This is what I found
Step-by-step explanation: <em>If you look at the figure, the angle marked red is equal to 70° because vertical angles are equal. So, that also means that the opposite angle 2 is also 70°. So, the first equation is:</em>
<em />
<em>70 = 5x + y</em>
<em />
<em>Next, the green angle as marked is equal to</em>
<em>Green angle = 180 - 70 = 110</em>
<em>Being vertical angles, angle 1 is then equal to 110°. So,the second equation is</em>
<em />
<em>110 = 5x + 3y</em>
<em />
<em>Subtract the two equations:</em>
<em />
<em> 5x + y = 70</em>
<em> - 5x + 3y = 110</em>
<em>________________</em>
<em> -3y = -40</em>
<em> y = -40/-3 = 13.33°</em>
<em />
<em>Substituting y to either one of the equations,</em>
<em>5x + 13.33 = 70</em>
<em>Solving for x,
</em>
<em>x = 11.33°</em>
<em />
Check the picture below.
![\bf \stackrel{area}{A}=length\cdot width\implies A(w)=(1000-2w)w \\\\\\ \boxed{A(w)=1000w-2w^2} \\\\\\ \cfrac{dA}{dw}=1000-4w\implies 0=1000-4w\implies 4w=1000 \\\\\\ w=\cfrac{1000}{4}\implies \boxed{w=\stackrel{width}{250}} \\\\\\\ [1000-2(250)]\implies 1000-500\implies \boxed{l=\stackrel{length}{500}}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Barea%7D%7BA%7D%3Dlength%5Ccdot%20width%5Cimplies%20A%28w%29%3D%281000-2w%29w%0A%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7BA%28w%29%3D1000w-2w%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7BdA%7D%7Bdw%7D%3D1000-4w%5Cimplies%200%3D1000-4w%5Cimplies%204w%3D1000%0A%5C%5C%5C%5C%5C%5C%0Aw%3D%5Ccfrac%7B1000%7D%7B4%7D%5Cimplies%20%5Cboxed%7Bw%3D%5Cstackrel%7Bwidth%7D%7B250%7D%7D%0A%5C%5C%5C%5C%5C%5C%5C%0A%5B1000-2%28250%29%5D%5Cimplies%201000-500%5Cimplies%20%5Cboxed%7Bl%3D%5Cstackrel%7Blength%7D%7B500%7D%7D)
and if you run a first-derivative test on say x = 249 and x = 251, you'll notice the slope is positive and negative respectively, meaning, is a maximum.
Answer:
0.3 chance of not drawing a blue marble.
Step-by-step explanation:
This problem can be found using the theoretical probability formula.
The formula is: P (desired outcome) = <u># of desired outcomes</u>
total number of outcomes
Now all you have to do is input the numbers into the equation.
P(not drawing a blue marble) = <u>3</u>
10
3/10 is equal to 0.3 as a decimal.
40 mph would be 120 miles in 3 hours (120/40)
80 mph is 120 miles in 1.5 hours(120/80)
3 - 1.5 = 1.5, not 3 hrs
Change the speed to 20 mph( 1/2 the speed) to double the hours.
20 mph = 6 hours(120/20)
40 mph = 3 hrs(120/40)
6 - 3 = 3 hours difference
