If f(x) is continuous on a closed interval, then it is enough to look at the points where f'(x) = 0 in order to find its absolute maxima and minima. Be prepared to justify your answer.

a. The line of the best fit is ŷ = -8.55485X + 118.39451.

b. The value of the correlation coefficient is  -0.8619.

A straight line that minimizes the gap between it and certain data is called a line of best fit. In a scatter plot containing several data points, a relationship is expressed using the line of best fit. It is a result of regression analysis and a tool for forecasting indicators and price changes.

Sum of X = 117.4

Sum of Y = 298

Mean X = 10.6727

Mean Y = 27.0909

The sum of squares (SSX) = 0.8618

The sum of products (SP) = -7.3727

Regression Equation = ŷ = bX + a

b = SP/SSX = -7.37/0.86 = -8.55485

a = MY - bMX = 27.09 - (-8.55*10.67) = 118.39451

ŷ = -8.55485X + 118.39451

X Values

∑ = 117.4

Mean = 10.673

∑(X - Mx)² = SSx = 0.862

Y Values

∑ = 298

Mean = 27.091

∑(Y - My)² = SSy = 84.909

X and Y Combined

N = 11

∑(X - Mx)(Y - My) = -7.373

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -7.373 / √((0.862)(84.909)) = -0.8619

Therefore, the line of the best fit is ŷ = -8.55485X + 118.39451

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The values a and b should be replaced to rewrite the given expression as (x + a)(x - b).

Generally speaking, the standard form of a quadratic function is given by this mathematical expression;

ax² + bx + c = 0

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

c represents the constant.

Next, we would solve the above quadratic function by using the factorization method;

x² + x - 72 = 0

x² - 8x + 9x - 72 = 0

x(x - 8) + 9(x - 8) = 0

(x + 9)(x - 8) = 0

(x + 9)(x - 8) = (x + a)(x - b).

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The solution is, the distance = √116.

The distance between two points is the length of the line joining the two points.

Formula: distance= √(x_2-x_1)²+(y_2-y_1)²

here, we have,

given that,

P (3√2,5√3), Q(√2,-√3)

so,  the distance d(P,Q).

by using the formula we get,

the distance = √108 + 8

                     = √116

Hence, The solution is, the distance = √116.

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Answer: The coordinates where the two lines intersect are (-5, -8).

Step-by-step explanation:
To find the coordinates where the two lines intersect, we need to solve the system of equations simultaneously. We can do this by substitution or elimination, but we'll use substitution here:

First, we set the two equations equal to each other:

x - 3 = 2x + 2

Next, we solve for x:

x - 2x = 2 + 3

-x = 5

x = -5

Now that we have the value of x, we can substitute it into one of the original equations to find the corresponding value of y. Let's use the first equation:

y = x - 3

y = (-5) - 3

y = -8

The equation for the nth term of this sequence is an = -4.5 + 2.5(n - 1)

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

a4 = 3

a10 = 18

An arithmetic sequence is represented as

an = a + (n - 1)d

Using the above as a guide, we have the following:

a + 3d = 3

a + 9d = 18

Subtract the equations

So, we have

6d = 15

Divide

d = 2.5

So, we have

a + 3 * 2.5 = 3

This gives

a = -4.5

So, the sequence is -4.5 + 2.5(n - 1)

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The solution of both inequalities is (-1, 2).

Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

We have the inequalities

x+ y >1.........(1)

-x+ y <3.........(2)

The graph for x+ y >1 is shown by the red shaded region.

and, the graph for -x+ y <3  is shown by the blue shaded region.

Also , the Inequality intersect at (-1, 2) which shows the solution of both inequalities.

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Answer:

Circumference = (3.14)(15) = 47.1 in

Step-by-step explanation:

Answer:

+5&-2

Step-by-step explanation:

Answer:

x=6.5

Step-by-step explanation:

I'm not sure if it's correct

The theoretical probability of selecting a red bead is 0.28.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Given that,

Color                     Frequency

Red                               17

Orange                         12

Yellow                          10

Green                           9

Blue                              8

Purple                           5

Color                      List A                      List B

Red                           33                            31

Orange                     27                            24

Yellow                       22                           18

Green                        30                           34

Blue                           18                            19

Purple                        12                            5

Probability of selecting a red bead = 17/61

= 0.28

Orange color would have a frequency closest to 24.

Therefore, the theoretical probability of selecting a red bead is 0.28.

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Answer: 6 and 1/3

Step-by-step explanation:

Assuming that sweet generous little Marcus here wants some muffins too, he has to share 19 blueberry muffins between 3 people (Marcus + friend 1 + friend 2.)

Most unfortunately, 19 isn't divisible by 3 to create a whole number (ie. a whole muffin).

Therefore you have 2 options:

Option 1:

19/3 = 6.333....

This means that each person will get 6 and 1/3 of a muffin

Option 2:

19/3 = 6 (and 1 remainder)

This means that each person will get 6 muffins each, but there will be a leftover muffin to feed the birds or something.

(I personally prefer option 2, but I think your teacher is looking for option 1.)

80 times, the house should be cleaned to buy the car.

Equation for the amount is y = 50t + 500

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.

Given,

Amount in the savings = $500

Amount to get the car = $4500

Grandma pays $50 for every time after cleaning

then, after t times, the amount will be

y = 50 t + 500

here, y is the total amount after working

t is number of times of cleaning the house

For $4500

4500 = 50t + 500

50t = 4500 - 500

50t = 4000

t = 4000/50

t = 80

Hence, we have to clean the house 80 times to have $4500.

equation for the amount is y = 50t + 500

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The milk bottle, item is the best example of an artifact from the passage that reveals something about sign. Thus, option (a) is correct.

The term “passage” refers to the explanation and description of a sentence in relation to a topic. The passage aimed to describe those details related to the theme of the story. The different passage is to justify to the different things as to clarify. The passage is to define the important terms.

The milk bottle sat on the central shelf, as mentioned in the passage. The artifact is a completely empty milk bottle. The section gives information regarding signs. The passage was Sig's refrigerator, which had been opened. A milk bottle sat on the middle shelf, its cap missing and no milk inside.

As a result, the milk bottle, item is the best example of an artifact from the passage that reveals something about sign. Therefore, option (a) is correct.

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The order from least to greatest would be as follows:

√3 - 1 < 2√10 ÷ 5 < √14 < 3√2 < √19 + 1 < 6

To order the numbers, we need to first simplify and evaluate each expression.

1. √3 - 1 = 1.73205080757 - 1 = 0.73205080757

2. 2√10 ÷ 5 = 1.265

3. √14 = 3.74166

4. 3√2 = 4.243

5. √19 + 1 = 5.359

6. 6 is simply 6

Therefore, the correct answer is as given above. It could then be concluded that the order from least to greatest is:

0.73205080757 < 1.265 < 3.74166 < 4.243 < 5.359 < 6

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Answer:

bottom-right

Step-by-step explanation:

the points on the graph are scattered and have no correlation whereas the others all remain in a relatively similar shape

The formulas are functionally the same, but 'n' (the sample size) is used instead of 'N' (the population size).

The sample mean is the average value for a set of observations which is derived from a population. While the population mean is the average value for the entire set of observation belonging to a particular study of interest.

The set of observation belonging to a population is denoted by 'N' ; while the sample size is denoted as 'n' :

The mean formula is written thus :

Population mean = Σx / N

Sample mean = Σx / n

Where, x = set of values.

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The height of the cone in discuss as required to be determined is; 16.38 cm.

Since the height of the cone is three times the length of the diameter of its base;

h = 3d;

d = h/3

Therefore, radius,

r = d/2

r = h/3 ÷ 2

multiply by the reciprocal of 2

r = h/3 × 1/2

r = h / 6.

Volume of a cone, V = (1/3) πr²h

128 = (1/3) × (22/7) × (h³/36)

h³ = 4398.55

h = 16.38 cm.

Ultimately, the height of the cone is; 16.38 cm.

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The Complete statement are:

1. 27/3 + 5 x 2

2. 81 + 1 - 8 x 4 x 1 = 60

Combining operands with a single arithmetic operator specifies an arithmetic operation. The  ADD, SUBTRACT, DIVIDE, and MULTIPLY can also be used to specify arithmetic operations.

Given:

we have to apply the operation to make

27 3 5 2 = 19

81 11 8 4 1 = 60

so, first 27 3 5 2 = 19

1. 27/ 3 = 9

2. 5 x 2= 10

3. 9+ 10 = 19

For second,

1.81 + 11 = 92

2. 8 x 4 x 1 = 32

3. 92-32 = 60

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Answer:

The point of intersection between 2x+3y=12 and 2x-y=4 is (3,2)

Step-by-step explanation:

Let's call the added amount of kg of mixed nuts that contain

40

%

peanuts

m

a

d

d

e

d

. If the new mixture contains

34

%

peanuts, then:

m

peanuts

m

total

=

0.34

The bag of

6

kg

already contained

0.3

⋅

6

=

1.8

kg

of peanuts. Furthermore,

40

%

of

m

added

will be peanuts. This means that:

m

peanuts

=

0.4

m

added

+

1.8

The total mass will be the original

6

kg

plus the added mass, so

m

total

=

m

added

+

6

.

This gives us the following equation.

0.4

m

added

+

1.8

m

added

+

6

=

0.34

Multiply both sides with

m

added

+

6

.

0.4

m

added

+

1.8

=

0.34

(

m

added

+

6

)

Multiply out the brackets.

0.4

m

added

+

1.8

=

0.34

m

added

+

2.04

Subtract

0.34

m

added

from both sides.

0.04

m

added

+

1.8

=

2.04

Subtract

1.8

from both sides.

0.06

m

added

=

0.24

Divide both sides by

0.06

.

m

added

=

4

Therefore, Jenny must add

4

kg

.

Answer:

[tex]\sqrt{13}[/tex]

Step-by-step explanation:

[tex]L^{2}[/tex]=[tex]3^{2}[/tex]+[tex]2^{2}[/tex]=9+4=13

L=[tex]\sqrt{13}[/tex]

Answer:

he circumference of the circle is approximately 56.52 millimeters.

Step-by-step explanation:

The circumference of a circle is given by the formula:

C = πd

where C is the circumference, d is the diameter, and π is a mathematical constant approximately equal to 3.14.

Substituting the given value of the diameter, we get:

C = πd = π(18) = 56.52 mm (rounded to two decimal places)

Therefore, the circumference of the circle is approximately 56.52 millimeters.

The factorization of 2x² - 2x - 3x + 9 using the box method is (2x - 3)(x - 3).

To factor the trinomial 2x² - 2x - 3x + 9 using the box method, we first draw a box and divide it into four sections:

   | 2x  -3 |

   |--------|

   | -2x  9 |

Then, we fill in the top left section with the coefficient of the leading term, 2x, and the bottom right section with the constant term, 9.

   | 2x  -3 |

   |--------|

   | -2x  9 |

Next, we find two numbers that multiply to 2x * 9 = 18 and add to the coefficient of the middle term, -2x - 3x = -5x.

One way to do this is to factor out 2 from the leading two terms, giving 2x² - 2x - 3x + 9 = 2x(x - 1) - 3(x - 3), and then finding the product of (x - 1) and (x - 3) using the AC method:

AC method:

2x(x - 1) - 3(x - 3) = 2x(x - 1) - 3x + 9 - 3(-1)

We can then place these two numbers in the remaining two sections of the box:

   | 2x  -3 |

   |--------|

   | -2x  9 |

   | 2x  -3 |

   |--------|

   | -2x  9 |

   |--------|

   | -3   1 |

We can now factor the trinomial by taking the common factor out of each row and column of the box:

2x(x - 1) - 3x + 9 - 3(-1)

= (2x - 3)(x - 3)

Therefore, the factorization of 2x² - 2x - 3x + 9 using the box method is (2x - 3)(x - 3).

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The area of the given triangle is approximately 204.2 square inches.

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.

To calculate the area of a triangle with given side lengths, we can use Heron's formula:

Area = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle (half of the perimeter), and a, b, and c are the lengths of the sides.

In this case, the lengths of the sides are a=32, b=22, and c=19. Therefore, the semi-perimeter is:

s = (a + b + c) / 2 = (32 + 22 + 19) / 2 = 36.5

Now we can plug in these values into the formula and simplify:

Area = √(36.5(36.5-32)(36.5-22)(36.5-19)) ≈ 204.16

Rounding this to 1 decimal place, the area of the triangle is approximately 204.2 square inches.

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250 in the function given represents the exponential constant.

Given is the exponential function as -

y = 250(2.3)ˣ

In the exponential function given, 250 represents the exponential constant.

An exponential function is of the form -

y = A(B)ˣ

Therefore, 250 in the function given represents the exponential constant.

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The equation of line passes through the points (- 7, -3) and (-3, 5) will be;

⇒ y = 2x + 11

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (- 7, -3) and (-3, 5).

Now,

Since, The equation of line passes through the points (- 7, -3) and (-3, 5).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (5 - (-3)) / (-3 - (-7))

m = 8 / 4

m = 2

Thus, The equation of line with slope 2 is,

⇒ y - (-3) = 2 (x - (-7))

⇒ y + 3 = 2 (x + 7)

⇒ y + 3 = 2x + 14

⇒ y = 2x + 14 - 3

⇒ y = 2x + 11

Therefore, The equation of line passes through the points (- 7, -3) and

(-3, 5) will be;

⇒ y = 2x + 11

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Answer: The correct answer is C. It represents a function only.

A function is a special type of relation where each input value is associated with only one output value. In other words, for every x in the domain of the function, there is only one corresponding y in the range.

In this equation, y = 2^x + 4, for every value of x, there is a unique corresponding value of y. So, it satisfies the requirement of a function and represents a function only.

Step-by-step explanation:

Answer:

D. It represents both a relation and a function

Hope this helps!

Step-by-step explanation:

All functions are relations, but not all relations are functions. The equation given is an Exponential function.

The probability that a randomly selected persons favorite restaurant is a deli is 9/50

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

The table of values

On the table, we have

Total = 100

Deli = 18

So, the probability is

P = Deli/Total

Substitute the known values in the above equation, so, we have the following representation

P = 18/100

Simplify

P = 9/50

Hence, the probability is (d) 9/50

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The triangle has vertices A(7,-2), B(5.25, -1.25), and C(5, -0.5).

What is a triangle ?

Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.

Let's call the vertex we know A, and the midpoints of the other two sides B and C, respectively.

Using the midpoint formula, we can find the coordinates of the other two vertices, which are the endpoints of the sides that have B and C as midpoints

Coordinates of B:

x-coordinate: (7 + 3.5)/2 = 5.25

y-coordinate: (-2 - 0.5)/2 = -1.25

So, B is (5.25, -1.25)

Coordinates of C:

x-coordinate: (7 + 3) / 2 = 5

y-coordinate: (-2 + 1)/2 = -0.5

So, C is (5, -0.5)

Therefore, The triangle has vertices A(7,-2), B(5.25, -1.25), and C(5, -0.5).

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