What is the end behavior of the polynomial function? Drag the choices into the boxes to correctly describe the end behavior of the function. f(x)=6x9−6x4−6 f(x)=−3x4−6x+4x−5


As x→−∞


As x→∞

What Is The End Behavior Of The Polynomial Function? Drag The Choices Into The Boxes To Correctly Describe

Answers

Answer 1

The end behavior of the polynomial function is as shown in the attached picture.

What is polynomial function?

Polynomial functions refers to equation that consists of variables that have non negative exponents or powers. The when there is only one term in the equation it is referred to as monomial

What is end behavior of polynomial function?

The end behavior refers to the behavior of the function at the extremes of the x direction.

The end behavior of a polynomial function is controlled by the term that has the leading terms

In the given question,

The first question has 6x^9 as the term that controls the end behavior hence substituting the -∞ and +∞ gives the end behavior as attachedSimilarly, the second function has -3x^4 as the leading term substituting the -∞ and +∞ gives the end behavior as attached

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What Is The End Behavior Of The Polynomial Function? Drag The Choices Into The Boxes To Correctly Describe

Related Questions

Mrs. McDonald passed out 189 photos that she had taken during the school year. If each of her 21 students received the same number of photos, how many did each receive?

Answers

Answer: 9. 189 divided by 21 is 9.

Step-by-step explanation:

In a company 80/ of workers are men if 1120 people workfor the company who aren’t men how many workers are there in all

Answers

Answer:

if you meant %, the answer is 2016

Step-by-step explanation:

1120 + 80% is 2016

PLSSSSS
WILL MARK BRAINLIEST!!!
SIMPLEEE
(Yr7)

Answers

Answer:

Step-by-step explanation:

the answer I have given below

kind regards

Sandra recorded the distances that 6 beetles crawled in 10 seconds down a 36 inch track. The fractions represent the distances that Sandra recorded. 7 2 1 11 5 17 18' 3' 9' 36' 18 3 36. Which list shows distances Sandra recorded in order from least to greatest?

Answers

Distances Sandra recorded in order from least to greatest is 1/9, 5/18, 11/36, 7/18, 17/36, 2/3.

Given that, the fractions represent the distances that Sandra recorded is 7/18, 2/3, 1/9, 11/36, 5/18, 17/36.

What is the fraction?

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Here, distance is 10/36

So, the equivalent fractions for the given fractions are

7/18 = 14/36

2/3 = 24/36

1/9 = 4/36

11/36

5/18 = 10/36

17/36

So, least to greatest is

4/36 < 10/36 < 11/36 < 14/36 < 17/36 < 24/36

1/9 < 5/18 <11/36 <7/18 <17/36 <2/3

Therefore, distances Sandra recorded in order from least to greatest is 1/9, 5/18, 11/36, 7/18, 17/36, 2/3.

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In today's recording, the first example was the function
f(x) = x² + 5x³ + 10x² + 20x + 24
After depressing our function twice and getting a quotient (depressed polynomial), which was the
resulting quadratic equation that we needed to solve?
O x²+4=0
O x²-4=0
O x² + 4x + 4 = 0
O x² + 4x = 0

Answers

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

How can you locate a polynomial's root?Set the equation's value to zero to get the polynomial's roots. Completely factor the polynomial expression. Then, in order to find the variable, set each factor equal to zero. The formula isx^4+5x^3-10x^2-20x+24Finding polynomial roots (zeroes) is the focus of this solution.

 ((((x4)+(5•(x3)))-(2•5x2))-20x)+24

((((x4) +  5x3) -  (2•5x2)) -  20x) +  24

Find the roots (zeroes) of F(x) = x4 + 5 x 3 x 10 x 2 x 20 + 24.The Polynomial Roots Calculator is a collection of techniques for identifying x values where F(x)=0.One of the tools discussed above is the rational roots test. Only numbers x that can be written as the quotient of two integers would be considered rational roots.According to the Rational Root Theorem, P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient if a polynomial zeroes for a rational integer P/Q.The Leading Coefficient in this situation is 1 and the Trailing Constant is 24.The element(s) are: of the Trailing Constant: 1, 1, 2, 3, 4, 6, 8, 12, and 24 of the Leading Coefficient: 1.According to the Factor Theorem, if P/Q is a polynomial's root, then q*x-p can be used to divide the polynomial. Keep in mind that q and p come from P/Q in its simplest form.In our situation, this means that 4 different polynomials, including x-2, can divide x4+5x3–10x2–20x+24.

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PLEASE PLEASE PLEASE HELP ME I WILL MARK BRAINLY ​

Answers

Answer:

pretty sure its WZX

Step-by-step explanation:

what two numbers multiply to be -6 and add up to be -5

Answers

Answer: -2 and -3

Step-by-step explanation:

Tara's family raises honey bees and sells the honey at the farmers' market. to get ready for market day, tara fills 28 equal sized jars with honey. she brings a total of 14 cups of honey to sell at the farmers' market. use an equation to find the amount of honey each jar holds. to write a fraction, use a slash ( / ) to separate the numerator and denominator.

Answers

The amount of honey each jar holds is 1/2 cup by jar

To solve this exercise we have to perform a mathematical operation of division with fractions:

Information about the problem:

Jars filled = 28 jarsCups brought = 14 cups

To find the amount of honey each jar holds we state the following equation:

Amount of honey by jar = Cups brought / Jars filled

Amount of honey by jar = 14 cups /28 jar

Simplifying to its minimum expression, we have:

Amount of honey by jar = 7 cups / 14 jar

Amount of honey by jar = 1 cup / 2 jar

Amount of honey by jar = 1/2 cup by jar

What is a fraction?

Is a number that expresses the portion of some number over a total. The number that expresses the portion is known as the numerator and the number that expresses the total is known as the denominator.

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Karyn proofreads 15 pages in 2 hours for $40. What is her proofreading rate in pages per hour? How much does she earn per hour?

Answers

The proofreading rate of Karyn in pages per hour is $20 per 7.5 pages per hour , and she earn $20 per hour .

In the question ,

it is given that

Karyn proofreads ⇒15 pages in 2 hours for $40

Karyn in 2 hour proofreads 15 pages ,

So, in 1 hour She will proofread = 15/2= 7.5 pages

and will get $40/2 = $20 for 1 hour ,

hence ,her rate in pages per hour is $20 per 7.5 pages per hour .

In 2 hour Karyn earns $40

So , in 1 hour Karyn will earn $40/2 = $20

hence , she earn $20 per hour .

Therefore , the proofreading rate of Karyn in pages per hour is $20 per 7.5 pages per hour , and she earn $20 per hour .

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1
What is the ratio of blue
circles to red circles?

Answers

Answer:

1:1 or one red circle to one blue circle

There is one red and one blue circle

Step-by-step explanation:

A woman is training for a cycling event. In the first week she cycles 20 km. In each subsequent week, she cycles 5 km more than she cycled the previous week.

How many kilometres has she cycled in total by the end of the 18th week?

Answers

The kilometres that she has cycled in total by the end of the 18th week is 105.

How to calculate the number of kilometers?

Based on the information, this is an arithmetic sequence and the formula is illustrated as

= a + (n - 1)d

where a = first term = 20

d = common difference = 5

n = numbers = 18

Therefore, the 18th term will be:

= a + (n - 1)d

= 20 + (18 - 1)5

= 20 + (17 × 5)

= 20 + 85

= 105

The number of kilometers is 105 kilometers.

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Students in a fitness class each completed a one-mile
Which statements are true about a histogram with one-
walk or run. The list shows the time it took each person
minute increments representing the data? Select three
to complete the mile. Each time is rounded to the
options.
nearest half-minute.
5.5, 6, 7, 10, 7.5, 8, 9.5, 9, 8.5, 8, 7, 7.5, 6, 6.5, 5.5
O A histogram will show that the mean time iS
approximately equal to the median time of 7.5
minutes.
O The histogram will have a shape that is left-skewed.
O The histogram will show that the mean time is greater iS
than the median time of 7.4 minutes.
O The shape of the histogram can be approximated with
a normal curve.
0 The histogram will show that most of the data is
centered between 6 minutes and 9 minutes.

Answers

In linear equation, The histogram will show that most of the data is centered between 6 minutes and 9 minutes.

What in mathematics is a linear equation?

An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x).The dependent variable in this scenario is y since it depends on the independent variable, x.

5.5+6+7+10+7.5+8+9.5+9+8.5+8+7+7.5+6+6.5+5.5=111.5

Since there are 15 values,

           their mean is 111.5/15=7.43 which is very close to the mean.

A)A histogram will show that the mean time is approximately equal to the median time of 7.5 minutes

D)The shape of the histogram can be approximated with a normal curve.

E)The histogram will show that most of the data is centered between 6 minutes and 9 minutes.

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My penMath The area of a triangle can be found using the formula: Area = 1/2 · base · height. Find the area of the triangle pictured below, where the measurements are given in meters (m) 2 m 10 m

Answers

Answer:

The area of the given triangle is 10 sq meters

Explanation:

The area of a triangle is given by the formula:

Area = 1/2 base . height

Given that the triangle has base = 10m, and height = 2m

Area = 1/2 * 10 * 2

= 10 square meters

An adult elephant weighs 2 2/5 tons. An adult hippo weighs 1 4/5 tons. How much will the animals weigh together?

Answers

Answer: If you want the result as a fraction it should be 3.7/5. but if you want a whole number it's 4.2. if you want a mixed number its 4 1/5

Step-by-step explanation:

Use the graph to write a linear function that relates y to x.

Answers

Answer:

y=4/3x+2

Step-by-step explanation:

Using the information found in these tables which of the following statements is true


Please helpppp

Answers

The first one is correct because the age/grade is independent and screen time: games is dependent on the independent

a school nurse can give 25 eye tests in a two-hour period. how long will it take the nurse to give eye tests to all 600 stuents in her school.

Answers

600/25 = 24
24•2 = 48

48 hours for all 600 students

How did the people of the Plymouth Colony fail to achieve the ideals of the Mayflower Compact? They did not come together to create a government. They did not write laws that protected everyone in the colony. They did not create an orderly community within the colony. They did not form a civil body that could preserve the colony.

Answers

The people of the Plymouth Colony fail to achieve the ideals of the Mayflower Compact as A. They did not come together to create a government.

What was Mayflower Compact?

The Mayflower Compact was the Plymouth colony's first government instrument. The Pilgrim Fathers, the emigrants who crossed the Atlantic on the Mayflower in search of religious freedom, wrote the manifesto. On November 11, 1620, it was signed on the sands of what is now Provincetown, near Cape Cod. The pilgrims knew they were in a land unfamiliar to the London Company when the Mayflower docked in Plymouth.

The strangers claimed that the Virginia Company contract was null and void. They believed that because the Mayflower landed outside of Virginia Company territory, they were no longer bound by the charter of the company. Because there was no official government over them, the stubborn strangers refused to acknowledge any regulations.

Many of the pilgrims were already weak from disease and a lack of food when they arrived in Plymouth. The journey had been lengthy, and they were running low on supplies. During the winter, the colony lost about half of its population owing to disease and famine.

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Answer:its A i did it on edge

Step-by-step explanation:

For any integer of n which of the following, n and n+2, n-1 and n+1, 2n and 2n+2, 2n-1 and 2n+1, 2n+ 1 and 2n+2, 2n and 2n+1 are always 2 consecutive even numbers

Answers

The number 2n and 2n + 2 will always are 2 consecutive even numbers.

What is termed as the consecutive even numbers?Consecutive numbers are numbers that obey one another in a regular adding up order or pattern. They are written in a series with a fixed difference here between numbers and no numbers skipped in between. We know that even numbers end in 0, 2, 4, 6, and 8. Consider a set of even numbers ranging from 2 to 12 but rather write those in ascending order. When written from smallest to largest, the numbers are organized as 2, 4, 6, 8, 10, 12. The difference between any former leader pair is 2, as we can see. As a result, these numbers comprise the collection of consecutive even numbers.

From the given option in the question;

2n and 2n + 2 will always be two consecutive even number.

For, n = 1, the numbers be 2 and 4.

For, n = 2, the numbers be 4 and 6.

For n = 3, the numbers be 6 and 8....and so on.

Thus, the number 2n and 2n + 2 will always are 2 consecutive even numbers.

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(-4k - 1) - (-6k - 6)

Answers

Answer:

2k + 5

Step-by-step explanation:

Since this is a subtraction problem, you need to change it to an addition problem. When you do this, you also need to change the sign of each term in the second set of parentheses.

(-4k - 1) - (-6k - 6)

(-4k - 1) + (6k + 6)

Remove the parentheses and add like terms.

-4k - 1 + 6k + 6

2k +5

-4k - 1 + 6k + 6
2K+5

A plumber charges $25 for a service call plus $50 per hour of service. Write an equation in slope-intercept form for the cost, C, after h hours of service. What will be the total cost for 8 hours of work? 10 hours of work? On a graph

Answers

The equation in slope intercept form is C(h) = 50h+25  ,the total cost for 8 hours of work is $425 , and for 10 hours of work  is  $525.

In the question;

it is given that

the fixed charge of plumber = $25

charge for per hour of service = $50

the hours of service be "h"

and the total cost be "C"

according to the question

C(h) = 50h+25

the equation in the slope intercept form is C(h) = 50h+25

to find the total cost for 8 hours of work , put h=8

C(8) = 50(8) + 25

= 400+25

= 425

to find the total cost for 10 hours of work , put h=10

C(10) = 50(10) + 25

= 500+25

= 525

Therefore , total cost for 8 hours of work is $425 , and for 10 hours of work  is $525 .

The given question is incomplete , the complete question is

A plumber charges $25 for a service call plus $50 per hour of service. Write an equation in slope-intercept form for the cost, C, after h hours of service. What will be the total cost for 8 hours of work? 10 hours of work?

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The slope of line ℓ
is greater than 0 and less than 1. Write an inequality for the slope of a line perpendicular to ℓ
.

Answers

By properties of perpendicular lines and algebra properties, the slope of the line perpendicular to line ℓ is represented by m' > 1.

How to represent an inequality associated with a line perpendicular to another line

Let m be the slope of a line, in accordance with analytic geometry, the slope of line perpendicular to the first one is equal to m' = - 1 / m. The statement can be summarized by the following inequality:

0 < m < 1

Then, by algebra properties for inequalities we find that that slope for the perpendicular line is:

0 < m · m⁻¹ < m⁻¹

0 < 1 < m⁻¹

1 < m⁻¹

- m⁻¹ > 1

- 1 / m > 1

m' > 1

The slope of the line perpendicular to line ℓ is represented by m' > 1.

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vehicle speed on a particular bridge in china can be modeled as normally distributed. (a) if 5% of all vehicles travel less than 39.18 m/h and 10% travel more than 73.27 m/h, what are the mean and standard deviation of vehicle speed? (round your answers to three decimal places.) mean standard deviation

Answers

The mean and standard deviation of the vehicle speed are 58.33 and 11.64 respectively.

The vehicle speed on a particular bridge in china has normal distribution.

5% represents the 5th percentile which is here, 39.18 m/h.

Since 10% travels more than 73.27 m/h, 90% travels less than 73.27 m/h.

So here the 90th percentile is 73.27 m/h.

Also the z-score, z = (x-μ)/σ, where μ is the mean of normal distribution and σ, the standard deviation.

So 39.18 corresponds to the z with p-value 0.05, i.e., z = -1.645 [from the normal tables]

Hence, z = (x-μ)/σ

⇒ -1.645 = (39.18 - μ)/σ

⇒ -1.645σ = 39.18 - μ

⇒ μ = 39.18 + 1.645σ  ----------(1)

Also 73.27 corresponds  to the z with p-value 0.9,i.e., z = 1.28.

Hence , z = (x-μ)/σ

⇒ 1.28 = (73.27 - μ)/σ

⇒ 1.28σ = 73.27 - μ

⇒ μ = 73.27 - 1.28σ  ----------(2)

Equating (1) and (2), we get,

39.18 + 1.645σ  =  73.27 - 1.28σ

2.925σ = 34.05

σ = 11.64

hence μ = 39.18 +1.645 x 11.64

⇒ μ = 58.33

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WRITE AN EQUATION TO DESCRIBE THE RELATIONSHIP BETWEEN J AND Mj | 4 | 12 | 20m | 3 | 9 | 15

Answers

First, we can use the points (4,3) and (20,15) to find the slope of the line:

[tex]\begin{gathered} s=\frac{m_2─m_1}{j_2─j_1}=\frac{15─3}{20─4}=\frac{12}{16}=\frac{3}{4} \\ s=\frac{3}{4} \end{gathered}[/tex]

Now we can find the relation function using the point (4,3) and the slope s=3/4

[tex]\begin{gathered} m─m_1=s(j─j_1) \\ \Rightarrow m─3=\frac{3}{4}(j─4)=\frac{3}{4}j─(\frac{12}{4})=\frac{3}{4}j─3 \\ m=\frac{3}{4}j \end{gathered}[/tex]

therefore, the equation to describe the relationship between J and M is m=3/4j

Which of the following equations have no solutions?Choose all answers that apply:-60x + 32 = 32x + 60 -60x + 32 = 32x - 60 -60x + 32 = -60x - 32-60x + 32 = -60x + 60

Answers

Answer:

-60x + 32 = -60x - 32

Step-by-step explanation:

The first step to solve this question is combining the like terms in each option.

In those that we end up with:

0x = c

In which c != 0, we have no solution. So

-60x + 32 = 32x + 60

-60x - 32x = 60 - 32

-92x = 28

No 0x, so it has solution

-60x + 32 = 32x - 60

-60x - 32x = -60 - 32

-92x = -92

No 0x, so it has solution

-60x + 32 = -60x - 32

-60x + 60x = -32 - 32

0x = -64

0x equaling a value different of 0, so no solution.

-60x + 32 = -60x + 60

Help help please please help help I need help 30 POINTS

Answers

Line b



Line of symmetry is basically a line in the middle or somewhere else that dictates where a shape would be symmetrical

Standard Questions
Question Progress
The average mass of a man is 84 kg and of a woman is 70 kg.
A lift can safely carry 720 kg.
Work out the maximum number of people the lift can safely carry.

Answers

We need to know simple division to solve the problem. The maximum number of men in the lift is 8 and the maximum number of women in the lift is 10.

We will be using the simple concept of division to find the number of people that the lift can carry. The average weight of a man is given to be 84 kg and the average weight of  a woman is given to be 70kg. The lift can carry 720 kg, we will find separately the number of men and women that can be carried in the lift. Inorder to find the maximum number of men we divide the total weight the lift can carry by the average weight of a man, we will similarly calculate the maximum number of women.

number of men= 720/84=8.57 which means that the number of men is 8

number of women =720/70=10.28 which means that number of women is 10.

Therefore the lift can carry at most 8 men and at most 10 women.

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I need help with these problems ASAP.

Answers

The following cases are described:

The rational function is (f / g) (x) = x - 6, whose domain is all the real numbers.The rational function is (f / g) (x) = 1 / (x + 2), whose domain is all the real numbers except x = - 2.

How to derive a rational function by division of functions and find its domain

Algebraically speaking, rational functions are expressions of the form f(x) = p(x) / q(x), such that q(x) ≠ 0, where p(x) is the numerator and q(x) is the denominator. Rational functions can be found by using the defintion of division between two functions:

(f / g) (x) = f(x) / g(x)

And the domain of (f / g) (x) is every value of x such that g(x) ≠ 0. Now we proceed to find all the required information for each case:

Case 1 - f(x) = x² - 3 · x - 18, g(x) = x + 3

Rule: (f / g) (x) = (x² - 3 · x - 18) / (x + 3)

         (f / g) (x) = [(x - 6) · (x + 3)] / (x + 3)

         (f / g) (x) = x - 6

Domain: Since the resulting expression is a linear function, then the domain of (f / g) (x) is all the real numbers.

Case 2 - f(x) = x - 3, g(x) = x² - x - 6

Rule: (f / g) (x) = (x - 3) / (x² - x - 6)

         (f / g) (x) = (x - 3) / [(x - 3) · (x + 2)]

         (f / g) (x) = 1 / (x + 2)

Domain: The domain of the rational function is any real number except x = - 2.

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HELP PLS ITS DUE TONIGHT

Answers

Answer:

1. 12

2. 4:5

3. 5

4. 30

5. 42

6. 15

7. 36

8. 1120

9. 10 2/3

Step-by-step explanation:

Answer:

In photo

Step-by-step explanation:

Determine if the table below is proportional?

Answers

The table represent a direct proportional relation.

How to determine if a table represents a proportional relation

In this question we find a table with four pairs of elements that have to be tested with respect to the direct proportional formula, which is defined below:

y = k · x

Where:

x - Independent variable.y - Dependent variable.k - Constant of proportionality.

The table represents a direct proportional relation if and only if there is only one constant of proportionality:

k₁

k₁ = 12 / 3

k₁ = 4

k₂

k₂ = 20 / 5

k₂ = 4

k₃

k₃ = 8 / 2

k₃ = 4

k₄

k₄ = 32 / 8

k₄ = 4

As k₁ = k₂ = k₃ = k₄, the table represent a proportional relationship.

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during a tennis match, a player serves the ball at 23.6 m/s, with the center of the ball leaving the racquet horizontally 2.37 m above the court surface. the net is 12m away and 0.90 m high. when the ball reaches the net, a) does the ball clear it? show your solution. b) what is the distance between the center of the ball and the top of the net? Who prioneered a manufacturing method based around the principle of take the work to the man, not the man to the work?. what advice about fat would you give someone who wants to lose weight? a. continue to incorporate fats into your diet but choose healthy ones and monitor portion size. b. fat has many uses in the body and should not be cut back. c. exercise more and eat high-fat foods that provide more energy. d. avoid foods that contain unhealthy fatty acids. e. cut out all fats in your diet so energy comes from muscle stores. The nutrition label on Erin's box of animal crackers states that 16 crackers contain 24 grams of carbohydrates. Erin ate 12 animal crackers from the box. What is the number of grams of carbohydrates in 12 animal crackers? A.8 grams B. 12 grams C. 18 gramsD. 20 grams when he was in treatment for his substance use disorder, wesley was taught to identify cues and situations that increased his drug cravings and how to effectively deal with those situations. this approach is known as: Whats the correct answer answer asap for brainlist Factor Pairs (MAJOR POINTS!) a small manufacturing company is considering purchasing a maintenance contract for its air conditioning systems. since all of its systems are new, the company plans to begin the contract in year four and continue through year ten. the cost of the contract is $3,200 per year and the company's minimum attractive rate of return is 12% per year. the present worth of the contract is nearest to: a) $6,605 b) $10,395 c) $14,604 d) $18,081 A family of four went to an amusement park for their vacation. They started the vacation with $426.They spent a total of $198 the first three days.If they divided the remainder of the money evenly between the family members for souvenirs, how much did each person have to spend? What two numbers multiplied give you 100 and added give you 21? how much would EZ Excavation charge to haul 40 cubic yards of dirt six distinct positive integers are randomly chosen between and , inclusive. what is the probability that some pair of these integers has a difference that is a multiple of ? A sample of unknown material weight 900N In air and and 400N when submerged in an alcohol solution with a density of 0.7 g/cm.What is the density of the material ? For each level of confidence o below, determine the corresponding normal confidence interval. Assume each confidence interval is constructed for the same sample statistics.Drag each normal confidence interval given above to the level of confidence a cyclist rides her bike at a speed of 30 kilometers per hour. what is the speed in miles per hour? how many miles will the cyclist travel in 5 hours? a scientist need to 6000 calories per day. Based on the percentage of total daily calories and the number of calories needed, how many biscuits, packages of pemmican, butter and coco does a person need each day? suppose alyssa is willing to drive across town to save 50 percent on a soccer ball with a list price of $40. if alyssa is rational, this implies that she would a certain compound is found to have the percent composition (by mass) of 85.63% c and 14.37% h. the molecular formula contains 6 carbon atoms. how many hydrogen atoms are contained in a molecular of this compound? What is anexample of actingin a self-centeredway?A. Throwing a surpriseparty for a friend.B. Wishing you didsomething in a differentway.C. Going to your friend'sbasketball game tosupport them.D. Visiting a friend who isgoing through a hard time. Why were Europeans looking for a sea route to the Indies?ResponsesMountains blocked the way from Europe to Asia.Mountains blocked the way from Europe to Asia.Muslim powers controlled most of the land routes.Muslim powers controlled most of the land routes.Camels and donkeys were becoming scarce.Camels and donkeys were becoming scarce.Merchants liked to travel by sea