Answer:
Peter ran 33 laps.
Step-by-step explanation:
Multiply Evelyn's 44 laps by 75% or 0.75 to get your answer.
44(0.75)=33
 
        
             
        
        
        
Answer:
Definition: The enclosing boundary of a curved geometric figure, especially a circle.
Step-by-step explanation:
 
        
             
        
        
        
Answer:
The volume of the pill is 
Step-by-step explanation:
Find the volume of the pill in cubic millimeters
we know that
The volume of the pill is equal to the volume of the cylinder plus the volume of a sphere (two hemisphere is equal to one sphere)
so
we have


assume

substitute

 
        
             
        
        
        
Answer:
Bias for the estimator = -0.56
Mean Square Error for the estimator = 6.6311
Step-by-step explanation:
Given - A normally distributed random variable with mean 4.5 and standard deviation 7.6 is sampled to get two independent values, X1 and X2. The mean is estimated using the formula (3X1 + 4X2)/8.
To find - Determine the bias and the mean squared error for this estimator of the mean.
Proof - 
Let us denote 
X be a random variable such that X ~ N(mean = 4.5, SD = 7.6)
Now,
An estimate of mean, μ is suggested as

Now
Bias for the estimator = E(μ bar) - μ
                                     = 
                                     = 
                                     = 
                                     = 
                                     = 
                                     = 3.9375 - 4.5
                                     = - 0.5625 ≈ -0.56
∴ we get
Bias for the estimator = -0.56
Now,
Mean Square Error for the estimator = E[(μ bar - μ)²]
                                                              = Var(μ bar) + [Bias(μ bar, μ)]²
                                                              = 
                                                              = 
                                                              = ![\frac{1}{64} ( [{3Var(X_{1}) + 4Var(X_{2})]  }) + 0.3136](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B64%7D%20%28%20%5B%7B3Var%28X_%7B1%7D%29%20%2B%204Var%28X_%7B2%7D%29%5D%20%20%7D%29%20%2B%200.3136)
                                                              = ![\frac{1}{64} [{3(57.76) + 4(57.76)}]  } + 0.3136](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B64%7D%20%5B%7B3%2857.76%29%20%2B%204%2857.76%29%7D%5D%20%20%7D%20%2B%200.3136)
                                                              = ![\frac{1}{64} [7(57.76)}]  } + 0.3136](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B64%7D%20%5B7%2857.76%29%7D%5D%20%20%7D%20%2B%200.3136)
                                                              = ![\frac{1}{64} [404.32]  } + 0.3136](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B64%7D%20%5B404.32%5D%20%20%7D%20%2B%200.3136)
                                                              = 
                                                               = 6.6311
∴ we get
Mean Square Error for the estimator = 6.6311
 
        
             
        
        
        
Step-by-step explanation:
let both unknowns be x and y
 x = 5y. ......(1)
x + y = 90. ......(2)
 sub eqn (1) into eqn (2)
 5y + y = 90
 6y = 90
 y = 90/6
 = 15
 sub y = 15 to eqn (1)
 x = 5y
 x = 5 × 15
 × = 75