Calculate the gradient of the given function; evaluate the gradient of the function at the point P, and calculate the directional derivative of the function in the direction of u. (a) f(x,y) = x In (x/y). P(3,1), u = -5/3i + 12/13j (b) g(x,y) = x sin(xy^2), P (phi/2,1), u = (1/sqrt(2), 1/sqrt(2))
Answers
(a) The gradient of f(x, y) is: ∇f = (∂f/∂x)i + (∂f/∂y)j = (ln(x/y) + 1)i - (x/y)j
Directional derivative of f in the direction of u = (-5/3)(ln(3)) + (12/13)(-3)
(b) The gradient of g(x, y) is: ∇g = (∂g/∂x)i + (∂g/∂y)j = (sin(xy^2) + y^2 cos(xy^2))i + (2xy cos(xy^2))j
Directional derivative = (sin(xy^2) + y^2 cos(xy^2) + 2xy cos(xy^2)) / sqrt(2)
(a) Let's calculate the gradient of the function f(x, y) = x ln(x/y):
Gradient of f(x, y) = (∂f/∂x)i + (∂f/∂y)j
To find ∂f/∂x, we differentiate f(x, y) with respect to x while treating y as a constant:
∂f/∂x = ln(x/y) + 1
To find ∂f/∂y, we differentiate f(x, y) with respect to y while treating x as a constant:
∂f/∂y = -x/y
The gradient of f(x, y) is:
∇f = (∂f/∂x)i + (∂f/∂y)j = (ln(x/y) + 1)i - (x/y)j
Now, let's evaluate the gradient of the function at point P(3, 1):
∇f(3, 1) = (ln(3/1) + 1)i - (3/1)j
= ln(3) i - 3j
Next, we can calculate the directional derivative of the function in the direction of u = -5/3i + 12/13j:
Directional derivative of f in the direction of u = ∇f · u
= (∇f · u_x)i + (∇f · u_y)j
= (∇f · (-5/3i))i + (∇f · (12/13j))j
= (-5/3)(ln(3) i - 3j) · i + (12/13)(ln(3) i - 3j) · j
(b) Let's calculate the gradient of the function g(x, y) = x sin(xy^2):
Gradient of g(x, y) = (∂g/∂x)i + (∂g/∂y)j
To find ∂g/∂x, we differentiate g(x, y) with respect to x while treating y as a constant:
∂g/∂x = sin(xy^2) + y^2 cos(xy^2)
To find ∂g/∂y, we differentiate g(x, y) with respect to y while treating x as a constant:
∂g/∂y = 2xy cos(xy^2)
Therefore, the gradient of g(x, y) is:
∇g = (∂g/∂x)i + (∂g/∂y)j = (sin(xy^2) + y^2 cos(xy^2))i + (2xy cos(xy^2))j
Now, let's evaluate the gradient of the function at point P(phi/2, 1):
∇g(phi/2, 1) = (sin((phi/2)(1)^2) + (1)^2 cos((phi/2)(1)^2))i + (2(phi/2)(1) cos((phi/2)(1)^2))j
Finally, to calculate the directional derivative of g in the direction of u = (1/sqrt(2), 1/sqrt(2)):
Directional derivative of g in the direction of u = ∇g · u
= (∇g · (1/sqrt(2))i) + (∇g · (1/sqrt(
Therefore, the directional derivative of g in the direction of u = (1/sqrt(2), 1/sqrt(2)) is:
Directional derivative = (sin(xy^2) + y^2 cos(xy^2) + 2xy cos(xy^2)) / sqrt(2)
To evaluate the directional derivative at a specific point, such as P(phi/2, 1), substitute the corresponding values of x and y into the expression for the directional derivative.
To know more about gradients, click here: brainly.com/question/30249498
#SPJ11
Related Questions
the city of covington is placing a statue in a triangular grassy area bounded by sidewalks on all 3 sides. if the city wants the statue to be an equal distance from all 3 sides of the grassy area, where should they place it?
Answers
To place the statue an equal distance from all three sides of the grassy area, the city should position it at the intersection of the perpendicular bisectors of the three sides.
Here's a step-by-step process to determine the placement:
Identify the three sides of the grassy area and locate their midpoints.
Construct the perpendicular bisectors of each side. A perpendicular bisector is a line that cuts a line segment into two equal parts at a right angle.
The point where the three perpendicular bisectors intersect is the desired location to place the statue. This point is equidistant from all three sides.
By placing the statue at this intersection point, it ensures that the distance from the statue to each side of the grassy area is equal.
To learn more about bisectors visit;
https://brainly.com/question/31893955
#SPJ11
How to convert teaspoons to cups
Answers
Answer: no idea
Step-by-step explanation:
Use the properties of the natural logarithm to expand each logarithmic expression. Round answers to 3
decimal places, if necessary. a. In(7x) = Preview 5x b. In Preview x + 3 c. In (x 8) = Preview d. 15,000 In(xy4) =
Answers
a. ln(7x) can be expanded as ln(7) + ln(x). b. ln(x + 3) remains as it is, since it cannot be simplified further. c. ln(x^8) can be expanded as 8ln(x). d. 15,000ln(xy^4) can be expanded as ln(x) + 4ln(y) + ln(15,000).
a. To expand the logarithmic expression ln(7x), we can use the property of the natural logarithm that states ln(ab) = ln(a) + ln(b).
Therefore, ln(7x) can be expanded as ln(7) + ln(x).
b. Similarly, the logarithmic expression ln(x + 3) can be expanded using the property ln(ab) = ln(a) + ln(b).
Hence, ln(x + 3) remains as it is since we cannot simplify it further.
c. Expanding the logarithmic expression ln(x^8) can be done using the property ln(a^b) = b * ln(a).
Thus, ln(x^8) becomes 8 * ln(x).
d. Expanding the logarithmic expression 15,000ln(xy^4) can be done by applying the property ln(ab) = ln(a) + ln(b).
Therefore, 15,000ln(xy^4) can be expanded as 15,000[ln(x) + ln(y^4)].
Learn more about expanded here
https://brainly.com/question/17921963
#SPJ11
During a sale, a shop allows 20% discount off the marked price of clothing. What will a customer pay for a dress with a marked price of $30? * 1 point
Answers
Answer:
$24
Step-by-step explanation:
Let the full price of $30 be 100%.
If the discount allowed is 20%, then the percentage of the original price that a customer will pay is:
\(P=100\%-20\%\\P=80\%\)
80% of a marked price of $30 is:
\(80\%*\$30\\\$24\)
A customer will pay $24.
. Visually compare the dot plot of heights of field hockey players to the dot plots for softball and basketball players. Shape: Center: Spread:
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Using visual comparison :
SHAPE :
Both plots are fairly left skewed as their peaks are more shifted to the right and tails to the left of the distribution.
The centre :
Both softball and basketball plots are centered around the median of the distribution. With softball having a centre (median value) of 5'4'' and basketball has a value of 5'8''.
Spread :
The softball plot spread from 4'9'' through 5'6''
While basketball spreads from 5'2'' through 6'0''
B is the midpoint of AC. AB = 2x + 12 and AC = 10x - 12.
Find the following:
x:
AB:
BC:
AC:
Answers
Answer:
Step-by-step explanation:
If B is the midpoint of AC, then AB = BC and AB+BC = AC
AB +AB = AC
2AB = AC
2(2x+12) = 10x-12
4x+24 = 10x-12
collect like terms:
4x-10x = -12-24
-6x = -36
x = -36/-6
x = 6
Get AB:
AB = 2x+12
AB = 2(6)+12
AB = 12+12
AB = 24
Since AB = BC, hence BC = 24
AC = AB+BC
AC = 24+24
AC = 48
Help me cuhhhh?????????
Answers
Answer:
D. 10.5 ft
Step-by-step explanation:
3 times 3.5 = 10.5.
Liz ha two piece of tring one 18cm other 24cm long. He want to cut them up to produce maller piece of tring that are all of the ame length with no tring leftover. What i the greatet length,in cm, that he can make them?
Answers
The greatest length that Liz can make using the strings is 6 cm.
Given,
In the question:
Liz has two piece of string one 18cm other 24cm long.
and, He want to cut them up to produce smaller piece of string that are all of the same length with no string leftover.
To find the greatest length, in cm.
Now, According to the question:
Let's know:
Greatest Common Factor (GCF):-
The GCF of a set of values (typically two) is the greatest factor that applies to every number.
We must find the GCF of 18 and 24:
List the factors of both values:
18: 1, 2, 3, 6, 9, 18
24: 1, 2, 3, 4, 6, 8, 12, 24
Let's identify the common factors between 18 and 24:
18: 1, 2, 3, 6, 9, 18
24: 1, 2, 3, 4, 6, 8, 12, 24
Hence, the GCF is 6.
The greatest length that Liz can make using the strings is 6 cm.
Learn more about Greatest Common factor at:
https://brainly.com/question/11221202
#SPJ4
solve: 3x^2+16x+5=0
I did it but apparently its wrong so, please help it would literally probably help me finish high school.
Answers
Answer:
(3x+1)(x+5)
Step-by-step explanation:
Sorry for my handwriting lol hope this makes sense
A company uses two vans to transport
workers from a free parking lot to the
workplace between 7:00 and 9:00 a.m.
One van has 6 more seats than the other.
The smaller van makes two trips every
morning while the larger one makes only
one trip. The two vans can transport 57
people, maximum.
How many seats does the larger van have?
Answers
y is the seats in the large van = (x + 6). Since the large has 6 more seats.
Since the 2 vans can transport 57 people.
Small van makes 2 trips = 2x.
Large van makes one trip = (x + 6).
2x + (x +6) = 57
2x + x + 6 = 57
3x + 6 = 57
3x = 57 -6
3x = 51
x = 51/3
x = 17.
The larger van has (x + 6) = (17 + 6) = 23.
The larger van has 23 seats.
Answer:
The larger van has 23 seats
Step-by-step explanation:
Create a system of Equations:
1. Define variables.
> let x=small van and y=larger van
2. create 2 equations based on the information given.
> y = 6 + x
> 2x + y = 57
3. Use any method to solve
Substitution: 2x + (6 + x) = 57. x=17
now plug x in to the original equation to solve for y (the larger van)
y = 6 + 17 and y = 23
Elimination: 2y = 12 + 2x
y = 57 - 2x
3y = 69 and y = 23
The amount of time (t) in minutes it takes to make a coffee at Starbucks is related to (n) the number of coffees purchased. The equation is t = 2n − 3. How long does it take if a customer buys 5 coffees?
A. 13 minutes
B. 7 minutes
C. 4 minutes
D. None of these choices are correct.
Answers
7 minutes
Step-by-step explanation:\(t=2n-3\)
\(when\ n=5\)
\(t=2\times 5-3=7\ minutes\)
I hope this helps you
:)
A spring is attached at one end to support B and at the other end to collar A represented in the figure. Collar A slides along the vertical bar between points C and D. In the figure, the angle is the angle created as the collar moves between points Cand D. When the spring is stretched and the distance from point A to point Bis 5.3 feet, what is the value of e to the nearest tenth of a degree? 3 ft B 00000 А
Answers
The Distance from point A to point B is: 3.4 ft when θ = 28° and The value of θ is: 54.8°
Given,
A spring is attached at one end to support B and at the other end to collar A.
Part A: Reference angle (θ) = 28°
We have to find out the distance of point A to point B.
Adjacent = 3 ft (given)
Apply the trigonometry function to find AB
cos θ = adj / hypotenuse
Substituting all the values ,
cos 28°= 3/AB
AB = 3/cos 28°
AB = 3.4 ft (nearest tenth of a foot)
Part B:
It is given that Distance from point A to point B is 5.2 feet
We have to calculate the Value of θ
adjacent = 3 ft
hypotenuse = AB = 5.3 ft
To find θ , We will again apply the trigonometry function
cos θ = adjacent/hypotenuse
Substituting all the given values
cos θ = 3/5.3
θ = cos⁻¹ ( 3 / 5.3)
θ = 54.8°
That is,
The length of point A to point B is 3.4 feet
The value of θ is 54.8°
Learn more about trigonometry here;
https://brainly.com/question/16381132
#SPJ4
1
3
2
4 and B=
6
5
1
A=
2
4
5
Find A + B.
O A. A + B =
O AOS
8
6
10
4
o
B. A + B = 7
8
9
12
16
O c. A + B = 5
6
8
7
10
O D. A+B=
5 12
3 8
15 24
Answers
Answer:
A is your correct answer .
1. A + B =
This is right answer
Suggest at least 3 ways that parametric equation of a
plane can be helpful to visualize vectors in a plane.
Answers
Parametric equations of a plane can be helpful in visualizing vectors in a plane in the following ways:
Plotting Points on the Plane: By using the parametric equations, we can plot points on the plane by varying the parameters. This allows us to visualize the distribution of points and identify patterns or structures within the plane.
Representing Vector Directions: Parametric equations allow us to express vectors in terms of their components in the plane. We can use the parameters in the equations to represent different magnitudes and directions of vectors. By manipulating the parameters, we can observe how the vectors change and visualize their directions in the plane.
Understanding Vector Operations: Parametric equations provide a framework for performing vector operations in the plane. We can use the equations to add, subtract, or scale vectors, and visualize the results. This helps in understanding vector arithmetic and the geometric interpretation of vector operations.
Parametric equations of a plane provide a mathematical representation of the plane in terms of parameters. These equations allow us to visualize vectors in the plane by plotting points, representing vector directions, and understanding vector operations.
By plotting points on the plane using the parametric equations, we can observe the distribution of points and gain insights into the structure of the plane. This visualization can be useful in various applications, such as analyzing data patterns, understanding geometric relationships, or solving optimization problems.
Parametric equations also enable us to express vectors in terms of their components in the plane. By varying the parameters in the equations, we can represent different magnitudes and directions of vectors. This allows us to visualize the vector directions and observe how they change based on the parameters.
Furthermore, parametric equations provide a framework for performing vector operations in the plane. We can use the equations to add, subtract, or scale vectors, and visually observe the effects of these operations. This helps in understanding vector arithmetic and the geometric interpretation of vector operations in the context of the plane.
Overall, the parametric equations of a plane offer a powerful tool for visualizing vectors in a plane, enabling us to analyze the distribution of points, represent vector directions, and explore vector operations.
Therefore, parametric equations of a plane can be helpful in visualizing vectors in a plane in the following ways:
Plotting Points on the Plane: By using the parametric equations, we can plot points on the plane by varying the parameters. This allows us to visualize the distribution of points and identify patterns or structures within the plane.
Representing Vector Directions: Parametric equations allow us to express vectors in terms of their components in the plane. We can use the parameters in the equations to represent different magnitudes and directions of vectors. By manipulating the parameters, we can observe how the vectors change and visualize their directions in the plane.
Understanding Vector Operations: Parametric equations provide a framework for performing vector operations in the plane. We can use the equations to add, subtract, or scale vectors, and visualize the results. This helps in understanding vector arithmetic and the geometric interpretation of vector operations.
Learn more about parametric equations of a plane here:
https://brainly.com/question/30754186
#SPJ4
a population of fruit flies grows exponentially by the formula y=a ebt , where t is the time in days and y is the number of fruit flies. assume that there are 63 flies after 3 days and 121 flies after 13 days. how many flies are after 37 days?
Answers
The calculated number of flies after 37 days is 2,047.
The given growth of fruit flies is demonstrated by a formula \(y=a*e^{bt}\)
therefore, using simple formulation depending on the concept of multiplication, division, and addition we can solve the given question.
there are two scenario provided which generate two cases
first scenarios = 63 flies in 3 days
second scenario = 121 flies in 13 days
Using the provided data to initiate the calculation
\(= > 63 = a*e^{3b}\) ------> first equation
\(= > 121=a*e^{13b}\)-------------> second equation
simplifying the form of the equation by dividing the first equation by the second
\(121/63=e^{10b}\)
taking ㏒ on both sides
㏒\((\frac{121}{63})=10b\)
calculating concerning b
\(b=\)㏒\((\frac{121}{63})/10\)
staging the value of b in the first equation we get,
\(a=63/e^{3b}\)
finally using the current value t find the total number of flies after 37 days
\(y=a*e^{(bt)}\)
\((63/e^{3b} )e^{(37b)}\)
\(= 2,047\)
The calculated number of flies after 37 days is 2,047.
To learn more about multiplication,
https://brainly.com/question/29793687
#SPJ4
Here are two vectors:
A
=4
i
^
+3
j
^
−2
k
^
,
B
=−5
i
^
+3
j
^
+2
k
^
. Determine the following: a)
A
+
B
b)
A
−
B
c)
A
⋅
B
d)
A
×
B
e)
A
⋅(
A
×
B
)
Answers
For the given two vectors the results are:
a) A + B = -i^ + 6j^
b) A - B = 9i^
c) A · B = -15
d) A × B = Calculations not provided
e) A · (A × B) = Not calculable without A × B
Let's calculate the requested values using the given vectors:
A = 4i^ + 3j^ - 2k^
B = -5i^ + 3j^ + 2k^
a) A + B:
Adding the corresponding components, we get:
A + B = (4i^ + 3j^ - 2k^) + (-5i^ + 3j^ + 2k^)
= 4i^ + (-5i^) + 3j^ + 3j^ - 2k^ + 2k^
= -i^ + 6j^
Therefore, A + B = -i^ + 6j^.
b) A - B:
Subtracting the corresponding components, we get:
A - B = (4i^ + 3j^ - 2k^) - (-5i^ + 3j^ + 2k^)
= 4i^ - (-5i^) + 3j^ - 3j^ - 2k^ - 2k^
= 9i^
Therefore, A - B = 9i^.
c) A · B (dot product):
The dot product is calculated by multiplying the corresponding components and summing them:
A · B = (4)(-5) + (3)(3) + (-2)(2)
Calculating the values:
A · B = -20 + 9 - 4
= -15
Therefore, A · B = -15.
d) A × B (cross product):
The cross product is calculated using the determinant method. The cross product is only defined for three-dimensional vectors, so we'll omit the calculations here since the vectors A and B are in three dimensions.
e) A · (A × B):
To calculate A × B, we need the cross product of vectors A and B. Once we have the cross product, we can calculate the dot product with A.
Since we haven't calculated the cross product A × B, we cannot proceed to find A · (A × B) at this point.
To learn more about vector
https://brainly.com/question/29286060
#SPJ11
3. Aneesa thinks that (8x)^1/2 is equivalent to 8x^1/2
Do you agree or disagree? Justify your answer.
Answers
Answer:
x= 0 I believe the answer would be false.
Which choice is equivalent to the quotient below?
\( \frac{ \sqrt{5} }{ \sqrt{45} } \)
A. 9
B. 1/3
C. 1/81
D. 3
Answers
√5/√45 <— simply both terms by 5
= √1/√9 <— √5÷5 = 1 and √45 ÷ 5 = √9
= 1/√9
= 1/3
√1 = 1
(you can write 1 directly instead of √1)
√9 = 3
Consider the rectangle shown
2x-1
3x +5
If the perimeter of the rectangle is 52, what is the value of
Answers
Step-by-step explanation:
Perimeter of a rectangle= 2L + 2W
let the length be 2x-1 and breadth/ width = 3x+5
52= 2x-1 + 3x+5
52= 5x +4
collect like terms;
52-4 = 5x
48=5x
divide by the co- efficient of X
x= 9.6.
hope it helps. pls like and follow :-):-)
find the lengths of the segments with variable expressions
Answers
Answer:
EF = 10; AD = 3 ; BC = 17
Step-by-step explanation:
The median (EF) of a trapezoid equal half the sum of the length of the two bases of the trapezoid (AD and BC)
EF = 1/2 (AD + BC)
x = 1/2( x - 7 + 2x - 3)
x = 1/2 (3x - 10)
2x = 3x - 10 Multiply all terms by 2 or x = 3/2x - 5
-x = -10 x - 3/2x = -5
x = 10 -1/2x = -5
x = 10
So EF = 10
AD = x - 7 BC = 2x - 3
AD = 10 - 7 BC = 2(10) - 3
AD = 3 BC = 20 - 3
BC = 17
Need a bit of help, please. :D
Answers
Answer:
c.
Step-by-step explanation:
Please note that the angle A and B are somewhat close to 45deg, so we expect AC and BC to be close in length.
We can drop answer a on that basis.
We can also drop abswer d on the basis that AC is longer than AB there and that cannot be the case in a right triangle.
We can verify that for both b and c the Pythagoras theorem holds, so we need to choose the answer that fits the angles A and B. Te can check the tan of the angle to get the ratio between BC and AC.
tan(48.8deg) ~= 1.1423
1.6/1.4 ~= 1.1429; close enough.
So we choose answer c.
Can someone help please?
Triangle not drawn to scale
Given: m&A= 62°,m&C=28°,c=24cm. Then a
_?__cm to the nearest hundredth.
Answers
Answer:
a = 45.14
Step-by-step explanation:
First we need to determine whether this is a non-right triangle or a right triangle.
Since we have two angles already, we can determine whether the third angle is a right or non-right angle:
The sum of all the angles in a triangle will always add up to 180, so we have
180 - (62 + 28) = 180 - 90 = 90
Since we have a right triangle and only one side, we can use trigonometry to find the measure of a.
If we use ∠A as the reference angle, side a is our opposite angle and side c is our adjacent angle.
This means we must use tangent as \(tan=\frac{opposite}{adjacent}\):
\(tan (62)=\frac{a}{24}\\ 24*tan(62)=a\\45.137=45.14 = a\)
Which of the following R-squared values is the most satisfactory?
Mutiple Choice
a. 0.3
b. 0.5
c. 0
d. 75
e. −0.5
Answers
Among the given options, an R-squared value of 0.5 is the most satisfactory as it indicates a moderate level of relationship between the variables. So, the correct option is b.
R-squared is a statistical measure that represents the proportion of the variance in the dependent variable that can be explained by the independent variable(s). It ranges from 0 to 1, with 1 indicating a perfect fit and 0 indicating no relationship between the variables.
In this case, an R-squared value of 0.5 means that 50% of the variance in the dependent variable can be explained by the independent variable(s). This is considered a moderate level of explanatory power.
To know more about variance, visit
https://brainly.com/question/33654267
#SPJ11
Pls help this is confusing :/
Use matrices to determine the coordinates of the vertices of the rotated figure. Then graph the pre-image and the image of the same coordinate grid. \(Rot_{270}\) for ΔUVW with vertices U(-3,8), V(8,4), and W(6,-8) This is for pre-calculus!
Answers
The coordinates of triangle U'V'W' include U'(8, 3), V'(4, -8) and W'(-8, -6) and this is represented by graph A shown in the image attached below.
What is a transformation?A transformation can be defined as the movement of a point on a cartesian coordinate from its original (initial) position to a new location.
The types of transformation.In Geometry, there are different types of transformation and these include the following:
DilationReflectionRotationTranslationBased on the information provided, triangle UVW would be rotated counterclockwise through an angle of 270 degree at origin to produce triangle U'V'W', we have:
\(\left[\begin{array}{ccc}0&1\\-1&0\end{array}\right]\)
Therefore, the image of triangle UVW would be given by this matrix:
\(\left[\begin{array}{ccc}0&1\\-1&0\end{array}\right]\) \(\left[\begin{array}{ccc}-3&8&6\\8&4&-8\end{array}\right]\)
Image = \(\left[\begin{array}{ccc}8&4&-8\\3&-8&-6\end{array}\right]\)
Based on the image above, we can logically deduce that the coordinates of triangle U'V'W' include U'(8, 3), V'(4, -8) and W'(-8, -6) and this is represented by graph A shown in the image attached below.
Read more on transformations here: https://brainly.com/question/12518192
#SPJ1
Answer:
hi friend
Step-by-step explanation:
z = 73i - 32
What is the real part of z ?
What is the imaginary part of z?
Answers
Answer:
real: -32imaginary: 73Step-by-step explanation:
The real part is everything that does not multiply i. The imaginary part is everything that does multiply i.
Conventionally, the real part is written first:
z = -32 +73i
Re(z) = -32
Im(z) = 73
A group of individuals containing b boys and g girls is lined up in random order: that is, each of the (b + g)! permutations is assumed to be equally likely. What is the probability that the person in the i^th position, 1 lessthanorequalto i lessthanorequalto b + g is a girl?
Answers
The probability is g / (b + g).
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are.
Let Gi be the event that the person in the ith position is a girl.
let the simple space S is all the ways to order (b + g) people, where b for boys and g for girls.
then, P(Gi) = \(\frac{|Gi|}{|s|}\)
|s| = (b + g)! / b! g!
for the purpose of this problems, individuals of the same sex are indistinguishable.
since, if we put a girl in the ith position, the other (b + g - 1) positions can be filled in randomly.
|Gi| = (b + g - 1)! / (g - 1)! b!
then, P(Gi) = \(\frac{|Gi|}{|s|}\)
P(Gi) = [ (b + g - 1)! / (g-1)! b! ] / [ (b + g)! / b! g! ]
P(Gi) = g / (b + g)
Therefore, the probability is g / (b + g).
To learn more about probability visit : brainly.com/question/11034287
#SPJ4
the price of a gallon of unleaded gas was $2.83 yesterday. Today, the price rose to $2.90. find tge percentage increase. round ur answer to the nearest tenth of a percent
Answers
The price rose by \(2.5\%\)
What is percentage?A percentage is a number or ratio that represents a fraction of 100.
The change in price is
\(2.90 - 2.83 = 0.07\)
The increase percentage is
\(\text{p}=\dfrac{0.07\times100}{2.83}\)
\(\text{p}=2.473\)
Learn more about Percentage:
https://brainly.com/question/13450942
A sandwich shop offers five types of sandwiches in three different sizes in four different kinds of bread. You can add six different fillings (tomatoes, pickles, lettuce, onions, jalapenos, mushrooms) for $0.50 each. In how many ways can you personalize your sandwich
Answers
Assuming that you can choose only one type of sandwich, one size, one type of bread, and any combination of fillings, you can personalize your sandwich in the following way : 5 (types of sandwich) x 3 (sizes) x 4 (types of bread) x 2^6 (choices of fillings) = 5 x 3 x 4 x 64 = 3840
So, you can personalize your sandwich in 3840 different ways by choosing one type of sandwich, one size, one type of bread, and any combination of six different fillings.
Hi! I'd be happy to help you determine the number of ways you can personalize your sandwich at this shop.
1. Sandwich type: There are 5 types of sandwiches to choose from.
2. Sandwich size: There are 3 different sizes available.
3. Bread type: You can select from 4 different kinds of bread.
Now, let's consider the fillings. Since there are 6 fillings, each one can either be included or not included. This results in 2 options (yes or no) for each filling.
To calculate the total number of personalized sandwiches, we can multiply the options for each aspect of the sandwich:
5 (types) * 3 (sizes) * 4 (breads) * 2^6 (fillings) = 5 * 3 * 4 * 64 = 3840
Therefore, you can personalize your sandwich in 3840 different ways.
Learn more about combination here : brainly.com/question/31596715
#SPJ11
witch of the following is the beast reason to use cash for making purchases A. knowing what you have spent your money on is simple B. splitting bills with friends is easier C. Getting more cash from an ATM machine is easy to do D. keeping track of how much you have spent is simple
Answers
Keeping track of how much you have spent is simple. Option D
How does purchasing get easier?
Having cash on hand makes your spending more concrete and visible. Cash payments make it simpler to keep track of your spending because you can actually see the cash leave your wallet or hand.
You may get a better idea of how much you have spent by keeping track of the cash you have on hand and comparing it to the amount you started with. This might be especially useful for people who prefer a simpler approach to budgeting and want to exert more control over their spending patterns.
Learn more about cash purchases:https://brainly.com/question/28392657
#SPJ1
Solve each quadratic equation using any method.
x²+x-6=0
Answers
The solutions to the quadratic equation x² + x - 6 = 0 are x = 2 and x = -3.
To solve the quadratic equation x² + x - 6 = 0, we can use factoring, completing the square, or the quadratic formula. Let's solve it by factoring: Write the quadratic equation in the form ax² + bx + c = 0:
x² + x - 6 = 0
Factor the quadratic expression:
(x - 2)(x + 3) = 0
Set each factor equal to zero and solve for x:
x - 2 = 0 or x + 3 = 0
Solving for x in the first equation:
x - 2 = 0
x = 2
Solving for x in the second equation:
x + 3 = 0
x = -3
So the solutions to the quadratic equation x² + x - 6 = 0 are x = 2 and x = -3.
Learn more about quadratic equation here :
https://brainly.com/question/29269455
#SPJ11