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SSSSS [86.1K]
3 years ago
9

3. Write an exponential equation for each coin that will give the coin's value, V, at any time, t. Use

Mathematics
1 answer:
Sloan [31]3 years ago
7 0

Answer:

Coin A : V(t)=25(1.07)^t

Coin B : V(t)=40(1.05)^t

Step-by-step explanation:

Consider the given formula is  

V(t)=P(1+r)^t

where, P is current value, V(t) is the value of the coin in t years, and r is annual appreciation rate.

For coin A, current value is 25 dollars and annual appreciation rate is 7%.

V(t)=25(1+0.07)^t

V(t)=25(1.07)^t

For coin B, current value is 40 dollars and annual appreciation rate is 5%.

V(t)=40(1+0.05)^t

V(t)=40(1.05)^t

Therefore, the required equations for coin A and B are V(t)=25(1.07)^t and V(t)=40(1.05)^t respectively.

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Answer:

Choice number one:

\displaystyle \frac{5}{10}\cdot \frac{4}{9}.

Step-by-step explanation:

  • Let A be the event that the number on the first card is even.
  • Let B be the event that the number on the second card is even.

The question is asking for the possibility that event A and B happen at the same time. However, whether A occurs or not will influence the probability of B. In other words, A and B are not independent. The probability that both A and B occur needs to be found as the product of

  • the probability that event A occurs, and
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5 out of the ten numbers are even. The probability that event A occurs is:

\displaystyle P(A) = \frac{5}{10}.

In case A occurs, there will only be four cards with even numbers out of the nine cards that are still in the bag. The conditional probability of getting a second card with an even number on it, given that the first card is even, will be:

\displaystyle P(B|A) = \frac{4}{9}.

The probability that both A and B occurs will be:

\displaystyle P(A \cap B) = P(B\cap A) =  P(A) \cdot P(B|A) = \frac{5}{10}\cdot \frac{4}{9}.

6 0
3 years ago
Pythagorean triples are given by the formulas x2 - y2, 2xy, and x2 + y2. Use the formulas for the Pythagorean triples to prove w
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Let k be an integer. Suppose there is a triangle with legs of length 16 and 2k+1. Then by the Pythagorean theorem, the length of the hypotenuse should be

\sqrt{16^2+(2k+1)^2}=\sqrt{4k^2+4k+257}

The formulas for Pythagorean triples say that if the legs are integers, then so must be the hypotenuse, because if x=16 and y=2k+1 are integers, then so are x^2-y^2, 2xy, and x^2+y^2.

However, 4k^2+4k+257 is not a perfect square trinomial, which means for any integer k, the length of the hypotenuse is not an integer, so such a triangle doesn't exist.
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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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3 years ago
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Answer:

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