The total amount of the food came to $47. 50. But the restaurant also charges 6% sales tax on the total. The server was not great, so you left a 15% tip. How much will they pay at the restaurant’s register, including sales tax and tip?

Answer: cluster sampling

Step-by-step explanation: got it right on edge:)

Answer:

A

Step-by-step explanation:

a)  the probability of exactly two breakdowns in the next month is approximately 0.224 or 22.4%

b)  the probability of at most one breakdown in the next month is approximately 0.199 or 19.9%.

To find the probability of the number of breakdowns in a month for the washing machine using the Poisson probability distribution, we need to know the average rate of breakdowns per month, which is given as three breakdowns.

The Poisson probability distribution formula is given by:

P(x; λ) = (\(e^{(-\lambda )\)* λ^x) / x!

Where:

P(x; λ) is the probability of x events occurring in a given interval,

λ is the average rate of events occurring in that interval,

e is the base of the natural logarithm, and

x! represents the factorial of x.

a) To find the probability of exactly two breakdowns, we substitute x = 2 and λ = 3 into the formula:

P(2; 3) = (\(e^{(-3)} * 3^2\)) / 2!

Calculating this, we get:

P(2; 3) ≈ 0.224

Therefore, the probability of exactly two breakdowns in the next month is approximately 0.224 or 22.4%.

b) To find the probability of at most one breakdown, we sum the probabilities of zero breakdowns and one breakdown:

P(0; 3) + P(1; 3)

Substituting x = 0 and λ = 3 into the formula for the first term:

P(0; 3) = (\(e^{(-3)} * 3^0)\) / 0! = \(e^{(-3)\)

Substituting x = 1 and λ = 3 into the formula for the second term:

P(1; 3) = (\(e^{(-3)} * 3^1\)) / 1! =\(3e^{(-3)\)

Calculating this sum, we get:

P(0; 3) + P(1; 3) = \(e^{(-3)} + 3e^{(-3)}\)

Approximating this value, we find:

P(0; 3) + P(1; 3) ≈ 0.199

Therefore, the probability of at most one breakdown in the next month is approximately 0.199 or 19.9%.

Using the Poisson probability distribution, we can determine the likelihood of different numbers of breakdowns occurring in a month for the washing machine in the laundromat.

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Answer: 50

Step-by-step explanation:

Greatest common factor of 200 and 150 is 50

200/50=4

150/50=3

Answer:

Its A

Step-by-step explanation:

Adding integer constraints to a linear programming model may or may not improve the optimal objective value.

When solving a linear programming problem, the standard approach is to relax the integer constraints and find an optimal solution in the continuous domain. This is known as linear programming (LP) relaxation. However, the optimal solution obtained from the LP relaxation may not satisfy the integer constraints. In such cases, if the integer constraints are added back to the problem, it becomes an integer programming (IP) problem.

The addition of integer constraints introduces discrete decisions into the problem, allowing for more precise control over the variables. In some cases, adding integer constraints can lead to a better optimal objective value because it forces the solution to select values that align with the discrete nature of the problem. This is especially true when the problem exhibits combinatorial or logical structures where discrete choices are crucial.

However, there are instances where adding integer constraints may not improve the optimal objective value. This can happen when the LP relaxation already provides an optimal solution that satisfies the problem's requirements. In such cases, the introduction of integer constraints may restrict the feasible solution space, making it harder to find a better solution.

In summary, while adding integer constraints to a linear programming model has the potential to improve the optimal objective value by incorporating discrete decisions, it is not guaranteed to do so. The impact of integer constraints depends on the problem structure and whether the LP relaxation already provides an optimal solution that meets the problem's criteria.

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Answer:

-3x + 7

Step-by-step explanation:

she used the y-intercept as the slope and the slope as the y- intercept.

Answer:

its y= -3x+7

Step-by-step explanation:

she used the x intercept for the y - intercept and the y- intercept for the c-intercept

The height of the mountain is 1.49 miles if in traveling across flat land you notice a mountain directly in front of you.

Given,

In the question:

Its angle of elevation (to the peak) is 3.5 degrees.

After you drove 13 miles closer, the angle of elevation is 9 degrees.

To find the approximate height of the mountain.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationship between the sides and angles of a right-angle triangle.

Now, According to the question:

It is given that:

In traveling across flat land you notice a mountain directly in front of you.

Applying tan ratio:

tan3.5 = h/(15+x)

Here h is the height of the mountain and x is the distance between the base of the mountain and to the second position of the car.

h = (15 + x) tan3.5

h = x tan9

(15 + x) tan3.5 = x tan9

x = 9.44

h = 9.44 tan9

h = 1.49 miles

Hence, the height of the mountain is 1.49 miles if in traveling across flat land you notice a mountain directly in front of you.

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Answer:

A. Opposite angles of a rhombus are congruent.

Step-by-step explanation:

Answer:

six and five thousands

Answer:

\( 85\degree \)

Step-by-step explanation:

By the property of intersecting chords inside a circle.

\( m\angle AEB=\frac{1}{2} (132\degree + 38\degree) \)

\( m\angle AEB=\frac{1}{2} \times 170\degree \)

\( m\angle AEB=85\degree \)

The current in an rlc circuit is described by d²i/dt² + 10di/dt + 25i = 0 if i(0) = 10 a and di(0)/dt = 0, then for t > 0, where a = 10 , b = 5 , and s = -5.

The given differential equation is:

d²i/dt² + 10di/dt + 25i = 0

The characteristic equation is:

r² + 10r + 25 = 0

Solving this quadratic equation, we get:

r = (-10 ± √(100 - 4*25))/2

r = -5

Since the roots are equal, the general solution of the differential equation is:

i(t) = (a + bt) \(e^{-5t}\)

Now, using the initial conditions i(0) = 10 and di(0)/dt = 0, we get:

i(0) = a = 10

di/dt = -5(a + bt)e \(e^{-5t}\) + b* \(e^{-5t}\)

At t=0, di/dt = 0

So, 0 = -5a + b

b = 5a

Substituting the value of a and b, we get:

i(t) = (10 + 5t) \(e^{-5t}\)

Therefore, for t > 0, i(t) = (10 + 5t) \(e^{-5t}\).

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Angle ABC is greater than angle C, as required. Given triangle ABC with AC greater than AB, and BD drawn such that AD is congruent to AB, we need to prove that angle ABC is greater than angle C.

To begin with, we can draw a diagram to visualize the situation. In the diagram, we see that BD is an altitude of triangle ABC, as well as a median since it divides the base AC into two equal parts. We also see that triangles ABD and ABC are congruent by the side-side-side (SSS) criterion, which means that angle ABD is equal to angle ABC.

Now, we can use this information to prove our statement. Since triangle ABD and triangle ABC are congruent, their corresponding angles are also equal. Therefore, we know that angle ABD is equal to angle ABC.

Next, we observe that angle ABD is a right angle, since BD is an altitude of triangle ABC. This means that angle ABC is the sum of angles ABD and CBD.

Since AD is congruent to AB, we also know that angles ABD and ADB are congruent. Therefore, angle CBD is greater than angle ADB.

Putting all of this together, we can conclude that angle ABC is greater than angle C, as required.

In summary, we have shown that given triangle ABC with AC greater than AB and BD drawn such that AD is congruent to AB, angle ABC is greater than angle C. This is because angles ABD and CBD add up to angle ABC, and angle CBD is greater than angle ADB.

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The value of n is 1/2 and it is not an even number or odd number

From the question, the steps are given as

n + n + 1 = 2n + 1

n + n + 1 = 2n+2-1

n + n + 1 = 2(n+1) -1

Also, from the question, we have the result of the expression to be

2

This means that

n + n + 1 = 2

Substitute n + n + 1 = 2(n+1) -1 in the equation n + n + 1 = 2

So, we have

2(n + 1) - 1 = 2

Add 1 to all sides of the equation

So, we have

2(n + 1) = 3

Divide both sides of the equation by 2

So, we have

n + 1 = 3/2

Subtract 1 from all sides

n = 1/2

The above implies that the number n is neither an even number, nor an odd number

This is so because the result is a fraction

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Answer:

Step-by-step explanation:

{ 2/3 x+y=6

+

{ -2/3x-y=2

= 0=6

Hence,no solution.

To find the maximums and minimums of the function f(x,y)=x^2+y^2+xy in the region {(x,y): x^2+y^2<=1}, we need to use the method of Lagrange multipliers.

First, we need to find the gradient of the function and set it equal to the gradient of the constraint (which is the equation of the circle x^2+y^2=1).

∇f(x,y) = <2x+y, 2y+x>
∇g(x,y) = <2x, 2y>

So, we have the equations:
2x+y = 2λx
2y+x = 2λy
x^2+y^2 = 1

Simplifying the first two equations, we get:
y = (2λ-2)x
x = (2λ-2)y

Substituting these into the equation of the circle, we get:
x^2+y^2 = 1
(2λ-2)^2 x^2 + (2λ-2)^2 y^2 = 1
(2λ-2)^2 (x^2+y^2) = 1
(2λ-2)^2 = 1/(x^2+y^2)

Solving for λ, we get:
λ = 1/2 or λ = 3/2

If λ = 1/2, then we get x = -y and x^2+y^2=1, which gives us the critical points (-1/√2, 1/√2) and (1/√2, -1/√2). We can plug these into the function to find that f(-1/√2, 1/√2) = f(1/√2, -1/√2) = -1/4.

If λ = 3/2, then we get x = 2y and x^2+y^2=1, which gives us the critical point (2/√5, 1/√5). We can plug this into the function to find that f(2/√5, 1/√5) = 3/5.

Therefore, the local maximum is (2/√5, 1/√5) with a value of 3/5, the local minimum is (-1/√2, 1/√2) and (1/√2, -1/√2) with a value of -1/4, and the absolute maximum is also (2/√5, 1/√5) with a value of 3/5, and the absolute minimum is on the border, which occurs at (0,1) and (0,-1) with a value of 0.

There are no critical points in the interior of the disk (not the border) that are not extremes or saddle points.
(i) Local extrema:
To find the local extrema, we first find the partial derivatives of f(x, y) with respect to x and y:

f_x = 2x + y
f_y = 2y + x

Set both partial derivatives equal to zero to find critical points:

2x + y = 0
2y + x = 0

Solving this system of equations, we find that the only critical point is (0, 0).

(ii) Absolute extrema:
To determine whether the critical point is an absolute maximum, minimum, or saddle point, we must examine the second partial derivatives:

f_xx = 2
f_yy = 2
f_xy = f_yx = 1

Compute the discriminant: D = f_xx * f_yy - (f_xy)^2 = 2 * 2 - 1^2 = 3

Since D > 0 and f_xx > 0, the point (0, 0) is an absolute minimum of the function.

(iii) Critical points and their classification:
The only critical point in the interior of the disk is (0, 0). As determined earlier, this point is an absolute minimum. No saddle points or other extrema are present within the interior of the disk.

To find any extrema on the boundary of the disk (x^2 + y^2 = 1), we use the method of Lagrange multipliers. However, as the boundary is not part of the domain specified in the question, we will not delve into that here.

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What is the first step to be performed when computing Σ(X + 2)2 option d) Sum the (X + 2) values. The first step in computing Σ(X + 2)2 is to perform the operation within the parentheses, which is adding 2 to each score. Once this is done, the resulting values of (X + 2) should be summed.

This is the explanation for the correct answer. Squaring each value (option a) or adding 2 points to each score (option b) are not the correct first steps in this calculation. Summing the squared values (option c) is also not the correct first step as the expression Σ(X + 2)2 requires summing the values before squaring them.

Therefore, the conclusion is that option d) is the correct first step in computing Σ(X + 2)2.

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Answer:

39 : 13 : 26 or 78 cookies total

Step-by-step explanation:

if following the rule, divide the normal amount of cookies by the total

(26 divided by 2 = 13)

then multiply that 13 with the other two numbers and thats your answer

y = e is the equation of the tangent line to the given curve at the specified point , y = \(e^{x}\) / x , (1, e)

Through the coordinate geometry formal of point-slope form, the equation of tangent and normal can be calculated.

The tangent has the equation (y - y1) = m(x - x1), and a normal travelling through this point and perpendicular to the tangent has the equation (y - y1) = -1/m (x - x1).

thus , y' =  \(\frac{e^{x}-xe^{x} }{x^{2} }\)

y'(1) = 0 = m

Our slope is indicated by the horizontal line.

y−\(y_{1}\)=m(x−\(x_{1}\))

Our line will simply be our y-coordinate because our slope(m) is 0:

e

Therefore:

The tangent line's equation is y=e.

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Answer:

28 girls.

Step-by-step explanation:

b - number of boys

g - number of girls

b = 2*g

b + g = 84

2*g + g = 84

3*g = 84

g = 84/3 = 28

And just in case:

b = 2*g = 2*28 = 56

b + g = 28 + 56 = 84; the answer checks out ;)

Answer:

28

Step-by-step explanation:

Let the number of girls be x .

number of boys = 2x

Number of students in class =84

A/q,

2x +x = 84

3x =84

x= 84/3

x= 28

So number of girls in class is 28

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The area of the triangle is 42.31 square units.Using Heron's formula, we found that the area of the triangle with side lengths a = 11.52, b = 7.62, and c = 14.5 is approximately 42.31 square units.

To find the area of the triangle using Heron's formula, we need to calculate the semi-perimeter (s) first. The semi-perimeter is given by the formula s = (a + b + c) / 2, where a, b, and c are the lengths of the sides of the triangle.

In this case, we have a = 11.52, b = 7.62, and c = 14.5. Thus, the semi-perimeter is:

s = (11.52 + 7.62 + 14.5) / 2 = 33.64 / 2 = 16.82.

Now, we can use Heron's formula to calculate the area (A) of the triangle:

A = sqrt(s(s - a)(s - b)(s - c)).

Substituting the values, we have:

A = sqrt(16.82(16.82 - 11.52)(16.82 - 7.62)(16.82 - 14.5))

A = sqrt(16.82(5.3)(9.2)(2.32))

A = sqrt(424.469728) ≈ 20.61.

Rounding the area to two decimal places, the area of the triangle is approximately 42.31 square units.

Using Heron's formula, we found that the area of the triangle with side lengths a = 11.52, b = 7.62, and c = 14.5 is approximately 42.31 square units.

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The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer:

\(\\\sf7x^3 - 2x^2 - 5\)

Step-by-step explanation:

\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)

Remove parenthesis.

6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3

Rearrange:

6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3

Combine like terms to get:

----------------------------------------

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Answer:

7x³ - 2x² - 5

Step-by-step explanation:

(6x³ + 3x² - 2) + (x³ - 5x² - 3)

Remove the round brackets.

= 6x³ + 3x² - 2 + x³ - 5x² - 3

Put like terms together.

= 6x³ + x³ + 3x² - 5x² - 2 - 3

Do the operations.

= 7x³ - 2x² - 5

____________

hope this helps!

Answer: 12

Step-by-step explanation: 13*3=39

39-3=36

36/3=12✅

a) It would take Anya approximately 4 years to accumulate $40,000 with an annual interest rate of 12%. b) Anya must earn an annual rate of return of approximately 12.6% to save $40,000 in 3 years.

a) To calculate the number of years it would take Anya to accumulate $40,000, we can use the future value formula for compound interest:

Future Value = Present Value * (1 + interest rate)ⁿ

Where:

Future Value = $40,000

Present Value = $25,000

Interest rate = 12% = 0.12

n = number of years

Substituting the given values into the formula, we have:

$40,000 = $25,000 * (1 + 0.12)ⁿ

Dividing both sides of the equation by $25,000, we get:

(1 + 0.12)ⁿ = 40,000 / 25,000

(1.12)ⁿ = 1.6

To solve for n, we can take the logarithm of both sides of the equation:

n * log(1.12) = log(1.6)

Using a calculator, we find that log(1.12) ≈ 0.0492 and log(1.6) ≈ 0.2041. Therefore:

n * 0.0492 = 0.2041

n = 0.2041 / 0.0492 ≈ 4.15

b) To calculate the required rate of return for Anya to save $40,000 in just 3 years, we can rearrange the future value formula:

Future Value = Present Value * (1 + interest rate)ⁿ

$40,000 = $25,000 * (1 + interest rate)³

Dividing both sides of the equation by $25,000, we have:

(1 + interest rate)³ = 40,000 / 25,000

(1 + interest rate)³ = 1.6

Taking the cube root of both sides of the equation:

1 + interest rate = ∛1.6

Subtracting 1 from both sides, we get:

interest rate = ∛1.6 - 1

Using a calculator, we find that ∛1.6 ≈ 1.126. Therefore:

interest rate = 1.126 - 1 ≈ 0.126

To express the interest rate as a percentage, we multiply by 100:

interest rate = 0.126 * 100 = 12.6%

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Answer:

69 hours

Step-by-step explanation:

The painter spends 3 hours working on a painting.

The sculptor spends 23 times as long as the painter.

The amount of time the sculptor spent is:

23 * 3 = 69 hours

The sculptor works for 69 hours.

The weight of the Avery's lunch box using given weights is equal to 0.92 pounds (rounded to two decimal places).

Total weight of the backpack= 2 2/3 pounds

                                                = 8/3 pounds

The weight of the each book =7/8 pounds.

Let x be the weight of the lunch box in pounds.

An equation that represents the total weight in Avery's backpack,

2(7/8) + x = 8/3

To solve for x, simplify and solve for x,

⇒14/8 + x = 8/3

Multiplying both sides by 24 the least common multiple of 8 and 3 to clear the fractions,

⇒42 + 24x = 64

Subtracting 42 from both sides,

⇒24x = 22

Dividing both sides by 24,

⇒x = 22/24

Simplifying the fraction,

⇒x = 11/12

     =  0.92 pounds (rounded to two decimal places).

Therefore, the  weight of the lunch box is equal to 0.92 pounds (rounded to two decimal places).

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Answer:

x=3

Step-by-step explanation:

6x-3

(6*3)-3

18-3

15

3x+6

(3*3)+6

9+6

15

5x

5*3

15

The value of x from the given equilateral triangle is 3.

The given triangle is equilateral triangle with sides 6x-3, 3x+6 and 5x.

An equilateral triangle is a triangle in which all three sides are equal and angles are also equal. The value of each angle of an equilateral triangle is 60° therefore, it is also known as an equiangular triangle.

Now, 6x-3=3x+6

⇒ 6x-3x=6+3

⇒ 3x=9

⇒ x=9/3 =3

and 6x-3=5x

⇒ 6x-5x=3

⇒ x=3

Therefore, the value of x from the given equilateral triangle is 3.

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Answer:

85

Step-by-step explanation:

out of 100 aka 100%, 15% is taken so subtract the too and you get 85