Answer:
see below
Step-by-step explanation:
butterfly = x minutes
breast = y minutes
total is 50 minutes
breast stroke = butterfly +20
Part A
x+y = 50 
y = x+20
Part B
Substitute the second equation into the first
x+ (x+20) = 50
2x+20 = 50
2x+20-20 = 50-20
2x = 30
2x/2 = 30/2
x = 15
y = x+20
y = 20+15
y = 35 minutes
35 minutes on the breast stroke
Part C
45 minutes on the butterfly is not reasonable
We only have a total of 50 minutes
50-45 = 5
But he spend more time on the breast stroke ( 20 minutes more), but if he spend 45 minutes on the butterfly, he would have to spend less on the breast stroke.
 
        
             
        
        
        
Answer:
 
 
So then the correct answer would be:
B) .9996
Step-by-step explanation:
The exact way to solve this problem is using the binomial distribution, assuming that our random variable of interest is "number of students living in apartments" represented by X and 
And we want this probability:
![P(200 \leq X \leq 400) [tex]In order to find this probability we can use the foloowing excel code:"=BINOM.DIST(400,600,0.4,TRUE)-BINOM.DIST(199,600,0.4,TRUE)"And we got:[tex] P(200 \leq X \leq 400) =0.999675[tex]But for this case the problem says that we need to approximate, so then we can use the normal approximation to the normal distribution. We need to check the conditions in order to use the normal approximation.
[tex]np=600*0.4=240\geq 10](https://tex.z-dn.net/?f=%20P%28200%20%5Cleq%20X%20%5Cleq%20400%29%20%5Btex%5D%3C%2Fp%3E%3Cp%3EIn%20order%20to%20find%20this%20probability%20we%20can%20use%20the%20foloowing%20excel%20code%3A%3C%2Fp%3E%3Cp%3E%22%3DBINOM.DIST%28400%2C600%2C0.4%2CTRUE%29-BINOM.DIST%28199%2C600%2C0.4%2CTRUE%29%22%3C%2Fp%3E%3Cp%3EAnd%20we%20got%3A%3C%2Fp%3E%3Cp%3E%5Btex%5D%20P%28200%20%5Cleq%20X%20%5Cleq%20400%29%20%3D0.999675%5Btex%5D%3C%2Fp%3E%3Cp%3EBut%20for%20this%20case%20the%20problem%20says%20that%20we%20need%20to%20approximate%2C%20so%20then%20we%20can%20use%20the%20normal%20approximation%20to%20the%20normal%20distribution.%20%3C%2Fp%3E%3Cp%3EWe%20need%20to%20check%20the%20conditions%20in%20order%20to%20use%20the%20normal%20approximation.%0A%3C%2Fp%3E%3Cp%3E%5Btex%5Dnp%3D600%2A0.4%3D240%5Cgeq%2010) 
 
So we see that we satisfy the conditions and then we can apply the approximation.
If we appply the approximation the new mean and standard deviation are:
 
 
And then 
And we are interested on the following probability:
 
 
So then the correct answer would be:
B) .9996
 
        
             
        
        
        
Answer:
x
=
4
or
x
=
−
4
Explanation:
First divide throughout by 
2
 to get
x
2
=
16
Now take the square root on both sides to get
x
=
±
4
.
You may now substitute the values of 
x
=
4
and
x
=
−
4
 back into the original equation and check that it satisfies the equation which it does.
Step-by-step explanation:
 
        
                    
             
        
        
        
Answer:
Steps shown in picture provided 
 
        
             
        
        
        
Answer:
for the triangle on top on side is 8 one side is 4 so if we use the theorem
64+16=80
a=9
so 
Side a = 19.8242
Side b = 17.66349
Side c = 9
Angle ∠A = 90° = 1.5708 rad = π/2
Angle ∠B = 63° = 1.09956 rad = 7/20π
Angle ∠C = 27° = 0.47124 rad = 3/20π
Area = 79.48573
Perimeter p = 46.4877
Semiperimeter s = 23.24385