A 3-foot piece of wire costs $0.76. What is the unit price, rounded to the nearest cent?

The sum of three even consecutive integers if the first integer is y is 3y+6.

What is an expression?

Expression in mathematics is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

It is given that the first even integer is y, than the second integer will be 2 more then the first one that is y+2 and the third even integer will be 2 more then the second one that is y+4. Now the sum of all these three integer will be :

sum = first number + second number + third number

       = y + (y+2) + (y+4)

       = 3y + 6

Therefore, the sum of three even consecutive integers if the first integer is y is 3y+6.

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Final answer:

To prove that a subset b of a well-ordered set a is also well-ordered, we can assume the opposite and show that it leads to a contradiction. If b is not well-ordered, it means that there exists an element in b smaller than all others, but since b is a subset of a this element must also be in a, contradicting the assumption that a is well-ordered. Therefore, b must be well-ordered as well.

Explanation:

To prove that if a is any well-ordered set of real numbers and b is a nonempty subset of a, then b is also well-ordered, we can use the fact that every well-ordered set has the least element. Let's assume that b is not well-ordered and does not have the least element. This means that there exists an element in b that is smaller than all other elements in b. However, since b is a subset of a, this element must also be in a. But this contradicts the assumption that a is well-ordered and has the least element. Therefore, b must be well-ordered as well.

B is the right answer

-2

The car used 70 gallons of gas to go 3 miles

The fraction 2/5 represents 2 of the 5 equal parts into which a whole is divided. This shows how fractions indicate the distribution of a whole into equal parts. Here, 2 slices out of 5 total slices illustrate the concept effectively.

Examples:

To calculate the cost of pizzas at Copper Creek Pizza with their special offer, we use provided formulas for up to 4 pizzas, and extend those to 20 pizzas. The total cost for 20 pizzas would be $178.50. If a group ordered together, they could save $34 by placing one order for 15 pizzas instead of separate orders.

To complete the table showing the cost of ordering up to 4 large pizzas from Copper Creek Pizza, we calculate the total cost based on the special deal provided. For any additional large pizza after the first one, the price is $8.50 each.

The explicit rule for the cost of n large pizzas is Cost = 17 + 8.50(n - 1), where n is the number of pizzas ordered.

The recursive rule is Costn = Costn-1 + 8.50, with the initial condition Cost1 = 17.

For part (c), the cost of ordering 20 large pizzas is calculated as: Cost = 17 + 8.50(20 - 1) = 17 + 8.50(19) = 17 + 161.50 = $178.50.

For part (d), if five people each make an order for 3 large pizzas, the total cost would be 5 x ($17 + 2 x $8.50) = 5 x ($34) = $170. If they placed one order for 15 pizzas, the cost would be $17 + 14 x $8.50 = $136. Therefore, they would have saved $170 - $136 = $34.

The greatest number of necklaces that can be made is 4, with each necklace containing 6 jade beads and 6 teak beads. This is determined by finding the GCD of 24 and 30, which is 6.

To determine the greatest number of necklaces the jewelry maker can make with 24 jade beads and 30 teak beads, we need to find the greatest common divisor (GCD) of the two numbers of beads. The GCD of 24 and 30 is 6.

This means the jewelry maker can make necklaces, each containing 6 beads of one type; 24 jade beads can make 4 necklaces, and 30 teak beads can also make 5 necklaces.

However, since each necklace must have the same number of jade and teak beads, the maximum number of necklaces is limited by the jade beads, which can only make 4 necklaces.

Therefore, the greatest number of necklaces that can be made is 4, with each necklace containing 6 jade beads and 6 teak beads.

Answer:   [tex]85.5\ in^2[/tex]

Step-by-step explanation:

Given : A sheet of paper has dimensions of 8.5 in x 11 in.

Then, the area if the sheet of paper will be :_

[tex]\text{Area}=8.5\times11=93.5\text{ in.}^2[/tex]

Also, we cut [tex]2 in^2[/tex] from each corner of the sheet.

Since, there are 4 corner in a sheet , then the combined area we cut will be :-

[tex]4\times2=8\ in.^2[/tex]

Now, the area of the sheet of paper will be  =[tex]93.5\text{ in.}^2-8\text{ in.}^2[/tex]

[tex]=85.5\ in^2[/tex]

Hence, the area of the sheet of paper will be [tex]85.5\ in^2[/tex]

In an exponential distribution scenario like bus waiting times, the formula P(T > t) = e^(-λt) can be used to calculate the probability of waiting more than a certain time. Substituting the given average waiting time in the formula, we get the probability of waiting more than 20 minutes for a bus is approximately 13.5%.

The question describes the waiting time for a bus as being exponentially distributed. In an exponential distribution, the probability that a variable (in this case, time until the next bus arrives) exceeds a certain value is calculated using the formula P(T > t) = e^(-λt) where, λ is the rate parameter - in this case, 1/10 (since the bus arrives every 10 minutes on average).

Thus, if we want to calculate the probability of waiting more than 20 minutes, we simply substitute t = 20 into the formula giving us: P(T > 20) = e^(-1/10 * 20), which simplifies to e^-2.

The number e^-2 is approximately 0.135, so the probability of having to wait more than 20 minutes for the bus is about 13.5%

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Based on the provided information, statement that is true about angles 1 and 2 is that they are complementary.

complementary angle can be explained as two angles are that has their measures adding to 90 degrees.

We can see that coloured portion is 90°, and  addition of ∠1 and ∠2= 90° since they are on straight line.

Therefore, option C is correct.

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To find the number of hamburgers sold on Saturday, we set up a system of equations and solve for the variable x.

To find the number of hamburgers sold, we can set up a system of equations using the given information. Let x represent the number of hamburgers sold. The number of cheeseburgers sold is two times the number of hamburgers sold, so the number of cheeseburgers is 2x. The total number of hamburgers and cheeseburgers sold is 336, so we can write the equation x + 2x = 336. Combining like terms, we have 3x = 336. Dividing both sides by 3, we find x = 112. Therefore, 112 hamburgers were sold on Saturday.

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By calculating the z-score for an attendance of 50,000 and referring to the z-table, we find that the probability that a randomly selected game had an attendance greater than 50,000 is approximately 18.67%.

In this question, we are given that the average attendance for a baseball season is 41,602 with a standard deviation of 9,440. We are asked to find the probability that a randomly selected game had an attendance greater than 50,000.

First, we have to find the z-score, which is calculated as: z = (X - μ) / σ , where X is the value from our dataset (in this case, 50,000), μ is the mean (41,602), and σ is the standard deviation (9,440). Plugging the numbers in, we get: z = (50000 - 41602) / 9440 ≈ 0.89.

Typically, the area to the right (greater than) of z = 0 is 0.5 in a standard normal distribution. However, we are interested in the area to the right of z = 0.89. To find this area, we can look at a z-table or use a calculator with a normal distribution function. The area to the right of z = 0.89 is approximately 0.1867, which means that the probability a randomly selected game had an attendance greater than 50,000 is roughly 18.67%.

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Final answer:

The solution to (4x10 to the 3rd power) x (3x10 to the 4th power) is 1.2x10 to the 8th power in scientific notation.

Explanation:

The solution to (4×103) × (3×104) in scientific notation involves multiplying the coefficients (4 and 3) and then adding the exponents of 10 (3 and 4). To multiply the coefficients, you do 4 × 3, which equals 12. To combine the powers of 10, you add the exponents: 103 × 104 becomes 103+4, which is 107. Therefore, the product in scientific notation is 12 × 107. Since scientific notation requires that the coefficient be between 1 and 10, we adjust the coefficient by dividing it by 10 and increasing the exponent by 1, resulting in 1.2 × 108.

The hourly unit rate of pay for the employee is $5.25.

Option A is the correct answer.

We have,

Let x be the unit rate.

i.e

Hourly rate of pay for the employee.

Then the employee earned a total of:

Total earnings = (hourly rate) x (number of hours worked) + tips

$400 = 28x + $253

Subtracting $253 from both sides, we get:

$147 = 28x

Dividing both sides by 28, we get:

x = $5.25

Therefore,

The hourly unit rate of pay for the employee is $5.25.

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