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Veseljchak [2.6K]
3 years ago
10

-16 = -5a -21. Plz help. Show work if possible. Pre-Algebra is hard. :(

Mathematics
1 answer:
Leona [35]3 years ago
5 0

Answer:

a = -1

Step-by-step explanation:

-16 = -5a - 21 (Given)

5 = -5a (Added 21 on both sides)

-1 = a (Divided -5 on both sides)

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The length of a rectangle is 5 centimeters less then twice it's width. The perimeter of the rectangle is 26 cm. What are the dim
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Answer:

The dimensions of the rectangle are length = 7cm and width = 6cm.

Step-by-step explanation:

In order to solve for the dimensions, you will need to set up two equations in order to solve for the missing variable.  Given the information that the length is 5 cm less then twice it's width, using 'L' for length and 'w' for width we get the following equation:  L = 2w - 5.  Perimeter is the sum of all the sides, or in the case of a rectangle P = 2w + 2L.  We can then use our expression for 'L' in our perimeter formula:  26 = 2w + 2(2w - 5).  First, using the distributive property we get: 26 = 2w + 4w - 10.  Next, we combine like terms:  26 = 6w - 10.  Then, we use inverse operations to isolate the variable:  26 + 10 = 6w - 10 + 10 to get 36 = 6w, divide both sides by 6 to get w = 6.  Lastly, plug in the value of 'w' to 'L':  L = 2(6) - 5 or L = 7.

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3 years ago
The number of hours a lightbulb burns before failing varies from bulb to bulb. The population distribution of burnout times is s
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ANSWER:

The average burnout time of a large number of bulbs has a sampling distribution that is close to Normal.

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The cental limit theorem states, that id the sample size is large (30 or more), then the sampling distribution of the sample means is approximately normal with mean ц and standar deviation б/\sqrt{n}

Thus the correct answer is the average burnout time of a large number of bulbs has a sampling distribution that is close to Normal.

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Parameterize the lateral face T_1 of the cylinder by

\mathbf r_1(u,v)=(x(u,v),y(u,v),z(u,v))=(2\cos u,2\sin u,v

where 0\le u\le2\pi and 0\le v\le3, and parameterize the disks T_2,T_3 as

\mathbf r_2(r,\theta)=(x(r,\theta),y(r,\theta),z(r,\theta))=(r\cos\theta,r\sin\theta,0)
\mathbf r_3(r,\theta)=(r\cos\theta,r\sin\theta,3)

where 0\le r\le2 and 0\le\theta\le2\pi.

The integral along the surface of the cylinder (with outward/positive orientation) is then

\displaystyle\iint_S(x^2+y^2+z^2)\,\mathrm dS=\left\{\iint_{T_1}+\iint_{T_2}+\iint_{T_3}\right\}(x^2+y^2+z^2)\,\mathrm dS
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=\displaystyle4\pi\int_{v=0}^{v=3}(v^2+4)\,\mathrm dv+2\pi\int_{r=0}^{r=2}r^3\,\mathrm dr+2\pi\int_{r=0}^{r=2}r(r^2+9)\,\mathrm dr
=136\pi
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If a=48Tg\pi then g=\frac{a}{48T\pi}.

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