You've been hired to plan a New Year's Eve party at the Governor's Mansion. The Mansion Charges: $1, 250 plus $20 per person.

I. Write an equation that can be used to the determine the cost of the party. Define the variables.

II. What is the cost if there is 300 people attending the party?

III. Represent the previous answer in a graph. ( Count by intervals of 50)

IV. There are 750 people who attended the party. Daryl said the cost will be $16,500. Is he correct ? Explain why or why not. Prove your answer by showing your work and including detailed reasoning.

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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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

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.

The fraction [tex]\frac{7}{35}[/tex] represents how many games Krista's softball team lost out of the 35 games Krista's team played.

To find the percent of games that Krista's team lost, we need to turn the fraction [tex]\frac{7}{35}[/tex] into a percent.

We can reduce [tex]\frac{7}{35}[/tex] by dividing both the numerator and denominator by the Greatest Common Factor of 7 and 35 using 7.

7 ÷ 7 = 1

35 ÷ 7 = 5

Now, we have our reduced fraction.

1 ÷ 5 = 0.2

0.2 × 100 = 20%

Therefore, Krista's softball team lost 20% of their games.

Step-by-step explanation:

Speed with which the players throw a small hard ball is 188 miles per hour. We need to convert the speed of the ball in kilometers per hour.

Firstly we can see the conversion from mile per hour to kilometer per hour as :

1 miles = 1609.34 meters

Also, 1 mile per hour = 1.60934 kilometer per hour

To convert 188 mph to km/h we can use the unitary method as :

188 mile per hour = 1.60934 × 188 kilometer per hour

188 mile per hour = 302.557 kilometer per hour

So, the speed of the ball is 188 miles per hour or 302.557 kilometer per hour. Hence, this is the required solution.

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.

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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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.

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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Answer: 2 x 40 = 80

Step-by-step explanation: there are two baskets of apple fruit labelled basket X and basket Y, each basket consists 150 green apple fruit.

You were asked to select 40 green apple fruit from each of the basket and put it together in basket Z.

40 green apples from both baskets X and Y equals 80 green apples in basket Z.

2 x 40 =80