Step-by-step explanation:
(72)¹⁴³ ≡ x (mod 7)
Since 72 ≡ 2 (mod 7),
72³ ≡ 2³ (mod 7) ≡ 1 (mod 7).
Therefore (72)¹⁴³ = (72³)⁴⁷ * (72²)
≡ 1⁴⁷ * 4 (mod 7) ≡ 4 (mod 7).
The answer is A.
Answer:
In a certain animal shelter, the ratio of the number of dogs to the number of cats is 15 to 7. If 12 additional cats were to be taken in by the shelter, the ratio of the number of dogs to the number of cats would be 15 to 11. How many dogs are in the shelter?
A. 15
B. 25
C. 30
D. 45
E. 60
Answer:

Step-by-step explanation:
The PDF of X is
The PDF of Y is
The means of X and Y are respectively,
so we can see that the larger the parameter, the smaller the mean. Hence the PDF of Z = min(X, Y) is an exponential with the largest parameter of the two.
Therefore, the PDF of Z is
Answer:
R { - 6, 6 }
Step-by-step explanation:
To find the range substitute the values of x from the domain into f(x)
f(- 1) = - 4(- 1) + 2 = 4 + 2 = 6
f(2) = - 4(2) + 2 = - 8 + 2 = - 6
Range { - 6, 6 }