First check for the critical points of f by checking where the first-order derivatives vanish.
[tex]\dfrac{\partial f}{\partial x}=4x-4=0\implies x=1[/tex]
[tex]\dfrac{\partial f}{\partial y}=2y-4=0\implies y=2[/tex]
Notice how the point (1, 2) lies on the line y = 2x ; at this point, we get a value of f(1, 2) = -5 (MIN).
Next, check the points where the boundary lines intersect, which occurs at the points (0, 0), (0, 2), and (1, 2). We already checked the last one. We find f(0, 0) = 1 (MAX) and f(0, 2) = -3.
Now check on the boundary lines themselves. If x = 0, then
[tex]f(0,y)=y^2-4y+1=(y-2)^2-3[/tex]
which has a maximum value of -3 when y = 2 (so we get the same critical point as before).
If y = 2, then
[tex]f(x, 2)=2x^2-4x-3=2(x-1)^2-5[/tex]
with a maximum of -5 when x = 1.
If y = 2x, then
[tex]f(x,2x)=6x^2-12x+1=6(x-1)^2-5[/tex]
with the same maximum of -5 when x = 1.
This question is based on the absolute maximum and absolute minimum.
We get this by differentiating the terms.
Given:
f(x,y) = [tex]2x^{2} - 4x + y^2 - 4y +1[/tex], bounded by the lines x=0,y=2,y=2x in the first quadrant,bounded by the lines x=0,y=2,y=2x in the first quadrant.
We need to determined the absolute maximum and absolute minimum of the function.
Now, partial differentiating wrt x and y.
[tex]\dfrac{\partial f}{ \partial x} = 4x -4 = 0 \Rightarrow x= 1 \\\dfrac{\partial f}{ \partial y} = 2y - 4 = 0 \Rightarrow y = 2[/tex]
Now, point (1, 2) lies on the line y = 2x ; at this point, we get a value of
f(1, 2) = -5 (MIN).
Next, check the points where the boundary lines intersect, which occurs at the points (0, 0), (0, 2), and (1, 2).
Now, find f(0, 0) = 1 (MAX) and f(0, 2) = -3.
Now check on the boundary lines themselves.
If x = 0, then we get,
[tex]f(0,y) = y^2 - 4y +1 = ( y-2)^2 -3\\[/tex]
which has a maximum value of -3 when y = 2 (so we get the same critical point as before).
If y = 2, then we get,
f(x,2) = [tex]2x^2-4x -3 = 2(x-1)^2 -5[/tex] with a maximum of -5 when x = 1.
If y = 2x, then we get,
f(x,2x) = [tex]6x^2 -12x +1 = 6(x-1)^2 -5[/tex] with the same maximum of -5 when x = 1.
For more details, prefer this link:
https://brainly.com/question/13774780
What is the slope of the lines 2,8 -6,-8
Answer:
2
Step-by-step explanation:
Slope is: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We are given the points (2,8) and (-6, -8) .
[tex]m=\frac{-8-8}{-6-2} =\frac{-16}{-8}=2[/tex]
The slope is 2.
Joshua has $4,200 to invest for college. If Joshua invests $4,200 for 3 years and earns $630, what is the simple interest rate? Joshua’s goal is to have $5,000 after 4 years. Is this possible if he invests with a rate of
return of 6%? Explain.
Answer:
The simple interest rate is 5%.
This is possible with a rate of 6%, since in this case, his amount earned will be $5,208.
Step-by-step explanation:
This is a simple interest problem.
The simple interest formula is given by:
[tex]E = P*I*t[/tex]
In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
After t years, the total amount of money is:
[tex]T = E + P[/tex]
Joshua has $4,200 to invest for college. If Joshua invests $4,200 for 3 years and earns $630, what is the simple interest rate?
We have that [tex]P = 4200, E = 630, t = 3[/tex]. We have to find I.
[tex]E = P*I*t[/tex]
[tex]630 = 4200*I*3[/tex]
[tex]I = \frac{630}{4200*3}[/tex]
[tex]I = 0.05[/tex]
The simple interest rate is 5%.
Joshua’s goal is to have $5,000 after 4 years. Is this possible if he invests with a rate of return of 6%?
We have to find T when [tex]P = 4200, t = 4, I = 0.06[/tex]
So
[tex]E = P*I*t[/tex]
[tex]E = 4200*0.06*4[/tex]
[tex]E = 1008[/tex]
[tex]T = E + P = 4200 + 1008 = 5208[/tex]
This is possible with a rate of 6%, since in this case, his amount earned will be $5,208.
The graph of g(x) = ax^2 opens downward and is narrower than the graph of f(x) = x^2. Which of the following could be the value of a?
The value of a should be less than -1.
Equation of parabola,The equation of a parabola is given by the following function,
[tex]y=f(x)=\pm a(x-h)^2+k[/tex]
where,
(h, k) denotes the coordinates of its vertex,
a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.
Given to us,[tex]f(x) = x^2[/tex]
[tex]g(x)=ax^2[/tex]
SolutionFor the parabola,g(x) to be narrower than the parabola f(x) the value of a should be less than 1. also for the parabola to open downward the value of a is needed to be negative.
Hence, the value of a should be less than -1.
Learn more about Equation of parabola:
https://brainly.com/question/4443998
Jake made a rectangular garden area as shown in the figure. He wants to add 3 inches of topsoil to the entire area.
36 in
15 in
How much topsoil does Jake need to get at the nursery?
540 in.
1,080 in.
1,386 in.
1,620 in.
Answer:
1,620in
Step-by-step explanation:
LxWxH
36 x 15 x 3 = 1,620 in
Answer:
1620
Step-by-step explanation:
What is the answer to this question–1 × –5?
Answer:
5
Step-by-step explanation:
a minus times by another minus makes a positive, so it is basically 1 x 5
Answer:
5
Step-by-step explanation:
Since the you are multiplying 2 minuses together they will cancel each other out to form a positive number. However if you have an example like this
-6 × 7
Then the answer will be -42 because there is only one negative
what is the volume of aright square prism whose length of side of the base is 6cm and height 10cm?
Answer: 360 cubic centimeters.
Step-by-step explanation:
Since it has a base shaped like a square and we know that it has a side length of 6 cm then we could square it an multiply it by the height.
6^2 = 36
36 * 10 = 360
A cylindrical metal pipe has a diameter of 8.4 millimeters and a height of 10 millimeters. A hole cut out of the center has a diameter of 6 millimeters.
A smaller cylinder is cut out of a larger cylinder. The smaller cylinder has a diameter of 6 millimeters. The larger cylinder has a diameter of 8.4 millimeters. Both cylinders have a height of 10 millimeters.
What is the volume of metal in the pipe? Use 3.14 for and round the answer to the nearest tenth of a cubic millimeter.
Answer:
[tex]271.3 mm^3\\[/tex]
Step-by-step explanation:
We have to find the volume of the hole and subtract it from the volume of the cylinder.
The volume of a cylinder is given as:
[tex]V = \pi r^2h[/tex]
where r = radius
h = height
A cylindrical metal pipe has a diameter of 8.4 mm and a height of 10 mm.
Its radius is 4.2 mm. Therefore, its volume is:
[tex]V = 3.14 * 4.2^2 * 10 = 553.9 mm^3[/tex]
A hole cut out of the center has a diameter of 6 mm. Its height is also 10 mm.
Its radius is 3 mm. Therefore, its volume is:
[tex]V = 3.14 * 3^2 * 10 = 282.6 mm^3[/tex]
Therefore, the volume of metal in the pipe is:
[tex]553.9 - 282.6 = 271.3 mm^3[/tex]
Answer:
B
Step-by-step explanation:
Find the slope of the line: 3x-2y=6
Answer:
slope = 3/2
Step-by-step explanation:
3x-2y=6
Get this equation in the form y = mx+b where m is the slope and b is the y intercept
Subtract 3x from each side
3x-3x-2y=-3x+6
-2y = -3x+6
Divide each side by -2
-2y/-2 = -3x/-2 +6/-2
y = 3/2x -3
The slope is 3/2 and the y intercept is -3
Answer:
3/2
Step-by-step explanation:
I got this answer by putting it in the form y=mx+b
Step 1: Subtract 3x from each side
-2y = -3x+6
Step 2: Divide each side by -2
y = 3/2x -3
The slope is 3/2 and the y intercept is -3 because m is the slope and b is the y-intercept.
A fire hydrant with a blue cap provides water at a rate of 1,500 gallons per minute. A fire hydrant with a green cap provides water at a rate of 1,000 gallons per minute. A fire hydrant with a purple cap provides water at half the rate of a fire hydrant with a green cap. What is the equation in fraction form
Answer:
Fire hydrant with a purple cap (with respect to a fire hydrant with a green cap):
[tex]\dot Q_{purple} = \frac{1}{2}\cdot \dot Q_{green}[/tex]
Step-by-step explanation:
The volume rate of the fire hidrant with a purple cap is equal to the product of the proportion factor and the volume rate of the fire hydrant with a concrete cap.
[tex]\dot Q_{i} = k \cdot \dot Q_{j}[/tex]
There are two different solutions:
Fire hydrant with a purple cap (with respect to a fire hydrant with a green cap):
[tex]\dot Q_{purple} = \frac{1}{2}\cdot \dot Q_{green}[/tex]
Fire hydrant with a purple cap (with respect to a fire hydrant with a blue cap):
[tex]\dot Q_{purple} = \frac{1}{2} \times \frac{1000\,gpm}{1500\,gpm}\cdot \dot Q_{blue}[/tex]
[tex]\dot Q_{purple} = \frac{1}{3}\cdot \dot Q_{blue}[/tex]
To prove a polygon is a rectangle which of the properties listed must be included in the proof
Answer:
if the diagonals of a parallelogram are congruent, then it's a rectangle (neither the reverse of the definition nor the converse of a property). If a parallelogram contains a right angle, then it's a rectangle (neither the reverse of the definition nor the converse of a property).
Step-by-step explanation:
Entrance to a prestigious MBA program in India is determined by a national test where only the top 10% of the examinees are admitted to the program. Suppose it is known that the scores on this test are normally distributed with a mean of 420 and a standard deviation of 80. Parul Monga is trying desperately to get into this program. What is the minimum score that she must earn to get admitted?
Answer:
The minimum score that she must earn to get admitted is 523.
Step-by-step explanation:
As the scores are normally distributed, we can calculate the probability using the z-score.
The distribution has a mean of 420 and a standard deviation of 80.
We have to calculate the z-score z* that satisfies:
[tex]P(z>z^*)=0.1[/tex]
This happens for z*=1.28155.
Then, we can calculate the score as:
[tex]X=\mu+z\cdot\sigma=420+1.28155\cdot 80=420+102.524=522.524[/tex]
A baseball player comes up to bat 3 times during a league game. He either gets a hit or gets an out. What is the probability that the player gets 3 hits in the three bats ?
Answer:
Since there are 2 possibilities for each bat (hit or out), the amount of total possibilities is 2 * 2 * 2 = 8. There is only one possibility out of those eight that gives us three hits, therefore the probability is 1 / 8 or 0.125.
Which explains why the graph is not a function?
Answer:
56
Step-by-step explanation:
A laptop has a listed price of $875.98 before tax. If the sales tax rate is 6.5%, find the total cost of the laptop with sales tax included.
Round your answer to the nearest cent, as necessary.
please!
Answer:
$932.92
Step-by-step explanation:
6.5% = 0.065
(875.98) + (875.98)(0065)
(875.98) + (56.9387)
932.9187
$932.92
Answer:
$[tex]932.92[/tex]
Step-by-step explanation:
[tex]6.5/100=0.65[/tex]
Next, multiply the price by the sales tax.
[tex]875.98*0.65=56.94[/tex]
Then, add.
[tex]875.98+ 56.94=932.92[/tex]
$[tex]932.92[/tex] is the total cost of the laptop.
The chess clubs of two schools consist of, respectively, 8 and 9 players. Four members from each club are randomly chosen to participate in a contest between the two schools. The chosen players from one team are then randomly paired with those from the other team, and each pairing plays a game of chess. Suppose that Rebecca and her sister Elise are on the chess clubs at different schools. What is the probability that
Answer:
A)1/18
B)1/6
C)13/18
Step-by-step explanation:
THIS IS THE COMPLETE QUESTION BELOW,
The chess clubs of two schools consist of, respectively, 8 and 9 players. Four members from each club are randomly chosen to participate in a contest between the two schools. The chosen players from one team are then randomly paired with those from the other team, and each pairing plays a game of chess. Suppose that Rebecca and her sister Elise are on the chess clubs at different schools. What is the probability that (a) Rebecca and Elise will be paired? (b) Rebecca and Elise will be chosen to represent their schools but will not play each other? (c) either Rebecca or Elise will be chosen to represent her school?
CHECK THE ATTACHMENT'S FOR STEP BY STEP EXPLANATION
Reflect on the concept of function. What concepts (only the names) did you need to accommodate the concept of function in your mind? What is the simplest function you can imagine? In your day to day, is there any occurring fact that can be interpreted as a function? Is it possible to view a function? What strategy are you using to get the graph of a function?
Answer:
Step-by-step explanation:
For this kind of question you'd be better off if you'd write down and share your own answers to these conceptual questions and then ask for Brainly feedback on what you have written. You'll need to understand the concept of "function" often in algebra and beyond.
What concepts (only the names) did you need to accommodate the concept of function in your mind? input, output, rule, domain, range, mapping, variation (direct and inverse)
Simplest function: y = c (there's only one x-value and y equals that value)
In your day to day, is there any occurring fact that can be interpreted as a function? An electronic parking meter: the amount of time you can park at the meter without risking getting a ticket is dependent upon the number of quarters you insert into the meter, e. g, 15 minutes for 25 centers, 30 minutes for 50 cents, and so on.
Is it possible to view a function? Sure. Graph the function.
What strategy are you using to get the graph of a function? Set up a coordinate plane. Label the horizontal axis "x" and the vertical axis "y". Choose x (input) values that are included in the domain of the function. If the domain includes '0' you will be finding the 'y-intercept' of the function. Write the input and output as a point: (x, y). Plot that point. Choose other x values within the domain and calculate the corresponding y value for each. Plot several more points and draw a line or a curve through them. Of course there are more sophisticated strategies for graphing functions. Remember: If you're working with a function, there is never more than one output or y value for any particular input value.
what is the value sin(?)= cos 28
Answer: 62
Step-by-step explanation:
Using the fact that cos(90-x)=sin(x) we get that 90-x=28, so x=62 and the answer is simply 62.
Hope that helped,
-sirswagger21
Please answer this correctly
Answer:
A =12.56 m^2
Step-by-step explanation:
Find the area of a circle with radius 4
A = pi r^2
A = 3.14 * 4^2
A =50.24
Since this is 1/4 of the circle, multiply by 1/4
A = 1/4 * 50.24
A =12.56 m^2
Answer:
12.56
Step-by-step explanation:
the formula for the area of a circle is the following:
[tex]\pi r^{2}[/tex]
so divide that formula by 4 to get a quarter and plug in the radius for r.
[tex](\pi )(4^2)/4= 12.56[/tex]
A study was conducted to determine how bacteria cells multiply over time in a controlled environment. In the study, the bacteria cells were counted once every hour for a total of 6 hours. which one is indepedent variable and dependent varible?
Answer:
Dependent variable → bacteria cell increase or population
Independent variable → time variable
Step-by-step explanation:
An independent variable has direct effect on the dependent variable. The independent variable can stand on it own and it is not change by the other variable you are trying to measure. The independent variable have direct effect on the dependent variable.
A dependent variable is actually the variable being tested in an experiment. The dependent variable is actually dependent on the independent variable.
The dependent variable in this scenario is the bacteria cell increase or the bacteria cell multiplication. The bacteria cell increase is dependent on the time . The time variable is the independent variable as it can stand on it own .
Dependent variable → bacteria cell increase or population
Independent variable → time variable
Solve the two-step equation.
-9x + 0.4 = 4
Which operation must be performed to move all the constants to the right side of the equation?
Answer:
x = -0.4
multi-step equation
Step-by-step explanation:
subtract 0.4 from 4 and 0.4 so it cancells out,
0.4 - 0.4 = 0 (cancelled out)
4 - 0.4 = 3.6
then bring down -9x and divide -9 from both sides
-9/-9 = 0 (cancelled out)
3.6 / -9 = -0.4
x = -0.4
Answer:
x = -0.4
Step-by-step explanation:
We have the equation:
-9x + 0.4 = 4
First, the operation to move all the constants to the right side is subtraction since we would have to subtract 0.4 from each side, let's see this:
Now, we have all the constants on the right side of the equation.
Now, the operation we need to perform to isolate the variable is division (since the x has a -9 that is being multiplied by x) we need to do the opposite operation:
Thus, the answer to this equation is x= -0.4
What is the value of n ??????????
Answer:
it's b 59° because it's at the side
I will give brainiest to the first to answer. The what
of the following set of data is 5.
13, 7, 9, 5, 2, 3, 5, 4, 10, 12
Answer:
it is the mode.
Step-by-step explanation:
i. e 5 is the most occuring number in the set of data listed above
Calculating a correlation can help describe a relation between two quantitative variables' ___ and ___ . However, it is not sufficient to use a correlation coefficient to describe two variables. The addition of ___ can provide other helpful details such as __ _."
Answer:
direction
shape
scatter plots
shape and outliers
Step-by-step explanation:
Correlation is defined as the degree of correspondence between two variables.
When the values increase together, correlation is positive and when one value decreases as the other increases, correlation is negative .
Calculating a correlation can help describe a relation between two quantitative variables' direction and shape. However, it is not sufficient to use a correlation coefficient to describe two variables. The addition of scatter plots can provide other helpful details such as shape and outliers
Determine the percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg. Interpret your answer in terms of sampling error.
Answer:
Percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg = 78.5%
The sampling error is 0.08083, in terms of the sampling error, 78.5% of samples of three men will have mean brain weights within (1.24×sampling error) of the mean.
Step-by-step explanation:
Complete Question
According to one study, brain weights of men are normally distributed with mean = 1.20 kg and a standard deviation = 0.14 kg.
Determine the percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg. Interpret your answer in terms of sampling error.
Solution
The Central limit theorem allows us to say
The mean of sampling distribution is approximately equal to the population mean.
μₓ = μ = 1.20 kg
And the standard deviation of the sampling distribution is given as
σₓ = (σ/√N)
σ = population standard deviation = 0.14 kg
N = sample size = 3
σₓ = (0.14/√3) = 0.08083
Percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg, that is, percentage of all samples of three men with mean brain weights within 1.10 kg and 1.30 kg.
P(1.10 ≤ x ≤ 1.30)
We first normalize or standardize 1.10 and 1.30
The standardized score for any value is the value minus the mean then divided by the standard deviation.
For 1.10 kg
z = (x - μₓ)/σₓ = (1.10 - 1.20)/0.08083 = -1.24
For 1.30 kg
z = (x - μₓ)/σₓ = (1.30 - 1.20)/0.08083 = 1.24
To determine the required probability
P(1.10 ≤ x ≤ 1.30) = P(-1.24 ≤ z ≤ 1.24)
We'll use data from the normal distribution table for these probabilities
P(1.10 ≤ x ≤ 1.30) = P(-1.24 ≤ z ≤ 1.24)
= P(z ≤ 1.24) - P(z ≤ -1.24)
= 0.89251 - 0.10749
= 0.78502 = 78.502%
The sampling error is 0.08083, in terms of the sampling error, 78.5% of samples of three men will have mean brain weights within (1.24×sampling error) of the mean.
Hope this Helps!!!
Simplify the answer pls
Answer:
[tex]\frac{9}{8}[/tex]
Step-by-step explanation:
27 ÷ 9 = 3
3 * 3 = 9
9 ÷ 8 = [tex]\frac{9}{8}[/tex]
The weights of college football players are normally distributed with a mean of 200 pounds and a standard deviation of 50 pounds. If a college football player is randomly selected, find the probability that he weighs between 170 and 220 pounds.
Answer:
[tex]P(170<X<220)=P(\frac{170-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{220-\mu}{\sigma})=P(\frac{170-200}{50}<Z<\frac{220-200}{50})=P(-0.6<z<0.4)[/tex]
And we can find this probability with this difference:
[tex]P(-0.6<z<0.4)=P(z<0.4)-P(z<-0.6)=0.655-0.274= 0.381 [/tex]
Step-by-step explanation:
Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(200,50)[/tex]
Where [tex]\mu=200[/tex] and [tex]\sigma=50[/tex]
We want to find the following probability:
[tex]P(170<X<220)[/tex]
And we can use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
And using this formula we got:
[tex]P(170<X<220)=P(\frac{170-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{220-\mu}{\sigma})=P(\frac{170-200}{50}<Z<\frac{220-200}{50})=P(-0.6<z<0.4)[/tex]
And we can find this probability with this difference:
[tex]P(-0.6<z<0.4)=P(z<0.4)-P(z<-0.6)=0.655-0.274= 0.381 [/tex]
i need to know £400 in euros and how to convert it
Answer:
449.40 Euro
Step-by-step explanation:
1 pound=1.12 euro
400*1.12=
The mean height of women in a country (ages 20minus29) is 64.2 inches. A random sample of 75 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 inches? Assume sigmaequals2.84. The probability that the mean height for the sample is greater than 65 inches is nothing.
Answer:
[tex] z=\frac{65-64.2}{\frac{2.84}{\sqrt{75}}} = 2.440[/tex]
And we can find the probability using the complement rule and with the normal standard table like this:
[tex] P(Z>2.440) =1-P(Z<2.440) = 1-0.993 =0.007[/tex]
The probability that the mean height for the sample is greater than 65 inches is 0.007
Step-by-step explanation:
Let X the random variable that represent the women heights of a population, and we know the following parameters
[tex]\mu=64.2[/tex] and [tex]\sigma=2.84[/tex]
We are interested on this probability
[tex]P(X>65)[/tex]
Since the sample size selected is 75>30 we can use the centrel limit theorem and the appropiate formula to use would be the z score given by:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
If we find the z score for 65 inches we got:
[tex] z=\frac{65-64.2}{\frac{2.84}{\sqrt{75}}} = 2.440[/tex]
And we can find the probability using the complement rule and with the normal standard table like this:
[tex] P(Z>2.440) =1-P(Z<2.440) = 1-0.993 =0.007[/tex]
The probability that the mean height for the sample is greater than 65 inches is 0.007
I promise brainliest and a exter 25 poinst to the first to answer What is the solution to the inequality 2x ≥ -4? Click the number line until the correct answer is shown...
:
Answer:
the answer is the arrow going to the right because its not a negative number and a closed circle
Step-by-step explanation:
so that means that 2x is at LEASt more than -4 opposed to this sign> wich just means greater than
because when you work with variables you usually cannot find the exact amount especially when you are rounding so you know that its biigger than no less than or at least -4
the answer is the arrow going to the right because its not a negative number and a closed circle
please please mark as brainliest
Simplify the answer pls
Answer:
Step-by-step explanation:
24/3 - 4
8 - 4 = 4