Use number patterns and powers of ten to complete the chart. Need help
Worth 23 points

Answer:

22

Step-by-step explanation:

The total cost of 4 sets of the fall candle gift set is represented by the expression 20v + 24p.

To find the total cost of 4 sets of the fall candle gift set, we first need to determine the cost of one set. Each set contains 4 vanilla candles and 6 pumpkin spice candles. If we let v represent the cost of each vanilla candle and p represent the cost of each pumpkin spice candle, then the cost of one set is 4v + 6p.

Since we want to find the cost of 4 sets, we multiply the cost of one set by 4:

[tex]\[ 4 \times (4v + 6p) \][/tex]

Now, distribute the 4 across the terms inside the parentheses:

[tex]\[ 4 \times 4v + 4 \times 6p \][/tex]

Simplify the expression by multiplying the coefficients:

[tex]\[ 16v + 24p \][/tex]

This expression represents the total cost for 4 sets of the fall candle gift set, with v being the cost per vanilla candle and p being the cost per pumpkin spice candle.

A real world problem reflected in the expression 5x + 10 can involve calculating the total cost of books plus a membership fee in a bookstore. The quadratic formula is used for solving quadratic equations, which have significant applications in various fields.

An example of a real world problem represented by the expression 5x + 10 is calculating the total cost of purchasing multiple items. Imagine you are at a bookstore, and each book costs $5. There is also a one-time membership fee to join the bookstore's readers club, which is $10. If x represents the number of books you decide to purchase, then 5x would represent the total cost of the books, and when you add the $10 membership fee, the expression for calculating your total cost would be 5x + 10.

Additionally, the concept of quadratic formula is significant in mathematics as it helps in finding solutions for quadratic equations, such as t² + 10t - 2000 = 0. This equation can be solved by rearranging to have 0 on one side and then applying the quadratic formula. Understanding quadratic equations is crucial not just in theoretical math but also practical real world applications like physics or economics.

Final answer:

The constant of proportionality of 1/3 means that for every unit increase in one variable, the other variable increases by 1/3 of that unit. It is a number that relates two quantities that are directly proportional to each other.

Explanation:

The question 'what is the constant of proportionality of 1/3' can be related to various contexts in Mathematics and Science. In mathematics, a constant of proportionality is a number that relates two quantities that are proportional to each other. If one quantity is always the product of the other quantity and a constant, this constant is called the constant of proportionality.

For example, if you have an equation y = (1/3)x, then the constant of proportionality between x and y is 1/3. This means for every unit increase in x, y increases by 1/3 of that unit. It can also appear in a science context, such as in Ohm's Law, where V = IR, and 'R' can be considered the constant of proportionality that relates voltage (V) and current (I), or in the specific heat equation, where the specific heat serves as the constant.

Answer:

It will take 2 hours for Jordan and Jake to earn the same amount of money

Step-by-step explanation:

Jordan earns $9 per hour

Let he worked for x hours

So, he earned in x hours = 9x

Jordan also gets a $10 weekly allowance.

So, his total earning in x hours = 10+9x

Jake earns $6.50 per hour at his job.

Let he worked for x hours

So, he earned in x hours = 6.50x

Jake also gets a $15 weekly allowance.

So, his total earning in x hours = 15+6.50x

Now to know How many hours will it take for Jordan and Jake to earn the same amount of money

[tex]10+9x=15+6.50x[/tex]

[tex]9x-6.5x=15-10[/tex]

[tex]2.5x=5[/tex]

[tex]x=\frac{5}{2.5}[/tex]

[tex]x=2/tex]

Hence it will take 2 hours for Jordan and Jake to earn the same amount of money

Laura’s hike can be described by the equation ( y = 6x ), where ( x ) represents time (in hours) and ( y ) represents distance (in miles).

Graph Description:

The graph depicts a linear relationship between time (in hours) and distance (in miles).

The x-axis represents time, ranging from 0 to 5 hours.

The y-axis represents distance, ranging from 0 to approximately 24 miles.

The line starts from the origin (0,0) and extends to the point (5,24), indicating that Laura covered a distance of approximately 24 miles in five hours.

Each grid square along the x-axis represents one hour, and each grid square along the y-axis represents approximately four miles.

Equation for the Graph:

To find the equation of the line, we’ll calculate the slope (m) and the y-intercept (b).

Let’s use two points on the line: (1,0) and (5,24).

The slope (m) can be calculated as follows: [tex][ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} = \frac{{24 - 0}}{{5 - 1}} = \frac{{24}}{{4}} = 6 ][/tex]

The y-intercept (b) is where the line crosses the y-axis (at point (0,0)). Therefore, ( b = 0 ).

The equation of Laura’s hike on the graph is: [ y = 6x ]

Explanation:

The equation ( y = 6x ) represents Laura’s hiking progress. For every hour she hikes, she covers a distance of 6 miles.

The slope of 6 indicates that her speed is consistent (6 miles per hour).

The y-intercept of 0 means that she started at the origin (0 miles) when the hike began.

In summary, Laura’s hike can be described by the equation ( y = 6x ), where ( x ) represents time (in hours) and ( y ) represents distance (in miles).

To determine the monthly charge for a cell phone plan with a flat fee and a fee per 50 MB of data used, we use a linear equation. For example, with a flat fee of $20 and a per 50MB data charge of $2, the equation for the monthly cost (C) would be C = 20 + 2D, where D reflects the number of 50MB increments used.

For the scenario you're describing, you would typically use a linear equation where one part is constant (the flat fee), and the other changes based on the amount of data (measured in 50 MB sets) the customer uses. Let's consider a scenario where you're charging a flat fee of $20 and a fee of $2 for every 50 MB of data used during the month. Then, the equation for the cost, C, each month would be:

C = 20 + 2D

In this equation, D reflects the number of 50MB data increments used by the customer. So, if a customer uses 150 MB of data in a month, D would equal 3, as 150 MB is three sets of 50 MB. The total cost for this customer would be:

C = 20 + 2(3)
C = $26

The set $20 is the flat fee and the varying part, 2D, reflects the data charge. Hence, the total bill for a customer any given month would depend on their data usage.

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To find the amount of yards of ribbon Kevin needs, he should first convert the ribbon length from feet to yards and then multiply by the number of ribbons. One ribbon is 0.75 yards long, and he requires 1,000 ribbons, totaling 750 yards needed.

How Kevin Can Determine the Total Yards of Ribbon Needed

Kevin needs to calculate the total length of ribbon required for a school event, with the requirement being 1,000 ribbons each 2.25 feet long. To find how many yards of ribbon he needs, Kevin can follow a two-step pattern. First, he should convert the length of each ribbon from feet to yards, knowing that 1 yard is equal to 3 feet. This means each ribbon is
2.25 feet / 3 feet/yard = 0.75 yards long.

Next, Kevin should multiply the length of one ribbon by the total number needed to find the total yardage required. So, 0.75 yards per ribbon × 1,000 ribbons = 750 yards of ribbon needed for the event.

By using this pattern, Kevin can easily calculate the amount of ribbon he needs to purchase, ensuring he has enough for the school event without buying excess material.

The X and Y intercepts of the given equation can be found by setting variables to zero in turn and solving for the other. The X intercept is -3 and the Y intercept is 6.

To find the X and Y intercepts of -8x + 4y =24, we should set each variable equal to zero in turn to solve for the other. The X intercept occurs when Y is zero, and the Y intercept happens where X is zero.

For finding X-intercept, place Y equal to zero in the equation, so we get -8x +4(0) = 24. Solving it leads us to X = -3.

For the Y-intercept, let’s place X equal to zero in the equation. Here we get -8(0) + 4y = 24. Solving this yields Y = 6. So, the X intercept is -3, and the Y intercept is 6.

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The given algebraic expression simplifies to 9a - 4b - 13 by first grouping together like terms (terms with the same variable and exponent), then adding them up.

To simplify the given algebraic expression 2a - 1 + 8b - 12b + 7a - 12, we first group together like terms. The 'like terms' are terms with the same variables and exponents. In this case, 2a and 7a are like terms, and 8b and -12b are like terms.

The expression becomes: (2a + 7a) + (-1 - 12) + (8b - 12b)

Adding these like terms together, we get 9a - 13 - 4b. So, the original expression simplifies to 9a - 4b - 13.

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