f(x, y) = x ² - 4xy + 5
has critical points where both partial derivatives vanish:
∂f/∂x = 2x - 4y = 0 ==> x = 2y
∂f/∂y = -4x = 0 ==> x = 0 ==> y = 0
The origin does not lie in the region R, so we can ignore this point.
Now check the boundaries:
• x = 1 ==> f (1, y) = 6 - 4y
Then
max{f (1, y) | 0 ≤ y ≤ 2} = 6 when y = 0
max{f (1, y) | 0 ≤ y ≤ 2} = -2 when y = 2
• x = 4 ==> f (4, y) = 12 - 16y
Then
max{f (4, y) | 0 ≤ y ≤ 2} = 12 when y = 0
max{f (4, y) | 0 ≤ y ≤ 2} = -4 when y = 2
• y = 0 ==> f (x, 0) = x ² + 5
Then
max{f (x, 0) | 1 ≤ x ≤ 4} = 21 when x = 4
min{f (x, 0) | 1 ≤ x ≤ 4} = 6 when x = 1
• y = 2 ==> f (x, 2) = x ² - 8x + 5 = (x - 4)² - 11
Then
max{f (x, 2) | 1 ≤ x ≤ 4} = -2 when x = 1
min{f (x, 2) | 1 ≤ x ≤ 4} = -11 when x = 4
So to summarize, we found
max{f(x, y) | 1 ≤ x ≤ 4, 0 ≤ y ≤ 2} = 21 at (x, y) = (4, 0)
min{f(x, y) | 1 ≤ x ≤ 4, 0 ≤ y ≤ 2} = -11 at (x, y) = (4, 2)
A football team has a probability of 0.76 of winning when playing any of the other four teams in its conference. If the games are independent, what is the probability the team wins all its conference games
Answer:
0.33362176
Step-by-step explanation:
Probability is the ratio of the number of possible outcomes to the number of total outcomes.
Given that a football team has a probability of 0.76 of winning when playing any of the other four teams in its conference, the probability that the team wins all its conference games
= 0.76 * 0.76 * 0.76 * 0.76
= 0.33362176
This is the probability that the teams wins the 4 matches played against the other teams in the conference.
Geometry Summer school workkkk worth 50 pointssss
White colour is painted in 2 ft wide which lies inside from both sides in the basketball court of length 78 ft and breadth 46 ft . find the area of the painted part.
Answer:
L1=78
W1=46
L2=78+4=82
W2=46+4=50
Area=L2×W2-L1×W1
82×50-78×46
Ans- 512ft^2
The firm had 15 billion VND of earnings before interest and tax (EBIT), corporate tax is 20%. The market price of stock is 60.000đ. Knowing that net income will be held 40% before using it for dividend. How much of the net income can be divided for shareholders?
Answer:
was assigned with this problem (the reference text is attached):
Which of the following, if included in a student's paper, would NOT be an example of plagiarism?
1. In the game of baseball, which is rather boring, the batter stands on home base (Hughes 1).
2. Baseball is rather surprisingly known as "America's Favorite Pastime."
3. Baseball is "a rather boring sport played between two teams of nine players" (Hughes 1).
4. All of these are plagiarism.
The answer tells that only the third choice is NOT a plagiarism. My question is, why is the first choice a plagiarismwas assigned with this problem (the reference text is attached):
Which of the following, if included in a student's paper, would NOT be an example of plagiarism?
1. In the game of baseball, which is rather boring, the batter stands on home base (Hughes 1).
2. Baseball is rather surprisingly known as "America's Favorite Pastime."
3. Baseball is "a rather boring sport played between two teams of nine players" (Hughes 1).
4. All of these are plagiarism.
The answer tells that only the third choice is NOT a plagiarism. My question is, why is the first choice a plagiarismwas assigned with this problem (the reference text is attached):
Which of the following, if included in a student's paper, would NOT be an example of plagiarism?
1. In the game of baseball, which is rather boring, the batter stands on home base (Hughes 1).
2. Baseball is rather surprisingly known as "America's Favorite Pastime."
3. Baseball is "a rather boring sport played between two teams of nine players" (Hughes 1).
4. All of these are plagiarism.
The answer tells that only the third choice is NOT a plagiarism. My question is, why is the first choice a plagiarismwas assigned with this problem (the reference text is attached):
Which of the following, if included in a student's paper, would NOT be an example of plagiarism?
1. In the game of baseball, which is rather boring, the batter stands on home base (Hughes 1).
2. Baseball is rather surprisingly known as "America's Favorite Pastime."
3. Baseball is "a rather boring sport played between two teams of nine players" (Hughes 1).
4. All of these are plagiarism.
The answer tells that only the third choice is NOT a plagiarism. My question is, why is the first choice a plagiarismwas assigned with this problem (the reference text is attached):
Which of the following, if included in a student's paper, would NOT be an example of plagiarism?
1. In the game of baseball, which is rather boring, the batter stands on home base (Hughes 1).
2. Baseball is rather surprisingly known as "America's Favorite Pastime."
3. Baseball is "a rather boring sport played between two teams of nine players" (Hughes 1).
4. All of these are plagiarism.
The answer tells that only the third choice is NOT a plagiarism. My question is, why is the first choice a plagiarismwas assigned with this problem (the reference text is attached):
Which of the following, if included in a student's paper, would NOT be an example of plagiarism?
1. In the game of baseball, which is rather boring, the batter stands on home base (Hughes 1).
2. Baseball is rather surprisingly known as "America's Favorite Pastime."
3. Baseball is "a rather boring sport played between two teams of nine players" (Hughes 1).
4. All of these are plagiarism.
The answer tells that only the third choice is NOT a plagiarism. My question is, why is the first choice a plagiarismwas assigned with this problem (the reference text is attached):
Which of the following, if included in a student's paper, would NOT be an example of plagiarism?
Two equal positive charges are placed x m apart. The equipotential lines are at 100 V interval. The work required to move a third charge, q = -e, from the +100 V line to b is:______
Answer:
+200 J
Step-by-step explanation:
The equally positive charges plates are placed at point x. Exponential lines are 100 V interval and therefore the charges on the potential line is positive. The potential for line c is +200 V which indicates that work required to move the third line is +200 J.
bHhHshsbsnsnsnsnsnsbsbsbckclccllcxldkdldkdkdk HELP
Answer:
Step-by-step explanation:
The reasons for each statement are inside the parentheses
1. <1 and <2 are complementary (given)
2. m<1 + m<2 = 90° (definition of complementary angles)
3. m<2 = 74° (given)
4. m<1 + 74° = 90° (Substitution)
5. m<1 = 16° (Subtraction property of equality)
This is gotten by subtracting 74° from both sides as follows:
m<1 + 74° - 74° = 90° - 74°
m<1 = 16°
∫[tex]\frac{x+2019}{x^{2}+9 }[/tex]
Split up the integral:
[tex]\displaystyle\int\frac{x+2019}{x^2+9}\,\mathrm dx = \int\frac{x}{x^2+9}\,\mathrm dx + \int\frac{2019}{x^2+9}\,\mathrm dx[/tex]
For the first integral, substitute y = x ² + 9 and dy = 2x dx. For the second integral, take x = 3 tan(z) and dx = 3 sec²(z) dz. Then you get
[tex]\displaystyle \int\frac x{x^2+9}\,\mathrm dx = \frac12\int{2x}{x^2+9}\,\mathrm dx \\\\ = \frac12\int\frac{\mathrm du}u \\\\ = \frac12\ln|u| + C \\\\ =\frac12\ln\left(x^2+9\right)[/tex]
and
[tex]\displaystyle \int\frac{2019}{x^2+9}\,\mathrm dx = 2019\int\frac{3\sec^2(z)}{(3\tan(z))^2+9}\,\mathrm dz \\\\ = 2019\int\frac{3\sec^2(z)}{9\tan^2(z)+9}\,\mathrm dz \\\\ = 673\int\frac{\sec^2(z)}{\tan^2(z)+1}\,\mathrm dz \\\\ = 673\int\frac{\sec^2(z)}{\sec^2(z)}\,\mathrm dz \\\\ = 673\int\mathrm dz \\\\ = 673z+C \\\\ = 673\arctan\left(\frac x3\right)+C[/tex]
Then
[tex]\displaystyle\int\frac{x+2019}{x^2+9}\,\mathrm dx = \boxed{\frac12\ln\left(x^2+9\right) + 673\arctan\left(\frac x3\right) + C}[/tex]
A coin is tossed three times. An outcome is represented by a string of the sort HTT (meaning a head on the first toss, followed by two tails). The
outcomes are listed in the table below. Note that each outcome has the same probability.
For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event.
Outcomes Probability
HHT HHH THH HTH HTT TTT TTH THT
Event A: Alternating tail and head (with either coming first)
Event B: No tails on the first two tosses
Event C: A tail on both the first and the last tosses
Answer:
Step-by-step explanation:
In this question, the sample space contains 8 elements and has been given as;
HHT HHH THH HTH HTT TTT TTH THT
1. For event A:
Outcomes of alternating tail and head = THH HTH HTT THT
= 4 outcomes
Pr(alternating tail and head (with either coming first)) = [tex]\frac{4}{8}[/tex]
= [tex]\frac{1}{2}[/tex]
2. For event B:
Outcomes of no tails on the first two tosses = HHT HHH
= 2 outcomes
Pr (No tails on the first two tosses) = [tex]\frac{2}{8}[/tex]
= [tex]\frac{1}{4}[/tex]
For event C:
Outcomes of a tail on both the first and the last tosses = THT TTT
= 2 outcomes
Pr(A tail on both the first and last tosses) = [tex]\frac{2}{8}[/tex]
= [tex]\frac{1}{4}[/tex]
It takes Jacob and Hannah a hours to do
a certain job, it takes Jacob and Ethan b
hours to do the same job and it takes
Hannah and Ethan c hours to do the
same job. How long would it take Jacob,
Hannah and Ethan to do the same job if
all of them worked together?
Step-by-step explanation:
Kym teaches sixth grade students in an urban school where most of the families in the community live below the poverty line. Each year the majority of the students in her school fail the statewide tests. Kym follows school district teaching guides and typically uses direct instruction in her Language Arts and Social Studies classes. The classroom assessments are designed to mirror those on the statewide tests so the students become familiar with the assessment format.
write your answer in simplest radical form
Answer:
[tex]8\sqrt{2}[/tex]
Step-by-step explanation:
Maybe this image can help you.
A recipe calls for 4 cups of flour and 6 cups of sugar. How many cups of sugar per cup of flour does the recipe require?
Answer:
3 cups of sugar per 2 cups of flour
Step-by-step explanation:
just flip and simplify the fraction
4/6 = 6/4 = 3/2
If r = 0.97, this indicates a ________ correlation. Question 10 options: A) weak negative B) weak positive C) strong negative D) strong positive
Answer:C
Step-by-step explanation:
A correlation of -0.97 is a strong negative correlation while a correlation of 0.10 would be a weak positive correlation
Answer:
C) strong negative.
Step-by-step explanation:
Leanne is planning a bridal shower for her best friend. At the party, she wants to serve 33 beverages, 33 appetizers, and 22 desserts, but she does not have time to cook. She can choose from 1313 bottled drinks, 77 frozen appetizers, and 1313 prepared desserts at the supermarket. How many different ways can Leanne pick the food and drinks to serve at the bridal shower
Answer:
She can pick the food and drinks in 780,780 different ways.
Step-by-step explanation:
The drinks, appetizers and desserts are independent of each other, so the fundamental counting principle is used.
Also, the order in which the beverages, the appetizers and the desserts are chosen is not important, which means that the combinations formula is used to solve this question.
Fundamental counting principle:
States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Beverages:
3 from a set of 13. So
[tex]C_{13,3} = \frac{13!}{3!10!} = 286[/tex]
Appetizers:
3 from a set of 7, so:
[tex]C_{7,3} = \frac{7!}{3!4!} = 35[/tex]
Desserts:
2 from a set of 13, so:
[tex]C_{13,2} = \frac{13!}{2!11!} = 78[/tex]
How many different ways can Leanne pick the food and drinks to serve at the bridal shower?
286*35*78 = 780,780
She can pick the food and drinks in 780,780 different ways.
I can’t solve plz help me ...
Your answer is in the attachment.
The equation of a line is (3)/(5)x+(1)/(3)y=(1)/(15) . The x-intercept of the line is , and its y-intercept is .
bxf-mgii-whr
Step-by-step explanation:
come I will teach
Let sin A = -3/5
with 270°
sinA/2
Answer:
-0.316227766
Step-by-step explanation:
0.316227766
An article in the Journal of Composite Materials describes the effect of delamination on thenatural frequency of beams made from composite laminates. Five such delaminated beams were subjected to loads, and the resulting frequencies were as follows (in Hz):
230.66, 233.05, 232.58, 229.48, 232.58
(a) Find a 90% two-sided CI on mean natural frequency. Round your answers to 2 decimal places.
(b) Do the results of your calculations support the claim that mean natural frequency is 235 Hz?
(A). _____________<= U<= _______________
(B). YES OR NO ?
Answer:
(230.21 ; 233.13)
Step-by-step explanation:
Given the data :
230.66, 233.05, 232.58, 229.48, 232.58
To calculate the 90% CI
WE obtain the mean and standard deviation of the sample data :
Mean of sample, ΣX /n = 1158.35/5 = 231.67
The standard deviation of the sample, s = 1.531 (Using calculator).
(The 90% Tcritical value, 2 sided, df = 4) = 2.132
The confidence interval, CI :
Mean ± Tcritical * s/√n
C.I = 231.67 ± (2.132 * (1.531/√5)
C. I = 231.67 ± 1.4597
(231.67 - 1.4597) ; (231.67 + 1.4597)
(230.21 ; 233.13)
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 2.1yd : 1.4yd
9514 1404 393
Answer:
3/2
Step-by-step explanation:
Multiplying numerator and denominator by 10 will convert the ratio to a ratio of whole numbers. Then dividing by the common factor of 7 will reduce it to simplest form.
[tex]\dfrac{2.1\text{ yd}}{1.4\text{ yd}}=\dfrac{2.1\times10}{1.4\times10}=\dfrac{21}{14}=\dfrac{3\times7}{2\times7}=\boxed{\dfrac{3}{2}}[/tex]
plot the following points on a xy-plane.
(5,2) , (-2, 1) , (-1,-3)
Answer: See below
Step-by-step explanation:
Answer:
Answer below
Step-by-step explanation:
Find the area of the plot of land shown below.
9514 1404 393
Answer:
3070.06 square inches
Step-by-step explanation:
The area of the left triangle can be found using Heron's formula:
s = semiperimeter = (53+71+58)/2 = 91
area = √(s(s -53)(s -71)(s -58)) = √2282280 ≈ 1510.72
The area of the right triangle can be found using the trig formula ...
area = 1/2ab·sin(C)
area = 1/2(55)(71)sin(53°) ≈ 1559.34
Then the total area is ...
1510.72 +1559.34 = 3070.06 . . . . . square inches
Instructions: State what additional information is required in order
to know that the triangles in the image below are congruent for the
reason given
Reasory. AAS Postulate
Step-by-step explanation:
AAS means angle angle side. so, we need 2 angles and 1 side.
the diagram shows us 1 angle in each triangle to be equal or congruent (C and G).
it also shows us implicitly, that the side AB is shared and is therefore truly the same for each triangle.
that means we need one more angle. either the one at A or the one at B. you pick.
A couple decide to have 5 children what if the probability that they will have at least one girl
Answer:
31/32
Step-by-step explanation:
There are 2^5, or 32 combinations.
There is only 1 combination which is all 5 children are boys.
So the probability that will have at least 1 girl is: 1 - 1/32 = 31/32
A regular six sided die is to be rolled once what is the probability that a number less than three is rolled
Answer:
1/3
Step-by-stepi
Answer anyone ? Tyia :)
Find the missing side lengths leave your answer as a racials simplest form
Find f(2) given f(x) = -3x^2 + 2x+11
Answer:
Answer:f(2)=-3(2)^2+2*2+11
Answer:f(2)=-3(2)^2+2*2+11 =-3*4+4+11
Answer:f(2)=-3(2)^2+2*2+11 =-3*4+4+11 =-12+4+11
Answer:f(2)=-3(2)^2+2*2+11 =-3*4+4+11 =-12+4+11 =3
hence, f(2)=3
Find the area of the sector round your answer to the nearest 10th
Answer:
63.4
Step-by-step explanation:
Area of sector=pi*r^2*(theta/360)
Area of sector=pi*121*(60/360)
Area of sector=63.4
In a food preference experiment, 80 lizards were given the opportunity to choose to eat one of three different species of insects. The results showed that 33 of the lizards chose species A, 12 chose species B, and 35 chose species C. They conducted a Chi-squared analysis to test for equal preference. What are the Null and Alternate hypothesis for this test
Answer:
H0 : The variables are independent
H1 : The variables are not independent
Step-by-step explanation:
In a Chisquare test ; The null hypothesis is used to lay claim that the variables are independent, that is no relationship exists between the categorical variables in the population while the alternative hypothesis negates the null thus claiming that the variables aren't independent.
The null hypothesis, H0 : The variables are independent, A = B = C
The alternative hypothesis ; H1 : The variables are not independent, A ≠ B ≠ C
Geometry homework due tonightttt worth 50 points
Answer:
Angle 2 = 180 - 76 = 104 (linear pair)
angle 3 = 76 (vertically opposite angles)
angle 4 = 104(vertically opposite angles)
Answer:
m∠2 = 104°m∠3 = 76°m∠4 = 104°Step-by-step explanation:
Concept:
Here, we need to know the idea of supplementary angles and linear pairs.
Supplementary angles are two angles or arcs whose sum is 180 degrees.
A linear pair of angles are formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. The measure of a straight angle is 180 degrees.
Linear pair and supplementary angles are conveying the same meaning. However, linear pair is describing the "appearance" of the two angles as they form a line which is 180 degrees. On the other hand, supplementary angles are the properties stating two angles adds up to 180 degrees, but are not required to be together.
If you are still confused, you can refer to the attachment below for a graphical explanation.
Solve:
∠1 and ∠2 are linear pairs and supplementary to each other forming 180°
m∠2 = 180 - 76 = 104°∠2 and ∠3 are linear pairs and supplementary to each other forming 180°
m∠3 = 180 - 104 = 76°∠3 and ∠4 are linear pairs and supplementary to each other forming 180°
m∠4 = 180 - 76° = 104°Hope this helps!! :)
Please let me know if you have any questions
13. Find the slope of the line that passes through (1, 8) and (-3, 12).
Answer:
-1
Step-by-step explanation:
Slope formula:
[tex]\frac{y2-y1}{x2-x1}[/tex]
x1 = 1
y1 = 8
x2 = -3
y2 = 12
[tex]\frac{12-8}{-3-1}[/tex]
[tex]\frac{4}{-4}[/tex] = -1
