 18%

= $7.56

b. New total;

Coupon of 15% off applies;

= 42 * (1 - 15%)

= $35.70

Add the tip;

= 35.70 + 7.56

= $43.26

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Answer:

42 m^2

Step-by-step explanation:

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3 years ago
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Gas is escaping from a spherical balloon at the rate of 12 ft3/hr. At what rate (in feet per hour) is the radius of the balloon
bija089 [108]

Answer:

This is the rate at which the radius of the balloon is changing when the volume is 300 ft^3 \frac{dr}{dt}=-\frac{3}{225^{\frac{2}{3}}\pi ^{\frac{1}{3}}} \:\frac{ft}{h}  \approx -0.05537 \:\frac{ft}{h}

Step-by-step explanation:

Let r be the radius and V the volume.

We know that the gas is escaping from a spherical balloon at the rate of \frac{dV}{dt}=-12\:\frac{ft^3}{h} because the volume is decreasing, and we want to find \frac{dr}{dt}

The two variables are related by the equation

V=\frac{4}{3}\pi r^3

taking the derivative of the equation, we get

\frac{d}{dt}V=\frac{d}{dt}(\frac{4}{3}\pi r^3)\\\\\frac{dV}{dt}=\frac{4}{3}\pi (3r^2)\frac{dr}{dt} \\\\\frac{dV}{dt}=4\pi r^2 \frac{dr}{dt}

With the help of the formula for the volume of a sphere and the information given, we find r  

V=\frac{4}{3}\pi r^3\\\\300=\frac{4}{3}\pi r^3\\\\r^3=\frac{225}{\pi }\\\\r=\sqrt[3]{\frac{225}{\pi }}

Substitute the values we know and solve for \frac{dr}{dt}

\frac{dV}{dt}=4\pi r^2 \frac{dr}{dt}\\\\\frac{dr}{dt}=\frac{\frac{dV}{dt}}{4\pi r^2} \\\\\frac{dr}{dt}=-\frac{12}{4\pi (\sqrt[3]{\frac{225}{\pi }})^2} \\\\\frac{dr}{dt}=-\frac{3}{\pi \left(\sqrt[3]{\frac{225}{\pi }}\right)^2}\\\\\frac{dr}{dt}=-\frac{3}{\pi \frac{225^{\frac{2}{3}}}{\pi ^{\frac{2}{3}}}}\\\\\frac{dr}{dt}=-\frac{3}{225^{\frac{2}{3}}\pi ^{\frac{1}{3}}} \approx -0.05537 \:\frac{ft}{h}

7 0
4 years ago
Which sequence can be defined by the recursive formula f (1) = 4, f (n + 1) = f (n) – 1.25 for n ≥ 1?
asambeis [7]

Answer:

4, 2.75, 1.5, 0.25, - 1, - 2.25, ...............

Step-by-step explanation:

Using the recursive formula with f(1) = 4, then

f(2) = f(1) - 1.25 = 4 - 1.25 = 2.75

f(3) = f(2) - 1.25 = 2.75 - 1.25 = 1.5

f(4) = f(3) - 1.25 = 1.5 - 1.25 = 0.25

f(5) = f(4) - 1.25 = 0.25 - 1.25 = - 1

f(6) = f(5) - 1.25 = - 1 - 1.25 = - 2.25

Sequence is 4, 2.75, 1.5, 0.25, - 1, - 2.25, .......

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4 years ago
The weather forecast in a city is that for every week, 3 days are sunny 2 are cloudy, and 2 are rainy. On any chosen day, descri
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It is more likely to be sunny than it is to be cloudy or rainy.
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it is equally likely to be cloudy or rainy.
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Evaluate the expression 5(9-4)^2-3^2
Kay [80]
<span>5(9-4)^2-3^2
5(5)^2-3^2
5(25)-9
125-9
116</span>
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3 years ago
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