Answer:
169.04 in² (nearest hundredth)
Step-by-step explanation:
Surface area of a cone =  r² +
r² +  r
r
(where r = radius of the base and  = slant height)
 = slant height)
Given slant height  = 10 and surface area = 188.5
 = 10 and surface area = 188.5
Surface area  =  r² +
r² +  r
r
188.5 =  r² + 10
r² + 10 r
r
  r² + 10
r² + 10 r - 188.5 = 0
r - 188.5 = 0
r =  = 4.219621117...
 = 4.219621117...
Volume of a cone = (1/3) r²h
r²h
(where r = radius of the base and h = height)
We need to find an expression for h in terms of  using Pythagoras' Theorem a² + b² = c², where a = radius, b = height and c = slant height
 using Pythagoras' Theorem a² + b² = c², where a = radius, b = height and c = slant height
r² + h² =  ²
²
h² =  ² - r²
² - r²
h = √( ² - r²)
² - r²)
Therefore, substituting found expression for h:
volume of a cone = (1/3) r²√(
r²√( ² - r²)
² - r²)
Given slant height  = 10 and r = 4.219621117...
 = 10 and r = 4.219621117...
volume = 169.0431969... = 169.04 in² (nearest hundredth)
 
        
                    
             
        
        
        
8[2] + 6[2] = c[2]
64 + 36 = c[2]
100 = c[2]
c = 10
8 + 6 + 10 = 24 units
        
                    
             
        
        
        
The answer is any whole number larger than 3
        
             
        
        
        
The formula for volume of a sphere is V = 4
/3 x π x r3 (cubed).
The original radius of the balloon is 10 ft, so when we plug that value into the equation we get 4188.79. When the balloon deflated, the new radius was 5 ft, so the new volume is 523.6. The question asks how much volume was lost, so we need to subtract 4188.79 - 523.6 and get approximately 3665.
Hope this helps! I hate taking usa test prep quizzes too haha.
 
        
             
        
        
        
Answer:

Step-by-step explanation:
<u>Probabilities</u>
When we choose from two different sets to form a new set of n elements, we use the so-called hypergeometric distribution. We'll use an easier and more simple approach by the use of logic.
We have 6 republicans and 4 democrats applying for two positions. Let's call R to a republican member and D to a democrat member. There are three possibilities to choose two people from the two sets: DD, DR, RR. Both republicans, both democrats and one of each. We are asked to compute the probability of both being from the same party, i.e. the probability is

Let's compute P(DD). Both democrats come from the 4 members available and it can be done in  different ways.
 different ways. 
For P(RR) we proceed in a similar way to get  different ways.
 different ways. 
The total ways to select both from the same party is

The selection can be done from the whole set of candidates in  different ways, so
 different ways, so

