Determine whether the points P and Q lie on the given surface.
r(u, v) = ⟨2u + 3v, 1 + 5u − v, 2 + u + v⟩
P(7, 10, 4), Q(5, 22, 5)

Answer:

The smaller cup has a height of 4cm

Step-by-step explanation:

The two cups have a proportional relationship. This means that the since the smaller cup has a capacity that is half of the larger cup, the height will also be half of the larger cup height.

.25 is half of .5

_ is half of 8

Hope this helped!

Herman must sell 27 glasses of lemonade to break even.

To create a linear cost function, we need to determine the relationship between the number of glasses of lemonade made (q) and the cost of making that quantity (c).

From the given data, we have two points: (19, $2) and (83, $5). We can use these points to find the slope of the line and then determine the cost function.

Using the formula for the slope of a line:

slope = (change in cost) / (change in quantity)

slope = ($5 - $2) / (83 - 19)

slope = $3 / 64

Now, let's use the point-slope form of a linear equation to find the cost function:

c - $2 = ($3 / 64)(q - 19)

To break even, the cost (c) should equal the revenue earned from selling the lemonade. Revenue is calculated by multiplying the number of glasses sold (q) by the selling price per glass ($0.15).

c = $0.15q

Setting the cost equal to revenue:

$0.15q = ($3 / 64)(q - 19) + $2

Solving this equation will give us the value of q when the cost equals the revenue (break-even point).

Simplifying the equation:

0.15q = (3/64)(q - 19) + 2

Solving for q:

0.15q = (3/64)q - (57/64) + 2

(49/64)q = (57/64) + 2

(49/64)q = (185/64)

q = (185/64) * (64/49)

q = 185/49

q ≈ 3.775

Since we cannot sell a fraction of a glass, Herman must sell at least 4 glasses of lemonade to break even.

Herman needs to sell at least 27 glasses of lemonade to break even. This calculation is based on the given cost data and the selling price per glass.

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Answer: Yes

Step-by-step explanation:

Imagine you have b = 2.

Plug 2 into the equation 2b + b = 3b

You get: 2(2) + 2 = 3(2)

Which solves to be 6 = 6

As long as the variable is the same, in this case b, and they are to the same power, in this case ^1, you can combine them.

Answer:

The answer is No they are not equvalient expression

Step-by-step explanation:

please mark as brailist

The triangle is a right triangle, and the length of segment BD is 16.30

Start by calculating the length CD using the following Pythagoras theorem

\(CD = \sqrt{28.9^2 - 24.2^2}\)

Evaluate

\(CD = \sqrt{249.57}\)

Take the square of both sides

CD^2 = 249.57

The length BD using the following Pythagoras theorem

\(BD = \sqrt{CB^2 - CD^2}\)

So, we have:

\(BD = \sqrt{22.7^2 - 249.57}\)

Evaluate

\(BD = \sqrt{265.72}\)

Evaluate the square root

BD = 16.30

Hence, the length of segment BD is 16.30

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The curl of the vector field

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

The divergence of the vector field

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

To find the curl of the vector field F(x, y, z) = 9ex sin(y), 2ey sin(z), 8ez sin(x), we need to compute the determinant of the curl matrix.

(a) Curl of F:

The curl of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

curl(F) = (∂R/∂y - ∂Q/∂z)i + (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)k

In this case, we have:

P(x, y, z) = 9ex sin(y)

Q(x, y, z) = 2ey sin(z)

R(x, y, z) = 8ez sin(x)

Taking the partial derivatives, we get:

∂P/∂y = 9ex cos(y)

∂Q/∂z = 2ey cos(z)

∂R/∂x = 8ez cos(x)

∂R/∂y = 0 (no y-dependence in R)

∂Q/∂x = 0 (no x-dependence in Q)

∂P/∂z = 0 (no z-dependence in P)

Substituting these values into the curl formula, we have:

curl(F) = (0 - 2ey cos(z))i + (8ez cos(x) - 0)j + (0 - 9ex cos(y))k

= -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

Therefore, the curl of the vector field F is given by:

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

(b) Divergence of F:

The divergence of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

div(F) = ∂P/∂x + ∂Q/∂y + ∂R/∂z

In this case, we have:

∂P/∂x = 9e^x sin(y)

∂Q/∂y = 2e^y sin(z)

∂R/∂z = 8e^z

Substituting these values into the divergence formula, we have:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

Therefore, the divergence of the vector field F is given by:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

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If the standard error for samples of a particular size (which is greater than 80) is calculated as 45.1, and you want to determine the standard error for a doubled sample size, we can use the following relationship:

Standard Error for the new sample size = Standard Error for the original sample size / √(New Sample Size / Original Sample Size)

Let's denote the original sample size as n and the standard error for the original sample size as SE_original.

SE_original = 45.1 (given)

Let's assume the new sample size is 2n (double the original sample size). The standard error for the new sample size, denoted as SE_new, can be calculated as follows:

SE_new = SE_original / √(2n / n)

SE_new = SE_original / √2

Substituting the given value of SE_original:

SE_new = 45.1 / √2

Calculating this expression, the standard error for the new sample size is approximately 31.92 (rounded to two decimal places).

Therefore, if you double the sample size, the standard error would be approximately 31.92.

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Answer:

see explanation below

Step-by-step explanation:

(secθ - cosθ)/secθ = (sinθ)^2

(secθ - cosθ)/secθ = (sinθ)^2

since secθ = 1/cosθ, you substitute

(secθ - cosθ)/(secθ)

= (1/cosθ  - cosθ)/(1/cosθ)

= cosθ(1/cosθ  - cosθ)

= 1 - cosθ^2

= sinθ^2

Answer:

the third one, the 6 one, and the last one

Step-by-step explanation:

i hope it help because it like asking you for the number who will give you positive, and if you know negative + negative = positive

The probability of rolling a number greater than 4 on a number cube is 1/3 or 0.33.

A number cube is a cube-shaped object with six sides, numbered from 1 to 6. When rolling the number cube, there are six possible outcomes, each with an equal chance of occurring. Since we are interested in finding the probability of rolling a number greater than 4, we need to determine how many of the six possible outcomes meet this condition.

There are two possible outcomes that satisfy the condition: rolling a 5 or rolling a 6.

So, as there are two outcomes = 2/6

= 1/3

Therefore, the probability of rolling a number greater than 4 is 1/3.

This can also be simplified to 0.33 or 33.3% as a decimal or percentage, respectively.

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Answer:

Actually, I am not sure about the Ans of 6 no.

please mark me brilliant

Radius of the largest tabletop that can be cut from a rectangular piece of wood measuring 1.20 m by 1.80 m is 0.60 m.

What is the largest tabletop radius that could be cut?

To find the largest tabletop that could be cut from the rectangular piece of wood, we need to maximize the radius of the tabletop while ensuring that it fits inside the rectangle.

Here, the rectangle represents the piece of wood, and the circle represents the tabletop we want to cut. The center of the circle is marked with the letter "o". We want to find the radius of the largest circle that can fit inside the rectangle.

We can see that the diameter of the circle is limited by the shorter side of the rectangle (1.20 m), because if the diameter were any larger, the circle would not fit inside the rectangle. Therefore, the radius of the circle is half the length of the shorter side of the rectangle:

radius = 1.20 m / 2 = 0.60 m

So the radius of the largest tabletop that could be cut is 0.60 meters.

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The answer is C aka answer 3

Answer: 77 suits

Step-by-step explanation:

Let sales of this month = x

Sales for last 4 months = 92, 28, 83, 75

Average = Sum of Observation ÷ No of Observation

Now, we can form an equation

(92+28 +83+75+x) ÷ 5 =71

(92+28 +83+75+x) = 71 × 5

278 + x = 355

x = 355 - 278

x = 77

Answer:

Step-by-step explanation:

\(25+12.5v\ge 130\\ \\ 12.5v\ge 105\\ \\ v\ge 8.4\)

Answer:

D) -4, 0

Step-by-step explanation:

find common difference.

the common difference appears to be +4 as you must add 4 to -12 to get to -8

now we find the missing terms.

the previous term of the first missing term is -8

if the common difference is +4 then the next term would be -8 + 4 = -4

the term after that would be -4 + 4 = 0

the two missing terms are -4 and 0

The isospin ⊗ spin wavefunctions for the four different spin states of a Δ0 particle, in terms of the wavefunctions of the quarks it is composed of, are:

|3/2, 3/2⟩ = |u↑d↑⟩

|3/2, 1/2⟩ = (√3/2)|u↓d↑⟩ + (√1/2)|u↑d↓⟩

|3/2, -1/2⟩ = (√1/2)|u↓d↑⟩ - (√3/2)|u↑d↓⟩

|3/2, -3/2⟩ = |u↓d↓⟩

The Δ baryons are composed of three quarks: two down (d) quarks and one up (u) quark. The isospin of a particle represents its behavior under rotations in the isospin space, which is related to the behavior of the particle under the strong force. The spin of a particle represents its intrinsic angular momentum.

For the Δ0 particle, which has isospin 3/2, there are four different spin states. Each spin state corresponds to a different combination of up and down quark spin projections along the z axis. The isospin ⊗ spin wavefunctions represent the composite wavefunctions of the quarks that make up the Δ0 particle for each spin state.

In the first spin state, |3/2, 3/2⟩, both the up and down quarks have their spins aligned in the upward direction. In the second spin state, |3/2, 1/2⟩, the up quark has its spin aligned upward while the down quark has its spin aligned downward. The third spin state, |3/2, -1/2⟩, has the up quark with its spin aligned downward and the down quark with its spin aligned upward. Finally, in the fourth spin state, |3/2, -3/2⟩, both the up and down quarks have their spins aligned in the downward direction.

These wavefunctions provide a mathematical description of the different spin states of the Δ0 particle, taking into account the wavefunctions of the constituent quarks. They help us understand the quantum mechanical properties and behavior of the Δ0 baryon in terms of its quark composition.

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9514 1404 393

Answer:

  A)  278.3

Step-by-step explanation:

Write your question as an equation and solve.

  46% × what = 128

Divide by the coefficient of 'what':

  what = 128/0.46 ≈ 278.3

It will cost $225 to pour 25 yd3 of concrete with 3 workers working at a rate of $15 per hour.

To determine the cost to pour 25 yd3 of concrete, you can use the following formula:

cost = (number of workers * worker rate per hour * number of hours)

In this case, the number of workers is 3, the worker rate per hour is $15, and the number of hours can be calculated by dividing the volume of concrete to be poured (25 yd3) by the rate at which the workers can pour concrete (5 yd3 per hour). Therefore, the number of hours it will take to pour 25 yd3 of concrete is 25/5=5 hours.

Plugging these values into the formula gives:

cost = (3 workers * $15/hour * 5 hours) = $<<3155=225>>225

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Answer:

8/5

Step-by-step explanation:

It rises 8 and runs 5. I used the points (-4, -4) and (1, 4)

Answer:

3

Step-by-step explanation:

y= mx +b

b the y-intercept and is 2  so is red or purple line

m is the slope = 1/2  so rise 1 and run 2 is the purple line

Answer: -2/10

Step-by-step explanation:

The pre-image of vertex A' by a reflection across the line y = x is (2, 10).

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

We have,

The coordinate of A(10 ,2)

Now, When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places.

Then, the pre image of vertex A' is (2, 10).

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The graph represents this system of inequalities:

F. y ≤ −x + 4

G. y ≤ 3x − 1

In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Next, we would determine the linear equation representing the line of f(x) which passes through the points (0, 4) and (4, 0) by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 0 = (4 - 0)/(0 - 4)(x - 4)

y - 0 = -1(x - 4)

y = -x + 4

Therefore, an inequality representing the line of f(x) is y ≤ -x + 4

For the line of g(x), we have:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-1) = (5 - (-1))/(2 - 0)(x - 0)

y + 1 = 3(x - 0)

y = 3x - 1

Therefore, an inequality which represents the line of g(x) is y ≤ 3x - 1.

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Complete Question:

In the graph, the area below f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area where f(x) and g(x) have shading in common is labeled AB. Graph of two intersecting lines. The line f of x is solid and goes through the points 0, 4, and 4, 0 and is shaded below the line. The other line g of x is solid, and goes through the points 0, negative 1 and 2, 5 and is shaded below the line. The graph represents which system of inequalities?

y ≤ −3x − 1

y ≤ −x − 4

y > −3x + 1

y ≤ −x − 4

y < 3x − 1

y ≤ −x + 4

y ≤ 3x − 1

y ≥ −x + 4

Answer:

18.84 ft

Step-by-step explanation:

¼×2×3.14×12 = 18.84 ft

Step-by-step explanation:

assuming 90° is the central angle measure then the degree measure of the arc would be 90°

though the question asks for length

to do this create a ratio of the degree measurement of the arc divided by the total degree measure of a circle which would be

90/360

next think about circumference, it's the measure of the length around a circle. that would be relevant to what the question is asking so calculate it the formula is C=2*pi*r

calculate and the circumference is 24pi

next multiply the total circumference by the ratio for the section we want in this case 90/360

arc length = 24pi * 90/360 = 6pi

therefore the answer is 6pi or 18.84 substituting 3.14 for pi

Answer:

12 adults

Step-by-step explanation:

We can solve this in a couple of simple steps. First, since there are 3 adults for every 8 students we add these two numbers together

3+8 = 11

Now we simply divide this number by the total amount of people that went to the trip in order to get how many times this set of adults and students repeats itself.

44 / 11 = 4

Finally, we multiply this number by the set of 3 adults in order to find out how many adults went to the trip.

4 * 3 = 12 adults

8 * 3 = 32 Students

Answer:

\(y = -\frac{3}{2}x -1\)

Step-by-step explanation:

Given

Perpendicular to \(y = \frac{2}{3}x + 2\)

Pass through \((-2,2)\)

Required

Determine the line equation

First, we need to determine the slope of \(y = \frac{2}{3}x + 2\)

An equation is of the form:

\(y = mx + b\)

Where

\(m = slope\)

In this case:

\(m = \frac{2}{3}\)

Next, we determine the slope of the second line.

Since both lines are perpendicular, the second line has a slope of:

\(m_1 = \frac{-1}{m}\)

\(m_1 = \frac{-1}{2/3}\)

\(m_1 = -\frac{3}{2}\)

Since this line passes through (-2,2); The equation is calculated as thus:

\(y - y_1 = m_1(x - x_1)\)

Where

\((x_1,y_1) = (-2,2)\)

This gives:

\(y - 2 = -\frac{3}{2}(x - (-2))\)

\(y - 2 = -\frac{3}{2}(x +2)\)

\(y - 2 = -\frac{3}{2}x -3\)

Add 2 to both sides

\(y - 2+2 = -\frac{3}{2}x -3 + 2\)

\(y = -\frac{3}{2}x -1\)

Answer:

10

Step-by-step explanation:

6,6,8,10,x is in order which means the mediam is 8 because it's the middle.

The average is the sum divided by 5 since there are 5 numbers. But this number is 8 since we are given the mean=median. So the sum is 5 times that.

So we have 6+6+8+10+x=5(8).

30+x=40

x=10 since 30+10=40.

The value of x in the triangle is 2.5√2

From the question, we have the following parameters that can be used in our computation:

The triangle

The value of x can be calculated using the following ratio

sin(30) = opposite/hypotenuse

Using the above as a guide, we have the following:

sin(30) = x/5√2

So, we have

x = 5√2 * sin(30)

Evaluate

x = 2.5√2

Hence, the value of x is 2.5√2

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\(2x(x - 1) \\ \\ {2x}^{2} - 2x\)