Answer:
In order to maximize profit, the company should sell each widget at $22.68.
Step-by-step explanation:
The amount of profit y made by the company for selling widgets at x price is given by the equation:
[tex]y=-34x^2+1542x-10037[/tex]
And we want to find to price for which the company should sell in order to maximize the profit.
Since our equation is a quadratic with a negative leading coefficient, its maximum will occur at the vertex point.
The vertex of a quadratic is given by the formulas:
[tex]\displaystyle \text{Vertex}=\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
In this case, a = -34, b = 1542, and c = -10037.
Find the x-coordinate of the vertex:
[tex]\displaystyle x=-\frac{(1542)}{2(-34)}=\frac{771}{34}\approx \$22.68[/tex]
So, in order to maximize profit, the company should sell each widget at $22.68.
Extra Notes:
In order to find the maximum profit, substitute the price back into the equation:
[tex]\displaystyle y\left(\frac{771}{34}\right)\approx\$7446.56[/tex]
There are 12 inches in 1 foot. This is equivalent to 60 inches in 5 feet. Which proportions can be used to represent this? Check all that apply.
Answer:
Step-by-step explanation:
12 inches 60 inches
---------------- is equivalent to ------------------
1 foot 5 feet
This can be seen if we multiply both numerator and denominator of the first ratio by 5 (each).
120 inches
------------------ is another equivalent fraction (or ratio).
10 feet
Answer:B and C
Step-by-step explanation:
12/1 = 60/5
1/12 = 5/60
A company plans to reduce the amount of energy used each year. This table shows the company's plan.
Answer:
the anserw would be B
Step-by-step explanation:
The relationship that explains the exponential relationship between the year and amount of energy used is: Option B: The amount of energy used decreases by different amount each year.
What is the rate of exponential function?Rate of an exponential function is in terms of exponential function itself. It's not constant, and always changing. For example, the rate of [tex]y = e^x[/tex] with respect to x is [tex]y' = e^x[/tex] itself, which increases as x increases.
The given table is:
Year(Serial no.) Amount of energy used (kWh)
1 1,000,000
2 900,000
3 810,000
4 792,000
The differences between each consequent years of the amount of energy used is:
1000000 - 900000 = 100000
900000 - 810000 = 90000
810000 - 792000 = 18000
So, we see that the decrement is done by decreasing amount.
So rate of change wasn't constant but continuosly changing.
Thus, Option C is clearly wrong.
We see that 100,000 is 10% of 1,000,000
and 90,000 is 10% of next years amount 900,000
but 18,000 is not 10% of next years amount which is 810,000
Thus, Option A is wrong too.
Option B is correct in its statement, and so as option D because we don't see any immediate pattern in the decrement, except that the energy is just decreasing, so its unexpected.
The rate of exponentially related variables is not unexpected though.
So, its only Option B which is closest (among other options) to the intention of telling that the relation between the year and the amount of energy used is exponential, although it doesn't prove that the relationship is exponential. (because, suppose the function i take is [tex]y = x^2[/tex], then its rate with respect to x is [tex]y' = 2x[/tex] and this rate is also non-constant, but the function wasn't exponential).
Thus, the relationship that explains the exponential relationship between the year and amount of energy used is: Option B: The amount of energy used decreases by different amount each year.
Learn more about rates of exponential functions here:
https://brainly.com/question/1497850
A city has a population of 340,000 people. Suppose that each year the population grows by 5.25%. What will the population be after 15 years?
Answer:
Future population = 720800
Step-by-step explanation:
Below is the calculation of population after 15 years.
Given the present population = 340000
Growth in population = 5.25%
Use below formula to find the values:
Future population = Present population ( 1 + r)^n
Future population = 340000 ( 1 + 5.25%)^15
Future population = 340000 (2.15)
Future population = 720800
The equations to this problem .
Answer:
The answer would be the third one.
in ΔABC, ∠ABC is a right angle, AB = 3 units, and BC = 2 units. ΔABC is dilated by a scale factor of 0.5 with point B as the center of dilation, resulting in the image ΔA′B′C′. Which statement about A′B′ is true?
Answer:
the first one i think
Step-by-step explanation:
Answer:
first one
Step-by-step explanation:
What is the midpoint of the line segment graphed below?
A. (4,7/2)
B. (8,7/2)
c. (4,3/2)
D (8, 3/2)
Answer:
a) (4,7/2)
Step-by-step explanation:
Midpoint Formula:
[(-1+9)/2], [(2+5)/2]
(8/2, 7/2) = (4, 7/2)
Of the 2 226 people on the ship, 703 survived and
1523 died.
What percentage of the passengers survived?
Answer:
32%
Step-by-step explanation:
703/2226=32%
what's the answer for this question please thank you :)
Answer:
Arc AB = 110
Step-by-step explanation:
<C = 55 degrees. That's the way the triangle is marked. AB = BC.
The central angle is twice the angle made by the end points of line AB
The central angle = 2*55 = 110
The measure of arc AB equals the central angle which makes arc AB = 110
find the slope of a line parallel to given line.
Answer:
-3
Step-by-step explanation:
If lines are parallel to each other, they will never touch so the slope will be the same.
So if the first line is already given in slope intercept form, that means the -3 is the slope.
So a line parallel to this would have the slope -3 and start at a different place on the y axis.
PLS HELP What type of line is PQ¯¯?
A. side bisector
B. median
C. altitude
D. angle bisector
Answer: Altitude
Step-by-step explanation:
Altitude is perpendicular line made from vertex to side
The line PQ is the altitude, the correct option is C.
What is a Triangle?A triangle is a polygon with three sides, three vertices and three angles.
The Triangle PSR is an obtuse angle triangle,
The line PQ makes 90 degree with the line SR extended up to Q.
The line is the height of the triangle.
To know more about Triangle
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#SPJ5
24.94 is 29% of what number?
Answer:
86
hope this helps!
add me as a friend if u can<3
Answer:
86
Step-by-step explanation:
Express 29% as a decimal, which is 0.29
Then divide 24.94 by 0.29, which gives you 86.
Rewrite y +2> +(6x –9) to isolate the y-term.
Rewrite y +2>2(6x-
Helppppp
Given:
The inequality is:
[tex]y+2>\dfrac{1}{3}(6x+9)[/tex]
To find:
The inequality after isolating the y-term.
Solution:
We have,
[tex]y+2>\dfrac{1}{3}(6x+9)[/tex]
On simplification, we get
[tex]y+2>\dfrac{1}{3}(6x)+\dfrac{1}{3}(9)[/tex]
[tex]y+2>2x+3[/tex]
Subtracting 2 from both sides of the above inequality, we get
[tex]y+2-2>2x+3-2[/tex]
[tex]y>2x+1[/tex]
Therefore, the required inequality is [tex]y>2x+1[/tex].
Factor the following 2x-18x+36=
Hey there!
2x - 18x + 36
COMBINE the LIKE TERMS
(2x - 18x) + 36
2x - 18x = -16x
36 = 36 because it doesn’t have any like terms
= -16x + 36
Answer: -16x + 36 or you could simply say
4(-4x + 9)
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
1) Marcos deseja comprar uma guitarra. Seu amigo possui um e quer vender a vista por R$850,00. Caso Marcos prefira, pode parcelar em 4 parcelas iguais, com vencimento para 30, 60, 90 e 120 dias, seu amigo aplicará sobre o valor do produto, uma taxa única de 12%. Nessa situação, o custo final da guitarra e o valor de cada parcela são respectivamente: *
1 ponto
a) R$102,00 e R$55,00.
b) R$850,00 e R$212,00
c) R$952,00 e R$238,00
d) R$980,00 e R$245,00.
2) Luiza está em dúvida sobre financiar uma moto nova no valor de R$25.000,00 ou fazer um consórcio. Como o desejo de Luiza em adquirir uma moto é algo que tem a mais de dois anos, ela já dispõe de uma reserva, aplicada na caderneta de poupança, de R$15.000,00. As propostas que lhe foram apresentadas na concessionária são: Financiamento de 36 prestações fixas de R$1.050,00 sem entrada.Financiamento de 36 prestações fixas de R$395,00 com entrada de R$14.000,00.Consórcio de 36 prestações reajustáveis de acordo com a inflação, sendo a primeira parcela no valor de R$800,00, com possibilidade de obter a moto, ao longo do período do consórcio, por meio de sorteio ou lance.Das opções apresentadas a mais vantajosa para Luiza é: *
1 ponto
a) O consórcio, pois, a prestação não é tão alta e ela ainda terá o valor de suas economias para usar em caso de alguma emergência.
b) O financiamento de 36 prestações fixas de R$1.050,00 sem entrada.
c) O financiamento de 36 prestações de R$395,00 fixas com entrada de R$14.000,00.
d) Todas as propostas são equivalentes, Luiza pode escolher qualquer uma delas.
Answer:
1)C
2)C
Step-by-step explanation:
Fiz no Classroom!!!
Find an equation of the circle whose diameter has endpoints (6,4) and (2,-6)
Answer:
[tex](x-4)^2+(y+1)^2=29[/tex]
Step-by-step explanation:
We want to find a circle whose diameter has the endpoints (6, 4) and (2, -6).
Since this is the diameter, its midpoint will be the center of the circle. Find the midpoint:
[tex]\displaystyle M=\left(\frac{6+2}{2}, \frac{4+(-6)}2}\right)=(4, -1)[/tex]
So, the center of our circle is (4, -1).
Next, to find the radius, we can find the length of the diameter and divide it by half.
Using the distance formula, find the length of the diameter:
[tex]\begin{aligned} d&=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\ &=\sqrt{(2-6)^2+(-6-4)^2}\\\\&=\sqrt{(4)^2+(-10)^2}\\\\&=\sqrt{116}\\\\&=2\sqrt{29}\end{aligned}[/tex]
So, the radius will be:
[tex]\displaystyle r=\frac{1}{2}d=\frac{1}{2}\left(2\sqrt{29}\right)=\sqrt{29}[/tex]
The equation for a circle is given by:
[tex]\displaystyle (x-h)^2+(y-k)^2=r^2[/tex]
Substitute:
[tex](x-4)^2+(y+1)^2=29[/tex]
Use the Pythagorean theorem to classify the triangle
formed by the three fences. Which is true about the
numbers 5, 12, and 13?
Answer:
they are equal
Step-by-step explanation:
The triangle with sides 5, 12, 13 is a right triangle because
a^2+b^2 = c^2
5^2+12^2 = 13^2
25+144 = 169
169 = 169
I'm using the pythagorean theorem converse.
If X and Y varies inversely, what would the value of X be? (-9,4) (x,-12)
Answer:
Use papa math
Step-by-step explanation:
Use papa math
The area of the base is 15cm. The height is 6 cm. What is the volume of the rectangular prism?
Answer:
you don't put the L value
Please please help me please
Answer:
Step-by-step explanation:
height of a triangle=4x-1
base=5x+2x-3
=7x-2
area of triangle=base*height/2
=(7x-2)(2x-3)/2
=7x*2x-7x*3-2*2x+2*3/2
=14x^2+21x-4x-6/2
=14^2+17x-6/2
area of rectangle=l*b
(7x-2)(4x+1)
7x(4x+1)-2(4x+1)
4x*7x+7x*1-2*4x-2*1
=28x^2+7x-8x-2
=28x^2-x-2
area of shaded part=area of rectangle-area of triangle
=[tex](28x^2-x-2 )-\frac{14x^2+17x-6}{2}[/tex]
If angle 3 is 142°, find angles 1, 2 and 4. Show your work.
PLEASE HELP - 60 POINTS
m<1=m<2 = 38°
m<3= m<4= 142°
Answer:
Angles 1 and 2 are vertically opposite and angles 3 and 4 are vertically opposite and as such the are congruent.
m∠3 = 142° ⇒ m∠4 = m∠3 = 142°Angles 1 and 3 are supplementary and angles 2 and 4 are supplementary and as such sum to 180°.
m∠1 = 180° - 142° = 38°m∠2 = m∠1 = 38°A surveyor is using indirect measurement to find the height of a cliff. He is 4 feet tall and is standing 32 feet away. How tall is the cliff?
Answer:
256 ft
Step-by-step explanation:
[tex]\frac{x}{32} =\frac{32}{4}[/tex]cross multiply
4x = 32(32)
4x = 1024
x =256
256 ft
Read what Sasha says. I am y years old. My mother's age is 3 times my age. My brother is 2 years younger than me. My father's age is 4 times my brother's age. The total of our four ages is 116 years.
a) Write an equation to show this.
b) Solve the equation.
c) How old is Sasha's father?
Answer:
please look at the picture l. it is solved there. hope this helps.. do mark me as brainliest
Answer:
a) y + 3y + (y - 2) + 4(y - 2) = 116
b) y = 14
c) 48
Step-by-step explanation:
Sasha says. I am y years old. y
mother's age is 3 times my age 3y
brother is 2 years younger than me y - 2
father's age is 4 times my brother's age 4(y - 2)
-------------------------------
total of our four ages is 116 years.
a) Write an equation to show this.
y + 3y + (y - 2) + 4(y - 2) = 116
b) Solve the equation.
distribute
y + 3y + y - 2 + 4y - 8 = 116
combine like terms
9y - 10 = 116
add 10 to both sides
9y = 126
Divide both sides by 9
y = 14
c) How old is Sasha's father?
4(y - 2)
4(14 - 2)
4(12)
48
PLZZ THIS IS DUE
Module 8: Directions: Respond to this question to demonstrate your understanding of the topic/content. Be sure to provide adequate and relevant details learned in the module to support your response. Pay close attention to organizing your response so it makes sense and uses correct grammar. Your response should be at least 5-7 sentences at a minimum.
Question: Explain what a chord is and determine if a diameter is or is not a chord?
Mr. Rankin took his family out to dinner last night and their subtotal was $88.24. The sales tax was 5%, and he left a 20% tip. If Mr. Rankin puts $120 on the table, how much change did he recieve?
Answer:
8.82
Step-by-step explanation:
subtotal- 88.24
total- 92.65
total with tip-111.18
change- 8.82
How could you use a model to find 7 divided by 2= 7/2
Answer:
[tex] \frac{7}{2} \\ = 3 \frac{1}{2} [/tex]
is my dad abusive? today he grabbed my ears so hard and they turned so red and he put his arms around my face. then he kicked me really hard to the point where I peed, he also pushed me a lot and started slapping me. he did more which I can't remember but he also smashed my phone :) this all happened within 20 minutes and I could barely breathe after that lol. this may not seem so much but it is. this is too personal ig lol and I started self-harming again bc of him yay.
Answer:
Step-by-step explanation:
OMG! Don't do that! I am so sorry this is happening to you. Look I don't know how to comfort you. IF he keeps doing this tell your mom or litterally call 911. If he did it just on that day then try confronting him on it. And ask him why he did that! Don't self-harm you deserve so much more than that! You are awesome!
Help pleasssere!!!!!!!!!!!
Step-by-step explanation:
I hope it helps...I just put it in point slope form
Geometry geometry help
Answer:
b = 7.14cm
Step-by-step explanation:
For this question, we need to use the pythagorean theorem, since it is a right triangle, and we know two sides. The formula for the Pythagorean theorem is c^2 = a^2 + b^2.
1. a = 5.8cm so a^2 will be 5.8 x 5.8 which is 33.64
2. c = 9.2cm so c^2 will be 9.2 x 9.2 which is 84.64
3. If we add these to our Pythagorean equation, it will be 84.64 = 33.64 + b^2. --> 51 = b^2 --> b = 7.141428....
4. Since we need to round it to two decimal places, b will be 7.14.
Two positive numbers have a difference of 21. The larger number is five more than twice the smaller. Find the two numbers.
Answer:
X = 29
Y = 8
Step-by-step explanation:
X - y = 21
X = 2y + 5
Substitute:
2y+5-y= 21
2y = 16
Y = 8
X-8 = 21
X = 29
Find the measure of x and y
Answer:
y - 41°
x - ?
Step-by-step explanation:
use method of Z equation
Z 41° so y is 41° too
make sense
