PLEASE HELP
The graph below shows a company's profit f(x), in dollars, depending on the price of pens x, in dollars, sold by the company:
Graph of quadratic function f of x having x intercepts at ordered pairs 0, 0 and 6, 0. The vertex is at 3, 120.
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 = 3 to x = 5, and what does this rate represent?
Part C: Describe the constraints of the domain.
Answers
Answer:
See below ↓
Step-by-step explanation:
Part A
The x-intercepts represents when the profit of the company is 0 dollars. It means they are making no profit when selling the pens at that pricePart B
y-value when x = 3 ⇒ 120y -value when x = 5 ⇒ 60rate of change = Δy/Δx = -60/2 = -30This rate represents the depreciating profit of the company when increasing the price of a pen from $3 to $5Part C
Domain of the graph is only true for positive values of yDomain ⇒ 0 ≤ x ≤ 6Answer:
Part A
The x-intercepts are when f(x) = 0.
Since x represents the price of pens, and f(x) represents the company's profit, the x-intercepts give the price of the pens when the profit is zero.
⇒ the profit is zero when the price of pens are $0 and $6
The maximum value of the graph (vertex) represents the cost of pens when the profit is at its highest. Therefore, the optimal amount to price the pens to get the maximum profit.
⇒ maximum profit of $120 occurs when the pens are priced at $3
Part B
[tex]\sf average \ rate \ of \ change=\dfrac{change \ in \ y}{change \ in \ x}[/tex]
From inspection of the graph, f(3) = 120 and f(5) ≈ 60
[tex]\sf \implies average \ rate \ of \ change=\dfrac{60-120}{5-3}=-30[/tex]
This means that as the price of the pens increases by $1 (between $3 and $5), the average profit decreases by approximately $30.
Part C
The domain is the set of input values (x-values). As the price of a pen cannot be less than zero, the domain will be x ≥ 0
Unless the company is happy to make a loss, the restricted domain should be 0 ≤ x ≤ 6
Related Questions
6.
Part I: Suppose a prism has a square base with each side of length 3.75 cm and a height
of 5.65 cm. Use the formula below to find the volume. Show your work and round your
answer to the nearest hundredth. (5 points)
Answers
79.45401²
Step-by-step explanation:[tex]1)\ V=B\ Sh[/tex]
[tex]\therefore\ V=3.15\times 3.75\times 5.65[/tex]
[tex]=79.403125[/tex]
[tex]\approx 79,45\ cm^3[/tex]
I hope this helps you
:)
Rounded to the nearest hundredth, the volume of the prism is approximately 79.50 cm^3.
To find the volume of a prism, we use the formula:
Volume = Base Area * Height
In this case, the prism has a square base with each side of length 3.75 cm and a height of 5.65 cm. The formula for the area of a square is:
Base Area = Side Length^2
So, the base area can be calculated as:
Base Area = 3.75 cm * 3.75 cm = 14.0625 cm^2
Now, we can find the volume using the formula:
Volume = Base Area * Height
Volume = 14.0625 cm^2 * 5.65 cm
Volume ≈ 79.5025 cm^3
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Help help help math math
Answers
Answer:
>
Step-by-step explanation:
Negative is that amount below zero. For example -3 is 0 - 3. This means that since -3 is 3 less than 0, -3 < 0. This can also be said as 0 > -3.
Answer:
Answer: 0 (> )-3
Step-by-step explanation:
Hope it helps
How is the graph of log (x + 3) translated from the graph of log x?
shifted down 3 units
shifted left 3 units
shifted up 3 units
shifted right 3 units
Answers
shifted left 3 units
Graphed Below:
red line: log (x + 3)blue line: log (x)Please help as soon as possible
Answers
Answer:
possibly (9, 9) (9, 5) (5, 9)
A map has a scale of 3 cm:20 km. If two cities are 30 cm apart on a map, how far are the cities actually apart?
Answers
The actual distance between the cities is 200 km using multiplication.
The scale of the map is 3 cm : 20 km. This means that for every 3 cm on the map, the actual distance in real life is 20 km.
If two cities are 30 cm apart on the map, we can use the scale to find the actual distance between them. First, we need to determine how many times the scale goes into the distance on the map. To do this, we divide the distance on the map by the length of the scale:
30 cm ÷ 3 cm/20 km = 30 ÷ 3 × 20 = 200 km
Therefore, the actual distance between the two cities is 200 km.
Alternatively, we can use the proportionality between the scale and the actual distance to set up a proportion and solve for the actual distance. Let x be the actual distance between the cities in kilometers:
3 cm / 20 km = 30 cm / x
Cross-multiplying and solving for x, we get:
x = (20 km / 3 cm) × 30 cm = 200 km
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A car travels 80 miles on 3 gallons of gas. At the same rate (in miles per gallon) l, how many miles will the car be expected to travel on 5 gallons of gas?
A. 48
B. 130
C. 133 1/5
D. 160
Answers
Answer:
C
Step-by-step explanation:
Karen drew a triangle with side lengths 3 centimeters, 4 centimeters, and 5 centimeters. What is the perimeter of the triangle?
Answers
Answer:
12 cm
Explanation:
The formula or method to find the area of any shape is to go around the shape.
In this case, they are 3, 4 and 5.
p = 3 + 4 + 5
p = 12 cm
Tadeo is a beekeeper. The table shows the weekly number of bees producing honey in a new hive. Which expression gives the number of bees in week 12?
Answers
The exponential equation that gives the number of bees in week 12 is of:
[tex]y = 4(3)^{11} = 708588[/tex]
What is an exponential function?It is modeled by:
[tex]y = ab^x[/tex]
In which:
a is the initial value.b is the rate of change.In this problem, considering that the initial week is the first, and the value triples every week, the expression for the number of bees after x weeks is given by:
[tex]y = 4(3)^{x - 1}[/tex]
Hence, after 12 weeks, the expression is:
[tex]y = 4(3)^{11} = 708588[/tex]
More can be learned about exponential equations at https://brainly.com/question/25537936
Answer:
4 • 3^11
Step-by-step explanation:
$6500 for 5 years at 5.5% compounded monthly
Answers
Answer:
$8,552.07
Step-by-step explanation:
The final balance is $8,552.07
The total compound interest is $2,052.07
Kaya rented a limousinefor prom. There was a one-time charge of $100 plus an hourly rate of $50 per hour. Her
total cost for the night was $300. How many hours did she rent the limo?
Answer using 2 step equations and X as variable
Answers
C = 50X + 100
Since C = 300,
50X + 100 = 300
50X = 200
X = 4 hours
x=4
She rented the limo for 4 hours($200) with the one time charge of $100
A high-altitude spherical weather balloon expands as it rises due to the drop in atmospheric pressure. Suppose that the radius r increases at the rate of 0.03 inches per second and that r=48 inches at time t=0. Determine a function that models the volume V of the balloon at time t and find the volume at t=300 seconds.
Answers
Considering a linear function for the radius, we have that:
The volume of the sphere is modeled by [tex]V(t) = \frac{4\pi(0.03t + 48)^3}{3}[/tex].After 300 seconds, it is of 775,735 in³.What is a linear function?A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value.What is the volume of a sphere?The volume of a sphere of radius r is given by:
[tex]V = \frac{4\pi r^3}{3}[/tex]
In this problem, radius r increases at the rate of 0.03 inches per second and that r=48, hence it is represented by the following linear function:
[tex]r(t) = 0.03t + 48[/tex]
Thus, the volume of the sphere is given by:
[tex]V = \frac{4\pi r(t)^3}{3}[/tex]
[tex]V(t) = \frac{4\pi(0.03t + 48)^3}{3}[/tex]
After 300 seconds, the volume in cubic inches is given by:
[tex]V(300) = \frac{4\pi(0.03(300) + 48)^3}{3} = 775735[/tex]
More can be learned about linear functions at https://brainly.com/question/24808124
Help me pls answer 1&2&3 pls brainless
Answers
Answer:
3,1,5
Step-by-step explanation:
QUICK PLEASE Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices.
Josiah’s Music
Sample 1
Sample 2
R & B
5
R & B
4
Pop
4
Pop
3
Classical
3
Classical
5
Jazz
2
Jazz
4
Rock
6
Rock
4
Josiah’s work:
StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x.
Answers
Answer:
Sample 1
Step-by-step explanation:
Can someone please help me
Answers
Answer:
BCDE
Step-by-step explanation:
An oblique cylinder with a base of radius 2 units is shown. The top
of the cylinder can be obtained by translating the base by the directed line segment
AB which has length 16 units. The segment AB forms a 30° angle with the plane of
the base. What is the volume of the cylinder?
Answers
The volume of the cylinder is the amount of space on it
The volume of the oblique cylinder is 174.19 cubic units
How to determine the volume of the cylinder?The given parameters are:
AB = 16 units
Radius (r) = 2 units
[tex]\theta = 30^o[/tex]
Start by calculating the height (h) using:
[tex]h = 16 * \cos(30^o)[/tex]
This gives
[tex]h = 13.86[/tex]
The volume of the cylinder is then calculated as:
[tex]V = \pi r^2 h[/tex]
This gives
[tex]V = 3.142 * 2^2 * 13.86[/tex]
[tex]V = 174.19248[/tex]
Approximate
[tex]V = 174.19[/tex]
Hence, the volume of the oblique cylinder is 174.19 cubic units
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Please help with this
Answers
Answer:
1) the quadratic formula2) factoring (zero product property)Step-by-step explanation:
1) using quadratic formula
(b)² - 4ac ----(always write the formula)
3 ( 4x + 1 )² - 5 =25
(12x + 1)² - 5 = 25 (using (a+b)^2)
144x² + 24x +1 - 5 = 25
144x²+ 24x - 4 = 25
144x² + 24x =29
144x² + 24x - 29= 0 (thus, formed and equation)
A=144, b= 24, c= -29
(24)² - 4(144 X -29)
576 - 4 X -4176
576 + 16704=0
17280>0, therefore it has 2 distinct real roots2) x²-8x+12=0
sum= -8, product= 12
-2,-6
so,
x²-2x -6x + 12
x ( x - 2 ) -6 ( x - 2 )
(x-2) (x-6)
X= 2, 6Hope it is correct and helpful
Stay safesorry for the late answerWhich of the following describes the solution to a system of linear inequalities?
A. The soultion is the region where both shaded parts overlap.
B. The solution is everything on the shaded graph.
Answers
Answer:
A. The solution is the region where both shaded parts overlap.
Step-by-step explanation:
The solution to a system of linear inequalities is the intersection region of the solution of both inequalities. Or you could also say that it's the region where the graphs of the inequalities in the system overlap.
The shaded area represents the solution and where the two inequalities overlap.
given that three points 15 raise to power 6 is equal to 3 raise to power 6 x b correct to four decimal places
Answers
Answer:
A. Directions: Encircle the letter of the correct answers
Step-by-step explanation:
1.the I in resign sounds like the I in.
A. hit B. High
Out of 100 people sampled, 36 had kids. Based on this, construct a 95% confidence interval for the true
population proportion of people with kids.
Give your answers as decimals, to four places
Answers
This is the same as saying 0.2659 < p < 0.4541
=========================================================
Work Shown:
At 95% confidence, the z critical value is about z = 1.96 which is determined through a table or calculator.
x = number of people who had kids = 36
n = sample size = 100
phat = sample proportion of those who had kids
phat = x/n
phat = 36/100
phat = 0.36
E = margin of error
E = z*sqrt(phat*(1-phat)/n)
E = 1.96*sqrt(0.36*(1-0.36)/100)
E = 0.09408
This value of E is approximate because z = 1.96 is approximate.
-------------
L = lower bound
L = phat - E
L = 0.36 - 0.09408
L = 0.26592
L = 0.2659
U = upper bound
U = phat + E
U = 0.36 + 0.09408
U = 0.45408
U = 0.4541
The values of L and U are approximate since E is approximate.
-------------
The confidence interval in the format (L, U) is (0.2659, 0.4541)
This is equivalent to writing 0.2659 < p < 0.4541
which is the format L < p < U
We're 95% confident that the true population proportion (p) is somewhere between 0.2659 and 0.4541; i.e. we're 95% confident the true percentage of people who had kids is somewhere between 26.59% and 45.41%
A 25-year, $1,000 par value bond has an 8.5% annual coupon. The bond currently sells for $875. If the yield to maturity remains at its current rate, what will the price be 5 years from now?
Answers
Given the current yield to maturity of the bond, the price of the bond five years for now is $883.10.
What is the price of the bond five years from now?The first step is to determine the yield to maturity of the bond. The yield to maturity is the return on the bond if the bond is held to matuity.
Yield to matuity can be determined using a financial calculator:
Cash flow in year 0 = -875
Cash flow each year from year 1 to 25 = 85
Cash flow in year 25 = $1000
Yield to matuity = 9.86%
Future price of the bond: (coupon x future price factor) + [FV / (1 + YTM)^n)]
Future price factor = [1 - (1/YTM)^n] / YTM
= [1 - 1/0.0986^20] 0.0986 = 8.595555
[85 x 8.595555 ] + 152.478323 = $883.10
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Caden deposited $300 into a checking account. Each week he withdraws $12 from his account.
a) Write an equation to describe this sequence.
b) How many weeks can Caden go before he runs out of money?
Answers
Answer:
B i had this text and made a 100
Step-by-step explanation:
b
Help help help help help
Answers
Answer:
49.12
Step-by-step explanation:
Area of triangle =1/2 x b x h
=24
semi circle =(pie rxr)divuded by 2
=25.12
so, 25.12 +24=49.12
SOMEONE PLSSS HELP ME FAST
WILL MARK BRAINLIEST
Answers
Answer:
D. 45
Step-by-step explanation:
To find out how many games will be played with 10 people, we need to first find the pattern of the given table. To start out, we can see that for the numbers of players added, it adds one each time it goes up one number. And, we can also see that starting at 1 games played, it adds 2 for the next and gets 3 games. Then it adds 3 to get 6 games. So, we can see that for every added person added, it starts at 1 and adds 2, then adds, 3, 4, 5, 6, etc... Knowing this, we can figure out how many games will be played with 10 people.
2 people gets 1 games
+1 +2
3 people get 3 games
+1 +3
4 people get 6 games
So, now we can simply skip to 6 and seven players becuase we know that the pattern holds true to itself.
6 people get 15 games
+1 +6
7 people get 21 games
+1 +7
8 people get 28 games
+1 +8
9 people get 36 games
+1 +9
10 people get 45 games
Graph the circle (x+5)^2+(y+2)^2=4
Answers
(x+5)² + (y+2)² = 4
(x - x0)² + (y - y0)² = r²
with circle center point (x0 ; y0) and r for circle radius
so you have to place the point (- 5 ; - 2) and graph the circle with r = 2
HELP ME ON TANGENTS, ARCS AND CHORDS! 1
Answers
Jogging is one of the few sports that has been consistently increasing over the past few years. The number of people jogging (in millions) from the years 2000 to 2009 is given by the equation y=x+22, where x is the number of years after 2000.
a. Use this equation or a graph of it to complete the ordered pair (4, ).
b. Write a sentence explaining the meaning of the answer to part (a).
c. If this trend continues, how many joggers will there be in 2021 ?
a. Complete ordered Pair
(4, )
Answers
Answer:
a. (4, 26)
b. The number of people jogging in 2004 was 26 million.
c. 43 million
Step-by-step explanation:
To complete the ordered pair, use the given first value of the pair as the value of the variable in the equation. Evaluate the equation to find the second value of the ordered pair:
a.y = x +22
y = 4 +22 = 26
The ordered pair is (4, 26).
__
b.The ordered pair tells you (years after 2000, number of joggers in millions). That means the ordered pair (4, 26) tells you 4 years after 2000, there were 26 million joggers.
__
c.21 years after 2000, the value of x is 21, so the value of y is ...
y = 21 +22 = 43
There will be 43 million joggers in 2021.
Please helppppppp thank you so much
Answers
Answer:
7 1/8
Step-by-step explanation:
1 1/8 + 1 1/8 is 2 2/8
2 2/8 + 4 7/8 is 6 9/8 = 7 1/8
I need help with this question?
Answers
Answer:
38.5 cm²
Find area of the full rectangle:
Length * Width
6 * 7
42 cm²
Find area of the missing triangle
1/2 * base * height
1/2 * 7 * 1
3.5 cm²
Area of the figure:
42 - 3.5
38.5 cm²
A thief steals an atm card and must randomly guess the correct five-digit pin code from a 8-key keypad. repetition of digits is allowed. what is the probability of a correct guess on the first try?
Answers
Answer:
The probability of a correct guess on the first try is 0.024%.
Since a thief steals an atm card and must randomly guess the correct four -digit pin code from a 8 -key keypad, and repetition of digits is allowed, to determine what is the probability of a correct guess on the first try the following calculation must be performed:
8 x 8 x 8 x 8 = X
8 ^ 4 = X
4096 = X
1/4096 = X
0.000244140625 = X
0.000244140625 x 100 = 0.024%
Therefore, the probability of a correct guess on the first try is 0.024%
Step-by-step explanation:
Need help with this geometric question ASAP, Thank you