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:
The probability the student studies Art and
Biology is 0.2143.
Step-by-step explanation:
Denote the events as follows:
A = a students studies Art
B= a students studies Biology
The information provided is:
N = 42
n (An B) = 9
n (A' n B) = 10
n (A' n B') =7
Then the number of students who study Art
but not Biology is:
n(An B') = N -n (An B) -n (A' nB) - n (A'n B')
= 42 - 10 - 7 - 9
= 16
The number of students who study Art but
not Biology is 16.
Compute the probability the student studies
Art and Biology as follows:
P(ANB)
n(ANB)
= 0.2143
Thus, the probability the student studies Art
and Biology is 0.2143.
Answer:
simple interest
Step-by-step explanation:
this is because r is interest rate, p is principal, and t is time
Answer:
Step-by-step explanation:
Area of the trapezoid = area of rectangle + 2 * area of triangle
Area of a triangle = 1/2 bh
= 1/2 * 13 * 7
= 45.5 units²
Area of a rectangle = L × B
= 15 × 13
= 195 units²
Area of the trapezoid = [195 + 2 * (45.5)]
= 195 + 91
= 286 units²
