The derivative of f at (a, b) is the gradient vector [4a - b, -a].
How to determine the derivative of f at (a, b)From the question, we have the following parameters that can be used in our computation:
f(x, y) = 2x^2 − xy
The two-variable function f(x, y) = 2x^2 - xy is differentiable at any point (a, b) if its partial derivatives exist and are continuous at that point.
This is represented as
∂f/∂x = 4x - y
∂f/∂y = -x
The derivative of f at (a, b) can be calculated by evaluating the partial derivatives of f at (a, b):
∂f/∂x(a, b) = 4a - b
∂f/∂y(a, b) = -a
Hence, the derivative of f is [4a - b, -a].
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A committee of 3 is to be formed from 5 men and 6 women. (a) What is the probability that a random committee is made up of 2 women and 1 man? (b) Suppose now that the committee consists of different positions: Chairperson, Vice-Chairperson, and Treasurer. What is the probability that the Chairperson and Vice Chairperson are both women and the Treasurer is a man?
Answer:
a) 0.4545 = 45.45% probability that a random committee is made up of 2 women and 1 man.
b) 0.1515 = 15.15% probability that the Chairperson and Vice Chairperson are both women and the Treasurer is a man
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
If the order of the people chosen is important, we use the permutations formula. If the order is not important, we use the combinations formula.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
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]
(a) What is the probability that a random committee is made up of 2 women and 1 man?
Order is not important, so we use the combinations formula.
Desired outcomes:
2 women from a set of 6, and a men from a set of 5. So
[tex]D = C_{6,2}*C_{5,1} = \frac{6!}{2!4!}*\frac{5!}{1!4!} = 15*5 = 75[/tex]
Total outcomes:
3 people from a set of 6 + 5 = 11. So
[tex]T = C_{11,3} = \frac{11!}{3!8!} = 165[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{75}{165} = 0.4545[/tex]
0.4545 = 45.45% probability that a random committee is made up of 2 women and 1 man.
(b) Suppose now that the committee consists of different positions: Chairperson, Vice-Chairperson, and Treasurer. What is the probability that the Chairperson and Vice Chairperson are both women and the Treasurer is a man?
Now, the order is important, which means that we use the permutations formula.
Desired outcomes:
2 women from a set of 6, and a men from a set of 5. So
[tex]D = P_{6,2}*P_{5,1} = \frac{6!}{4!}*\frac{5!}{4!} = 30*5 = 150[/tex]
Total outcomes:
3 people from a set of 11. So
[tex]T = P_{11,3} = \frac{11!}{8!} = 990[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{150}{990} = 0.1515[/tex]
0.1515 = 15.15% probability that the Chairperson and Vice Chairperson are both women and the Treasurer is a man
Find the vertex of the graph of the quadratic function f(x)=7x2+14x+10
Answer:
plazzz get lost bro fast
what is 23 + 23 - 789
Answer:
743
Step-by-step explanation:
23+23=46
789-46=743
Answer:
743
Step-by-step explanation:
Using the Distributive Property, rewrite 2x + 16 as a product of two factors. *
1. 2x + 8
2. 2(16x)
3. 2(x + 8)
4. 2(x + 16)
5,3,1,-1, common difference or common ratio
Answer:
Common
Step-by-step explanation:
Jocelyn boils 24 eggs. From experience, she knows that the shell of any given during the boiling process. If shells crack independently, what is the probability the boiling process with a cracked shell? Round to 2 decimal places.
Answer:
.62
Step-by-step explanation:
Keep it nice and simple.
Answer:
.62
Step-by-step explanation:
100% of what equals 12
Answer:
12
Step-by-step explanation:
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*..
IM GIVING 40 POINTS !! DONT SKIP :((.
The solution set in interval notation is ??
Answer:
Step-by-step explanation:
Evalute 4+(7-5)⁴?
PLEASE HELP
Answer:
The answer is 20
Step-by-step explanation:
(7-5)=2
2^4 = 16
16 + 4 = 20
What is the area of the figure?
Answer:
졌던 냥 샷 세 새 새 휴 여ㅔ헤헤헤헤헤헤하리ㅎㄴ하왕허웋ㅇ헝후오ㅡ아ㅗ여ㅏㅕ라ㅕ라ㅗㅇ렁셔 요 쇽뎌ㅕ려래ㅛ요ㅓㅓㅛ요ㅏ다ㅛ 또훙서 유ㅓ가ㅗㅗ히ㅓ
ㅍ피ㅓ리ㅓ히ㅓㅓ히ㅗ챠ㅗㅗ료ㅡ쵸ㅏㅇ
Step-by-step explanation:
ㅇㅎ겨개ㅛ교ㅑ아ㅛ려ㅐㄹ서넣요ㅏㅗㅏ차ㅗ셔ㅏ 로 홀ㅛㅕㅑ쇼ㅑ겻효ㅕ 껴ㅛㅕㅛ교ㅑ교ㅐ료ㅏ래ㅕ새ㅕ리ㅕㅐㅕㅔㅑㅣㅕ셔ㅐ ㅕㅣ셔ㅐㄱㅕㅔ샹샹허텋요ㅑ오툐ㅏ어ㅣ래ㅕ촤쳐ㅐ료ㅑ와타ㅛ낳와탸ㅛ와촤야ㅛ 유ㅗㅡ촤우ㅗ퇴롸러ㅣ혀ㅣ라ㅛㅌ샤 ㅗㅣ래ㅛ려ㅣ랴ㅛ아ㅗ처ㅣ촤여ㅣ리ㅕㅓ쵸ㅐ려ㅣㅓㅓㅣ리ㅓㄹㅗㅏ려ㅣ려ㅣ려ㅣㅣㅕㅛㅑㅓㅛ나굣이셔서ㅣㅣ시서ㅣ서소니서서서성섯여ㅣ햐ㅔㅅ하ㅕㅓ퍄샤도ㅕㅐ요ㅏㅗ럇냐ㅛ려ㅔㅐㅈ서ㅕㅣ세ㅕ엿처억 ㅣㅕ려
find the perimeter and area of the rectangle with vertices (1, -2), (1, 7), (-3, 7), and (-3, -2)
Answer:
26
Step-by-step explanation:
9+4+9+4=26
Is the set of the following numbers ordered from greatest to least or least to greatest
Answer: Your answer should be least to greatest I believe
A bucket contains 13 & 1/3 gallons of water and is 5/6 full. How many gallons of water would be in a full bucket?
Answer:
16
Step-by-step explanation:
Answer:
17 2+2+2+2+2+2+2+2+1
Step-by-step explanation:
the bucket contains 13 and 6
Name all digits that can be the last digit of prime numbers.
Answer:
1,2,3,5,7,9
Step-by-step explanation:
I started by seeing all the digits (0-9) which are prime numbers.
8) Which of the Prime number are
even numbers?
C
a) 0 & 2
b) 1 & 2
c) 2
ОО
d) None
Can someone explain to me how to do this problem?
x • 1 + x/1 =
Do
10 cm
10 cm
20 cm
form an triangle?
Answer:
No it is unable to form a triangle.
Step-by-step explanation:
It cannot be because one side is two times the other side, and there are two of the "other sides". It cannot form a triangle.
Answer:
Step-by-step explanation:
A submarine is 84 feet below the surface of the water and descends 10 feet
deeper every minute. How many minutes will it take for the submarine to be
located 219 feet below the surface? Write and solve an equation,
Answer:
13.5
Step-by-step explanation:
219-84=135
10*13.5=135
so it would take 13.5 minutes to get to 219 since 84+135=219
A playground is 45 feet wide
convert the wind to yards
This is the question I need the answer in 24 house or less please and thank u
Answer:
Vertex: (–9, 1)
Axis of Symmetry: x = –9
Step-by-step explanation:
x = 9 is the lowest point on the graph. This makes it the x-coordinate of the vertex and the axis of symmetry. Now count how many squares above the x-axis it is. It's 1 square above, right? This means the vertex is (–9, 1).
Hope this helps you. Have a great day!
The earth travels 1,050 miles per hour.
At this rate, how many miles does the earth travel per day?
Plz Help God will Bless You!!
The earth travels 1,050 miles in an hour.
There are 24 hours in a day.
So multiply 1,050 by 24.
And you get 25,200.
The earth travels 25,200 miles in a day.
You enter an elevator and go down 7 floors you exit on the 10th floor. Write an equation you can use to find the floor where you entered the elevator
Probability is a measure of how likely an event is to occur. Choose the probability that best matches each of the following statements: (a) This event is impossible: [ Select ] (b) This event will occur more often than not, but is not extremely likely: [ Select ] (c) This event is extremely unlikely, but it will occur once in a while in a long sequence of trials: [ Select ] (d) This event will occur for sure: [ Select ]
Answer:
(a) 0
(b) 0.6
(c) 0.01
(d) 1
Step-by-step explanation:
Given
Probabilities: 0, 0.01, 0.3, 0.6, 0.99, and 1 ---> Missing information
Required
Match the probabilities with appropriate values
(a) Impossible:
An impossible event will always have a probability of 0
(b) Occurrence is more often than not, but not extremely likely:
An event that will occur more often than not will have a probability greater than 0.5 but less than 1
However, if the likelihood is not extremely likely, the probability will be closer to 0.5 and 1.
The probability that matches this description is 0.6
(c) Occurrence is extremely unlikely, but will occur once in a while
An event that is extremely unlikely will have a value greater than 0 and the value will be very close to 0.
The probability that matches this description is 0.01
(d) A certain event:
A certain event has a probability of 1
Solve the equation
2x2 + 12x - 7 = 0
by completing the square.
Give your answers correct to 2 decimal places.
Show step by step please!!!!
Step-by-step explanation:
4+12x=7
12x=7-4
12x=3
X=3/12
X=0.25
which explains how to find the quotient of the division below -3 1/3 / 4/9
19 tens is the same
as
Count forward by fives.
Here again are the results of a survey that students conducted at a mall. The students conducted this survey as part of a statistics project to determine if younger adults are more likely to have tattoos. At least one tattoo No tattoo Row Totals Age 18 - 29 170 320 490 Age 30 - 50 60 445 505 Column Totals 230 765 995 Which proportions are most useful in analyzing the relationship between age and tattoos? Group of answer choices 170 / 230 and 60 / 230
Answer:
1. 170/490 and 60/505
2. 320/490 and 445/505
Step-by-step explanation:
No options were given, but the question can still be answered
Given
[tex]\begin{array}{cccc}{} & {\ge 1\ tattoo} & {0\ tattoo} & {Row\ Total} & {18 -29} & {170} & {320} & {490} & {30 - 50} & {60} & {445} & {505} & {Column\ Total} & {230} & {765} & {995}\ \end{array}[/tex]
Required
Which proportion best compares age and tattoos?
The row data represents the age range of each group while the column data represents the amount of tattoo by each group.
So, to make comparison:
You simply pick a cell data and compare it to the row total.
Take for instance
For those who have at least 1 tattoo. The proportion to use are:
170/490 --- For age range: 18 - 29
60/505 --- For age range: 30 - 29
For those without tattoo. The proportion to use are:
320/490 --- For age range: 18 - 29
445/505 --- For age range: 30 - 29
(05.07 MC)
The net of a square pyramid is shown below
3 inches
2 inches
3 inches
2 inches
What is the surface area of the solid?
16 square inches
24 square inches
28 square inches
Previous Question
Question 1 (Answered)
Answer:
16 2x3 divided by 2 x4=12 + 2x2=16 I think hopefully this helps :)
Factor out the GCF from the terms of the polynomial 2x^3 − 5x^2 + 25.
Answer:
Step-by-step explanation:
The polynomial is already factored.