Answer:
 
  
Now we can calculate the p value with the following probability:
 
  
Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true proportion for this case is higher than 0.5
Step-by-step explanation:
Data given and notation 
n=75 represent the random sample taken
 estimated proportion of interest
 estimated proportion of interest
 is the value that we want to test
 is the value that we want to test
 represent the significance level
 represent the significance level
Confidence=95% or 0.95
z would represent the statistic 
 represent the p value
 represent the p value 
System of hypothesis
We want to verify if the true proportion is higher than 0.5:  
Null hypothesis: 
  
Alternative hypothesis: 
  
The statistic is given by:
 (1)
 (1)  
Replacing the info given we got:
 
  
Now we can calculate the p value with the following probability:
 
  
Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true proportion for this case is higher than 0.5
 
        
             
        
        
        
Answer:
Center: (-9, -7)
Radius: 5
Step-by-step explanation:
 
        
                    
             
        
        
        
Answer:
18.8 cubic inches 
Step-by-step explanation:
✔️Amount of juice Cup B will hold than Cup A = Volume of cup B - volume of cup A
✔️Volume of Cup B = Volume of cylinder = πr²h
radius (r) = ½ of 2 = 1 in.
height (h) = 7 in.
Volume of cup B = π*1²*7 = 21.99 in.³
✔️Volume of Cup A = Volume of cone = ⅓πr²h
radius (r) = ½ of 2 = 1 in.
height (h) = 3 in.
Volume of cup B = ⅓*π*1²*3 = 3.14 in.³
✔️Amount of juice Cup B will hold than Cup A = 21.99 in.³ - 3.14 in.³ = 18.8 in.³ (nearest tenth)
 
        
             
        
        
        
Answer:
64-63=1 so she drove 1 extra miles the second month
Step-by-step explanation:
 
        
             
        
        
        
Step-by-step explanation:
(1 - cos²A) (1 + tan²A) = tan²A
(sin²A)(sec²A) = tan²A
(sin²A)(1/cos²A) = tan²A
(sin²A)/(cos²A) = tan²A
tan²A = tan²A → <u>Proved</u>