The diagram shows a roller-coaster track. Assume that the system is closed.


At which point on the track will a roller-coaster car have the greatest potential energy due to gravity?

A. A
B. D
C. B
D. C

Please HELP!!!

1) Unit Rate of the given options are;

$0.05 for 1 ounce

24 bottles per case

16 ounces per bottle

2) Rate of the given options are;

5 bottles for $5

$1 per 16 ounces

A unit rate (or unit ratio) describes how many units of the first type of quantity corresponds to one unit of the second type of quantity. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second.

Meanwhile, a rate is the ratio between two different units of measure.

Thus;

1) Unit Rate of the given options are;

$0.05 for 1 ounce

24 bottles per case

16 ounces per bottle

2) Rate of the given options are;

5 bottles for $5

$1 per 16 ounces

3) The option that is neither a unit rate nor a rate is; 36 bottles

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The area of a sidewalk that surrounds a rectangle of 4 ft by 6 ft  is 56 ft²

The given situation can be depicted in the attached picture.

Recall the formula to calculate the area of a rectangle:

  A = l ⨉ w

Where:

l = length

w = wide

In the attached picture, the area of the sidewalk is the one with green color.

Notice that:

Area of sidewalk = area of bigger rectangle – area of smaller rectangle

Parameters of the bigger rectangle:

l = 6 + 2 + 2 = 10 ft.

w = 4 + 2 + 2 = 8 ft.

Area of bigger rectangle = 10 x 8 = 80 ft²

Parameters of the smaller rectangle:

l = 6 ft.

w = 4 ft.

Area of bigger rectangle = 6 x 4 = 24 ft²

Hence,

Area of sidewalk = 80 - 24 = 56 ft²

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Cameron's current service charge of $0.95 per song, and the new service charge of $0.89 per song and $12 fee for joining, gives;

To Formulate

The charges for songs on the current music service is, C1 = 0.95•s

The charges for the new download service is, C2 = 12 + 0.89•s

Where the $12 is the joining fee

When the cost is the same for both service, we have;

C1 = C2

Which gives;

The equation to represent when the cost for both service is the same is therefore;

0.95•s = 12 + 0.89•s

Computing;

The number of songs that gives the same costs is therefore;

0.95•s = 12 + 0.89•s

12 = 0.95•s - 0.89•s = 0.06•s

s = 12 ÷ 0.06 = 200

Interpreting the solution;

The interpretation is, the cost of songs downloaded on both service will be the same, when 200 songs are downloaded.

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Answer:

Ramon deposited $204 monthly

Step-by-step explanation:

Step 1: Firstly convert 2 years to month

1 year = 12 month

∴ 2 years = 24 month

Step 2: Divide $4896 by 24

➟ 4896 ÷ 24

➟ 204

B(4015) is the [tex]2008^{th[/tex]term of the sequence.

What is the sequence?

Since the mean of the first terms is, the sum of the first terms is n². Thus, the sum of the first 2007 terms is 2007² and the sum of the first 2008 terms is 2008² Hence, the 2008th term of the sequence is

2008² - 2007² = (2008 + 2007) (2008 - 2007) = 4015

Note that n² is the sum of the first n odd integers.

From inspection, we see that the sum of the sequence is n². We also notice that n² is the sum of the first n odd integers.

Because 4015 is the only odd integer, B is the answer.

B(4015) is the [tex]2008^{th[/tex]term of the sequence.

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Answer:

nnk;'/mnhjjfn;h;;vhxpycoyyoly,

Step-by-step explanation:

I]o]ogi-gogoig]gogh]o]v]b]bob]b]k k k lgg]goghjppkngghhjjl

No generalizations can be made because the sample size is too small. Therefore, the correct option is option A.

A restaurant is an institution of business which prepares and provides clients with food and beverages. Although many restaurants now provide take-out as well as food delivery services, meals are often served and consumed on the premises.

A restaurant serves breakfast, lunch, and dinner. The restaurant offers a daily special. To estimate the percentage of customers who order the daily specials, the restaurant selected a random sample of customers who had lunch during 2 month period. From the results, the restaurant determined that 25% of these customers ordered the daily special. No generalizations can be made because the sample size is too small.

Therefore, the correct option is option A.

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The equation 3(4x + 12) = 2(6x + 8) has no solution because the variable x was neglected as it equals 0.

It should be noted that the equation given is illustrated as:

3(4x + 12) = 2(6x + 8)

Open the parentheses

12x + 36 = 12x + 16

Collect like terms

12x - 12x = 16 - 36

0 = -20

Therefore, it has no solution.

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Answer:

629.3 cm3

Step-by-step explanation:

This is known as a rectangular prism aka cuboid.

The formula for the volume is Length x width x height

so 14.5x7x6.2 = 629.3 cm cubed

answer

ex 17

2 3/4 ×8

=11/4×8/1

=11/24

ex 18

9/2× 5/4

=36/10

4

Answer:

Rise is 4

Run is 5

Slope is 4/5

Step-by-step explanation:

The 2 points on the line (4,-3) and (9,1)

Rise is 4

Run is 5

Slope is 4/5

Answer:

The answer is 6.

Step-by-step explanation:

A negative and a negative makes a positive when the problem is written as
x - (-x)

So 2 - (-4) equals 2 + 4

which is simply 6

Answer:

6

Step-by-step explanation:

Two negatives cancel out a positive.

2-(4) should turn into 2 +4

2+4 =6

The location of the y value of R' after using the translation rule is -10

The translation rule is given as:

(x + 4, y - 7)

The pre-image of R is located at (-17, -3)

Rewrite as

R = (-17, -3)

When the translation rule is applied, we have:

R' = (-17 + 4, -3 - 7)

Evaluate

R' = (-13, -10)

Remove the x coordinate

R'y = -10

Hence, the location of the y value of R' after using the translation rule is -10

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Step-by-step explanation:

gradient = slope or several other words.

it describes how strongly a line (or tangent to a bent curve) is going up or down or ... if it is changing at all.

it is represented by the ratio

(y coordinate change / x coordinate change)

when going from one point on the line to another.

in our case, when going from A to B we have

x changes by -2k (from 3k to k).

y changes by -11 (from 8 to -3).

so, the gradient or slope is

-11/-2k = 3

11/2k = 3

11 = 3×2k = 6k

k = 11/6

A = (33/6, 8) = (11/2, 8)

B = (11/6, -3)

Answer:

1)  -5x² + 13x + 6

2) B(x)  =(4x + 1 )(2x + 3)

  A(x) = (5x +2)(3-x)

Step-by-step explanation:

1) Expand the equation by using distributive property. Then simplify  by combining the like terms.

A(x) = (3 -x)2² - (x -3)(7x+ 4) - 18 + 2x²

         = (3 - x)4 - [x*7x + x*4 - 3*7x - 3*4] - 18 + 2x²

         = 3*4 - x*4 - [7x² + 4x - 21x - 12] - 18 + 2x²

         = 12 - 4x - 7x² - 4x + 21x + 12 - 18 + 2x²

        = 2x² - 7x² -4x - 4x + 21x + 12 + 12 - 18

       = -5x² + 13x + 6

B(x) = (3x + 2)² - (x - 1)²

Identities:

(a + b)² = a² + 2ab + b² ; Here a =3x & b = 2

(m -n)² = m² - 2mn + n² ; Here m = x & n = 1

2) B(x) = (3x)² + 2*3x*2 + 2² - [x² - 2*x*1 + 1]

      = 9x² + 12x + 4 - [x² - 2x + 1]

      = 9x² + 12x + 4 - x²+ 2x - 1

     = 9x² - x² + 12x + 2x  + 4 - 1

     = 8x² + 14x +3

Product = 8*3 = 24

Sum = 14

Factors = 2 , 12    {2*12 = 24 & 2 +12= 14}

    = 8x² + 2x + 12x + 3    {Rewrite the middle term}

    = 2x(4x + 1) + 3(4x + 1)      

   = (4x + 1 )(2x + 3)

  A(x) = - 5x² + 13x + 6

       = -5x² + 15x -2x + 6

       = 5x(-x +3) +2 (-x + 3)

       = (5x +2)(3-x)

4) B(x) - 3 = 8x² + 14x + 3 - 3

                = 8x² + 14x

                = 2x *4x + 2x *7

                =2x(4x + 7)

Hence proved.

                           B(x) = 3

            8x²  + 14x + 3 = 3

        8x² + 14x + 3 - 3 = 0

           8x² + 14x         = 0

              2x(4x + 7)     = 0

2x = 0   or    4x + 7 = 0

 x = 0   or          4x = -7

                            [tex]\sf x = \dfrac{-7}{4}[/tex]

  x = 0 or    [tex]\sf \dfrac{-7}{4}[/tex]

Answer:

x<-5/4 or x>2

Step-by-step explanation:

-4x -11 > 5

    +11   +11

-4x>5

/      /

-4   -4   Switch the sign when divided by a negative.

x<-5/4

8x - 7 > 9

    +7   +7

8x>16

/      /

8    8

x>2

Answer:

1

Step-by-step explanation:

a) Flip the equation

4x - 2 = 2

b) Add 2 to both sides

4x - 2 + 2 = 2 + 2

4x = 4

c) Divide both sides by 4

4x/4 = 4/4

x = 1

The amount of the discount that was given is $300.

A discount reduces the price of an item. When a discount is given, the item becomes cheaper. VAT is value added tax. VAT increases the price of an item.

The equation that can be used to represent the total cost of the bicycle is:

Total cost after VAT and discount = (1 + VAT) x (marked price - discount)

1921 = (1 + 0.13) x (2,000 - d)

1921 = 1.13 x (2,000 - d)

In order to determine the value of discount, take the following steps:

Divide both sides of the above equation by 1.13

1921 / 1.13 = 2000 - d

1,700 = 2,000 - d

Combine similar terms: 2000 - 1700 = d

Add similar terms together: d = 300

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The equation of the line is x = 5

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, let's find the slope and y-intercept

(5, 0)(5, - 2)

m = -2 - 0 / 5 - 5

m = -2 / 0

m = infinity

Hence,  It is a vertical line, since the x is the same for both of them, and it is equal to  both times.

Therefore, the equation of the line is x = 5

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Answer:

A) The unit prices are the same.

Step-by-step explanation:

First convert dollars to cents to make the calculation easier

Package of 50 paper plates costs $2.50
$2.50 = 2.50 x 100 = 250¢
So the unit price, which is the price per paper plate = 250/50 = 5¢

Package of 80 paper plates costs $4.00
$4.00 = 4.00 x 100 = 400¢
So the unit price, which is the price per paper plate = 400/80 = 5¢

So the unit prices of both packages are the same

Using scientific notation, the first step in simplifying the expression is given by:

a. Addition and subtraction requires the terms to be "like terms" with the same power of the base 10, so you would need to change the second number to (0.026 x 10^5).

A number in scientific notation is given by:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex].

For two numbers in scientific notation to be added or subtracted, they need to have the same exponent, which removes options b and c.

Moving the second number for 10^3 to 10^5 would be equivalent to a multiplication by 100, hence we have to divide by 100 at the base, that is:

2.6 x 10^3 = (2.6/100) x 10^5 = 0.026 x 10^5.

Hence option a is correct.

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From the calculation below, the equivalent to the fraction represented by point M on the number line is [tex]\frac{1}{4}[/tex].

On the number line, it can be observed that there are eight points starting from the first point after 0 up to 1.

Since M is on the second point on the number line, we can have:

P = Point at which M is located on the number line = 2

T = Total number of points on the number line = 8

Therefore, we have:

[tex]M =\frac{P}{T}[/tex]

[tex]M=\frac{2}{8}[/tex]

[tex]M =\frac{1}{4}[/tex]

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Based on the price of the current model of a sports car, the price increase for the next model will be $1,564

The price of the next model of the sports car will be $35,564.

The increase in price in dollar terms for the next model of the sports car can be found by the formula:
= Current cost of current model x Price increase in percentage

= 34,000 x 4.6%

= $1,564

The price of the next model is therefore:

= Current price of current model + Price increase

= 34,000 + 1,564

= $35,564

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The solution to the inequality using William's template is x  > 21.5/19

The inequality expression is given as

-1.5(4x + 1) > 45 - 25(x + 1)

For parentheses: Distribute

So, we have

-6x - 1.5 > 45 - 25x - 25

2. If necessary: Combine Terms

So, we have

19x  > 21.5

3. Apply properties: Divide both sides by 19

x  > 21.5/19

Hence, the solution to the inequality using William's template is x  > 21.5/19

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The company must produce 25 t-shirts to break even.

Here, we are given that a company producing t-shirts charges $125 for the design and set up plus $5 per tee.

This means-

fixed cost of producing the t-shirts = $125

Variable cost of producing a t-shirt = $5

Let x be the number of t-shirts produced

Thus, the total cost of producing t-shirts will be-

Total cost = 125 + 5x

Further, the selling price of 1 t-shirt = $10

Thus, selling price of x t-shirts = $10x

Now, at the break even point, the profit is 0, this implies-

Selling price = cost price

⇒ 10x = 125 + 5x

10x - 5x = 125

5x = 125

x = 125/5

x = 25

Thus, the company must produce 25 t-shirts to break even.

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Answer:

he traveled 900 feet

Step-by-step explanation:

250 + 650 = 900

Mr. Carter traveled a total distance of 900 feet from his boat to where he ended up.

Here, we have to find the total distance that Mr. Carter traveled from his boat to where he ended up, we need to calculate the sum of the distances above and below sea level.

The distance above sea level is 250 feet (his house boat's level), and the distance below sea level is 650 feet (where he ended up after jumping).

Total distance traveled = Distance above sea level + Distance below sea level

Total distance traveled = 250 feet + 650 feet

Total distance traveled = 900 feet

Mr. Carter traveled a total distance of 900 feet from his boat to where he ended up.

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Answer:

exact form: 17/10

decimal form: 1.7

mixed number form: 1  7/10

Step-by-step explanation:

Answer: it is upside down

Step-by-step explanation:

cant see the problem