290 million = 290,000,000
scientific notation would be 2.9 x 10^8
the 8 comes from the number of spaces you need to move the decimal point to the left to get 2.9
Given:
15. 
17. 
19. 
To find:
The values of the given logarithms by using the properties of logarithms.
Solution:
15. We have,
Using property of logarithms, we get
![[\because \log_aa=1]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Clog_aa%3D1%5D)
Therefore, the value of is 1.
17. We have,
Using properties of logarithms, we get
![[\because \log_a\dfrac{m}{n}=-\log_a\dfrac{n}{m}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Clog_a%5Cdfrac%7Bm%7D%7Bn%7D%3D-%5Clog_a%5Cdfrac%7Bn%7D%7Bm%7D%5D)
Therefore, the value of is -1.
19. We have,
Using property of logarithms, we get
![[\because a^{\log_ax}=x]](https://tex.z-dn.net/?f=%5B%5Cbecause%20a%5E%7B%5Clog_ax%7D%3Dx%5D)
Therefore, the value of is 100.
Answer:
The solution to this equation could not be determined.
Step-by-step explanation:
Simplifying
a(c + -1b) = d
Reorder the terms:
a(-1b + c) = d
(-1b * a + c * a) = d
(-1ab + ac) = d
Solving
-1ab + ac = d
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Combine like terms: d + -1d = 0
-1ab + ac + -1d = 0
The solution to this equation could not be determined.
Answer:
The probability that event B will occur is 0.45
Step-by-step explanation:
Given;
probability that event A occurs, P(A) = 0.4
the probability that events A and B both occur, P(A ∩ B) = 0.25
the probability that either event A or event B occurs, P(A ∪ B) = 0.6
To determine the probability that event B will occur, we use probability addition rule;
P(A) + P(B) = P(A ∩ B) + P(A ∪ B)
0.4 + P(B) = 0.25 + 0.6
0.4 + P(B) = 0.85
P(B) = 0.85 - 0.4
P(B) = 0.45
Therefore, the probability that event B will occur is 0.45
Answer:
area of a rectangle = 4(length × width)
