Use graphing technology (TI calculator or Desmos) to find the linear regression equation that models the data. Let x equal the hours of sleep and y equal test score. Explain the steps you use.

Use the equation to determine the approximate test score of a student who sleeps an average of 7.5 hours a night. Show your work.

The coordinates of the location where the facility should be built are (7, 0).

We are given the coordinates of three cities J(5, 2), K(-7, 2) and L(-5, -8).

A television station wants to build a new broadcast facility that is equidistant from the three cities.

We need to find out the coordinates of the location where the facility should be built.

We can use the distance formula to find the distance between two points (x1, y1) and (x2, y2):d

= √[(x₂ - x₁)² + (y₂ - y₁)²]

Let (x, y) be the coordinates of the broadcast facility.

We know that the distance from the facility to city J is equal to the distance from the facility to city K, and also equal to the distance from the facility to city L.

Using the distance formula, we can write these three equations:√[(x - 5)² + (y - 2)²]

= √[(x + 7)² + (y - 2)²]  [Distance from facility to city J = distance from facility to city K]

√[(x - 5)² + (y - 2)²]

= √[(x + 5)² + (y + 8)²]

[Distance from facility to city J = distance from facility to city L]√[(x + 7)² + (y - 2)²]

= √[(x + 5)² + (y + 8)²]

[Distance from facility to city K = distance from facility to city L]

Squaring both sides of these equations, we get: (x - 5)² + (y - 2)² = (x + 7)² + (y - 2)²  ...

(1)Simplifying this equation, we get: x = -1

Similarly, (x - 5)² + (y - 2)² = (x + 5)² + (y + 8)²  ...

(2)Simplifying this equation, we get: x² + y² - 10x - 4y + 90 = 0

Similarly, (x + 7)² + (y - 2)² = (x + 5)² + (y + 8)²  ..

.(3)Simplifying this equation, we get: x² + y² - 4x - 10y - 6 = 0

Now, we need to solve equations (2) and (3) for y and x respectively.x² + y² - 10x - 4y + 90 = 0

[Equation (2)]x² + y² - 4x - 10y - 6 = 0 [Equation (3)]

Multiplying equation (2) by 10, and equation (3) by 4,

we get:10x² + 10y² - 100x - 40y + 900 = 0  ...(4)

4x² + 4y² - 16x - 40y - 24 = 0  ...

(5)Subtracting equation (5) from equation (4),

we get:6x² + 6y² - 84x + 924 = 0

Simplifying this equation by dividing both sides by 6,

we get:x² + y² - 14x + 154 = 0

Completing the square, we get:(x - 7)² + y² = 95

This is the equation of a circle with center at (7, 0) and radius √95 units.

Therefore, the coordinates of the broadcast facility are (7, 0).

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16 Ounces makes two cups.

In cooking and baking, measuring ingredients is an important step to ensure that recipes come out correctly. Ounces and cups are both units of measurement used to quantify the amount of ingredients in a recipe.

One cup is equal to 8 fluid ounces, so two cups is equal to 16 fluid ounces. This means that if a recipe calls for 2 cups of an ingredient, you would need 16 fluid ounces of that ingredient to make the recipe.

It's important to note that fluid ounces and ounces are not the same thing. Fluid ounces are a measure of volume, while ounces can refer to both weight and volume, depending on the context. When measuring ingredients, it's important to use the correct units of measurement to ensure that the recipe turns out as intended.

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Answer:

f(x) = -(x + 8)(x -14)

= -(x2 - 112 - 6x)

= -x2 + 6x + 112 --- (1)

We know the graph of an equation y = ax2 + bx + c where a ≠ 0 is a parabola. The parabola opens upwards if a > 0 and opens downwards if a < 0. The vertex of the parabola is the point where the axis and parabola intersect. Its x coordinate x = -b/2a and its y coordinate is found out by substituting x = -b/2a in the parabola equation.

The parabola given in the problem statement has a negative coefficient of x2 and hence it is a parabola which opens downwards. Also for the equation

a = -1, b = 6 and c = 112. Therefor the x-coordinate of the vertex is

x = -b/2a

= -(6)/[2(-1)]

= 3

Substituting the value of x = 3 in equation (1) we get,

Now y = -(3)2 + 6(3) + 112

= -9 + 18 + 112 = 121

So the vertex point coordinates are (3, 121) and the y value is 121.

The graph below verifies the vertex point.

vertex of the graph

What is the y-value of the vertex of the function f(x) = -(x + 8)(x - 14)?

Summary:

The y-value of the vertex of the function f(x) = -(x + 8)(x - 14) is 121.

This can be derived using Chebyshev's inequality, as Chebyshev's inequality and the law of large numbers are different in nature.

Let M_n be the maximum of n independent U(0, 1) random variables.

To derive the exact expression for P(|M_n − 1| > ε), we need to follow the below steps:

First, we determine P(M_n ≤ 1-ε). The probability that all of the n variables are less than 1-ε is (1-ε)^n

So, P(M_n ≤ 1-ε) = (1-ε)^n

Similarly, we determine P(M_n ≥ 1+ε), which is equal to the probability that all the n variables are greater than 1+\epsilon

Hence, P(M_n ≥ 1+ε) = (1-ε)^n

Now we can write P(|M_n-1|>ε)=1-P(M_n≤1-ε)-P(M_n≥1+ε)

P(|M_n-1|>ε) = 1 - (1-ε)^n - (1+ε)^n.

Thus we have derived the exact expression for P(|M_n − 1| > ε) as P(|M_n-1|>ε) = 1 - (1-ε)^n - (1+ε)^n

Now, to show that $lim_{n\to\∞}$ P(|M_n - 1| > ε) = 0 , we can use Chebyshev's inequality which states that P(|X-\mu|>ε)≤{Var(X)/ε^2}

Chebyshev's inequality and the law of large numbers are different in nature as Chebyshev's inequality gives the upper bound for the probability of deviation of a random variable from its expected value. On the other hand, the law of large numbers provides information about how the sample mean approaches the population mean as the sample size increases.

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Answer:

I only know that for table e the bottom under 4 is 6.

Step-by-step explanation:

The y-intercept of a function is the value of y = -9 when x = 0. Therefore, the functions have the same y-intercept.

How to find y-intercept?

A function's y-intercept is the value of y at x = 0. It is, in other words, the location of the graph's intersection with the y-axis.

the point on a line, curve, or surface where the y-axis touches that point.

Therefore,

Function 1:

r = 5 / 8 t - 9

r = 5 / 8 (0) - 9

r = -9

hence, the y-intercept is -9

Function 2:

when t = 0, r = -9

Hence, the value of  y-intercept is -9

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Answer:

Pretty sure its function 1

Step-by-step explanation:

Answer:

The base is 90 sq

Step-by-step explanation:

Formula for Area= 1/2*b*h

where b is unknown and area = 54sq

1/2 *b*12 = 54sq

12b = 54*2

12b /12 = 54*2/12

b = 9sq

Answer:

I believe 70

Step-by-step explanation:

Answer:

i) Gas mileage = 31 miles

ii) 2170 miles = 70 gallons

310 miles on 10 gallons of gas.

⇒ 310 miles = 10 gallons

⇒ 310/10 miles = 10/10 gallons

⇒ 31 miles = 1 gallon

Gas mileage = 31 miles

⇒ 31 miles = 1 gallon

⇒ 31 x 70 miles = 1 x 70 gallon

⇒ 2170 miles = 70 gallons

Answer:

11

Step-by-step explanation:

i just need 11 more than ill be fine

Answer:

3x^2-6x+3=0

x^2-2x+1=0

x^2-x-x+1=0

x(x-1)-(x-1)=0

(x-1)(x-1)=0

x=1,1

so x has only one answer

so it intersects only one time

The equation Chad should program is \(y = -0.04x^2 + 20x.\)

The equation that Chad should program into his rocket launcher to win is:

\(y = -0.04x^2 + 8x\)

This is a quadratic equation in standard form, where the coefficient of x^2 is negative, indicating that the path of the rocket is a downward facing parabola. The coefficient of x^2 is -0.04, which means that the parabola is relatively flat, ensuring that the rocket will travel a horizontal distance of 20 feet when it reaches a height of 100 feet.

To sketch the rocket’s path, we can plot points on the graph of the equation. For example, when x = 0, y = 0, so the rocket starts at the origin. When x = 50, y = 200, so the rocket reaches its maximum height at x = 50 and y = 100. When x = 100, y = 0, so the rocket lands 20 feet away from the launch pad at ground level. We can connect these points to sketch the path of the rocket.

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Answer:

The fraction can be written as 43/50

Step-by-step explanation:

Place the Percentage Value at the top over 100.

= 86/100

On reducing the fraction, we get the exact form: 43/50

Answer:

43/50

Step-by-step explanation:

Place the Percentage Value at the top over 100.

= 86/100

On reducing the fraction, we get the exact form: 43/50

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx

where

k is the constant of proportionality or slope

In this problem

we have a proportional relationship between the land planted and the wheat produced

Let

l ----> number of acres

w ----> wheat produced

so

w=kl

take the point (1,50)

Find teh value of k

k=w/l

k=50/1=50

therefore the equation is equal to

w=50l

Answer:

x < 45

Step-by-step explanation:

Let's call that number x. x/3 - 5 < 10, and we can add by five on both sides then multiply by 3 on both sides to get that x < 45.

I would prefer leaving the answer as a radical number as √5 since it is a shorter form and exact form of the answer.

My reasons for leaving it as a radical form or a decimal approximation are;

1) If we are trying to find an exact answer, then we should leave it as √5. For example, if we are told a square has an area of 5 square units, then it means that the exact length of the side is √5 units.

2) If √5 is the length of an object that has to be made to that specific length, then we would require an approximation. For example, if you are asked to make a square out of cardboard whose area is 5 square feet, then we will definitely need an approximation of √5 ft = 2.24 ft, which would help us make each side of the cardboard square in the length of 2.24 ft.

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Unfortunately, you have not provided the example data set that you would like to graph, analyze, and conclude. Therefore, I will provide general steps on how to accurately graph data, interpret the graph, analyze it, and conclude.

Graph the data set on the appropriate graph. For example, if you have time series data, plot it on a line graph. If you have categorical data, plot it on a bar graph. Ensure to use appropriate labeling for the x-axis and y-axis, including units.

Interpret the graph Analyze the graph by observing its key features such as the shape, trend, and distribution. For example, observe if there is a positive, negative, or no correlation. If there is a trend, is it linear or non-linear What is the range and variability of the data Write the analysis Write the analysis based on your observations State whether the hypothesis was supported or rejected and how the data set contributed to understanding the research question or the phenomenon being studied.

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The scale factor of two similar circles is equal to the ratio of their radii.

This can be expressed mathematically as a fraction, where the numerator is the radius of the larger circle, and the denominator is the radius of the smaller circle. For example, if the radii of the two circles are 3 cm and 6 cm, then the scale factor is 3/6 or 1/2. To find the scale factor, divide the radius of the larger circle by the radius of the smaller circle. For example, if the radii of the two circles are 10 cm and 4 cm, then the scale factor is 10/4, or 5/2.

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Answer:

I'm pretty sure it's the first one

Answer:

Step-by-step explanation:

Let the integers be:

Their sum is 42:

The numbers are: 13, 14 and 15

∂g/∂u is equal to 21u⁵cos⁴(v)sin⁴(v)(cos(v) + u³cos⁴(v)sin²(v)sin(v)).

To find the indicated derivative, we need to use the chain rule. Let's differentiate step by step:

Given:

g(u, v) = f(x(u, v), y(u, v))

f(x, y) = 7x³y³

x(u, v) = ucos(v)

y(u, v) = usin(v)

To find ∂g/∂u, we differentiate g(u, v) with respect to u while treating v as a constant:

∂g/∂u = (∂f/∂x) * (∂x/∂u) + (∂f/∂y) * (∂y/∂u)

To find ∂f/∂x, we differentiate f(x, y) with respect to x:

∂f/∂x = 21x²y³

To find ∂x/∂u, we differentiate x(u, v) with respect to u:

∂x/∂u = cos(v)

To find ∂f/∂y, we differentiate f(x, y) with respect to y:

∂f/∂y = 21x³y²

To find ∂y/∂u, we differentiate y(u, v) with respect to u:

∂y/∂u = sin(v)

Now, we can substitute these partial derivatives into the equation for ∂g/∂u:

∂g/∂u = (21x²y³) * (cos(v)) + (21x³y²) * (sin(v))

To find the simplified form, we substitute the given values of x(u, v) and y(u, v) into the equation:

x(u, v) = ucos(v) = u * cos(v)

y(u, v) = usin(v) = u * sin(v)

∂g/∂u = (21(u * cos(v))²(u * sin(v))³) * (cos(v)) + (21(u * cos(v))³(u * sin(v))²) * (sin(v))

Simplifying further, we get:

∂g/∂u = 21u⁵cos⁴(v)sin⁴(v)(cos(v) + u³cos⁴(v)sin²(v)sin(v))

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\(\tt Step-by-step~explanation:\)

\(\tt Area:\)

To solve for the area of a triangle, we multiply the length and height, then divide that by two. L = 10. H = 7.

\(\tt 10*7=70\\70/2=35\\35=A\)

\(\tt Perimeter:\)

\(\tt Step~1:\)

To solve for the perimeter, or edges, of the triangle, we need to use the Pythagorean Theorem: a² + b² = c² to solve for the third side. We already know two measures: 10 and 7. Now we need to square them, add them together to get c², then take the root of that number.

\(\tt 7^2=49\\10^2=100\\100+49=\sqrt{149}\\\sqrt{149\)

We cannot simplify √149, so we either leave it, or round it.

\(\tt \sqrt{149}\\12.2066\)

This is rounded to the nearest 10,000.

\(\tt Step~2:\)

Now that we have the measure of the longest side, we can add all three sides together to get the perimeter of the triangle.

\(\tt 10+7+\sqrt{149}=17+\sqrt{149}=P\\Rounded~to~the~nearest~1,000th:~29.207=P\)

\(\large\boxed{\tt Our~final~answer: ~A=35,~P=17+\sqrt{149}}\)

The maximum profit if the profits per acre are $75 for corn and $40 for soybeans is $371,255.83. Therefore, the correct option is c.

To find the maximum profit from planting corn and soybeans, we can use linear programming. Let's first define the variables and write the constraints.

Let x be the number of acres of corn and y be the number of acres of soybeans.

1. Total acre constraint: x + y ≤ 6,000

2. Fertilizer/herbicide constraint: 9x + 3y ≤ 40,501

3. Labor constraint: 0.75x + y ≤ 5,250

The objective function to maximize is the profit function: P(x,y) = 75x + 40y

Now, we will use the Solver to find the maximum profit:

Step 1: Set up a spreadsheet with the constraints and the objective function.

Step 2: Go to the Data tab and click on Solver. If Solver is not available, you may need to add it in Excel Options.

Step 3: Set the objective function by selecting the cell with the profit function.

Step 4: Choose "Max" for the objective.

Step 5: Add the constraints by selecting the corresponding cells.

Step 6: Click on "Solve" and the Solver will find the optimal values for x and y.

After using Solver, we find that the optimal values are x = 4,363.89 (corn) and y = 1,636.11 (soybeans), which yields a maximum profit of $371,255.83. Therefore, the correct answer is c: $371,255.83

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Answer:

the new selling price would be 15 + 6.75 = $<<15+6.75=21.75>>21.75.

Step-by-step explanation:

To calculate the markup on the necklace, you need to first calculate the amount of the markup by multiplying the cost of the necklace by the markup percentage. In this case, the markup would be 15 * 0.45 = $<<15*0.45=6.75>>6.75.

To determine the new selling price of the necklace, you would then add the markup to the cost of the necklace. So the new selling price would be 15 + 6.75 = $<<15+6.75=21.75>>21.75.

Step-by-step explanation:

x = 7

3 + 4x = 5x - 4

3 + 4(7) = 5(7) - 4

3 + 28 = 35 - 4

31 = 31

Option C

The equations having the solutions 7 are 65−2x=6x+9 and 3+4x=5x−4. the correct options are A and C.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that we have to check all the equations having solution 7.

Checking option A,

65−2x=6x+9

65 - ( 2 x 7 ) = ( 6 x 7 ) + 9

51 = 51

Checking option B,

x²+1=8x−5

(7²) + 1 = ( 8 x 7 ) - 5

50≠ 51

Checking option C,

3 + 4x = 5x - 4

3 + 4(7) = 5(7) - 4

3 + 28 = 35 - 4

31 = 31

Checking option D,

9 - x = 14x

9 - 7 = 14 x 7

2≠ 98

Therefore, the equations having the solutions 7 are 65−2x=6x+9 and 3+4x=5x−4. the correct options are A and C.

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De acuerdo con la información, se puede inferir que los divisores de 12 serían: 1, 2, 3, 4, 6 y 12.

Para calcular los divisores de un número debemos probar dividiendo este número desde el uno en adelante hasta llegar al mismo número. Para que un número sea considerado divisor de otro es cuando al dividirlo por ese número da como resultado un número entero.

En el caso de 12, los números que servirían como divisores son:

De acuerdo con lo anterior, los divisores de 12 son: 1, 2, 3, 4 ,6 y 12.

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Number of ways 5 gymnasts participate including exactly two from Lia , Bella , Priscilla is equal to 252.

As given in the question,

Total number of gymnasts = 12

Number of gymnasts to be participates = 5

Condition:

Exactly two gymnasts from Lia , Bella , Priscilla

Number of ways 5 gymnasts participates

= ⁹C₃ × ³C₂

= ( 9!)/ ( 9 - 3)! 3! × 3!/ ( 3-2)! 2!

= [( 9× 8 ×7 × 6!)/ 6! ( 3× 2× 1)] × ( 3 × 2!)/ 2!

= [( 9× 8 ×7)/ ( 3× 2× 1)] × 3

= 252

Therefore, the number of ways 5 gymnast can participate out of 12 with the given condition is 252.

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