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andrew11 [14]
3 years ago
9

The figures below are based on semicircles and squares. Find the perimeter and the area of each shape. Give your answer as a com

pletely simplified exact value in terms of π (no approximations).

Mathematics
1 answer:
Nuetrik [128]3 years ago
4 0
To find the area, move each semicircle to fill up the square, you'll see there are three squares, each with an area of 4*4=16, so the total area is 3*16=48
Now the perimeter:
the perimeter of a circle is π times the diameter.
perimeter of each semicircle: (1/2)π*4=2π
there are altogether 6 arches and two straight sides, so the total is
2π*6+4*2=12π+8

the area is 48 square units, the perimeter is 12π+8 units.

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Juli2301 [7.4K]

Answer:

c

Step-by-step explanation:

7 0
3 years ago
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25 points for right answers
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You divide by 16 so you can get each ingredient per serving then you multiply that by 4 and you get your answer

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A space telescope on a mountaintop is housed inside of a cylindrical building with a hemispheric dome. If the circumference of t
Vlad1618 [11]

Answer:

 185553.7\text{ feet}^3

Step-by-step explanation:

GIVEN: A space telescope on a mountaintop is housed inside of a cylindrical building with a hemispheric dome. If the circumference of the dome is 84\text{ feet}, and the total height of the building up to the top of the dome is 91\text{ feet}.

TO FIND: what is the approximate total volume of the building.

SOLUTION:

let the height of the mountaintop be h\text{ feet}

As the dome hemispherical.

circumference of a hemisphere =\frac{1}{2}\times2\pi\times radius

                                                    =\pi\times radius

                                                    \frac{22}{7}\times radius=84

                                                    radius=26.75\text{ feet}

total height of the building up to the top of the dome =\text{radius of hemisphere}+\text{height of mountaintop}

=26.75+h=91

h=64.25\text{ feet}

Volume of building =\text{volume of cylindrical mountaintop}+\text{volume of dome}

                                =\pi(radius)^2h+\frac{2}{3}\pi(radius)^3

as radius of mountain top is same as dome

putting values

                                =3.14(26.75)^264.75+\frac{2}{3}3.14(26.75)^3      

                               =145484.6+40069.1

                               185553.7\text{ feet}^3

Hence the total volume of the building is 185553.7\text{ feet}^3                                      

5 0
3 years ago
Sergio is working on a research project involving the ages of students at Brooklyn College. After interviewing 500 students, he
Zinaida [17]

Answer:

The probability of of a randomly chosen student being exactly 21 years old.

= 1.293

Step-by-step explanation:

<u><em>Step(i):-</em></u>

<em>Given Population  size n = 500</em>

<em>Mean of the Population = 20 years and 6 months</em>

<em>                                        = </em>20 + \frac{6}{12} = 20 +0.5 = 20.5 years<em></em>

<em>Standard deviation of the Population = 2 years</em>

Let 'X' be the range of ages of the students on campus follows a normal distribution

Let   x =21

            Z = \frac{x-mean}{S.D}

            Z = \frac{x-mean}{S.D} = \frac{21-20.6}{2} =0.2

<em>The probability of a randomly chosen student being exactly 21 years old.</em>

<em>P( Z≤21) =  0.5 + A( 0.2) </em>

            = 0.5 +0.793

           =  1.293

           

6 0
3 years ago
6. How many 4 digit odd numbers can be formed if no digit can be repeated?
ale4655 [162]
1, 3, 5, 7, 9 are the possible digits

meaning you have 5! possible combinations or 120 combinations
6 0
3 years ago
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