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3 years ago

15

Find the cost of lodging: What is the average lodging cost per night if a family had motel bills of $79.00, $146.00, and $104.60

for three different nights?

2 answers:

kumpel [21]3 years ago

6 0

Answer:

$109.86

Step-by-step explanation:

Rudiy273 years ago

4 0

Answer: 108.87

Step-by-step explanation:

To find the average

Sum of numbers÷how many numbers

(76+146+104.6) ÷ 3 numbers

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The sum of the first 6 terms of a geometric series is 15,624 and the common ratio is 5.

nikitadnepr [17]

Answer:

4

Step-by-step explanation:

The sum of n terms of a geometric series with first term a1 and common ratio r is given by ...

Sn = a1·(r^n -1)/(r -1)

for r=5 and n=6, this becomes ...

15624 = a1·(5^6 -1)/(5 -1) = a1·(15624/4)

Then we have ...

1 = a1/4 . . . . . divide by 15624

4 = a1 . . . . . . multiply by 4

The first term of the series is 4.

5 0

3 years ago

Please help and provide work for help!!

Stella [2.4K]

Answer:

Step-by-step explanation:

1)

Tri. prism:

B = base = 1/2 a c

base = 1/2 * 6 * 6 = 18

volume = Bh

v = 18*4

v = 72

Rec. prism

volume = 4*6*6

v = 144

total volume = 144+72

vt = 212

2)

top rec. = 2*3*5=30

bot rec. = 4*5*6=120

vt = 30 + 120

vt = 150

7 0

3 years ago

99 POINT QUESTION, PLUS BRAINLIEST!!!

VladimirAG [237]

First, we have to convert our function (of x) into a function of y (we revolve the curve around the y-axis). So:

$y=100-x^2\\\\x^2=100-y\qquad\bold{(1)}\\\\\boxed{x=\sqrt{100-y}}\qquad\bold{(2)} \\\\\\0\leq x\leq10\\\\y=100-0^2=100\qquad\wedge\qquad y=100-10^2=100-100=0\\\\\boxed{0\leq y\leq100}$

And the derivative of x:

$x'=\left(\sqrt{100-y}\right)'=\Big((100-y)^\frac{1}{2}\Big)'=\dfrac{1}{2}(100-y)^{-\frac{1}{2}}\cdot(100-y)'=\\\\\\=\dfrac{1}{2\sqrt{100-y}}\cdot(-1)=\boxed{-\dfrac{1}{2\sqrt{100-y}}}\qquad\bold{(3)}$

Now, we can calculate the area of the surface:

$A=2\pi\int\limits_0^{100}\sqrt{100-y}\sqrt{1+\left(-\dfrac{1}{2\sqrt{100-y}}\right)^2}\,\,dy=\\\\\\= 2\pi\int\limits_0^{100}\sqrt{100-y}\sqrt{1+\dfrac{1}{4(100-y)}}\,\,dy=(\star)$

We could calculate this integral (not very hard, but long), or use (1), (2) and (3) to get:

$(\star)=2\pi\int\limits_0^{100}1\cdot\sqrt{100-y}\sqrt{1+\dfrac{1}{4(100-y)}}\,\,dy=\left|\begin{array}{c}1=\dfrac{-2\sqrt{100-y}}{-2\sqrt{100-y}}\end{array}\right|= \\\\\\= 2\pi\int\limits_0^{100}\dfrac{-2\sqrt{100-y}}{-2\sqrt{100-y}}\cdot\sqrt{100-y}\cdot\sqrt{1+\dfrac{1}{4(100-y)}}\,\,dy=\\\\\\ 2\pi\int\limits_0^{100}-2\sqrt{100-y}\cdot\sqrt{100-y}\cdot\sqrt{1+\dfrac{1}{4(100-y)}}\cdot\dfrac{dy}{-2\sqrt{100-y}}=\\\\\\$

$=2\pi\int\limits_0^{100}-2\big(100-y\big)\cdot\sqrt{1+\dfrac{1}{4(100-y)}}\cdot\left(-\dfrac{1}{2\sqrt{100-y}}\, dy\right)\stackrel{\bold{(1)}\bold{(2)}\bold{(3)}}{=}\\\\\\= \left|\begin{array}{c}x=\sqrt{100-y}\\\\x^2=100-y\\\\dx=-\dfrac{1}{2\sqrt{100-y}}\, \,dy\\\\a=0\implies a'=\sqrt{100-0}=10\\\\b=100\implies b'=\sqrt{100-100}=0\end{array}\right|=\\\\\\= 2\pi\int\limits_{10}^0-2x^2\cdot\sqrt{1+\dfrac{1}{4x^2}}\,\,dx=(\text{swap limits})=\\\\\\$

$=2\pi\int\limits_0^{10}2x^2\cdot\sqrt{1+\dfrac{1}{4x^2}}\,\,dx= 4\pi\int\limits_0^{10}\sqrt{x^4}\cdot\sqrt{1+\dfrac{1}{4x^2}}\,\,dx=\\\\\\= 4\pi\int\limits_0^{10}\sqrt{x^4+\dfrac{x^4}{4x^2}}\,\,dx= 4\pi\int\limits_0^{10}\sqrt{x^4+\dfrac{x^2}{4}}\,\,dx=\\\\\\= 4\pi\int\limits_0^{10}\sqrt{\dfrac{x^2}{4}\left(4x^2+1\right)}\,\,dx= 4\pi\int\limits_0^{10}\dfrac{x}{2}\sqrt{4x^2+1}\,\,dx=\\\\\\=\boxed{2\pi\int\limits_0^{10}x\sqrt{4x^2+1}\,dx}$

Calculate indefinite integral:

$\int x\sqrt{4x^2+1}\,dx=\int\sqrt{4x^2+1}\cdot x\,dx=\left|\begin{array}{c}t=4x^2+1\\\\dt=8x\,dx\\\\\dfrac{dt}{8}=x\,dx\end{array}\right|=\int\sqrt{t}\cdot\dfrac{dt}{8}=\\\\\\=\dfrac{1}{8}\int t^\frac{1}{2}\,dt=\dfrac{1}{8}\cdot\dfrac{t^{\frac{1}{2}+1}}{\frac{1}{2}+1}=\dfrac{1}{8}\cdot\dfrac{t^\frac{3}{2}}{\frac{3}{2}}=\dfrac{2}{8\cdot3}\cdot t^\frac{3}{2}=\boxed{\dfrac{1}{12}\left(4x^2+1\right)^\frac{3}{2}}$

And the area:

$A=2\pi\int\limits_0^{10}x\sqrt{4x^2+1}\,dx=2\pi\cdot\dfrac{1}{12}\bigg[\left(4x^2+1\right)^\frac{3}{2}\bigg]_0^{10}=\\\\\\= \dfrac{\pi}{6}\left[\big(4\cdot10^2+1\big)^\frac{3}{2}-\big(4\cdot0^2+1\big)^\frac{3}{2}\right]=\dfrac{\pi}{6}\Big(\big401^\frac{3}{2}-1^\frac{3}{2}\Big)=\boxed{\dfrac{401^\frac{3}{2}-1}{6}\pi}$

Answer D.

6 0

3 years ago

Read 2 more answers

If n2 = 1/16, then n could be which of the following?<br> -8<br> -1/4<br> 1/4

andreyandreev [35.5K]

$n^2=\dfrac{1}{16}\\\\n=-\dfrac{1}{4} \vee n=\dfrac{1}{4}$

6 0

3 years ago

Given the angles inscribed in the circle, find m ∠ DBC.

Cloud [144]

Answer:

m∠DBC = 51°

Step-by-step explanation:

<u>Circle Theorem vocabulary</u>

Chord: A straight line joining two points on the circle.
Inscribed angle: The angle formed when two chords meet at one point on a circle.
Intercepted arc: The arc that is between the endpoints of the chords that form the inscribed angle.

<u>Inscribed Angle Theorem</u>

The measure of an <u>inscribed angle</u> is half the measure of the <u>intercepted arc</u>.

Therefore:

$\sf \implies \angle DBC=\dfrac{1}{2}\:\overset{\frown}{BC}$

$\sf \implies \angle DBC=\dfrac{1}{2}\:(102^{\circ})$

$\sf \implies \angle DBC=51^{\circ}$

Learn more about the Inscribed Angle Theorem here:

brainly.com/question/27934538

brainly.com/question/27943630

6 0

2 years ago

Read 2 more answers