the zagat restaurant survey provides food, decor, and service ratings for some of the top restaurants across the united states. for 18 restaurants located in a certain city, the average price of a dinner, including one drink and tip, was $48.60. you are leaving on a business trip to this city and will eat dinner at three of these restaurants. your company will reimburse you for a maximum of $50 per dinner. business associates familiar with these restaurants have told you that the meal cost at one-third of these restaurants will exceed $50. suppose that you randomly select three of these restaurants for dinner. (round your answers to four decimal places.)

The matching between polynomial with its factorization is:

Letter A - Number 5

Letter B - Number 1

Letter C - Number 2

Letter D - Number 4

Letter E - Number 6

Letter F - Number 3

In math, the factoring or factorization is used to write an algebraic expression in factors.

The question gives a polynomial and asks your respective factorization. For solving this exercise, you should calculate the multiplication between the terms and after that you should match the result with given equations.

      Multiplying the terms, you will have:

      x²-3x+5x-15=x²+2x-15

     Therefore, the letter a match with the equation 5.

      Multiplying the terms, you will have:

      2(x²+4x-4x-16)=2(x²-16)=2x²-32

     Therefore, the letter b match with the equation 1.

      Multiplying the terms, you will have:

      (x-8)*(x-8)=x²-8x-8x+64=x²-16x+64

     Therefore, the letter c match with the equation 2.

      Multiplying the terms, you will have:

      7x-x²+21-3x= -x²+4x+21

     Therefore, the letter d match with the equation 4.

      Multiplying the terms, you will have:

      x+2-5x²-10x= -5x²-9x+2

     Therefore, the letter e match with the equation 6.

      See, the equation 6 is 4-9x-2-5x²=-5x²-9x+2.

      Multiplying the terms, you will have:

     ( x – 3)( x + 3)( x² + 9)= (x²-3x+3x-9)(x²+9)= (x²-9)(x²+9)= x²-81

     Therefore, the letter f match with the equation 3.

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The percent increase in the interstate highway system from 1960 to now is 381%.

option A.

The percent increase from 16,000 km to 77,000 km is difference between the old value and new value divided by the old value expressed in 100%.

percent increase =  100% x (new value - old value) / old value

percent increase = 100% x  (77,000 - 16,000) / 16,000

percent increase = 100% x 61,000 / 16,000

percent increase = 381.25%

Thus, the percent increase in the interstate highway system from 1960 to now is approximately 381%, which is option A.

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An angle drawn in standard position measuring 10 radians has its terminal ray lying in the third quadrant. The reasoning behind this can be explained by understanding the relationship between the angle measurement and the quadrants in the coordinate plane.

In the standard position, an angle is drawn with its initial side along the positive x-axis and its terminal side determined by the angle measurement. In the coordinate plane, the quadrants are divided into four sections: first quadrant (positive x and y), second quadrant (negative x, positive y), third quadrant (negative x and y), and fourth quadrant (positive x, negative y).

In this case, the angle measures 10 radians, which is greater than π radians (approximately 3.14). Since π radians is half of a circle (180 degrees) and represents the boundary between the second and third quadrants, an angle measuring 10 radians is greater than π and thus falls in the third quadrant.

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Answer:

Step-by-step explanation:

45

If the lengths of all the sides of a polygon are tripled, but the angles remain the same, the area of the polygon will increase by a factor of 9. This is because the area of a polygon is directly proportional to the square of its side length. Therefore, tripling the side lengths will increase the area by a factor of 3^2, which is 9.

When the lengths of all the sides of a polygon are tripled while the angles remain the same, the new polygon will be similar to the original one but with larger sides. To determine what happens to the area of the polygon in this case, let's consider the following steps:

1. All the sides of the polygon are tripled. This means that each side's length is now 3 times its original length.

2. The angles of the polygon remain the same, so the overall shape is preserved.

3. To find the area of the new polygon, we can use the formula for the area of a similar polygon: (New area) = (scale factor)^2 * (Original area), where the scale factor is the ratio of the new side length to the original side length.

4. In this case, the scale factor is 3 (since the lengths of the sides are tripled). So, we have (New area) = (3)^2 * (Original area).

5. Therefore, the new area is 9 times the original area.

In conclusion, when the lengths of all the sides of a polygon are tripled and the angles remain the same, the area of the polygon increases by a factor of 9.

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Answer: 20.8

Step-by-step explanation:

Since it is an equilateral triangle, we know the bottom is also 24. We also know that line E is bisecting the base. So using the smaller right triangle we know that the hypotenuse is 24 and one leg is 12. So use the Pythagorean theorem.

\(a^{2} +b^{2} =c^{2} \\12^{2} +b^{2} =24^{2} \\144+b^{2} =576\\b^{2} = 432\\b= 20.8\)

Step-by-step explanation:

what I don't understand is why the distance around the window has to be written twice.

but let's start with the circumference of the complete circle :

2×pi×r = 2×22/7 × 3.5

or as the boxes are lined

22/7 × 2 × 3.5 = 22/7 × 7 = 22 ft

the circumference of half the circle is then about

22/2 = 11 ft

the distance around the window is then

11 + 3.5×2 = 11 + 7 = 18 ft

The value of a gold coin picturing the head of the Roman Emperor Marcus Aurelius is increasing at the rate of 11% per year, $362.45  it will  be worth in 11 years.

What is Compound Interest?

We can solve this problem using the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the final amount

P = the initial amount

r = the annual interest rate (as a decimal)

n = the number of times interest is compounded per year

t = the number of years

In this case, the initial amount (P) is $115, the annual interest rate (r) is 11%, and we want to know the final amount (A) in 11 years (t).

We are not given the number of times interest is compounded per year (n), so we will assume it is compounded annually (n = 1).

Plugging in the numbers, we get:

\(A = 115(1 + 0.11/1)^{(1*11)\)

\(A = 115(1.11)^{11\)

A = $362.45

Therefore, the coin will be worth $362.45 in 11 years. The answer is (A) $362.45.

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Answer:

5.77in

Step-by-step explanation:

A cube has 6 square faces, so each face would have area 200 sq in/6=33.33 sq in

Since the area of each face equals the square of the sides, the edge of the cube would be sqrt%2833.33sq+in%29= approx. 5.77 in

To determine the exact concentration of the solution made, one can divide the mass of the solute with the volume of the solution.

A solution is the substance formed by the mixture of solute in solvent. The solute may or may not be dissolved in the solution. One can determine the exact concentration of the solution if the mass of solute added in the specific volume of solution is known. If the solution is made by someone else, then its concentration can be determined by process of titration.

The concentration of a solution is expressed in the form of moles or grams per unit liter. If the solution is unknown and only its dissolved chemical is known, then titration will help in determining the closest value of concentration if performed without human error. In titration, the use of glassware that that is more precise than the flasks, beakers, and graduated cylinders are used.

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Refer to complete question below:

How do we determine concentration a solution? If it is a solution that we have made up, we can readily do the calculations required. But what if it is a solution that someone else has made? What technique can be used to gather information about a solution that we are given with no other information than the name of the chemical dissolved.

These values of h and k are specific to the given system of equations and may not apply to other systems.

(a) The system has no solution when h = 16.
(b) The system has a unique solution for any value of h ≠ 16.
(c) The system has many solutions when h = 16.

To determine the values of h and k that result in different solutions for the given system of equations, let's analyze the coefficient matrix of the system:
```
2   4
8   h
```
(a) To have no solution, the coefficient matrix must be inconsistent. This occurs when the determinant of the matrix is zero. In this case, the determinant is 2h - 32. So, to have no solution, we need 2h - 32 = 0. Solving this equation, we find h = 16. Therefore, the system has no solution when h = 16.

(b) To have a unique solution, the coefficient matrix must be consistent and have a non-zero determinant. This means that 2h - 32 ≠ 0. Since the determinant of the coefficient matrix is 2h - 32, we can conclude that the system has a unique solution for any value of h such that h ≠ 16.
(c) To have many solutions, the coefficient matrix must be consistent and have a determinant of zero. In this case, we need 2h - 32 = 0, which gives us h = 16. Therefore, the system has many solutions when h = 16.

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The area of the given trapezoidal site is 250,000 sq. ft.

The area of the trapezoidal with the dimensions of both bases and the height is given by the formula,

Area = 1/2 × height × (base1 + base2)

Units: square units

The given trapezoidal site has a base of 150 feet, i.e., base1 = 150 ft; a height of 2000 ft, i.e., height = 2000 ft and a parallel base of 100 feet, i.e., base2 = 100 ft.

Then, the area of the trapezoidal is

= 1/2 × 2000 × (150 + 100)

= 1/2 × 2000 × 250

= 250,000 sq. ft

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Answer:

The hand moved \(\bf \frac{3}{4}\) of a complete turn.

Step-by-step explanation:

The hand moved from 3 to 12, that is, it moved:

12 - 3 = 9 hours

In a clock, 12 hours represent a complete turn.

∴ Using the unitary method:

12 hours    ⇒     1 turn

1 hour        ⇒     \(\frac{1}{12}\) turns

9 hours     ⇒     \(\frac{1}{12}\)  × 9 = \(\frac{9}{12}\)

                                     = \(\bf \frac{3}{4}\) turns    (simplified)

∴ The hand moved \(\bf \frac{3}{4}\) of a complete turn.

The answer is  \(\boxed{\frac{3}{4}}\).

To find the fraction of a complete turn it moved in this case, take the ratio between hours covered between 3 and 12, and the hours covered in a complete turn.

Answer:

Ax + By = C is standard form.

y + 1 = (2/3)(x - 8)

distribute the (2/3)

y + 1 = (2/3)x - (16/3)

Multiply each term by 3 to clear the fractions.

3y + 3 = 2x - 16

Subtract 2x from both sides.

-2x + 3y + 3 = - 16

Subtract 3 from both sides.

-2x + 3y = - 19

Correct form typically has the leading coefficient as a positive number so multiply each term by - 1.

2x - 3y = 19

Step-by-step explanation:

Answer:

The answer is 2x + -3y = 19

Step-by-step explanation:

got it right on edge

Answer:

Step-by-step explanation:

1256cm^2

The Values of (a+b)ab are undefined.

Given that, a = 3an and db = -2We need to find the values of (a+b)

Now, we have a = 3an... equation (1)Also, we have db = -2... equation (2)From equation (1), we get: n = 1/3... equation (3)Putting equation (3) in equation (1), we get: a = a/3a = 3... equation (4)Now, putting equation (4) in equation (1), we get: a = 3an... 3 = 3(1/3)n = 1

From equation (2), we have: db = -2=> d = -2/b... equation (5)Multiplying equation (1) and equation (2), we get: a*db = 3an * -2=> ab = -6n... equation (6)Putting values of n and a in equation (6), we get: ab = -6*1=> ab = -6... equation (7)Now, we need to find the value of (a+b).For this, we add equations (1) and (5),

we get a + d = 3an - 2/b=> a + (-2/b) = 3a(1) - 2/b=> a - 3a + 2/b = -2/b=> -2a + 2/b = -2/b=> -2a = 0=> a = 0From equation (1), we have a = 3an=> 0 = 3(1/3)n=> n = 0

Therefore, from equation (5), we have:d = -2/b=> 0 = -2/b=> b = ∞Now, we know that (a+b)ab = (0+∞)(0*∞) = undefined

Therefore, the values of (a+b)ab are undefined.

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To determine how many pieces of the press must be purchased, we need to consider the production rate, operating hours, efficiency, and scrap rate.

Number of units processed per day = 10,000

Machine efficiency = 95%

Punching operation time = 10 seconds

Number of shifts per day = 2

Number of hours per shift = 8

To calculate the required number of presses, we can use the following formula:

Number of presses = (Number of units processed per day / (Machine efficiency * Number of shifts * Number of hours)) * (Punching operation time / 3600)

Number of presses = (10,000 / (0.95 * 2 * 8)) * (10 / 3600) = 52.08

Therefore, approximately 52 presses would be needed to meet the production requirements.

If the press has a scrap rate of 10%, we need to consider the effect of scrapped units on the required number of presses.

Number of scrapped units per day = 10,000 * 0.10 = 1,000

Number of units that can be reworked = 1,000 * 0.70 = 700

To modify the formula for the new scenario, we subtract the reworked units from the total units processed per day:

Number of units processed per day (after rework) = 10,000 - 700 = 9,300

Number of presses (after considering scrap and rework) = (9,300 / (0.95 * 2 * 8)) * (10 / 3600) = 48.48

Therefore, approximately 48 presses would be needed when considering the scrap rate and rework capability.

The new answer is different from Exercise 11 because the scrap rate reduces the effective production rate, resulting in a lower requirement for punch presses. By accounting for scrap and rework, the company can optimize its resource allocation and production planning to meet the desired output while considering the potential loss due to scrap.

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Answer:

rectangular pyramid, 5, 8,5

Step-by-step explanation:

Answer:

✔ rectangular pyramid

This figure will have

✔ 5

faces,

✔ 8

edges, and

✔ 5

vertices.

the person above is correct

The provided sequence is a recursive sequence and the next four terms of the sequence are 4, 6.5, 9, and 11.5.

To determine whether the provided sequence is recursive or explicit, we need to examine the relationship between the terms.

A recursive sequence is defined in terms of previous terms in the sequence, typically using a recurrence relation or formula.

In this case, the formula Aₙ = Aₙ₋₁ + 2.5 defines the nth term in terms of the previous term.

An explicit sequence, on the other hand, can be directly calculated using a formula that does not rely on previous terms.

The formula provides a direct expression for calculating any term of the sequence.

In the provided formula Aₙ = Aₙ₋₁ + 2.5, the current term Aₙ is defined in terms of the previous term Aₙ₋₁.

Therefore, this sequence is a recursive sequence.

Now let's compute the next four terms of the sequence using the provided initial term A₁ = 1.5:

Term 1 (A₁) = 1.5

Term 2 (A₂) = A₁ + 2.5 = 1.5 + 2.5 = 4

Term 3 (A₃) = A₂ + 2.5 = 4 + 2.5 = 6.5

Term 4 (A₄) = A₃ + 2.5 = 6.5 + 2.5 = 9

Term 5 (A₅) = A₄ + 2.5 = 9 + 2.5 = 11.5

Therefore, the next four terms of the sequence are 4, 6.5, 9, and 11.5.

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Answer: 75.2

Step-by-step explanation:

Well, if it isn't the most confusing question ever.

First of all, what is P?

I'll assume its the perimeter...

2*(1.2*2)+4*(8.8*2)

Or

2*2.4+4*17.6

75.2

We know that

• 2/5 are strawberries.

• 1/4 of the strawberries are chocolate covered.

We have to find 1/4 of 2/5, let's multiply these fractions.

Answer:

9\(\frac{75}{84}\)

get a common denominator between 6,12,7,2 = 84

Step-by-step explanation:

\($x$: $x = \frac{x}{6} + \frac{x}{12} + \frac{x}{7} + 5 + \frac{x}{2} + 4$\)

The solution is x = 84

The value of the equation is A = 84

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

x = ( x/6 ) + ( x/12 ) + ( x/7 ) + 5 + ( x/2 ) + 4   be equation (1)

On simplifying the equation , we get

x = [ ( x/6 ) + ( x/12 ) + ( x/7 ) + ( x/2 ) ] + 9

Now , on further simplification , we get

x = [ ( x/7 ) + ( x/2 ) ] + [ ( 2x + x ) / 12 ] + 9

x = ( 3x/12 ) + [ ( 2x + 7x ) / 14 ] + 9

x = ( 3x/12 ) + ( 9x/14 ) + 9

On simplifying the equation , we get

x = ( x/4 ) + ( 9x/14 ) + 9

x = [ ( 14x + 36x ) / 56 ] + 9

x = ( 50x / 56 ) + 9

Subtracting ( 50x/56 ) on both sides of the equation , we get

9 = x - ( 50x/56 )

9 = ( 56x - 50x ) / 56

6x/56 = 9

Multiply by 56 on both sides of the equation , we get

6x = 504

Divide by 6 on both sides of the equation , we get

x = 504/6

x = 84

Therefore , the value of x is 84

Hence , the equation is A = 84

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To find the sum of 305 and 84, proceed as follows:

The answer is 389.

Answer:

Step-by-step explanation:

She collected 2/6 gallon of orange juice from two trees and 2/3 from the last tree.  To add these two fractions, both must have common denominators.

Multiply both the numerator and denominator of 2/3 by 2.  This results in 4/6.

Now you have 4/6 + 2/6 which equals 8/6.  This can be converted to 1 and 2/6, further simplified to 1 and 1/3.  Therefore, Sue collected a total of 1 and 1/3 gallons of orange juice.

.....It's D on Ap3x....

Answer:

308 cm³

Step-by-step explanation:

volume of cylinder = πr²h

volume = (22/7)*(7/2)*(7/2)*8

volume = 308cm³

Option B) George's arrival changes the mood because he complains that Beneatha is giving them a lecture on their African past

In Act 2 of A Raisin in the Sun, George Murchison's arrival changes the mood of the scene as he complains that Beneatha is giving them a lecture on their African past. George's comments create tension and conflict among the characters, particularly with Beneatha, who is exploring her African heritage. His attitude towards Beneatha's interest in her roots is dismissive and condescending, which generates discomfort and disagreement among the characters. George's arrival highlights the cultural differences between him and the Younger family and demonstrates the generational and ideological divides within the African American community. Thus, his presence is a catalyst for revealing deeper tensions and conflicts within the play.

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Complete question:

How does the arrival of George Murchison change the mood of the scene?

A) George's arrival changes the mood because he doesn't take part in the dance

B) George's arrival changes the mood because he complains that Beneatha is giving them a lecture on their African past

C) George's arrival changes the mood because he was rich, and they didn't like that a rich white person was in their house

D) George's arrival changes the mood because he had a gun

Initial estimates of the probabilities of events are known as Prior Probabilities.

Prior Probabilities can be defined as the probability of the event before the event takes place.

For Example ,Let there be three wells X,Y,Z with water in it . it is given that one of the wells have the water that is fit for drinking. So the prior probability that Well Z can have drinking water is 1/3 i.e. 0.333  .

Therefore , the Initial estimates of the probabilities of events are known as Prior Probabilities.

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