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.
If i walk 4 miles an hour how long will it take to walk 1 mile
Find an explicit formula for the sequence 30\,,\,150\,,\,750\,,\,3750,...30,150,750,3750,...30, space, comma, space, 150, space, comma, space, 750, space, comma, space, 3750, comma, point, point, point.
Answer:750+3750=4,500
Step-by-step explanation:
An equation of a function y(t) is shown. y(t)=−t2+14t−40 Which of the following statements are true about the graph of y(t) for 6≤t≤8 and WHY? a. The value of y(t) increases over the interval 6≤t≤7. b. The value of y(t) increases over the interval 7≤t≤8. c. The average rate of change over the interval 6≤t≤8 is 0. d. The value of y(t) is constant over the interval 6≤t≤8. e. The average rate of changer over the interval 6≤t≤7 is the same as the average rate of change over the interval 7≤t≤8. Make sure you use complete sentences and capitalize!
What is the excluded value of
-2x/17
a. x=0
b. x=2
c. x=17
d. no excluded values
Which of the following is equivalent to the midpoint between the points (8, -9) and (0, 5)?
(4, -2)
(4, 2)
(-2, 4)
(2, 4)
another geometry file upload
The ratio of height between Joey and his girlfriend is 8:7. If Joey is 72 inches tall, how tall is his girlfriend in inches
A rectangular crate has the dimensions of 32.1 inches by 28.2 inches by 1 foot.What is the volume of the crate? Round your answer to the nearest tenth, if necessary
a)6.3 cubic feet
b)16. cubic feet
c)18.4 cubic feet
d)905.22 cubic feet
Graph the function y = 6/x . Draw a chart to show the ordered pairs that are on the graph.
Answer:
x y
-3
-2
-1
1
2
3
Answer:
see the attachment for the graph and chart
Step-by-step explanation:
A spreadsheet or graphing calculator is convenient for making a chart of ordered pairs.
Baby Kelsey wants to arrange 12 blocks in a row. How many different arrangements can she make?
To find the number of arrangements Baby Kelsey can make with 12 blocks, we calculate 12 factorial (12!), which equals 479,001,600. This represents the total number of unique ways to arrange the blocks in a row.
Explanation:The student has asked how many different arrangements can be made with 12 blocks in a row. To determine the number of different arrangements, we use the concept of factorial, which is represented by an exclamation mark (!). In this case, we want to find 12!, which represents the product of all positive integers from 1 to 12.
Specifically, the calculation is 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1. This multiplication results in the number of unique ways to arrange the 12 blocks since each block is distinct and can be placed in any position within the arrangement.
Therefore, there are 479,001,600 different arrangements possible when organizing 12 unique blocks in a row, showcasing the vast number of combinations for even a small number of objects.
3 red pens, 9 blue pens, 8 green pens
What is the probability of picking a blue? In a decimal
the probability of picking a blue is 0.45.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
3 red pens, 9 blue pens, 8 green pens
now, we get,
There are a total of 20 pens.
There are 9 blue pens out of 20 total pens.
In decimal format,
i.e. 9/20
=0.45
you have a chance of 0.45 .
hence, the probability of picking a blue is 0.45.
To learn more on probability click:
brainly.com/question/11234923
#SPJ2
What is the input to a trigonometric function?
a ratio
the x position of a point on the circle
a central angle of a circle
the y position of a point on the circle
Answer: A central angle of a circle
Step-by-step explanation:
The trigonometric functions are also known as circular functions.
The two fundamental trigonometric functions are defined as the coordinates of a any point A travelling around on the unit circle of radius 1 .
The input variable in trigonometric functions is the central angle of the circle 'x' such that we get sin x and cos x which give the x and y coordinates of A.
Hence, the input to a trigonometric function is a central angle of a circle.
What is the exact area of a circle with a diameter of 20 cm?
400πcm^2
10πcm^2
100πcm^2
20πcm^2
The exact area of a circle with a diameter of 20 cm is 100π cm². This is found using the formula Area = πr², with 'r' being the radius of the circle.
Explanation:The subject of this question falls under the category of Mathematics, specifically geometry. In order to find the area of a circle, we use the formula: Area = πr², where r is the radius of the circle.
The diameter of the circle is given as 20 cm, so the radius, which is half the diameter, would be 10 cm. Substituting the radius value into the formula gives us: Area = π(10 cm)² = 100π cm². Therefore, the exact area of the circle with a diameter of 20 cm is 100π cm².
Learn more about Area of a Circle here:https://brainly.com/question/28642423
#SPJ3
A package of cookies contains 6 cookies. Each package of cookies costs $1.49.
A function, f(x), is written to represent the cost of purchasing x packages of cookies.
What is the practical domain for the function f(x)?
A: all positive integers
B: all real numbers
C: all whole numbers that are multiples of 6
D: all whole numbers
Given are 6 cookies in a package.
Given that the cost of a package = 1.49 dollars.
Let's assume we purchase 'x' numbers of packages.
So, total cost of 'x' packages = '1.49x' dollars.
f(x) is the function that represents the cost of 'x' packages, i.e. f(x) = 1.49x
Since the number of packages can not be negative or can't be decimal numbers, so 'x' should be positive integral values.
So, the practical domain of f(x) would be "positive integral values".
Hence, option A is correct, i.e. "all positive integers".
How do I find the solution for this quadratic?
Tammy and Wyatt are sales associates at the same used car dealership. Their supervisor is planning to promote the employee with the best sales numbers, on average. The box plots below show their sales, in thousands of dollars, for the past 2 weeks:
box plot labeled Tammy with min at 19, Q1 at 21, median at 25.5, Q3 at 26.75, max at 27.75. Box plot labeled Wyatt with min at 18.5, Q1 at 20.5, median at 24, Q3 at 27.5, max at 28.25
Who should get the promotion, and why?
A) Wyatt should get the promotion. His data is more evenly distributed, so his sales are more consistent.
B) Wyatt should get the promotion because he had the highest sales in a single day.
C) Tammy should get the promotion because her lowest value is higher than Wyatt's lowest value.
D) Tammy should get the promotion. She has a higher median with a smaller IQR, so her sales are better on average.
Answer:
Tammy should get the promotion. She has a higher median with a smaller IQR, so her sales are better on average.
Find the volume of a right prism with height h=10 cm, if: a The base is equilateral triangle with side 4 cm, base altitude of ≈ 3.5 cm. Help me!!!
To find its Volume of Right prism we multiply the base of the triangle times the height and divide that by 2.Then, multiply the area times the length, or the depth, of the prism to find the volume.
Area of the equilateral triangle = [tex]\frac{1}{2}x4x3.5.[/tex]
Area of triangle = 7 square cm.
Volume of the right prism = Area of triangle x Height of prism = 7x10 =70 cubic cm.
Volume of right prism = 70 cubic cm.
A circle is centered at (−8, −13) and has a radius of 13.
What is the equation of the circle?
Enter the equation in the box using lower case variables x and y.
A 9 cm tall cone shaped paper cup can hold up to 58.9 cm cubed of water. What is the minimum amount of paper needed to make the paper cup, assuming no overlap in the paper? Use 3.14 for π.
Please help with geometry
Which is closer to the x-axis (1.4 , 2.2) and (4.1 , 2.4) or (3.9) and (8,9) or (1 1/4 , 2) and 1 1/4 , 8)?
What is 40.15 divided by 7.3, written as a decimal?
Final answer:
To calculate 40.15 divided by 7.3, we can use long division. The final quotient is 5.5, and there is no remainder. Therefore, 40.15 divided by 7.3 written as a decimal is 5.5.
Explanation:
To calculate 40.15 divided by 7.3, we can use long division.
First, we write the division problem with 40.15 as the dividend and 7.3 as the divisor:
5.5
________
7.3 | 40.15
We start by dividing 40.15 by 7.3. The quotient is 5.5.
Next, we subtract 5.5 multiplied by 7.3 from 40.15:
5.5
________
7.3 | 40.15
- 36.5
________
37.65
Since the remainder, 37.65, is greater than the divisor, 7.3, we can continue dividing.
We bring down the next digit from the dividend, which is 0, and divide it by 7.3:
5.5
________
7.3 | 40.15
- 36.5
________
4.15
3.65
We repeat the process of dividing and subtracting until the remainder is less than the divisor:
5.5
________
7.3 | 40.15
- 36.5
________
4.15
3.65
5.5
0
The final quotient is 5.5, and there is no remainder. Therefore, 40.15 divided by 7.3 written as a decimal is 5.5.
9. Find the value of x. Round to the nearest tenth. The diagram is not drawn to scale
[Geometry Basics] I'm just checking if this is correct:
~ Endpoint: (-9, -1), midpoint: (8,14)
Answer I got: (25, 31)
~ Endpoint: (10,12), midpoint: (6,9): (2,6)
I will give you brainiest if it's correct :) And 20 pts.
Find the slope of the line
-4
-1/4
1/4
4
if f(x) = x-1 and g(x) =2x-3 find the sum, difference, product and quotient of these two functions
Jack's father let jack use a rectangular section of the back yard that had dimensions of 10 feet by 12 feet for his garden. he wanted to put a fence around the outside of the garden. how long should the piece of fencing he needs to buy be?
Chris plants a sunflower that is 6 inches tall. The sunflower is expected to grow at an average rate of 1.5 inches per day during the next month.
A. Create an equation that Chris can use to find the number of days, x, it will take the sunflower to grow to a height of 45 inches.
B. How many days will it take the sunflower to grow to a height of 45 inches?
The volume of two spheres are 327\pi in^{3} and 8829\pi in^{3}
What is the ratio of their radii?
The median is 28; 16,24,x,48