Answer:
a = 
Step-by-step explanation:
Given:
f(x) = log(x)
and,
f(kaa) = kf(a)
now applying the given function, we get
⇒ log(kaa) = k × log(a)
or
⇒ log(ka²) = k × log(a)
Now, we know the property of the log function that
log(AB) = log(A) + log(B)
and,
log(Aᵇ) = b × log(A)
Thus,
⇒ log(k) + log(a²) = k × log(a) (using log(AB) = log(A) + log(B) )
or
⇒ log(k) + 2log(a) = k × log(a) (using log(Aᵇ) = b × log(A) )
or
⇒ k × log(a) - 2log(a) = log(k)
or
⇒ log(a) × (k - 2) = log(k)
or
⇒ log(a) = (k - 2)⁻¹ × log(k)
or
⇒ log(a) = 
(using log(Aᵇ) = b × log(A) )
taking anti-log both sides
⇒ a =
Answer:
261.8 in^3
Step-by-step explanation:
The formula for the volume of a cone is V = (1/3)(base)(height), where "base" is the area of the base.
In this case, with the radius being 5 in and the height 10 in, we get:
V = (1/3)*π*(5 in)^2*(10 in), which simplifies to 261.8 in^3.
If "a" and "b" are two values of x-coordinate, and "m" is the midpoint between them, it means the distance from one end to the midpoint is the same as the distance from the midpoint to the other end
... a-m = m-b
When we add m+b to this equation, we get
... a+b = 2m
Solving for m gives
... m = (a+b)/2
This applies to y-coordinates as well. So ...
... The midpoint between (x1, y1) and (x2, y2) is ((x1+x2)/2, (y1+y2)/2)
_____
Jennifer had (x1, y1) = (-4, 10) and (x2, y2) = (-2, 6). So her calculation would be
... midpoint = ((-4-2)/2, (10+6)/2) = (-6/2, 16/2) = (-3, 8)
Brandon had (x1, y1) = (9, -4) and (x2, y2) = (-12, 8). So his calculation would be
... midpoint = ((9-12)/2, (-4+8)/2) = (-3/2, 4/2) = (-1.5, 2)
Answer:
Therefore the mean and standard deviation of his total score if he plays a full 18 holes are 160 and 
respectively.
Step-by-step explanation:
Given that,
For the first 9 holes X:
E(X) = 80
SD(X)=13
For the second 9 holes Y:
E(Y) = 80
SD(Y)=13
For the sum W=X+Y, the following properties holds for means , variance and standard deviation :
E(W)=E(X)+E(Y)
and
V(W)=V(X)+V(Y)
⇒SD²(W)=SD²(X)+SD²(Y) [ Variance = (standard deviation)²]
∴E(W)=E(X)+E(Y) = 80 +80=160
and
∴
Therefore the mean and standard deviation of his total score if he plays a full 18 holes are 160 and respectively.
