Answers
Answer:
y =293(1.06) ^x
y = 370 after 4 years
Step-by-step explanation:
If we are using the model for growth
y = a ( 1+b)^x
a is the initial population
b is the increase rate
We can substitute the values into the equation
y =293 (1+.06) ^ x
y =293(1.06) ^x
Let x equal 4 for the 4 years
y = 293(1.06)^4
y=369.9
Related Questions
find the area of a triangle with the given base and height
7ft, 2in
Answers
Answer:
A = 84 inches^2
Step-by-step explanation:
We know that the formula for the area of a triangle is given by
A = 1/2 b*h
Let's substitute what we know
We need the units to be the same
Convert 7 ft to inches
1 ft = 12 inches
Multiply both sides by 7
7 ft = 84 inches
A = 1/2 *84*2
A = 84 inches^2
7ft = 84 in
84 • 2 = 168
168 • 1/2 (/2) = 84
Area is 84 sq in or 7 sq ft
Write a sentence to represent the equation 4 m = -8.
Answers
Answer:
The product of 4 and m is -8.
Without numbers: The product of four and the variable m is negative eight.
Step-by-step explanation:
4m means m is multiplied by 4. The result of the multiplication operation is called a "product." The equal sign translates to "is".
The sentence 'Four times a certain number equals negative eight' corresponds to the equation 4m = -8, indicating that multiplying a number by four yields negative eight.
The sentence to represent the equation 4 m = -8 might be: "Four times a certain number equals negative eight." This sentence encapsulates the equation by specifying that the product of the number m and four is equivalent to negative eight, implying that m will have a negative value since it is equal to a negative number when multiplied by a positive.
Prove that u(n) is a group under the operation of multiplication modulo n.
Answers
Answer:
The answer is the proof so it is long.
The question doesn't define u(n), but it's not hard to guess.
Group G with operation ∘
For all a and b and c in G:
1) identity: e ∈ G, e∘a = a∘e = a,
2) inverse: a' ∈ G, a∘a' = a'∘a = e,
3) closed: a∘b ∈ G,
4) associative: (a∘b)∘c = a∘(b∘c),
5) (optional) commutative: a∘b = b∘a.
Define group u(n) for n prime is the set of integers 0 < i < n with operation multiplication modulo n.
If n isn't prime, we exclude from the group all integers which share factors with n.
Identity: e = 1. Clearly 1∘a = a∘1 = a. (a is already < n).
Closed: u(n) is closed for n prime. We must show that for all a, b ∈ u(n), the integer product ab is not divisible by n, so that ab ≢ 0 (mod n). Since n is prime, ab ≠ n. Since a < n, b < n, no factors of ab can equal prime n. (If n isn't prime, we already excluded from u(n) all integers sharing factors with n).
Inverse: for all a ∈ u(n), there is a' ∈ u(n) with a∘a' = 1. To find a', we apply Euclid's algorithm and write 1 as a linear combination of n and a. The coefficient of a is a' < n.
Associative and Commutative:
(a∘b)∘c = a∘(b∘c) because (ab)c = a(bc)
a∘b = b∘a because ab = ba.
Answer:
The answer is the proof so it is long.
The question doesn't define u(n), but it's not hard to guess.
Group G with operation ∘
For all a and b and c in G:
1) identity: e ∈ G, e∘a = a∘e = a,
2) inverse: a' ∈ G, a∘a' = a'∘a = e,
3) closed: a∘b ∈ G,
4) associative: (a∘b)∘c = a∘(b∘c),
5) (optional) commutative: a∘b = b∘a.
Define group u(n) for n prime is the set of integers 0 < i < n with operation multiplication modulo n.
If n isn't prime, we exclude from the group all integers which share factors with n.
Identity: e = 1. Clearly 1∘a = a∘1 = a. (a is already < n).
Closed: u(n) is closed for n prime. We must show that for all a, b ∈ u(n), the integer product ab is not divisible by n, so that ab ≢ 0 (mod n). Since n is prime, ab ≠ n. Since a < n, b < n, no factors of ab can equal prime n. (If n isn't prime, we already excluded from u(n) all integers sharing factors with n).
Inverse: for all a ∈ u(n), there is a' ∈ u(n) with a∘a' = 1. To find a', we apply Euclid's algorithm and write 1 as a linear combination of n and a. The coefficient of a is a' < n.
Associative and Commutative:
(a∘b)∘c = a∘(b∘c) because (ab)c = a(bc)
a∘b = b∘a because ab = ba.