20 points! If u can provide an explanation that would be great if not just tell me how certain that's the answer. Thanks a bunch
Answers
Let
x = number of trays of corn muffins
y = number of trays of bran muffins
Given info: "baking a tray of corn muffins takes 4 cups of milk and 3 cups of wheat flour"
If we focus on the milk only then baking x trays of corn muffins means we use up 4*x (or simply 4x) cups of milk. Focus now on the wheat flour and it takes 3*x or 3x cups of wheat flour
Also given: "Baking a tray of bran muffins takes 2 cups of milk and 3 cups of wheat flour"
So we use up 2y cups of milk and 3y cups of wheat flour
-----------------
So far we have used 4x cups of milk for the corn muffins plus 2y more cups of milk for bran muffins giving a total of 4x+2y cups of milk used. We only have 16 cups of milk which means we can say this
4x + 2y <= 16
where the "<=" symbol without quotes means "less than or equal to". That inequality above is one of the constraints placed.
-----------------
Another constraint is this inequality
3x+3y <= 15
because
* we use 3x cups of wheat flour for the corn muffins
* we use 3y cups of wheat flour for the bran muffins
* we have a max of 15 cups of wheat flour
-----------------
Additional contraints are:
x >= 0
y >= 0
indicating that we cannot have x or y be negative
-----------------
The four constraints are:
4x + 2y <= 16
3x+3y <= 15
x >= 0
y >= 0
If you graph all of these inequalities and do the proper shading, you'll get what you see in the attached image. Specifically I'm talking about the blue shaded region. This region is known as the feasible region.
Now turn your attention to the red corner points aka the vertices. These points will be plugged into the objective function
P(x,y) = 3x+2y
This represents the profit (in dollars) of making x trays of corn muffins and y trays of bran muffins.
3x = 3*x = profit from just the corn muffins only
2y = 2*y = profit from just the bran muffins only
3x+2y = total profit (selling both corn and bran muffins)
The four corner points are:
A = (3,2)
B = (0,5)
C = (0,0)
D = (4,0)
Plug each of these points into P(x,y) = 3x+2y
-----------------------------
Plug in A = (x,y) = (3,2)
P(x,y) = 3x+2y
P(3,2) = 3*3+2*2
P(3,2) = 13
We earn a profit of $13 if we sell 3 trays of corn muffins and 2 trays of bran muffins
-----------------------------
Plug in (x,y) = (0,5) which is point B
P(x,y) = 3x+2y
P(0,5) = 3*0+2*5
P(0,5) = 10
The profit dropped to $10, so we can ignore point B. So far point A leads to the most profit.
-----------------------------
Plug in point C, which is (x,y) = (0,0)
P(x,y) = 3x+2y
P(0,0) = 3*0+2*0
P(0,0) = 0
The profit drops even further. Ignore this point.
-----------------------------
Plug in point D: (x,y) = (4,0)
P(x,y) = 3x+2y
P(4,0) = 3*4+2*0
P(4,0) = 12
The profit has gone back up but not at the same height as $13 back for point A. So we can cross this off the list too
-----------------------------
The max profit happens at point A which again was
(x,y) = (3,2)
x = 3 ----> selling 3 trays of corn muffins
y = 2 ----> selling 2 trays of bran muffins
----------------------------------------------------------
----------------------------------------------------------
So the final answer is choice A "3 trays of corn muffins and 2 trays of bran muffins"
Related Questions
Use the Law of Syllogism to draw a conclusion from the given information.
Given: If two lines are perpendicular, then they form right angles. If two lines meet at a 90 angle, then they are perpendicular. Two lines meet at a 90 angle.
a.Conclusion: The lines are parallel.
b.Conclusion: The lines are perpendicular and meet at a 90 angle.
c.Conclusion: The lines meet at a 90 angle.
d.Conclusion: The lines form a right angle.
Answers
hope i helped
Find the difference quotient please
Answers
[tex]f(x) = \frac{x}{x+6} [/tex]
Answers:
[tex]f(a) = \frac{a}{a+6} [/tex]
[tex]f(a+h) = \frac{a+h}{a+h+6} [/tex]
[tex] \frac{f(a+h)-f(a)}{h} = \frac{6}{(a+h+6)(a+6)} [/tex]
Explanation:
[tex]f(a+h)-f(a) = \frac{(a+h)(a+6)-a(a+h+6)}{(a+h+6)(a+h)} \\ = \frac{a^{2}+6a+ah+6h-(a^{2}+ah+6a)}{(a+h+6)(a+6)} \\= \frac{6h}{(a+h+6)(a+6)} [/tex]
[tex] \frac{f(a+h)-f(a)}{h} = \frac{6}{(a+h+6)(a+6)} [/tex]
Which is the graph of 4x – 3y = 12?
Answers
Answer:
its the last graph pictured
The graph of 4x - 3y = 12 is given below.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
The given linear equation is 4x - 3y = 12.
Rearranging it into slope intercept form, we get,
y = 4/3 x - 4
In order to find the points through which it passes, put some of the values of x.
When x = -3, y = -4 - 4 = -8
When x = 0, y = 0 - 4 = -4
When x = 3, y = 4 - 4 = 0
When x = 6, y = 8 - 4 = 4
...........
So the graph passes through (-3, -8), (0, -4), (3, 0) and (6, 4).
Hence the graph of the given equation is given below.
Learn more about Linear Equations here :
https://brainly.com/question/29739212
#SPJ2
Simplify the expressions. (use only positive exponents in your answers.) (a) (9x4)(-9x-3) = incorrect: your answer is incorrect.
Answers
36(-9x-3)
-324x-108
What is the cube root of 27?
A.3
B.4
C.5
D.6
Answers
because 3 x 3 x 3 = 27
your answer is A.3
hope this helps
You have 2 types of bread, 3 types of meat, and 2 types of cheese. How many different sandwiches can you make if each sandwich has 1 type of bread, 1 type of meat, and 1 type of cheese?
Answers
The king has only one sibling. what is the probability that the sibling is a male
Answers
so, the required probability is 1/2
Answer:
theres a 40% chance it will be a boy or a 60% change of a boy.
Step-by-step explanation:
40% because over half the population are girls but for the 60% its more common for boy twins.
hope you understand ^_^
Problem page a delivery truck is transporting boxes of two sizes: large and small. the large boxes weigh 45 pounds each, and the small boxes weigh 15 pounds each. there are 120 boxes in all. if the truck is carrying a total of 3300 pounds in boxes, how many of each type of box is it carrying?
Answers
l= number of large boxes
equation 1: s+l=120
equation 2: 15s+45l=3300
solve by elimination, multiply equation 1 by -15.
-15(s+l=120) = -15s-15l=-1800 add to equation 2.
-15s+15s-15l+45l=-1800+3300 = 30l=1500
30l=1500 , l=50
s+l=120, s+50=120 --> s=70
The mean score of a competency test is 65, with a standard deviation of 4. use the empirical rule to find the percentage of scores between 53 and 77. (assume the data set has a bell-shaped distribution.)
Answers
To solve this problem, we use the t statistic. The z score is calculated as:
z = (x – u) / s
where x is the sample value = 53 and 77, u is the mean score = 65 while s is the standard deviation = 4
when x = 53
z = (53 – 65) / 4 = -3
From the standard distribution tables, the p value at z = -3 is:
P (z=-3) = 0.0013
when x = 77
z = (77 – 65) / 4 = 3
From the standard distribution tables, the p value at z = 3 is:
P (z=3) = 0.9987
The percentage P between the two would be the difference:
P (53 < x < 77) = 0.9987 – 0.0013 = 0.9974
Answer:
0.9974 or 99.74%
Carl deposited $5,142 into a savings account 20 years ago. The account has an interest rate of 3.8% and the balance is currently $10,994.58. How often does the interest compound? daily monthly quarterly annually
Answers
The answer is it is compounded monthly which is 365/yr.
This is done using trial and error but I got it right at the first try.
Solution:
A = P (1+r/n) ^nt
Where:
A is the accrued amount or also known as the future value
P is the principal amount = $5,142
r is the nominal interest rate = 0.038
n is the number of compounding units = 365
t is time = 20
A = 5,142 (1 + 0.038/365) ^ 365(20)
= 5,142 (1.0001041095890410958904109589041)^7300
= 5.142 (2.13819163)
= $10994.58
An urn contains six chips, numbered 1 through 6. two are chosen at random and their numbers are added together. what is the probability that the resulting sum is equal to 5?
Answers
Final answer:
The probability of drawing two chips from an urn numbered 1 through 6 such that their sum is 5 is 4/15, since there are four favourable outcomes (1,4), (2,3), (3,2), and (4,1) out of the total 15 possible combinations.
Explanation:
The question involves calculating the probability of drawing two chips from an urn, each numbered 1 through 6, such that their sum equals 5. To solve the problem, let's consider all possible combinations of two different chips that can be drawn at random:
(1, 4)(2, 3)(3, 2)(4, 1)There are 4 favourable combinations that result in a sum of 5. As each chip can be drawn only once, the total number of pairs can be given by the combination formula C(n, k) = n! / (k!(n-k)!)), where n is the total number of chips and k is the number of chips drawn. In this case, C(6, 2) = 6! / (2!4!) = 15, and so there are 15 possible pairs that can be drawn from our urn.
Therefore, the probability of getting a sum of 5 is the number of favourable outcomes divided by the total number of outcomes, which is 4 favourable combinations divided by 15 possible combinations, resulting in a probability of 4/15.
What is the area of the trapezoid shown? (1) angle a = 120 degrees (2) the perimeter of trapezoid abcd = 36?
Answers
Neither statement alone is sufficient to determine the area of the trapezoid.
Explanation:The area of a trapezoid can be found using the formula:
Area = (1/2) * (sum of parallel sides) * height
To find the area of the trapezoid, we need the lengths of the parallel sides and the height.
(1) The given angle does not provide information about the lengths of the sides, so it is not sufficient to find the area.
(2) The perimeter of the trapezoid does not directly give information about the lengths of the sides, so it is also not sufficient to find the area.
Therefore, neither statement alone is sufficient to determine the area of the trapezoid.
Learn more about Area of a trapezoid here:https://brainly.com/question/15640807
#SPJ2
simplify
(-6i)(-7-6i)-(7i)(3-2i)
Answers
(-6i)(-7-6i) becomes 42i + 36i^2, or 42i -36
-(7i)(3-2i) becomes -[21i - 14i^2], or -[21i + 14]
Combine these two products.
42i-21i -36 -14
21i - 50 (answer)
James earned a total of $900 this week. this total was $20 less than four times the amount he earned last week. how much money did james earn last week
Answers
4x = 900+20
4x = 920
x = 920/4
x = 230
he earned $230
Given two points on the graph of the line, the equation of the line can be found.
True
False
Answers
Which transformation is not isometric?
Answers
martha can complete 15 activities a day at summer camp. she can choose between crafts or sports.
1. Define two variables and create an equation to represent the situation? 2. what are 3 possible combinations of crafts and sports that Martha can do?
Answers
Given that Martha can complete 15 activities a day at summer camp and she can choose between crafts or sports.
Let x be the number of crafts activity Martha did and let y be the number of sports activity Martha did.
The equation representing the situation is given by
x + y = 15
Part B:
There are many possible combinations of crafts and sports that Martha can do.
3 possible combinations of crafts and sports that Martha can do are
7 crafts and 8 sports
4 crafts and 11 sports
8 crafts and 7 sports
What is surface area
Answers
2 * 3.61 * 11 = 79.42
Area of the front and back =
2 * (2 * 3) = 12
Total Area = 91.42 cm
in 1996,Donovan Bailey of Canada ran the 100 meter dash in 9.84 seconds.How fastis that to the nearst second?to the nearst tenth of a second
Answers
HELP PLEASE!! 30 POINTS!!
John's credit card company calculates a finance charge based upon a periodic rate of 1.75% on all unpaid balances. If John has an unpaid balance of $475, determine the finance charge that he will be assessed.
A. $8.31
B. $349.00
C. $346.30
D. $469.33
Answers
Final answer:
The finance charge for John is calculated by multiplying his unpaid balance by the periodic rate. The calculation results in a finance charge of $8.31, which is option A.
Explanation:
John's finance charge on his credit card, based on a periodic rate of 1.75% on an unpaid balance of $475, can be calculated using the formula: Finance Charge = Periodic Rate × Unpaid Balance. To find the finance charge, multiply 1.75% (or 0.0175 in decimal form) by $475. Therefore, the finance charge would be 0.0175 × $475 = $8.3125. When rounded to the nearest cent, this is $8.31, which corresponds to option A.
A rectangular garden has a length that is five less than twice the width. the garden perimeter is 50 meters. what are the dimensions of the garden?
Answers
2(2W-5)+2W=50
4W-10+2W=50
6W-10=50
6W=60
W=10
Donnavan is measuring the angles of a triangle. he measures the first two angles and gets 10° and 120°. what should be the measure of the third angle?
a.25° eliminate
b.50°
c.130°
d.230°
Answers
10+120=130
180-130=50
Therefore the last angle must be 50°
please help me! thanks :)
Answers
Angles STU and STR are supplementary angles.
Angles R and STR are congruent.
m<STU + m<STR = 180
8x + m<STR = 180
m<STR = 180 - 8x
m<R = m<STR = 180 - 8x
m<RST + m<R + m<STR = 180
7x - 54 + 180 - 8x + 180 - 8x = 180
-9x + 360 = 180
-9x = -126
x = 14
also m < SRT = 180-8x ( because side RS = side ST, so isosceles triangle)
So
7x - 54 + 180 - 8x = 8x (ext. angle of triangle =sum of opposite internal angles)
7x - 8x - 8x = -180 + 54 = -126
-9x = -126
x = 14 answer
What geometric formula relates the radius of a circle to its area?
Answers
r = radius
[tex] A = \pi r^{2} [/tex]
The geometric formula for the radius of a circle to its area will be;
A = πr²
Where, A is area of circle , r is radius of circle.
What is Circle?
Circle is a closed two dimensional figure in which the set of all points in the plane is equidistance from the center of circle.
Let radius of a circle = r
And, Area of a circle = A
Then, The geometric formula for the radius of a circle to its area will be;
A = πr²
Thus, The geometric formula for the radius of a circle to its area will be;
A = πr²
Where, A is area of circle , r is radius of circle.
Learn more about the circle visit:
https://brainly.com/question/24810873
#SPJ2
whats the chance to not get 33% chance 3 times in a row
Answers
What was the name of the treatise in which Euclid compiled all the existing geometric knowledge, along with some of his own observations, to provide a logical structure and progression for geometry?
Earth Measurements
The Pythagorean Theorem
The Elements
Logic and Geometry
Answers
Answer:
The correct answer is The Elements.
This is the right answer for Edmentum and Plato users
Like and Rate
The sun is 30 ∘ above the horizon. it makes a 60 m -long shadow of a tall tree. how high is the tree
Answers
To calculate the height of a tree with a 60-meter long shadow when the Sun is 30 degrees above the horizon, use the tangent trigonometric function. The tree's height is calculated to be around 34.62 meters tall.
Explanation:The student is asking how to calculate the height of a tree given the length of its shadow when the Sun is 30 degrees above the horizon. This is a trigonometry problem involving a right-angled triangle, where the tree represents the opposite side, the shadow represents the adjacent side, and the angle given is the angle of elevation of the Sun. Since we have the angle and the length of the adjacent side, we can use the tangent trigonometric ratio to find the height of the tree. The tangent of an angle in a right-angled triangle is the ratio of the opposite side to the adjacent side (tangent = opposite/adjacent).
Therefore, the tree is approximately 34.62 meters tall.
Please help guys!!
What set of transformations is performed on LMNO to form L'M'N'O'?
A 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left
A 270-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left
A translation 1 unit to the left followed by a 270-degree counterclockwise rotation about the origin
A translation 1 unit to the left followed by a 90-degree counterclockwise rotation about the origin
Answers
Answer:
Its b and can you give me the brainlist
Step-by-step explanation:
Which of the following illustrates the truth value of the following mathematical statements? 6 + 3 = 9, and 5 • 5 = 20
A. T T → T
B. F T → F
C. T F → F
D. F F → F
Answers
C. T F → F
How many kilograms are in 5500 g? Show all work
Answers
When converting gram to kilogram (smaller unit to larger unit), you must divide by 10. This means that you must move each unit to the left. For example:
Kilo, hectogram, decagram, gram... you must move 3 steps to the left which means 5500 grams is equal to 5.5 Kilograms