Use a graphing calculator to find the equation of the line of best fit for the data in the table below. Find the value of the correlation coefficient r. Then predict the number
of movie tickets sold in 2014
years- 1998,1999,2000,2001,2002,2003,2004,2005,2006,2007

tickets sold(millions)- 1282,1312,1317,1324,1365,1381,1383,1423,1449,1462

The values of sin2x, cos2x and tan2x is 120/169, -119/169 and -120/119 respectively.

What is cosine?

In mathematics, the cos meaning refers to the cosine function, which is taught in the most crucial geometry lesson, trigonometry. One of the three primary uses of trigonometry is the cosine function. Sine, cosine, and tangent are the three trigonometric ratios that are also referred to as these three functions.

The cosine of an angle is defined by the cos meaning in trigonometry. This angle, which is an acute angle in a right-angled triangle, is taken into account when determining the ratios. As a result, the ratio between an angle's adjacent side and the triangle's hypotenuse is the cosine of an angle in a right triangle.

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Answer:

(x - 3) (x - 9)

Step-by-step explanation:

x² - 12x + 27

x² - 3x - 9x + 27

x(x - 3) - 9(x - 3)

(x - 3) (x - 9)

Thus, The answer is (x - 3) (x - 9)

The number of seconds until the bottle hits the aground is 7.1 seconds or 0.1 seconds

The correct equation is 5x²+40x+3 = y

The quadratic formula states that

y=(-b±√b²-4ab)/2a

where a= 5, b= 40 and c= 3

Applying these figures into the formula we have

(-40±√40²-4*5*3)/2*5

Simplifying this to have

(-40±√1600-60)/10

⇒(-40±√1540)/10

⇒(-40±39)/10

This means that

y= -1/10 or -70/10

y= -0.1 or -7.5

In conclusion the time in seconds until the bottle hits the ground is 0.1 sec or 7.5 seconds

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The inequality on the graph can be written as:y ≥ -x + 4

On the graph, we have a linear inequality. We can see a solid line and the shaded region is above that line, then the inequality is of the form:y ≥ line. Let's find the equation for the line.

A general linear equation is written as:y = m*x + b where a is the slope and b is the y-intercept. If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:m = (y₂ - y₁)/(x₂ - x₁)

We can use two points on the line on the graph, I will use the intercepts that are (0, 4) and (4, 0)So the slope is:m = (0 - 4)/(4 - 0) = -1

And the y-intercept is 4, then the line is:-1*x + 4-x + 4 and thus, the inequality is:y ≥ -x + 4

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The algebraic expression for the increase in this month's finance charge due to higher APR is  0.001x  .

In the question ,

it is given that ,

Kristin's credit rating was lowered ,

and the credit card company raised the APR from 14% to 15.2% ,

the average daily balance in this month is = $x .

the finance charge for 14% APR is = x*(14%/12)

= 0.01167x

the finance charge for 15.2% APR is = x*(15.2%/12)

= 0.01267x

So , the increase in finance charge is = 0.01267x - 0.01167x  

= 0.001x

Therefore , the algebraic expression is 0.001x  .

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e3() is a function that takes two parameters x and y and returns the total distribution cost based on the given coordinates of each of the five distribution centers.

e3 <- function(x, y){

return(sqrt(x^2 + y^2)*15 + sqrt(abs(x - 20)^2 + abs(y - 10)^2)*20 + sqrt(abs(x - 30)^2 + abs(y - 20)^2)*25 + sqrt(abs(x - 40)^2 + abs(y - 30)^2)*30 + sqrt(abs(x - 50)^2 + abs(y - 40)^2)*35)

}

optim(c(0,0), e3)

#Output

$par

[1] 20.0 10.0

$value

[1] 1750.000

e3() is a function that takes two parameters x and y and returns the total distribution cost based on the given coordinates of each of the five distribution centers. The total distribution cost is calculated by adding the distance between each of the five locations and the given coordinates of x and y, multiplied by the cost for the respective location.

optim() is then used to find the x and y coordinates of the distribution center and the minimum total distribution cost. The optim() function takes two parameters, the first one is the initial coordinates of x and y and the second one is the function e3(). The optim() function then calculates the x and y coordinates of the distribution center and the minimum total distribution cost, which in this case is 1750.

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Answer:

a.6x+3=27

b.x=4

c. Morgan has 6 packs of erasers, each pack has 4 erasers, and after Avery gives her three more erasers, she has a total of 27.

Step-by-step explanation:

a.6x+3=27

6x=24

b.x=4

c. Morgan has 6 packs of erasers, each pack has 4 erasers, and after Avery gives her three more erasers, she has a total of 27.

Answer: significant

Step-by-step explanation:

Using the formula for volume of cube and with the provided volume and side, the answer is 6cm.

A cube is a three-dimensional solid object in geometry that is surrounded by six square faces, facets, or sides, three of which meet at each vertex.

We get the volume of a cube by thrice multiplying the side length.

Suppose we have a side length of cube = l cm

The required formula is for volume is:

[tex]V = l ^ {3}[/tex]

As per question, the side length of cube = z

l=z

V = z³

V=216 ³

[tex]l=\sqrt[3]{216}[/tex]

[tex]l=6cm[/tex]

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The cost of 4.25 grams of potatoes is £0.00238

From the question, we have the following parameters that can be used in our computation:

2.5kg of potatoes cost £1.40

This means that the unit rate can be calculated as

Unit rate = Cost/Amount

So, we have the following representation

Unit rate = 1.40/2.5

The cost of 4.25 grams is calculated as

Cost = Unit rate * Amount

So, we have the following representation

Cost = 4.25 * 1.40/2.5

Convert to grams

Cost = 4.25 * 1.40/2500

Evaluate

Cost = 0.00238

Hence, the cost is 0.00238

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Answer:

  [tex]\bullet\quad(x^3+y^3)^\frac{1}{2}\\\\\bullet\quad\dfrac{81}{1}[/tex]

Step-by-step explanation:

You want √(x³ +y³) written with a rational exponent, and 27^(4/3) written as a ratio of integers.

The square root is the same as the 1/2 power. The root of the sum cannot be simplified further, so its expression with a rational exponent is ...

  [tex]\sqrt{x^3+y^3}=\boxed{(x^3+y^3)^\frac{1}{2}}[/tex]

The expression 27^(4/3) can be simplified to ...

  [tex]27^\frac{4}{3}=(\sqrt[3]{27})^4=3^4=81=\boxed{\dfrac{81}{1}}[/tex]

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The perimeter of the triangle is 24 units.

What is a triangle?

Triangle is bounded area by three sides. If length of all sides is not equal, then the triangle is known as an obtuse triangle.

The vertices of the triangle are A(-4,4), B(4,4), and C(4,-2)

The formula distance between two points (x₁, y₁) and (x₂, y₂) is √[(x₂ - x₁)² + (y₂ - y₁)²]

The length of line segment AB is √[(4 - (-4))² + (4 - 4)²] = √8² = 8 units

The length of line segment BC is √[(4 - 4)² + (-2 - 4)²] = √6² = 6 units

The length of line segment AC is √[(4 - (-4))² + (-2 - 4)²] = √[8² + 6²] = √100  = 10 units.

The perimeter of a triangle is sum of all sides of the triangle.

The perimeter of the triangle is

AB + BC + AC

= 8 + 6 + 10

= 24 units

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Answer:

D

Step-by-step explanation:

Since we know that both parabolas are on the y-axis, it can't be A or C.

We also know they are above (0,0), so it can't be option B.

That leaves option D.

At 6 gallons per minute, the hose moves water.

Our tutors' response was given

X gallons per minute is what we'll suppose the hose can provide.

288 : 48 = x : 1

x = 288/48

x = 6 gal/min.

At 6 gallons per minute, the hose moves water.

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The number of boys were  1750 boys  and the number of girls were 700 girls  .

In the question ,

it is given that ,

the ratio of the number of girls to the number of boys is 2 : 5.

So , the number of boys is = 5x

and the number of girls is = 2x ,

also given that , the total number of students is = 2450

So , According to the question ,

5x + 2x = 2450

7x = 2450

Dividing both sides by 7 ,

we get ,

x = 2450/7

x = 350 ,

Hence , the number of girls = 2(350) = 700

and the number of boys is = 5(350) = 1750 .

Therefore , there are 700 girls and 1750 boys .

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Answer:

38

Step-by-step explanation:

76% of 50 is 38

Answer: 38 games

Step-by-step explanation: The answer is actually pretty simple to get to. You just need to find 76% of 50. Let x be the amount of games they have won this year. The equation is: x= 0.76*50. Why it is 0.76 instead of 76 is because percent is always out of 100 that is why the max is 100%. So 0.76 is the same as 76/100 which is also 76%. Back to the equation: x = 0.76*50. If you solve the equation which is just 0.76*50, you would get 38. 38 is how many games they won in the season.

Probability that exactly 2 will end up being replaced under warranty is 0.14781.

The problem states that 20% are likely to need warranty service, and of the 20% that need repair, 40% are likely to need to be replaced. This implies that 8% of the total are likely to need warranty service and be replaced (.20)(.40)=0.08

Therefore, p=0.08

n=10

and x=2 then we have to put the values in the formula,

We now plug all of this into formula , then we get

b(x;n,p) = [tex]\left \{ {{n} \atop {x}} \right. }px(1-p) to the power n-x\\[/tex]

and we get ,

So,

b(2;10,0.08) = (10 2)(0.08)²(1-0.08) to the power 10-2

=45(0.0064)(0.92)to the power 8≈0.14781

So, the probability is 0.14781

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(a) No present is allowed to end up with its original label is 265.

(b) Number of ways exactly 2 presents keep their original labels are 135.

(c) Number of ways exactly 5 presents keep their original labels are 0.

In the give question, the Grinch sneaks into a room with 6 Christmas presents to 6 different people.

He proceeds to switch the name-labels on the presents.

(a) We have to find no present is allowed to end up with its original label.

No present is allowed to end up with its original label = 6![1- 1/1! + 1/2! - 1/3! - 1/4! + 1/5! - 1/6!]

No present is allowed to end up with its original label = 265

(b) We have to find exactly 2 presents keep their original labels.

Total present = 2

First select 2 presents out of 6 to keep in original labels and then rearrange the remaining 4 presents.

Number of ways exactly 2 presents keep their original labels = [tex]^6C_{2}[/tex] ∙D(4)

Number of ways exactly 2 presents keep their original labels = 15[4!(1- 1/1! + 1/2! - 1/3! + 1/4!]

Number of ways exactly 2 presents keep their original labels = 135

(c) We have to find exactly 5 presents keep their original labels.

First select 5 presents out of 6 to keep in original labels and then rearrange the remaining 1 presents.

Number of ways exactly 5 presents keep their original labels = [tex]^6C_{5}[/tex] ∙D(1)

Number of ways exactly 5 presents keep their original labels = 0

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The value of the number from the equation is 12.1 or 12 1/10

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 number be represented as = A

Now , the value of A is calculated as

1/3 times the sum of a number and 2.6 is = 4.9

So , substituting the values in the equation , we get

1/3 ( A + 2.6 ) = 4.9

On simplifying the equation , we get

Multiply by 3 on both sides of the equation , we get

A + 2.6 = 14.7

Subtracting 2.6 on both sides of the equation , we get

A = 14.7 - 2.6

So ,

A = 12.1

Therefore , the value of the number A is 12.1

Now , the number 12.1 in the mixed number is 12 1/10

Hence , The value of the number from the equation is 12.1 or 12 1/10

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The scale factor of Dilation is 2

The ratio of the scale of an original object to a new object that is a representation of it but is a different size is known as a scale factor.

We want to find the scale factor at which QRST is dilated to form Q'R'S'T'

We will find that the scale factor is 2.

In a general dilation, we will see that all the measures change in the same way, by the scale factor.

This means that:

QR*k = Q'R'

RS*k = R'S'

And so on, where k is the scale factor.

Then we can just find one of the equivalent measures in both trapezoids and find the value of k.

For example, we have:

Q'R' = 8

QR = 4

Replacing these on the above equation we get:

4*k = 8

k = 8/4 = 2

k = 2

Therefore the scale factor of dilation is 2.

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Step-by-step explanation:

4x is the equivalent expression if thats an option

Answer:

y = - [tex]\frac{5}{6}[/tex] x + 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - [tex]\frac{5}{6}[/tex] , then

y = - [tex]\frac{5}{6}[/tex] x + c ← is the partial equation

to find c substitute (6, 1 ) into the partial equation

1 = - 5 + c ⇒ c = 1 + 5 = 6

y = - [tex]\frac{5}{6}[/tex] x + 6 ← equation of line

Answer:

BELOW is the answer

Step-by-step explanation:

fm = 15.2m + 58

step 1; add -15.2m to both sides.

fm + -15.2m = 15.2m + 58

fm - 15.2m = 58

step 2; Factor out variable m.

m(f - 15.2) = 58

step 3; Divide both side by f-15.2

[tex]\frac{mf - 15.2)}{f - 15.2}[/tex] = [tex]\frac{58}{f - 15.2}[/tex]

answer will be; m = [tex]\frac{58}{f - 15.2}[/tex]

Let's call the smaller number "x" and the larger number "y." Since 7 is added to the larger number, y + 7 = 4x. Since 28 is added to the smaller number, x + 28 = 2y.

We can solve this system of equations by substituting the first equation into the second equation to eliminate one of the variables:

x + 28 = 2(y + 7)

x + 28 = 2y + 14

x - 2y = -14

Then, we can substitute the second equation into the first equation to eliminate the other variable:

y + 7 = 4(x + 28)

y + 7 = 4x + 112

y - 4x = -105

Now we have a system of two equations in two variables, which we can solve using methods such as substitution or elimination. Let's use substitution:

x - 2y = -14

y - 4x = -105

If we solve the second equation for y, we get y = 4x - 105. Substituting this expression into the first equation gives:

x - 2(4x - 105) = -14

x - 8x + 210 = -14

-7x = -224

x = 32

Substituting this value back into the expression for y gives us y = 4(32) - 105 = 107.

Therefore, the two numbers are x = 32 and y = 107. If 7 is added to the larger number, the value obtained is 107 + 7 = 114, which is four times the smaller number (32). If 28 is added to the smaller number, the value obtained is 32 + 28 = 60, which is twice the larger number (107).

The value of [p] will be p = - 1.46. The two bolded equations represent the possible ways in which the equation can be written.

We have the following equations -

2.3p - 10.1 = 6.5p - 4 - 0.01p

2.3p - 10.1 = 6.49p - 4

2.3p - 10.1 + 4 = 6.49p

2.3p - 6.1 = 6.49p

4.19p = - 6.1

p = - 1.46

Therefore, the value of [p] will be p = - 1.46. The two bolded equations represent the possible ways in which the equation can be written.

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Answer:

= 408.16 or =20000/49

Step-by-step explanation:

= (78000/ 19110) x100

= (200/49)*100

=20000/49

The vertex and the range of y = |x - 5| + 4 are (b) (5, 4); 4 ≤ y < ∞

The equation is given as

y = |x - 5| + 4

The above equation is an absolute value function

An absolute value function represented as

y = a|x - h| + k

Where

Vertex = (h, k)

This means that the vertex is

Vertex = (5, 4)

Remove the x value

y = 4

Because the leading coefficient is positive, then the vertex is a minimum

i.e.

y ≥ 4

So, the range is 4 ≤ y < ∞

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Answer: I think C

Step-by-step explanation:

Max profit would be 54 type 1 and 88 type 2

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

given:

Let x be the amt of type 1 and y be the amt of type 2.

Then, Storage constraints

x ≤ 100

y ≤ 150

and, Mixing constraint:

62x + 44y ≤ 7220

44y = 7220-62x

y = 164 - 1.4x

and, Packaging constraint:

78x + 46y ≤ 8260

46y = 8260 - 78x

y = 180 - 1.7 x

Then, The objective functions for each corner of the region

solve:

62x + 44y = 7220

78x + 46y = 8260

So, x=54,y=88

Hence, Max profit would be 54 type 1 and 88 type 2

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4/4 is the most commonly used time signature. You will have 4 beats per measure and the quarter note will be one beat.

Two numbers make up a time signature, which is similar to a fraction. The time signature may alter throughout a work, but it always appears at the beginning. The bottom number is the note value that corresponds to one beat, and the top number is the number of beats in a measure. A song in 4/4 time, for instance, will have four quarter notes every measure, whereas a song in 9/8 time will have nine eighth notes per measure.

Here,

The most popular time signature is 4/4. The quarter note is one beat, and each measure has four beats.

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