Kennedy is working two summer jobs, making $11 per hour babysitting and making $8 per hour clearing tables. In a given week, she can work at most 17 total hours and must earn no less than $160. If x represents the number of hours babysitting and y represents the number of hours clearing tables, write and solve a system of inequalities graphically and determine one possible solution.
Using graphical method of Linear programing problem, the system of inequalities are x + y ≤ 17 and 11x +8y ≥ 160. The maximum value of z=145, x=8,y=14 .
What is linear programing problem?Linear programing problem is" a system of process of finding maximum or minimum value of any variables".
What is inequalities?Inequalities is statement of an order relationship, "greater than or greater than or equal to, less than or less than or equal to between two numbers or algebraic expressions" .
According to the question,
Let 'x' represents the number of hours clearing tables and 'y' represents the number of hours clearing tables.
maximum of z =11x+8y
x + y ≤ 17 → (1)
11x +8y ≥ 160 → (2)
Using graphical method, we can solve this Linear programing problem(LPP).
In inequality(1) put x=0, we get y=17 and y=0, we get x=17 therefore in equation (1) we get (17,17) draw this point on graph.
In inequality(2) put x=0 we get y=20 and put y=0 we get x=14.54 from equation(2) we get (14.54,20) draw this point on graph.
To find maximum value of z solve this equation
x + y =17 →(3)
11x +8y =160 →(4),
multiply (3) by 8 we get, 8x+8y=136 and subtract the equation (3) from the equation (4)
11x+8y=160
8x+8y=136 [multiply by(-) on both sides]
we get x=3 substitute this 'x' value in equation (3)
3+y=17
y = 14.
The maximum z = 11x+8y
z = 11(3)+8(14) [substitute (3,14)]
maximum z =145.
Hence, using graphical method of Linear programing problem, the system of inequalities are x + y ≤ 17 and 11x +8y ≥ 160. The maximum value of z=145, x=8,y=14 .
Learn more about Linear programming problem here
https://brainly.com/question/27580242
#SPJ2
A 32-foot ladder is leaning against a building and forms a 29.37° angle with the ground. How far away from the building is the base of the ladder? Round your answer to the nearest hundredth.
15.69 feet
18.01 feet
27.89 feet
36.72 feet
Answer:
hope this helps, brainlist? (OwO)
Step-by-step explanation:
I think the answer is 27.89 feet, C
The building is 27.89 feet far from the base of the ladder if a 32-foot ladder is leaning against a building and forms a 29.37° angle with the ground.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have:
Lenght of the ladder = 32 foot
The angle formed between the ladder and the ground = 29.37°
The ladder, wall of the building, and the ground are making a right-angle triangle.
Let's suppose the base of the ladder is x feet far from the building.
Applying the Cos ratio to find the value of x:
[tex]\rm Cos29.37\°=\frac{x}{32}[/tex]
x = 27.887 feet or (Cos29.37° = 0.871)
x = 27.89 feet
Thus, the building is 27.89 feet far from the base of the ladder if a 32-foot ladder is leaning against a building and forms a 29.37° angle with the ground.
Know more about trigonometry here:
brainly.com/question/26719838
SPJ2
Pls pls pls help ,,,,,,,,
Answer:
72 (d)
Step-by-step explanation:
I did the math
need help asap please
Answer:
16°
Step-by-step explanation:
We know that in parallelogram opposite angles are equal so
4u - 8° = 6u - 40°
6u - 4u = 40° - 8°
2u = 32°
u = 32° /2
u = 16°
The value of u should be 16° to make PQRS parallelogram.
Hope it will help.
Answer:
[tex]\displaystyle 16 = u[/tex]
Step-by-step explanation:
Diagonal, opposite angles are congruent in every parallelogram:
[tex]\displaystyle [5u + 44]° = [14u - 100]° → -144 = -9u; 16 = u \\ \\ AND/OR \\ \\ [6u - 40]° = [4u - 8]° → -32 = -2u; 16 = u[/tex]
No matter which pair you take, you will ALWAYS arrive at the same exact solution.
I am joyous to assist you at any time.
What is the slope of the line in the graph?
5
W
4
3
3 2 1
2 3 4 5 X
-5 -4 -3 7-11
-2
-3
-5
1
Answer:
the slope of this line is 1
Answer:
The slope of this line is 1
If 0 = 35, then solve for X.
X
9
Round to the nearest hundredth.
Answer:
x = 15.69
Step-by-step explanation:
Given that,
Height, h = 9
Hypotenuse, H = x
Angle, [tex]\theta=35[/tex]
We need to find the value of x.
The relation between height, Hypotenuse and the angle is given by :
[tex]\sin\theta=\dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\\sin(35)=\dfrac{9}{x}\\\\x=\dfrac{9}{\sin(35)}\\\\x=15.69[/tex]
So, the value of x is 15.69.
A planner assembles party favor bags filled with glow sticks and temporary tattoos for a client. There are 24 glow sticks and 30 temporary tattoos to divide evenly among the bags.
If there are no leftover items, what is the greatest number of bags the planner can assemble
Answer: The greatest number of bags is 6.
Step-by-step explanation:
In each bag, there would be 4 glow sticks and 5 tattoos, which is the greatest number that can be put in each bag without having any left.
Suppose that a chemist is mixing two acid solutions, one of 15% concentration and the other of 25% concentration. Which of the following concentrations could not be obtained?
Choose the correct answer below.
Answer: d. 29%
Step-by-step explanation:
The mixture of the two concentrations should equal a concentration that is between the concentration percentages of the two solutions.
This is because the lower concentration percentage will pull the higher one down while the higher concentration will pull the lower one up. It will not be possible to get a mixture concentration that is lower than the lower concentrated acid or higher than the higher concentration acid.
Mixture concentration must be between 15% and 25%.
Option D at 29% is therefore not possible.
112 yards
R
Sand
15 yards
Trap
20 yards s
If RS is parallel to AB, what is the width of the sand trap?
149 yards
82 yards
107 yards
84 yards
Answer:
my teacher has cancer please help her at #snowmanchallenge
Step-by-step explanation:
try to spread the help every snowman is ten dollars for her
Answer:
84
Step-by-step explanation:
112/20= 5.6
5.6*15=84
brainly is easy
SOMEONE PLEASE HELP ME THIS IS ALMOST DUE AND I NEED THE RIGHT ANSWER PLZ!!!
Answer:
Option A: 8 yards
Step-by-step explanation:
From the given graph, we have;
Coordinate of point A = (1, -4)
Coordinate of point B = (-3, 3)
Now,he threw baseball from point A to point B.
Distance between two coordinates is;
√((y2 - y1)² + (x2 - x1)²)
AB = √((3 - (-4))² + (-3 - (1))²)
AB = √(7² + (-4)²)
AB = √(49 + 16)
AB = √65 yards
AB = 8.06 yards
Approximating to a whole number gives;
AB ≈ 8 yards
find the area or this triangle
Answer:
Area of triangle = 15 square units
Step-by-step explanation:
We need to find area of the triangle, given the vertices:
A=(4,0)
B=(1,5)
C=(7,5)
The formula used is: [tex]Area\:of\:triangle=\frac{1}{2}(x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2))[/tex]
We have: [tex]x_1 =4, y_1 =0, x_2 =1, y_2=5, x_3=7 , y_3=5[/tex]
Putting values and finding area
[tex]Area\:of\:triangle=\frac{1}{2}(x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2))\\Area\:of\:triangle=\frac{1}{2}(4(5-5)+1(5-0)+7(0-5))\\Area\:of\:triangle=\frac{1}{2}(4(0)+1(5)+7(-5))\\Area\:of\:triangle=\frac{1}{2}(0+5-35)\\Area\:of\:triangle=\frac{1}{2}(-30)\\Area\:of\:triangle=-15[/tex]
We will be ignoring negative sign, because area of triangle is positive.
So, Area of triangle = 15
solve the questions bellow
Answer:
1. 29.67°
2. 68.96°
3. 89.85°
Step-by-step explanation:
1. Reference angle = x
Opposite = 45 cm
Adjacent = 79 cm
Therefore:
[tex] tan(x) = \frac{45}{79} [/tex]
[tex] tan(x) = 0.569620253 [/tex]
[tex] x = tan^{-1}(0.569620253) [/tex]
[tex] x = 29.67 [/tex] (nearest hundredth)
2. Reference angle = B
Opposite = 14
Hypotenuse = 15
Therefore:
[tex] sin(B) = \frac{14}{15} [/tex]
[tex] sin(B) = 0.93333 [/tex]
[tex] B = sin^{-1}(0.93333) [/tex]
[tex] B = 68.96 [/tex] (nearest hundredth)
3. Reference angle = x
Adjacent = 238,900 mi
Hypotenuse = 92,955,807 mi
Therefore:
[tex] cos(x) = \frac{238,900}{92,955,807} [/tex]
[tex] x = cos^{-1}(\frac{238,900}{92,955,807}) [/tex]
[tex] x = 89.85 [/tex] (nearest hundredth)
You roll a six sided die . What is the probability that the value of the roll will be a two or six ?
Answer:
2 out of 6
Step-by-step explanation:
I think its this because out of the 6 sides you are hoping that two of the outcomes are true
Please help me with this :,)
Answer:
alright gotcha!
Step-by-step explanation:
I am attaching the photo gimme some time
10% of ________ is 7
25% of ________ is 6
Answer:
I got
10% of 70 is 7
Answer:
First one is 70
Second one is 24
Step-by-step explanation:
First one :7*100=700
700÷10=70
The second one :6*100=600
600÷25=24
What is the decimal Expansion of the following fraction?
Answer:
B
Step-by-step explanation:
1/25 = 0.04 only. this is surely the anwer
Bernard designs motorized bicycles at Smart Gear Technologies. His total earnings are
$54,000 this year. Bernard pays $201 in payroll taxes for every $1,000 he earns.
What is Bernard's net income for this year?
Answer:
600
Step-by-step explanation:
Are the ratios 1:2 and 2:3 equivalent?
Answer:
Step-by-step explanation:
No
Answer:
No, Picture it as fractions. 1:2 is the same as 1/2, and 1:3 the same as 1/3
Which equation is a linear function?
y= 2 + 3
y = 22 - 1
y= 22 +7
Any method to solve the quadratic equetion below over the set of complex numbers.
2x(x+6)=(x-4)(x+3)
Simplify this expression.
6x + 3 – 4x + 2y + 7
Answer:
2x + 10 + 2y
Step-by-step explanation:
6x + 3 – 4x + 2y + 7
(6x - 4x) = 2x
2x + 3 +2y + 7
(3 + 7) = 10
Answer: 2x + 10 + 2y
Translate and solve: fifty times n is at most 500.
Answer:
n must be less than or equal to 10
Step-by-step explanation:
Pls help extra points and mark brainlist
Step-by-step explanation:
that seems like a decimal? 2.8?
9+6²-2.8
9+36-2.8
42.2
hope it helps.
have a great day :)
Lynnetta gets paid weekly for completing household chores. The amount of money she earns for doing dishes, D, is
approximately Normally distributed with a mean of $53 and a standard deviation of $3.60. The amount of money she
earns for doing laundry, L, is approximately Normally distributed with a mean of $47 and a standard deviation of
$4.10. Assume that D and L are independent random variables.
What is the probability that Lynnetta will earn more than $110 in a randomly selected week?
0.034
0.097
0.249
0.966
Answer:
its a
Step-by-step explanation:
i guessed on edge lol
A certain lottery has 31 numbers. In how many different ways can 4 of the numbers be selected?
Which of the following expressions has the greatest value?
110
33
52
25
Answer:
2^5
,,,,,,,,,,, ,,,,,,,,,
Use your knowledge of special right triangles to find y. Write your answer in simplest radical form.
Please be quick
Answer:
[tex] \sin(30°) = \frac{10}{y} \\ \frac{1}{2} = \frac{10}{y} \\ \boxed{y = 20 \: mi}[/tex]
or,
[tex] \cos(60°) = \frac{10}{y} \\ \frac{1}{2} = \frac{10}{y} \\ \boxed{y = 20 \: mi}[/tex]
20 mi is the right answer.The classes at the middle school want to raise money.
The sixth grade runs a bake sale for 5 hours and makes $170.
The seventh grade sets up a dunking booth for 4 hours and makes $112.
The eighth grade has a car wash and makes $192 in 6 hours.
Which class has the highest rate for raising money?
Seventh grade
Sixth grade
Eighth grade
All classes had the same hourly rate.
Answer:
This is a multiple step question. Before you can answer it you must find what it is asking, which is the highest rate for making money, or the greatest rate of change. To compare the rate of change between each grade, you must first have them in common units, which can be done by finding how much money was made by each grade in one hour. To find this, divide the number of dollars made by the number of hours it was made in to get how much was made in one hour. Doing this shows that the sixth grade made 34 dollars an hour (170 divided by 5), seventh made 28 dollars an hour (112/4), and the eighth grade made 32 dollars an hour (192/6). Then compare the numbers to see that the greatest amount earned in one hour was 34 dollars, by the sixth grade, which then becomes your answer: The sixth grade had the highest rate for raising money.
Please solve if so thank you so much!!
Answer:
60 x 4
Step-by-step explanation:
Answer:
y=35x+60
x=4
Step-by-step explanation:
There are 4 boys eating oranges. Each boy eats 1 / 2 of an orange. How many oranges did the boys eat?
Answer:
2 oranges
Step-by-step explanation:
Two halves make a whole orange, and since there's four of them, they are eating 2 oranges.
Answer:they would have eaten 2 because 1/2+1/2 is a whole and since there are 4 boys eating 1/2 of an orange they would have eaten 2 oranges