Mav is working two summer jobs, making
$15 per hour lifeguarding and making $10
per hour landscaping. In a given week, she
can work at most 12 total hours and must
earn no less than $140. If x represents the
number of hours lifeguarding and y
represents the number of hours
landscaping, write and solve a system of
inequalities graphically and determine
one possible solution.
Inequality 1: y ≥û
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
y
Inequality 2: y ≥û
0 1 2 3
4
5
switch shade
plot
6
switch shade
plot
7
8 9 10 11 12 13 14 15 16 17 18 19 20
Xx
Answers
This solution satisfies both constraints, as x + y = 4 + 8 = 12, which is less than or equal to 12, and 15x + 10y = 15 * 4 + 10 * 8 = 120, which is greater than or equal to 140.
What is inequality?
In mathematics, a relationship between two expressions or values that are not equal to each other is called 'inequality. ' So, a lack of balance results in inequality.
We can write the first inequality as x + y <= 12
This inequality represents the constraint that Mav can work at most 12 hours in total between both jobs.
The second inequality represents the constraint that Mav must earn no less than $140 in a given week, which can be written as:
15x + 10y >= 140
To graph the system of inequalities, we can plot the lines corresponding to x + y = 12 and 15x + 10y = 140 on the coordinate plane and shade the region that satisfies both inequalities.
The solution to the system of inequalities will be the values of x and y that lie in the shaded region.
One possible solution is x = 4 and y = 8, which means that Mav works 4 hours of lifeguarding and 8 hours of landscaping in a given week, earning a total of 15 * 4 + 10 * 8 = $120.
Hence, This solution satisfies both constraints, as x + y = 4 + 8 = 12, which is less than or equal to 12, and 15x + 10y = 15 * 4 + 10 * 8 = 120, which is greater than or equal to 140.
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Answer:
y ≤ 12 -xy ≥ 14 -1.5x(x, y) = (4, 8) — 4 hours lifeguarding, 8 hours landscapingStep-by-step explanation:
You want inequalities, their graph, and a possible solution satisfying Mav's requirement for at most 12 total hours spent lifeguarding at $15 per hour and landscaping at $10 per hour, with an income of at least $140.
SetupThe required relations can be written ...
x + y ≤ 12 . . . . . . . total hours
15x +10y ≥ 140 . . . . total earnings
InequalitiesThe inequalities need to be solved for y to match the answer format requirements.
inequality 1: y ≤ 12 -x . . . . . . . . . . subtract x
inequality 2: y ≥ 14 -1.5x . . . . . . divide by 10, subtract 1.5x
SolutionThe attached graph shows a couple of possible solutions. The solution space is the doubly-shaded area bounded by vertices ...
(4, 8), (12, 0), and (9 1/3, 0)
Mav will make the most money working 12 hours lifeguarding (x, y) = (12, 0).
She can just meet her income requirements by working 8 hours lifeguarding and 2 hours landscaping (x, y) = (8, 2).
One possible solution is 4 hours lifeguarding and 8 hours landscaping.
Related Questions
QUESTION FOR FOR LIH04
Answers
Which proportion can be used to find the length of sides ik
Answers
The proportion i/k = 12 can be used to find the length of sides i and k if the perimeter is 12 units. To solve for the length of each side, the equation i + k = 12 is used, and then the two sides are divided by each other to get the proportion i/k = 12.
The proportion i/k = 12 can be used to find the length of sides i and k of a shape if the perimeter is 12 units. In order to solve for the length of each side, the equation i + k = 12 is used to determine the sum of the sides. The two sides are then divided by each other, resulting in the proportion i/k = 12. This proportion can then be used to find the length of sides i and k. For example, if the length of side i is 8, then the length of side k is 4. This can be determined by dividing 8 by 4, which results in the proportion i/k = 2. If the perimeter is 12 units, then the equation i + k = 12 can be used to determine that the length of side i is 6 and the length of side k is 6, since 6 + 6 = 12. The proportion i/k = 12 can then be used to confirm that the length of side i is 6 and the length of side k is 6.
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The complete question is
Which proportion can be used to find the length of sides ik if the perimeter is 12 units?
Using the image below, identify the following angles:
Column A
1.
<1 and <4
2.
<2 and <6
3.
<1 and <8
4.
<3 and <5
Column B
a. Corresponding
b. Alternate Exterior
c. Same-Side Interior
d. Vertical
Answers
Answer:
1) Vertical angles
2) Corresponding
3) Alternate exterior
4) Same-Side Interior
Step-by-step explanation:
Convert milligrams per liter to micrograms per (fluid ounce)
Answers
To convert milligrams per liter (mg/L) to micrograms per fluid ounce (µg/fl oz), we can use the conversion factor of 29.5735.
This conversion factor takes into account the difference in volume between a liter and a fluid ounce.
1 fl oz = 29.5735 mL
1 L = 1000 mL
So, to convert from milligrams per liter to micrograms per fluid ounce, we divide by 29.5735 and multiply by 1000:
(mg/L) * 1000 / 29.5735 = (µg/fl oz)
Therefore, to convert a value x from milligrams per liter to micrograms per fluid ounce:
x (µg/fl oz) = x (mg/L) * 1000 / 29.5735
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calculate the cost of producing container A using surface area
Answers
The program to cost of each container and the total cost of producing all the containers is given below.
How to depict the C ProgramThe program based on the information will be:
#include <iostream>
using namespace std;
int main() {
int r,h,c,n;
cout<<"Enter the base radius : ";
cin>>r;
cout<<"\nEnter the height : ";
cin>>h;
cout<<"\nEnter the cost per square cm : ";
cin>>c;
cout<<"\nEnter the number of containers : ";
cin>>n;
int s_area = (3.14*r*2)+(2*3.14*r*h);
int cost = c*s_area;
int t_cost = n*cost;
cout<<"\nCost of each container : "<<cost<<endl;
cout<<"Total cost : "<<t_cost<<endl;
}
Based on the above, we've created a program to take the radius of the base, the height of the container, the cost per square centimeter of the material cost.
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A manufacturer wishes to determine the cost of producing an open-top cylindrical container. The surface area of the container is the sum of the area of the circular base plus the area of the outside (the circumference of the base times the height of the container). Create C program to take the radius of the base, the height of the container, the cost per square centimeter of the material (cost), and the number of containers to be produced (quantity). Calculate the cost of each container and the total cost of producing all the containers.
Segment has endpoints (−7, 14) and (11, 5). Point lies on at (−3, 12).
What is the ratio of to ?
Last time I asked the question Brainly decided to delete like 90% of my question.
Answers
The ratio of the coordinate point on the line is 2 to 7.
What is the ratio of the point on the coordinate?The ratio of the coordinate point on the line is calculated as follows;
Let the coordinate points = (xp, yp)
Let the ratio of the line = a:b
xp = x₁ + (a/(a+b) (x₂ - x₁)
yp = y₁ + (a/a+b) (y₂ - y₁)
-3 = -7 + ( a/a+b)(11 - - 7)
-3 = -7 + (a/a+b)(18)
-3(a + b) = -7(a+b) + 18a
7(a + b ) - 3(a+b) = 18a
7a + 7b - 3a - 3b = 18a
4b = 14a
4/14 = a/b
2/7 = a/b
2 : 7 = a : b
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what does the degree of a vertex in the hollywood graph represent? what does the neighborhood of a vertex repre- sent? what do the isolated and pendant vertices represent?
Answers
The degree of a vertex represents the number of other actors or actresses that an actor or actress has worked with in movies.
The neighborhood of a vertex represents the set of actors or actresses that an actor or actress has worked with in movies.
Isolated vertices represent actors or actresses who have not worked with any other actors or actresses in any movie, while pendant vertices represent actors or actresses who have only appeared in one movie with another actor or actress in the Hollywood graph.
The Hollywood graph is an undirected graph because the relationship between actors and actresses is mutual.
Each vertex in this graph represents an actor or actress, and the degree of a vertex represents the number of other actors or actresses that they have worked with in movies. In other words, the degree of a vertex represents the number of edges that are connected to that vertex.
The neighborhood of a vertex in a graph refers to the set of all vertices that are adjacent to it. In the context of the Hollywood graph, the neighborhood of a vertex represents the set of actors or actresses that a particular actor or actress has worked with in movies.
An isolated vertex in a graph is a vertex that has no edges connected to it. In the context of the Hollywood graph, an isolated vertex represents an actor or actress who has not worked with any other actors or actresses in any movie.
A pendant vertex in a graph is a vertex that has only one edge connected to it. In the context of the Hollywood graph, a pendant vertex represents an actor or actress who has only appeared in one movie with another actor or actress in the Hollywood graph.
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78miles on 3gallons is it 26
Answers
Answer:
Yes, 26
Step-by-step explanation:
78 miles ÷ 3 gallons = 26 mpg
when a researcher rejects the null hypothesis, the difference is declared to be: select one: a. statistically significant. b. statistically insignificant. c. statistically unimportant. d. statistically strong.
Answers
Answer:
C
Step-by-step explanation:
In a family the oldest child is 7 years older than the youngest child what is a equation to represent this situation
Answers
The equation to represent the situation where the oldest child is 7 years older than the youngest child, using x for the age of the youngest child and y for the age of the oldest child, is y = x + 7.
If we let x represent the age of the youngest child in a family, then we can say that the oldest child is 7 years older than the youngest child. We can represent the age of the oldest child using the expression "x + 7", because if we add 7 to the age of the youngest child, we get the age of the oldest child.
Therefore, we can write an equation to represent this situation by equating the age of the oldest child to the age of the youngest child plus 7. This can be written as:
x + 7 = Oldest child's age
where x is the age of the youngest child, and "Oldest child's age" represents the age of the oldest child in the family. This equation tells us that if we know the age of the youngest child, we can find the age of the oldest child by adding 7 to it.
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pls help due now!!!!!!!!!!!!!!!
Answers
Answer: D. 6 cm
Step-by-step explanation:
V = 4/3πr^3
r = (3 V/4π)^1/3 = (3* 900/4*π)^1/3 = 5.98942
Geometry and 60 POINTS!!!!!!
Answers
Answer:
a = 6 ft.
------------------------------
Given is an isosceles right triangle.
As per property of a such triangle, its hypotenuse is √2 times its leg.
That is:
a√2 = 6√2, divide both sides by √2a = 6Answer:
a = 6 ft
Step-by-step explanation:
We have to find,
→ The value of a in the diagram.
Formula we use,
=> Using Pythagoras theorem.
→ (Hyp)² = (Opp)² + (Base)²
Forming the equation,
→ (6√2)² = (a)² + (a)²
Now the value of a will be,
→ (6√2)² = (a)² + (a)²
→ (a)² + (a)² = (6√2)²
→ 2a² = 36 × 2
→ 2a² = 72
→ a² = 72 ÷ 2
→ a² = 36
→ a = √(36)
→ [ a = 6 ft ]
Hence, the value of a is 6 ft.
Write the equation in standard form of the line y=1/9x+5
Answers
The equation in standard form is x - 9y = -45.
What is the Equation of a Line in Standard Form?The equation of a line in standard form is Ax + By = C, where x and y are variables and A, B and C are integers.
Given equation is y = 1/9 x + 5.
Here 1/9 is not an integer.
So multiplying the equation throughout by 9, we get,
9y = x + (5 × 9)
9y = x + 45
Subtracting both sides by x,
9y - x = 45
-x + 9y = 45
Multiplying throughout by -1,
x - 9y = -45, which is in standard form.
Hence the equation is x - 9y = -45 in standard form.
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Need this for a math lesson
Answers
The upper quartile score on the final exam is 83.
What is Upper quartile?Upper quartile, represented as Q₃, also known as third quartile is the value in a data set such that 75% of the points in the data set are below this value, after arranging in an ascending order.
Given data set is the scores for the final exam in an 8th grade math class.
58, 72, 74, 92, 84, 40, 74, 81, 76, 83.
First arrange the data in an ascending order.
40, 58, 72, 74, 74, 76, 81, 83, 84, 92.
Median is the middle element.
Median = (74 + 76) / 2 = 75
Upper quartile is the median of the second half.
Consider the second half.
76, 81, 83, 84, 92.
Median = 83
Third quartile = 83
Hence 83 is the upper quartile score on the final exam.
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uppose that shoe sizes of american women have a bell-shaped distribution with a mean of 8.06 and a standard deviation of 1.52 . using the empirical rule, what percentage of american women have shoe sizes that are between 6.54 and 9.58 ?
Answers
Using the empirical rule, we can conclude that approximately 68% of American women have shoe sizes between 6.54 and 9.58.
Using the empirical rule, we can say that approximately 68% of the data falls within one standard deviation of the mean, approximately 95% of the data falls within two standard deviations of the mean, and approximately 99.7% of the data falls within three standard deviations of the mean.
To find the percentage of American women who have shoe sizes between 6.54 and 9.58, we first need to standardize these values by subtracting the mean and dividing by the standard deviation:
z1 = (6.54 - 8.06) / 1.52 = -1.00
z2 = (9.58 - 8.06) / 1.52 = 1.00
Now, we can use the empirical rule to find the percentage of women with shoe sizes between z = -1.00 and z = 1.00. Since this interval corresponds to one standard deviation from the mean, we know that approximately 68% of the data falls within this range.
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What is the exact volume of a cylinder with a height of 5 feet and a radius of 2 feet?
Answers
Answer:
V = 62.83ftStep-by-step explanation:
V≈62.83ft³
I hope it helped you out.
7. Find the value of w in the regular heptagon
whose interior angle has a measure of
(w + 8). Round your answer to the nearest
hundredth.
Answers
Answer: 96
The sum of the interior angles of a regular heptagon is equal to (n-2)180 degrees, where n is the number of sides of the polygon.
Since a regular heptagon has 7 sides, the sum of its interior angles is (7-2)180 = 720 degrees.
Therefore, the measure of each interior angle is 720 degrees / 7 = 104 degrees.
If the measure of an interior angle is (w + 8) degrees, then w + 8 = 104.
Solving for w, we get w = 96.
1. You need to dig a tunnel. You begin at the surface of the ground. The tunnel slopes downward for 83 meters. The final depth below ground is 52 meters. Find the angle of depression of the tunnel's descent. Round your answer to the nearest tenth. Draw a diagram to illustrate your problem.
Answers
Answer: 38.8°
Step-by-step explanation:
See the attached diagram:
From it we can tell that the tunnel forms a right triangle, with the length of a leg and the hypotenuse given. We can use the sine function to easily answer this, (letting θ be the angle we need to find)
sinθ = 52/83
.: θ = arcsin(52/83)
(Note: arcsin is the inverse of the sine function)
.: θ ≅ 38.8°
Edward and his little brother made up
a game using coins. They flip the coins
towards a cup and receive points for
every one that makes it in. Edward
starts with 20 points, and his little
brother starts with 18 points. Edward
gets 2 points for every successful
shot, and his brother, since he is
younger, gets 3 points for each
successful shot. Eventually, the
brothers will have a tied score in the
game. How many additional shots will
each brother have made? How many
points will they both have?
Edward and his brother will have each
made ________
shots, for a tied score
of ________
Answers
His little brother made 4
5. Rajah 2 menunjukkan sebuah silinder dan sebuah kuboid. Diagram 2 shows a cylinder and a cuboid. Guna / Use = 271 30 cm Rajah 2/ Diagram 2 Diberi bahawa isi padu silinder dan kuboid adalah sama. Cari nilai x dan berikan jawapan anda betul kepada dua tempat perpuluhan. It is given that the volume of the cylinder and the cuboid are the same. Find the value of x and give your answer correct to two decimal places. Jawapan / Answer: 7 cm 8 cm [3 markah/ 3 marks] For Examine Us
who can help me pls
Answers
Answer:
Step-by-step explanation:
5. Diagram 2 shows a cylinder and a cuboid. Diagram 2 shows a cylinder and a cuboid. Fold / Use = 271 30 cm Find the value of x and give the correct answer to the multiple of two places. It is given that the volume of the cylinder and the cuboid are the same. Find the value of x and give your answer correct to two decimal places. Answer / Answer: 7 cm 8 cm [3 markah/ 3 marks] For Examine Us
Alonzo is going to watch a movie in his collection. He has 3 action movies, 11 comedies, and 9 dramas.
He will randomly select one movie. What is the probability that the movie he selects is not a comedy?
Write your answer as a fraction.
Answers
The probability that he does not select a comedy is 12/23
What is the probability that the movie he selects is not a comedy?If we assume that all the movies have the same probability of being randomly selected, then the probability of selecting a movie that is not a comedy is equal to the quotient between the number of movies that aren't comedies and the total number of movies.
There are:
3 action ones.
11 comiedies.
9 dramas
For a total of 23 movies, and 12 of them are not comedies, then:
P = 12/23
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f(x) = -2x
g(x) = 8x² - 5x+7
Find (f g)(x).
O-16x³5x+7
O 16x4 + 10x³ - 14x²
O-16x² + 10x - 14x
O-16x³ + 10x² - 14x
Answers
Answer:
-16x² + 10x - 14.
Step-by-step explanation:
To find the composition of two functions, (f g)(x), we first evaluate g(x) and then substitute the result into f(x).
So, let's first evaluate g(x):
g(x) = 8x² - 5x + 7
Next, substitute g(x) into f(x):
(f g)(x) = f(g(x)) = f(8x² - 5x + 7) = -2(8x² - 5x + 7) = -16x² + 10x - 14
Therefore, (f g)(x) = -16x² + 10x - 14.
Please help me on this I am confused find the value of x pls pls pls pls pls pls pls pls pls pls pls pls pls.
Answers
The value of x is given as follows:
x = 130º.
How to obtain the value of x?To obtain the value of x, we must consider the exterior angle theorem, which states that each interior angle is supplementary with it's interior angle, meaning that the sum of their measures is of 180º.
As the interior angle is of 50º, the measure of the exterior angle x is given as follows:
x = 180 - 50
x = 130º.
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During a 36 - year period, lightning killed 2,457 people in the United States. Assuming that rate holds true today and is constant throughout the year. Find the probability that tomorrow: (a) No one in the United States will be struck and killed by lightning. (b) One person will be struck and killed.
(c) More than one person will be struck and killed.
Answers
Answer: A
Step-by-step explanation: This is how to solve: 3239 / (36 *365)
That's 0.246499239 kills per day, so none died
I hope this helped!
write x=[tex]\sqrt{y^2-3}[/tex] as a set of parametric equations with x =[tex]\sqrt{} t[/tex]
Answers
The set of parametric equations are
[tex]x=\sqrt{t}[/tex]
[tex]y=\sqrt{3+t[/tex]
Parametric Equations:A parametric equation uses a parameter, which is an independent variable (often represented by the notation t), and dependent variables, which are expressed as continuous functions of the parameter and are independent of other variables.
Using one or more independent variables known as parameters, a parametric equation defines a set of quantities as functions.
Given the equation:
[tex]x= \sqrt[]{y^{2}-3 }[/tex]
Let's find a set of parametric equation for the given equation given the parameter:
[tex]x = \sqrt{t}[/tex]
From the parameter:
[tex]x = \sqrt{t}[/tex]
Now, substitute [tex]\sqrt{t}[/tex] for x in the given equation:
[tex]x=\sqrt{y^2-3} \\\\\sqrt{t} = \sqrt{y^2 - 3} \\\\t=y^2-3\\\\y^2=3+t\\\\y=\sqrt{3+t}[/tex]
Therefore, the set of parametric equations is:
• [tex]x=\sqrt{t}[/tex]
• [tex]y=\sqrt{3+t}[/tex]
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A right triangle has legs measuring 20 in. and 28 in. what is the length of the hypotenuse? round to the nearest tenth. responses 8.0 in. 8.0 in. 19.6 in. 19.6 in. 34.4 in. 34.4 in. 1184.0 in.
Answers
The length of the hypotenuse of a right triangle with legs measuring 20 inches and 28 inches is approximately 34.4 inches, found using the Pythagorean theorem.
The length of the hypotenuse of a right triangle with legs measuring 20 inches and 28 inches can be calculated using the Pythagorean theorem, which states that the square of the sum of the squares of the lengths of the legs determines the length of the hypotenuse.
So, if we call the length of the hypotenuse "h", we have [tex]h^{2}[/tex] = [tex]20^2 + 28^2[/tex]
Solving for h:
[tex]h^2 = 20^2 + 28^2[/tex]
[tex]h^2[/tex] = 400 + 784
[tex]h^2[/tex] = 1184
h = [tex]\sqrt{1184}[/tex]
h ≈ 34.4 in.
So, the length of the hypotenuse is approximately 34.4 inches, rounded to the nearest tenth.
The Pythagorean theorem is a fundamental mathematical relationship that states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal tothe squared lengths of the two legs added together. In this case, the two legs have lengths of 20 inches and 28 inches, and the length of the hypotenuse can be found by solving for the square root of the total of the leg squares.
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16. The diagram shows a sketch of the graph y = ab^x where b>0
The curve passes through the points A (1, 10) and B (4,80).
The point C (-1, k) lies on the curve.
Find the value of k.
I don’t what exponential graphs are and I don’t understand what the question means!!!
Answers
Answer:
k is 2.5.
Step-by-step explanation:
To find the value of k, we can use the information given about points A and B to find the value of the parameters a and b. Since we know that the curve passes through A (1, 10) and B (4, 80), we can substitute these points into the equation y = ab^x to find the values of a and b.
Starting with point A:
10 = a * b^1
Next, using point B:
80 = a * b^4
We can now use these two equations to find the value of b:
10 = a * b^1
80 = a * b^4
Dividing the second equation by the first equation:
8 = b^3
Taking the cube root of both sides:
b = 2
We can now use either of the two equations to find the value of a:
10 = a * b^1
a = 10/2 = 5
Now that we have found the values of a and b, we can substitute the point C (-1, k) into the equation y = ab^x to find the value of k:
k = 5 * 2^(-1) = 5 * (1/2) = 2.5
So the value of k is 2.5.
At a construction site, sand is poured from a truck into a conical pile. The pile has a diameter of 12
feet and is 10 feet tall. Which of the following best describes the volume of the sand?
Answers
The volume of the sand which is equal to the volume of the cone will be 376.8 cubic feet.
What is the volume of the cone?Let h be the height of the cone and A be the base area of the cone.
Then the volume of the cone will be given as,
Volume = (1/3) × A × h
At a construction site, sand is poured from a truck into a conical pile. The pile has a diameter of 12 feet and is 10 feet tall.
The base area of the cone is given as,
A = π × (d/2)²
A = 3.14 × (12 / 2)²
A = 3.14 × 36
A = 113.04 square feet
Then the volume of the cone is given as,
V = 1/3 × 113.04 × 10
V = 376.8 cubic feet
The volume of the sand which is equal to the volume of the cone will be 376.8 cubic feet.
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hey can someone help me
Answers
60 children choose their favourite fruit out of apples bananas and watermelon 30% chose apples and 25% chose bananas How many children chose watermelon
Answers
Answer:
27 children.
Step-by-step explanation:
Let's call the number of children who chose apples x. Then, the number of children who chose bananas is 0.25x. The number of children who chose watermelon is 60 - x - 0.25x = 60 - 1.25x.
Since 30% of the children chose apples, we know that:
0.30 * 60 = x
So, x = 18, which means 18 children chose apples.
And since 25% of the children chose bananas, we know that:
0.25 * 60 = 0.25x = 15
So, 15 children chose bananas.
Finally, the number of children who chose watermelon is:
60 - 18 - 15 = 27 children.
