Answer:
There are an absolute minimum (x = 6) and an absolute maximum (x = 12).
Step-by-step explanation:
The correct statement is described below:
Find the absolute maximum and minimum values of the function below:
[tex]f(x) = x^{3}-9\cdot x^{2}+ 3[/tex], [tex]2 \leq x \leq 12[/tex]
Given that function is a polynomial, then we have the guarantee that function is continuous and differentiable and we can use First and Second Derivative Tests.
First, we obtain the first derivative of the function and equalize it to zero:
[tex]f'(x) = 3\cdot x^{2}-18\cdot x[/tex]
[tex]3\cdot x^{2}-18\cdot x = 0[/tex]
[tex]3\cdot x \cdot (x-6) = 0[/tex] (Eq. 1)
As we can see, only a solution is a valid critical value. That is: [tex]x = 6[/tex]
Second, we determine the second derivative formula and evaluate it at the only critical point:
[tex]f''(x) = 6\cdot x -18[/tex] (Eq. 2)
x = 6
[tex]f''(6) = 6\cdot (6)-18[/tex]
[tex]f''(6) =18[/tex] (Absolute minimum)
Third, we evaluate the function at each extreme of the given interval and the critical point as well:
x = 2
[tex]f(2) = 2^{3}-9\cdot (2)^{2}+3[/tex]
[tex]f(2) = -25[/tex]
x = 6
[tex]f(6) = 6^{3}-9\cdot (6)^{2}+3[/tex]
[tex]f(6) = -105[/tex]
x = 12
[tex]f(12) = 12^{3}-9\cdot (12)^{2}+3[/tex]
[tex]f(12) = 435[/tex]
There are an absolute minimum (x = 6) and an absolute maximum (x = 12).
help! 50 points and brainliest if u answer all of em
Answer:
The first one is C the second and third are correct.
Step-by-step explanation:
Un abuelo quiere repartir una cierta cantidad de manera proporcional entre sus tres nietos de 14, 10 y 6 años de edad ¿A quién le corresponde más? Resuelve el problema apoyándote con los videos previos. Una vez resuelto, planteen el tema a alguien de su familia y juntos comenten cómo utilizan las relaciones proporcionales en sus quehaceres.
Answer:
El nieto de 14 años de edad recibirá la mayor cantidad.
Step-by-step explanation:
En este problema, debemos tener en mente que la cantidad aportada es directamente proporcional a la edad de quien recibe, esta cantidad es igual al producto de la cantidad total y la razón de la edad de quien recibe y la suma de todas las edades.
Bajo este razonamiento, podemos concluir que el nieto de 14 años de edad recibirá la mayor cantidad.
You can buy a pack of 12 batteries
for $6. What is the unit price?
Answer:
Each battery costs .5 dollars or 50 cents
Step-by-step explanation:
6/12=.5
Answer:
total units 12
cost per unit $ 0.5000
Step-by-step explanation:
Hope this helps! :)
A dietician is considering three food types to be served at a meal she is particularly concerned with the amount of one vitamin provided?
5 years ago
at this meal ,. One ounce of food 1 provide 8 milligrams of the vitamin , an ounce of food 2 provides 24 milligram and an ounce of food 3 provides 16 milligrams . The minimum daily requirements for vitamin is 120 milligram
a. If x equals the number of ounces of food type j served at meal, determine the equation which ensure the meal satisfies MDR exactly.
i want linear equation solution of this
Answer:
8* x₁ + 24*x₂ + 16*x₃ ≥ 120
Step-by-step explanation:
food 1 provides 8 mgrs of vitamin
food 2 provides 24 mgrs of vitamin
food 3 provides 16 mgrs of vitamin
If xj ( j = 1 ,2,3 ) is the quantity in ounces of food ( 1, 2, 3 ) then:
8* x₁ + 24*x₂ + 16*x₃ ≥ 120
I need help please thanks
find x when y = 18, if y = 9 when x = 8
ASAP PLEASE
so
y=9 -> y=18
*2
x=8 -> x=16
*2
so x = 16
Answer:
the only logical way solving this question is:
if y=9 then x=8
if y=18 then x should be 16
Step-by-step explanation:
I cant find any other way to solve
A candy company claims that 20% of the candies in its bags are colored green. Steve buys 30 bags of 30 candies, randomly selects one candy from each, and counts the number of green candies. If there are 5, 6, or 7 green candies, Steve will conclude that the company’s claim is correct. What is the probability of Steve agreeing with the company’s claim? Use a TI-83, TI-83 plus, or TI-84 calculator to find the probability.
Answer:
The probability of Steve agreeing with the company’s claim is 0.50502.
Step-by-step explanation:
Let X denote the number of green candies.
The probability of green candies is, p = 0.20.
Steve buys 30 bags of 30 candies, randomly selects one candy from each, and counts the number of green candies.
So, n = 30 candies are randomly selected.
All the candies are independent of each other.
The random variable X follows a binomial distribution with parameter n = 30 and p = 0.20.
It is provided that if there are 5, 6, or 7 green candies, Steve will conclude that the company’s claim is correct.
Compute the probability of 5, 6 and 7 green candies as follows:
[tex]P(X=5)={30\choose 5}(0.20)^{5}(1-0.20)^{30-5}=0.17228\\\\P(X=6)={30\choose 6}(0.20)^{6}(1-0.20)^{30-6}=0.17946\\\\P(X=7)={30\choose 7}(0.20)^{7}(1-0.20)^{30-7}=0.15328[/tex]
Then the probability of Steve agreeing with the company’s claim is:
P (Accepting the claim) = P (X = 5) + P (X = 6) + P (X = 7)
= 0.17228 + 0.17946 + 0.15328
= 0.50502
Thus, the probability of Steve agreeing with the company’s claim is 0.50502.
idk the answer at all
Answer:
y-1=3/2(x+3)
Step-by-step explanation:
Calculate the slope m of the given line using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 2, - 4) and (x₂, y₂ ) = (2, 2) ← 2 points on the line
m=2+4/2+2=6/4=3/2
Parallel lines have equal slopes.
The equation of a line in point-slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = 3/2 and (a, b) = (- 3, 1), thus
y - 1 = 3/2 (x - (- 3)), that is
y - 1 = 3/2 (x + 3) ← equation in point- slope form
Sequence: 49, 36, 25, 16, 8, 4, 1 * Is this a arithmetic or geometric sequence? and if it is arithmetic find the common difference and if it is geometric find the common ratio? and please do not give me a stupid answer only smart people answer this if you know the answer to this you are smart. 1
Answer:
The given sequence [tex]49,36,25,16,8,4,1[/tex] is neither a arithmetic nor a geometric sequence
Step-by-step explanation:
A sequence is said to be an arithmetic sequence if difference between the terms is same.
A sequence is said to be a geometric sequence if ratio of the terms is same.
Given sequence is [tex]49,36,25,16,8,4,1[/tex]
Here,
[tex]36-49=-13\\25-36=-11\\36-49\neq 25-36[/tex]
So, this sequence is not an arithmetic sequence.
Also,
[tex]\frac{36}{49}\neq \frac{25}{36}[/tex]
So, this sequence is not a geometric sequence.
Therefore,
The given sequence [tex]49,36,25,16,8,4,1[/tex] is neither a arithmetic nor a geometric sequence
Somebody tell me whats the answer and how do i find the oder pair thing
Answer:
( 2,0)
Step-by-step explanation:
The line crosses the Y intercept at the coordinates at (2,0)
Answer:
the y-intercept of the graph is 2
the ordered pair is (0,2)
Step-by-step explanation:
The y-intercept is the point where the line crosses the "y" line. Ordered pair are written (x,y) (the x is always in the front)
So, if we look at the "y" line we can see they y point is a 2, and if we look at line "x", the 2 is "above" the point 0 on the line labeled x.
The population of Philadelphia, Pennsylvania, is about 1.5 × 106 people. The population of Moscow, Russia, is about 8 times greater than the population of Philadelphia. Drag the buttons to the correct places to show how to use a calculator to find the population of Moscow.
Answer:
8 x (1.5EE6)
Step-by-step explanation:
hurry i'm doing a test so
what is the value of x in the equation 5.5x = 17.6?
Answer:
x=3.2
Step-by-step explanation:
Answer:
x=3.2
Step-by-step explanation:
Divide each term by 5.5 and simplify.
x = 3.2
4(3x + 1)
What is the answer to 4(3x + 1)
Answer:
Answer is 12x+4. Hope that helped.
an airplane is change in alitude before landing is shown in the table
Answer:
wheres the table can you please provide one
Step-by-step explanation:
AnswerA= -4,000m
Step-by-step explanation:
1 35,000
2 31,000
3 27,000
4 23,000
Youre subtracting 4,000 everytime.
Analyzing a System
Solve the system of inequalities.
x² - gpg
v> 2
Which describe the solution set of the given system?
Check all that apply
The solution set is unbounded.
The point (1, 0) is in the solution set.
There is one point of intersection of the boundary
curves
The boundaries of the overlapping region are in the
solution set.
The boundary curves intersect at approximately
(-3,0).
Answer:
A, C, E
Step-by-step explanation:
took the assignment on edge
Answer:
a , c and e
Step-by-step explanation:
got it right on edg ^u^
What integer represents the situation ""6 yards behind the winner""?
Answer:
-6
Step-by-step explanation:
An integer is a whole number that can either be positive, negative or zero.
Now, we want to write the integer that represents 6 yards behind the winner.
Now, a distance of 6 yards behind the winner means a deficit distance of 6 yards behind the winner. Which in turn means a negative distance which is -6 yards behind the winner.
Thus, the integer is -6
How can you express (15+30) as a multiple of us some of her numbers with no common factor?
HELP : calculating slope between two points.
Answer:
(1.)3.5 (2.)-3 (3)0
Step-by-step explanation:
if right comment please
Help!NOW please!! I’ll do anything!
Answer:
16 1/2
Step-by-step explanation:
find the absolute value of both and add them, there's you answer
Answer:
re08uwahrewrai098nyryvrhheuaviufvsdsavad <<< Don't do this please
-16 1/2 units away
Find the unknown angle measure.
Answer:
x=22
Step-by-step explanation:
180-77=103
103+55=158
180-158=22
x=22
Solve x2 - 4x + 1 = 0.
x= 2 + 2i15
x = 4+ V3
x = 2/3
x= -2-3
Answer:
x = 2 ± √ 3
Step-by-step explanation:
A car dealership finds that a certain model of new car has something wrong with its transmission 15% of the time. How likely is it that a particular model of that car has something wrong with its transmission? Select the correct answer below: Very likely, the probability is close to 1. Somewhat likely, the probability is closer to 1 than to 0. Unlikely, the probability is close to 0. Somewhat unlikely, the probability is closer to 0 than it is to 1. Equally likely, the probability is 0.5.
Answer:
Unlikely, the probability is close to 0
Step-by-step explanation:
Given
[tex]Transmission = 15\%[/tex]
Required
Determine the likelihood
The given probability, 0.15 is close to 0. This implies that the event is unlikely.
From the list of given options, option C answers the question
Winter coats are marked 70% off on February 1st. if a coat costs $57.75 on January 31st, how much will it cost on February 1st.
Answer:
57.75-(57.75*0.7)=17,325
Or 100-70=30
So 57.75*0.3=17.325
Answer:
$40.425
Step-by-step explanation:
hope it helps good luck
890 g of copper is mixed with 100 g of zinc to form brass. The density of copper is 8.9 g/cm³ and the density of zinc is 7.1 g / cm ³ .
a ) What is the volume of copper and zinc used to make the brass ?
b ) Calculate the density of the brass .
Density ρ is equal to mass m per unit volume v, or
ρ = m / v
Solve for volume:
v = m / ρ
(a) 890 g of copper, which has a density of 8.9 g/cm³, has a volume of
v = (890 g) / (8.9 g/cm³) = 100 cm³
100 g of zinc, with density 7.1 g/cm³, has a volume of
v = (100 g) / (7.1 g/cm³) ≈ 14.08 cm³
(b) The density of brass is then
ρ = (890 g + 100 g) / (100 cm³ + 14.08 cm³) ≈ 8.68 g/cm³
(HELP PLEASE) Lines a and d are
-non-coplanar.
-parallel.
-perpendicular.
-skew.
Hanna lost 4 points on a test and earned 4 points on an extra-credit question
Answer:
the total points earned and lose cancel eachother out to be 0. she did not lose any points
Answer:
the total points earned and lose cancel eachother out to be 0. she did not lose any points
Step-by-step explanation:
4y-27=3y then y is equal to ?
Answer:
y=4/3y -9
Step-by-step explanation:
just divide both sides of the equation by 3
Aloma, a university graduate who started a successful business, wants to start an endowment in her name that will provide scholarships to ChE students. She wants the scholarship to provide $13,000 per year and expects the first one to be awarded on the day she fulfills the endowment obligation. If Aloma plans to donate $240,000, what rate of return must the university realize in order to award the annual scholarship forever?
The rate of return that the university must realize in order to award the annual scholarship forever is _____%.
Answer:
5.73%
Step-by-step explanation:
Calculation for the rate of return that the university must realize
Using this formula
Rate of return = Initial payment/(Plan to donate- Initial payment)
Let plug in the formula
Rate of return=$13,000/($240,000-$13,000)
Rate of return=$13,000/$227,000
Rate of return=0.0573*100
Rate of return =5.73%
Therefore The rate of return that the university must realize in order to award the annual scholarship forever is 5.73 %.
The product of two integers is -40. If
the sum of the two integers is -3, what
are the two integers?
Answer:
-20
Step-by-step explanation:
no cap
What is the midpoint of the segments with endpoints (3,7) and (9,15)
Answer:
(6,11)
I can confirm that this question is right.
12/2 22/2
(6 , 11)
The table shows the makeup of a New Year’s Eve television show. What fraction of the show will be for the audience to speak?
Table:
Introduction: 10%
Skits: 25%
Guests: 45%
Audience: 20%
Answer:
1/5
Step-by-step explanation:
We need to find the fraction of the show will be for the audience to speak. Here, the part of the audience is 20%.
We know that, percent means we need to divide the value by 100 i.e.
[tex]20\%=\dfrac{20}{100}\\\\=\dfrac{2}{10}\\\\=\dfrac{1}{5}[/tex]
So, the required fraction is 1/5.
