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2 years ago

The group wants to leave a 15% tip on the $14.40 bill. What will be the amount of the tip?

Mathematics

1 answer:

Sedbober [7]2 years ago

5 0

Answer:

$2.16

Step-by-step explanation:

To find the tip amount, you multiply the price by the tip percentage.

14.40*0.15 = 2.16

So...

Tip = $2.16

Hope this helps!

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A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of lengths 3, 4, and 5. What

krok68 [10]

The area of the required triangle is <u>9/π²(3 + √3)</u> sq. units.

In the question, we are given that a triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of lengths 3, 4, and 5.

We are asked for the area of the triangle.

Now, the circumference of the circle = 3 + 4 + 5 = 12 units.

The formula for the circumference is 2πr, which gives is:

2πr = 12,

or, r = 6/π.

The length of the arcs are proportional to its central angle, making the angles: 3θ, 4θ, and 5θ, which needs to sum up to 360°, giving us θ = 360°/12 = 30°.

Thus, the three arcs subtends angles of θ₁ = 3θ = 90°,θ₂ = 4θ = 120°, and θ₃ = 5θ = 150°.

The area of the circle can be calculated as:

Area = (1/2)r² sin θ₁ + (1/2)r² sin θ₂ + (1/2)r² sin θ₃ = r²/2(sin θ₁ + sin θ₂ + sin θ₃).

Substituting the values, we get:

Area = 36/2π²(sin 90° + sin 120° + sin 150°),

or, Area = 36/2π²( 1 + √3/2 + 1/2),

or, Area = 9/π²(3 + √3).

Thus, the area of the required triangle is <u>9/π²(3 + √3)</u> sq. units.

Learn more about a triangle at

brainly.com/question/13734546

#SPJ4

5 0

1 year ago

Suppose after 2500 years an initial amount of 1000 grams of a radioactive substance has decayed to 75 grams. What is the half-li

krok68 [10]

Answer:

The correct answer is:

Between 600 and 700 years (B)

Step-by-step explanation:

At a constant decay rate, the half-life of a radioactive substance is the time taken for the substance to decay to half of its original mass. The formula for radioactive exponential decay is given by:

$A(t) = A_0 e^{(kt)}\\where:\\A(t) = Amount\ left\ at\ time\ (t) = 75\ grams\\A_0 = initial\ amount = 1000\ grams\\k = decay\ constant\\t = time\ of\ decay = 2500\ years$

First, let us calculate the decay constant (k)

$75 = 1000 e^{(k2500)}\\dividing\ both\ sides\ by\ 1000\\0.075 = e^{(2500k)}\\taking\ natural\ logarithm\ of\ both\ sides\\In 0.075 = In (e^{2500k})\\In 0.075 = 2500k\\k = \frac{In0.075}{2500}\\ k = \frac{-2.5903}{2500} \\k = - 0.001036$

Next, let us calculate the half-life as follows:

$\frac{1}{2} A_0 = A_0 e^{(-0.001036t)}\\Dividing\ both\ sides\ by\ A_0\\ \frac{1}{2} = e^{-0.001036t}\\taking\ natural\ logarithm\ of\ both\ sides\\In(0.5) = In (e^{-0.001036t})\\-0.6931 = -0.001036t\\t = \frac{-0.6931}{-0.001036} \\t = 669.02 years\\\therefore t\frac{1}{2} \approx 669\ years$

Therefore the half-life is between 600 and 700 years

5 0

2 years ago

How to write in words .102

Nutka1998 [239]

One hundred an two

hope it help you

4 0

3 years ago

Read 2 more answers

Michael is paid $9 per hour to work at the movie theater and $7 per hour when he helps his aunt at her bakery. Michael cannot wo

evablogger [386]

if he works at the theater he can make $288 in 32 hours, if he works at his aunts he can make $224 in 32 hours. he should work at the theater to meet his goal.

I really hope this helps

4 0

2 years ago

Read 2 more answers

Simplify: 0.810×0.00048 all over 0.000400×0.027

elixir [45]

Answer:

Step-by-step explanation:

Okay! This question is a very simple one, but without a calculator, your answer could easily vary from others! So, let´s do this one together!

The equation:

0.810x0.00048/0.000400x0.027

Let´s do the top :

0.810 x 0.00048 = 0.0003888

I will leave these numbers the same until the last part, lets not round them.

Bottom:

0.0004 x 0.027 = 0.0000108

And again I am not going to round this number.

Now we can divide!

0.0003888/0.0000108 = 36

I hope this helped!

4 0

3 years ago

Read 2 more answers