Answer:
Mai
Step-by-step explanation:
To find the rate, you must determine who is going faster per minute. To do this, you must divide the total number of miles by the total number of minutes.
Mai: 5 miles / 15 minutes = 1/3 miles per minute
Jada: 4 miles / 14 minutes = 2/7 miles per minute 
Then, use a common denominator to make calculations easier:
Mai: 1/3 * 7/7
Jada: 2/7 * 3/3
You should get:
Mai: 7/21 miles per minute
Jada: 6/21 miles per minute
By looking at this, you can see that Mai is traveling slightly faster, going more miles than Jada per minute.
 
        
             
        
        
        
<span> b4 + b3 - 45b2 - 27b + 25
—————————————————————————
b2 </span>
        
                    
             
        
        
        
Answer:
 
      
Step-by-step explanation:
We have to find the equation of plane that is parallel to the vectors

The plane also passes through the point (2,0,-1).
Hence, the equation of plane s given by:
![\displaystyle\left[\begin{array}{ccc}x-2&y-0&z+1\\3&0&3\\0&1&3\end{array}\right]\\\\=(x-2)(0-3) - (y-0)(9-0) + (z+1)(3-0)\\=-3(x-2)-9y+3(z+1)\\\Rightarrow -3x + 6 - 9y + 3z + 3 = 0\\\Rightarrow 3x + 9y -3z -9 = 0\\\Rightarrow x + 3y -z - 3 = 0](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx-2%26y-0%26z%2B1%5C%5C3%260%263%5C%5C0%261%263%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%3D%28x-2%29%280-3%29%20-%20%28y-0%29%289-0%29%20%2B%20%28z%2B1%29%283-0%29%5C%5C%3D-3%28x-2%29-9y%2B3%28z%2B1%29%5C%5C%5CRightarrow%20-3x%20%2B%206%20-%209y%20%2B%203z%20%2B%203%20%3D%200%5C%5C%5CRightarrow%203x%20%2B%209y%20-3z%20-9%20%3D%200%5C%5C%5CRightarrow%20x%20%2B%203y%20-z%20-%203%20%3D%200)
It is the required equation of plane.
 
        
             
        
        
        
General Idea:
If we have a quadratic function of the form f(x)=ax^{2} +bx+c , then the function will attain its maximum value only if a < 0 & its maximum value will be at x=-\frac{b}{2a} .
Applying the concept:
The height h is modeled by h = −16t^2 + vt + c, where v is the initial velocity, and c is the beginning height of the firecracker above the ground. The firecracker is placed on the roof of a building of height 15 feet and is fired at an initial velocity of 100 feet per second. Substituting 15 for c and 100 for v, we get the function as  .
.
Comparing the function f(x)=ax^{2} +bx+c with the given function  , we get
, we get  ,
,  and
 and  .
.
The maximum height of the soccer ball will occur at t=\frac{-b}{2a}=\frac{-100}{2(-16)} = \frac{-100}{-32}=3.125 seconds 
The maximum height is found by substituting  in the function as below:
 in the function as below:

Conclusion:
<u>Yes !</u> The firecracker reaches a height of 100 feet before it bursts. 
 
        
             
        
        
        
Answer:
Step-by-step explanation:
Given that in a sample of 800 U.S. adults, 199 think that most celebrities are good role models. Two Two U.S. adults are selected at random from the population of all U.S. adults without replacement. 
In 800 adults 199 are favourable and remaining 601 are against.
a) The probability that both adults think most celebrities are good role models is ________= Prob of selecting both from 199
= 
=0.062
b) The probability that neither adult thinks most celebrities are good role models is _______=P(both selecting from 601)
=  
=0.564
c) The probability that at least one of the two adults thinks most celebrities are good role models ______
=1-Prob that neither thinks 
= 1- 0.564
= 0.436