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Drupady [299]
3 years ago
9

Addy’s monthly water bills for last year are $27, $31, $30, $26, $25, $27, $37, $33, $32, $28, $26, $26. Express the formula for

the mean using sigma notation and calculate the mean water bill for the year. Extend Your Understanding
Mathematics
1 answer:
Sav [38]3 years ago
7 0

Answer:

Σ( xi ) / n ; $29

Step-by-step explanation:

Given the following data:

X= $27, $31, $30, $26, $25, $27, $37, $33, $32, $28, $26, $26

Number of observations (n) = 12

Mean formula (m) = ( Σ xi ) / n

Where i = each individual value in X

Mean water bill for the years is thus :

m = Σ [(27 + 31 + 30 + 26 + 25 + 27 + 37 + 33 + 32 + 28 + 26 + 26)] / 12

m = 348 / 12

m = 29

Hence, the mean water bill for the year is $29

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2 (x-3) + 3 = 6x - 5​
anygoal [31]

Answer:

x = \frac{1}{2}

Step-by-step explanation:

2x-6+3=6x-5

2x-3=6x-5

2x-6x=-5+3

-4x=-2

x=.5or 1/2

5 0
3 years ago
In a science report, Mia finds that the average adult
Paul [167]
Equation would be b = 14m
8 0
3 years ago
Sketch the domain D bounded by y = x^2, y = (1/2)x^2, and y=6x. Use a change of variables with the map x = uv, y = u^2 (for u ?
cluponka [151]

Under the given transformation, the Jacobian and its determinant are

\begin{cases}x=uv\\y=u^2\end{cases}\implies J=\begin{bmatrix}v&u\\2u&0\end{bmatrix}\implies|\det J|=2u^2

so that

\displaystyle\iint_D\frac{\mathrm dx\,\mathrm dy}y=\iint_{D'}\frac{2u^2}{u^2}\,\mathrm du\,\mathrm dv=2\iint_{D'}\mathrm du\,\mathrm dv

where D' is the region D transformed into the u-v plane. The remaining integral is the twice the area of D'.

Now, the integral over D is

\displaystyle\iint_D\frac{\mathrm dx\,\mathrm dy}y=\left\{\int_0^6\int_{x^2/2}^{x^2}+\int_6^{12}\int_{x^2/2}^{6x}\right\}\frac{\mathrm dx\,\mathrm dy}y

but through the given transformation, the boundary of D' is the set of equations,

\begin{array}{l}y=x^2\implies u^2=u^2v^2\implies v^2=1\implies v=\pm1\\y=\frac{x^2}2\implies u^2=\frac{u^2v^2}2\implies v^2=2\implies v=\pm\sqrt2\\y=6x\implies u^2=6uv\implies u=6v\end{array}

We require that u>0, and the last equation tells us that we would also need v>0. This means 1\le v\le\sqrt2 and 0, so that the integral over D' is

\displaystyle2\iint_{D'}\mathrm du\,\mathrm dv=2\int_1^{\sqrt2}\int_0^{6v}\mathrm du\,\mathrm dv=\boxed6

4 0
3 years ago
Multiply: (4x – 7)(2x – 9)
Marizza181 [45]
Hello there!


Let's use foil.

First: 4x * 2x = 8x^2

Outside: 4x * -9 = -36x

Inside: -7 * 2x = -14x

Last: -7 * -9 = 63


Now, let's combine these.

8x^2 - 36x - 14x + 63

Finally, we can simplify this

8x - 50x + 63



I hope I helped!

Let me know if you need anything else!

~ Zoe


7 0
3 years ago
Penny is counting the days until her grandma comes to visit. There are 98 days left. How many weeks are left until Penny's grand
Burka [1]
98 divided by 7

98/7 = 14

Answer: There are 14 weeks left.
3 0
3 years ago
Read 2 more answers
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