The table shows the average cost, in dollars, of a movie ticket in the United States for different years. Calculate the correlation coefficient. Round to the nearest hundredth.

Year Cost
1948 0.36
1963 0.86
1974 1.89
1978 2.34
1985 3.55
1991 4.21
1997 4.59
2005 6.41
2010 7.89



0.12

0.96

0.93

1

The one side of rectangle is 11 feet and other side is 19 feet.

Step-by-step explanation:

Given,

Area of rectangle = 209 square feet

Let one side of rectangle = w

other side of rectangle = 2w-3

Area of rectangle = One side * other side

[tex]209=w*(2w-3)\\209=2w^2-3w[/tex]

[tex]0=2w^2-3w-209\\2w^2-3w-209=0[/tex]

[tex]2w^2+19w-22w-209=0\\w(2w+19)-11(2w+19)=0\\(2w+19)(w-11)=0[/tex]

Either;

2w+19=0        =>2w=-19

Or,

w-11=0            => w=11

As length cannot be negative, therefore,

One side of rectangle = 11 feet

Other side of rectangle = 2w-3 = 2(11)-3 = 22-3 = 19 feet

The one side of rectangle is 11 feet and other side is 19 feet.

Keywords: rectangle, area

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Answer:

b. Shift left 3 units

Step-by-step explanation:

You're given

y = √(x + 3)

y = √(x - (-3))

y = √(x - amount_shifted)

amount shifted = -3

so shifted 3 units and the negative means it's shifted to the left

Answer:

10.32

Step-by-step explanation:

10.31988

the 9 makes the 1 to a 2 so...

10.32

Step-by-step explanation:

the farmer plants 0.4 of the total field which is 2.3 acres

⇒0.4×2.3= 0.92 acres

now draw a grid of area 2.3 acres and in that area shade 0.92 acres.Use a proper scale to draw the grid. It will a be pictorial representation of the proper and its solution.

Answer:

Step-by-step explanation:

a) The maximum number of houses Sam can build in 24 hours is 8, so the constraint is in construction, not decoration. For each small house Sam constructs, he makes $10/3 = $3.33 per hour of work. For each large house Sam constructs, he makes $15/5 = $3.00 per hour. The most money is to be made by building only small houses.

Sam should make 8 small houses and 0 large houses in 24 hours.

__

b) If Sam works 8-hour days, then he can complete at most 80 small houses. The constraint remains in construction, so the answer is the same: build only small houses.

_____

If Sam works more than 16 2/3 hours per day, he can build 100 large houses or more, so the constraint moves to decoration. The decorator makes more money by decorating large houses, so all the effort should go to construction of large houses.

If Sam works between 10 and 16 2/3 hours per day, the best revenue will come from some mix. The problem statement is unclear as to how many hours Sam works in 30 days.

Answer:

Part A) 170.66$ would be the original price.

Part B) 256$ would be the price that the store paid for the music player.

Part B) What you need to balance is your markup, meaning how much to raise your price, and your markdown or discount, meaning, how to much to decrease prices.

Step-by-step explanation:

Part A) Determining the Original Price

Note: when a shopkeeper devalues of a certain product or commodity as he/she is being unable to sold the product or commodity at the original selling price that was planned, it normally means the product or commodity is being markdown due to certain issues.

So, a music player was marked down by 1/4 of the original price, and we have to calculate the original price if the sales price is $128.

Let 'p' be the original price

As a music player was marked down by 1/4 of the original price

So, Markdown = 1/4p

As the sales price is $128

As the Sale price = [tex]p - \frac{p}{4}[/tex] ⇒ [tex]\frac{3p}{4}[/tex]

[tex]128 = \frac{3p}{4}[/tex]

[tex]552 =3p[/tex]

[tex]p =170.66[/tex]          

Hence, 170.66$ would the original price.

Part B) Determining the Price that the store paid for the music player

When an amount is added to the cost price of a product or commodity in order to determine the selling price, it means the the product or commodity is being marked up.

So, as the music player was marked up by 1/2 before it was placed on the sales floor and we have to determine the price that store paid for the player.

So, dividing the original price by 2 and adding the result to the original price would give us the price that store had to pay for the music player.

As the original price is 170.66.

So, the price that the store paid for the music player can be calculated as:

price = 170.66 + 170.66/2

price = 170.66 + 85.33

price = 255.99$  ≈ 256$

Therefore, 256$ was the price that the store paid for the music player.

Part C) Determining the difference between the discount price and the price that the store paid for the music

For example, let suppose you are a shopkeeper and have a jeans fabric business. You want to make money from it. But, in order to earn money from selling jeans fabric, you have to make sure that your price must be at the right value price both in terms of generating money and also giving your customer a great value for the money to given them a decent deal.

What you need to balance is your markup, meaning how much to raise your price, and your markdown, meaning, how to much to decrease prices.

In business, the conditions may never always remain favorable due to certain circumstance, hence bad days. Sometimes, the conditions get ideal for business, hence good days.

As I earlier sated that when a shopkeeper devalues of a certain product or commodity as he/she is being unable to sold the product or commodity at the original selling price that was planned, it normally means the product or commodity is being markdown due to certain issues.

For example, the cost price of 1 Jeans fabric is 10$, and you want to earn profit. So, you mark up your fabric to 30$.  As $30 is $20 more than $10. So, markup value will be 2. In terms of percentage, it means you have a markup of 200%.

But, due to certain issues, your sales are being effected due to certain condition. In order to not affect the sales, you want to markdown the price - a kind of discount. Your starting price was $30 and want to decrease the price to $20. It means the difference is $10. So, you have made a markup or given a discount of $30/$10 = 0.33. In terms of percentage, it is around 33%. So, you have given the discount of 33% to hope for the great sales.

So, in the question, when the music player was marked down by 1/4 of the original price, it means the discount of 1/4 of the original price was provided. As the sale price was $128, and original price was $170.66. So, discount of 1/4 or 25% was offered.

As the original price was $170, and it was marked up by 1/2 by the owner or creator of music player before it was placed on the sales floor. So, 256$ was the price that the store paid for the music player.

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[tex]

2(x+3)=12 \\

x+3=6 \\

x=3

[/tex]

Hope this helps.

Answer:

The answer is 1 solution.

Step-by-step explanation:

2(x+3)=12

First, do the multiplication by multiplying two times everything in the parentheses

2x+6=12

Then, subtract six from twelve.

2x+6=12

   -6    -6

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

2x=6

Finally, divide everything by two.

x=3

It has one solution, and the solution is x=3!

Answer:

Post the questions and I'll do my best to help

Step-by-step explanation:

Answer:

[tex]\sum\limits^{n=6}_{n=1} {(-4+8n)}[/tex] is the notation to represent the sum of first six terms of the sequence 4, 12, 20, ....

So, the option "the summation from n equals 1 to 6 of negative 4 plus 8 times n" is the correct option as:    [tex] \sum\limits^{n=N}_{n=1} {(-4+8n)}[/tex].

Step-by-step explanation:

Let us consider the sequence

4, 12, 20, ....

As d = 12-4 = 20 - 12 = 8

Hence, the sequence is an arithmetic as the common difference between consecutive terms is same (constant).

So,

For the arithmetic sequence,

a, a + d, a + 2d, a + 3d.........a + (n - 1)d

The nth term = a + (n - 1)d

a = first term, d = common difference

For the given sequence 4, 12, 20,...

a = 4, d = 8

Lets put these values in Summation Formula.

Sigma notation to represent the sum of the first six terms of the following sequence:  [tex] \sum\limits^{n=N}_{n=1} {a+(n-1)d}[/tex]

⇒   [tex] \sum\limits^{n=N}_{n=1} {4+(n-1)8}[/tex]

⇒   [tex] \sum\limits^{n=N}_{n=1} {(4+8n-8)}[/tex]

⇒   [tex] \sum\limits^{n=N}_{n=1} {(-4+8n)}[/tex]

Hence, [tex]\sum\limits^{n=6}_{n=1} {(-4+8n)}[/tex] is the notation to represent the sum of first six terms of the sequence 4, 12, 20, .....

So, the option "the summation from n equals 1 to 6 of negative 4 plus 8 times n" is the correct option as:  [tex] \sum\limits^{n=N}_{n=1} {-4+8n}[/tex].

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Answer:

the summation from n equals 1 to 6 of negative 4 plus 8 times n

Answer:

0ne week= 8 miles

W=5n

Answer:

(3, - 25 )

Step-by-step explanation:

Given a quadratic in standard form : y = ax² + bx + c : a ≠ 0

The the x- coordinate of the turning point is

x = - [tex]\frac{b}{2a}[/tex]

Given

y = (x + 2)(x - 8) ← expand factors using FOIL

  = x² - 6x - 16 ← in standard form

with a = 1 and b = - 6, thus

x = - [tex]\frac{-6}{2}[/tex] = 3

Substitute x = 3 into the equation for corresponding value of y

y = (3 + 2)(3 - 8) = 5(- 5) = - 25

turning point at (3, - 25 )

Answer:

y=3

Step-by-step explanation:

Add the y and divide

7y=21

21/7=3

y=3

Answer:

it's already simplified :) your welcome

Answer:

It sold for $9.20 more in 1992 than in 1982.

It sold for $20.70 in 1992.

Step-by-step explanation:

The price in 1982 was $11.50.

The price increased by 80% of $11.50.

We need to find 80% of $11.50.

To find a percent of a number, multiply the percent by the number.

80% of $11.50 =

= 80% * $11.50

= 0.8 * $11.50

= $9.20

It sold for $9.20 more in 1992.

The price in 1992 is the original price of the belt plus the amount of increase.

$11.50 + $9.20 = $20.70

It sold for $20.70 in 1992 than in 1982.

Answer:

see the explanation

Step-by-step explanation:

Verify the range of each quadratic function

case 1) we have

[tex]f(x)=(x-4)^2+5[/tex]

This is a vertical parabola open upward (the leading coefficient is positive)

The function is written in vertex form

The vertex represent a minimum

The vertex is the point (4,5)

The range is the interval [5,∞)

[tex]y\geq 5[/tex]

case 2) we have

[tex]f(x)=-(x-4)^2+5[/tex]

This is a vertical parabola open downward (the leading coefficient is negative)

The function is written in vertex form

The vertex represent a maximum

The vertex is the point (4,5)

The range is the interval (-∞,5]

[tex]y\leq 5[/tex]

case 3) we have

[tex]f(x)=(x-5)^2+4[/tex]

This is a vertical parabola open upward (the leading coefficient is positive)

The function is written in vertex form

The vertex represent a minimum

The vertex is the point (5,4)

The range is the interval [4,∞)

[tex]y\geq 4[/tex]

case 4) we have

[tex]f(x)=-(x-5)^2+4[/tex]

This is a vertical parabola open downward (the leading coefficient is negative)

The function is written in vertex form

The vertex represent a maximum

The vertex is the point (5,4)

The range is the interval (-∞,4]

[tex]y\leq 4[/tex]

Answer:

  (a) d = 0.012v^2

  (b) 4.8 m

  (c) 25 m/s

Step-by-step explanation:

(a) Writing an equation to fit a bunch of data is often a matter of trial and error. You can often get an idea of the sort of function that is involved by graphing the data points.*

When we do that, we see the relationship is non-linear with an upward curvature. It might be described by a polynomial or exponential function.

When we try a quadratic equation, we find the fit is really quite good. The graphing calculator that does this quadratic regression analysis tells us the equation is essentially ...

  d = 0.012·v^2

__

(b) The equation predicts a depth of 4.8 m.

  d = 0.012·20^2 = 4.8

__

(c) Solving for speed, we get a speed of 25 m/s.

  7.5 = 0.012v^2

  625 = v^2 . . . . . . divide by .012

  25 = v . . . . . . . . . take the square root

_____

* The energy of a falling object is proportional to the square of its speed. If we assume that the depth of penetration into the clay is proportional to the energy absorbed, then it is not surprising to see a quadratic relationship between speed and distance. What is surprising is that this relationship would show up in middle school math problem, not a high-school physics problem.

Essentially, you have to assume the form of the equation, then find the coefficients that make it so. Working with the evenly spaced table values of 5, 10, 15 m/s can simplify the effort.

A graphing calculator or spreadsheet can do the bulk of the work once the data is entered.

Answer:

30,000 cm^2.

Step-by-step explanation:

The area  = 3*1 = 3 square meters.

There are 100^2 = 10,000 cm^2 in a square meter

So the area in square centimeters is 3 * 10,000 = 30,000.

Answer:

Table #4

Step-by-step explanation:

because for every one x added, 2 y are added( if that makes any sense)

Answer:

Second from the top

The answer you have selected:

40:8 , 50:10, 60:14, 90:18

Proportions can be viewed as fractions:

40/8, 50/10, 60/14, 90/18

Now we have to simplify these fractions

5 , 5 , 4.3, 5

Unfortunately, they do not all come out to the same number, so this answer is incorrect

The second answer from the top:

4/2 , 7/3.5, 8/4, 10/5

These all equal 2 when simplified

2, 2, 2, 2

This shows a proportional relationship between x and y. If you would like to continue to make sure the bottom two are incorrect, you can use the steps that I have used for the first two. Hope this helps :)

Answer:135,136,137

Step-by-step explanation:

408 divided by 3=136

136-1=135

136+1=137

135,136,137

The largest number of the three consecutive even numbers that sum to 408 is 138.

The problem is a classic arithmetic sequence problem in mathematics, where a common difference exists between each number. For consecutive even numbers, this difference is 2. If the sum of three consecutive even numbers is 408, we can form the equation 3n+6=408 (since the first number is 'n', the next is 'n+2', and the following is 'n+4'). Solving this equation gives us n=134, hence the sequence of numbers is 134, 136 and 138. The largest number in this sequence is 138.

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Answer:

1) $250

2) $200 + $50x

Step-by-step explanation:

1)

$200 (start up fee) + $50 * ( 1 month ) = $200 + $50 = $250

2)

$200 (start up fee) + $50 * ( x months ) = $200 + $50x

Hope this helps :)

Answer:

4 terms

Step-by-step explanation:

Terms are separated by adding or subtracting.

The terms are:

14m

-8.8n

5p

-1

The variables are not separate terms because they are multiplying with the coefficient, not adding or subtracting.

The garden view hotel is 235 feet tall

Step-by-step explanation:

The given is:

We need to find the height of the garden view hotel

Assume that the height of garden view hotel is x feet and the height of the plaza hotel is y feet

∵ The height of the garden view hotel = x feet

∵ The height of the plaza hotel = y feet

∵ The height of the garden view hotel is 17 less than twice the

    height of the plaza hotel

- That means x is less than 2 × y by 17, equate x by the difference

   of 2 × y and 17

∴ x = 2y - 17 ⇒ (1)

∵ Their combined height = 361 feet

∴ x + y = 361

- Find y in terms of x by subtraction x from both sides

∴ y = 361 - x ⇒ (2)

Substitute y in equation (1) by equation (2)

∵ x = 2(361 - x) - 17

- Simplify the right hand side

∴ x = 722 - 2x - 17

- Add like terms

∴ x = 705 - 2x

- Add 2x to both sides

∴ 3x = 705

- Divide both sides by 3

∴ x = 235

The garden view hotel is 235 feet tall

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The height of the Gardenview Hotel is 235 feet, which we found by first creating a system of equations using the information given and then solving by substitution.

To find the height of the Gardenview Hotel, let's create a system of equations based on the information given. Let G be the height of the Gardenview Hotel and P be the height of the Plaza Hotel. We are told that the Gardenview Hotel is seventeen less than twice the height of the Plaza Hotel, which we can express as G = 2P - 17. Additionally, we know their combined height is 361 feet, so G + P = 361.

Now we can solve the system of equations step by step:

Substitute the expression for G from the first equation into the second equation: (2P - 17) + P = 361.

Combine like terms: 3P - 17 = 361.

Add 17 to both sides of the equation: 3P = 378.

Divide both sides of the equation by 3 to find the height of the Plaza Hotel: P = 126.

Now use the value of P to solve for G using the first equation: G = 2(126) - 17.

Simplify to find the height of the Gardenview Hotel: G = 252 - 17.

Thus, the height of the Gardenview Hotel is 235 feet.

Answer:

The roots of the equation are -2.5 and -2

Step-by-step explanation:

We are given a quadratic equation and we are supposed to find the roots of the equation.

y = [tex]2x^{2}+9x+10[/tex]

To find the roots put y= 0.

We can factorize the given equation to get the roots.

[tex]2x^{2}+ 4x + 5x + 10[/tex] = 0

2x ( x + 2 ) + 5 ( x + 2 ) = 0

( 2x + 5 )( x + 2 ) = 0

x = -[tex]\frac{5}{2}[/tex]  and  x = -2

Hence the roots of the quadratic equation are -2.5 and -2.

Answer:

5≤u

Step-by-step explanation:

Put the words and numbers into an equation:

-5u+27≤2

Put all like terms on one side:

27-2≤5u ---> Do you see what I did there? Now you don't have to work with negatives. :)

Simplify:

25≤5u

Solve:

5≤u

:)

Answer:

25

Step-by-step explanation:

If a two digit number is a multiple of 5, then it ends with 0 or with 5.

If a two digit number ends with 0, then the number of ones is 0 and the number of tens must be 3 less that is impossible.

Hence, this two digit number must end with 5. If it ends with 5, then the number of ones is 5 and number of tens must be 5 - 3 = 2.

Therefore, the number is 25.

The question is about two-digit numbers that are multiples of 5 and have fewer tens than ones. Numbers such as 15, 25, 35, 45, 50, 65, 75, 85, and 95 satisfy these conditions.

The subject of this question is a mathematical problem solving task regarding two-digit numbers and their properties. The most important criteria are that the number is a multiple of 5 and has less tens than ones. First, multiples of 5 are numbers that end in 0 or 5. Secondly, having less tens than ones implies that the digit in the ones place must be greater than the digit in the tens place.

An example of a number that fulfills these conditions would be 15. Here, the digit in the ones place (5) is greater than the digit in the tens place (1). Also, 15 is a multiple of 5 because it can be divided by 5 without leaving a remainder.

However, 15 is just one of many possible answers. Other numbers that satisfy these conditions are: 25, 35, 45, 50, 65, 75, 85, and 95.

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Answer:

A

Step-by-step explanation:

We know that negative numbers are smaller than positive numbers, so let's compare the 2 negative numbers. Unlike positive numbers, the more negative it has, the smaller it is. So we know the smallest is -20. Without looking at the other numbers (even though I did just in case) we know that this is correct. They say least to greatest, so -20 should be first. A is the only one that starts with -20.

The one should pay [tex]2\frac{3}{16}[/tex] dollars

Step-by-step explanation:

Let us revise how to multiply a mixed number by a proper fraction

∵ One yard of a ribbon costs [tex]3\frac{1}{2}[/tex] dollars

∵ We need to find the cost of [tex]\frac{5}{8}[/tex] yards

- Multiply the cost of 1 yard by [tex]\frac{5}{8}[/tex]

∵ [tex]3\frac{1}{2}[/tex] = [tex]\frac{3(2)+1}{2}[/tex] = [tex]\frac{6+1}{2}[/tex]

∴ [tex]3\frac{1}{2}[/tex] = [tex]\frac{7}{2}[/tex]

∵ The cost = [tex]\frac{7}{2}[/tex] × [tex]\frac{5}{8}[/tex]

∴ The cost = [tex]\frac{7(5)}{2(8)}[/tex]

∴ The cost = [tex]\frac{35}{16}[/tex]

Change the improper fraction to a mixed number

∵ 35 ÷ 16 = 2 and remainder 3 ⇒ (16 × 2 = 32)

∴ [tex]\frac{35}{16}[/tex] = [tex]2\frac{3}{16}[/tex]

∴ The cost = [tex]2\frac{3}{16}[/tex] dollars

The one should pay [tex]2\frac{3}{16}[/tex] dollars

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Answer:

2.1875

Step-by-step explanation:

You would have to sell approximately 52 bracelets per week in order to pay your fee.

190 ÷ 3.60 = 52.7

This is your net profit after covering both the cost of the glow sticks and the booth fee. The actual profit you make will depend on how many glow sticks you manage to sell at the convention.

To determine the profit you make from selling glow sticks at the Star Wars convention, you can calculate the profit per unit and the total profit considering the costs and selling price.

Here are the key values:

Cost per glow stick: $2.02

Fixed weekly fee for the booth: $190

Selling price per glow stick: $3.60

Now, let's calculate the profit per unit:

Profit per unit = Selling price per unit - Cost per unit

Profit per unit = $3.60 - $2.02 = $1.58

This means you make a profit of $1.58 for each glow stick you sell.

To find the total profit, you need to consider how many glow sticks you sell. Let's assume you sell 'x' glow sticks. Your total profit can be calculated as:

Total Profit = Profit per unit × Number of Units Sold

Total Profit = $1.58x

Now, you need to take into account the fixed weekly booth fee of $190. So, your total profit after deducting the booth fee will be:

Total Profit - Booth Fee = $1.58x - $190

This is your net profit after covering both the cost of the glow sticks and the booth fee. The actual profit you make will depend on how many glow sticks you manage to sell at the convention.

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Final answer:

Jada's speed (⅔ mile per minute) is three times faster than her cousin's speed (⅔ mile per minute); thus, Jada is moving faster.

Explanation:

To determine who is moving faster between Jada and her cousin, we need to calculate their swimming speeds and compare them. Speed can be calculated by dividing the distance by the time it takes to cover that distance.

Jada's Speed:

Jada swims 2 miles in 12 minutes. To find her speed, we use the formula:

Speed = Distance ÷ Time

Speed = 2 miles ÷ 12 minutes = ⅔ mile per minute

Jada's Cousin's Speed:

Jada's cousin swims 1 mile in 24 minutes. Using the same formula:

Speed = 1 mile ÷ 24 minutes = ⅔ mile per minute

Comparison and Result:

Jada's speed is ⅔ mile per minute, whereas her cousin's speed is ⅔ mile per minute. Jada is swimming at a higher speed because she covers more distance in less time compared to her cousin. Specifically, she swims three times faster, evidenced by comparing their speeds:

Jada's speed ÷ Cousin's speed = ⅔ mile per minute ÷ ⅔ mile per minute = 3

Therefore, Jada is moving three times faster than her cousin.