Read the following scenario and develop a method for answering the question posed. Be sure to define all variables used, justify your thinking mathematically, and fully answer the questions posed in complete sentences. Orbital Toys sells two types of sets of magnetic spheres, silver, and brass. The store owner, Lucy Ball, pays $8 and $16 for each one set of silver magnetic spheres and brass magnetic spheres respectively. One set of silver magnetic spheres yields a profit of $5 while a set of brass magnetic spheres yields a profit of $7. Ms. Ball estimates that no more than 2000 sets of magnetic spheres will be sold every month and she does not plan to invest more than $20,000 in the inventory of these sets. How many sets of each type of magnetic spheres should be stocked in order to maximize her total monthly profit? What is her maximum monthly profit?
Answers
8 dlls for silver
16 dlls for brass
5 dlls profit silver
7 dlls profit spheres
Then the price is
8+5= 13 dlls for silver
16+7=23 dlls for brass
Let S and B be the amount of magnetic silver and brass sphers that are sold, respectively.
Then, Ms. Ball estimation is that
[tex]S+B\leq2000[/tex]Also, she doesn't want to invest more than 20000, so
[tex]\begin{gathered} 8S+16B\leq20000 \\ S+2B\leq2500 \end{gathered}[/tex]The objective function is
[tex]V=5S+7B[/tex]Subjected to:
[tex]\begin{gathered} S+B\leq2000 \\ S+2B\leq2500 \\ S\ge0,\text{ B}\ge0 \end{gathered}[/tex]GRAPH
The interection is at
[tex]\begin{gathered} S=2000-B \\ S=2500-2B \\ 2000-B=2500-2B \\ B=500 \\ S=2000-500 \\ S=1500 \end{gathered}[/tex]So, the extremes must be at (0,1250), (1500,500), (2000,0) , (0,0).
So, if we replace the points
[tex]\begin{gathered} V(0,1250)=5(0)+7(1250)=8750 \\ V(1500,500)\text{ = 5(1500)+7(500)=}11000 \\ V(2000,0)=5(2000)+7(0)=10000 \end{gathered}[/tex]So, the amount she will need to stock to maximize her profit is 1500 of silver and 500 of brass, and the maximum profit is going to be 11000 dlls.
Related Questions
Darcy mounted a motion sensor so it would light a path to the door on her deck. If you know AB=10 feet, and BE and BD trident angle ABC, what is the perimeter of the deck area to the right of the beam of light ?PART 1: what others angles or sides of triangle BDC can you label given that side AB is 10 feet, BE and BD trisect angle ABC? Label the diagram accordingly, and explain your reasoning
Answers
Part 1
The labelled disgram is shown below.
We would apply the pythagorean theorem which is expressed as
hypotenuse^2 = one leg^2 + other leg^2
Considering triangle ABE
Sin 60 = 10/BE
BE = 10/Sin60 = 11.55
tan60 =10/AE
AE = 10/tan60 = 5.77
Part 1
Side DC of triangle BDC = 10 feet(opposite sides of a rectangle are congruent)
angle DBC = 30 degrees because BE and BD trisect angle ABC. 90/3 = 30
The sum of the angles in a triangle is 180 degrees. Thus,
angle DBC + angle DCB + angle BDC = 180
30 + 90 + angle BDC = 180
angle BDC = 180 = 180 - (30 + 90 = 180 - 120
angle BDC = 60
Sin 30 = CD/BD = 10/BD
BD = 10/Sin30
BD = 20
tan 30 = DC/BC = 10/BC
BC = 10/tan30
BC = 17.32
Perimeter of deck area to the right of the beam of light = perimeter of triangle BDC
= BD + DC + BC
= 20 + 10 + 17.32
Perimeter = 47.32 feet
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BRAINLIEST!!!!! AND 100
POINTS!!!!!
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Answer:
it would be the same since reflection doesn't change the andle
Answer:
A: It would have the same measure as the original angle.
Step-by-step explanation:
Well, reflecting is where you take the original image, which you see now, and flipping it like a mirror image. So, I think the answer would be: A It would have the same measure as the original angle. Because, it is literally the same thing, just in a mirror image. Like, if you look in the mirror, you see yourself, still the same.
in this quadratic trinomial 20 is the _____. 3x^2 -7x-20
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A trinomial has three terms. The first term contains the squared variable, the second term contains the variable with an exponent of 1, and the third term does not have any variable. That term is called the independent term.
In the polynomial:
[tex]3x^2-7x-20[/tex]The term -20 is the independent term because it does not depend on the value of the variable x.
I need help with my math
Answers
Answer:
Histogram Tells you how many pumpkins had mass below 6 kg
The box plot can be used to determine that the median was 8
Explanation:
A histogram is a chart the plots frequency of a certain quantity.
In our case, the histogram given tell us how many pumpkins fall within a certain mass range. Therefore, to find out how many pumpkins are below 6 kg, we use a histogram.
On the other hand, the box plot summarizes the numerical data. In our case, it can be used to find the median weight of the pumpkins by just reading off the position of the median line.
What is the line of reflection for
Answers
SOLUTION:
Step 1:
In question 12, we are meant to find the line of reflection for Triangle ABC and its image based on the diagram:
Step 2:
The line of reflection for Triangle ABC and its image is:
[tex]\text{y = x --- OPTION D}[/tex]Find the savings plan balance after 6 months with an APR of 8% and monthly payments of $300.
Answers
316.21 is the savings plan balance after 6 months with an APR of 8% and monthly payments of $300.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
We need to find the savings plan balance after 8 months with an APR of 8% and monthly payments of $300.00.
Let 8% is changed to decimal value by dividing with hundred.
8/100=0.08.
Now we are required to find the growth factor.
growth factor = (1 + (0.08 / 12)) per month = 1.00667
After 9 months, the balance is
($300.00)*(1.00667)8
316.21 is the balance after 6 months.
Hence 316.21 is the savings plan balance after 6 months with an APR of 8% and monthly payments of $300.
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Given the figure below, determine the angle that is a same side interior angle with respect to
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We remember that two interior angles are those inside the are of the lines, Thus, the angles in the area:
Are interior. Now, we identify two sides, the right side, and the left side, which have been separated by the transversal line.
Thus, the angle that is is the same side as ∡3, and also that is interior is ∡5.
Find the volume of a cylinder and cinema given the following dimensions
Answers
Given:
The radius , r=20 ft.
The height , h=23 ft.
The volume of the cylinder can be calculated as,
[tex]\begin{gathered} V=\pi r^2h \\ =\pi\times20^2\times23 \\ =28902.65ft^2 \end{gathered}[/tex]Therefore, the volume of the cylinder is 28902.65 sq.ft.
The volume of the cone can be calculated as,
[tex]\begin{gathered} V=\frac{1}{3}\pi\times r^2h \\ =\frac{1}{3}\pi\times20^2\times23 \\ =9634.22ft^2 \end{gathered}[/tex]Therefore, the volume of the cone is 9634.22 sq.ft.
Question 8 of 20If f(x) = 2x²+2 and g(x)=x2-1, find (f- g)(x).O A.3x²+3O B.x2²+1 O C.3x2² +1O D.x² +3
Answers
Solution
Step 1
Write the two functions:
[tex]f\mleft(x\mright)=2x²+2\text{ }and\text{ }g\left(x\right)=x2-1[/tex]Step 2
(f- g)(x) = f(g) - g(x)
[tex]\begin{gathered} \left(f-g\right)\left(x\right)=2x²+2\text{ - \lparen}x^2-1) \\ \\ (f-g)(x)=2x^2+\text{ 2 - x}^2\text{ + 1} \\ \\ (f-g)(x)=x^2+3 \end{gathered}[/tex]Final answer
D. x² +3
Written as a percent, what is the probability of getting an odd number on a spinner with 5 equal parts numbered 1 to 5?A.20%B.40%C.60%D.80%
Answers
Given:
There are given that the spinner with 5 equal parts numbered 1 to 5.
Explanation:
In the given spinner, there are given the number: 1, 2, 3, 4, 5.
Now,
From all the given numbers, there are 3 odd numbers: 1, 3, and 5.
So,
From the probability:
[tex]P=\frac{Total\text{ number of odd numbers in the given spinner}}{Total\text{ numbers on the spinner}}[/tex]Then,
[tex]\begin{gathered} P=\frac{3}{5} \\ P=0.6 \end{gathered}[/tex]Now,
For the percentage:
[tex]\begin{gathered} P=0.6\times100\% \\ P=60\% \end{gathered}[/tex]Final answer:
Hence, the correct option is C.
do you know the north Zone at the football stadium has 95 Rose there are 48 seats in a row how many people will the North end zone seat
Answers
The North zone at the football stadium has 95 rows.
There are 48 seats in a row.
How many people will the North end zone seat?
Since there are 95 rows and each row has 48 seats, multiply them to get the total number of seats.
[tex]\begin{gathered} total\: seats=rows\times seats \\ total\: seats=95\times48 \\ total\: seats=4560 \end{gathered}[/tex]Therefore, there are 4560 people sitting in the North zone.
1: Are the two slopes parallel.
perpendicular or neither?
Answers
The slopes of two parallel lines are the same, while the slopes of two perpendicular lines are the opposite reciprocals of each other. Each line has infinitely many lines that are parallel to it and infinitely many lines that are perpendicular to it.
P.S hopes this helps
Write a linear function f with f(0) = 3.75 and f(-6) =3.75
f(x) = ???
Answers
The linear function will be;
⇒ f (x) = 3.75
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The values are,
⇒ f (0) = 3.75
And, f (-6) = 3.75
Now,
Let the linear function is,
f (x) = ax + b
Since, The values is given as;
f (0) = 3.75
And, f (-6) = 3.75
So, We can substitute the given values in the linear function, we get;
f (x) = ax + b
Substitute x = 0 we get;
f (0) = a × 0 + b
f (0) = b
3.75 = b
b = 3.75
And, We can substitute x = -6 and f(0) = 3.75 we get;
f (-6) = a × -6 + b
3.75 = -6a + 3.75
- 6a = 0
a = 0
So, Substitute a = 0 and b = 3.75 in linear function we get;
f (x) = ax + b
f (x) = a × 0 + 3.75
f (x) = 3.75
Therefore,
The linear function will be;
⇒ f (x) = 3.75
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write the equation of the line passing through the given points write your awnser in slope intercept form Y=mx+b (5 1) and (-3 17)
Answers
The given points are (5, 1) and (-3, 17).
First, we have to find the slope using the following formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]\begin{gathered} x_1=5 \\ x_2=-3 \\ y_1=1 \\ y_2=17 \end{gathered}[/tex]Let's use the coordinates above to find the slope.
[tex]m=\frac{17-1}{-3-5}=\frac{16}{-8}\Rightarrow m=-2[/tex]The slope is -2.
Now, we use the point-slope formula to find the equation.
[tex]y-y_1=m(x-x_1)[/tex]Let's use the same coordinates x_1 and y_1, and the slope m = -2.
[tex]y-1=-2(x-5)[/tex]Now, we solve for y to express the equation in slope-intercept form.
[tex]y-1=-2x+10\Rightarrow y=-2x+10+1\Rightarrow y=-2x+11[/tex]Therefore, the slope-intercept form of the equation is[tex]y=-2x+11[/tex]A company purchased 10,000 pairs of men'sslacks for $18.66 per pair and marked them up $22.93. What was the selling price of each pair of slacks? Use the formulaS=CMThe selling price of each pairs of slacks is ?
Answers
Given:
A company purchased slacks for $18.66 per pair.
Mark up= $22.93
[tex]\begin{gathered} \text{Selling price= cost price +mark up} \\ \text{Selling price=}18.66+22.93 \\ \text{Selling price= \$41.59} \end{gathered}[/tex]Can you help me with this problem? I will send a screenshot of the problem and the answer choices.
Answers
Given:
Distance of her beagle = 25/4 meters to the right
Distance of her labrador = 51/20 meters directly to her left.
Let's determine the expression which represents how far apart the two dogs are.
We have the following:
Since the beagle is to the right, the distance is = 25/4 meters
Since the labrador is to the left, the distance is = -51/20 meters.
Now, to find how far apart the two dogs are, let's use the absolute value expression:
[tex]\lvert\frac{25}{4}-(-\frac{51}{20})|[/tex]Therefore, the expression which represents how far the two dogs are is:
[tex]\lvert\frac{25}{4}-(-\frac{51}{20})\rvert[/tex]ANSWER:
[tex]\lvert\frac{25}{4}-(-\frac{51}{20})\rvert[/tex]What’s eight less than four times a number in algebraic expression
Answers
Answer:
4x - 8, 4x just means four of x, and eight less means to subtract 8.
Step-by-step explanation:
Answer:
The answer is 4x - 8 and it equals -32
The diameter of a circle is 6 ft. Find its circumference in terms of \piπ.
Answers
The circumference of circle with diameter 6 feet will be 6π feet.
According to the question,
We have the following information:
Diameter of the circle = 6 feet
Now, we will find the radius of the circle. We know that the radius of the circle is half that of its diameter.
Radius of the circle = Diameter/2
Radius of the circle = 6/2 feet
Radius of the circle = 3 feet
We know that the following formula is used to find the circumference of the circle:
Circumference of the circle = 2πr
Circumference of the circle = 2π*3
Circumference of the circle = 6π feet
Hence, the circumference of the circle is 6π feet.
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Ashley watches a giant that has 16 equally spread seats. Identify w.
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The angle formed outside the circle by the intersection of a tangent and a secant is equal to half of the difference of the intercepted arcs. The bigger arc is 180º, because the starting point of the secant and the starting point of the tangent are precisely on the opposite position of each other(we can see that by counting the same amount of seats between them on both sides). The smaller arc is equal to 90º, therefore
[tex]w^o=\frac{1}{2}(180^o-90^o)=45^o[/tex]A linear equation written in the form y = mx + b is in ?
Answers
A linear equation is written in the form
[tex]y=mx+b[/tex]it is the Slope-intercept form
How many area codes of the form (XYZ) are possible if the digit 'X' and 'Y' can be any number ( through 9 but they can't repeat and the digit 7 can be any number 1 through 9?
Answers
Start to see the possible options
[tex]XYZ=-\cdot-\cdot-_{}[/tex]The first digit will have 10 possible numbers to choose from 0 to 9, however in the second digit since it cannot repeat there will be only 9 possible to choose from. As for ther third number 0 is not an option meaning that there are 9 to choose as well.
[tex]\begin{gathered} XYZ=10\cdot9\cdot9 \\ XYZ=810 \end{gathered}[/tex]Write in terms of confunction of a complementary angle:tan 26°
Answers
ANSWER
The cofunction of tan 36 degrees is cot 54 degrees
STEP-BY-STEP EXPLANATION
Given information
[tex]\text{tan 26}\degree[/tex]Co function of tan can be written below as
[tex]\begin{gathered} \tan \text{ }(A)\text{ = cot (B)} \\ \text{if, A + B = 90} \end{gathered}[/tex][tex]\begin{gathered} \text{tan 36 = cot (90 - 36)} \\ \tan \text{ 36 = cot 54} \end{gathered}[/tex]Therefore,
tan 36 = 0.7265
cot 54 = 0.7265
Hence, the cofunction of tan 36 is cot 54
im having a hard time understanding this could you please help me
Answers
Given -
The odds against winning a prize in the raffle = 9:1
To Find -
Probability of winning prize =?
Step-by-Step Explanation -
Total possible outcome = 9 + 1 = 10
Favourable outcome = 9
So,
Probability = Total outcome / Favourable outcome
Probability = 9/10 = 0.9
Final Answer -
Probability of winning prize = 0.9
Which system of equations best represents the situation below?A farmer grew his own tomatoes (a), eggplants (b), and potatoes (c). Hedecided to package his vegetables and price them as follows:1 tomato, 1 eggplant, 2 potatoes for $102 tomatoes, 1 eggplant, 3 potatoes for $144 tomatoes, 3 eggplants, 5 potatoes for $20
Answers
Solution
- The cost of the crops are $(a) for tomatoes, $(b) for eggplants, and $(c) for potatoes.
- We simply need to follow the statements about the farmer's pricing in order to determine the correct set of equations.
Statement 1:
- "1 tomato, 1 eggplant, 2 potatoes for $10"
- If there is 1 tomato, it implies that, this tomato is priced at $(a). Similarly, 1 eggplant would be priced at $(b), but 2 potatoes would be $(c) + $(c) = $2(c).
- We are told that the total cost for this package is $10.
- Thus, the first equation must be:
[tex]a+b+2c=10[/tex]- We can interprete the other packages in a similar manner.
Statement 2:
"2 tomatoes, 1 eggplant, 3 potatoes for $14"
- This implies that the farmer would price the packages as follows:
2 tomatoes: 2(a)
1 eggplant: 1(b)
3 potatoes: 3(c)
- Since the total cost is $14, we can write the second equation as follows:
[tex]2a+b+3c=14[/tex]Statement 3:
"4 tomatoes, 3 eggplants, 5 potatoes for $20"
- This implies that the farmer would price the packages as follows:
4 tomatoes: 4(a)
3 eggplants: 3(b)
5 potatoes: 5(c)
- Since the total cost is $20, we can write the third equation as follows:
[tex]4a+3b+5c=20[/tex]Final Answer
The 3 equations are:
[tex]\begin{gathered} a+b+2c=10 \\ 2a+b+3c=14 \\ 4a+3b+5c=20 \end{gathered}[/tex]OPTION C
Help please not sure if I am right or wrong thank you
Answers
Given:
[tex]-1+\sqrt[]{-4}[/tex]To find the simplified complex number
[tex]\begin{gathered} -1+\sqrt[]{-4}=-1\pm2i \\ -1+\sqrt[]{-4}=-1+2i,-1-2i \end{gathered}[/tex]27–34: Describing Distributions. Consider the following distributions.-How many peaks would you expect the distribution to have? Explain.-Make a sketch of the distribution.-Would you expect the distribution to be symmetric, left-skewed, or right-skewed? Explain.-Would you expect the variation of the distribution to be small, moderate, or large? Explain.#29The annual snowfall amounts in 50 randomly selected American cities
Answers
Answer:
Step-by-step explanation:
Error Analysis On a math test a student, Sarah, has to identify all the coefficients and constantsof the expression y +n + 2. Sarah says that 6 is a coefficient and 2 is a constant. Identify all thecoefficients and constants of the expression. What error might Sarah have made?The coefficient(s) of the expression is/are
Answers
the coefficients are the numbers that accompany a variable on this case we have 2 variables y and n so the numbers that accompany each one are 1 for y and 6 for n
so there area 2 coefficients 1 and 6
the constant are the numbers without a variable on this case only the 2
1. 3 In right AXYZ, the length of the hypotenuse YZ is 85 inches and tan Z= 3/4 What is the length, in inches, of the leg XY?
Answers
We have a right triangle XYZ.
The length of the hypotenuse is YZ=85.
We also know that the tangent of Z is 4.
We have to find the length of XY.
We can start by drawing the triangle and writing the data:
The tangent of an angle can be related with the sides by the following trigonometric ratio:
[tex]\tan (Z)=\frac{\text{Opposite}}{\text{Adyacent}}=\frac{XY}{XZ}=\frac{3}{4}[/tex]We can not find the value of the legs from the trigonometric ratio, but we have a proportion between them. We can write the previous result as:
[tex]\begin{gathered} \frac{XY}{XZ}=\frac{3}{4} \\ XZ=\frac{4}{3}\cdot XY \end{gathered}[/tex]Now we can relate XY with the hypotenuse YZ using the Pythagorean theorem:
[tex]\begin{gathered} XY^2+XZ^2=YZ^2 \\ XY^2+(\frac{4}{3}XY)^2=YZ^2 \\ XY^2+\frac{16}{9}XY^2=YZ^2 \\ (\frac{16}{9}+1)XY^2=YZ^2 \\ \frac{16+9}{9}XY^2=YZ^2 \\ \frac{25}{9}XY^2=YZ^2 \\ XY^2=\frac{9}{25}YZ^2 \\ XY=\sqrt[]{\frac{9}{25}YZ^2} \\ XY=\frac{3}{5}YZ \\ XY=\frac{3}{5}\cdot85 \\ XY=51 \end{gathered}[/tex]Answer: the length of the leg XY is 51 inches.
A pair of jeans is on sale for $30. If this price represents a 20% discount from the original price, what is the original price to the nearest cent ?
Answers
Given Data:
The sale price of the jeans is: s=$30
The discount is: d=20%
The expression to calculate the original price is,
[tex]s=P\times\frac{d}{100}[/tex]Here P represents the original price.
[tex]\begin{gathered} 30=P\times\frac{20}{100} \\ P=30\times\frac{100}{20} \\ =30\times5 \\ P=150 \end{gathered}[/tex]Thus, the original price of the jeans is $150.
Use the order of operations to demonstrate that the Distributive Property holds by showing that both sides of each equation are equal.
2/5(4/3-1/3)=2/5*4/3-2/5*1/3
LHS= 2/5(4/3-1/3)
=2/5(4-1/3)
=2/5( /3)
= /15
= 2/5
RHS= 2/5*4/3-2/5*1/3
= /15-2/15
= -2/15
= /15
=2/5
Answers
The Distributive Property holds as both sides of the given equality are equal.
Distributive PropertyThe distributive property means that the outer time of the expression multiplies each of the inner terms of the expression. Then, these terms may be combined, if they contain like-terms.
The left-hand side of the expression is given as follows:
2/5(4/3 - 1/3).
Applying the distributive property, it is found that:
2/5 x 4/3 = 8/15.2/5 x 1/3 = 2/15.Subtracting them, it is found that:
2/5(4/3 - 1/3) = 8/15 - 2/15 = 6/15 = 2/5. (as both 6 and 15 are divided by 3).
Precedence of operationsThe right-hand side of the expression is:
2/5 x 4/3 - 2/5 x 1/3
Multiplication takes precedence over subtraction, hence:
2/5 x 4/3 - 2/5 x 1/3 = 8/15 - 2/15
Same denominator, hence the numerators can be subtracted as follows:
8/15 - 2/15 = 6/15 = 2/5. (as both 6 and 15 are divided by 3).
Both sides of the expression have the same value, hence the distributive property holds for this problem.
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