An engineer is using a polynomial function to model the height of a roller coaster over time x, as shown.
On a coordinate plane, a curve increases from quadrant 3 and crosses the y-axis at (0, 4). It then decreases and crosses the x-axis at (5, 0). It continues to decrease and then starts to increase and crosses the x-axis at (8, 0).
The engineer wants to modify the roller coaster design by transforming the function. Which represents 2 f (0.3 x minus 1) + 10, the modified design of the roller coaster?
On a coordinate plane, a curve increases from quadrant 3 and crosses the y-axis at (0, 10). It then decreases and goes through (20, 10). It continues to decrease and then starts to increase and goes through (30, 10).
On a coordinate plane, a curve increases from quadrant 3 and crosses the y-axis at (0, negative 10). It then decreases and goes through (20, negative 10). It continues to decrease and then starts to increase and goes through (30, negative 10).
On a coordinate plane, a curve increases from quadrant 3 and crosses the y-axis at (0, 20). It then decreases and then increases again.
On a coordinate plane, a curve increases from quadrant 3 and crosses the y-axis at (0, 10). It then decreases and goes through (20, negative 10). It continues to decrease and then starts to increase and goes through (30, negative 10).

Answer:

325 miles

Step-by-step explanation:

speed = distance/time

=> distance = speed x time = 65 x 5 = 325 miles

Step-by-step explanation:

If you drive at a constant speed of 65 miles per hour for 5 hours, you would cover a distance of:

Distance = Speed x Time

Distance = 65 mph x 5 hours

Distance = 325 miles

Therefore, your grandmother's house is 325 miles away from yours.

La nueva temperatura de la congeladora industrial es de -3°C.

Si una congeladora industrial se mantiene a -8°C y aumenta su temperatura en 5°C, podemos encontrar su nueva temperatura sumando -8°C y 5°C:

-8°C + 5°C = -3°C

Por lo tanto, la nueva temperatura de la congeladora industrial es de -3°C.

La temperatura es una magnitud física que mide el grado de calor o frío de un objeto, sustancia o ambiente. Esta magnitud está relacionada con la energía cinética promedio de las moléculas que componen el objeto o sustancia, y se expresa en unidades de medida como grados Celsius (°C), grados Fahrenheit (°F) o kelvin (K).

Es importante tener en cuenta que una temperatura de -3°C sigue siendo fría, pero es importante asegurarse de que la congeladora se mantenga a la temperatura adecuada para preservar los alimentos y evitar su descomposición.

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The volume of the container is 127.23 cubic cm

The given parameters are

Number of balls = 6

Height of ball = 3 cm

This means that

Height of cylinder, h = 6 * 3 cm = 18 cm

Radius of cylinder, r = 3/2 cm = 1.5 cm

So, we have

Volume = πr²h

Volume = π * 1.5² * 18

Volume = 127.23

The volume of a ball is

Ball = 4/3πr³

For 6 balls, we have

Balls = 6 * 4/3πr³

Balls = 8πr³

So, we have

Balls = 8π * 1.5³

Balls = 84.82

So, the unoccupied space is

Space = 127.23 - 84.82

Space = 42.41

This is calculated as

Area = 2πrh + 2πr²

So, we have

Area = 2π * 1.5 * 18 + 2π * 1.5²

Area = 183.78

Hence, the surface area is 183.78 square cm

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When the shape R is reflected R' the coordinates of C (2, 5) when translated to R" C (1, -1).

What are Transformations:

Transformations are changes made to a geometric figure in a plane or space. There are three main types of transformations: translation, rotation, and reflection.

Rotation is a transformation where a figure is turned around a fixed point, called the center of rotation. This can be a clockwise or counterclockwise turn, and the degree of rotation is determined by the angle between the original and final positions of the figure.

Here we have a shape R

From the graph,

The coordinate of C is (-4, 5)  

Shape R is reflected in line x = -1 to give R'

=> (x, y )  →  (-x - 2, y)

=> (-4, 5) → (4- 2, 5)  

=> Coordinates of C are (2, 5)

R' is then translated by (-1, -6) to give R''

Hence, the R is moved 1 unit left words and 6 units downwards

=> (2, 5) → (-1 + 2, 5 - 6)

=> (2, 5) → (1, -1)

Therefore,

When the shape R is reflected R' the coordinates of C (2, 5) when translated to R" C (1, -1).

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The solution of the inequality is x ≤ - 7 / 2 or x > 1

Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.

Therefore, let's solve the inequalities. The variable in the inequality is x. A variable is a number represented with letter in an equality or inequality.

Therefore,

x + 1 / 2 ≤ - 3 or x - 3 > - 2

Let's solve them individually,

x + 1 / 2 ≤ - 3

subtract 1 / 2 from both sides of the inequality

x ≤ - 3 - 1 / 2

x ≤ - 7 / 2

Hence,

x - 3 > - 2

add 3 to both sides of the inequality

x - 3 + 3 > - 2 + 3

x > 1

Hence,

x ≤ - 7 / 2 or x > 1

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If he sweets are all red, yellow or green in the ratio of 6 : 4 : 4, there are 36 yellow sweets in the packet.

To solve this problem, we need to use the concept of ratios. The ratio of red, yellow, and green sweets is 6:4:4, which means that for every 6 red sweets, there are 4 yellow and 4 green sweets.

We can use this ratio to find out how many yellow sweets there are in the packet. Since the ratio of yellow sweets to the total number of sweets is 4:14 (6+4+4=14), we can write:

Yellow sweets / 126 = 4 / 14

To solve for the number of yellow sweets, we can cross-multiply and simplify:

Yellow sweets = 126 x 4 / 14

Yellow sweets = 36

We can also use the same method to find the number of red and green sweets:

Red sweets = 126 x 6 / 14

Red sweets = 54

Green sweets = 126 x 4 / 14

Green sweets = 36

To check our answer, we can verify that the total number of sweets is equal to the sum of red, yellow, and green sweets:

54 + 36 + 36 = 126

Therefore, our answer is correct.

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The radius of a circle is half of the diameter. Therefore, the radius of the circle is 7 yards and the diameter of the circle is 14 yards.

The above shape is a circle. The area of the circle is given as 49πyards square. The radius of a circle is the distance of the circumference to the centre of a square. The diameter of a circle is twice the radius of the circle.

Therefore, let's find the radius and diameter of a circle as follows:

area of a circle  = πr²

where

Area of the circle = πr²

49π = πr²

divide both sides of the equation by π

r² = 49

square root both sides of the equation

r = √49

r = 7 yards

Therefore,

diameter = 7 × 2

diameter = 14 yards

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2/3 in its simplest form.

3-(7)/(3) can be simplified to 2/3 by performing the following steps:

1. First, divide 7 by 3 to get 7/3.

2. Then, subtract 7/3 from 3 to get 3-(7/3), which equals 2/3.

Therefore, the answer is 2/3 in its simplest form.

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11 square units

Given the vertices of a triangle in coordinate geometry, find its area by using the determinant method. The given vertices of the triangle are (-2, 3), (3, 2), and (-1, -8).Step-by-step explanation: The formula for calculating the area of the triangle with given vertices using determinant method is given as, \[\frac{1}{2}\begin{vmatrix}x_1 & y_1 & 1 \\x_2 & y_2 & 1 \\x_3 & y_3 & 1 \\\end{vmatrix}\]Here, x1, y1, x2, y2, x3, y3 are the coordinates of the given vertices. Now, substitute the given values and evaluate the determinant as shown below. \[\frac{1}{2}\begin{vmatrix}-2 & 3 & 1 \\3 & 2 & 1 \\-1 & -8 & 1 \\\end{vmatrix}=\frac{1}{2}((-2)(2(-8)-(-1)(3))+3(1(-8)-(-1)(-1))+1(3(2)-(-1)(3)))\]After multiplying, we get, \[\frac{1}{2}(-16+29+9)=\frac{1}{2}(22)=11\] Therefore, the area of the triangle whose vertices are (-2, 3), (3, 2), and (-1, -8) is 11 square units.

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2x²-9x-5

2x²-x-10x-5

(x-5)(2x+1)

You have some standard six-sided dice. So, the probability of rolling a total of ten when you roll three dice is 5/216.

To find the probability of rolling a total of ten when rolling three dice, we can use the formula:

P(event) = desired outcomes / total outcomes

Given that we have six-sided dice, we know that the total outcomes for rolling one die is six.

Therefore, the total outcomes for rolling three dice would be[tex]6^3[/tex]= 216.

To find the desired outcomes, we can use combinations.

There are three ways we can roll a total of ten with three dice:

1-3-62-4-43-5-24-3-34-2-45-1-5

Therefore, there are five combinations that result in a total of ten.

Therefore, the probability of rolling a total of ten when rolling three dice is:

P(event) = 5/216

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Answer: 2

Step-by-step explanation:

The inequality expression 4y > 12x - 48 when evaluated is y > 3x - 12

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

4y>12x-48

Express properly

4y > 12x - 48

Multiply 1/4 to both sides of the inequality

So, we have the following representation

1/4 * 4y > 12x * 1/4 - 48 * 1/4

Evaluate the products

y > 3x - 12

Hence, the solution is y > 3x - 12

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The questiοn is an illustratiοn οf inequalities and mathematical οperatiοns the amοunt between $2 and $10 is $8.

The amοunt between $10 and $20 is $10

$100 is greater than $50

In mathematics, an inequality is a cοnnectiοn that is nοt equal between twο expressiοns οr values. Cοnsequently, imbalance leads tο inequity. In mathematics, an inequality cοnnects twο unrelated values. Inequality is distinct frοm equality. When twο values are nοt equal, the nοt equal sign is mοst usually used ().

Variοus inequalities are emplοyed tο cοntrast values, nο matter hοw small οr huge. Many basic inequalities can be sοlved by altering the twο sides until the variables are all that remain. Yet, a variety οf factοrs cοntribute tο inequality: Negative values οn bοth sides are split οr added. Trade οff the left and right.

(a) Amοunt between $2 and $10.

The amοunt is calculated as:

Hence, the amοunt between $2 and $10 is $8

(b) Amοunt between $10 and $20.

The amοunt is calculated as:

Hence, the amοunt between $10 and $20 is $10

(c) Amοunt greater than $50.

An amοunt greater than $50 is an amοunt that have an higher value.

Take fοr instance: $100

$100 is greater than $50, because it has a higher value.

There is nο enοugh infοrmatiοn tο sοlve the οther questiοns

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The  equation she will use to determine how much money she'll have after 2 years is: A = 49,000*(1+0.153/12)^(2*12).

After 2 years she'll have $70,960.36.

The formula for compound interest is: A = P * (1 + r/n)^(n*t).  In the formula, we convert the annual interest rate to a monthly rate by dividing it by 12 (the number of months in a year), and we multiply the number of years by 12 to get the number of months.

Using this formula, we can calculate how much money Lara will have after 2 years:

A = 49000 * (1 + 0.153/12)^(12*2)

A = $70,960.36

Therefore, Lara will have $70,960.36 after 2 years of compounding her investment monthly at 15.3%.

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Answer:

10^0

Step-by-step explanation:

Anything that has a exponent of 0 will always equal 1 therefore if 10^-3/10^-3 it will equal 1 so they both are 1

Answer: A 10^0

10^-3  is 0.001.  0.001 divided into 0.001 is 1.

A- 10^0 is 1 so this correct.

B- 10^-6 is 1.0e-6, so this is incorrect.

C-10^1 is 10, so this is incorrect.

D.10^6 is 1000000, so this is incorrect.

After solving our equation 10^-3/ 10^-3, we have concluded that that answer is 1, meaning that answer choice A, 10^0 is our correct answer.

Notes- ^ means to the power of, which is an exponent.

I hope this helped & Good Luck <3!!!!

Answer:

The coefficient is 3.

Answer:

3

Step-by-step explanation:

Here 2xy² + x³ – x⁵ + xy², there are two like terms

2xy² and xy², so the coefficient of xy² = 2 + 1

Coefficient of xy² in the given expression is 3.

Answer:

x = 6

Step-by-step explanation:

7x = 42

To solve the equation, divide each side by 7.

7x/7 = 42/7

x = 6

One package of sugar cookie dough costs $6 and one package of double chocolate cookie dough costs $11.

How to solve the variables?

Let's use the following variables:

Let x be the cost of one package of sugar cookie dough.

Let y be the cost of one package of double chocolate cookie dough.

We can create a system of two equations to represent the information given in the problem:

Equation 1: 7x + y = 53 (from Kayla's sales)

Equation 2: x + y = 17 (from Maria's sales)

We can solve for x and y by using the substitution method, which involves solving one equation for one variable and substituting the result into the other equation. Here's how we can do it:

Solve Equation 2 for y:

y = 17 - x

Substitute y = 17 - x into Equation 1 and solve for x:

7x + (17 - x) = 53

6x + 17 = 53

6x = 36

x = 6

Substitute x = 6 into Equation 2 and solve for y:

y = 17 - x

y = 17 - 6

y = 11

Therefore, one package of sugar cookie dough costs $6 and one package of double chocolate cookie dough costs $11.

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Answer:

We can use the formula for the length of an arc of a circle, which is:

length of arc = (angle/360) × 2πr

where angle is the angle subtended by the arc at the center of the circle, r is the radius of the circle, and π is approximately 3.14.

In this problem, the angle subtended by the arc at the circumference of the circle is 86 degrees. Since the radius of the circle is 8 cm, the diameter is 2 × 8 = 16 cm, and the circumference is 2πr = 2π(8) = 16π cm.

Using the hint given in the problem, we can find the angle subtended by the arc at the center of the circle:

angle at center = 2 × angle at circumference

= 2 × 86

= 172 degrees

Substituting into the formula, we have:

length of arc = (172/360) × 2π(8)

≈ 7.5 cm

Rounding to the nearest whole number, the length of the arc is 8 cm.

Answer:

x^2-2x-8<0

Step-by-step explanation:

It is difficult visualizing the expressions, so lets change them to equations by substituting a "y" in place of the 0 of the inequality.  This will allow us to graph the expressions.  Then if we focus on only the y=0 line in the graph, we can find the correct inequality.

All four expressions are graphed with this substitution and included on the attached worksheet.  Note the marked their marked differences.  The two points on the given number line (-4,0) and (2,0) are marked on each graph.

What we should focus on first is which graphs actually intersect the two end values of x given on the number line:  -4 and 2.  Since we used y instead of "0" in the expressions, we are seeing everything, for all values of x.  But what we really want are -4 and 2, which we can mark with (-4,0) and (2,0).

Only two graphs intersect (-4,0) and (2,0):  the first and third (lower left).  The first (x^2-2x-8<y)  has the interior of the parabola colored blue - these are the valid points for the inequality.  The number line between (-4,0) and (2,0) in included.  The third (x^2-2x-8>y) is colored everywhere outside the parabola, and thus exclues the number line in the region we are interested.  So the equation for this graph is not a valid possibility.

We may conclude that graph 1 is correct.  The important section of the graph is expanded at the bottom.  Since the graph line is dotted, the two points (-4,0) and (2,0) are not actually included on the line - they are simply a boundary, due to the < function.  They would be included if the expression had said ≤ or ≥    (with the = sign).      

The expression that represents the solution set is x^2-2x-8<0    

On solving the above question, As a result, the polynomials f(x) zeros are x = 9 and x = 44/5.

A polynomial is a mathematical statement composed of coefficients and variance that exclusively uses additions, subtractions, operations such as addition, and nonzero powers of variables. The form x2 4x + 7 indicates a single determinate x algebraic. A polynomial expression in mathematics is made up of determinants (also known as freshly made) and polynomials that may be multiplied, subtracted, repeated, and raised through negative integer ones of – anti. A polynomial is an algebraic statement that includes variables and coefficients. An expression can really only incorporate the operations addition, deletion, duplication, and non-negative integer factors. These expressions are referred to as polynomials.

If x - 9 is a factor of f(x), we get:

f(x) = (x - 9)g(x) (x)

g(x) denotes a polynomial.

When we plug this into the supplied f(x) equation, we get:

5x^3 - 44x^2 - 13x + 36 = (x - 9)g (x)

Using polynomial long division to expand the right side, we get:

x(g(x)) = 5x3 - 44x2 - 13x + 36 - 9g(x) (x)

When we multiply the coefficients of similar terms on both sides, we get:

5 = g(x) (x)

-44 = g'(x) (x)

-13 = g''(x) (x)

36 = -9g''(x) (x)

When we solve these equations, we get:

5 g'(x) = -44 g"(x) = -13/2 g"'(x) = -12

Hence, g(x) is a constant function, and g'(x) = -44 suggests that x = 44/5 is the sole real root of g(x).

As a result, the f(x) zeros are x = 9 and x = 44/5.

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The inequality for the given sentence would be:

4x ≥ 18. This means that the product of x and 4 is greater than or equal to 18.

The inequality "4x ≥ 18" is read as "four times x is greater than or equal to 18". This means that the value of x must be equal to or greater than 4.5 for the inequality to hold true.

To solve the inequality, we can divide both sides by 4, which gives us:

x ≥ 4.5

This means that any value of x that is equal to or greater than 4.5 will satisfy the original inequality.

For example, x = 5 would satisfy the inequality because: 4(5) = 20, which is greater than or equal to 18.p

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Therefore, the exact value of sec(θ) sec(A) in simplest radical form using a rational denominator is 41/16.

Trigonometry is based on the ratios of the sides of a right triangle, which are defined in terms of the angles of the triangle. The three main trigonometric functions are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively. These functions are used to relate the angles of a triangle to the lengths of its sides, and can be calculated using a scientific calculator or a table of values.

Here,

We can start by using the definition of cotangent:

cot(θ) = adjacent / opposite

From the given information, we have cot(θ) = -4/5. Since θ is in Quadrant II, we know that the adjacent side is negative and the opposite side is positive. We can use the Pythagorean theorem to find the hypotenuse:

a² + b² = c²

(-4)² + 5² = c²

16 + 25 = c²

c² = 41

c = √(41)

Now we can use the fact that secant is the reciprocal of cosine:

sec(θ) = 1 / cos(θ)

cos(θ) = adjacent / hypotenuse

cos(θ) = -4 / √(41)

cos(A) = adjacent / hypotenuse

cos(A) = 4 / √(41)

sec(θ) sec(A) = (1/cos(θ))(1/cos(A))

sec(θ) sec(A) = (√(41) / -4)(√(41) / 4)

sec(θ) sec(A) = (41 / 16)

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Angles congruent to ∠1= ∠4,∠8,∠5

Angles congruent to ∠2= ∠3,∠7,∠6

Angles congruent to ∠6= ∠3,∠7,∠2

Angles congruent to ∠7= ∠3,∠6,∠2

The opposing angles created by the connection of two straight lines are known as vertical angles or vertically opposed angles.

(Vertically opposite angle ∠1=∠4

Vertically opposite angle ∠8=∠5

consecutive exterior angle ∠4=∠8)

Angles congruent to ∠2= ∠3,∠7,∠6

Hence, Angles congruent to ∠1= ∠4,∠8,∠5

(Vertically opposite angle ∠2=∠3

Vertically opposite angle ∠7=∠6

consecutive exterior angle ∠3=∠7)

Angles congruent to ∠7= ∠3,∠6,∠2

(Vertically opposite angle ∠7=∠6

Vertically opposite angle ∠2=∠3

consecutive exterior angle ∠6=∠2)

Hence, Angles congruent to ∠6= ∠3,∠7,∠2

(Vertically opposite angle ∠6=∠7

Vertically opposite angle ∠3=∠2

consecutive exterior angle ∠7=∠3)

Hence, Angles congruent to ∠2= ∠3,∠7,∠6

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The solution of the absolute inequality is as follows:

x < 22 / 5 or x > 6 / 5

The absolute inequalities can be solved as follows:

An absolute value inequality is an inequality that has an absolute value sign with a variable inside, modulus of a complex number.

Therefore,

|14 - 5x| > 8

let's find x as follows:

|14 - 5x| > 8

14 - 5x > 8  or 14 - 5x < - 8

-5x > 8 - 14  or - 5x < - 8 - 14

-5x > -6  or - 5x < - 22

Therefore,

x > 6 / 5 or x < 22 / 5

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Answer:

D. x^2-x-9-12/x-2

Step-by-step explanation:

We can use synthetic division to divide (x^3 - 3x^2 - 7x + 6) by (x - 2). First, we set up the division as follows:

    2 |   1   -3   -7    6

       |______2___-2__-18

       | 1   -1   -9  -12

The numbers on the bottom row of the synthetic division table represent the coefficients of the quotient polynomial. Therefore, the quotient is x^2 - x - 9, and the remainder is -12.

So, we have:

(x^3 - 3x^2 - 7x + 6) / (x - 2) = x^2 - x - 9 + (-12 / x - 2)

Therefore, the correct option is D: x^2 - x - 9 - 12/(x - 2).

(a) The covariance for X and Y Cov(X, Y) = -1.05

(b) The correlation number (rho) is rho = Cov(X, Y)/(X, Y) = -1.05/(5).

The expected values of X and Y must first be determined in order to find the covariance and correlation coefficient for X and Y.

The amount of X is anticipated to be:

(a) E(X) = xP(X=x) = (0.03) + (5) (0.04 + 0.15 + 0.01) + (10) (0.06 + 0.20 + 0.15 + 0.13) + (15) (0.02 + 0.10 + 0.01) = 8.4

E(Y) = yP(Y=y) = (0.05) + (5) (0.04 + 0.01) + (10) (0.06 + 0.15 + 0.15) + (15) (0.02 + 0.20 + 0.13 + 0.01) = 10.5

X and Y's correlation is:

Cov(X, Y) = XY - XE (Y)

Each number of X and Y must be multiplied by their combined probability before the products are added to determine E(XY):

(0)(0)(0.05) + (0)(5)(0.03) + (0)(10)(0.06 + 0.01) + (0)(15)(0.02) + (5)(0)(0.04) + (5)(5)(0.15) + (5)(10)(0.20) + (5)(15)(0.10) + (10)(0)(0.01) + (10)(5)(0.15) + (10)(10)(0.13) + (10)(15)(0.01) + (15)(0)(0.02) + (15)(5)(0.10)

Therefore: Cov(X, Y)=E(XY)-E(X)E(Y) =119.25-(8.4)(10.5) = -1.05

As a result, X and Y have a correlation of -1.05.

(b) The standard errors of X and Y must also be computed in order to determine the correlation coefficient:

sqrt(Var(X)) = sqrt(E(X) - [E(X)]) = sqrt((0^2)(0.03) + (5^2)(0.04 + 0.15 + 0.01) + (10^2)(0.06 + 0.20 + 0.15 + 0.13) + (15^2)(0.02 + 0.10 + 0.01) - (8.4)^2) ≈ 5.23

The expression "_Y = sqrt(Var(Y)) = sqrt(E(Y)2 - [E(Y)]2)" = sqrt((0^2)(0.05) + (5^2)(0.04 + 0.01) + (10^2)(0.06 + 0.15 + 0.15) + (15^2)(0.02 + 0.20 + 0.13 + 0.01) - (10.5)^2) ≈ 5.07

The correlation number (rho) is rho = Cov(X, Y)/(X, Y) = -1.05/(5).

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Answer:

28%

Step-by-step explanation:

Answer:  45% of the 6th graders surveyed prefer superhero movies.

Step-by-step explanation:

To find the percentage of 6th graders who prefer superhero movies, we need to divide the number of 6th graders who prefer superhero movies by the total number of 6th graders, and then multiply by 100 to get a percentage.

According to the table, there are 17 6th graders who prefer superhero movies. The total number of 6th graders is:

10 + 11 + 17 = 38

Therefore, the percentage of 6th graders who prefer superhero movies is:

(17 / 38) x 100% = 44.74%

Rounded to the nearest whole number percent, the answer is:

45%

So approximately 45% of the 6th graders surveyed prefer superhero movies.

Answer:

y = 1/3x - 2

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

We know

m = 1/3

Y-intercept is located at (0, -2)

So, the equation is y = 1/3x - 2