Answer:
Attached is your answer.
Step-by-step explanation:
Hope it helps you!!
The congruence theorems or postulates could be given as reasons why LMN is congruent to OPQ are LA and AAS.
<h3>What is
congruence theorems?</h3>
Congruence theorems is one that explain that in a case whereby three sides of two triangles are equal to another, we can say they are congruent to each other.
From the given figure, there are two angles as well as one non-included side which is seen to be a congruent.
According to LA theorem , a triangle is congruent in a case whereby, leg as well as an acute angle of one right triangle of two right triangles are congruent to each other.
AAS theorem also explains that incase two angles and any of the side of a triangle are congruent to each other , the triangles are congruent.
Therefore, with these theorem, congruence theorems or postulates could be given as reasons why LMN is congruent to OPQ are LA and AAS.
CHECK THE FIQURE FOR THE COMNPLETE QUESTION
Learn more about congruence theorems from
brainly.com/question/17239468
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You roll a 6 sided die, and am trying to get a number 3. You have a 1/6 chance of getting the number
The probability of getting a heads tossing a coin is half, because there is only two sides.
Multiply the two fractions together:
1/6 x 1/2 = 1/12
B) 1/12 is your answer
hope this helps
We split [2, 4] into
subintervals of length
,
![[2,4]=\left[2,2+\dfrac2n\right]\cup\left[2+\dfrac2n,2+\dfrac4n\right]\cup\left[2+\dfrac4n,2+\dfrac6n\right]\cup\cdots\cup\left[2+\dfrac{2(n-1)}n,4\right]](https://tex.z-dn.net/?f=%5B2%2C4%5D%3D%5Cleft%5B2%2C2%2B%5Cdfrac2n%5Cright%5D%5Ccup%5Cleft%5B2%2B%5Cdfrac2n%2C2%2B%5Cdfrac4n%5Cright%5D%5Ccup%5Cleft%5B2%2B%5Cdfrac4n%2C2%2B%5Cdfrac6n%5Cright%5D%5Ccup%5Ccdots%5Ccup%5Cleft%5B2%2B%5Cdfrac%7B2%28n-1%29%7Dn%2C4%5Cright%5D)
so that the right endpoints are given by the sequence
![x_i=2+\dfrac{2i}n=\dfrac{2(n+i)}n](https://tex.z-dn.net/?f=x_i%3D2%2B%5Cdfrac%7B2i%7Dn%3D%5Cdfrac%7B2%28n%2Bi%29%7Dn)
for
. Then the Riemann sum approximating
![\displaystyle\int_2^42x\,\mathrm dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_2%5E42x%5C%2C%5Cmathrm%20dx)
is
![\displaystyle\sum_{i=1}^nf(x_i)\dfrac{4-2}n=\frac8{n^2}\sum_{i=1}^n(n+i)=\frac8{n^2}\left(n^2+\frac{n(n+1)}2\right)=\frac{12n+4}n](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bi%3D1%7D%5Enf%28x_i%29%5Cdfrac%7B4-2%7Dn%3D%5Cfrac8%7Bn%5E2%7D%5Csum_%7Bi%3D1%7D%5En%28n%2Bi%29%3D%5Cfrac8%7Bn%5E2%7D%5Cleft%28n%5E2%2B%5Cfrac%7Bn%28n%2B1%29%7D2%5Cright%29%3D%5Cfrac%7B12n%2B4%7Dn)
The integral is given exactly as
, for which we get
![\displaystyle\int_2^42x\,\mathrm dx=\lim_{n\to\infty}\frac{12n+4}n=12](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_2%5E42x%5C%2C%5Cmathrm%20dx%3D%5Clim_%7Bn%5Cto%5Cinfty%7D%5Cfrac%7B12n%2B4%7Dn%3D12)
To check: we have
![\displaystyle\int_2^42x\,\mathrm dx=x^2\bigg|_2^4=4^2-2^2=16-4=12](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_2%5E42x%5C%2C%5Cmathrm%20dx%3Dx%5E2%5Cbigg%7C_2%5E4%3D4%5E2-2%5E2%3D16-4%3D12)
Answer:
$1346.40
Step-by-step explanation:
Find the volume of the pool first:
volume = cubiod + triangular prism
volume = (8*6*8) + (8*6*6)/2
volume = 528 cubic feet
price = price per cubic foot * cubic feet
price = $2.55 * 528 cubic feet
price = $1346.40