Answer:
The profit decreases by $ 375 for every $ 1 increase in the selling price.
Step-by-step explanation:
From the definition of the secant line we get that the average rate of change of [tex]P(x) = -0.015\cdot x^{2}+1.2\cdot x -11.5[/tex], where [tex]x[/tex] is the selling price of the product, measured in dollars per unit, is:
[tex]r = \frac{P(55)-P(50)}{55-50}[/tex] (1)
Now we evaluate the function at each bound:
x = 50
[tex]P(50) = -0.015\cdot (50)^{2}+1.2\cdot (50)-11.5[/tex]
[tex]P(50) = 11[/tex]
x = 55
[tex]P(55) = -0.015\cdot (55)^{2}+1.2\cdot (55)-11.5[/tex]
[tex]P(55) = 9.125[/tex]
Then, the average rate of change is:
[tex]r = \frac{9.125-11}{55-50}[/tex]
[tex]r = -0.375[/tex]
Hence, the profit decreases by $ 375 for every $ 1 increase in the selling price.
The statements that best interprets the average rate of change from x = 50 to x = 55 is (b) The profit decreases by $375 for every $1 increase in the selling price.
The profit function is given as:
[tex]P(x) = -0.015x^2 + 1.2x - 11.5[/tex]
Calculate P(x), when x = 50.
So, we have:
[tex]P(50) = -0.015(50)^2 + 1.2(50) - 11.5[/tex]
[tex]P(50) = 11[/tex]
Calculate P(x), when x = 55.
So, we have:
[tex]P(55) = -0.015(55)^2 + 1.2(55) - 11.5[/tex]
[tex]P(55) = 9.125[/tex]
The average rate of change from x = 50, to 55 is then calculated using:
[tex]m = \frac{P(55) - P(50)}{55-50}[/tex]
So, we have:
[tex]m = \frac{9.125 - 11}{55-50}[/tex]
[tex]m = \frac{-1.875}{5}[/tex]
Divide
[tex]m = -0.375[/tex]
The function is in 1000 units.
So, we have:
[tex]m = -0.375\times 1000[/tex]
[tex]m = -375[/tex]
-375 implies a decrease of $375 for every $1 increase in sales
Hence, the correct statement is (b)
Read more about average rates at:
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A map has a scale of 1 inch = 20 miles. The distance on a map between two cities is 3 1/4 inches. How far apart are the two cities?
For a soccer game, Mr Morant prepared 32 hot dogs. He sold 1/2 of the hot dogs to the fans. He sold 1/4 of the hot dogs to the coaches. How many hot dogs were left?
Answer:
it is nothing
Step-by-step explanation:
1-1=2
You make a necklace using blue,purple and green beads in ratio of 1:3:5. You use a total of 126 beads. How many green beads are in the necklace?
Answer:
Step-by-step explanation:
x + 3x + 5x = 126
9x = 126
x = 14 (blue beads)
3(14) = 42 (purple beads)
5(14) = 70 (green beads)
Please I’m really confused which one it is please help
Answer:
The top one on the left
Step-by-step explanation:
Martin traveled at an average rate of 40 miles per hour for the first half of his trip. For the second half of his trip, he traveled at a rate of 60 miles per hour. How far did he travel in the 4-hour trip?
Answer:
Total distance traveled = 200 miles
Step-by-step explanation:
Total time taken for the trip = 4 hours
∴ The trip can be divided into two halves of 2 hours each.
1st half:
speed = 40 miles per hour
distance = speed × time
when time = 2 hours
distance = 40 × 2 = 80 miles
2nd half:
distance = speed × time
speed = 60 miles per hour
time = 2 hours
∴ distance = 60 × 2 = 120 miles
Combined distance traveled = 80 + 120 = 200 miles
1.5m^6(-2m^2)^4
find the product
(1,-19),(-2 -7) finnd the slope to this equation
Answer:
slope is 4
Step-by-step explanation:
ax = bc - c solve for x
Answer:
X = c - b/a
Step-by-step explanation:
Answer:
x=bc/a - c/a
You simplify it like you would any equation, only difference is it does not have numbers.
What's the answer help pls
Answer:
48°
Step-by-step explanation:
The m in front of the angle notation refers to the measure of the angle labeled A, B and C (with vertex at B)
Two Angles are Supplementary when they add up to 180 degrees.
HENCE,
∠A + ∠B =180 (given)
⇒4x - 16 +8x + 4 = 180°
⇒12x - 12 = 180°
⇒12x = 192
⇒x = 16 ----1
substituting eq1 in ∠A,
=> 4(16) -16
=> 64 - 16
=> ∠A = 48°
Answer:
48
Step-by-step explanation:
The definition of supplementary means that the two angles add up to 180. so you set both expressions up to where they add to 180. like this
4x-16+8x+4=180
combine like terms
12x-12=180
12x=192
divide to get x
x=16.
You need the measure of angle A so you plug it back in
4(16)-16
64-16
48 is the measure of angle A, and since these angles are supplementary, that means angle B is 132
The midpoint of a segment with endpoint (8,a) and (b,4) is (-1,-1)
What’s the value of a and b
Answer choices is
A. 10 b. 6
A.6 b.10
A. -6 b. -10
A. -10 b.-6
Answer:
(-10,-6)
Step-by-step explanation:
(8 + b) / 2 = - 1
(8 + b) = - 1 * 2
8 + b = - 2
b+8-8 = -2 - 8
b = - 10
=====================
(a + 4)/2 = -1
(a + 4) = - 2
a + 4 = -2
a + 4-4 = - 2 - 4
a = - 6
A brand new car costs $18,000, this price depreciates at 25% every year, how much would the car be after 12 years? 20 years?
Answer:
C(12)=$570.18
C(20)=$57.08
Step-by-step explanation:
Exponential Decay Function
The exponential function is often used to model natural growing or decaying processes, where the change is proportional to the actual quantity.
An exponential decaying function is expressed as:
[tex]C(t)=C_o\cdot(1-r)^t[/tex]
Where:
C(t) is the actual value of the function at time t
Co is the initial value of C at t=0
r is the decaying rate, expressed in decimal
The depreciation of goods is often modeled as an exponential function. The new car costs $18,000 and its price depreciates at r=25%= 0.25 every year.
The depreciation model is:
[tex]C(t)=18,000\cdot(1-0.25)^t[/tex]
Operating:
[tex]C(t)=18,000\cdot 0.75^t[/tex]
At t=12 years, the price will be:
[tex]C(12)=18,000\cdot 0.75^{12}[/tex]
C(12)=$570.18
At t=20 years, the price will be:
[tex]C(20)=18,000\cdot 0.75^{20}[/tex]
C(20)=$57.08
help meeeeeeeeee plzzzzzzzzzzzzz
Answer:
91 x
Step-by-step explanation:
Nov 06, 7:43:52 PM
Which equation represents a line which is parallel to the line y =
= -x - 8?
O 8x + 3y = -6
O 8x – 3y = 3
Submit Answer
8y - 3x = -48
3x + 8y = 48
O
Answer:
8x-3y=3
Step-by-step explanation:
Its the only one that would give you a negative x
Write the expression in simplest form.
(11 + 3) – 2(- 4 1 - 1) =
NIO
Answer:
11+3=14
-41-1=-42
14-2(-42)
-2(-42)
14+84
98
I hope this is good enough:
slope of (-3, 1), (1, 9) and slope of (-2, -9), (-1, -7)
Answer:
8/4 and 2/1(or just 2)
Step-by-step explanation:
slope formula- (y2-y1)/(x2-x1)
plug in the numbers-
(9-1)/(1+3) and (-7+9)/(-1+2)
Can someone plzz answer this!!?
Answer: B Angle Side Angle
Step-by-step explanation:
Since line AB and CD are parallel angles D and A are congruent by the alternate interior theorem and both angles AOB and DOC are congruent by the vertical angle theorem and it already shows line OC and line OB are congruent.
Is 46 a number in the sequence generated by 5n + 1
Answer:
231
Step-by-step explanation:
5.46+1
230+1
231
answer this?
Answer:
yes
Step-by-step explanation:
Equate 5n + 1 and 46 to find n, that is
5n + 1 = 46 ( subtract 1 from both sides )
5n = 45 ( divide both sides by 5 )
n = 9
Thus 46 is the ninth term in the sequence
Lines a and b are parallel. Line c is a transversal. FInd the measures of all angles formed by a, b, and c, given each scenario. One of the angles measures 150 degrees.
Answer:
30° and 150°
Step-by-step explanation:
Given
Parallel lines a and b
Transversal c
Angle = 150°
Required
Determine the list of possible angles
A transversal divides a parallel line into two measure which add up to 180°
Given that one of the angles is 150°, the other angle would be 180° - 150°
Other angle = 180° - 150°
Other angle = 30°
Aside 30° and 150°, there's no other possible angle that can be formed by the given information
Answer:
30 and 150
Step-by-step explanation:
Given
Parallel lines a and b
Transversal c
Angle = 150°
Required
Determine the list of possible angles
A transversal divides a parallel line into two measure which add up to 180°
Given that one of the angles is 150°, the other angle would be 180° - 150°
Other angle = 180° - 150°
Other angle = 30°
Aside 30° and 150°, there's no other possible angle that can be formed by the given information
Can a right triangle have sides of 12, 16, and 20?
The graph shows that the distance a dog runs is proportional to the time the dog is running. You want to use only one plotted point to find the unit rate. Which of the three plotted points could you choose? Select all that apply.
(0,0)
(1,9.7)
(4,38.8)
Question 2
The unit rate is
feet per second.
Answer:
2
Step-by-step explanation:
2
Which of the following mathematical properties is described by the statement, “whatever is done on one side of the equation must also be done on the other side of the equation”?
Identity Property of Addition
Associative Property
Communitive Property
Property of Equality
today guys please
Answer:
Property of Equality
Step-by-step explanation:
Answer:Property of Equality
STEP BY STEP EXPLANATION HAS BEEN CANCELED ITS EASY:
PLEB
True or False: A system of two equations in two variables whose graphs are a parabola and a circle can have four real ordered-pair solutions.
The parabola can intersect the circle four times as the graph shows below. Each intersection point is a solution in the form (x,y).
Please help me I will really appreciate it!!!
Answer:
t = [tex]\sqrt{\frac{-2(h-1)}{a} }[/tex]
Step-by-step explanation:
solve for t
h = -[tex]\frac{1}{2}[/tex]a[tex]t^{2}[/tex] + 1; multiply both sides by -2
-2h = a[tex]t^{2}[/tex] - 2; add 2 to both sides
-2h + 2 = a[tex]t^{2}[/tex]; divide by a
(-2h + 2) / a = [tex]t^{2}[/tex] ; take the square root
t = [tex]\sqrt{\frac{-2(h-1)}{a} }[/tex]
Translate the following statement: "Your grade, g, must be at least
75 to pass this class."
Answer:
"Your grade, g, must be at least 75 to pass this class'' is translated as:
g ≥︎ 75Step-by-step explanation:
Given the grade is denoted by 'g'.
In algebra '≥︎' denotes that something must be 'greater than or equal to'. In other words, it means 'at least'.
As the gade must be at least 75, it means it can be greater than 75, but it can not be less than 75.
Therefore, "Your grade, g, must be at least 75 to pass this class'' is translated as:
g ≥︎ 75Estimate the area of the figure. Each square represents 2 units^2.
Answer:
60 units²Step-by-step explanation:
Approximate area is about 50 units²
The closest option is the last one
WORTH 15 POINTS
⚠️MAKE SURE TO USE SURDS ⚠️
ANSWER ASAP WILL GIVE BRAINLIEST
Answer:
i got 1.23 don't think its right though so someone check me
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
First thing is you have to do the square root of 3. Which will give you a crazy long decimal but then after you square it, it becomes 3 perfectly.
Which pair of radicals is a pair of like radicals
Will mark brainliest!! Please answer ASAP
Will give extra points!!!
Please let me know if the picture above answer is correct or not and tell me the right answer!
Second question-
Which linear equation can be used to represent a line parallel to the x axis that passes through the point (8,5)
1) y=5
2) y=x+8
3) y=x+5
Answer:
y=5
Step-by-step explanation:
y= 5 is always parallel to x axis
A museum has 6,000 visitors in its first month of operation. The museum staff predicts that the number of visitors will increase by 5% each month. Assuming that this prediction is true, how many visitors does the museum expect on the 7th month of operation?
Multiply 5 by 6000 aka 30,000 then multiply 7 then to 210,000 please give brainliest
8100 visitors in 7th month.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
given:
Visitor in first month= 6000
If the visitors will increase at the rate of 5% then
Visitors in second month
=6000+ 6000 x 5/100
=6000 + 300
=6000
So, the visitors in 7 month
=6000+ 7(300)
=6000 +2100
=8100
Hence, there 8100 visitors in 7th month.
Learn more about unitary method here:
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Extremely easy question marking Brainliest answer
Answer:
It is hard to tell from this image, but I believe the word you are looking for is Integer. Integers are any positive or negative whole number.