The graph below shows a company's profit f(x), in dollars, depending on the price of erasers x, in dollars, being sold by the company:
graph of quadratic function f of x having x intercepts at ordered pairs 0, 0 and 8, 0. The vertex is at 4, 270
Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit?
Part B: What is an approximate average rate of change of the graph from x = 1 to x = 4, and what does this rate represent?
Answers
Answer:
A. x-intercepts: prices at with profit is zero
maximum: price at which profit is a maximum
increasing: (-∞, 3); decreasing: (3, ∞) — profit increases with increasing pen price below $3, decreases with increasing pen price above $3
B. -26 2/3; loss of profit for each dollar increase in pen price
Step-by-step explanation:
Part A:
The definition of the function tells you what points on the graph represent. The x-intercept at x=0 tells you the company's profit will be zero when the price of pens sold by the company is zero.
The x-intercept at x=6 tells you the company's profit will be zero when the price of pens sold is $6.
The maximum value of 120 at x=3 tells you the company's profit will be $120 when the price of pens sold is $3.
The graph goes "uphill" for x < 3, so the function is increasing for x < 3. The function goes "downhill", so is decreasing, for x > 3. This tells you profit increases with pen price when the price is below $3, and decreases with pen price above $3.
__
Part B:
The equation of the function describing the graph is ...
f(x) = -120/9x(x -6)
so, at x=5, the value is ...
f(5) = -120/9(5)(-1) = 600/9 = 66 2/3
Then the average rate of change from x=3 to x=5 is ...
m = (f(5) -f(3))/(5 -3) = (66 2/3 -120)/2 = (-53 1/3)/2 = -26 2/3
This represents the average change in profit for each dollar increase in the price at which pens are sold.
Related Questions
Answer the question below
Answers
Answer:
Step-by-step explanation:
The side length of the larger pentagon is 3, but the side length of the smaller pentagon is 2, so the scale factor is 2/3.After this. we want the points that stick the farthest out to map onto each other, so they need to have the same y coordinate. So, translate down 2 units.Finally, reflect over the y axis.This shows the pentagons are congruent.Solve the equation.
6x+7=8x-15
Answers
The answer to the question is 11
Answer:x=11
Step-by-step explanation:
I know the answer just need someone explain to me how to solve it
Answers
The logarithm of a quotient can be written as a difference of logarithms:
[tex]\log_3\left(\dfrac uv\right) = \log_3(u) - \log_3(v)[/tex]
You can also think of this as a combination of the product-to-sum and reciprocal/power properties of logarithms:
[tex]\log_3\left(\dfrac uv\right) = \log_3\left(u \times \dfrac1v\right) = \log_3(u) + \log_3\left(\dfrac1v\right) = \log_3(u) - \log_3(v)[/tex]
To summarize,
[tex]\log_b(mn) = \log_b(m)+\log_b(n)[/tex]
[tex]\log_b\left(\dfrac mn\right) = \log_b(m) - \log_b(n)[/tex]
[tex]\log_b\left(m^n\right) = n \log_b(m)[/tex]
In a soccer league with four teams, each team played four games with every other team. Each team received 3 points for a win, 1 point for a tie, and no points for a loss. After all the games, the point tallies were as follows: Team A won 22 points, team B won 19 points, team C won 14 points, and team D won 12 points. How many games ended in a tie?
Answers
The number of game that ended in a tie are= 67
Calculation of total number of tiesThe number of points that makes up a win = 3
The number of points that makes up a tie = 1
The number of points that makes a loss = 0
Team A = 22 points
Team B = 19 points
Team C = 14 points
Team D = 12 points
The total of points gotten by the whole team is = the games that ended in a tie.
That is , 22+19+14+12 = 67
Learn more about addition here:
https://brainly.com/question/24536701
#SPJ1
6) Which of the following equations is of a parabola with a vertex at (3, 0)?
a) y = x2 + 3
b) y = x2-3
c) y = ( x + 3) 2
d) y = ( x - 3)2
Answers
Answer: Second option is correct.
Step-by-step explanation:
Since we have given that
We need a parabola with a vertex at (0,-3)
If we select the equation:
[tex]y=x^2-3[/tex]
When we put x = 0, we get
[tex]y=0-3[/tex]
[tex]y=-3[/tex]
And similarly, when we put y = -3, we get
[tex]-3=x^2-3[/tex]
[tex]0=x^2[/tex]
[tex]x=0[/tex]
Hence, second option is correct.
3. Determine the 5-day SMA for the 10 consecutive-day closing prices for
Sherwin-Williams Co listed below.
$242.50 $273.98 $278.16 $293.94 $285.04
$290.80 S296.02 $291.01 $293.41 $286.85
Answers
The 5-day SMA for the 10 consecutive-day closing prices are:
Day 2-6=$284.384Day 2-6=$284.384Day 3-7=$288.792Day 4-8=$291.362Day 5-9=$291.256Day 6-10=$291.618 5-day SMA for the 10 consecutive-dayDay 1-5:
Day 1-5 =$242.50+$273.98+$278.16 +$293.94+ $285.04÷5
Day 1-5=$1,373.62÷5
Day 1-5=$274.724
Day 2-6:
Day 2-6=$273.98+ $278.16 +$293.94 +$285.04+$290.80÷5
Day 2-6=$1,421.92÷5
Day 2-6=$284.384
Day 3-7:
Day 3-7=$278.16 +$293.94+ $285.04+$290.80 +S296.02÷5
Day 3-7=$1,443.96÷5
Day 3-7=$288.792
Day 4-8:
Day 4-8= $293.94 +$285.04+$290.80+$296.02+ $291.01÷5
Day 4-8=$1,456.81÷5
Day 4-8=$291.362
Day 5-9:
Day 5-9=$285.04+$290.80+$296.02 +$291.01 +$293.41÷5
Day 5-9=$1,456.28÷5
Day 5-9=$291.256
Day 6-10:
Day 6-10=$290.80+$296.02+ $291.01 +$293.41+ $286.85÷5
Day 6-10=$1,458.09÷5
Day 6-10=$291.618
Therefore the 5-day SMA for the 10 consecutive-day closing prices are:
$284.384; $284.384; $288.792; $291.362; $291.256; $291.618.
Learn more about 5-day SMA for the 10 consecutive-day here: https://brainly.com/question/5549040
#SPJ1
Find x and find angle b
Answers
60 + 15x + 5 + 22x + 4 = 180
69° + 37x = 180
37x = 180° - 69°
37x = 111°
x = 111/37
x = 3
B = 22x + 4
B = 22(3) + 4
B = 66 + 4
B = 70
What does 3/4 + 3/4 + 3/4 + 3/4 =
Answers
Answer:
3
Step-by-step explanation:
3/4 = 0.75
0.75 x 4 = 3
0.75 + 0.75 + 0.75 + 0.75 = 3
Step-by-step explanation:
[tex] = \frac{3}{4} + \frac{3}{4} + \frac{3}{4} + \frac{3}{4} \\ [/tex]
[tex] = \frac{3 + 3 + 3 + 3}{4} \\ [/tex]
[tex] = \frac{12}{4} \\ [/tex]
change into lowest term
[tex] = \frac{6}{2} \\ [/tex]
[tex] = \frac{3}{1} \\ [/tex]
hope it helped !!!
Corbin made a scale model of the San Jacinto Monument. The monument has an actual height of 604 feet. Corbin's model used a scale in which 1 inch represents 100 feet. What is the height in inches of Corbin's model?
Answers
Answer: 6.04 inches
Step-by-step explanation:
The actual height of the monument = 604 feet
The scale used by Corbins is 1 inch = 100 feet
The height of the Corbins model in inches= [tex]\frac{604}{100}[/tex] = 6.04 inches
the height of the Corbins model = 6.04 inches
simplify the expression by combing like terms. write the twins from the highest to the lowest power of the variable. 15a + 12b - 14c * 3a + 19b -6c
Answers
Answer:
−42+15+31−6
Step-by-step explanation:
Combine the terms
The principal would like to assemble a committee of 7 students from the 13-member
tudent council. How many different committees can be chosen?
Answers
If the committee requires 7 students to be on it, and 7 can only go into 13 once (13 is a prime number), you can only have one committee
What is the measure of y
Answers
Just add the angles up.
Todd orders pictures from a photographer. Each picture costs $7.50. A one-time shipping fee of $3.25 is added to the cost of the order. The total cost of Todd's order before tax is $85.75. How many pictures did Todd order? Solve this problem using two different methods or strategies. Label your strategies.
Answers
Equation in slope intercept form
y=mx+by=7.5x+3.25So
Total paintings is x
85.75=7.5x+3.257.5x=82.5x=11 paintingsAnswer:
11 pictures
Step-by-step explanation:
Method 1Create an algebraic equation from the given information, defining the unknown quantity as a variable, then solve for the variable.
Given:
Cost of one picture = $7.50Shipping fee (one time) = $3.25Total cost of order = $85.75Let x = number of pictures ordered
⇒ Cost of one picture × number of pictures ordered + shipping fee = total
⇒ 7.5x + 3.25 = 85.75
⇒ 7.5x + 3.25 - 3.25 = 85.75 - 3.25
⇒ 7.5x = 82.50
⇒ 7.5x ÷ 7.5 = 82.50 ÷ 7.5
⇒ x = 11
Therefore, Todd ordered 11 pictures.
Method 2Logic and trial and error.
Given:
Cost of one picture = $7.50Shipping fee (one time) = $3.25Total cost of order = $85.75If the shipping fee is a one time cost, then if we subtract this from the total cost of the order, we know how much Todd spent on the pictures alone:
⇒ $85.75 - $3.25 = $82.50
We have been told that each picture costs $7.50.
Therefore, 10 pictures costs $75.00 (when multiplying by 10, we simply move the decimal point one place to the right).
$75.00 is less than $82.50. So what happens if we add another $7.50 to $75.00?
⇒ $75.00 + $7.50 = $82.50
Therefore, Todd ordered 10 + 1 = 11 pictures.
i need helpp ..
I'm stuck here just to suffer
this is not my exam
just help mee
Answers
There are 60 cubic units in the provided three-dimensional figure, and the units are mm³, cm³, and m³.
What is volume?It is defined as a three-dimensional space enclosed by an object or thing.
We have a three-dimensional shape shown in the picture with dimensions.
The total cubic units = 4×3×5 = 60 cubic cm
We can measure the volume with units of mm³, cm³, m³, km³
We can draw a relation between them:
mm³<cm³ <m³< km³
For the first picture, the unit mm³ would be best for measuring the volume.
For the second picture, the unit cm³ would be best for measuring the volume.
For the third picture, the unit m³ would be best for measuring the volume.
Thus, there are 60 cubic units in the provided three-dimensional figure, and the units are mm³, cm³, and m³.
Learn more about the volume here:
https://brainly.com/question/16788902
#SPJ1
What is the surface area of the model, including the bottom face?
Answers
Answer:
D. 483.84 ft^2.
Step-by-step explanation:
we have 2 triangles and 7 rectangles, 5 of which are 8.4*8.4 squares.
Area = 2 * 1/2 * 4 * 8.4 + 2*5.8*8.4 + 5 * 8.4^2
= 33.6 + 97.44 + 352.8
= 483.84 ft^2.
Which of the following examines relationships and patterns?
descriptive survey
predictive survey
exploratory survey
explanatory survey
Answers
which expression represents four less than half a number, n? (show your work)
1. 4-1/2n
2. 1/2n-4
3. 1/2 (4-n)
4. 1/2 (n-4)
Answers
Multiplying a number n by 1/2 is the same as dividing that number by 2.
Detailed Explanation:
It represents 4 being subtracted from the half of n. It can also be further simplified to n/2 - 4
A cube has an edge length of 9 meters. What is its volume, in cubic meters?
Answers
Work Shown:
volume = side*side*side
volume = 9*9*9
volume = 729
A slight shortcut would be to say 9^3 = 729
Polygon a b c d is shown with exterior angles. exterior angle a is 25 degrees, exterior angle b is 146 degrees, and exterior angle d is 149 degrees. what is the measure of angle bcd? 25º 40º 140º 155º
Answers
The measure of angle bcd of the polygon abcd is 40°.
Hence, option b) 40° is the correct answer.
What is a polygon?A polygon is simply a two-dimensional a plane shape enclosed by line segments called sides.
The sum of the exterior angles of a regular polygon will always equal 360
Given that;
Exterior angle a = 25 degreesExterior angle b = 146 degreesExterior angle d = 149 degreesExterior angle c = ?25° + 146° + 149° + c = 360°
320° + c = 360°
c = 360° - 320°
c = 40°
The measure of angle bcd of the polygon abcd is 40°.
Hence, option b) 40° is the correct answer.
Learn more about polygons here: brainly.com/question/22408868
#SPJ4
Answer:
C. 140 degrees
Step-by-step explanation:
Got it right Edge2022
Please help!!!!!
A coin is tossed on the board shown. Which is the probability that it will land in region II?
A. 75%
B. 45%
C. 55%
Answers
Answer: B
Step-by-step explanation:
The area of the entire rectangle is (10+30)(15+10) = 1000, and the area of region II is (30)(15)=450. Hence, the desired probability is 450/1000 = 45%.
Help me on this please!
Answers
Answer:
B-a population growth of 3% each year
Step-by-step explanation:
The 1.03 would mean that the exponential function is increasing by 3% every year because it is 0.03 units above 1.
Is it appropriate to use the geometric distribution to
calculate probabilities in this situation?
a medical device company knows that the percentage
of patients experiencing injection-site reactions with
the current needle is 11%. a nurse will collect data by
performing injections with this type of needle until five
people experience injection-site reactions.
yes, the geometric distribution is appropriate.
no, since each trial is not independent of the other
trials.
no, because it is not looking for the first occurrence
of success.
no, since the probability of success is not the same
for each of the trials.
Answers
The hypergeometric distribution should not be used, hence the correct option is given by:
no, because it is not looking for the first occurrence of success.
When the hypergeometric distribution should be used?These two conditions should be respected:
We should be looking for the probability of x successes on n trials, not the number of trials until n successes.The trials should not be independent, that is, the probabilities on each trial should be different.None of these conditions are true in this case, hence the correct option is given by:
no, because it is not looking for the first occurrence of success.
More can be learned about the hypergeometric distribution at https://brainly.com/question/24826394
#SPJ1
name four fractions whose values are between 1/4 and 3/4
Answers
Answer:
ok don't panic it's organic
Answer:
[tex]\frac{1}{3} , \frac{1}{2} , \frac{3}{8} , \frac{5}{8}[/tex]
Step-by-step explanation:
Lori wants to spend less than $20 on her school lunches this week. If she plans to buy all her lunches at school this week, on average, how much can she spend in a day?
Inequality:
Answers
Answer:
average = amount/ days
the answer is 4
Trains Two trains, Train A and Train B, weigh a total of 355 tons. Train A is heavier than Train B.
The difference of their weights is 183 tons. What is the weight of each train?
Answers
Answer:
A = 269 T B = 86 T
Step-by-step explanation:
A-B = 183 or A = 183 +B
A+B = 355 SUB IN THE VALUE ABOVE FOR A
183 + B + B = 355
183 + 2B = 355
B= 86 THEN A = 183 +B = 269
What is the solution to this equation?
X- 17 = -5
Answers
-5+17=12 - this is the quickest way to solve an easy equation like this
For what value of k will k + 11, 2k – 1 and 2k + 7 are the consecutive terms of an A.P.?
1st answer will be marked brainliest and no glibberish answers
Answers
[tex]\text{For arithmetic series, the common difference will be same. }\\\\~~~~~~(2k-1)-(k+11) = (2k+7)-(2k-1)\\\\\implies 2k-1-k-11 = 2k+7-2k+1\\\\\implies k-12=8\\\\\implies k=8+12\\\\\implies k=20[/tex]
A box contains six black balls and four white balls.
What is the probability of selecting a black ball at
random from the box?
(15 points!!!)
Thank you! :)
Answers
For probability questions, it is just the sum of the object you need to find, over the total sum of all objects.
Hope this helps!
Can someone help me with this question? Thanks!
Answers
The probability that the student loses his earbuds in cherry st. in the path of home to school is 0.2857 or 28.57%.
What is probability?Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
The path of the student from the home to school consists of:
0.2 miles of cherry st.0.4 miles of park st.0.1 miles of pine st.Total distance of the path of student from the home to school is,
d=0.2+0.4+0.1
d=0.7 miles
Now, the distance of cherry st. is 0.2 miles. Thus, the probability that he loses his earbuds in this st. is,
P=(0.2)/(0.7)
P=0.2857
P=28.57 %
Thus, the probability that the student loses his earbuds in cherry st. in the path of home to school is 0.2857 or 28.57%.
Learn more about the probability here;
https://brainly.com/question/24756209
#SPJ1
Consider the parallelogram below.
Find the value of y.
Enter each line of work as an equation.
Answers
Answer: 10
Step-by-step explanation:
Opposite sides of a parallelogram are congruent, so [tex]17=y+7 \longrightarrow y=10[/tex]
