a. Let us say that c(x) is the cost of one t shirt based on the number of increases therefore:
c = 10 + x
b. Say that t(x) is the number of t shirts sold based on the number of increases so:
t = 2500 – 100 x
b. The revenue is simply the product:
r(x) = (10 + x) (2500 – 100 x)
Combining:
r(x) = 25000 – 1000 x + 2500 x – 100 x^2
r(x) = 25000 + 1500 x – 100 x^2
Taking the 1st derivative and setting dr / dx = 0 to get the maxima:
dr / dx = 1500 – 200 x
1500 = 200 x
x = 7.5
t = 2500 – 100 x = 2500 – 100 (7.5) = 1750
Hence 1750 shirts should be sold.
A wire 360 in. long is cut into two pieces. one piece is formed into a square and the other into a circle. if the two figures have the same area, what are the lengths of the two pieces of wire (to the nearest tenth of an inch)?
The length of piece of wire for square = 230 inches
The length of piece of wire for circle = 130 inches.
The given length of wire = 360 inches
Now let it cuts into lengths r' and r
Therefore,
⇒ r' + r = 360 ...(i)
Now let with length r' square is formed
Therefore,
Area of square = r'xr'
= (r')²
And with length of r circle is formed,
Area of circle = π r²
According to the question
Both area are same,
⇒ (r')² = π r²
Taking square root both sides,
⇒ r' = √π r ......(ii)
Now from (i) and (ii);
⇒ √π r + r = 360
⇒ r(1 + √π) = 360
⇒ 2.77 r = 360
⇒ r = 129.96 ≈ 130 in
Then r' = 360 - 130
= 230
Hence length are 130 inches and 230 inches.
Learn more about the circle visit:
https://brainly.com/question/24810873
#SPJ1
"the sum of the squares of two consecutive odd integers is 2594. find the two integers."
Final answer:
To find two consecutive odd integers whose squares sum to 2594, a quadratic equation is set up and solved, revealing that the integers are 35 and 37.
Explanation:
To solve for two consecutive odd integers whose squares sum to 2594, we can set up equations based on the characteristics of odd integers. Let the smaller integer be n, then the next consecutive odd integer would be n + 2.
The equation based on the sum of the squares of the two numbers is then:
n2 + (n + 2)2 = 2594
Solving this equation:
n2 + n2 + 4n + 4 = 25942n2 + 4n - 2590 = 0n2 + 2n - 1295 = 0Solving the quadratic equation we find that n = 35 and n + 2 = 37. Hence, the two consecutive odd integers are 35 and 37.
Which number(s) below belong to the solution set of the inequality? Check all that apply.x + 16 < 51.
A. 80
B. 35
C. 38
D. 32
E. 34
F. 16
please help me
That would be 32, 16 and 34.
What's the answer of the photo I just sent you
(42 pts) What is the value of g(−3) when g(x)=2x−2 ? Enter your answer in the box.
equation = g(x) = 2x-2
when g(-3) replace x with -3
so you get g(-3) = 2(-3)-2
2*-3 = -6-2 = -8
g(-3) = -8
Archie is putting 24 books on 2 shelves. Each shelf holds 16 books.
How many more books can Archie put on the shelves?
Point A is located at –24 and point C is located at 36 on the number line below. Which value would represent point B, halfway between point A and point C?
Answer:
Point B will be 6
Step-by-step explanation:
We have point A= -24 and point B = 36, we want to know point B which is halfway between points A and C.
To find the middle between two points we have to add the two numbers and divide them by 2:
We would have:
(A+C)/2
We substitute the values of A and C:
B = (-24+36)/2
B = 12/2
B = 6.
We can also write this on a number line and get point B by counting how many numbers there are in between point A and C, and this result divides it by 2. This is in the attachment.
2(4x-3)-8=4+2x solving equations plz help ASAP show work and ill give brainliest
Is this true 1/2 >0.25
Determine whether the following pair of lines is parallel, perpendicular or neither 2x+3y=3: 2y=3x-4
If 3cot^2x - 5cotx = -2, then cotx = _____.
A. -2, -1/3
B. -1, -2/3
C. 1, 2/3
D. 2, 1/3
The hood of Christina's car is the shape of a trapezoid. The base bordering the windshield measures 30 inches and the base at the front of the car measures 24 inches. What is the width of the median of the hood?
The width of the median of the hood is
_______inches.
30-24 = 6
6/2 = 3
24 + 3 = 27
median width = 27
a. Write an expression that represents the following expression using the variable b: "Billy's age in 8 years." b. Write an equation using the expression above if in 8 years Billy will be 21 years old. c. How old is Billy now? d. Write and solve a word problem that matches the equation: a - 6 = 10.
Answer:
"Billy's age in 8 years", this refers to a future age, which implies adding 8 years to the present age. The expression would be:
[tex]B+8[/tex]
"In 8 years Billy will be 21 years", this expression, using the first one too, would be:
[tex]B+8=21[/tex]
How old is Billy now?
The answer to this question is the solution of the second equation:
[tex]B+8=21\\B=21-8=13[/tex]
Billy is 13 years old now.
A problem for the expression [tex]A-6=10[/tex] could be:
Six years ago Adam was 10 years old.
The six years in the past refers subtracting, and the age back then is the result of that difference.
Suppose three candidates are running in the texas democratic primary for governor. what happens if candidate x wins 45% of the vote, candidate y receives 30% of the vote, and candidate z wins 25% of the vote?
Final answer:
Since no candidate won an absolute majority in the Texas Democratic Primary for governor, a runoff election is necessitated between Candidate X and Candidate Y, the top two vote-getters, to ensure the nominee is chosen by a majority.
Explanation:
In the scenario where Candidate X wins 45% of the vote, Candidate Y receives 30%, and Candidate Z wins 25% in the Texas Democratic Primary for governor, no candidate has achieved an absolute majority, as required by Texas law to win the primary outright. An absolute majority means that a candidate must have more than 50% of the votes, specifically fifty percent plus one vote. Since this did not happen, a runoff election is triggered.
The runoff will take place between the two candidates who received the most votes, which in this case, would be Candidate X and Candidate Y. This runoff ensures that the final nominee for governor from the Democratic Party will have the support of a majority of its voters, reflecting a more democratic outcome. The system prevents a candidate from winning the primary nomination with only a plurality of the vote, which could be less representative of the party's voters as a whole.
Evaluate the expression 3(7 + 4)2 − 14 ÷ 7. (5 points)
50
361
363
586
Do not just give me the answer, walk me through it. I am literally so shallow minded when it comes to Algebra and I am trying really hard to understand it.
Which of the following inequalities is shown in the graph
The inequality y ≤ [tex]\frac{5}{2}[/tex] x+5 represents the given graph. Therefore, option D is the correct answer.
What is an inequality?In mathematics, inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.
From the graph the inequality intersect lines at (-2, 0) and (0, 5).
The graph is shaded below the line.
So, inequality y ≤ [tex]\frac{5}{2}[/tex] x+5.
The inequality y ≤ [tex]\frac{5}{2}[/tex] x+5 represents the given graph. Therefore, option D is the correct answer.
To learn more about the inequality visit:
https://brainly.com/question/20383699.
#SPJ5
the tour boats at the Laguna can carry 8 passengers. jacob watched 6 floats by. one of the board has 2 empty seats. the other were full. how many passengers were on the 6 boats?
Which expression is equivalent to the expression −2\3 (3- 1\2) (-1)?
Question 3 options:
-2 + 1\3 + 2\3
2 - 1\3
-2 +1\3-1
2 + 1\3
The Answer Is B.2-1/3
Hope It Helps Mark Me The Brainlyest
The expression −2/3(3-1/2)(-1) is equivalent to -5/3.
Explanation:To simplify the expression −2/3(3-1/2)(-1), we can start by simplifying the expressions within the parentheses.
3-1/2 = 6/2 - 1/2 = 5/2
Next, we can multiply the expression −2/3(5/2)(-1).
−2/3(5/2)(-1) = -2/3 * 5/2 * -1 = -10/6 = -5/3
Therefore, the expression is equivalent to -5/3.
What is the perimeter of the rectangle shown on the coordinate plane, to the nearest tenth of a unit? a.13.4 units b.17.9 units c.26.8 units d.40.0 units
A coordinate plane is a graphical image that shows two number lines. These number lines have a y-axis and x-axis. The y-axis is the vertical number line and the x-axis is the horizontal number line.
The perimeter of the rectangle is 26.8 units
We would be applying Pythagoras Theorem to find the length and breadth of the rectangle.
Pythagoras Theorem states that:
c² = a² + b²
Note that c = The length or breadth of the rectangle
Step 1 : Looking at upper part, and dividing the rectangle into a triangle,We have 4 units and 8 units.
a = 4 units
b = 8 units
Using the Pythagorean Theorem, you can calculate the length of the hypotenuse to be
c² = 4² + 8²
c² = 80
c = √ 80
c = 8.9 units
Applying this to the lower part,
We have 4 units and 2 units.
a = 2 units
b = 4 units
Using the Pythagorean Theorem, you can calculate the length of the hypotenuse to be
c² = 2² + 4²
c² = 20
c = √20
c = 4.5 units
Step 2: We find the Perimeter of a rectangleFormula = 2L + 2B
Where
L = Length = 8.9 units
B = Breadth = 4.5 units
Hence:
8.9 x 2 + 4.5 x2 = 26.8 units
Therefore, the perimeter of the rectangle is 26.8 units
Option C is the correct answer
To learn more, visit the link below:
https://brainly.com/question/1972439
miss. Nikkel want to divide her class of 23 students into 4 equal teams.is this reasonable?why or why not
Writing are the equations m + 3 = -5 and m = -2 equivalent? explain
PLZZZZZZ HEEEEELLLLLLPPPPPPPP!!!!!!!!!!
Given the system of equations, what is the solution?
3x - 2y + 10 = 0
5y = 4x + 8
A.){(-34/7, 16/7)}
B.){(34/7, -16/7)}
C.){(-34/7, -16/7)}
I can confirm that Option C is correct, just finished the assignment.
If two pyramids are similar and the ratio between the lengths of their edges is 3:11, what is the ratio of their volumes?
Answer: The ratio of the volumes of two pyramids is 27 : 1331.
Step-by-step explanation: Given that two two pyramids are similar and the ratio between the length of their edges is 3 : 11.
We are to find the ratio of the volumes of two pyramids.
Let a units and b units be the lengths of the edges of the two pyramids.
The, according to the given information, we have
[tex]a:b=3:11.[/tex]
We know that the ratio of the volumes of two similar pyramids is equal to the ratio of the cubes of the lengths of edges of the two pyramids.
Therefore, the ratio of the volumes of two pyramids will be
[tex]V:V'=\dfrac{V}{V'}=\dfrac{a^3}{b^3}=\left(\dfrac{a}{b}\right)^3=\left(\dfrac{3}{11}\right)^3=\dfrac{27}{1331}=27:1331\\\\\\\Rightarrow V:V'=27:1331.[/tex]
Thus, the ratio of the volumes of two pyramids is 27 : 1331.
which equation is an identity?
a. 11- (2v + 3) = -2v - 8
b. 5w + 8 - w = 6w - 2( w - 4)
c. 7m - 2 = 8m + 4 - m
d. 8y + 9 = 8y - 3
Answer:
Option b - [tex]5w + 8 - w = 6w - 2( w - 4)[/tex]
Step-by-step explanation:
To find : Which equation is an identity?
Solution :
Option a - [tex]11- (2v + 3) = -2v - 8[/tex]
If we open the parenthesis,
[tex]11- 2v -3 = -2v - 8[/tex]
[tex]-2v+8\neq -2v - 8[/tex]
No identity applied.
Option b - [tex]5w + 8 - w = 6w - 2( w - 4)[/tex]
If we apply distributive property, [tex]a(b+c)=ab+ac[/tex]
[tex]5w + 8 - w = 6w - 2w+8[/tex]
[tex]4w+8= 4w+8[/tex]
Distributive identity is applied.
Option c - [tex]7m - 2 = 8m + 4 - m[/tex]
Solve by subtracting in RHS
[tex]7m - 2 \neq 7m + 4[/tex]
No identity applied.
Option d- [tex]8y + 9 = 8y - 3[/tex]
This is not possible as [tex]8y + 9 \neq 8y - 3[/tex]
No identity applied.
Therefore, Option b is correct.
A box containing 4 identical books weighs 5kg. if the weight of the box is 600g, what is the weight of each book? answer key
Answer:
1100 grams
Step-by-step explanation:
Which expression is equivalent to 1/5(15 + 10x-5)?
A. 2 + 2x
B. 2 - 2x
C. -2 + 2x
D. -2 - 2x
how do i sketch the graph of each function?
If 20 pounds of flour were needed to make 31 pounds of bread, how many pounds of other ingredients would be needed to produce 60 pounds of bread?
What is the value of x?
Triangle PQR has vertices at the following coordinates : P(0,1) Q(3,2) R(5,-4) . Determine wether or not triangle PQR is a right triangle . Show all calculations for full credit .
The sum of the squares of two sides is not equal to the square of the third side, the triangle PQR is not a right triangle.
What is Pythagoras Theorem?According to Pythagoras Theorem, in a right angled triangle the square of the side opposite to the right angle is equal to the sum of squares of the other two sides.
Height² + Base² = Hypotenuse²
If a triangle is a right angle, then its sides should satisfy Pythagoras theorem.
The distance formula will be used to determine the length of the sides.
PQ² = ( 3 - 0)² + (2-1)²
PQ² = 10
PQ = √10
RQ² = ( 5 - 3)² + (-4-2)²
RQ² = 40
RQ = √40
RP² = ( 5 - 0)² + (-4-1)²
RQ² = 25 + 36
RQ² = 61
Applying the Pythagoras's Theorem,
61 ≠ 40 + 10
Therefore, it is not a right angled triangle.
To know more about Pythagoras Theorem
https://brainly.com/question/343682
#SPJ5