Answer:
f(x) = 54(two-thirds) Superscript x minus 1
Step-by-step explanation:
Given that:
First peak : 36 / 54=2/3
Second peak : 24 / 36 = 2/3
The common ratio here is 2/3 ; which mean each bounce height is 2/3 of previous height
Modeling this using geometric progression :
An=a1r^(n-1)
An = nth term of a geometric progression
a1=first term
r=common ratio = 2/3
n = nth term
a1=54
Substituting into the above formular :
An=54(2/3)^(n-1)
Answer:
(a) E(X) = -2p² + 2p + 2; d²/dp² E(X) at p = 1/2 is less than 0
(b) 6p⁴ - 12p³ + 3p² + 3p + 3; d²/dp² E(X) at p = 1/2 is less than 0
Step-by-step explanation:
(a) when i = 2, the expected number of played games will be:
E(X) = 2[p² + (1-p)²] + 3[2p² (1-p) + 2p(1-p)²] = 2[p²+1-2p+p²] + 3[2p²-2p³+2p(1-2p+p²)] = 2[2p²-2p+1] + 3[2p² - 2p³+2p-4p²+2p³] = 4p²-4p+2-6p²+6p = -2p²+2p+2.
If p = 1/2, then:
d²/dp² E(X) = d/dp (-4p + 2) = -4 which is less than 0. Therefore, the E(X) is maximized.
(b) when i = 3;
E(X) = 3[p³ + (1-p)³] + 4[3p³(1-p) + 3p(1-p)³] + 5[6p³(1-p)² + 6p²(1-p)³]
Simplification and rearrangement lead to:
E(X) = 6p⁴-12p³+3p²+3p+3
if p = 1/2, then:
d²/dp² E(X) at p = 1/2 = d/dp (24p³-36p²+6p+3) = 72p²-72p+6 = 72(1/2)² - 72(1/2) +6 = 18 - 36 +8 = -10
Therefore, E(X) is maximized.
Example 1<span>
<span><span>verbose explicit high3 <span>plus </span>4 <span>cross </span>2 <span>minus </span><span>minus </span>2 <span>equals </span>3 <span>plus </span>8 <span>plus </span>2 <span>equals </span>1 3</span><span>verbose explicit high semantics3 <span>plus </span>4 <span>times </span>2 <span>minus </span><span>negative </span>2 <span>equals </span>3 <span>plus </span>8 <span>plus </span>2 <span>equals </span>13</span><span>verbose explicit high semantics high3 <span>plus </span>4 <span>times </span>2 <span>minus </span><span>negative </span>2 <span>equals </span>3 <span>plus </span>8 <span>plus </span>2 <span>equals </span>13</span></span>
</span>
For most fractions, the beginning is indicated with "start fraction", the horizontal line is indicated with "over", and the end of the fraction is indicated by "end fraction". For the semantic interpretation, most numeric fractions are spoken as they are in natural speech. Also if a number is followed by a numeric fraction, the word "and" is spoken in between.
Answer:
Step-by-step explanation:
length of rectangle = circumference of circle = πd = 6π cm
area of rectangle = 2×6π = 12π cm
area of one circle = πr² = 9π cm²
surface area = 12π + 2(9π) = 30π ≅ 90 cm²
