let's find the maximum and minimum values of . to answer this question, recall that we consider two types of candidates for max/min: some are values attained at points in the interior of , and some are values attained at points in the boundary of . show that a critical point of in
Answers
To find the maximum and minimum values of a function, we consider two types of candidates: values attained at points in the interior of the function's domain and values attained at points on the boundary. It is important to show that critical points of the function lie within the domain.
To find the maximum and minimum values of a function, we examine critical points, which are points where the derivative of the function is zero or undefined. These critical points can occur both in the interior of the function's domain and on the boundary.
In the interior of the domain, we use the first derivative test or the second derivative test to identify local maxima and minima. The critical points in the interior can be points where the derivative changes from positive to negative (maxima) or from negative to positive (minima).
On the boundary of the domain, we evaluate the function at the boundary points to identify potential extreme values. These values can be considered as candidates for the maximum and minimum values of the function.
To ensure that the critical points lie within the domain, we need to verify that these points satisfy the constraints or conditions defined by the function's domain. This step is crucial in finding the maximum and minimum values accurately.
In conclusion, to find the maximum and minimum values of a function, we consider both the critical points in the interior and the values at the boundary points. It is essential to ensure that the critical points lie within the domain to determine the actual maximum and minimum values.
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Related Questions
Diego tried to solve the equation 1/3(x+15)=3 what was his mistake
Answers
Diego's mistake was that he forgot to distribute the 1/3 across the parentheses, so he should have solved the equation like this: 1/3x + 5 = 3, which can be rearranged to x = 14.
Given equation is 1/3(x+15)=3. For solving this equation we have to simplify this equation as follows:
Multiplying both sides by 3 to eliminate the fraction; we get(x + 15) = 9. Distributing the number 1/3 to both terms inside the parenthesis we get (x/3) + 5
Combining like terms we get(x/3) = -2. Multiplying both sides by 3 we get x = -6.
the solution to the given equation is x = -6.So, Diego's mistake was that he didn't eliminate the fraction first.
An equation is a mathematical statement that asserts the equality of two expressions. Equations typically involve variables, which are symbols that represent numbers or other mathematical objects whose specific value or identity is unknown or unspecified.
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What is the slope of the line?
3(y - 1) = 2x + 2
WHOEVER ANSWERS IT WILL GET BRAINIST !!!!! PLEASE HELP DUE IN 5 MINS
Answers
Answer:2/3
Step-by-step explanation:
plug it into y = mx + b and it results to m = 2/3
*ANSWER PLS TY* Find The Volume Of The Pyramid
Answers
Answer: A. 1120 in³
Step-by-step explanation:
the formula for the volume of the pyramid: \(V=\frac{1}{3} lwh\)
l (length)=16
w (width)=14
h (height)=15
\(V=\frac{1}{3} lwh\)
\(V=\frac{1}{3} (16)(14)(15)\)
\(V=\frac{1}{3} 3360\)
\(V=1120\)
Answer:
The answer is option A.
Step-by-step explanation:
Hey there!!
Given,
Length (l)= 16 in.
breadth (b)= 14 in.
height (h)= 15 in.
we have,
\(v. of \: pramid = \frac{1}{3} \times a \: of \: base \times height\)
or, volume = {1/3 × (16×14)×15} cubic inch.
by simplifying it we get,
The volume is 1120 cubic inch.
Hope it helps..
Help Ive been stuck on this for days
Jamie took 20 pieces of colored paper and put them in a hat. Eight pieces were red, three pieces were blue, and the rest were green. She pulls a piece of paper out of the hat. What are the chances that the paper is red?
A. 0.04
B. 0.4
C. 1.6
D. 1.2
Answers
Answer:
B. 0.4
Step-by-step explanation:
Probability (picking red paper) = preferred/sample
Preferred outcome (picking red) = 8 pieces.
Sample size is total outcome (paper in hat) = 20 pieces.
P(picking red paper) = 8/20
P(red) = 0.4 or 40%
Hope this helped :)
Can 0.43721… be a fraction
Answers
Answer:
43721/100000
Step-by-step explanation:
To write 0.43721 as a fraction you have to write 0.43721 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
0.43721 = 0.43721/1 = 4.3721/10 = 43.721/100 = 437.21/1000 = 4372.1/10000 = 43721/100000
Answer:
43,721/99,999
Step-by-step explanation:
A non-terminating, repeating decimal can be written as a fraction.
How many digits repeat?
If the digits 43721 repeat, and the decimal number is
0.437214372143721..., then we can convert it into a fraction.
Let x = 0.437214372143721... Eq. 1
Then 100,000x = 43,721.4372143721... Eq. 2
Now we subtract Eq. 1 from the Eq. 2.
100,000x = 43,721.4372143721...
(-) x = 0.4372143721...
--------------------------------------------------
99,999x = 43,721
x = 43,721/99,999
Answer: 43,721/99,999
in 2012, gallup asked participants if they had exercised more than 30 minutes a day for three days out of the week. suppose that random samples of 100 respondents were selected from both vermont and hawaii. from the survey, vermont had 65.3% who said yes and hawaii had 62.2% who said yes. what is the value of the sample proportion of people from vermont who exercised for at least 30 minutes a day 3 days a week? group of answer choices unknown 0.6375 0.653 0.622
Answers
The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week is 0.653.
We have,
Vermont had 65.3% of respondents who said yes to exercising for at least 30 minutes a day, 3 days a week.
To find the sample proportion, you can convert the percentage to a decimal by dividing the percentage by 100.
Step 1:
Convert the percentage to a decimal.
65.3 / 100 = 0.653
Thus,
The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week is 0.653.
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can someone please give me the answer to #1
Answers
Answer:
x: -8, 0, 8, 16, 24
y: -8, -5, -2, 1, 4
Step-by-step explanation:
For the X values, it is going up by 8.
For the Y values, plug in the X value into the equation.
Given the line of best fit for a set of data points with the equation y=5x-2.5, what is the residual for the point (3,6)?
Answers
========================================================
Explanation:
For the x value x = 3, the observed y value is y = 6 which is from the point (3,6).
The predicted y value is found by plugging x = 3 into the line of best fit equation
y = 5x-2.5
y = 5(3)-2.5
y = 12.5
The residual is the difference between the two y values
e = residual
e = (observed y value) - (predicted y value)
e = 6 - 12.5
e = -6.5
The negative residual tells us the observed y value is smaller than the predicted y value for this given x value.
Joy recently hired a roofer to do some necessary work. On the final bill, Joy was charged a total of $1487.
$365 was listed for parts and the rest for labor. If the hourly rate for labor was $66, how many hours of labor
was needed to complete the job?
(A) First write an equation you can use to answer this question. Use as your variable.
The equation is
(B) Solve your equation in part (A) to find the number of labor hours needed to do the job.
Answer: The number of labor hours was
Answers
The equation is 365 + 66x = 1487 and the number of labor hours was 17
Write an equation you can use to answer this question.The given parameters are:
Total charges = 1487
Parts = 365
Hourly rate = 66
Let the number of hours be x.
So, we have the following equation
Parts + Hourly rate * x = Total charges
Substitute the known values in the above equation
365 + 66x = 1487
Hence, the equation is 365 + 66x = 1487
Solve your equation in part (A) to find the number of labor hours needed to do the job.In (a), we have:
365 + 66x = 1487
Subtract 365 from both sides
66x = 1122
Divide both sides by 66
x = 17
Hence, the number of labor hours was 17
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Real quick please. At a carnival it costs $6.54 for 3 tickets. Write an equation that can be used to express the relationship between the total cost (t) and the number of tickets(n) you buy.
Answers
Answer:
t=2.18n
Step-by-step explanation:
Total cost is 6.54 for 3 tickets so divide 6.54 by 3 and you get price per ticket which is 2.18. Multiply that by how many tickets you want and you get your final price.
you randomly choose one shape from the bag. find the number of ways the event can occur. find the favorable outcomes of the event
Answers
(a) The number of ways that the event can occur is 6.
(b) Probabilities are :
1) 1/2, 2) 1/6 and 3) 1/3.
(a) Given a bag of different shapes.
Total number of shapes = 6
So, if we select one shape from random,
total number of ways that the event can occur = 6
(b) Number of squares in the bag = 3
Probability of choosing a square = 3/6 = 1/2
Number of circles in the bag = 1
Probability of choosing a circle = 1/6
Number of stars in the bag = 2
Probability of choosing a star = 2/6 = 1/3
Hence the required probabilities are found.
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Make it simple thanks
Write about what you should look for when trying to decide how many solutions an equation has.
Answers
Answer:
You can look for these:
Step-by-step explanation:
The factors of the equation:
For example, if multiplication, the factors 2x2=4
if addition, the addends 2 + 2= 4
So just look for the numbers before the equal sign and any key words in the problem.
Hope this helps!
Answer:
solution:we think
first to factordoing either and or equal to 0.Step-by-step explanation:
it may have many solutions.
A decision maker has five potential independent variables with which to build a regression model to explain the variation in the dependent variable. At step 1, variable x3 enters the regression model. Which of the following indicates which of the four remaining independent variables will be next to enter the model?A) The variable with the highest coefficient of partial determinationB) The variable that has the next highest correlation with the dependent variableC) The variable that will provide the next largest value for the slope coefficientD) Can't be determined without seeing the correlation matrix.
Answers
When building a regression model provided the given information from the four remaining independent variables the variable to be entered next (second) would be variable with the highest coefficient of partial determination. (Option A)
A regression model refers to a function that illustrates the relationship between one or more independent variables and a response, target, dependent variable. The primary uses of regression analysis are forecasting, time series modeling and identifying the cause-and-effect relationship between variables. When building a regression model with five potential independent variables to explain the variation in the dependent variable, at step 1, variable x3 enters the regression model. Of the four remaining independent variables, the variable entered next into the model would be the variable with the highest coefficient of partial determination. A coefficient of partial determination refers to the measurement of marginal (extra) contribution of X variable or percentage of variation in the response variable that can be explained by the explanatory variables and can be used to measure how strongly two variables are related to one another.
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A principal of $4,570 is placed in an account that earns 4.5% interest. If the interest is compounded annually, how much money will be in the account at the end of 5 years?
a.
$4654.15
b.
$4775.65
c.
$5638.75
d.
$5695.05
Answers
Answer:
d
Step-by-step explanation:
The amount of money that will be in the account at the end of 5 years given the principal and annual compounding is $5695.05.
How much would be in the account after 5 years?When interest is compounded annually, it means that both the principal and interest already accrued increases in value once in year.
The formula for calculating future value:
FV = P (1 + r)^nm
FV = Future value P = Present value R = interest rate m = number of compoundingN = number of years$4750 x (1.045^5) = $5695.05
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7. The quality control division of Rothschild's Blueberry Farm randomly inspects 100 of the containers in the truck being
sent to Stop and Shop. Identify the population and sample given in this scenario.
Answers
The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.
Population: The containers of blueberries that are being sent to Stop and Shop.
Sample: The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.
Therefore, the 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.
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please help! find m<5 and m<8 will give brainliest
Answers
M<5=132 degrees
M<8=48 degrees
Which Riemann sum represents the illustration shown?
The highlighted answer was just a misclick, i dont know if its the answer or not
Answers
The Riemann sum that represents the illustration on the graph is the second option as i goes from 1 to 4:
\(1∑2 {(xᵢ)}^{2} \)
What is the Riemann sumThe Riemann sum is a mathematical concept used to approximate the area under a curve. It is named after the German mathematician Bernhard Riemann.
The idea behind the Riemann sum is to divide the area under the curve into a series of rectangles, where the height of each rectangle is determined by the function being integrated, and the width of each rectangle is determined by the size of the intervals used to divide the domain of the function. The area of each rectangle is then calculated and added together to get an approximation of the total area under the curve.
The Riemann sum is written in the following form:
\(∑f(xᵢ)Δxᵢ\)
where f(xᵢ) is the value of the function at the ith point in the interval, Δxᵢ is the width of the ith rectangle, and the sum is taken over all i intervals.
Thus, the Riemann sum that represents the illustration on the graph as i goes from 1 to 4 is:
\(1∑2 {(xᵢ)}^{2} \)
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Need help with this geometry
Answers
Answer:
y = 2
Step-by-step explanation:
The mid segment HJ is half of the third side GK , that is
HJ = \(\frac{1}{2}\) GK , substitute values
2y = \(\frac{1}{2}\) (y + 6) ← multiply both sides by 2 to clear the fraction
4y = y + 6 ( subtract y from both sides )
3y = 6 ( divide both sides by 3 )
y = 2
Jason is in the business of manufacturing phones. He must pay a daily fixed cost of $500 to rent the building and equipment, and also pays a cost of $150 per phone produced for materials and labor. Make a table of values and then write an equation for C,C, in terms of p,p, representing total cost, in dollars, of producing pp phones in a given day.
Answers
Total cost of phone in a day $650
What is Algebra ?
One of the many branches of mathematics is algebra. Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of mathematical symbols and the rules for using these symbols in formulas.
Total cost of rent in a day = $500
Total cost of per phone = $150
The equation which represents values in term of c:
150p + 500 = C
The total cost he had in a day :
= 150 + 500
= $650
Hence, the total cost throughout the day is $650
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How do you solve this math problem?
Answers
Answer: 34.8
Step-by-step explanation:
Using a local telephone book to select a simple random sample could introduce _____ bias.
Answers
Answer:
Undercoverage
Step-by-step explanation:
Using a local telephone book to select a simple random sample could introduce UNDERCOVERAGE bias.
I hope it helps! Have a great day!
is it a acute, obtuse, or Right
Answers
Answer:
Right triangle
Step-by-step explanation:
it has one 90 degree angle
Answer:
Right Triangle
Step-by-step explanation:
select the number that comes next in the sequence of numbers below 6 12 20 26 34 40
Answers
GIVE BRAINLIEST PLEASE!
thank you and have a good day :)
Answer:
48
Step-by-step explanation:
the sequence of numbers alternates between adding 6 and 8.
6 + 6 = 12
12 + 8 = 20
20 + 6 = 26
26 + 8 = 34
34 + 6 = 40
40 + 8 = 48!
i hope this helps :)
Answer:48
Step-by-step explanation:The sequence adds 6 first then adds 8
I can't find the solution, 1+1! It hurts my brainnnnnn help please
Answers
Answer:
two
Step-by-step explanation:
Answer:
two lol
Step-by-step explanation:
Find the sum of the first 31 terms of the following series, to the nearest integer.
5, 14,23,...
Answers
Answer:
4340.
Step-by-step explanation:
14-5 = 9 and 23-14 = 9 so this is an arithmetic series with common difference of 9.
Sum of n terms = (n/2)[2a1 + d(n - 1)]
Here n = 31, d = 9 and a1 = 5.
So, substituting, we have:
Sum of 31 terms = (31/2)[2*5 + 9(31-1)]
= 15.5 * 280
= 4340.
NEED HELP NEED HELP please if you know show me how you got the answer
Answers
Answer:
It says to Graph y = 1/2x - 4
So equation y = 1/2x - 4
this corresponds to slope intercept form which is y = mx + b
M = slope = rise / run
B = y - intercept
First, start at the origin, (0,0)
Then go down 4, you should now be on the coordinate (0,4)
Now we need to use the slope.
The slope is 1 / 2, this means rise 1, run 2 (in this case 2 to the right because it is positive)
So, start at (0 , 4) and go up 1 unit then 2 to the right, then place a dot, keep repeating until you meet the end of the paper.
Then do the opposite so that you can graph the other side.
Down 1 and 2 to the left.
Answer:
Graph Points (0.-4) and (8,0) and connect the dots into a line
Step-by-step explanation:
To graph y=1/2x-4 you will need to find the y and x-intercept. To find an intercept you have to substitute the x and y variables with 0 one at a time. I first substitute the x variable with an 0 and got the equation y=-4 so my y-intercept is (0.-4). Then I substituted the y variable with 0 and got 0=1/2x-4, I added 4 on each side to get rid of it and got 4=1/2x. I then multiplied both sides by 2 to get the x by itself and got 8=x so my x-intercept is (8,0). Whenever your graphing slope-intercept form equations just find the y and x-intercepts, graph them, connect the dots.
Hope this helps you
Please find the range of these numbers
Answers
Answer:7
Step-by-step explanation:range is highest number subtracted by lowest
Answer:
17
Step-by-step explanation:
The formula for range is max-min.
The max is 91 and the min is 74
91-74=17
Plz help I’ll give brainliest
Answers
Answer:
2) 4/5
3) 3
Step-by-step explanation:
2) 4/8-3=4/5
3)5x-4=3x+2
2x=6
x=3
Answer:
2) 4/5
3)x=3
Step-by-step explanation:
1) 4/8-3= 4/5
2) 5x-4=3x+2
bring 3x to left side and bring -4 to right side (remember signs will be reversed that is 3x becomes -3x and -4 will be 4
5x-3x=4+2
2x=6
x=6/2
x=3
put 3 in place of x
5*3-4=3*3+2
15-4=9+2
11=11
Find the remaining sides of a 30-60-90 degree triangle if the longest side is 11.
Answers
The remaining sides are 11/2 and 11√3/4.
What is the Pythagorean theorem?Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We have,
In a 30-60-90 triangle,
The length of the side opposite the 30-degree angle = 1/2 x the length of the hypotenuse.
The length of the side opposite the 60-degree angle = √3/2 x the length of the hypotenuse.
The length of the hypotenuse = 2 x the length of the side opposite the 30-degree angle.
Now,
The length of the hypotenuse = 2x.
So,
2x = 11
x = 11/2
Now,
The lengths of the other two sides are:
= √3/2 x 11/2
= 11√3/4
And,
= 11/2
Thus,
The remaining sides are 11/2 and 11√3/4.
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Which triangle would be impossible to create?
A. Right Isosceles
B. Acute Scalene
C. Obtuse Equilateral
D. Right Scalene
Or none of these
Answers
Obtuse equilateral, because an obtuse triangle needs one angle that is greater than 90 degrees, but in an equilateral triangle all the angles are 60 degrees because all the sides are equal.
If all sides are equal, then all their non-touching angles are equal.
Hope this helps!