![\huge\text{$k=\boxed{117}$}](https://tex.z-dn.net/?f=%5Chuge%5Ctext%7B%24k%3D%5Cboxed%7B117%7D%24%7D)
![\displaystyle\frac{k}{3}-5=34](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7Bk%7D%7B3%7D-5%3D34)
To find the value of
, we need to isolate it on one side of the equation. Add
to both sides of the equation, then multiply both sides of the equation by
.
![\displaystyle\begin{aligned}\frac{k}{3}-5+5&=34+5\\\frac{k}{3}&=39\\\frac{k}{3}*3&=39*3\\k&=\boxed{117}\end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cbegin%7Baligned%7D%5Cfrac%7Bk%7D%7B3%7D-5%2B5%26%3D34%2B5%5C%5C%5Cfrac%7Bk%7D%7B3%7D%26%3D39%5C%5C%5Cfrac%7Bk%7D%7B3%7D%2A3%26%3D39%2A3%5C%5Ck%26%3D%5Cboxed%7B117%7D%5Cend%7Baligned%7D)
Answer:
48 liters
Step-by-step explanation:
First container = x
Second container has twice as much oil.
Second container = 2x
13 liters of oil was used from first container.
x - 13
7 liters of oil was used from the second container.
2x - 7
Second container has 3 times more oil than the first one.
2x - 7 = 3(x - 13)
x - 7 = 3(x - 13)
x - 7 = 3x - 39
2x = 32
x = 16
First container = 16 liters
second container = 16 x 2 = 32 liters
Total = 16 + 32 = 48 liters
Answer:
Step-by-step explanation:
tan (40) = x/12
x = 12*tan(40)
Answer:
x = (74-28)/2
Step-by-step explanation:
We find the perimeter of a triangle by adding the sides together
s1 +s2+s3 = P
The perimeter is 74
s1 +s2+s3 = 74
We know one of the sides is 28
28 +s2+s3 = 74
The other two sides are equal in length, call them x
28 +x+x = 74
Combine like terms
28+2x = 74
We want to solve for x
Subtract 28 from each side
28-28+2x = 74-28
2x = 74-28
Divide each side by 2
2x/2 = (74-28)/2
x = (74-28)/2
Answer: It is believed that exactly 20% of Evergreen Valley college students attended the opening night midnight showing of the latest harry potter movie.
Step-by-step explanation:
Since we have given that
n = 84
x = 11
So, ![\hat{p}=\dfrac{x}{n}=\dfrac{11}{84}=0.13](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%3D%5Cdfrac%7Bx%7D%7Bn%7D%3D%5Cdfrac%7B11%7D%7B84%7D%3D0.13)
p = 0.20
So, hypothesis:
![H_0:p=\hat{p}\\\\H_a:\hat{p}](https://tex.z-dn.net/?f=H_0%3Ap%3D%5Chat%7Bp%7D%5C%5C%5C%5CH_a%3A%5Chat%7Bp%7D%3Cp)
so, test statistic value would be
![z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\z=\dfrac{0.13-0.20}{\sqrt{\dfrac{0.2\times 0.8}{84}}}\\\\z=-1.604](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B%5Chat%7Bp%7D-p%7D%7B%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%7D%7D%5C%5C%5C%5Cz%3D%5Cdfrac%7B0.13-0.20%7D%7B%5Csqrt%7B%5Cdfrac%7B0.2%5Ctimes%200.8%7D%7B84%7D%7D%7D%5C%5C%5C%5Cz%3D-1.604)
At 1% level of significance, critical value would be
z= 2.58
Since 2.58>-1.604
So, We will accept the null hypothesis.
Hence, It is believed that exactly 20% of Evergreen Valley college students attended the opening night midnight showing of the latest harry potter movie.