Jordan flipped a coin 492 times. Which of the following would be a good estimate of the number of times the coin landed on heads? A.171 B.231 C.346 D.442

The length of the opposite side is the same as the length of the hypotenuse (they are the same side in this case), the ratio is:

sin(90 degrees) = 1 / 1 = 1

Thus, sin(90 degrees) equals 1.

In trigonometry, the sine function (abbreviated as sin) is defined based on the angles of a right-angled triangle.

Specifically, for a given angle θ in a right-angled triangle, the sine of θ is defined as the ratio of the length of the side opposite θ to the length of the hypotenuse (the longest side of the triangle, which is always opposite the right angle).

In a standard coordinate system, consider a right-angled triangle where one of the angles is 90 degrees (a right angle).

This angle is often denoted as π/2 radians in radians or 90 degrees in degrees.

In this triangle, the side opposite the angle θ (the side opposite the right angle) is the vertical side, and the hypotenuse is the longest side.

For a right-angled triangle with a 90-degree angle, the sine of θ is defined as:

sin(90 degrees) = length of opposite side / length of hypotenuse

Since the length of the opposite side is the same as the length of the hypotenuse (they are the same side in this case), the ratio is:

sin(90 degrees) = 1 / 1 = 1

Thus, sin(90 degrees) equals 1.

In radians, sin(π/2 radians) is also equal to 1 since it is the same angle as 90 degrees but measured in radians.

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Answer:

The answers are as follows:

5. c

6. b

7. not sure, sorry

8. b

Step-by-step explanation:

Answer:

The finalbank account amount will be $10,412.50, earning$7,012.50 in interest.

General Formulas and Concepts:
Algebra I

Simple Interest Rate Formula:

• A is the final amount
• P is the principle amount
• r is rate
• t is time

Step-by-step explanation:

Step 1: Define

Identify given variables.

P = $3,400

r = 0.0825

t = 25

Step 2: Find Interest

1. [Simple Interest Rate Formula] Substitute in variables:
   
2. Evaluate:
   

∴ the bank account will gain$7,012.50 and have a net balance of $10,412.50.

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Topic: Algebra I
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Final answer:

Using the formula for compound interest, we can find out that the sum of $3400, invested for 25 years at 8.25% annual interest compounded yearly, will amount to approximately $26358.85.

Explanation:

The question relates to calculating compound interest rather than simple interest. We're given $3400 as the principal, an annual interest rate of 8.25% and 25 years as the time period. We assume that the interest is compounded annually. Typically, we use the formula A=P(1+r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate in decimal form, n is the number of times that interest is compounded per unit t, t is the time the money is invested for.

Applying Formula

In this situation, r = 8.25/100 = 0.0825, P = $3400, t=25, and since it's yearly compounded n=1. Therefore, the equation becomes A = $3400 * (1+0.0825/1)^(1*25). The eventual amount will be approximately $26358.85. Thus, $26358.85 will be in the account after 25 years to the nearest cent.

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