is there a vector field g on ℝ3 such that curl(g) = x sin(y), cos(y), z − 3xy ?
Answers
Yes, there exists a vector field g on ℝ3 such that curl(g) = x sin(y), cos(y), z − 3xy.
To find such a vector field g, we can use the fundamental theorem of vector calculus. Let g(x,y,z) = P(x,y,z) i + Q(x,y,z) j + R(x,y,z) k be the vector field we are looking for.
Since the curl of g is given by curl(g) = ( ∂R/∂y - ∂Q/∂z ) i + ( ∂P/∂z - ∂R/∂x ) j + ( ∂Q/∂x - ∂P/∂y ) k, we can equate the components of curl(g) with the given function x sin(y), cos(y), z − 3xy to obtain a system of partial differential equations:
∂R/∂y - ∂Q/∂z = x sin(y)
∂P/∂z - ∂R/∂x = cos(y)
∂Q/∂x - ∂P/∂y = z − 3xy
Solving this system of equations, we can obtain the expressions for P, Q, and R. One possible solution is:
P(x,y,z) = z cos(y) - yz^2/2 + C1
Q(x,y,z) = x sin(y) + xz^2/2 - C2
R(x,y,z) = xz - y cos(y) - C3
where C1, C2, and C3 are constants of integration. It can be verified that the curl of this vector field is indeed equal to the given function.
For more questions like Vector click the link below:
https://brainly.com/question/29740341
#SPJ11
Related Questions
Let S = {v1 , , vk} be a set of k vectors in Rn, with k < n. Use a theorem about the matrix equation Ax = b to explain why S cannot be a basis for R^n Let A be an mx n matrix. Consider the statement. "For each b in R^m, the equation Ax -b has a solution." Because of a fundamental theorem about such matrix equations, this statement is equivalent to what other statements? Choose all that apply A. The columns of A span R^m B. Each b in R^m is a linear combination of the columns of A C. The rows of A span R^n D. The matrix A has a pivot position in each row. E. The matrix A has a pivot position in each column.
Answers
S cannot be a basis for \(R^{n }\)
What is Matrix ?
A matrix is a rectangular array of numbers or symbols arranged in rows and columns. Matrices are commonly used in mathematics, physics, engineering, computer science, and other fields to represent systems of linear equations, transformations, and other mathematical objects and operations.
The statement "For each b in \(R^{m }\), the equation Ax - b has a solution" is equivalent to the following statements:
A. The columns of A span \(R^{m }\)
B. Each b in \(R^{m }\) is a linear combination of the columns of A.
E. The matrix A has a pivot position in each column.
To explain why S cannot be a basis for \(R^{n }\) , we can use the fact that a set of vectors S = {v1, ..., vk} is a basis for \(R^{n }\) if and only if the matrix whose columns are the vectors in S is invertible. In this case, since k < n, the matrix whose columns are the vectors in S cannot be invertible because it has more columns than rows.
Therefore, S cannot be a basis for \(R^{n }\).
To learn more about Matrix from given link.
https://brainly.com/question/31017647
#SPJ1
Write an equation parallel to the line determined by the points (15, -6) and (-3, 13), through: (4, 2)
Answers
Answer:
The answer is
\(y = - \frac{19}{18} x + \frac{76}{2} \)Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the parallel line we must first find the slope of the original line
That's
Slope of the through points
(15, -6) and (-3, 13) is
\(m = \frac{13 - - 6}{ - 3 - 15} = - \frac{19}{18} \)Since the lines are parallel their slope are also the same
So slope of parallel line = - 19/18
Equation of the line using point (4,2) and slope -19/18 is
\(y - 2 = - \frac{19}{18} (x - 4) \\ y - 2 = - \frac{19}{18} x + \frac{38}{9} \\ y = - \frac{19}{18} x + \frac{38}{9} + 2\)We have the final answer as
\(y = - \frac{19}{18} x + \frac{76}{2} \)Hope this helps you
Answer:y=-1.583x-8.332
Step-by-step explanation:
First find slope from two points (-6-13)/(15+3)=-1.583
Now line is parallel so the slope would be same for the other line passing through (4,2) now as the general equation of line is
y=mx+c
2=-1.583(4)+c
Solving for c equals to -8.332
So final equation is
y=1.583x-8.332
2/x+4 = 3^x + 1
the approximate solution to the given equation after three iterations of successive approximations is when x is about.
answer choices are
-39/16
-35/-6
-37/16
-33/16
pls help :,)
Answers
After three iterations of successive approximations, the approximate solution to the given equation is when x is about -37/16.
To find the approximate solution to the equation 2/x + 4 = \(3^{x}\) + 1, we can use an iterative method such as the Newton-Raphson method. Starting with an initial guess, we can refine the estimate through successive iterations. After three iterations, we find that x is approximately -37/16.
The Newton-Raphson method involves rearranging the equation into the form f(x) = 0, where f(x) = 2/x + 4 - \(3^{x}\) - 1. Then, the iterative formula is given by:
x[n+1] = x[n] - f(x[n]) / f'(x[n])
By plugging in the initial guess into the formula and repeating the process three times, we arrive at an approximate solution of x ≈ -37/16.
It is important to note that the solution is an approximation and may not be exact. However, after three iterations, the closest option to the obtained approximate solution is -37/16, which indicates that -37/16 is the approximate solution to the given equation.
Learn more about iterations here:
https://brainly.com/question/30941646
#SPJ11
Given that
P
=
x
+
y
.
Find
P
when:
x
=
−
25
and
y
=
−
25
Answers
hope this helps
The results of a paired-difference test are shown below to the right. d = 5.6
a. Construct and interpret a 99% confidence interval estimate for the paired difference Sd =0.25 in mean values.
b. Construct and interpret a 90% confidence interval estimate for the paired difference n=16 in mean values_ (Round to two decimal places as needed:) Choose the correct answer below:
OA This interval will contain the true population mean 90% of the time_
OB. There is a 90% chance that the true population mean is contained in the interval.
Oc: If many random samples of this size were taken and intervals constructed, 90% of them would contain the true population mean: 0
D. Approximately 90% of the differences will be contained in the interval.
Answers
If many random samples of this size were taken and intervals constructed, 90% of them would contain the true population mean. In repeated sampling, about 90% of the constructed confidence intervals will capture the true population mean difference. The correct answer is C.
When we construct a confidence interval, it is important to understand its interpretation. In this case, the correct answer (Oc) states that if we were to take many random samples of the same size and construct confidence intervals for each sample, approximately 90% of these intervals would contain the true population mean difference.
This interpretation is based on the concept of sampling variability. Due to random sampling, different samples from the same population will yield slightly different sample means.
The confidence interval accounts for this variability by providing a range of values within which we can reasonably expect the true population mean difference to fall a certain percentage of the time.
In the given scenario, when constructing a 90% confidence interval for the paired difference, it means that 90% of the intervals we construct from repeated samples will successfully capture the true population mean difference, while 10% of the intervals may not contain the true value.
It's important to note that this interpretation does not imply a probability or chance for an individual interval to capture the true population mean. Once the interval is constructed, it either does or does not contain the true value. The confidence level refers to the long-term behavior of the intervals when repeated sampling is considered.
Learn more about confidence interval at https://brainly.com/question/15576092
#SPJ11
find the minimum cost of a rectangular box of volume 170 cm3 whose top and bottom cost 8 cents per cm2 and whose sides cost 9 cents per cm2.
Answers
Therefore the minimum cost of a rectangular box of volume is x = 4.641588834 cents.
What is the volume of cuboid?A cuboid is a six-faced solid known as a hexahedron in geometry. Four-sided quadrilaterals make up its faces. A cuboid is a hexahedron, a solid with six faces, and the word "cuboid" means "like a cube" in the sense that a cuboid can become a cube by changing the length of its edges or the angle between its faces and edges. Four-sided quadrilaterals make up its faces. A cuboid can be made to look more like a cube by varying the lengths of its edges or the angles between its faces and edges. A cuboid's volume is equal to the sum of its length, breadth, and height. The opposite faces of a cuboid on a rectangular cuboid are equal, and all the angles are at right angles.
To know more about volume ,visit:
brainly.com/question/28770143
#SPJ4
the curve of a model that performs well on false positives and true positives is in what quadrant (or region) of a roc curve?
Answers
The more that the ROC curve hugs the top left corner of the plot, the better the model does at classifying the data into categories
A true positive result is one in which the model accurately predicts the positive class. A true negative, on the other hand, is a result in which the model correctly predicts the negative class.
A false positive is an outcome in which the model forecasts the positive class inaccurately. A false negative is an outcome in which the model forecasts the negative class inaccurately.
The ROC curve is obtained by plotting the true positive rate (TPR) against the false positive rate (FPR) at various threshold values.
The true-positive rate is also known as sensitivity, recall, and likelihood of detection.
To learn more about Receiver operating characteristic
brainly.com/question/28197236
#SPJ4
Find a recursive definition for a function called "duplicate". The function will take a list as a parameter and return a new list. Each element in the original list will be duplicated in the ne' list. For example, duplicate (⟨1,2,3⟩) would return ⟨1,1,2,2,3,3⟩.
Answers
A recursive definition for the function called "duplicate" that takes a list as a parameter and returns a new list in which each element of the original list is duplicated can be defined as follows:
- If the input list is empty, the output list is also empty.
- If the input list is not empty, the output list is obtained by first duplicating the first element of the input list and then recursively applying the "duplicate" function to the rest of the input list.
More formally, the recursive definition for the "duplicate" function can be expressed as follows:
- duplicate([]) = []
- duplicate([x] + L) = [x, x] + duplicate(L)
- duplicate([x1, x2, ..., xn]) = [x1, x1] + duplicate([x2, x3, ..., xn])
This definition can be read as follows: if the input list is empty, the output list is also empty; otherwise, the output list is obtained by duplicating the first element of the input list and then recursively applying the "duplicate" function to the rest of the input list.
In summary, the recursive definition for the "duplicate" function takes a list as a parameter and returns a new list in which each element of the original list is duplicated.
Know more about recursive definition here:
https://brainly.com/question/28105916
#SPJ11
At Lara' party, 4 gallon of fruit punch are hared equally among 18 friend. How much fruit punch will each peron get?
Answers
Answer: About 0.2 gallons
Step-by-step explanation: 4/18=0.2 repeating, so each person gets about 0.2 gallons.
Each of her friend will get 4 and a half gallons of juice.
What is division?Division is one of the four main arithmetical operations by which we find the equal distribution of something.
Given that, At Lara's party, 4 gallon of fruit punch are shared equally among 18 friend.
To find how much each of them got, we will divide total amount of punch by total number friends
Amount of juice each of them gets, = 18/4 = 4.5
Hence, Each of her friend will get 4 and a half gallons of juice.
For more references on divisions, click;
https://brainly.com/question/21416852
#SPJ2
Testing more properties of the Cobb-Douglas utility function Check if the Cobb-Douglas utility function u(x
1
,x
2
)=x
i
α
x
2
β
, where α,β>0, satisfies the following properties: (a) local nonsatiation, (b) decreasing marginal utility for both goods 1 and 2, (c) quasi-concavity, and (d) homotheticity.
Answers
The Cobb-Douglas utility function satisfies the properties of local non-satiation, decreasing marginal utility for both goods, quasi-concavity, and homotheticity.
The Cobb-Douglas utility function u(x1, x2) = xi^(α) * x2^(β), where α and β are both greater than zero, satisfies the following properties:
(a) Local non-satiation:
This property states that at each point of the consumption set, there is always another bundle that is arbitrarily close and strictly preferred. Thus, the function has local non-satiation.
(b) Decreasing marginal utility for both goods 1 and 2: The marginal utility of a good measures the utility obtained by consuming one more unit of it. The marginal utility of x1 can be obtained as:
MU1 = α * xi^(α−1) * x2^(β)
The marginal utility of x2 can be obtained as:
MU2 = β * xi^(α) * x2^(β−1)
Therefore, both marginal utilities are decreasing in x1 and x2, satisfying this property.
(c) Quasi-concavity:
The Cobb-Douglas function is quasi-concave. This means that the upper contour set of any level set of the function is convex. This can be proved by taking the second partial derivative of the function and checking whether it is negative or not.
(d) Homotheticity:
The Cobb-Douglas function is homothetic. This means that its shape is independent of the total level of utility. The proof can be achieved by checking whether the function is homogeneous of degree one or not. This is true, since multiplying the inputs by any positive scalar λ leads to a proportional increase in the output.
In conclusion, the Cobb-Douglas utility function satisfies all four properties - local non-satiation, decreasing marginal utility for both goods 1 and 2, quasi-concavity, and homotheticity.
Learn More About marginal utility from the below link:
https://brainly.com/question/15050855
#SPJ11
Write an equation in slope intercept form plz help
Answers
The slope-intercept form is \(y = mx + b\)where m is the slope and b is the y-intercept.
The equation is already in slope-intercept form.
\(y = - x + 4\)
Answer:
Step-by-step explanation:
Q8:
y= -x+4 (given)
Slope of given the line=-1
For required slope which is passing through (6,5):
Using Point slope form:
\(y-y_{1} = m(x-x_{1} )\)
y-5=-1(x-6) (m=-1 because lines are parallel)
y-5=-x+6
x+y-5-6=0
x+y-11=0
Q9:
y=-4x-7
slope of the given line:
m=-4
Slope of required line:
m=1/4
Using Point slope form:
\(y-y_{1} = m(x-x_{1} )\)
y+1=1/4(x-8)
4y+4=x-8
x-4y-8-4=0
x-4y-12=0
Which of the following is not a polynomial?
a.4/x+x/7
b.x^2-4
c.-4/7
d.x^2-4+7x
Answers
The expression which does not represent a polynomial among the given answers choices is; Choice A; 4/x + x/7.
Which answer choice does not represent a polynomial?As evident in the task content; the answer choice which is not a polynomial is to be identified.
On this note, recall that a polynomial requires that the power of the variables is greater or equal to zero.
Since x exists as a denominator (with power -1) in the answer choice A;
Ultimately, the expression which is not a polynomial is; Choice A: 4/x + x/7.
Read moee on polynomial;
https://brainly.com/question/4142886
#SPJ1
Write an equation in slope-intercept form for the line that passes through (0,4) and is parallel to the line described by y=3x-7
Answers
slope-intercept form of a line (L1): y = mx + b; where m is the slope and b the y - intercept.
If two lines are parallel, that means the slope of both equations are equal.
L2: y = 3x - 7, m = 3
So, m for L1 is m = 3.
Now we just need to find y - intercept, as follows:
L1 passes through (0,4), then:
4 = 3(0) + b
4 = 0 + b
b = 4
The equation for the line is y = 3x + 4
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give a counterexample.
(a) lim x→4 2x x − 4 − 8 x − 4 = lim x→4 2x x − 4 − lim x→4 8 x − 4
(b) If lim x→5 f(x) = 0 and lim x→5 g(x) = 0, then lim x→5 f(x) g(x) does not exist.
(c) If f(3) = 2 and lim x→3+ f(x) = 2, then lim x→3− f(x) = 2.
(d) If lim t→0 h(t) does not exist, then h(0) cannot exist.
Answers
lim x→4 2x x − 4 − 8 x − 4 = lim x→4 2x x − 4 − lim x→4 8 x − 4, If lim x→5 f(x) = 0 and lim x→5 g(x) = 0, then lim x→5 f(x) g(x) does not exist, If f(3) = 2 and lim x→3+ f(x) = 2, then lim x→3− f(x) = 2, If lim t→0 h(t) does not exist, then h(0) cannot exist all these Limits statement are False
What do you mean by limits?A limit in mathematics is a value that a function approaches when the input gets closer to a certain value. Limits are used to find a function's derivative and integral as well as to characterize how a function behaves around particular places.
lim x -> c f(x) = L
(a) False.
According to the rules of limits, if both limits are present, the limit of a sum of two functions is equal to the total of their limits. The assertion, however, cannot be valid if one or both of the boundaries do not exist.
(b) False.
According to the limit laws, if the sum of two functions approaches 0, then the sum of their limits also does. The opposite of this statement is untrue, though.
In this instance, even if x approaches 5 and both f(x) and g(x) approach 0, the product of their limits, f(x)g(x), may not exist at all or may approach a non-zero value.
(c) False.
A function's limit as x gets closer to a number from the right is not always the same as the limit as x gets closer to the same number from the left.
Although f(3) = 2 in this instance and lim x3+ f(x) = 2, the limit of f(x) as x approaches 3 from the left may not be 2.
(d) False.
The absence of a limit does not imply the existence of the function's value at that time.
In this instance, the value of h(0) may still exist even though the limit of h(t) as t approaches 0 does not exist.
To know more about function visit:
brainly.com/question/29796477
#SPJ4
All these given Limit statement are False.
(a) lim x→4 2x x − 4 − 8 x − 4 = lim x→4 2x x − 4 − lim x→4 8 x − 4
(b) If lim x→5 f(x) = 0 and lim x→5 g(x) = 0, then lim x→5 f(x) g(x) does not exist
(c) If f(3) = 2 and lim x→3+ f(x) = 2, then lim x→3− f(x) = 2
(d) If lim t→0 h(t) does not exist, then h(0) cannot exist.
What do you mean by limits?A limit in mathematics is a value that a function approaches when the input gets closer to a certain value. Limits are used to find a function's derivative and integral as well as to characterize how a function behaves around particular places.
lim x -> c f(x) = L
(a) False.
According to the rules of limits, if both limits are present, the limit of a sum of two functions is equal to the total of their limits. The assertion, however, cannot be valid if one or both of the boundaries do not exist.
(b) False.
According to the limit laws, if the sum of two functions approaches 0, then the sum of their limits also does. The opposite of this statement is untrue, though.
In this instance, even if x approaches 5 and both f(x) and g(x) approach 0, the product of their limits, f(x)g(x), may not exist at all or may approach a non-zero value.
(c) False.
A function's limit as x gets closer to a number from the right is not always the same as the limit as x gets closer to the same number from the left.
Although f(3) = 2 in this instance and lim x3+ f(x) = 2, the limit of f(x) as x approaches 3 from the left may not be 2.
(d) False.
The absence of a limit does not imply the existence of the function's value at that time.
In this instance, the value of h(0) may still exist even though the limit of h(t) as t approaches 0 does not exist.
To know more about functions visit:
brainly.com/question/29796477
#SPJ4
Pls hurry!! It’s a quick question
Answers
Answer:
3/2
Step-by-step explanation:
. Carrie and Brad both ordered medium pizzas from Pizzazz. Carrie's pizza had 3 toppings
and cost $12.75 while Brad's pizza had 5 toppings and cost $14.25. Which equation
models this linear relationship where x represents the number of toppings and y represents
the total cost of the pizza?
Answers
Answer: It will be 0.75x+10.5
Step-by-step explanation:
Because if we were to do 12.75-10.5, we get 2.25, 2.25/0.75=3, it matches Carrie's pizza's amount of toppings, same with Brad. Goodluck on your DLA as you are on Aware Testing for Cinco, I won't tell you the school name because I don't want stalkers to track us down.
Find the length (distance) of a pen that starts at the 4.1 inch mark on a ruler and ends at 11 inches
Answers
Answer:
All we need to do is 11 - 4.1. we know to turn 4.1 into a 5, we need to add 0.9. With this knowledge, we can do the equation 6.9 + 4.1, which equals 11. So, the length of the pen is 6.9 inches.
A brainliest would help a lot!
Have a good day!
Sincerely,
didntask
Find the value of x. Round to the nearest tenth.
Answers
x = 30sin21 = 10.75 = 10.8 (to nearest tenth)
Someone already asked this question but wrong answer. PLS HELP!!!
[x/(y-1)](-4)-[xy+(-3)]/(-1) if x= -5 and y= -2
Answers
The worth of expression at x = - 5 and y = - 2 is,
⇒ 1/3
A numerical expression is characterized as the assortment of numbers factors and works by utilizing operations like expansion, deduction, multiplication, and division.
Considering that;
The expression is,
⇒ ([x/(y - 1)](- 4) - [xy + (- 3)]/(- 1)
Presently, We can place x and y in the above expression as;
⇒ ([x/(y - 1)](- 4) - [xy + (- 3)]/(- 1)
⇒ [- 5/(- 2 - 1) ] (- 4) - [-5×-2 + (- 3)]/(- 1)
⇒ [ - 5/ - 3 ] (- 4) - [10 - 3]/(- 1)
⇒ - 20/3 + 7
⇒ 1/3
In this way, The worth of expression at x = - 5 and y = - 2 is,
⇒ 1/3
to know more about multiplication click here:
https://brainly.com/question/1135170
#SPJ4
Human finger nails grow an average of 3.47mm per month. How much will they grow in 20 months
Answers
....................
Alex defeated 10 gyms today! She started with four hundred and forty coins and now has five hundred and forty coins
Find the Percent of increase
Answers
The percentage increase is 22.72%
How to determine the percentage increase?The given parameters are:
Initial = 440 coins
Final = 540 coins
The percentage increase is calculated as:
%Increase = (Final - Initial)/Initial * 100%
So, we have:
%Increase = (540 - 440)/440 * 100%
Evaluate the difference
%Increase = 100/440 * 100%
Evaluate the quotient
%Increase = 0.2272 * 100%
Evaluate the product
%Increase = 22.72%
Hence, the percentage increase is 22.72%
Read more about percentage increase at:
https://brainly.com/question/11360390
#SPJ1
Round off 2876.987 to nearest unit.
pls answer
Answers
222222345678975433382616273485
Using the data below, what is the value of the absolute percent error for week 3? Week Time Series Value Forecast 1 7 5.00 2 5 8.00 3 4 3.00 4 3 6.00 Submit Answer format: Number: Round to: 2 decimal places.
Answers
The value of the absolute percent error for week 3 is 25.00%.
To calculate the absolute percent error for week 3, we need to find the absolute difference between the forecasted value and the actual value, and then divide it by the actual value. Finally, we multiply the result by 100 to convert it to a percentage.
To find the absolute percent error for week 3, we'll use the formula:
Absolute Percent Error = |(Actual Value - Forecasted Value) / Actual Value| * 100
For week 3:
Actual Value = 4.00
Forecasted Value = 3.00
Absolute Percent Error = |(4.00 - 3.00) / 4.00| * 100
= |1.00 / 4.00| * 100
= 0.25 * 100
= 25.00
Therefore,For week three, the absolute percent error value is 25.00%.
learn more about percent from given link
https://brainly.com/question/24877689
#SPJ11
For a large order of brownies. Ms. Perry made 8/8 kg of fudge in her kitchen. She then got 1/6 kg from Mrs. Marshall. If she needs a total of 1 1/8kg for brownies, how much more fudge does she needs to make?
Answers
Answer:
Ms. Perry needs to make an additional 1/24 kg of fudge.
Step-by-step explanation:
Ms. Perry has a total of 8/8 + 1/6 = 13/6 kg of fudge. She needs 1 1/8 kg of fudge for the brownies, which is equivalent to 9/8 kg. To find how much more fudge she needs to make, we can subtract the amount of fudge she already has from the amount she needs:
9/8 - 13/6 = 27/24 - 26/24 = 1/24
Therefore, Ms. Perry needs to make an additional 1/24 kg of fudge.
a 25 foot ladder is leaned against the side of a building 2 feet from the base of the building. how far up the wall does the ladder reach and what is the angle of elevation for the ladder both to the nearest tenth?
Answers
Answer:
The ladder reaches up to 23.2 feet up the side of the building and the angle of elevation is 78.7 degrees to the nearest tenth. To calculate these values, you can use the Pythagorean Theorem. Let x be the distance the ladder reaches up the wall, and let y be the distance from the base of the building to where the ladder is leaning against the wall. Then, the Pythagorean Theorem states that x2 + y2 = 252, or x2 = 252 - y2. Since y = 2, then x2 = 252 - 22 = 676. Solving for x gives us x = 26, so the ladder reaches up to 26 feet. To calculate the angle of elevation, we can use trigonometry. We know that the opposite side is 26 feet and the adjacent side is 2 feet, so by using the tangent function, we can calculate the angle of elevation as tan-1(26/2) = 78.7 degrees.
the median and mean of : 24 , 44 , 10 , 22
Answers
To find the mean, we add up all the numbers and divide by the total number of numbers.
Mean = (24 + 44 + 10 + 22) / 4 = 25
Answer:
The mean is 25 and the median is 23
Tính đạo hàm của hàm số sau
y=x^3+x^2+1
Answers
\(y = {x}^{3} + {x}^{2} + 1 \\ y = {x}^{5} + 1 \\ y - 1 = {x}^{5} \)
which of the following would be considered a fee for a checking account?
A. Monthly service fee
B. Debit card fee
C. Overdraft fee
D. All of the above
Answers
Answer:
you're answer would be d
Answer:
D. All of the above
Step-by-step explanation:
Can someone help me with this 7th-grade math problem it is ratios I will give brainliest if it is correct so make sure it is correct
Answers
Answer:
c
Step-by-step explanation:
15 divided by 10= 1.5
21 divided by 14= 1.5
Answer: C is correct
Step-by-step explanation:
If you put in the fractions into a calculator you will see that both ratios are equal to 1.5
what is the probability of picking a blue marble randomly out of a bag of 6 blue marbles, 3 black marbles, and 8 orange marbles while rolling a 3 on a 6-sided dice at the same time?
Answers
Using the concepts of probability, we got that 0.063 is the probability of picking a blue marble randomly out of a bag of 6 blue marbles, 3 black marbles, and 8 orange marbles while rolling a 3 on a 6-sided dice at the same time
We know very well that probability is defined as the fraction of number of favorable outcomes to the total number of outcomes.
Here, we are rolling a 6-faced dice.
Getting 3 on the top face of dice is same as the any number getting from 1 to 6 on the top face of the dice.
So, every number has equal probability to come on the top face, therefore the probability of getting 3 on the top face of dice is (1/6)
Now, similarly total number of marbles in the bag=6 blue +3 black+8 orange marble=17 marbles.
Now, picking one marble from 17 marble is can be done in \(^1^7C_1\) ways, similarly choosing 1 blue marble from 6 marble can be done in \(^6C_1\) ways.
So, probability of picking 1 blue marble randomly=6/17
Now, the probability of picking 1 blue marble from 17 marbles along with rolling dice probability is given by =(6/17)×(1/6)=(1/17)=0.063
Hence, the probability of picking a blue marble randomly out of a bag of 6 blue marbles, 3 black marbles, and 8 orange marbles while rolling a 3 on a 6-sided dice at the same time is 0.063
To know more about probability, visit here:
https://brainly.com/question/11234923
#SPJ4