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4 years ago

A massage therapist charges a

Mathematics

2 answers:

Alexeev081 [22]4 years ago

7 0

Answer: 31.05

Step-by-step explanation:

30 mins massage = $15

Base fee. = $12

Total = $ 27

15% tip of total. = $4.05

Grand total. = $31.05

Andrew [12]4 years ago

4 0

Base fee = 12
Massage = 3x additional charge = 15

Tip:
15+12 = 27
27 x 0.15 = 4.05

Add everything together 27+40.4 = 31.05

Answer: Total cost = 31.05$

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If there are 63 peaches in 7 bowls, how many peaches are in one bowl?

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Answer:

Step-by-step explanation:

63/7 is 9

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3 years ago

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The table below shows the probability distribution of student ages in a high school with 1500 students. What is the expected val

lorasvet [3.4K]

Answer:

15.31

Step-by-step explanation:

The expected value, E(X) is given by :

E(X) = Σx*p(x)

From the table above :

E(X) = (13 * 0.01) + (14 * 0.27) + (15 * 0.30) + (16 * 0.25) + (17 * 0.16) + (18 * 0.01)

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3 years ago

a rectangle is constructed with its base on the x-axis and two of its vertices on the parabola y=121-x^2. what are the dimension

insens350 [35]

Answer:

the length is $\dfrac{22}{\sqrt{3}}$ and the width is $121-\left(\dfrac{11}{\sqrt{3}}\right)^2=121-\dfrac{121}{3}=\dfrac{242}{3}.$

Step-by-step explanation:

Let points A and B be placed on the x-axis. Their coordinates are $A(x_0,0)\ (x_0>0)$ and $B(-x_0,0)$ (because of parabola symmetry). Two other vertices lie on the parabola, then $C(-x_0,121-x_0^2)$ and $D(x_0,121-x_0^2).$ The length of the side AB is $2x_0$ and the length of the side AD is $121-x_0^2.$ Thus, the area of the rectangle ABCD is

$A=2x_0\cdot (121-x_0^2)=242x_0-2x_0^3.$

Find the derivative A':

$A'=242-2\cdot 3x_0^2=242-6x_0^2.$

Equate A' to 0:

$242-6x_0^2=0,\\ \\x_0^2=\dfrac{121}{3},\\ \\x_0=\dfrac{11}{\sqrt{3}}.$

The maximum area of the rectangle is

$A_{max}=242\cdot \dfrac{11}{\sqrt{3}}-2\cdot \left(\dfrac{11}{\sqrt{3}}\right)^3=\dfrac{2662}{\sqrt{3}}-\dfrac{2662}{3\sqrt{3}}=\dfrac{5324}{3\sqrt{3}}\ un^2.$