This ladder is extended to a length of 18 feet. The bottom of the ladder is 4. 5 feet from the base of the building. What angle does the ladder make with the ground?

The larger cup can hold 144.51 in³ more water than the smaller cup.

The volume of a cone of radius r and height h is given by one third of the multiplication of pi = 3.14 by the radius squared by the height, hence:

V = 3.14r²h/3

V = 1.0472r²h.

For the smaller cup, the dimensions are r = 2 in and h = 3 in, hence the volume is given as follows:

V = 1.0472 x 2² x 3

V = 12.57 in³.

For the larger cup, the dimensions are r = 5 in and h = 6 in, hence the volume is given as follows:

V = 1.0472 x 5² x 6

V = 157.08 in³.

Then the difference is of:

157.08 - 12.57 = 144.51 in³.

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Answer:

  9/4

Step-by-step explanation:

You want to know the value required to complete the square in the equation 1 = x² -3x.

Your picture shows the required value: (-3/2)² = 9/4.

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Answer:

6h² + 3h + 5

Step-by-step explanation:

7h² + 2h + 5 - h² + h

= 7h² - h² + 2h + h + 5

= 6h² + 3h + 5

Answer:

No

Step-by-step explanation:

g(x,y)=c (circle)

(0,5) is a point on the circle iff (if and only if) (0,5) is a solution of g(x,y)=c

In other words, g(0,5) must be equal to 1

LHS:

g(0,5)=(0+1)²+(5-4)²

= 1+1

= 2 ≠ 1

Answer:

I think so it is false

Hope it helps you

Answer: 3x + 5

Let's think the number as,"x".

So, 3x + 5

I can only think of this expression. But I don't know if I am correct.

Answer:

18 region

Step-by-step explanation:

step 1. 11+11+1=23

step 2. 23-41= -18 region

The number of different menu combinations Mr. Carlos' family can choose is 60.

To find the total menu combinations, you need to use the multiplication principle. Since there are 3 choices of appetizers, 5 choices of entrees, and 4 choices of cake, you simply multiply these numbers together. Here's the step-by-step explanation:

1. Multiply the number of appetizer choices (3) by the number of entree choices (5): 3 x 5 = 15
2. Multiply the result (15) by the number of cake choices (4): 15 x 4 = 60

So, there are 60 different menu combinations possible for Mr. Carlos' family to choose for their reception.

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Answer:

Step-by-step explanation:

Let the total is x.

10% or total is 66, find x:

Answer:

121

Step-by-step explanation:

Answer:

D, 122°F

Step-by-step explanation:

°F = 9/5°C + 32

°F = 9/5(50) +32

°F = 90 + 32

°F = 122

Answer:

I need the answer tooo

The required answers given  complex number sets can be represented as:

V = {z: 1 < |z| ≤ 2}

F = {2 : Re(z) < 1}

Let's break down the sets and explain their representations:

V: This set represents the region in the complex plane where the absolute value of z is greater than 1 but less than or equal to 2. In other words, it consists of all complex numbers that lie outside the unit circle but inside the circle centered at the origin with radius 2.

F: This set represents the complex number 2, but with a condition. It includes the complex number 2 only if the real part of z is less than 1. So, F consists of all complex numbers whose real part is strictly less than 1.

Therefore, the required answers given  complex number sets can be represented as:

V = {z: 1 < |z| ≤ 2}

F = {2 : Re(z) < 1}

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The equation of variable is m= -9, x = -2, b = 10, w = 4. There was a final answer of solving this in equation.

Solving equation of m,

4m - 5 = - 41

4m =  - 41 + 5

4m = -36

m = -36 / 4

m = - 9.

Solving equation of x.

- 11 = 1 - 6x

-11 -1 = -6x

-12 = -6x

- 12/6 = x

x = -2

Solving equation of b.

4/5b + 5 = 13

4/5b = 13 - 5

4/5b = 8

b = 8 x 5/4

b = 40/4

b = 10

Solving equation of w.

- 1/2w - 8 = -6

-1/2w = -6 + 8

-1/2w = 2

w = 2 x 2/1

w = 4/1

w = 4

Hence. the answer is -9, -2, 10, 4.

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Answer:

\(sin \theta = - \frac{1}{5}\)

Step-by-step explanation:

We Know

            \(sin ^2 \theta + cos^2 \theta = 1\\\)

            \(sin^2 \theta = 1 - cos^2 \theta\)

                     \(= 1 - (-\frac{\sqrt{24} }{5})^2\)                   \([\ given : cos \theta = -\frac{\sqrt{24} }{5} \ ]\)

                      \(= 1 - \frac{24}{25}\\\\= \frac{25 - 24}{25}\\\\=\frac{1}{25}\)

     \(sin ^2 \theta = \frac{1}{25}\\\\sin \theta = \sqrt {\frac{1}{25}}\\\\sin \theta = \pm \frac{1}{5}\\\\Since \ \theta \ is \ in \ III \ Quadrant \ sin \theta = -\frac{1}{5}\)

Answer:

$5.66lb variety : 8 lbs used

$8.86 variety: 2 lbs used

Step-by-step explanation:

Let x be the lbs of $5.66 variety

Let y be the lbs of $8.86 variety

Total weight = x + y lbs

Total cost = 5.66 + 8.86y

The final mixture weighs x + y pounds and costs a total of 5.66x + 8.86y

So the cost per pound of the final mixture:

Total Cost/Total Weight

\(\dfrac{ 5.66x + 8.86y}{x + y}\)

We are given that the final selling rate is $6.30

We are also given that the total weight is 10 lbs; so
\(x + y = 10\dots[1]\)

So we get

\(\dfrac{ 5.66x + 8.86y}{x + y} = 6.30\\\\\)

\(\longrightarrow \dfrac{ 5.66x + 8.86y}{10} = 6.30\\\\\longrightarrow 5.66x + 8.86y = 10 \times 6.30\\\\\\\longrightarrow 5.66x + 8.86y = 63\dots[2]\\\\\)

Let's re-write equations [1] and [2] below and solve for them

\(x + y = 10\dots[1]\)

\(5.66x + 8.86y = 63\dots[2]\\\\\)

Eliminate one of the variable terms by making their coefficients equal

Multiply equation [1] by 8.86 to make the y terms equal

[1]  x 8.86
\(\longrightarrow 8,86x + 8.86y = 8.86 \times 10\\\\\longrightarrow 8,86x + 8.86y = 88.6 \dots [3]\)

Subtract equation [2] from equation [3]:

\(8,86x + 8.86y = 88.6 \\-\\5.66x + 8.86y = 63.0\\\\----------\\3.20x \;\;\;\;\ + 0y= 25.6\\ \\\)

\(3.20x = 25.6\\\)

Divide both sides by 3.20 to get

\(x = \dfrac{25.6}{3.20} = 8\\\\\text{From equation [1] we get:}x + y = 10\\8 + y = 10\\y = 2\\\)

Answer:
$5.66lb variety : 8 lbs used

$8.86 variety: 2 lbs used

the criteria used when deciding upon the inclusion of a variable are A - Theory, B - t-statistic, C - Bias, and D - Adjusted R^2.

When deciding upon the inclusion of a variable, the following criteria are commonly used:

A - Theory: Theoretical justification is often considered to include a variable in a model. It involves assessing whether the variable is relevant and aligns with the underlying theory or conceptual framework.

B - t-statistic: The t-statistic is used to determine the statistical significance of a variable. A variable with a significant t-statistic suggests that it has a meaningful relationship with the dependent variable and may be included in the model.

C - Bias: Bias refers to the presence of systematic errors in the estimation of model parameters. It is important to consider the potential bias introduced by including or excluding a variable and assess whether it aligns with the research objectives.

D - Adjusted R^2: Adjusted R^2 is a measure of the goodness of fit of a regression model. It considers the trade-off between the number of variables included and the overall fit of the model. Adjusted R^2 helps in assessing whether the inclusion of a variable improves the model's explanatory power.

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Answer:

c₁₅ = 44

Step-by-step explanation:

substitute n = 15 into the formula

c₁₅ = 3(15) - 1 = 45 - 1 = 44

Answer:

44

Step-by-step explanation:

Substitute 15 for n in the term, then solve.

\(c_{15} = 3(15) - 1\\c_{15} = 45 - 1\\c_{15} = 44\)

The volume of the octahedron is (Base area ×Height)/3 when two pyramids can be formed from an octahedron, the volume of an octahedron is twice that of a pyramid.

Given that,

An octahedron is made by connecting the centers of the faces of the right rectangular prism in the illustration below.

We have to find what is the octahedron's volume.

The Greek term "Octahedron," which means "8 faces," is the source of the English word "octahedron." Eight faces, twelve edges, six vertices, and four edges that intersect at each vertex make up an octahedron, a polyhedron. It is one of the five platonic solids with equilateral triangle-shaped faces.

Since two pyramids can be formed from an octahedron, the volume of an octahedron is twice that of a pyramid. We can compute the volume of one pyramid, then multiply it by two to obtain the volume of an octahedron.

The pyramid's volume is equal to (Base area ×Height)/3.

Since the pyramid's base is square, its base area is equal to a².

Therefore, The volume of the octahedron is (Base area ×Height)/3 when two pyramids can be formed from an octahedron, the volume of an octahedron is twice that of a pyramid.

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Answer:

x = 24.8

Step-by-step explanation:

2x + 12.8 + 117.6 = 180

Then solve.

2x + 130.4 = 180

2x = 4.6

x = 24.8

Answer:

24.8

Step-by-step explanation:

you just told me to say something so i did.

Answer:

24 inches

Step-by-step explanation:

I divided 84 by 3.5 getting 24 as my answer. So i knew that the stage is 24 inches wide on the drawing.

The smaller number is 25, and the larger number is 68. The larger number is 18 more than twice the smaller number, and their sum is 93.

To solve this word problem using the 3-step process, we need to find the two numbers given that the larger number is 18 more than twice the smaller and the sum of the two numbers is 93.
Step 1: Let's assign variables to the unknown numbers. Let's say the smaller number is "x" and the larger number is "y".
Step 2: Translate the given information into equations. From the problem, we know that the larger number is 18 more than twice the smaller. So, we can write the equation as: y = 2x + 18.
We also know that the sum of the two numbers is 93. So, we can write another equation as: x + y = 93.
Step 3: Solve the system of equations. We have two equations:
y = 2x + 18
x + y = 93
We can solve this system of equations by substitution method or elimination method. Let's use substitution.
Substitute the value of y from the first equation into the second equation:
x + (2x + 18) = 93
3x + 18 = 93
3x = 93 - 18
3x = 75
x = 75 / 3
x = 25
Now, substitute the value of x back into the first equation to find y:
y = 2(25) + 18
y = 50 + 18
y = 68
So, the smaller number is 25 and the larger number is 68.

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The maximum length of each of the three sides is 13.5 feet.

A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides. The parallel sides are called bases while the non parallel sides are called legs.

Perimeter =  sum of lengths of sides of a trapezoid

58.5 = 3s + 18

58.5 - 18 = 3s

40.5 = 3s

s = 40.5 / 3

s = 13.5 feet

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Answer:

Wait... their is no r s and q in the quadratic formula....

Step-by-step explanation:

Answer:

C6.5

Step-by-step explanation:

LOL B-)

Answer: Its C 6.5 I got it right on a test but not sure if its right for you but i think its B also like the other guy said

The double integral of the curl of F over the surface S is given by -10A.

To verify Stokes's Theorem for the vector field F(x, y, z) = (-y + z)i + (x - z)j + (x - y)k over the surface S defined by z = 25 - x^2 - y^2, we'll evaluate both the line integral and the double integral.

Stokes's Theorem states that the line integral of the vector field F around a closed curve C is equal to the double integral of the curl of F over the surface S bounded by that curve.

Let's start with the line integral:

(a) Line Integral:

To evaluate the line integral, we need to parameterize the curve C that bounds the surface S. In this case, the curve C is the boundary of the surface S, which is given by z = 25 - x^2 - y^2.

We can parameterize C as follows:

x = rcosθ

y = rsinθ

z = 25 - r^2

where r is the radius and θ is the angle parameter.

Now, let's compute the line integral:

∫F · dr = ∫(F(x, y, z) · dr) = ∫(F(r, θ) · dr/dθ) dθ

where dr/dθ is the derivative of the parameterization with respect to θ.

Substituting the values for F(x, y, z) and dr/dθ, we have:

∫F · dr = ∫((-y + z)i + (x - z)j + (x - y)k) · (dx/dθ)i + (dy/dθ)j + (dz/dθ)k

Now, we can calculate the derivatives and perform the dot product:

dx/dθ = -rsinθ

dy/dθ = rcosθ

dz/dθ = 0 (since z = 25 - r^2)

∫F · dr = ∫((-y + z)(-rsinθ) + (x - z)(rcosθ) + (x - y) * 0) dθ

Simplifying, we have:

∫F · dr = ∫(rysinθ - zrsinθ + xrcosθ) dθ

Now, integrate with respect to θ:

∫F · dr = ∫rysinθ - (25 - r^2)rsinθ + r^2cosθ dθ

Evaluate the integral with the appropriate limits for θ, depending on the curve C.

(b) Double Integral:

To evaluate the double integral, we need to calculate the curl of F:

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

where P, Q, and R are the components of F.

Let's calculate the partial derivatives:

∂P/∂z = 1

∂Q/∂y = -1

∂R/∂x = 1

∂P/∂y = -1

∂Q/∂x = 1

∂R/∂y = -1

Now, we can compute the curl of F:

curl F = (1 - (-1))i + (-1 - 1)j + (1 - (-1))k

       = 2i - 2j + 2k

The curl of F is given by curl F = 2i - 2j + 2k.

To apply Stokes's Theorem, we need to calculate the double integral of the curl of F over the surface S bounded by the curve C.

Since the surface S is defined by z = 25 - x^2 - y^2, we can rewrite the surface integral as a double integral over the xy-plane with the z component of the curl:

∬(curl F · n) dA = ∬(2k · n) dA

Here, n is the unit normal vector to the surface S, and dA represents the area element on the xy-plane.

Since the surface S is described by z = 25 - x^2 - y^2, the unit normal vector n can be obtained as:

n = (∂z/∂x, ∂z/∂y, -1)

  = (-2x, -2y, -1)

Now, let's evaluate the double integral over the xy-plane:

∬(2k · n) dA = ∬(2k · (-2x, -2y, -1)) dA

            = ∬(-4kx, -4ky, -2k) dA

            = -4∬kx dA - 4∬ky dA - 2∬k dA

Since we are integrating over the xy-plane, dA represents the area element dxdy. The integral of a constant with respect to dA is simply the product of the constant and the area of integration, which is the area of the surface S.

Let A denote the area of the surface S.

∬(2k · n) dA = -4A - 4A - 2A

            = -10A

Therefore, the double integral of the curl of F over the surface S is given by -10A.

To verify Stokes's Theorem, we need to compare the line integral of F along the curve C with the double integral of the curl of F over the surface S.

If the line integral and the double integral yield the same result, Stokes's Theorem is verified.

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Answer:

Step-by-step explanation:

The answer is B. His budget is $250 so it has to be less than or equal to. $60 a crew member (x = the crew members) and $45 to use the forklift, so $60x + $45 is less than or equal to $250

Answer:

B is the correct answer.

Step-by-step explanation:

According to the problem, the contractor can spend AT MOST $250 a day, meaning $250 is the limit. Therefore, that gives you less than or equal too, or ≤. Next, it costs $45 a day, including $60, which you would add to get the final amount, or +.

Therefore, 60x + 45 ≤ 250

Answer:

1/ 6

7/ 12

Step-by-step explanation:

Answer:

7a) 1/7

7b) 7/12

Step-by-step explanation:

For 7a) you know that the denominator of 5/6 is equal to 6 so that means you should make 1 have a denominator of 6. To do that, you have to multiply the denominator and the numerator by 6 to get 6/6-5/6=?. With this, you could easily solve the two fractions because they have equal denominators. You subtract the numerator and keep the denominator. 6-5=1 so the answer is 1/6.

For 7b) I would first convert 1 3/12 into an improper fraction. To do that, you have to multiply the whole number by the denominator then add the numerator. It will look like this 12x1+3/12 which is equal to 15/12. This makes the question easier to solve. You then want to convert 2/3 to have a denominator of 12. To do that, you have to multiply 4 on the numerator and denominator. This will turn the fraction into 8/12. After you do that, you can easily subtract the fractions again. you do 15-8/12 which is equal to 7/12.

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