Use the quadratic formula to find the solutions.<span><span><span><span>−b</span>±<span>√<span><span>b2</span><span><span>−4</span><span>(<span>ac</span>)</span></span></span></span></span><span>2a</span></span><span><span><span>-b</span>±<span><span>b2</span><span><span>-4</span><span>ac</span></span></span></span><span>2a</span></span></span>Substitute the values <span><span>a=5</span><span>a=5</span></span>, <span><span>b=<span>−3</span></span><span>b=<span>-3</span></span></span>, and <span><span>c=<span>−4</span></span><span>c=<span>-4</span></span></span> into the quadratic formula and solve for <span>xx</span>.<span><span><span>3±<span>√<span><span><span>(<span>−3</span>)</span>2</span><span><span>−4</span>⋅<span>(<span>5⋅<span>−4</span></span>)</span></span></span></span></span><span>2⋅5</span></span><span><span>3±<span><span><span>-3</span>2</span><span><span>-4</span>⋅<span>5⋅<span>-4</span></span></span></span></span><span>2⋅5</span></span></span>Simplify.Tap for more steps...<span><span>x=<span><span>3±<span>√89</span></span>10</span></span><span>x=<span><span>3±89</span>10</span></span></span>The result can be shown in both exact and approximate form.<span><span>x=<span><span>3±<span>√89</span></span>10</span></span><span>x=<span><span>3±89</span>10</span></span></span><span>x≈1.24339811,<span>−<span>0.64339811</span></span></span>
Answer:
Option C
Step-by-step explanation:
Assuming P represents the number of outcomes, n the number of competitors and r the number of places to be awarded....
![P = n! / ( n - r )!\\P = 8! / ( 8 - 3 )!\\P = 8! / 5!\\\\Algebra, P = 336 \\Solution = Option C](https://tex.z-dn.net/?f=P%20%3D%20n%21%20%2F%20%28%20n%20-%20r%20%29%21%5C%5CP%20%3D%208%21%20%2F%20%28%208%20-%203%20%29%21%5C%5CP%20%3D%208%21%20%2F%205%21%5C%5C%5C%5CAlgebra%2C%20P%20%3D%20336%20%5C%5CSolution%20%3D%20Option%20C)
There are 336 different possible ways for the winners to be chosen.
<u><em>Hope that helps!</em></u>
Answer:
About 30%
Step-by-step explanation:
1) figure out how many people didn't respond: 1334-931=403
2) divide small number by big number(nearest tenth): 403/1334=.30
3) move decimal to the right two times: 20%
<u>Given</u>:
The given equation is ![q+\log _{2}(6)=2 q+2](https://tex.z-dn.net/?f=q%2B%5Clog%20_%7B2%7D%286%29%3D2%20q%2B2)
We need to determine the approximate value of q.
<u>Value of q:</u>
To determine the value of q, let us solve the equation for q.
Hence, Subtracting
on both sides of the equation, we get;
![q=2 q+2-\log _{2}(6)](https://tex.z-dn.net/?f=q%3D2%20q%2B2-%5Clog%20_%7B2%7D%286%29)
Subtracting both sides of the equation by 2q, we have;
![-q=2-\log _{2}(6)](https://tex.z-dn.net/?f=-q%3D2-%5Clog%20_%7B2%7D%286%29)
Dividing both sides of the equation by -1, we have;
![q=\log _{2}(6)-2](https://tex.z-dn.net/?f=q%3D%5Clog%20_%7B2%7D%286%29-2)
Now, substituting the value of
, we have;
![q=2.585-2](https://tex.z-dn.net/?f=q%3D2.585-2)
Subtracting the values, we get;
![q=0.585](https://tex.z-dn.net/?f=q%3D0.585)
Thus, the approximate value of q is 0.585
Hence, Option C is the correct answer.