The usual margin of error we strive for is a 95% probability that our estimate is within the margin. Assuming a normal distribution (and that we have a big enough sample not to worry about t tests) that corresponds to between minus and plus two standard deviations of the mean (remember the 68-95-99.7 rule). So our margin of error is plus or minus two standard deviations.
Answer: ±2%
Step 1
<u>Find the value of x</u>
we know that
-------> by corresponding angles, because the given lines are parallel
Solve for x
![(x-1)\°=74\°\\x=74+1 \\ x=75\°](https://tex.z-dn.net/?f=%28x-1%29%5C%C2%B0%3D74%5C%C2%B0%5C%5Cx%3D74%2B1%20%5C%5C%20x%3D75%5C%C2%B0)
Step 2
<u>Find the value of y</u>
we know that
![(x-1)+40+(y-2)=180](https://tex.z-dn.net/?f=%28x-1%29%2B40%2B%28y-2%29%3D180)
substitute the value of x and solve for y
![(75-1)+40+(y-2)=180](https://tex.z-dn.net/?f=%2875-1%29%2B40%2B%28y-2%29%3D180)
![74+40-2+y=180](https://tex.z-dn.net/?f=74%2B40-2%2By%3D180)
![112+y=180](https://tex.z-dn.net/?f=112%2By%3D180)
![y=180-112](https://tex.z-dn.net/?f=y%3D180-112)
![y=68\°](https://tex.z-dn.net/?f=y%3D68%5C%C2%B0)
therefore
<u>the answer is the option B</u>
![x=75\°, y=68\°](https://tex.z-dn.net/?f=x%3D75%5C%C2%B0%2C%20y%3D68%5C%C2%B0)
Answer : Distance between the ships to the nearest miles = 106.03 ≈ 106 mi.
Explanation :
Since we have shown in the figure below :
a=70 mi.
b=52 mi.
c=x mi.
![\text{Since two ships leaves the same port in different directions forming a }120\textdegree\text{angle between them.}](https://tex.z-dn.net/?f=%5Ctext%7BSince%20two%20ships%20leaves%20the%20same%20port%20in%20different%20directions%20forming%20a%20%7D120%5Ctextdegree%5Ctext%7Bangle%20between%20them.%7D)
So, we use the cosine rule , which states that
![c^2=a^2+b^2-2ab.cosC\\\\x^2=70^2+52^2-2\times 70\times 52\times cos(120\textdegree)\\\\x^2=4900+2704-7280\times (-0.5)\\\\x^2=7604+3640\\\\x^2=11244\\\\x=\sqrt{11244}\\\\x=106.03](https://tex.z-dn.net/?f=c%5E2%3Da%5E2%2Bb%5E2-2ab.cosC%5C%5C%5C%5Cx%5E2%3D70%5E2%2B52%5E2-2%5Ctimes%2070%5Ctimes%2052%5Ctimes%20cos%28120%5Ctextdegree%29%5C%5C%5C%5Cx%5E2%3D4900%2B2704-7280%5Ctimes%20%28-0.5%29%5C%5C%5C%5Cx%5E2%3D7604%2B3640%5C%5C%5C%5Cx%5E2%3D11244%5C%5C%5C%5Cx%3D%5Csqrt%7B11244%7D%5C%5C%5C%5Cx%3D106.03)
So, c = x= 106.03 mi.
Hence, distance between the ships to the nearest miles = 106.03 ≈ 106 mi.
Step-by-step explanation:
2x + 2x + 2 = 4x + 2 <em>combine like terms</em>
4x + 2 = 4x + 2 <em>subtract 4x from both sides</em>
4x - 4x + 2 = 4x - 4x + 2
2 = 2 TRUE
<h2>CONCLUSION:</h2><h3>This equation has an infinitely many solutions. The solution to this equation is any real number.</h3>
10 is the least common multiple of 5 and 2