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Answer: 100(pi)/9

Step-by-step explanation:

We use the equation (theta/360)(2)(pi)(r)

Theta = 100 (100 degrees of a 360 degree circle)

r = 10 (not 20 because that is the whole needle, we need half of 20 for the radius)

Plugging this in: 100/360 (2)(pi)(10)

2,000(pi)/360

Divide by 20 to simplify:

Final answer:

The sales tax on an item costing $5 with a tax rate of 5.4% will be $0.27. This is calculated by converting the percentage to a decimal (0.054) and multiplying by the original cost ($5).

Explanation:

The subject of this question is mathematics, specifically, it's a problem of calculating the sales tax. In this scenario, if the tax rate is 5.4% and the initial price of the item is $5, you can calculate the amount of tax to pay by multiplying the original price of the item by the tax rate in decimal form.

So, step 1 is converting the percentage into a decimal by dividing by 100. That gives us 5.4 / 100 = 0.054.

Step 2 is multiplying this tax rate by the original price of the item:  $5 * 0.054 = $0.27.

Therefore, the tax you would pay on an item that costs $5 before sales tax is approximately $0.27, rounding up to the nearest cent.

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Answer:

Let's find the recursive formula, explicit formula, and the indicated term for the given arithmetic sequences.

Sequence 1: 1, 4, 1, 10, ...

To find the recursive formula, we need to identify the pattern between consecutive terms. Looking at the sequence, we can see that each term alternates between adding 3 and subtracting 3.

Recursive formula:

a1 = 1 (the first term)

an = an-1 + (-1)^(n+1) * 3

For example, to find the 4th term (a4) using the recursive formula:

a1 = 1 (the first term)

a2 = a1 + (-1)^(2+1) * 3 = 1 + (-1) * 3 = -2

a3 = a2 + (-1)^(3+1) * 3 = -2 + 1 * 3 = 1

a4 = a3 + (-1)^(4+1) * 3 = 1 + (-1) * 3 = -2

Explicit formula:

To find the explicit formula, we need to identify the common difference. In this case, since the terms alternate between adding 3 and subtracting 3, the common difference is not constant.

Indicated term:

To find the indicated term, we need to know which term is being referred to. Please provide the term number or the position of the term in the sequence so that I can assist you further.

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Sequence 2: 12, 7, 2, -3, ...

To find the recursive formula, we need to identify the pattern between consecutive terms. Looking at the sequence, we can see that each term decreases by 5.

Recursive formula:

a1 = 12 (the first term)

an = an-1 - 5

For example, to find the 4th term (a4) using the recursive formula:

a1 = 12 (the first term)

a2 = a1 - 5 = 12 - 5 = 7

a3 = a2 - 5 = 7 - 5 = 2

a4 = a3 - 5 = 2 - 5 = -3

Explicit formula:

To find the explicit formula, we need to identify the common difference. In this case, the common difference is -5.

Explicit formula:

an = 12 + (n - 1)(-5)

Indicated term:

To find the indicated term, we need to know which term is being referred to. Please provide the term number or the position of the term in the sequence so that I can assist you further.

Please provide the term number or the position of the term in the sequence so that I can help you find the indicated term.

Step-by-step explanation:

Answer:

x = -2 u got this

Step-by-step explanation:

-7x = 4x + 22

-11x = 22

x = -2

Easy bro

Final answer:

To solve the system of equations by substitution, solve one equation for one variable and substitute the expression into the other equation. In this case, solve the first equation for y, then substitute that value of y into the second equation. Solve for x and substitute the value back into the first equation to find y. The solution to the system of equations is x = -2 and y = 14.

Explanation:

To solve the system of equations by substitution, we need to solve one equation for one variable and substitute that expression into the other equation.

In this case, we can solve the first equation for y:

y = −7x

Now we substitute this value of y into the second equation:

−7x = 4x + 22

Next, we solve this equation for x:

−7x - 4x = 22

-11x = 22

x = -2

Finally, we substitute this value of x back into the first equation to find y:

y = -7(-2)

y = 14

Therefore, the solution to the system of equations is x = -2 and y = 14.

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▹ Answer

30 miles

▹ Step-by-Step Explanation

Multiply mph by hours:

15 mph * 2 hrs = 30 miles

Hope this helps!

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