Alex is a writer who writes poems and short stories. For an upcoming writer's workshop Alex wants to write some new works. He needs to determine how many poems and short stories he will have ready for the workshop. Alex figures that each poem will take him 30 hours and each short story will take him 70 hours. For the workshop Alex wants to have at least 4 poems and 3 short stories to display. If Alex has 840 hours of work time available, what solution represents the maximum number of works that he could write while staying in his time budget
Answers
Answer:
The maximum number of works that he can write while staying in his time budget is 24.
21 poems and 3 short stories
Step-by-step explanation:
In order to solve this problem we must first determine what our variables are. In this case it's the number of poems and short stories he can write.
p = # of poems
s = # of short stories
Next, we must build our objective function which will represent the total number of works he can write.
N=p+s
where N is the number of works.
Next, we must write the constrains based on the information provided by the problem.
The problem tells us that it takes him 30 hours to write a poem and 70 hours to write a short story and that he has 840 hours available to write them, so that constrain will be the following:
[tex]30p+70s \leq 840[/tex]
it also tells us that he wants to write at least 4 poems and 3 short stories so there we have our other two constrains.
[tex]p \geq 4[/tex]
[tex]s \geq 3 [/tex]
once we got our constrains we can go ahead and graph them to see how they will behave. (See attached picture)
In the graph p is the horizontal axis and s is the vertical axis.
On the graph we can see a polygon that is formed by the restriction. The vertices of the polygon will represent the optimal conditions for this linear programming problem. There are three optimal solutions there, so we need to test them to see which will return the greatest number of works he can write while keeping the given conditions.
Option 1:
4 poems and 3 short stories
N=4+3
N= 7 works
Option 2:
4 poems and 10 short stories
N=4+10
N=14 works
Option 3:
21 poems and 3 short stories
N=21+3
N=24 works
So the optimal solution will be given by option 3 with 21 poems and 3 short stories.
Related Questions
What are the coordinates of the solution of these two linear equations
Answers
Hi there! The solutions of two linear equations can be broken into 3 types:
Infinitely Many SolutionsOne Solution No SolutionThis is from the system of equations where you solve for the y-value and x-value by substitution method or elimination method.
From the question above, the question asks you to find the coordinate of the solution of the equations. But how do we know the coordinate point of the solution if we aren't given any equations? They don't give equatione but they give a graph instead.
Now I would like you to take a look at the graph. You notice that both graphs have one intersect point, right? That point is our solution!
Hence, we can say that an intersection point of two graphs is the solution of both equations.
The graphs intersect each others at (2,1). Thus the answer to this question is (2,1)
Questions can be asked through comment.
Furthermore, an intersection point of two graph is the solution to the equation of the graphs.
Hope this helps, and Happy Learning! :)
What is the formula for surface area? Giving brainliest to the correct answer
Answers
Answer: Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area
Find x if x : 10 = 10 : x
A) 10 B) 20 C) 16
Answers
Answer:
10 is the correct answer
Answer:
A) 10
Step-by-step explanation:
given,
x:10=10:x
x/10=10/xx²=100x=√100x=10hope it helps.
stay safe healthy and happy.Polygon ABCDE ~ Polygon FGHIJ
What is the scale factor of polygon ABCDE to polygon FGHIJ?
Answers
The scale factor of polygon ABCDE to polygon FGHIJ will be 9/2. Then the correct option is C.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
There is no effect of dilation on the angle.
Polygon ABCDE is similar to the Polygon FGHIJ.
Then the scale factor is given as,
Scale factor = 27 / 6
Simplify the equation, then we have
Scale factor = 27 / 6
Scale factor = 9 / 2
The scale factor of polygon ABCDE to polygon FGHIJ will be 9/2. Then the correct option is C.
More about the dilation link is given below.
https://brainly.com/question/2856466
#SPJ1
Help Please! I've been stuck and options are below!
Answers
Answer:
first question is b second is d
Step-by-step explanation:
A photograph measuring 4 inches wide and 5 inches long is enlarged to make a wall mural. If the mural is 150 inches wide, how long is the mural?
A. 120 inches
B. 600 inches
C. 750 inches
D. 187.5 inches
Answers
you would get this by doing the following
150/4 = 37.5
5 x 37.5 = 187.5
which triangles are similar?
Answers
Answer:
triangle a and b
Step-by-step explanation:
because its common knowledge
Each cement block weighs 1 1/4 pounds. How much do 8 cement blocks weight in total?
Answers
Answer:
10
Step-by-step explanation:
[tex]1 \frac{1}{4} \times 8 = 10[/tex]
Answer:
10 pounds.
Step-by-step explanation:
1 * 8 + 1/4 * 8
= 8 + 2
= 10 pounds.
Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 6.8 parts/million (ppm). A researcher believes that the current ozone level is at an insufficient level. The mean of 10 samples is 6.4 ppm with a standard deviation of 1.1. Does the data support the claim at the 0.05 level
Answers
Answer:
The test statistics fall in the critical region and hence null hypothesis is to be rejected.
Step-by-step explanation:
The null hypothesis : H0 : Mean = 6.80
Alternative hypothesis: Ha: Mean is not equal to 6.80
As per the z statistics
z = (x’-mean)/(sigma/sqrt n)
Substituting the given values, we get –
z = 6.4-6.8/(1.1/sqrt 10)
z = -1.149
z test statistics is -1.149
Critical value for two tailed test at 98% confidence is .10749
The test statistics fall in the critical region and hence null hypothesis is to be rejected.
Find the quotient of -4 1/6 and -3 1/3
A) 13 8/9
B) -5/6
C) -7 1/2
D) 1 1/4
Answers
Answer:
B -5/6
Step-by-step explanation:
if you add 5 over 8 + 5 over 8.. how do you simplify it and write it as a mixed number?
Answers
Answer:
its equal to 10 over 8
Step-by-step explanation:
then u divide the numerator and denominator by 2 over 2 which will give you 5 over 4
since it's 5 over 4 you 1 whole number which become 1 and 1 over 4
ellus
Find the surface area of the composite figure.
2 cm
7 cm
2 cm
12 cm
12 cm
7 cm
7 cm
SA = [?] cm2
Answers
Answer:
SA = 484 cm²
Step-by-step explanation:
Surface area of the composite figure = surface area of the larger rectangular prism + (surface area of the smaller rectangular prism - base area of the smaller rectangular prism)
✔️Surface are of the larger rectangular prism = 2(LW + LH + WH)
L = 7 cm
W = 7 cm
H = 12 cm
S.A = 2(7*7 + 7*12 + 7*12) = 434 cm²
✔️Surface are of the smaller rectangular prism = 2(LW + LH + WH)
L = 7 cm
W = 2 cm
H = 2 cm
S.A = 2(7*2 + 7*2 + 2*2) = 64 cm²
✔️Base area of the smaller rectangular prism = L*W
L = 7 cm
W = 2 cm
Area = 7*2 = 14 cm²
✅Surface area of the composite figure = 434 + (64 - 14)
= 434 + 50
= 484 cm²
In the diagram A, B, and C are the points on the circle. Use the diagram to prove the theorem which states that:
if O is the center of the circle then AÔB = 2Ĉ.
Answers
9514 1404 393
Explanation:
Here's one way to go at it.
Draw segments AB and CO. Define angles as follows. (The triangles with sides that are radii are all isosceles, so their base angles are congruent.)
x = angle OAB = angle OBA
y = angle OAC = angle OCA
z = angle OBC = angle OCB
Consider the angles at each of the points A, B, C.
At A, we have ...
angle CAB = x + y
At B, we have ...
angle CBA = x + z
At C, we have ...
angle ACB = y + z
The sum of the angles of triangle ABC is 180°, as is the sum of angles in triangle ABO. This gives ...
x + x + ∠AOB = (x+y) +(x+z) +(y+z)
∠AOB = 2(y+z) = 2∠ACB
This shows ∠AOB = 2×∠C, as required.
the lee family eats at a restaurant for a total bill of 45$ they decided to give a tip of 18% how much tip will they give
Answers
How to Do it/ Work:
18 * 0.45 = 8.1
USE TABLE AOR TABLE RFOR
SERVING UP A LARGE FEAST?
96"
42"
A А
B
R=45"
SHOW AN EXPLANATION ON WHICH TABLE YOU CHOOSE!!!
Answers
Answer:
use table B
Step-by-step explanation:
the perimeter of table A =
2×(96+42) = 2× 138 = 276 inches
the perimeter of table B =
2×3.14×45 = 282.6 inches
table B > table A
Help I will brainliest your answer
Answers
Answer: y=12
Step-by-step explanation:
96=8y
96/8=y
12=y
Similar Triangles
Write the ratio of corresponding sides for the similar triangles and reduce the ratio to lowest terms.
a. 4/15 = 5/12 = 4/15
b. 4/5 = 12/15 = 4/5
c. 4/12 = 5/15 = 1/3
d. 5/4 = 15/12 = 5/4
Please select the best answer from the choices provided
Answers
Answer:
C. 4/12 = 5/15 = 1/3
Step-by-step explanation:
I calculated it logically
Answer:
The answer is A
Step-by-step explanation:
simply log 64 - log 128 + log 32
Answers
Answer:
log(16)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra II
Logarithmic Property [Multiplying]: [tex]\displaystyle log(ab) = log(a) + log(b)[/tex]Logarithmic Property [Dividing]: [tex]\displaystyle \displaystyle log(\frac{a}{b}) = log(a) - log(b)[/tex]Step-by-step explanation:
Step 1: Define
Identify
log(64) - log(128) + log(32)
Step 2: Condense
Logarithmic Property [Dividing]: log(1/2) + log(32)Logarithmic Property [Multiplying]: log(16)los niños están jugando bingo con las tablas de multiplicar, 9 números deben ser las respuestas de las tablas de multiplicar del 1 al 9 y para ir marcando una persona sacará los PO de las tablas .. responde : a) que números eligirias tú para que tengas más posibilidades de ganar ? b) gloria eligió los siguientes números 54,6,8,9,12,16,18,24,36.. Jorge eligió los números 1,2,3,5,7,25,49,64,81 quien tiene más posibilidades de ganar el bingo ?? explica el por qué ??
Answers
Answer: el fredo en y multa verdad thress
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
Please answer the ones you know or all of them
Answers
Answer:
solve each equation :
12) B) {0}
13)(B) {-3}
14) (C) {4}
Find the inverse function of the function f(x) = 5x/7
f-(x) = -7x/5
f-'(x) = – 5x/7
f-l(x) = 5x/7
f-'(x) = 7x/5
Answers
What is the value of log6 49?
Round your answer to two places.
Answers
Answer: 2.17
Step-by-step explanation: To get the answer you count the first two numbers on the Decimal Form, starting behind the period.
(2.17206626)
Please help and thank you
( ignore the answer I clicked)
Answers
Answer:
Step-by-step explanation:
Answer:
your answer is correct. a trapezoid can be defined by it's set of parallel sides
Step-by-step explanation:
If the shape you're looking at doesn't have at least one set of parallel sides, it's not a trapezoid;
7=-1/4+b solve for b
Answers
Answer:
b = 7 1/4
Step-by-step explanation:
7 = -1/4 + b
Add 1/4 to both sides
7 1/4 = b
b = 7 1/4
Successfulness of the Competition policy in South Africa- support and graphs
Answers
Answer:
Answer to the following question is a follows;
Step-by-step explanation:
The following are a few examples of how South Africa's competitiveness policy has been successful:
⇒ Consumers or buyers were given a variety of product options as well as competitive prices.
⇒ In 1984, practises like horizontal cooperation and resale price maintenance and control were ruled illegal.
Write the percent as a fraction and as a decimal.
2%
_
4
What is the fraction equivalent?
Answers
2%- fraction 1/50
4- fraction 2/5
4-decimal0.04
A gumball machine has various colors of gumballs. There is a 10% chance that the next
gumball from the machine is red and 0.8 chance it is orange.
Is the next gumball more likely to be red or orange? Explain your reasoning.
Answers
Answer:
It is red
Step-by-step explanation:
There are 5 blue dogs for every 2 green cats. How many green cats are there for 1 blue dog?
Answers
Answer:
2/5
Step-by-step explanation:
The ratio is 5:2 , simplify an you'll get 1:2/5
A pair of sneakers costs $60. Dahlia bought them on sale for $45. What is the percent decrease in the price of the sneakers?
Answers
Answer:
the answer is %25
Step-by-step explanation:
Need help with this scatter plots question. How do I solve it?
Answers
Answer:
No Trend
Step-by-step explanation:
Scatter plots usually have 1 or 2 outlier points if they're to show a positive or negative trend. There is a kind-of negative trend in the graph, but for me personally, I think the outliers kind of cancel the pattern out since there's way to much other points around it. It can't be constant since constant means that the points have to be in one place, and obviously its not really the case here. Therefore, you're left with a no-trend graph!