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3 years ago

Find the area of the trapezoid A. 168 in^2 B. 94.5 ft^2 C. 72 ft^2 D. 84 ft^2

Mathematics

1 answer:

Rainbow [258]3 years ago

4 0

Answer:

D. 84 ft^2

Step-by-step explanation:

Formula for area of a trapezoid:

$A=\frac{a+b}{2} h$

where a and b = bases and h = height

The trapezoid shown has the following dimensions

base 1 = 9ft

base 2 = 12ft

height = 8ft

Using the following information we plug in the values into the formula

$A=\frac{9+12}{2} \\9+12=21\\\frac{21}{2} =10.5\\10.5*8=84$

Hence, the area of the trapezoid is 84ft² and your answer is D

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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

The graph of a system of linear equations shows 2 lines with different slopes.

pochemuha

they are the same lines

x and y are the same

Step-by-step explanation:

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3 years ago

According to a certain website, wine critics generally use a wine-scoring scale to communicate their opinions on the relative qu

const2013 [10]

Answer:

$\bar x = 82$

$\sigma = 9.64$

Step-by-step explanation:

Given

$n = 12$

$87\ 91\ 86\ 82\ 72\ 91\ 60\ 77\ 80\ 79\ 83\ 96$

Solving (a); Point estimate of mean

To do this, we simply calculate the sample mean

$\bar x = \frac{\sum x}{n}$

$\bar x = \frac{87+ 91+ 86+ 82+72+91+60+77+80+79+83+96}{12}$

$\bar x = \frac{984}{12}$

$\bar x = 82$

Solving (b); Point estimate of standard deviation

To do this, we simply calculate the sample standard deviation

$\sigma = \sqrt{\frac{\sum(x-\bar x)^2}{n - 1}$

$\sigma = \sqrt\frac{(87-82)^2+ (91-82)^2+ ....+ (79-82)^2+ (83-82)^2+ (96-82)^2}{12-1}$

$\sigma = \sqrt\frac{1022}{11}$

$\sigma = \sqrt{92.91}$

$\sigma = 9.64$

<em>Note that: The sample mean and the sample standard deviation are the best point estimators for the mean and the standard deviation, respectively.</em>

<em>Hence, the need to solve for sample mean and sample standard deviation</em>

3 0

3 years ago

Ms. Bell's mathematics class consists of 12 sophomores, 8 juniors, and 9 seniors. How many different ways can Ms. Bell create a

shtirl [24]

Answer:

792

Step-by-step explanation:

It's a combination question. The order is of no consequence. Also the fact that there are juniors and seniors is not important either.

So the answer is

12C5

12!

====

(12 - 5)! * 5!

12 * 11 * 10 * 9 * 8

==============

5 * 4 * 3 * 2 * 1

792

7 0

3 years ago

Can someone help me with 7 1/2 ÷ 1 9/10 please and thank you

Evgen [1.6K]

7 1/2÷ 1 9/10 = 15/2 ÷19/10 = 15/2x10/19 = 159/38 = 4 7/38

4 7/38 (Answer)
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38 )159
152
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4 0

3 years ago

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