There are seven ice skaters in a competition. How many different possibilities are there for the top three places? (A different ordering of the same three skaters counts as a different possibility.)

Answer:

That's the correct answer!!

Step-by-step explanation:

76 adult tickets were sold.

Let's assume the number of adult tickets sold is x. Since the number of student tickets sold was three times the number of adult tickets sold, we can represent it as 3x.

According to the problem, the total number of tickets sold was 304. So, we can write the equation:

x + 3x = 304

Combining like terms, we get:

4x = 304

Divide both sides by 4:

x = 76

Therefore, 76 adult tickets were sold.

The system of equations that can be used to determine the price of the mountain bike at each store is:

s - 2d = -290

s - d = 304

Let's determine the correct system of equations to find the prices of the mountain bike at Speed Cycling (s) and Downhill Racing (d).

Given:

The price at Speed Cycling (s) is $290 less than twice the price at Downhill Racing (d). This can be expressed as s = 2d - 290.

The price difference between Speed Cycling and Downhill Racing is $304. This can be expressed as s - d = 304.

Now, we have the two equations:

s = 2d - 290

s - d = 304

These equations form a system that can be used to determine the prices of the bike at each store.

To solve for s and d, you can use the method of substitution or elimination. By substituting the value of s from the first equation into the second equation, you can find the prices of the bike at each store:

Substitute s from the first equation into the second equation:

(2d - 290) - d = 304

Now, solve for d:

d - 290 = 304

Add 290 to both sides:

d = 304 + 290

d = 594

Now that you've found the price at Downhill Racing (d), you can find the price at Speed Cycling (s) by using the first equation:

s = 2d - 290

s = 2 * 594 - 290

s = 1188 - 290

s = 898

So, the price of the mountain bike at Downhill Racing (d) is $594, and the price at Speed Cycling (s) is $898.

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To calculate g(3/2) for the function g(x) = 4x - 4^x, we first multiply 4 by 3/2 to get 6, then calculate 4 raised to the power of 3/2 to get 8, and subtract the latter from the former to obtain the final result of -2.

To find the value of g(3/2) for the function g(x) = 4x - 4x, we simply substitute x with 3/2. The calculation involves two parts: multiplying 4 by 3/2, and then raising 4 to the power of 3/2.

Therefore, the value of g(3/2) is -2.

If [tex]g(x) = 4x - 4^x[/tex], what is the value of g(3/2) is  -2.

To find the value of g(3/2), you need to substitute x = 3/2 into the given function [tex]g(x) = 4x - 4^x.[/tex]

g(3/2) = [tex]4(3/2) - 4^\frac{3}{2}[/tex]

Now, let's simplify this expression:

[tex]g(3/2) = 6 - 4^\frac{3}{2}[/tex]

The value of 4^(3/2) is the square root of 4 cubed, which is [tex]2^3[/tex] = 8. Therefore:

g(3/2) = 6 - 8

Now, subtract 8 from 6:

g(3/2) = -2

So, the value of g(3/2) is -2.

Final answer:

Sarah's original investment was calculated by dividing the final amount of $448 by 1 plus the percentage increase in decimal form, which gives us $350 as the original investment before a 28% growth.

Explanation:

The student is asking to calculate the original investment amount before a 28% increase resulted in a final amount of $448. To find the original investment, we divide the final amount by 1 plus the percentage increase in decimal form. In this case, the percentage increase is 28%, which is 0.28 in decimal form.

The formula to find the original investment (O) is:

O = Final Amount / (1 + Percentage Increase)

So, the original investment would be calculated as follows:

O = $448 / (1 + 0.28) = $448 / 1.28

After performing the division, we find the original investment is:

O = $350

Therefore, Sarah originally invested $350 in JetBlue stock.

Final answer:

Using the Pythagorean theorem, we find that the side lengths of the right triangle are 9m for the shorter leg, 12m for the longer leg, and 15m for the hypotenuse.

Explanation:

We are asked to find the side lengths of a right triangle, with the condition that the longer leg is 3m longer than the shorter leg, and the hypotenuse is 6m longer than the shorter leg. We can name the shorter leg 'x'. Therefore, the longer leg will be 'x + 3' and the hypotenuse will be 'x + 6'. According to the Pythagorean theorem (a² + b² = c²), we can set up the equation x² + (x + 3)² = (x + 6)².

First, we expand the equations: x² + (x² + 6x + 9) = (x² + 12x + 36).

Combining like terms, we get 2x² + 6x + 9 = x² + 12x + 36. Simplifying further, we get x² - 6x - 27 = 0.

This is a quadratic equation that can be factored as (x - 9)(x + 3) = 0, which gives us the solutions x = 9 and x = -3. Since a side length cannot be negative, we discard the negative value.

Thus, the lengths of the sides of the triangle are: shorter leg x = 9m, longer leg x + 3 = 12m, and hypotenuse x + 6 = 15m.

The value of the expression at a - 10 = 0 is 169.

We have,

Expression:

a² + 6a + 9 _________(1)

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

From the expression a - 10 = 0.

Find the value of a.

a = 10

Now,

Substituting a = 10 in (1).

a² + 6a + 9

Simplify the expression.

10² + 6 x 10 + 9

100 + 60 + 9

Add the like terms in the expression.

100 + 69

169

Thus,

The value of the expression at a - 10 = 0 is 169.

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The complete question:

what are the steps to solve a^2 + 6a + 9 when a - 10 = 0.

To win the lottery by betting on numbers 2 and 9, the combined probability is calculated by multiplying the individual probabilities of drawing each number. The probability of drawing number 2 is 1/10, and subsequently drawing number 9 is 1/9, resulting in a combined probability of 1/90.

The question asks about the probability of winning a lottery by correctly guessing two specific numbers out of ten. To determine this probability, we must consider the two stages of the lottery separately. Initially, any one of the ten balls can be drawn, so the probability of drawing the first number you bet on, which is 2 in this case, is 1/10. Once the first ball is chosen, it is not replaced, meaning the second selection will be made from the remaining nine balls. Therefore, the probability of drawing the second number you bet on, number 9, after having already drawn number 2, is 1/9. We use the product rule because we need the outcome of drawing both numbers.

Using the product rule, the combined probability of drawing both numbers in the correct order is calculated by multiplying the probabilities of each individual event. Therefore, the combined probability is (1/10) x (1/9), which simplifies to 1/90. This is the probability of winning the lottery by betting on numbers 2 and 9.

[tex]log_6(17w)[/tex] can be expressed as [tex]log_6(17) + log_6(w)[/tex] using the sum of logarithms property.

To express log base 6 of 17w as the sum of logarithms, you can use the properties of logarithms, specifically the product rule for logarithms:

[tex]log_b(xy) = log_b(x) + log_b(y)[/tex]

In this case, you have log base 6 of 17w, and you want to express it as the sum of logarithms. You can do this as follows:

[tex]log_6(17w) = log_6(17) + log_6(w)[/tex]

So, log base 6 of 17w can be expressed as the sum of log base 6 of 17 and log base 6 of w.

This is a straightforward application of the product rule for logarithms, where you split the logarithm of a product into the sum of the logarithms of the individual factors.

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The total interest paid for a mortgage at 8% interest rate with a $800 monthly payment.

A. To find the maximum loan amount you can afford:

B. Total payment over 30 years = Monthly payment * 12 months * 30 years.

C. Total interest paid = Total payment - Loan amount.