a bucket that weighs 4 pounds and a rope of negligible weight are used to draw water from a well that is 83 feet deep. the bucket is filled with 35 pounds of water and is pulled up at a rate of 1.8 feet per second, but water leaks out of a hole in the bucket at a rate of 0.25 pounds per second. find the work done pulling the bucket to the top of the well. your answer must include the correct units. (you may enter lbf or lb*ft for ft-lb.)

To evaluate the vectors 2v - u given u = (1, -3) and v = (-4, 2), you have to first determine the values of 2v and then subtract u from the resulting vector.

To get 2v, you can multiply v by 2 as shown below:2v = 2(-4, 2)

= (-8, 4)

To subtract u from 2v, you can subtract the x-component of u from the x-component of 2v and also subtract the y-component of u from the y-component of 2v.

That is:(-8, 4) - (1, -3) = (-8 - 1, 4 - (-3)) = (-9, 7)

Therefore, the vector 2v - u is (-9, 7).

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Im so sorry i don't know.

Answer:

1/2cup

as if 3and1/2cup is divided into 4people then in every one will get half cup.

Answer:

Each person gets \(\frac{7}{8}\) cup of pudding.

Step-by-step explanation:

The problem is essentially asking;

\(3\frac{1}{2}\) ÷ 4

(4 because the pudding has to be divided amongst Regina and her 3 friends, hence 4 people)

To divide fractions, first one has to convert from improper fractions to mixed numbers;

\(\frac{7}{2}\) ÷ 4

Next, one has to reciprocate the second fraction, since the second number is an integer, one simply has to put the number as the denominator, and set the numerator to 1.

\(\frac{7}{2}\) * \(\frac{1}{4}\)

Now, one has to perform the multiplication, simply multiply the numerators and denominators together (there is no way of simplifying in this problem);

\(\frac{7}{8}\)

Each person gets \(\frac{7}{8}\) cup of pudding.

1.1)Consider the vectors u = (3,-4,-1) and v = (0,5,2). Find u v and determine the angle between u and v.

Solution:Given vectors areu = (3,-4,-1) and v = (0,5,2).The dot product of two vectors is given byu.v = |u||v|cosθ

where, θ is the angle between two vectors.Let's calculate u.vu.v = 3×0 + (-4)×5 + (-1)×2= -20

Hence, u.v = -20The magnitude of vector u is |u| = √(3² + (-4)² + (-1)²)= √26The magnitude of vector v is |v| = √(0² + 5² + 2²)= √29

Hence, the angle between u and v is given byu.v = |u||v|cosθcosθ = u.v / |u||v|cosθ = -20 / (√26 × √29)cosθ = -20 / 13∴ θ = cos⁻¹(-20 / 13)θ ≈ 129.8°The angle between vectors u and v is approximately 129.8°2.1)Determine if the three vectors u = (1,4,-7), v = (2,-1, 4) and w = (0, -9, 18) lie in the same plane or not.Solution:

To check whether vectors u, v and w lie in the same plane or not, we can check whether the triple scalar product is zero or not.The triple scalar product of vectors a, b and c is defined asa . (b × c)

Let's calculate the triple scalar product for vectors u, v and w.u . (v × w)u . (v × w) = (1,4,-7) . ((2, -1, 4) × (0,-9,18))u . (v × w) = (1,4,-7) . (126, 8, 18)u . (v × w) = 0Hence, u, v and w lie in the same plane.2.3)Determine if the line that passes through the point (0, -3, -8) and is parallel to the line given by x = 10 + 3t, y = 12t and z=-3-t passes through the xz-plane.

If it does give the coordinates of the point.Solution:We can see that the given line is parallel to the line (10,0,-3) + t(3,12,-1). This means that the direction ratios of both lines are proportional.

Let's calculate the direction ratios of the given line.The given line is parallel to the line (10,0,-3) + t(3,12,-1).Hence, the direction ratios of the given line are 3, 12, -1.We know that a line lies in a plane if the direction ratios of the line are proportional to the direction ratios of the plane.

Let's take the direction ratios of the xz-plane to be 0, k, 0.The direction ratios of the given line are 3, 12, -1. Let's equate the ratios to check whether they are proportional or not.3/0 = 12/k = -1/0We can see that 3/0 and -1/0 are not defined. But, 12/k = 12k/1Let's equate 12k/1 to 3/0.12k/1 = 3/0k = 0

Hence, the direction ratios of the given line are not proportional to the direction ratios of the xz-plane.

This means that the line does not pass through the xz-plane.2.4)Determine the equation of the plane that contains the points P = (1, -2,0), Q = (3, 1, 4) and Q = (0,-1,2).Solution:Let the required plane have the equationax + by + cz + d = 0Since the plane contains the point P = (1, -2,0),

substituting the coordinates of P into the equation of the plane givesa(1) + b(-2) + c(0) + d = 0a - 2b + d = 0This can be written asa - 2b = -d ---------------(1

)Similarly, using the points Q and R in the equation of the plane givesa(3) + b(1) + c(4) + d = 0 ---------------(2)and, a(0) + b(-1) + c(2) + d = 0 ---------------(3)E

quations (1), (2) and (3) can be written as the matrix equation shown below.[1 -2 0 0][3 1 4 0][0 -1 2 0][a b c d] = [0 0 0]

Let's apply row operations to the augmented matrix to solve for a, b, c and d.R2 - 3R1 → R2[-2 5 0 0][3 1 4 0][0 -1 2 0][a b c d] = [0 -3 0]R3 + R1 → R3[-2 5 0 0][3 1 4 0][0 3 2 0][a b c d] = [0 -3 0]3R2 + 5R1 → R1[-6 0 20 0][3 1 4 0][0 3 2 0][a b c d] = [-15 -3 0]R1/(-6) → R1[1 0 -3⅓ 0][3 1 4 0][0 3 2 0][a b c d] = [5/2 1/2 0]3R2 - R3 → R2[1 0 -3⅓ 0][3 -1 2 0][0 3 2 0][a b c d] = [5/2 -3/2 0]Now, let's solve for a, b, c and d.3b + 2c = 0[3 -1 2 0][a b c d] = [-3/2 1/2 0]a - (6/7)c = (5/14)[1 0 -3⅓ 0][a b c d] = [5/2 1/2 0]a + (3/7)c = (3/14)[1 0 -3⅓ 0][a b c d] = [1/2 1/2 0]a = 1/6(2) - 1/6(0) - 1/6(0)a = 1/3Hence,a = 1/3b = -2/3c = -1/7d = -5/7The equation of the plane that passes through the points P = (1, -2,0), Q = (3, 1, 4) and R = (0,-1,2) is given by1/3x - 2/3y - 1/7z - 5/7 = 0.

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Check the picture below.

The weight of an object is given by the formula weight = mass * gravity, where gravity is approximately 9.8 m/\(s^2\). So, in this case, the weight of the object is 10 kg * 9.8 m/\(s^2\) = 98 N.

Since the displacement of the object from its equilibrium position is 9.8 cm = 0.098 m, we can set up the equation:

98 N = K * 0.098 m

Solving for K, we find:

K = 98 N / 0.098 m = 1000 N/m

Now, let's formulate the initial value problem for y(t). The displacement of the object from its equilibrium position is denoted by y(t), and we need to find the equation involving y(t), its first derivative y'(t), its second derivative y''(t), and time t.

Using Newton's second law, the sum of the forces acting on the object is equal to the mass of the object times its acceleration. The forces acting on the object are the force exerted by the spring, given by -K * y(t), and the force F(t) given in the problem. So, we have:

m * y''(t) = -K * y(t) + F(t)

Substituting the values for m and K, we have:

10 kg * y''(t) = -1000 N/m * y(t) + 70 N * cos(8t)

This is the initial value problem for y(t).

To solve the initial value problem for y(t), we need to find the equation of motion for y(t). This is a second-order linear non-homogeneous differential equation. The general solution to this type of equation is a sum of the complementary solution (the solution to the homogeneous equation) and a particular solution (any solution that satisfies the non-homogeneous part).

The complementary solution is found by setting F(t) to zero:

10 kg * y''(t) = -1000 N/m * y(t)

The characteristic equation for this homogeneous equation is:

10\(r^2\) + 1000 = 0

Solving for r, we find r = ±sqrt(-100) = ±10i

So, the complementary solution is:

y_c(t) = c1 * cos(10t) + c2 * sin(10t)

Now, we need to find a particular solution. In this case, since F(t) is of the form A * cos(8t), a particular solution can be assumed to be of the form:

y_p(t) = A * cos(8t)

Substituting this into the differential equation, we get:

-1000 N/m * (A * cos(8t)) = 70 N * cos(8t)

Simplifying, we find A = -0.07 m.

Therefore, the particular solution is:

y_p(t) = -0.07 * cos(8t)

The general solution is the sum of the complementary and particular solutions:

y(t) = y_c(t) + y_p(t)

     = c1 * cos(10t) + c2 * sin(10t) - 0.07 * cos(8t)

To determine the maximum excursion from equilibrium made by the object, we need to find the maximum value of |y(t)|.

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L((7,8)) = (-9,23).  To find the value of L((7,8)), we can use the linearity property of the linear operator L.

Since L is a linear operator, we can express any vector in R² as a linear combination of the basis vectors (1,0) and (0,1).

We have L((1,2)) = (-2,3) and L((1,-1)) = (5,2). Therefore, we can express (7,8) as (7,8) = 7(1,2) + 1(1,-1).

Using the linearity property, we can distribute the linear operator L over the linear combination:

L((7,8)) = L(7(1,2) + 1(1,-1))

= 7L((1,2)) + L((1,-1))

= 7(-2,3) + (5,2)

= (-14,21) + (5,2)

= (-9,23)

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Answer:

Answer is (D)    x2 – 4x – 12

Step-by-step explanation:

edge 2020 test

The study would use a simple random sampling because it would be easy to randomly select. The study would use cluster sampling because the of fall into naturally occurring subgroups. The study would use stratified sampling because it would be important to have members from each segment of the population.

The study is a sample survey, because the population is for it to be practical to record all of the responses.

a. The study would use a simple random sampling because it would be easy to randomly select members of the population. Simple random sampling is a type of probability sampling that is used when the population is homogenous and every member has an equal chance of being selected for the sample.

b. The study would use cluster sampling because the members of the population fall into naturally occurring subgroups. Cluster sampling is a type of probability sampling that is used when the population is heterogeneous and can be divided into naturally occurring subgroups.

c. The study would use stratified sampling because it would be important to have members from each segment of the population. Stratified sampling is a type of probability sampling that is used when the population is heterogeneous and can be divided into segments or strata based on certain characteristics.

d. The study is a sample survey, because the population is too large for it to be practical to record all of the responses. Sample survey is a type of survey that collects data from a sample of the population, rather than the entire population. This is often done when the population is too large or when it is not practical to survey the entire population.

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Answer: a) To find the equation of line PS, we first need to find the slope of the line L1 which is given by:

slope = (y2 - y1) / (x2 - x1)

= (3 - 5) / (-2 - 0)

= 2/2

= 1

Since PS is parallel to L1, it also has the same slope. We can now use the point-slope form of the equation of a line to find the equation of PS, using the point P(1,2):

y - y1 = m(x - x1)

y - 2 = 1(x - 1)

y - x + 2 = 0

Therefore, the equation of line PS is y - x + 2 = 0.

b) To find the coordinates of S, we know that S lies on line PS and also on the line passing through points (6,4) and P(1,2). Let's call the coordinates of S as (x,y). Since S lies on line PS, we know that y - x + 2 = 0. We can also use the slope formula to find the slope of line PS:

slope_PS = (y - 2) / (x - 1)

Since PS is parallel to line L1, we know that slope_PS = 1. Therefore, we can write:

(y - 2) / (x - 1) = 1

y - 2 = x - 1

y = x + 1

Now, we can use the fact that S also lies on the line passing through points (6,4) and P(1,2). This line has the equation:

(y - 4) / (x - 6) = (2 - 4) / (1 - 6)

(y - 4) / (x - 6) = -2/-5

(y - 4) / (x - 6) = 2/5

We can solve for y in terms of x:

y - 4 = (2/5)(x - 6)

y = (2/5)x - 8/5 + 4

y = (2/5)x + 6/5

Now, we can set the two equations for y equal to each other, since they both represent the y-coordinate of point S:

x + 1 = (2/5)x + 6/5

Solving for x, we get:

x = 2

Substituting x = 2 into either of the equations for y, we get:

y = 3

Therefore, the coordinates of S are (2,3).

c) To find the coordinates of Q, we can use the fact that PQ is parallel to SR and PS is parallel to QR. This means that PQRS is a parallelogram and its opposite sides are parallel. Since we know the coordinates of P and S, we can find the coordinates of Q and R by adding or subtracting the appropriate vector from P and S.

The vector that we need to add to P to get Q is the same vector that we need to add to S to get R, which is given by the displacement vector PS = <5,1>. Therefore:

Q = P + PS

= <1,2> + <5,1>

= <6,3>

Therefore, the coordinates of Q are (6,3).

d) To find the equation of line L2 which is the perpendicular bisector of line QR, we first need to find the midpoint of QR. The midpoint formula is given by:

midpoint = [(x1 +)]

We can then find the midpoint of QR using the midpoint formula:

midpoint of QR = ((-4 + 1)/2, (7 + 4)/2) = (-1.5, 5.5)

So the slope of L2 is the negative reciprocal of the slope of QR:

slope of L2 = -1/slope of QR = -(7-5)/(1+4) = -2/5

We can use the point-slope form of the equation of a line to find the equation of L2. We know that L2 passes through the midpoint of QR, so we can use the point (-1.5, 5.5):

y - 5.5 = (-2/5)(x + 1.5)

Simplifying and rearranging, we get:

y = (-2/5)x + 7.5

Therefore, the equation of line L2 is y = (-2/5)x + 7.5.

The time-series model that assumes that demand in the next period will be equal to the most recent period's demand is A) Naive approach.

This model is based on the simplest assumption of all, that the next period's demand will be equal to the current period's demand. It is called the naive approach because it assumes no underlying pattern in the data and provides a baseline prediction. The formula for the naive approach is as follows:

y(t) = y(t-1) where y(t) represents the demand in period t and y(t-1) represents the demand in the previous period.

Although this model is simple, it is often used as a benchmark for comparison with more complex models and can provide reasonable results for stable demand patterns.

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Number of square feet of wall painted in 1 hour is 243 square feet. Therefore, option C is the correct answer.

Given that, it takes Zach 10 minutes to paint \(40\frac{1}{2}\) square feet of his bedroom wall.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Here,  square feet = 40.5 square feet

Rate at which he paints the wall =40.5/10

= 4.05 square feet per minute

As we know 1 hour =60 minutes

Now, number of square feet

= 4.05×60

= 243 square feet

Number of square feet of wall painted in 1 hour is 243 square feet. Therefore, option C is the correct answer.

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Answer:

The answer would be b=7.

Step-by-step explanation:

The reason for this is that cot x = 3/4. That means tan x = 4/3. In tangent 4/3 is opposite/adjacent. So 4 is opposite and 3 is adjacent.

The picture is below if you needed it.

The answer is not 4 though because we need to put it into ratio form. 10.5 = to the 3 and 2b is equal to the 4.

Since we understand this information we now cross multiply to get the answer.

3/10.5 = 4/2b

When you cross multiply you get 7 = b.

This is the answer. To check you can put it into the ration again.

3 divided by 4 is 0.75 as is 10.5 divided by 2(7) or 14.

This is how to answer and check the problem

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The value of b from the given diagram is 7.

Given the following parameters:

\(cot(x)=\frac{3}{4} \\tan(x)=\frac{4}{3}\)

From the given diagram, the opposite is 4 and the adjacent is 3

Substitute the sides of the triangle:

\(tan(x)=\frac{2b}{10.5} \\\frac{4}{3}= \frac{2b}{10.5} \\6b=42\\b =\frac{42}{6}\\b=7\)

Hence the value of b from the given diagram is 7.

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There are 6 possible itineraries with Thailand as the last stop.

To find the number of possible itineraries with Thailand as the last stop, you need to consider the possible arrangements for the other three destinations (Singapore, Hong Kong, and Bali).

Since there are 3 remaining destinations, there are 3! (3 factorial) ways to arrange them.

3! = 3 × 2 × 1 = 6.

Therefore, there are 6 possible itineraries with Thailand as the last stop.

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Answer:

Undefined

Step-by-step explanation:

you can't divide by 0

(-2-0)/(2-2)

According to gift economy A registered person has received a gift that's valued at $150 from the finra member firm through which her firm clears trades. this gift is considered Excessive.

According to the statement

we have given that the person has received a gift that's valued at $150 from the FINRA member firm through the traders. And we have to find about the type gift.

So, For this purpose, we know that the

A gift economy is one in which services or goods are given without an agreement as to a suitable payment or trade to be made in return.

And

The gift economy recognizes that in the real world, this is only a partial understanding of what motivates individuals and communities. The gift economy places greater value on qualitative relationships between dependent people. The commodity economy places greater value on quantitative trade of goods.

That's why, A registered person has received a gift that's valued at $150 from the finra member firm through which her firm clears trades. this gift is considered Excessive.

So, According to gift economy. A registered person has received a gift that's valued at $150 from the finra member firm through which her firm clears trades. this gift is considered Excessive.

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Answer:

This represents 3 and one-third divided by two-thirds because 10/3 = 3 and 1/3.

Answer:

It is 3 and 1/3 divided by 2/3.  None of the choices given work.

Hope it helps <3

Answer:

0.11111111111

Step-by-step explanation:

Answer:

10 in long

Step-by-step explanation:

Answer:

A photographer needs a frame for a 16 x 20 inch picture, such that the total area is 340 in2. Calculate the width of the frame. Which of the following quadratic equations would be used when solving this?

Step-by-step explanation:

who df deleted my answer

BebeHowILook

Answer: 4x^2+72x=20

Step-by-step explanation: I took the quiz.

Answer: A function is a relation between domain and range such that each value in the domain corresponds to only one value in the range. Relations that are not functions violate this definition. They feature at least one value in the domain that corresponds to two or more values in the range.

Step-by-step explanation:

Answer:

Hello...

Step-by-step explanation:

A)It is similar but not congruent.

B)segment AB.

C)angle A.

HOPE IT HELPS YOU DEAR.....

The answers to all parts are given below.

A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

The sum of two sides of a triangle is greater then the third side. Mathematically -

a + b > c

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given is a triangle PQR and line segment AB, which is parallel to QR.

[A] -

ΔPQR is similar to ΔPAB as -

∠P = ∠P (Common)

∠PAB = ∠PQR (Corresponding angles)

∠PBA = ∠PRQ (Corresponding angles)

Using AAA similarity rule, ΔPQR is similar to ΔPAB.

[B] -

Line segment AB corresponds to line segment QR

[C] -

∠A in ΔPAB corresponds to ∠Q.

Therefore, the answers to all parts are given above.

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Answer:

A and A

the equation of a parabola in vertex form is

y = a(x - h)² + k

where ( h, k ) are the coordinates of the vertex and a is a multiplier

y = - 2(x + 3)² + 2  is in this form

with vertex = ( - 3, 2)

To find the y-intercept let x = 0

y = - 2(3)² + 2 = - 18 + 2 = - 16

Similarly

y = - 2(x + 2)² + 2 is in vertex form

vertex = ( - 2 , 2)

x = 0 : y = - 2(2)² + 2 = - 8 + 2 = - 6 ← y- intercept

hope this helped

You can infer causality from a correlational result, but only when the r value is greater than b. 0.5

A correlation coefficient, generally denoted by the symbol "r," is a metric that evaluates the degree and direction of a linear relationship between two variables. r has a value between -1 and 1, with -1 indicating a strong negative correlation, +1 indicating a high positive correlation, and 0 indicating no connection.

A correlation value of 0.5 or above is regarded moderate or strong, and it might indicate that a causal link exists between the two variables. It is crucial to remember, however, that correlation does not imply causation, and that other factors such as confounding variables, spurious correlations, or reverse causality may be contributing to the apparent association.

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Answer:

4

Step-by-step explanation:

You can count on your fingers if you need to or use a calculator.

Answer:

2+2 is 4

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

I answered it on edge

2.45 seconds will it take for the egg to reach the ground.

Height can be defined the vertical distance from the top to the base of the object.

Given

Height h(t) = 90 ft

Acceleration due to gravity a = -16 ft/\(s^{2}\)

Initial velocity  v = 0

\(h_{0}\) = 0

\(h(t) = at^{2} +vt+h_{0}\)

90 = 16\(t^{2}\) + 0

90 =  16\(t^{2}\)

\(t^{2} = \frac{90}{16}\)

\(t^{2}=5.625\)

t = \(\sqrt{5.625}\)

t = 2.45

Hence, 2.45 seconds will it take for the egg to reach the ground.

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