Given the function g(x) = -x² − 9x + 27, determine the average rate of change
of the function over the interval -9 ≤x≤-1.

Answers

Answer 1

The rate of change of the function g(x) in the interval -9 ≤ x ≤ -1 is  1

How to determine the rate of change?

The rate of change of a function y = f(x) on the interval [a, b] is given by the formula below:

R = (f(b) - f(a))/(b - a)

Here the function is g(x) = -x² − 9x + 27 and the interval is [-9, -1], we can evaluate g(x) in both ends of our interval, then we will get the two values needed for the numerator, here we will get:

g(-1) =  -(-1)² − 9*-1 + 27 = -1 + 9 + 27 = 35

g(-9) = -(-9)² -9*-9 + 27 = 27

Replacing that in the formula we can get the rate of change is:

R = (35 - 27)/(-1 + 9) = 8/8 = 1

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Related Questions

Gabriel finds some wooden boards in the backyard with lengths of 5 feet, 2.5 feet and 4 feet. He decides he wants to make a triangular garden in the yard and uses the triangle inequality rule to see if it will work. Which sums prove that the boards will create a triangular outline for the garden? Select all that apply. 5 + 2.5 > 4 5 + 2.5 < 4 4 + 2.5 > 5 4 + 2.5 < 5 4 + 5 > 2.5

Answers

So the correct possible triangular outline for the garden is:

5 + 2.5 > 4

4 + 2.5 > 5

4 + 5 > 2.5

Given information:

Gabriel finds some wooden boards in the backyard with lengths of 5 feet, 2.5 feet, and 4 feet.

He decides he wants to make a triangular garden in the yard and uses the triangle inequality rule to see if it will work.

The sums that prove that the boards will create a triangular outline for the garden are:

5 + 2.5 > 4

4 + 2.5 > 5

4 + 5 > 2.5

So the correct options are:

5 + 2.5 > 4

4 + 2.5 > 5

4 + 5 > 2.5

These sums satisfy the triangle inequality rule, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.

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Women in the age group of 20-29 have total cholesterol levels with a mean of 183 mg per dl and the standard deviation of 37. 2mg per dl. if 250 women were randomly selected about how many would you expect to have a total cholesterol level greater than 240mg/dl?

Answers

Answer:

Sidama Cofee Football Team, the Ethiopian premier league club in Yiregalem, plays 70 percent of their games at night and 30 percent during the day. The team wins 50 percent of their night games and 90 percent of their day games. According to today’s news, they won yesterday. What is the probability the game was played at night?

Best represents the population

Answers

The equation that best represents the population of the town, which increases exponentially at the rate of 6% every year, after x years is C. y = 158,260(1.06)ˣ.

What is exponential growth?

Exponential growth refers to a constant percentage or rate of growth per period.

The opposite of exponential growth is exponential decay and refers to the constant rate of decay in value per period.

The town's initial population = 158,260

Growth rate per year = 6%

Let x = the number of years of growth

Let y = the population after x years

Equation:

y = 158,260(1 + 0.06)^x

Thus, the correct equation representing population growth after x years is Option C.

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A study is testing the effectiveness of a new allergy medication. Sixty people who reported they have allergies volunteered to be part of the study and were randomly assigned to one of two groups, as shown in the design web.

Which of the following accurately describes the benefit of comparison in the experiment shown in the design web?

A. The level of allergic symptoms in both groups can be compared to see if the new medication had a significant effect.
B. The overall level of allergic symptoms can be used to determine if the new allergy medication had a significant effect.
C. The level of allergic symptoms in the group who received the medication can be used to determine if the medication had a significant effect.
D. The level of allergic symptoms in both groups cannot be compared to determine if the medication had a significant effect because one group only received a placebo.

Answers

The level of allergic symptoms in both groups cannot be compared to determine if the medication had a significant effect since, one group only received a placebo accurately describes the benefit of comparison in the experiment shown in the design web.  Thus option A is correct.

A scientific experiment inside that carry out a sequence of tasks and closely monitor their results to discover new information. An investigation is a method that used to confirm or deny a hypothesis, as well as assess the likelihood or effectiveness of something that hasn't been tried before.

Although one sample only obtained a placebo inside the investigation depicted in the design web, which is difficult to compare the severity of allergic rhinitis in both groups to establish whether the drug had a substantial impact.

Hence, option A is the correct option.

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Find the maximum volume of the cylindrical can such that the sum of its height and its circumference is 45 cm.

Answers

The maximum volume of the cylindrical can such that the sum of its height and its circumference is 45 cm is  337.5 cm³

Let's denote the radius of the cylindrical can as r, and its height as h.

The circumference of the base of the can is 2πr, so the sum of the height and the circumference can be written as:

h + 2πr = 45..(1)

We want to find the maximum volume of the can, which is given by:

V = πr²h..(2)

From (1), h = 45 - 2πr

Substitute h value in equation above

V = πr²(45-2r)

V = 45πr² - 2π²r³

To find the maximum volume, we have to find the differentiation of V

dV/dr = 90πr - 6π²r² = 0

Solving for r, we get:

r = 15/π cm

Now plug in r value in h

V = π(15/π)²(15)

= 337.5 cm³

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Gustave Eiffel built the Eiffel Tower (1887-89) for the______In 1889.

World's Fair

Panama Pacific Exhibition

Salon

Great Exhibition

Answers

Answer:

World's Fair. Is the correct answer

What is the volume of the following rectangular prism? 3 1/3 1 2/5

Answers

Area of rectangular prism: Base x Height.

so 3x1/3x2/5=0.4 0r 2/5

x2+10x+=()2
step by step

Answers

The value of the expression x² + 10x, when x = 2 is 24.

In the expression x² + 10x, x represents a variable, which is a placeholder for a value that can change. We are given that x = 2, which means we substitute 2 for x in the expression:

x² + 10x = 2² + 10(2)

Here, 2² means 2 raised to the power of 2, which is 2 multiplied by itself: 2² = 2 x 2 = 4.

10(2) means 10 multiplied by 2, which is 20.

So we can substitute these values in the expression:

x² + 10x = 2² + 10(2)

= 4 + 20

= 24

Therefore, when x is equal to 2, the value of the expression x² + 10x is 24.

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The complete question:

Evaluate the expression x² + 10x, when x = 2.

which can be represented using the product (50)*(-5) ?

Answers

The expression that can be represented by product (50)*(-5) is 250

Which expression represented using the product (50)*(-5) ?

Any number that can be expressed as the product of 50 and -5 can be represented using the expression (50)*(-5).

For example, if we multiply 50 and -5, we get -250. Therefore, -250 can be represented using the expression (50)*(-5).

Similarly, if we multiply 50 and -5 by any other number, we can represent the product using the expression (50)*(-5).

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Find the pair of numbers that completes the factorization. x^2 - 3x - 40 = (x +?)(x-?)
a- 5,8

b- 4,10

c- 10,4

d- 8,5

Answers

answer

a. 5,8

explanation

use numbers in each answer choice

+5 * -8 = - 40

+5 -8 = -3

Consider the form [tex]x^2+bx+c[/tex]. Find a pair of integers whose product is [tex]c[/tex] and whose sum is [tex]b[/tex]. In this case, whose product is -40 and whose sum is -3.

[tex]\longrightarrow\boxed{\bold{(-8,5)}}[/tex]

Write the factored form using these integers.

[tex](x-8) \ (x+5)[/tex]

a cylinder with a height of 32 mm and a diagonal 40 mm what is the surface area

Answers

The surface area of the cylinder is calculated as approximately:

8,444.6 mm².

How to Find the Surface Area of a Cylinder?

The surface area of a cylinder (SA) = 2πrh + 2πr², where:

r is the radius

h is the height of the cylinder.

Given the following:

Diagonal of cylinder = 40 mm

Height of cylinder (h) = 32 mm

Radius (r) = √(40² - 32²) = 24 mm [based on Pythagorean Theorem]

Plug in the values:

surface area of the cylinder (SA) = (2 * π * 24 * 32) + (2 * π * 24²)

≈ 8,444.6 mm²

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GIVING BRINLIET
Question
The set shows the absolute values of a set of rational numbers in increasing order.

{0.4, 1, 212
, 4, 5.3, 7, 9.8}

Can you determine the order of the rational numbers themselves? Explain why.
Responses
A No, it is not possible to determine the order of the rational numbers because we only know the signs of the rational numbers.No, it is not possible to determine the order of the rational numbers because we only know the signs of the rational numbers.
B Yes, it is possible to determine the order of the rational numbers because we know the size of the rational numbers.Yes, it is possible to determine the order of the rational numbers because we know the size of the rational numbers.
C No, it is not possible to determine the order of the rational numbers because we do not know the signs of the rational numbers.No, it is not possible to determine the order of the rational numbers because we do not know the signs of the rational numbers.
D Yes, it is possible to determine the order of the rational numbers because we know that all of the rational numbers are positive.

Answers

Answer:

C. No, it is not possible to determine the order of the rational numbers because we do not know the signs of the rational numbers.

For each graph below, state whether it represents a function. I don’t know if I got these right.

Answers

Answer:

you got them all right except graph 4 is a function! The trick is to use the vertical line test. Put your pencil vertically on your paper and move it across the graph. If your pencil passes through the same point twice, it's not a function. :)

Step-by-step explanation:

Solve for x. Round to the nearest tenth, if necessary.

Answers

Step-by-step explanation:

For a RIGHT triangle   tan Φ = opposite leg / adjacent leg

 for this triangle

         tan 71 = x / 5.7

       5.7 * tan 71 = x    =   16.6  units

I have to factor, solve, and sketch a parabola for the following, but I do not know how.

2x(x-7)

(x+4)(x-4)

Answers

The parabola for the expression are given in attachment.

A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line, which is known as the directrix

y=2x(x-7)

Let us take few values of x and y and draw the parabola

Similarly we draw the graph for (x+4)(x-4)

Hence, the parabola for the expression are given in attachment.

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The average number of chocolate chips in one ounce is 63 with a standard deviation of 1.8. Find the probability that a randomly selected ounce of chocolate chips will contain between 62 and 66 chocolate chips .

Answers

The probability that a randomly selected ounce of chocolate chips will contain between 62 and 66 chocolate chips is 0.6644.

How to find the probability that a randomly selected ounce of chocolate chips will contain between 62 and 66 chocolate chips

Using the z-score formula to standardize the values and find the probability using a standard normal distribution table:

z1 = (62 - 63) / 1.8 = -0.56

z2 = (66 - 63) / 1.8 = 1.67

Using the standard normal distribution table, we find that the area to the left of z1 is 0.2881 and the area to the left of z2 is 0.9525.

Therefore, the probability that a randomly selected ounce of chocolate chips will contain between 62 and 66 chocolate chips is:

P(62 < x < 66) = P(z1 < z < z2) = P(z < z2) - P(z < z1)

= 0.9525 - 0.2881

= 0.6644

Therefore, the probability is approximately 0.6644.

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Find the Fourth vertex

Answers

The vertex of the parallelogram is (5, 13)

We know that in a parallelogram the opposite sides are equal

AB=√(-3-4)²+(-6+3)²

=√49+9

=√58 units

BC=√(6-4)²+(2+3)²

=√4+25

=√29 units

AD=√(-3-x)²+(-6-y)²

AD=√58 units

√58 units=√(-3-x)²+(-6-y)²

58 units=(-3-x)²+(-6-y)²

Now CD=√(6-x)²+(2-y)²

29 units=(6-x)²+(2-y)²

x=5 and y=13 satisfies the equation

Hence, the vertex of the parallelogram is (5, 13)

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If-4x - 6y = 8 and 6x + 5y = 7 are true equations, what would be the value
of 2x - y?

Answers

answer:

15

step-by-step explanation:

you would need to use elimination to solve thisthis can be done by adding both equations

-4x - 6y = 8

+ (6x + 5y = 7)

__________

2x - y = 15

Complete the following statement. Write your answer as a decimal or whole number.
% of $800,000 = $360,000
Submit

Answers

Answer:

45%

Step-by-step explanation:

Divide $360,000 by $800,000 to find the percentage

360,000/800,000=.45

To conver the decimal to a percentage, move the decimal point two places to the right, so .45 becomes 45%

Complete the ratio table

Answers

The first blank is 57 so it makes
57/438
The second blank is 584 so it makes
76/584

Help !!!!!!!!!!!!!!!!!!!!

Answers

Step-by-step explanation:

Upper problem:

The transformation is a translation of 3 units down.

Lower problem:

The transformation is a translation of 2 units left and 5 units down.

You need to arrange 7 of your favorite books along a small shelf. How many different ways can you arrange the​ books, assuming that the order of the books makes a difference to​ you?

Answers

There are 5,040 different ways you can arrange your 7 favorite books on the small shelf.

The organization or positioning of a group of items or components in relation to one another is referred to as an arrangement. It can be used in a variety of situations, such as mathematics, art, or event planning, and can relate to the arrangement, positioning, or grouping of things.

The number of different ways you can arrange 7 books in a specific order is given by the permutation formula:

P(7,7) = 7!

where "!" denotes the factorial operation.

Thus, the number of ways you can arrange your 7 favorite books along a small shelf, assuming that the order of the books makes a difference to you, is:

7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040

Therefore, there are 5,040 different ways you can arrange your 7 favorite books on the small shelf.

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Use three different values of n to demonstrate that 2n + 3n is equivalent to 5n.

Answers

The three different values of n to demonstrate that 2n + 3n is equivalent to 5n are 1, 4 and 10.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = 2n + 3n

On simplifying the equation , we get

A = 5n

when n = 1 , we get

2n + 3n = 2(1) + 3(1) = 2 + 3 = 5

5n = 5(1) = 5

Therefore, both expressions give the same result of 5.

when n = 4 , we get

2n + 3n = 2(4) + 3(4) = 8 + 12 = 20

5n = 5(4) = 20

Again, both expressions give the same result of 20.

when n = 10 , we get

2n + 3n = 2(10) + 3(10) = 20 + 30 = 50

5n = 5(10) = 50

Hence , the equation is solved

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CAN SOMEONE HELP WITH THIS QUESTION?✨

Answers

The value of the linear sum ∑(i = 1 to 124) (29a_i - 13b_i) is -30.

We have,

Using the linearity of the sum, we have:

∑(i = 1 to 124) (29a_i - 13b_i)

= 29∑(i = 1 to 124)a_i - 13∑(i = 1 to 124)b_i [Distributive property]

= 29(-10) - 13(-20) [Substitute the given sums]

= -290 + 260

= -30

Therefore,

The value of ∑(i = 1 to 124) (29a_i - 13b_i) is -30.

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What is the volume of this figure?

Enter your answer in the box.

Answers

Answer:6720m^2

Step-by-step explanation:

Jared's class took a survey to see how many students owned a trampoline. Of the 24 students in the class, 14 students said they owned a trampoline. If you chose a student at random from Jared's class, what is the probability that the student does not own a trampoline?

Answers

The  probability that the student does not own a trampoline is given by the relation P ( A' ) = 5/12

Given data ,

Let the probability that the student does not own a trampoline be P ( A ' )

Given that there are 14 students who own a trampoline out of 24 students in total, the probability of owning a trampoline is 14/24. Therefore, the probability of not owning a trampoline is:

1 - 14/24 = 10/24 = 5/12

So, the probability that a student chosen at random from Jared's class does not own a trampoline is 5/12

Hence , the probability is 5/12

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please help!!!!!!!!!!!​

Answers

The value of x in the given diagram is 12.

option C.

What is the value of x?

The value of x in the given diagram is calculated by apply the principle of intersecting chord theorem as shown below;

The intersecting chord theorem states that angle formed at the circumference is twice the angle at the tangent.

the angle at circumference = 360 - (6 + 20x)

tangent angle = 4x + 9

360 - (6 + 20x) = 2 (4x + 9)

360 - 6 - 20x = 8x + 18

-28x = -336

x = 336/28

x = 12

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PLEASE HELP
What is the difference between the median math test score in the morning and the
afternoon?

Answers

Answer:

difference = 12.5

Step-by-step explanation:

the median score is the value of the line inside the box.

median in afternoon = 75

median in morning = 87.5

difference = 87.5 - 75 = 12.5

What is the value of x?
cos 63° = sin x
Enter your answer in the box
X= ​

Answers

Answer:

x = 27°

Step-by-step explanation:

using the co-function identity

cos x = sin(90 - x) , then

cos63° = sin(90 - 63)° = sin27° with x = 27°

Determine whether the given ordered list of numbers is a solution of the the system of equations

Answers

It should be noted that to evaluate whether an organized array of numbers serves as a resolution for a combination of equations, one can apply this method.

How to explain the method

Write down the arrangement of equations that you wish to evaluate the solution for. For illustration, let us say that we have this system:

2x + 3y = 7

x - y = 2

Inject the data from the orderly list into the equations. For example, if the ordered list is (x=1, y=3), then we have:

2(1) + 3(3) = 7

1 - 3 = -2

Verify whether the outcome of the equations are equivalent to the values in the ordered list. If they are, then the orderly list is a resolution of the arrangement of equations. On the other hand, if not, then it is not a solution.

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a bar of width is formed of three uniform segments with lengths and areal densities given by: matlab mathematica python r sympy from sympy import * w which of the following statements is not true regarding the day-to-day challenges of growing a firm? strong bases completely to produce in water. the resulting solution conducts electricity well; hence these compounds are classified as electrolytes. As you drive down the road at 14 m/s, you press on the gas pedal and speed up with a uniform acceleration of 1.22 m/s^2 for 0.65 s. If the tires on your car have a radius of 33 cm, what is their angular displacement during this period of acceleration? for a particular liquid-air interface the critical angle (for total internal reflection) is 54.6 degrees. the index of refraction of air is 1.00029. what is the index of refraction of the liquid? what lead to the evolution between prokaryotic and eukaryotic cells and caused the evolution of eukaryotic cells? During S1 which valve closes first? why What is the value of x? true/false. labor unions question 1 options: raise wages in unionized industries. create labor shortages in non-unionized industries. play a larger role in the current u.s. economy than in european countries such as norway and sweden. prefer to operate in states with right-to-work laws. __________was a young Carmelite nun who dies young but write. Journal about her spiritual life, the symbol of which was the "little flower." T/F Having control over how much money is spent, otherwise known as budgetary powers, allows the governor to exert influence over state policy. Un granjero tiene para vender 1800 pollo primero vende 2/5 del total luego los 5/6 del resto y si se mueren 37 pollo cuantos pollos le quedan todavia? (6x10^1) + (9x10^1) in scientific notation Consider using the following Product class. public class Product { private String code; private String description; private double price; protected static int count = 0; // counts number of subclasses public Product() { code = ""; description = price = 0.0: 3 public void setCode(String c) { code = c;} public void setDescription(String d) {description = d; } public void setPrice(double p) { price = p; } public String getCode) { return code; } public String getDescrintion { return description; } public double getPricel) { return price; } public static int getCount) { return count; } public String toStringo { String message = "Code: " + code + "\n" + "Description" + description + "\n" + "Price:" + price + "\n"; return message: } } Use this class as a superclass to implement a hierarchy of related classes: Class Book Software MusicCD Data Author Version Artist Write the declarations for each of the subclasses. For each subclass, supply private instance variables. Complete the constructors, and toString methods. a. A kicker punts a football. The height (in yards) of the football is represented by f(x)=-1/9(x-30)^2+25 , where x is the horizontal distance (in yards) from the kicker's goal line.Find the domain and range.b. On the next possession, the kicker punts the football again. The height of the football is represented by g(x)=f(x+5) .Find the domain and range.c. Compare the graphs.d. On which possession does the kicker punts closer to his goal line? Explain. what is the main reason mountaintops are so cold? group of answer choices the winds are stronger at higher altitudes. mountaintops are above much of the greenhouse gas in the atmosphere. the air is thinner at higher altitudes. there is more water vapor at higher altitudes, causing there to be more snow. in a topographic profile, what would be the horiziontal scale when the vertical scale is 1:50,000 and the vertical exaggeration is 5 binary variables question content area bottom part 1 a. exclude certain individuals from your sample. b. are generally used to control for outliers in your sample. c. can take on only two values. d. can take on more than two values. 2. Marcus worked the following problem out in his notebook. Is his answer correct? Did he do the work correctly? If not,explain to Marcus what he did right and also what he needs to do to correct his work.13--13'-1169 Expecting the price of a popular brand of canned soup to increase in the future, a supermarket orders extra cases of the soup. this is an example of holding inventory because of changes in the _____________ of the inventory.