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just olya [345]
3 years ago
5

Allison’s cupcake and cookie budget for her party is $105. She would like to have at least 40 cupcakes and cookies combined, and

would like to have at most 5 more cupcakes than cookies. If cupcakes sell for $2.50 and cookies for $1.50, which system of inequalities could help Allison determine possible numbers of cupcakes (a) and cookies (b) that she should buy? ( a ≥ 0 , b ≥ 0 )
Mathematics
1 answer:
FinnZ [79.3K]3 years ago
4 0

Answer:

a + b ≥ 40

a + 5 ≤ b

2.50a + 1.50b ≤ 105

Step-by-step explanation:

We are told she would like to have at least 40 cupcakes and cookies combined.

If a is number of cupcakes and b is number of cookies, then this inequality is;

a + b ≥ 40

Secondly, we are told she would like to have at most 5 more cupcakes than cookies.

Thus, the inequality is;

a + 5 ≤ b

Lastly, we are told that cupcakes sell for $2.50 and cookies for $1.50

Thus, the inequality is;

2.50a + 1.50b ≤ 105

Finally, the 3 inequalities are;

a + b ≥ 40

a + 5 ≤ b

2.50a + 1.50b ≤ 105

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Answer:

The answer is 5300 units.

Step-by-step explanation:

The equation will be exactly lie below if the price is 5$:

5=-0.05x^2-0.3x + 8\\0=-0.05x^2-0.3x+3

Roots of the parabol will be:

x_{1}=-11.3\\x_{2}=5.3

In fact that there will be no negative production, The consumer surplus will be 5300 units

6 0
3 years ago
While in flight, a hot air balloon decreases its elevation by 83 2/5 meters and then increases its elevation by 83.7 meters
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An inequality which compares the changes in elevation of this hot air balloon while in flight is given by L - 83 2/5 ≤ L ≤ L + 83.7.

<h3>What is an elevation?</h3>

An elevation is also referred to as an altitude and it can be defined as the vertical distance (height) above a natural satellite or the surface of planet Earth such as land or sea level.

This ultimately implies that, an elevation (altitude) simply refers to the vertical height (elevation) of an object or physical body above a particular location or planetary reference plane such as land or sea level on planet Earth.

<h3>What is an inequality?</h3>

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments (symbols):

  • Less than (<).
  • Greater than (>).
  • Less than or equal to (≤).
  • Greater than or equal to (≥).

For this exercise, let the variable L represent the initial height of this balloon. Also, since the hot air balloon decreased its elevation by 83 2/5 and increases its elevation by 83.7 meters, we have the following:

  • The lower limit is equal to: L - 83 2/5.
  • The upper limit is equal to: L + 83.7.

In this context, an inequality which models the changes in elevation of this hot air balloon is L - 83 2/5 ≤ L ≤ L + 83.7.

Read more on inequality here: brainly.com/question/6666926

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Step-by-step explanation:

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4 0
3 years ago
Jenny drives from Paris to Rochefort, a distance of 483 km. her average speed on the journey is 84 km/h, she leaves at 9:50. Wha
Mrrafil [7]

The correct answer is 3: 35

Explanation:

To calculate at what time Jenny will arrive in Rochefort, the first step is to calculate the approximate time of the trip. Now, to calculate this consider the time of a movement (t) equals to the distance (d) divided by the speed (s), the process is shown below:

t = 483 km / 84 km/h

t = 5.75 hours

In this number 5 refers to the hours and 0.75 represents 45 minutes considering 0.75 x 60 minutes in one hour = 45 minutes. Therefore, the total time from Paris to Rochefort is 5 hours and 45 minutes. Now, to calculate the time of arrival add this result to the time of departure.

Add the hours: 5 hours + 9 hours: 14 hours

Add the minutes: 50 minutes + 45 minutes =95 minutes

95 minutes are equivalent to 1 hour (60) minutes and 35 minutes

Calculate the total

Hours: 14 hours + 1 hour = 15 hours or 3  in the 12 hour system (15 hours - 12 hours = 3 p.m.)

Minutes: 35 minutes

4 0
3 years ago
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