Larry's lemons is a street vendor business that sells lemonade and lemon bars. A cup of lemonade sells for $2 and a lemon bar sells for $1.50. When all related business expenses are included, a cup of lemonade costs $0.25 to prepare and a lemon bar costs $0.20 to prepare. Last Monday, one of the vendors selling Larry's Lemons sold at least $500 worth of lemonade and lemon bars and its expenses were no more than $100. At least 150 cups of lemonade were sold. Let x be the number of cups of lemonade sold last Monday and y be the number of lemon bars sold last Monday. Which ordered pair representing a combination of cups of lemonade and lemon bars could have been sold last Monday and make sense in the context of the situation?
The one possible ordered pair that satisfies all conditions is (x, y) = (150, 134).
The ordered pair (x, y) that satisfies the following conditions:
1. The total revenue from selling x cups of lemonade and y lemon bars is at least $500. This gives us the inequality:
[tex]\[ 2x + 1.50y \geq 500 \][/tex]
2. The total expenses for preparing x cups of lemonade and y lemon bars is no more than $100. This gives us the inequality:
[tex]\[ 0.25x + 0.20y \leq 100 \][/tex]
3. At least 150 cups of lemonade were sold, which gives us the inequality:
[tex]\[ x \geq 150 \][/tex]
To find a combination of x and y that satisfies all these conditions, we can start by considering the minimum number of lemonade cups sold, which is 150. We can then calculate the revenue and expenses for this minimum number and see how many lemon bars would be needed to meet the revenue requirement while keeping the expenses within the limit.
Let's start with the minimum number of lemonade cups:
[tex]\[ x = 150 \][/tex]
The revenue from lemonade alone would be:
[tex]\[ 2 \times 150 = \$300 \][/tex]
The expenses for lemonade alone would be:
[tex]\[ 0.25 \times 150 = \$37.50 \][/tex]
Now, we need to find out how many lemon bars (y) would be needed to make up the remaining revenue to at least $500 while keeping the total expenses at or below $100.
Let's denote the remaining revenue needed as R and calculate it:
[tex]\[ R = 500 - 300 = \$200 \][/tex]
The revenue from selling y lemon bars is $1.50y, so we have:
[tex]\[ 1.50y \geq 200 \][/tex]
[tex]\[ y \geq \frac{200}{1.50} \][/tex]
[tex]\[ y \geq 133.33 \][/tex]
Since we cannot sell a fraction of a lemon bar, we round up to the nearest whole number, so at least 134 lemon bars must be sold.
Now let's check the expenses for the lemon bars. We have $100 - $37.50 = $62.50 left for expenses. The cost to prepare each lemon bar is $0.20, so we calculate the maximum number of lemon bars (y) that can be prepared with the remaining expenses:
[tex]\[ 0.20y \leq 62.50 \][/tex]
[tex]\[ y \leq \frac{62.50}{0.20} \][/tex]
[tex]\[ y \leq 312.5 \][/tex]
Combining the two conditions for y, we find that y must be at least 134 but no more than 312.
Therefore, one possible ordered pair that satisfies all conditions is (x, y) = (150, 134). This means that at least 150 cups of lemonade and at least 134 lemon bars were sold last Monday to meet the revenue and expense conditions.
Consider the system of inequalities and its graph. y ≤ –0.75x y ≤ 3x – 2 In which section of the graph does the actual solution to the system lie?
A. 1
B. 2
C. 3
D. 4
Answer:
4
Step-by-step explanation:
trust me
Lamar’s teacher extended the graph as shown below and asked Lamar to write the function for the graph shown below using f(x) for the function name
If four times a number plus 3 is 11, what is the number? A. 16 B. 5 C. 2 D. 4
The tiles below represent the polynomial 2x2 + 5x + 3.
What is the factorization of 2x2 + 5x + 3?
A. (2x + 3)(x + 1)
B. (x + 3)(x + 3)
C. (x + 3)(x + 1)
D. (2x + 3)(x + 3)
Answer:
Factorization of 2x²+5x+3 is:
A. (2x + 3)(x + 1)
Step-by-step explanation:
We have to factorize the expression:
2x²+5x+3
We will solve this expression by splitting the middle term method
2x²+5x+3
=2x²+2x+3x+3
=2x(x+1)+3(x+1)
=(2x+3)(x+1)
Hence, factorization of 2x²+5x+3 is:
A. (2x + 3)(x + 1)
Jessica is trying to win this game of pool. She needs to hit the cue ball (white ball) 10 in. into the yellow ball so it will travel 15 in. to bounce off the back wall, travel across the table, and then land in the pocket. Determine the distance (d) that the yellow ball must travel after hitting the back wall to land in the pocket. A. 32 in.
In the diagram, SR = 4sqrt 2 and QR = sqrt 10. What is the perimeter of parallelogram PQRS?
A. sqrt 10 units
B. 8 sqrt 2 + sqrt 10 units
C. 16 sqrt 2 units
D. 8 sqrt 2 + 8 units
Answer: B
Step-by-step explanation:
Use logarithms to solve each equation
2x 9/8=111
A. 18.9561
B.25.8961
C. 10.2587
D. 35.5208
Solve this problem: –282 – (+1,017) = ? A. 1,299 B. 735 C. –735 D. –1,299
PLEASE HELP :( i'm stuck
What are the amplitude and midline?
Amplitude: 1; midline: y = 1
Amplitude: 0; midline: y = 0
Amplitude: 2; midline: y = 1
Amplitude: 2; midline: y = 0
Answer:
Amplitude: 1; midline: y = 1
Step-by-step explanation:
From the graph we can conclude that it is a sine or cosine function. In their standard form, these functions are given by the following equations:
[tex]y(t)=Acos(\omega t +\phi)\\\\or\\\\y(t)=Asin(\omega t+ \phi)[/tex]
Where:
[tex]A=Amplitude=\frac{|A_m_i_n-A_m_a_x|}{2}\\\omega=Angular\hspace{3}frequency\\\phi=Initial \hspace{3}phase[/tex]
And:
[tex]A_m_a_x=Maximum\hspace{3}amplitude\\A_m_i_n=Minimum\hspace{3}amplitude[/tex]
On the other hand, we can define the midline of these kind of functions as the halfway between the maximum and minimum amplitude of the function, Therefore:
[tex]Midline=M_l=\frac{A_m_a_x+A_m_i_n}{2}[/tex]
From the graph you can see that the maximum value of the function(maximum amplitude) is 2 and the minimum value of the function (minimum amplitude) is 0, thus:
[tex]A=\frac{|A_m_i_n-A_m_a_x|}{2} =\frac{|0-2|}{2} =\frac{|-2|}{2} =\frac{2}{2} =1[/tex]
And:
[tex]M_l=\frac{A_m_a_x+A_m_i_n}{2}=\frac{2+0}{2} =\frac{2}{2} =1[/tex]
what is the fifth term of the arithmetic sequence 7,3,-1....
Select from the drop-down menu to correctly compare the numbers. 4.5872...[ ] 14−−√
>
<
=
4.5872 > [tex]\sqrt{14}[/tex]
We have two numbers.
We have to compare these two numbers.
The square root of a number is always less than ?The square root of a number is always less then the number itself.
According to the question, we have -
A = 4.5872
B = [tex]\sqrt{14}[/tex]
Now -
The value of B = 3.472.
Clearly, A > B
Hence, 4.5872 > [tex]\sqrt{14}[/tex].
To solve more questions on comparing numbers, visit the link below-
https://brainly.com/question/15451569
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How many radii does a circle have? Explain.
Answer:
one because the distance stay the same and infinite because the are infinite positions that the radii could be in
Step-by-step explanation:
You bought a new car for $15,000 and know that it loses 1 5 of its value every year. The equation that models the value of your car is y = 15000( 4 5 )x. Which is the MOST reasonable domain for this function?
Answer:
0 < X < 20
Step-by-step explanation:
Need answer asap evaluate the limit or state that the limit does not exist 7n-8n/2n
Lincoln Technical College has 856 students. They expect 700 guests for a special speaker. The custodian has set up 1,500 chairs. How many more chairs are needed if everyone is to have a seat? 3. Draw a picture or a chart that shows the information and the question
57 chairs are needed if everyone is to have a seat
To calculate the number of additional chairs needed, we first need to determine the total number of seats required. This is the sum of the students, guests, and speaker. Then, we subtract the number of chairs already set up to find out the additional chairs needed.
Let's break it down step by step:
1. Total number of seats required:
- Students: 856
- Guests: 700
- Speaker: 1 (assuming the speaker needs a seat)
Total seats required = 856 (students) + 700 (guests) + 1 (speaker) = 1,557 seats
2. Number of chairs already set up: 1,500
3. Additional chairs needed:
Total seats required - Chairs already set up = 1,557 - 1,500 = 57
So, Lincoln Technical College needs 57 more chairs to accommodate everyone if all students, guests, and the speaker are to have a seat.
Lincoln Technical College has 856 students and expects 700 guests for a special speaker, making the total number of attendees 1,557. The custodian has already set up 1,500 chairs. To find out how many more chairs are needed, we subtract the number of chairs already set up from the total seats required. This calculation reveals that 57 additional chairs are needed to ensure that everyone has a seat. It's essential to consider all attendees, including students, guests, and the speaker, to accurately determine the total seating requirements.
Complete question:
Lincoln Technical College has 856 students. They expect 700 guests for a special speaker. The custodian has set up 1,500 chairs. How many more chairs are needed if everyone is to have a seat?
The flower garden has the shape of a right triangle. 68 ft of a perennial border forms the hypotenuse of the triangle, and one leg is 28 ft longer than other leg. find the lengths of the legs.
The shorter leg of the triangle is 32 feet long.
The longer leg of the triangle is 60 feet long.
In this case, we are given that the hypotenuse of the triangle is 68 feet, and one leg is 28 feet longer than the other leg. Let's call the length of the shorter leg "x". Then, the length of the longer leg is "x + 28".
Using the Pythagorean theorem, we can write the following equation:
68^2 = x² + (x + 28)²
Simplifying this equation, we get:
4624 = 2x² + 56x + 784
Solving for x, we find that:
x = 32 or x = -60
Since the length of a side of a triangle cannot be negative, we reject the solution x = -60. Therefore, the length of the shorter leg is 32 feet, and the length of the longer leg is 32 + 28 = 60 feet.
Ginger makes pies and sells them for $14 each. Write an equation that represents the situation, if y represents the money that Ginger earns and x represents the number of pies sold.
Which of the following has 8.012 in written form?A.eight and twelve hundredthsB.eight and twelve thousandthsC.eight and twelve thousandsD.none of the above
2,400 principal earning 2%, compounded annually, after 7 years. Find the balance in the account
The balance in the account after 7 years will be approximately $2,747.70.
How did we get the value?To calculate the balance in the account after 7 years with a principal of $2,400 earning 2% interest compounded annually, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future balance
P = the principal amount ($2,400)
r = the annual interest rate (2% or 0.02 as a decimal)
n = the number of times the interest is compounded per year (annually, so n = 1)
t = the number of years (7 years)
Plug these values into the formula:
A = 2400(1 + 0.02/1)^(1*7)
A = 2400(1 + 0.02)⁷
A = 2400(1.02)⁷
A = 2400(1.144877)
A ≈ $2,747.70
So, the balance in the account after 7 years will be approximately $2,747.70.
learn more about interest compounded: https://brainly.com/question/3989769
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write the product in its simplest form:
8y^7*6y^7
Find the total area of the regular pyramid.
Answer:
Area of the regular pyramid = 16.64 square units.
Step-by-step explanation:
Given : Regular pyramid .
To find: Find the total area of the regular pyramid.
Solution : We have given that regular pyramid.
Area = 4 ( area of triangle ) + area of base .
Area of the regular pyramid = 4 ( [tex]\frac{1}{2} * base * height + side * side[/tex].
Area of the regular pyramid = [tex]4(\frac{1}{2}* 2* \sqrt{10} + 2*2[/tex]
Area of the regular pyramid = [tex]4( \sqrt{10} ) + 4[/tex]
Area of the regular pyramid = (4 [tex]( \sqrt{10} ) \+\ 1[/tex].
Area of the regular pyramid = 16.64 square units.
Therefore, Area of the regular pyramid = 16.64 square units.
The altitude to the hypotenuse of a right triangle has a length of 12. what could be the lengths of the two segments of the hypotenuse ?
answer this question
PLEASE HELP I REALLY NEED IT
What are the x-intercepts of the quadratic function?
f(x)=x2−3x−10
Enter your answers in the boxes.
_______ and ________
Group terms that contain the same variable, and move the constant to the opposite side of the equation
(x²−3x)=10
Complete the square. Remember to balance the equation by adding the same constants to each side.
(x²−3x+2.25)=10+2.25
Rewrite as perfect squares
(x-1.5)²=12.25----------> (+/-)[x-1.5]=3.5
Answer:
5 and -2 :)
explanation:
The number of boys varies directly as the number of girls and inversely as the number of teachers when there are 24 boys and 16 girls there are 2 teachers how many girls are there when there are 73 boys and 1 teacher?
In a right rectangles pyramid with base edges a= 18 cm and b= 10 cm the slant height toward a is k= 13 cm while the slant height towards b is l= 15 cm. What is the surface area of the pyramid
express the product of 2x2 + 6z - 8 and x + 3 in standard form
Answer:
[tex]2x^3+12x^2+10x-8[/tex]
Step-by-step explanation:
The product is found using the distributive property.
[tex](x+3)(2x^2+6x-8)\\x*2x^2 + x*6x+x*(-8)=2x^3+6x^2-8x\\\\and\\\\3*2x^2+3*6x+3*(-8)=6x^2+18x-8[/tex]
Now combine the two products by adding like terms together.
[tex]2x^3+6x^2-8x + 6x^2+18x-8\\2x^3+12x^2+10x-8[/tex]
Kelly was building a bed for her dollhouse. She used her bed, which is 4 feet × 6 feet, as a guide. She scaled down the dimensions of her bed by a factor 1 over 5. What are the dimensions of the model bed she built?
0.8 foot × 1.2 feet
0.4 foot × 0.6 foot
0.08 foot × 0.12 foot
0.04 foot × 0.06 foot
The answer is A, 0.8 foot x 1.2 feet.
Hopefully this helps!
The 70-foot rope was cut into two pieces. one of the pieces was 10 feet longer than three times the length of the other piece. how long was each piece?