Answer:
V = 34,13*π cubic units
Step-by-step explanation: See Annex
We find the common points of the two curves, solving the system of equations:
y² = 2*x x = 2*y ⇒ y = x/2
(x/2)² = 2*x
x²/4 = 2*x
x = 2*4 x = 8 and y = 8/2 y = 4
Then point P ( 8 ; 4 )
The other point Q is Q ( 0; 0)
From these two points, we get the integration limits for dy ( 0 , 4 )are the integration limits.
Now with the help of geogebra we have: In the annex segment ABCD is dy then
V = π *∫₀⁴ (R² - r² ) *dy = π *∫₀⁴ (2*y)² - (y²/2)² dy = π * ∫₀⁴ [(4y²) - y⁴/4 ] dy
V = π * [(4/3)y³ - (1/20)y⁵] |₀⁴
V = π * [ (4/3)*4³ - 0 - 1/20)*1024 + 0 )
V = π * [256/3 - 51,20]
V = 34,13*π cubic units
Answer: the smallest number of people required for the sample to meet the conditions for performing inference is 100
Step-by-step explanation:
Given that;
36% of US population has never been married
32% are divorced
27% are married
5% are widowed
Taking a simple random sample of individuals to test this claim;
we need expected count in each cell to be at least 5, here the smallest proportion is 5% = 0.05
so we only need to satisfy condition for its expected count;
n × 0.05 ≥ 5
n = 5 / 0.05 = 100
Therefore the smallest number of people required for the sample to meet the conditions for performing inference is 100
Answer:
n + 5/5 = -9
Step-by-step explanation:
Answer:
x=16
Step-by-step explanation:
(whole secant) x (external part) = (tangent)^2
(8+24) * 8 = x^2
32*8 = x^2
256 =x^2
Take the square root of each side
sqrt(256) = sqrt(x^2)
16 = x
Answer:
<em>Option A; the tournament did begin with 128 teams</em>
Step-by-step explanation:
We can see that this equation is represented by compound interest, in other words an exponential function, either being exponential growth or exponential decay;
f ( x ) = a + ( b )^x, where a ⇒ start value, b ⇒ constant, x ⇒ ( almost always considered ) time, but in this case rounds
Option A; The equation is given to be t ( x ) = 128 * ( 1/2 )^x. Given by the above, 128 should represent the start value, hinting that the tournament <em>did indeed begin with 128 teams</em>
Option B; As the rounds increase the number of teams approach 128. Now mind you 128 is the start value, not the end value, which would mean that <em>this statement is false</em>
Option C; The tournament began with 1/2 teams. Theoretically that would not be possible, but besides that the tournament began with 128 teams, only differed by 1/2 times as much every round. <em>This statement is thus false</em>
Option D; This situation actually represents exponential decay. If each round the number of teams differed by 1/2 times as much, the number of teams remaining is less than before, and thus this models exponential decay, not growth<em> ( statement is false )</em>
<em>Answer : Option A; the tournament did begin with 128 teams</em>
