Find the absolute extrema of f(x) =3x^2 -2x+ 4 over the interval [0,5].
Find the absolute extrema of f(x) =3x^2 -2x+ 4 over the interval [0,5].
Answers
The absolute minimum value of the function f(x) = 3x^2 - 2x + 4 over the interval [0, 5] is 4, and the absolute maximum value is 69.
To find the absolute extrema of the function f(x) = 3x^2 - 2x + 4 over the interval [0, 5], we need to evaluate the function at the critical points and endpoints of the interval.
Find the critical points
To find the critical points, we take the derivative of f(x) and set it equal to zero:
f'(x) = 6x - 2
Setting f'(x) = 0 and solving for x:
6x - 2 = 0
6x = 2
x = 2/6
x = 1/3
Evaluate the function at the critical points and endpoints
Evaluate f(x) at x = 0, x = 1/3, and x = 5:
f(0) = 3(0)^2 - 2(0) + 4 = 4
f(1/3) = 3(1/3)^2 - 2(1/3) + 4 = 4
f(5) = 3(5)^2 - 2(5) + 4 = 69
Compare the values
To find the absolute extrema, we compare the values of the function at the critical points and endpoints:
The minimum value is 4 at x = 0 and x = 1/3.
The maximum value is 69 at x = 5.
Therefore, the absolute minimum value of f(x) = 3x^2 - 2x + 4 over the interval [0, 5] is 4, and the absolute maximum value is 69.
To learn more about critical points visit : brainly.com/question/7805334
#SPJ11
Related Questions
Hits on a personal website occur quite infrequently. They occur randomly and independently with an average of five per week. Required:
a. Find the probability that the site gets 10 or more hits in a week. Please give the answer to four decimal places. b. Determine the probability that the site gets 20 or more hits in 2 weeks. Please give the answer to four decimal places.
Answers
A. The probability of getting 10 or more hits in a week is approximately 0.0131 using the Poisson distribution. B.The probability of getting 20 or more hits in 2 weeks is approximately 0.0175 using the Poisson distribution.
a. The probability that the site gets 10 or more hits in a week is approximately 0.0131.
To calculate this probability, we can use the Poisson distribution, which is commonly used to model the number of events that occur in a fixed interval of time when the events are rare and independent. In this case, the average number of hits per week is given as 5.
Let X be the random variable representing the number of hits in a week. The probability of getting 10 or more hits can be calculated as the complement of the probability of getting less than 10 hits.
Using the Poisson distribution formula, the probability mass function is given by:
P(X = k) = (e^(-λ) * λ^k) / k!
Where λ is the average number of hits per week, and k is the desired number of hits.
To calculate the probability of getting less than 10 hits, we sum the probabilities for k = 0 to 9:
P(X < 10) = P(X = 0) + P(X = 1) + ... + P(X = 9)
Using the formula, we substitute λ = 5 and calculate the individual probabilities. Finally, we subtract this sum from 1 to find the probability of getting 10 or more hits:
P(X ≥ 10) = 1 - P(X < 10)
Evaluating this expression, we find that the probability is approximately 0.0131.
b. The probability that the site gets 20 or more hits in 2 weeks is approximately 0.0175.
To calculate this probability, we need to consider the number of hits over a two-week period. The average number of hits per week is still 5, so the average number of hits over two weeks is 10.
Let Y be the random variable representing the number of hits in two weeks. We can again use the Poisson distribution, but this time with λ = 10.
Similar to part a, we calculate the probability of getting less than 20 hits over two weeks:
P(Y < 20) = P(Y = 0) + P(Y = 1) + ... + P(Y = 19)
Using the Poisson distribution formula with λ = 10, we evaluate this sum. Finally, we subtract this sum from 1 to find the probability of getting 20 or more hits:
P(Y ≥ 20) = 1 - P(Y < 20)
Evaluating this expression, we find that the probability is approximately 0.0175.
To know more about the Poisson distribution, refer here:
https://brainly.com/question/30388228#
#SPJ11
Name the kind or kinds of symmetry the following figure has: point, line, plane, or none. (o)
Answers
Answer is Line
What will be the output of the following code snippet and why? public static void main(string[] args) { int num = 2; int dividend = 5; dividend /= num; system.out.println(dividend); }
Answers
2 will be the output of the following code snippet.
What is a snippet in coding?
A code Snippet is a programming term that refers to a small portion of re-usable source code, machine code, or text. Snippets help programmers reduce the time it takes to type in repetitive information while coding. Code Snippets are a feature on most text editors, code editors, and IDEs.What does a code snippet look like?
Code snippets are templates that make it easier to enter repeating code patterns, such as loops or conditional-statements. In Visual Studio Code, snippets appear in IntelliSense (Ctrl+Space) mixed with other suggestions, as well as in a dedicated snippet picker (Insert Snippet in the Command Palette).The output will be 2 because when two integers are divided in Java, the decimal portion is always truncated.
Learn more about code snippet
brainly.com/question/15003151
#SPJ4
The complete question is -
The following snippet of code would produce what outcome? public static void main(String 2 [] args) { int day = 5; switch (day) { case 1: System.out.println("Monday "); case 2: System.out.println("Tuesday "); case 3: System.out.println("Wednesday "); case 4: System.out.println("Thursday "); case 5: System.out.println("Friday "); case 6: System.out.println("Saturday "); case 7: System.out.println("Sunday "); break; default: System.out.println("Invalid Day "); } } Invalid Day Friday Saturday Sunday Invalid Day Friday Friday Saturday Sunday What will be the output of the following code: int x = 20; int y = 40; if (x > 10) { if (y > 50) { System.out.println("Hello, Friend."); } else { System.out.println("Goodbye, Friend."); } } else { if (y > 50) { System.out.println("Hello, Enemy:"); } else { System.out.println("Goodbye, Enemy."); } } Hello, Friend. Hello, Enemy. Goodbye, Friend. Goodbye, Enemy.
Sarah needs 3 feet of fabric for a project she is working on, but the store only sells the fabric in meters. One meter of fabric costs $1.20. How much will the fabric cost? [1 ft = 0.305 m]
Answers
Answer:
The 3 feet fabric will cost $ 1.09728 almost $ 1.10
Step-by-step explanation:
First we will find out how many meters 3 feet will be.
1 feet = 0.3048 meters
She needs 3 feet of fabric
3 *1 feet = 3* 0.3048 ( multiplying both sides by 3)
3 feet = 0.9144 meters
Using the unitary method we will find the cost of 3 feet of fabric
1 meter costs $ 1.20
0.9144 *1 meter costs $ 1.20 * 0.9144 ( multiplying both sides by 0.9144)
0.9144 meter = $ 1.09728
The 3 feet fabric will cost $ 1.09728 almost $ 1.10
Answer: 1.10
Step-by-step explanation: I did the test on FLVS, and got the answer right
Point D is located at (-1, 6) on the coordinate plane. Point D is reflected over the
y-axis to create point D'. Point D'is then reflected over the r-axis to create point
D". What ordered pair describes the location of D"?
Answers
Answer:
(1, -6)
Step-by-step explanation:
After reflecting over y axis: (1, 6)
After reflecting (1, 6) over x axis: (1, -6)
I think you made a typo in your question. I think you meant "x-axis" instead of "r-axis"
1/2x-3=7
(Show all work)
Answers
Answer:
X= 5
Step-by-step explanation:
1/2x -3 = 7
first you + 3 to both sides to get the x by it's self on one side of the (=)
Why +3 and not -3? because if you add 3 to the -3 on that side it goes to 0 witch means there is nothing there!
1/2x= 10
now you (/) by 2
10/2 =5
x=5
Answer:
x=20
Step-by-step explanation:
1/2x-3=7
add 3 to both sides
1/2x=10
divide both sides by 1/2
10/.5= 20
x=20
yu has 12 coins, consisting of 5 pennies, 4 nickels and 3 dimes. he tosses them all in the air. what is the probability that the total value of the coins that land heads-up is exactly 30 cents? express your answer as a common fraction.
Answers
If Yu has 12 coins , that consists of 5 pennies , 4 nickels and 3 dimes , then the probability that total value of coins that lands up exactly 30 cents is 5/120 .
Yu have 12 coins, consisting of 5 pennies, 4 nickels and 3 dimes, and he tosses them all in the air,
we have to find the probability that total value of the coins that land heads up is exactly 30 cents ,
number of pennies ⇒ 0.01 = 5 ;
number of nickels ⇒ 0.05 = 4 ;
number of dimes ⇒ 0.10 = 3 ;
there will be 5 "30cent" combinations ;
the combinations are :
⇒ 0.10 × 3
⇒ 0.10 × 2 + 0.05 × 2
⇒ 0.10 × 2 + 0.05 × 1 + 0.01 × 5
⇒ 0.10 × 1 + 0.05 × 4
⇒ 0.10 × 1 + 0.05 × 3 + 0.01 × 5
so , the probability that total value lands up exactly 30 cents is = 5/(5×4×3×2)
= 5/120 ;
Therefore, the probability that the total value of the coins that land heads-up is exactly 30 cents is 5/120 .
Learn more about Probability here
https://brainly.com/question/10650737
#SPJ4
points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints.
Answers
Points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints.
True
help for homework
with the steps please
and make sure it's in surd form
for brainliest
Answers
Answer:
\( \frac{ 8\sqrt{18} }{18} \)
Express the product of (x + 3)
and
(3+5) as a trinomial in simplest form.
Answers
Answer:
The answer would be 8x + 24. And it's not a trinomial form. Why? Maybe the given is not just (3+5), it's (3x+5). So that we can get trinomial product.
Sol.
(x + 3) (3x + 5)
Each parenthesis has a binomial (two numbers)
A. Note that whenever you have two parenthesis next to each other like this, it implies factoring. So let's factor.
3x^2 + 5x + 9x + 15
We get a quartnomial (containing 4 numbers), but we're looking for a trinomial. Can we reduce this?
B. Yeah, so we reduce
3x^2 + 14x + 15
There you go, this is a trinomial.
Which values represent solutions to the equation? Tangent (StartFraction 3 pi Over 4 EndFraction minus 2 x) = negative where x Is an element of [0, Pi]
Answers
Answer: we need a picture to solve this, please repost with a picture of your assignment
Step-by-step explanation:
Answer:
D.) 0, pi/2, pi 3pi/2
Step-by-step explanation:
if the marks of students in a class are [110,70,30,80,90,64] then what is the median of these marks?
Answers
Answer:
The Median is 75
Step-by-step explanation:
Medianmedian is the middle number in a set of given numbers
arranging in order will be
30,64,70,80,90,110
the middle numbers are 70 and 80
Median=80+70/2
=150/2
Median=75
While walking her dog, Sylvia noticed that 32 houses had a pot of red flowers on their
front step and 24 had a pot of yellow flowers. Write the ratio of red to yellow pots of
flowers three different ways. There is part a part b and part c pls helppp
Answers
The ratio of red to yellow pots of flowers in three different ways are
16 : 12, 8 : 6, and 4 : 3
As per the given data Sylvia while walking with her dog, she noticed that the 32 houses had a pot of red flowers on their front step.
Also, 24 houses had a pot of red flowers on their front step.
Here we have to determine that the ratio of red pots of flowers to yellow pots of flowers in three different ways.
The three different ways will be part a part b and part c.
The ratio of red to yellow pots of flowers.
32 : 24
Simplify the above ratio.
16 : 12
Also, we have to simplify further.
We get:
8 : 6
Then:
4 : 3
Therefore the ratios are 16 : 12, 8 : 6, and 4 : 3
For more questions on ratios
https://brainly.com/question/21106746
#SPJ4
Tori received $28.50 for 2 hours of work. How
much did she earn if she worked 15 hours?
Answers
Answer:
Hey! I hope this helps. I used ratio, I divided $28.50 by 2 to find out how much she worked for in an hour then I multiplied by 15.
True or False, in an analysis of variance, the larger the differences between the sample means are, the larger the f-ratio will be.
Answers
The statement is True.
In an analysis of variance (ANOVA), the larger the differences between the sample means are, the larger the F-ratio will be. The F-ratio compares the between-group variability to the within-group variability, and a larger F-ratio indicates more significant differences between the groups.
To know more about the analysis of variance visit:
https://brainly.in/question/8643242
#SPJ11
americium-241 is widely used in smoke detectors. calculate the amount of americium-241 consumed in a smoke detector (initially containing 4.50 µg of am), in micrograms, that has been used for one year if the half-life is 433 years.
Answers
The amount of americium-241 consumed in a smoke detector, initially containing 4.50 µg, after one year can be calculated to be approximately 0.0104 µg.
The decay of americium-241 over time can be modeled using the radioactive decay formula:
A(t) = A₀ * (1/2)^(t / T₁/₂)
where:
A(t) is the amount of americium-241 remaining after time t,
A₀ is the initial amount of americium-241,
t is the time elapsed,
T₁/₂ is the half-life of americium-241.
In this case, the initial amount of americium-241 is 4.50 µg, and the half-life is 433 years. We want to calculate the amount remaining after one year.
Substituting the given values into the decay formula:
A(1 year) = 4.50 µg * (1/2)^(1 / 433)
Calculating this expression:
A(1 year) ≈ 4.50 µg * 0.998005
A(1 year) ≈ 4.492 µg
Therefore, the amount of americium-241 consumed in the smoke detector after one year is approximately 4.50 µg - 4.492 µg ≈ 0.0104 µg.
After one year, approximately 0.0104 µg of americium-241 would be consumed in a smoke detector initially containing 4.50 µg of americium-241, considering its half-life of 433 years.
To know more about amount, visit;
https://brainly.com/question/26574670
#SPJ11
What is the final cost of a pair of jeans that cost $65 if the sales tax is 6%
Answers
Answer: 68.9
Step-by-step explanation:
65 x 0.06 = 3.9
3.9 + 65 = 68.9
Please Help!!!!!!!
Will mark brainliest
Answers
Answer:
○ \(\displaystyle x^2 + 4x + 13\)
Step-by-step explanation:
Sinse this expression is unfactourable with rational quantities, use the Quadratic Formula:
\(\displaystyle -B ± \frac{\sqrt{B^2 - 4AC}}{2A} = x\\ \\ -4 ± \frac{\sqrt{[-4]^2 - 4[1][13]}}{2[1]} = x \hookrightarrow -4 ± \frac{\sqrt{16 - 52}}{2} = x \hookrightarrow -4 ± \frac{\sqrt{-36}}{2} = x \hookrightarrow \frac{-4 ± 6i}{2} = x \\ \\ \boxed{-2 - 3i, -2 + 3i = x}\)
I am joyous to assist you at any time.
Please answer correctly !!!!!!! Will mark brainliest answer !!!!!!!!
Answers
Answer:
A is the answer i believe
Step-by-step explanation:
simplify 60 61 62 63 64 65 66 67 by using a formula covered in the lecture. do not evaluate your final answer.
Answers
By simplifying 60 61 62 63 64 65 66 67 by using the formula for arithmetic series, we get the answer to be 8 * 127 / 2.
To simplify the given expression, we can use the formula for the sum of an arithmetic series: Sn = n * (a1 + an) / 2, where Sn is the sum of the series, n is the number of terms, a1 is the first term, and an is the last term.
In this case, n = 8, a1 = 60, and an = 67. Plugging these values into the formula, we get:
S8 = 8 * (60 + 67) / 2
S8 = 8 * 127 / 2
S8 = 508
So the simplified expression is 508. However, since the question specifies to not evaluate the final answer, we can leave it in the form S8=8 * 127 / 2.
To know more about arithmetic series refer here:
https://brainly.com/question/16415816#
#SPJ11
Find the products in simplest form. 8 21 • 5 16 = 12 25 • 15 16 =.
Answers
Answer:
5/42 and 3/4
Step-by-step explanation:
8/21 x 5/16 =
in simplest form = 5/42
12/25 x 15/16
in simples form = 3/4
Answer:
1. 5/42
2. 9/20
Step-by-step explanation:
(2x – 1) (2x + 1) (4x2 + 1)(16x4 + 1) + 1
Answers
Answer:
Escribí esto, así que espero que quede claro.
Step-by-step explanation:
Maybe 256x square 8
(9x+29)+(93-5x)+(10x+2)
Answers
Answer:
14x + 124
General Formulas and Concepts:
Algebra I
Combining Like TermsStep-by-step explanation:
Step 1: Define Expression
(9x + 29) + (93 - 5x) + (10x + 2)
Step 2: Simplify
Combine like terms (x): 14x + 29 + 93 + 2Combine like terms (Z): 14x + 124Step-by-step explanation:
1, Rearrange the problem.
(9+29)+(9−5)+(10+2)
(9x+29)+(93−5x)+(10x+2)
(9+9)+(−5+93)+(10+2)
2, Solve.
14x+124
Answer:14x+124
A group of 40 students went on a field trip. Exactly 8 student wore blue shirt. what percent of the students on field trip wore blue shirt
Answers
20% wore a blue shirt
Answer:
20% student wore blue shirts
Step-by-step explanation:
Express m in terms of e and v and find the mass of an object whose energy and speed are 1800joules and 25m/s respectively
Answers
The object has a mass of 5.76 kg.
We may represent "m" in terms of "e" (energy) and "v" (speed) using the kinetic energy formula, assuming that "m" relates to the mass of the object:
The energy an object possesses as a result of its motion is known as kinetic energy. It is described as the energy that a moving object contains as a result of its motion, which is dependent on the mass and velocity of the object.
The formula for calculating an object's kinetic energy is KE = 1/2 * m * v2.
To solve for "m," we can rearrange this formula:
m = 2 x KE /
We obtain the following by substituting the given values:
m = 2 x 1800 / 25
m = 2 x 1800 J / 625
m= 5.76 (rounded to two decimal places)
To learn more about Kinetic energy :
https://brainly.com/question/28109294
#SPJ4
Idk which one it is can someone tell me :(
Answers
Answer:
A
A would be the best answer since it asking how much did it change.
1. If a researcher accepts a true null hypothesis, she has made a _______ decision.a. businessb. hypotheticalc. incorrectd. correct
Answers
Answer:
d. correct
Step-by-step explanation:
if it helped u please mark me a brainliest :))
PLS HELP ME ASAP WILL MARK THE BRAINLIEST
Answers
Answer:
Check images
Step-by-step explanation:
Gonna be completely honest, not confident in the third one but I tried my best.
if the station stocks 600 gallons at the start of the week, what is the probability that thry sell more than 250 gallons
Answers
The exact probability cannot be determined without additional information such as the average daily sales rate.
To find the probability of selling more than 250 gallons, we need to find the cumulative distribution function (CDF) of the number of gallons sold, which is the probability of selling a certain amount or less. Since the amount sold follows a Poisson distribution with an average of 200 gallons, the CDF can be calculated using the Poisson cumulative distribution function formula:
P(X <= x) = e^(-μ) * (μ^x) / x!
Where μ is the average number of gallons sold and x is the amount sold. To find the probability of selling more than 250 gallons, we subtract the CDF for 250 gallons or less from 1. This gives us the probability of selling more than 250 gallons.
Learn more about average here:
https://brainly.com/question/16956746
#SPJ4
help me 20 POINTS
math math math by the way do questions 10 and 13 on page 176
Answers
Answer:
Step-by-step explanation:
12.
13. Yes it is propoitinal because they are even
