n = 8
the sum to n terms of a geometric sequence is
=
where a is the first term and r the common ratio
here a = 16 and r = = = - 2
= ( 16( 1 - ( - 2 )^n )/1 - (- 2 )) = - 1360
( 1 - (- 2 )^n ) = - 1360
multiply both sides by
1 - (- 2 )^n = - 255
- (- 2 )^n = - 256
)-2)^n = 256
note that and = 256
hence n = 8
Answer:
Let p be a prime number. Suppose that a and n are positive numbers such that gcd(a, p) = 1 and gcd(n, p − 1) = 1.
Determine the number of solutions of the congruence x n ≡ a (mod p). Solution.
Let g be a primitive root modulo p. Since gcd(a, p) = 1, we can find an integer l such that a ≡ g l (mod p). In addition, since x ≡ 0 (mod p) is not a solution, we can write x ≡ g k (mod p) for some integer k.
Now the congruence can be written as g kn ≡ g l (mod p), which is equivalent to kn ≡ l (mod p − 1). This congruence can be solved in k by k ≡ ln−1 (mod p − 1) as gcd(n, p − 1) = 1, yielding a unique solution x ≡ g k (mod p) of the congruence x n ≡ a (mod p).
Step-by-step explanation:
Answer:
Plug this in a calculator and the answer will pop up.
Step-by-step explanation:
The values of x in the rectangles will be:
a. x = -3
b. x = 1
<h3>How to calculate the value?</h3>
It should be noted that the variables given in the rectangle will be equated. This will be:
3x + 18 = 24 + 5x
Collect like terms
5x - 3x = 18 - 24
2x = -6
x = -6/2 = -3
b. The value of x will be:
-4 + 9x = 5x
Collect like terms
9x - 5x = 4
4x = 4
x = 4/4
x = 1
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The percent markup of the sweatshirt is 60%
Here, we want to calculate the percenatge of profit made by the store
Mathematically;
From the question, we can deduce the following;
cost price is the price the store bought the sweatshirt = $12
sales price is the amount in which they sold the sweatshirt = $19.20
Thus, we proceed to substitute these values into the markup equation above;