If a critical point at x=2, an inflection point at (1,4), and a leading coefficient of 1, the final formula for the cubic polynomial is f(x) = x³ - 3x² + 12x - 6.
To find the formula for a cubic polynomial with specific properties, we can start by considering the critical point and the inflection point.
Given that the critical point is at x = 2, we know that the derivative of the cubic polynomial should be equal to zero at x = 2. This means that the slope of the polynomial at x = 2 is zero. Taking the derivative of the cubic polynomial, we have:
f'(x) = 3ax² + 2bx + c.
Setting this equal to zero and substituting x = 2, we get:
3a(2)² + 2b(2) + c = 0.
12a + 4b + c = 0.
Now, let's consider the inflection point at (1,4). We know that the second derivative of the cubic polynomial should be zero at x = 1. Taking the second derivative, we have:
f''(x) = 6ax + 2b.
Setting this equal to zero and substituting x = 1, we get:
6a(1) + 2b = 0.
6a + 2b = 0.
Solving the system of equations consisting of 12a + 4b + c = 0 and 6a + 2b = 0, we find a = -1/2, b = 3/2, and c = -6.
Therefore, the formula for the cubic polynomial is:
f(x) = -1/2x³ + 3/2x² - 6x + d.
The leading coefficient is 1, so we have:
f(x) = x³ - 3x² + 12x + d.
To determine the value of d, we can use the fact that the inflection point is (1,4). Substituting x = 1 and y = 4 into the equation, we get:
4 = 1 - 3 + 12 + d.
4 = 10 + d.
d = -6.
Therefore, the final formula for the cubic polynomial is:
f(x) = x³ - 3x² + 12x - 6.
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Complete question is:
Find the formula for a cubic polynomial, ax³+bx²+cx+d, with a critical point at x=2, an inflection point at (1,4), and a leading coefficient of 1.
The box plots below show the distribution of salaries, in thousands, among employees of two small companies.
A box plot titled Salaries in Dollars at Company 1. The number line goes from 25 to 80. The whiskers range from 25 to 80, and the box ranges from 26 to 34. A line divides the box at 30.
Salaries in Dollars at Company 1
A box plot titled Salaries in Dollars at Company 2. The number line goes from 35 to 90. The whiskers range from 36 to 90, and the box ranges from 38 to 44. A line divides the box at 40.
Salaries in Dollars at Company 2
Which measures of center and variability would be best to use when making comparisons of the two data sets?
Answer:
Mean and IQR
Step-by-step explanation:
The measure of centre gives the central or the measure which gives the best mid term of a distribution. Based in the details of the box plot, the median is the value which divides the box in the box plot.
For company A:
Range = 25 to 80 with a median value at 30 ; this means the median does not give a good centre measure of the distribution ad it is very close to the minimum value. This goes for the Company B plot too; with values ranging from (35 to 90) and the median designated at 40.
Hence, the mean will be the best measure of centre rather Than the median in this case.
For the variability, the interquartile range would best suit the distribution. With the lower quartile and upper quartile both having reasonable width to the minimum and maximum value of the distribution.
Answer:
B
Step-by-step explanation:
Can some help me pls
Answer:
1. 0=0
2. x= -3
3. 14=0
Step-by-step explanation:
I tried I'm sorry if it's wrong
I think it’s A but I think that I am incorrect. I’m in desperate need of the answer.
Answer:
It would be D
Step-by-step explanation:
Select all of the prime numbers from the list that can divide the number 10 exactly.
A2
B 3
C 5
D 7
E 11
F 13
G 17
H 19
I 23
Answer:
2 and 5
Step-by-step explanation:
2×5 = 10 or visa versa
10 ÷5=2
10 ÷2 =5
Find the exact value of the integral fx=-2² dx. -2x² 500 dx
The given integral is: $$\int (-2x^2 + 500)dx$$
To solve the above integral, we integrate both terms separately. Using the integral formulas, $$\int x^n dx= \frac{x^{n+1}}{n+1}+ C$$$$\int kf(x)dx= k\int f(x)dx$$
where C is a constant of integration and k is a constant.
The integral $\int -2x^2 dx$ is:\begin{align*} \int -2x^2 dx &= -2\int x^2 dx\\&= -2\times \frac{x^{2+1}} {2+1} + C\\&= -\frac {2}{3}x^3+ C\end{align*}
The integral $\int 500 dx$ is:\begin{align*}\int 500 dx &= 500\int dx\\&= 500\times x + C\\&= 500x + C\end{align*}
Thus, the integral $\int (-2x^2 + 500) dx$ is:\begin{align*}\int (-2x^2 + 500) dx &= \int -2x^2 dx + \int 500 dx\\&= (-\frac {2}{3}x^3+ C_1) + (500x + C_2)\\&= -\frac {2}{3}x^3+ 500x + C\end{align*}
where C is a constant of integration and $C=C_1+C_2$.
Therefore, the exact value of the integral is $-\frac {2}{3}x^3+ 500x + C$.
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1.There are 270 students at an elementary school. There are 5 boys for every 4 girls. How many boys attend the school?
2. 4 small candies cost $0.96. How much do 6 candies cost?
3. 3 bags of chips cost $5.55. How much does 2 bags of chips cost?
4. 5 movie tickets cost $55. At this rate, what is the cost per ticket?
Answer:
Step-by-step explanation:
1. Not sure...
2. $ 1.44
3. $ 3.70
4. $11 per ticket
Which of these is a nonlinear function. 20 points...
A. x=0
B. x=y/4
C. y=√x
D. y=√5
Plzz help everything is in the screen shot
Answer:
#1
Yesy = x + 1#2
Yesy = -2x#3
No#4
NoA rectangle prism has a length of 10m, a height of 9m, and a width of 15m. What is its volume, in cubic meters
Answer:
1350 m³
Step-by-step explanation:
To find the volume of a rectangular prism, we have to multiply its length, width, and height together.
The dimensions of this prism are 9, 10, and 15.
9 · 10 · 15 = 1350
The volume is 1350 meters³.
I hope this helps ^^
When performing polynomial regression, we should use the
smallest degree that provides a good fit. Why?
When performing polynomial regression, it is advisable to use the smallest degree that provides a good fit.
Polynomial regression involves fitting a polynomial function to a set of data points. The degree of the polynomial represents the highest power of the independent variable in the equation.
By using the smallest degree that provides a good fit, we aim to strike a balance between model complexity and overfitting.
Using a smaller degree helps prevent overfitting, which occurs when a model becomes too complex and captures noise or random fluctuations in the data. Overfitting leads to poor generalization, meaning the model may perform well on the training data but poorly on new, unseen data.
By using the smallest degree that provides a good fit, we minimize the risk of overfitting and ensure that the model captures the underlying trend in the data without incorporating unnecessary complexity.
This approach helps create a more robust and reliable model for making predictions on new data.
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Define a sequence a,, so that ao = 2, a₁ = 3, and an = 6an-1-8a-2.
The sequence {aₙ} defined by a₀ = 2, a₁ = 3, and aₙ = 6aₙ₋₁ - 8aₙ₋₂ produces the terms:
2, 3, 2, -12, -88, -432, ...
To define the sequence {aₙ}, given a₀ = 2, a₁ = 3, and the recursive formula aₙ = 6aₙ₋₁ - 8aₙ₋₂, we can calculate the subsequent terms of the sequence.
Using the given initial conditions, we have:
a₀ = 2
a₁ = 3
To find a₂, we substitute n = 2 into the recursive formula:
a₂ = 6a₁ - 8a₀
= 6(3) - 8(2)
= 18 - 16
= 2
To find a₃, we substitute n = 3 into the recursive formula:
a₃ = 6a₂ - 8a₁
= 6(2) - 8(3)
= 12 - 24
= -12
Continuing this process, we can find the subsequent terms of the sequence:
a₄ = 6a₃ - 8a₂
= 6(-12) - 8(2)
= -72 - 16
= -88
a₅ = 6a₄ - 8a₃
= 6(-88) - 8(-12)
= -528 + 96
= -432
and so on.
Therefore, the sequence {aₙ} defined by a₀ = 2, a₁ = 3, and aₙ = 6aₙ₋₁ - 8aₙ₋₂ produces the terms:
2, 3, 2, -12, -88, -432, ...
Please note that if you need the general formula for the nth term of the sequence, it may require a different approach as the given recursive formula is not a linear recurrence relation with constant coefficients.
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What was her score on this exam, rounded to the nearest integer
Answer:
Where is the number I need to round to?
(Please don't give me a bad rating i'm trying to help :) )
daniel bought 6 shirts for $28.93 if he paid the same price for each shirt how much would he spend if he bought 15 shirts?
Answer:
i dont know do it yourself chump
Step-by-step explanation:
I NEED HELP WITH THIS PLS ASAP!!!
Suppose that in a large batch of chocolate chip cookies, the number of chips in a given cookie is in a normal distribution with mean 7.5 and standard diviation 1.2.
(a) What is the probability that a cookie has less than 9 chips?
(b) What is the probability that a random sample of 4 cookies has an average of less than 9 chips per cookie?
If a normal distribution with a mean of 7.5 and a standard deviation of 1.2. (a) The probability that a cookie has less than 9 chips is 0.8944. (b) The probability that a random sample of 4 cookies has an average of fewer than 9 chips per cookie is 0.9938.
As μ = 7.5, σ = 1.2. The number of chips in a given cookie is in a normal distribution. We need to estimate the following probabilities:
(a) For this, we need to identify the probability of a Z-score when X=9. We can calculate it using the formula,
Z = (X-μ)/σ.
Therefore,
Z = (9-7.5)/1.2 = 1.25.
Now we can use the standard normal distribution table or calculator to identify the probability associated with the Z-score of 1.25. Using the calculator, P(Z < 1.25) = 0.8944.
(b) For this, we need to identify the probability of the Z-score when X = 9, n=4. We can calculate it using the formula,
Z = (X-μ)/(σ/√n).
Therefore,
Z = (9-7.5)/(1.2/√4) = 2.5.
Now we can use the standard normal distribution table or calculator to identify the probability associated with the Z-score of 2.5. Using the calculator, P(Z < 2.5) = 0.9938.
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Please help it’s due today, if you explain you get brainliest
5. At the end of the performance, the band marches off the field to the right, moving the entire sine curve. Asa grabs his camera to takes a picture of the entire football field. At the instant he takes the picture, the first person forming the curve now stands at the 5 yard line. What is the equation of the sine curve representing the position of the band members in Asa’s picture?
While playing, they move, but still maintain the sinusoidal function, ... 5.At the end of the performance, the band marches off the field to the ... Asa grabs his camera to takes a picture of the entire football field. At the instant he takes the picture, the first person forming the curve now stands at the 5 yard line.
a las 6 am un termometro marca 6°c bajo cero, a las 9 am la temperatura aumento a 4°c, a las 12 pm la temperatura subio 10°c, a las 15 pm la temperatura ascedio 13°c, a las 18 pm la temperatura descendio 13°c, a las 21 pm la temperatura bajo 11°c representa la temperatura en una recta numerica y determina la temperatura a las 21 pm
uh yeah I’m this bad at math I need help on number 4
Answer:
36
Step-by-step explanation:
To find the area of a triangle, multipy the base and height of a triangle, then divide it in half
8x9=72/2=36
(c) Let X and Y be independent random variables such that XY is degenerate at c≠0 i.e., P(XY = c) = 1. Show that X and Y are also degenerate.
(a) Suppose two buses, A and B, operate on a route. A person arrives at a certain bus stop on this route at time 0. Let X and Y be the arrival times of buses A
(c) Let X and Y be independent random variables such that XY is degenerate at c≠0 i.e., P(XY = c) = 1. Show that X and Y are also degenerate.
5. (a) Suppose two buses, A and B, operate on a route. A person arrives at a certain bus stop on this route at time 0. Let X and Y be the arrival times of buses A
(a) Let X and Y be the arrival times of buses A and B respectively, it is given that buses A and B are independent and hence X and Y are independent random variables.
Therefore, X and Y are also degenerate at c.
Since a person arrives at the bus stop at time 0, the arrival times of buses A and B cannot be negative
i.e., X, Y ≥ 0.
Also, both buses cannot arrive at time 0
i.e., P(X = 0, Y = 0) = 0.
Now, suppose that X and Y are not degenerate. T
hen, their joint distribution function is given by:
F(X, Y) = P(X ≤ x, Y ≤ y) > 0, for some x, y ≥ 0.
Using the independence of X and Y, we get:
F(X, Y) = P(X ≤ x)P(Y ≤ y) > 0,
for some x, y ≥ 0.
Since P(XY = 0) = 0,
we have XY ≠ 0 and
hence P(XY = c) > 0,
for some c ≠ 0.
Now, for a fixed ε > 0,
let Bε = {(x, y) : |xy - c| < ε}.
Then, P((X, Y) ∈ Bε) > 0.
Similarly, let B'ε = {(x, y) : x < ε} and
B''ε = {(x, y) : y < ε}.
Then, P((X, Y) ∈ B'ε) > 0
and P((X, Y) ∈ B''ε) > 0.
Now, we have:
Bε ⊆ B'ε ∪ B''ε and (X, Y) ∈ B'ε
if and only if X < ε and (X, Y) ∈ B''ε
if and only if Y < ε.So,
using the union bound and taking ε small enough, we get:
P(X < ε) + P(Y < ε) > P((X, Y) ∈ Bε) > 0.
This contradicts the assumption that P(X = 0, Y = 0) = 0.
Therefore, X and Y must be degenerate.
Now, we will show that if XY is degenerate at c ≠ 0
i.e., P(XY = c) = 1,
then X and Y are also degenerate at the same point.
To see this, note that for any Borel sets A, B ⊆ R, we have:
P(X ∈ A, Y ∈ B) = P(XY ∈ A × B) = P(XY = c)
= 1, if (c ∈ A × B) or (c is an isolated point of A × B).
Therefore, X and Y are also degenerate at c.
This completes the proof of the required statement.
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What kind of equation is shown below?
x2 + 6x - 13 = 0
Answer:
quadratic equation
Step-by-step explanation:
Answer:
the equation shown here is a quadratic equation
On Tuesday afternoon at camp, Eve did archery and sailing before dinner. Archery started at 12:30p.m. Eve spent 1 hours and 25 minutes at archery and 45 minutes sailing. What time did sailing end?
Answer:
2:40
Step-by-step explanation:
Add 85 minutes to 45 minutes and then add that to 12:30
What is the equation of the above graph in vertex form?
Answer:
https://brainly.com/question/3677306
Step-by-step explanation:
Solve 12/y = 4/3
Solution is____
Answer:
y=9
Step-by-step explanation:
12/y=4/3
3×12/y=3×4/3
36/y=4
y×36/y= 4×y
36=4y
36/4=4y/4
9=y
Need actual help (please hurry)
A figure is made up of with seven X rodes and five Y rodes . If X= 3 and Y= 5 calculate the perimeter with the formula.
OPTIONS:
8
46
50
40
Solve the system of equations using the elimination method
2y - 3y = -9
-x + 3y = 6
(-3,3)
(1,3)
(3,3)
(-3,1)
right answer gets brainliest
9514 1404 393
Answer:
(d) (-3, 1)
Step-by-step explanation:
We assume a typo in the problem statement, and that the equations are supposed to be ...
[tex]2x -3y = -9\\-x +3y = 6[/tex]
Adding the two equations gives ...
x = -3
Substituting for x in the second equation gives ...
3 +3y = 6
1 + y = 2 . . . . divide by 3
y = 1 . . . . . . . subtract 1
The solution is (x, y) = (-3, 1).
what is the circumference of a circle with a radious of 8
Answer:
The circumference is 16π or 50.2654 depending on whether they ask you for an exact value or in terms of pi.
Step-by-step explanation:
2r=d
2(8)=d
16=d
C=πd
C=π16
So, the circumference is 16π or 50.2654 depending on whether they ask you for an exact value or in terms of pi.
Answer:
50.2654
Step-by-step explanation:
file:///C:/Users/TOSHIBA/Downloads/SISTEMA%20DE%20MEDICION%20ANGULOS%20(1).pdf
necesito solo las respuestas de la ultima pregunta, por favor
Answer:
I was unable to see this link. Sorry.
Step-by-step explanation:
How do I solve this arithmetic sequence?
Answer:
The 16ᵗʰ term of this sequence is 82
Step-by-step explanation:
Here,
First Term = a₁ = 9
Common Difference = (d) = 2
Now, For 16ᵗʰ term, n = 16
aₙ = a + (n - 1)d
a₁₆ = 7 + (16 - 1) × 2
a₁₆ = 7 + 15 × 5
a₁₆ = 7 + 75
a₁₆ = 82
Thus, The 16ᵗʰ term of this sequence is 82
-TheUnknownScientist