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MariettaO [177]
2 years ago
11

Which is the area of a rectangle with a length of 21 feet and a width of 15 feet?

Mathematics
2 answers:
nexus9112 [7]2 years ago
8 0

Answer:

315 ft ²

Step-by-step explanation:

The formula for the area of a rectangle is Area=Length × Width

Area=21×15

Area=315 ft ²

MA_775_DIABLO [31]2 years ago
3 0

Answer:

315

Step-by-step explanation:

Area = Length x Width

Area = 21 x 15

Area = 315

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120-3/4y=60 solve for y
navik [9.2K]
120 - 3/4y=60
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480y-3=240y
480y-240y=3
240y=3
y=3/240
y=1/80

Answer: y=1/80
5 0
3 years ago
A cylinder has a height of 4 meters and a radius of 1.5 meters. What is the approximate radius of a sphere that has the same sur
Mama L [17]

If the surface area of the cylinder is 12π square meters. Then the radius of the sphere will be 1.7 meters.

<h3>What is a cylinder?</h3>

A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.

A cylinder has a height of 4 meters and a radius of 1.5 meters.

Then the approximate radius of a sphere that has the same surface area as the cylinder.

We know that the Surface area of the cylinder will be is given as

Surface area = 2πrh

Surface area = 2 x π x 1.5 x 4

Surface area = 12π square meters

Then we have

Surface area of sphere = surface area of cylinder

                              4πr² = 12π

                                  r² = 3

                                   r = 1.7 meters

More about the cylinder link is given below.

brainly.com/question/3692256

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4 0
2 years ago
An article contained the following observations on degree of polymerization for paper specimens for which viscosity times concen
devlian [24]

Answer:

(a) A 95% confidence interval for the population mean is [433.36 , 448.64].

(b) A 95% upper confidence bound for the population mean is 448.64.

Step-by-step explanation:

We are given that article contained the following observations on degrees of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range:

420, 425, 427, 427, 432, 433, 434, 437, 439, 446, 447, 448, 453, 454, 465, 469.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                              P.Q.  =  \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }  ~ t_n_-_1

where, \bar X = sample mean = \frac{\sum X}{n} = 441

            s = sample standard deviation = \sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }  = 14.34

            n = sample size = 16

            \mu = population mean

<em>Here for constructing a 95% confidence interval we have used One-sample t-test statistics as we don't know about population standard deviation.</em>

<em />

<u>So, 95% confidence interval for the population mean, </u>\mu<u> is ;</u>

P(-2.131 < t_1_5 < 2.131) = 0.95  {As the critical value of t at 15 degrees of

                                             freedom are -2.131 & 2.131 with P = 2.5%}  

P(-2.131 < \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } } < 2.131) = 0.95

P( -2.131 \times {\frac{s}{\sqrt{n} } } < {\bar X-\mu} < 2.131 \times {\frac{s}{\sqrt{n} } } ) = 0.95

P( \bar X-2.131 \times {\frac{s}{\sqrt{n} } } < \mu < \bar X+2.131 \times {\frac{s}{\sqrt{n} } } ) = 0.95

<u>95% confidence interval for</u> \mu = [ \bar X -2.131 \times {\frac{s}{\sqrt{n} } } , \bar X +2.131 \times {\frac{s}{\sqrt{n} } } ]

                                      = [ 441-2.131 \times {\frac{14.34}{\sqrt{16} } } , 441+2.131 \times {\frac{14.34}{\sqrt{16} } } ]

                                      = [433.36 , 448.64]

(a) Therefore, a 95% confidence interval for the population mean is [433.36 , 448.64].

The interpretation of the above interval is that we are 95% confident that the population mean will lie between 433.36 and 448.64.

(b) A 95% upper confidence bound for the population mean is 448.64 which means that we are 95% confident that the population mean will not be more than 448.64.

6 0
3 years ago
hurrrrrrrrrry!!!!! There are 2 Senators from each of 50 states. We wish to make a 3-Senator committee in which no two members ar
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Answer:

You can choose one senator in 2 ways from the first of the 3 states; in 2 independent ways from the second of the 3 states; and in 2 independent ways from the third of the 3 states.

Step-by-step explanation:

So the answer to that question is 2*2*2*19600 which = 156800 way

Step-by-step explanation:

8 0
3 years ago
Show tan(???? − ????) = tan(????)−tan(????) / 1+tan(????) tan(????)<br> .
anyanavicka [17]

Answer:

See the proof below

Step-by-step explanation:

For this case we need to proof the following identity:

tan(x-y) = \frac{tan(x) -tan(y)}{1+ tan(x) tan(y)}

We need to begin with the definition of tangent:

tan (x) =\frac{sin(x)}{cos(x)}

So we can replace into our formula and we got:

tan(x-y) = \frac{sin(x-y)}{cos(x-y)}   (1)

We have the following identities useful for this case:

sin(a-b) = sin(a) cos(b) - sin(b) cos(a)

cos(a-b) = cos(a) cos(b) + sin (a) sin(b)

If we apply the identities into our equation (1) we got:

tan(x-y) = \frac{sin(x) cos(y) - sin(y) cos(x)}{sin(x) sin(y) + cos(x) cos(y)}   (2)

Now we can divide the numerator and denominato from expression (2) by \frac{1}{cos(x) cos(y)} and we got this:

tan(x-y) = \frac{\frac{sin(x) cos(y)}{cos(x) cos(y)} - \frac{sin(y) cos(x)}{cos(x) cos(y)}}{\frac{sin(x) sin(y)}{cos(x) cos(y)} +\frac{cos(x) cos(y)}{cos(x) cos(y)}}

And simplifying we got:

tan(x-y) = \frac{tan(x) -tan(y)}{1+ tan(x) tan(y)}

And this identity is satisfied for all:

(x-y) \neq \frac{\pi}{2} +n\pi

8 0
3 years ago
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