Use the graph of each function to estimate intervals to the nearest 0.5 unit on which the function is increasing, decreasing, or constant. Support the answer numerically.
f(x)=x^3-x^2-2x+3
It appears that from graph that the function is increasing in the interval (-∞,-1) and (1,∞). Also the function is decreasing in the interval (-1,1) and (0.0.5).The function is not constant anywhere.
To check if this is correct, we will find the relative extrema of the function,
f(x) = x³-x²-2x+3
Find it derivative f'(x) = 3x²-2x-2
f'(x) = 0
⇒ x = 2 ± √(4+24)/3
= 3.77 , -1.1
Find the second derivative f''(x) = 6x -2
f''(3.77) = 20.62>0
So the function has a relative minimum at x = 3.77.
f''(-1.1) = -8.6<0
So the function has a relative maximum at x = -1.1
Now we can conclude with the intervals where the function is increasing is before the relative maximum and after the relative minimum.
i.e., the intervals (-∞,-1) and (3.5,∞) [rounding to the nearest 0.5 unit]
So the interval in which the function is decreasing is between the relative maximum and minimum. i.e., the interval (-1, 3.5)
The function is nowhere constant.
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W
Which graph represents the solution of the system
{x² + y² = 4
x-y = 1
The graph is plotted in the following figure .
To plot a graph we need 2 pts .
First eqn is of a circle ( [tex]x^{2}[/tex] ) + ( [tex]y^{2}[/tex] ) = 4
Second eqn is of a line x - y = 1
The center of circle is ( 0 , 0 )
The circle passes through ( 2 , 0 ) , ( 0 , 2 ) , ( - 2 , 0 ) , ( 0 , - 2 ) .
The line passes through ( 0 , 1 ) , ( 0 , - 1 ) .
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The difference in the x-coordinates of two points is 3, and the difference in the y-coordinates of the two points is 6. What is the slope of the line that passes through the points? 2 3 6 9
Solution :
the differences in the X coordinates and Y coordinates:
The x-coordinate tells you how many steps you have to take to the right (positive) or left (negative) on the x-axis. And the y-coordinate tells you have many steps to move up (positive) or down (negative) on the y-axis.
Given : difference in the x-coordinates of two points is 3
the difference in the y-coordinates of the two points is 6
The slope of the line :
In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate.
The net change in the y-coordinate is represented by Δy and the net change in the x-coordinate is represented by Δx.
Hence, the change in y-coordinate with respect to the change in x-coordinate is given by,
m = change in y/change in x = Δy/Δx
Where “m” is the slope of a line.
Tan θ = Δy/Δx can also represent the slope of the line
So, tan θ to be the slope of a line.
Generally, the slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says (x1,y1) and (x2,y2) can be easily determined by finding the difference between the coordinates of the points. The letter ‘ m’ usually represents the slope.
If P(x1,y1) and Q(x2,y2) are the two points on a straight line, then the slope formula is given by:
Slope,
m = Change in y-coordinates/Change in x-coordinates
m = (y2 – y1)/(x2 – x1)
Therefore, based on the above formula, we can easily calculate the slope of a line between two points.
In other terms, the slope of a line between two points is also said to be the rise of the line from one point to another (along the y-axis) over the run (along the x-axis). Therefore,
Slope, m = Rise/Run
Use the slope formula.
the slope of a line given the coordinates of two points on the line. The slope formula is m=(y2-y1)/(x2-x1), or
the change in the y values over the change in the x values.
The coordinates of the first point represent x1 and y1. The coordinates of the second points are x2, y2. It does not matter which point you label as the first point and which you label as the second. Don't forget to include the correct sign of each value. Simplify to get the value of the slope. Check the your answer by graphing the points and verifying that the vertical distance between the two points and the horizontal distance between the two points is captured by the numerator and denominator of the slope
Ponit (2,3) & (6,9)
Slope of Line = y2-y1/x2-x1
= 9-3/3-2
=6/1
Slope of Line = 6
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I need help I need it in 1 min please help 13 and 14
i) 9⁻⁴=1/6561
ii1/2⁻⁶=64
Positive exponent: An exponent defines the number of times a number is multiplied by itself. For example, 32. It means that the number 3 has to be multiplied twice. Here, the number 3 is a base number and 2 is an exponent. The exponent can be positive or negative.
Nagative exponent: We know that the positive exponent tells us how many times a number is multiplied by itself. Whereas, the negative exponent tells us how many times we have to divide the base number. In other words, the negative exponent describes how many times we have to multiply the reciprocal of the base. An example of negative exponents is 3-2.
Thus, x-2 is written as (1/x²).
i)Rewrite expression using a positive exponent 9⁻⁴
We know that positive exponent.
9⁻⁴=1/94
9⁻⁴=1/6561.
ii)Rewrite expression using a positive exponent 1/2⁻⁶
1/2⁻⁶=26
⇒1/2⁻⁶=64.
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Write the composite function in the form f(g(x)). [identify the inner function u = g(x) and the outer function y = f(u).] y = 3 1 5x
Answer:
It's really hard to really solve cause I'm a student in learning.
Find the distance between the two points rounding to the nearest tenth (if necessary).
(-6, 5) and (3,-7)
Answer: 15
Step-by-step explanation:
Distance formula: a^2+b^2=c^2 where c is the distance.
a^2=
(-6-3)^2=
(-9)^2=81
b^2=
(5-(-7))^2=
(5+7)^2=
12^2=144
c^2=81+144=225
If c^2=225, then what's c?
c=15
See attachments!
Paolo wrote the following equation for the perimeter of a rectangle.
Which equation is equivalent to the equation Paolo wrote?
Answer:
p = 2 + l w
Step-by-step explanation:
Heyy! Could you guys possibly help with the answer to this question? I’m stuck.
The codes of the countries are 34, 35 and 36
How to determine the codes of the countries?The given parameters are
Sum of codes = 105
Where the numbers are consecutive numbers
This means that
B = A + 1
C = A + 2
So, we have
A +A + 1 + A + 2 = 105
Evaluate the like terms
3A = 102
Divide through by 3
A = 34
So, we have
B = A + 1 = 34 + 1 = 35
C = A + 2 = 34 + 2 = 36
Hence, the codes of the countries are 34, 35 and 36
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A road sign in Canada gives the distance to Toronto as 140 kilometers. What is this distance to the nearest mile?
Converting 140 kilometers to miles, the distance from a road sign in Canada to Toronto is 87 miles.
In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.
A conversion factor is a number used to change one set of units to another, either by multiplying or dividing.
From the problem, we must convert the distance of 140 kilometers into miles.
Converting kilometers to miles, we must use the conversion
1 kilometer = 0.621371 mile
140 kilometers = 140 (0.621371 mile)
140 kilometers = 86.992 miles
Rounding off to the nearest mile,
140 kilometers = 86.992 miles = 87 miles
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Write the number 86,360,000 using the number word "million" and then round to one decimal place.
million
M
The number 86,360,000 using the number word "million" and then round to one decimal place is Eighty-six million three hundred sixty thousand.
The writing style used to express numbers in India is known as the Indian numeral system. In this case, numbers are divided into several time periods or groupings. This numbering scheme uses ten distinct symbols, including the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
The order of the digits when using the Indian number system is one, ten, hundreds, thousands, ten thousand, lakhs, lakhs, crores, and crores. The era and locations are shown in the table below according to the amount of digits in a number.
Given number: 86,360,000
Eighty-six million three hundred sixty thousand in numbers
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total u.s. land area is 3.537 million square miles. what percentage of u.s. land is national park system land ?
The percentage of u.s. land is national park system land is approximately 41.8%
PercentageConvert acres to square miles
945,000,000 acres = 1476562.5 square milesPercentage of u.s. land is national park system land = national park system land / Total U.S. land area × 100
= 1476562.5 square miles / 3,537,000 square miles × 100
= 0.417461832061068 × 100
= 41.74618320610687%
Approximately,
41.8%
Therefore, the percentage of u.s. land is national park system land is approximately 41.8%
Complete question:
Total U.S. land area is 3.537 million square miles. Total U.S. national park system land occupies 954 million acres. What percentage of U.S. national park system land?
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NEED HELP
Which of the following is and isn't a function? ( There may be more than one answer ). Explain Clearly
Using the function concept, we have that:
Items, a, and d are functions.Item b and c are not functions.When does a relation represents a function?A relation represents a function when each value of the input is mapped to only one value of the output.
On a graph, it means that each value of x is mapped to only one value of y, that is, there are no vertically aligned points on the graph.
For this problem, relation c does not represent a function, as there are multiple values of x are related to two values of y, and there are vertically aligned points on the graph.
In item b, when x = 6, there are two values of y, hence this is also not a function. For items a and d, each value of x is mapped to only one value of y, hence they are functions.
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Georgia is on the prom committee. She wants to hang a dozen congruent triangles from the ceiling so that they are parallel to the floor. She sketched out one triangle on a coordinate plane with coordinates (0,4),(3,8) , and (6,0) . If each triangle is to be hung by one chain, what are the coordinates of the point where the chain should attach to the triangle?
The coordinates of the point where the chain should attach to the triangle are (3, 4).
Given that, a triangle is on a coordinate plane with coordinates (0,4), (3,8), and (6,0).
We need to find the coordinates of the point where the chain should attach to the triangle.
What is the centroid of the triangle?The centroid is the centre point of the object. The point at which the three medians of the triangle intersect is known as the centroid of a triangle. It is also defined as the point of intersection of all three medians. The median is a line that joins the midpoint of a side and the opposite vertex of the triangle. The centroid of the triangle formula is G = ((x1+x2+x3)/3 , (y1+y2+y3)/3).
Now, centroid = ((0+3+6)/3, (4+8+0)/4)
=(3, 4)
Therefore, the coordinates of the point where the chain should attach to the triangle are (3, 4).
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44. the total cost for tuition plus room and board at state university is 2,584 dollars. tuition costs 704 dollars more than room and board. what is the tuition fee?
If total cost for tuition plus room and board at state university is 2,584 dollars and tuition costs 704 dollars more than room and board, then the tuition fees is 1644 dollars
Given,
The total cost for tuition plus room and board = 2584 dollars
Consider the cost for room and board as x
Tuition costs 704 dollars more than room and board.
Therefore the tuition fees = 704+x
Then the total cost = Cost for tuition fees+ Cost for room and board
2584 = (704+x)+x
2584= 704+2x
2x= 1880
x= 940 dollars
Then the tuition fees = 704+x
=704+940
=1644 dollars
Hence, if total cost for tuition plus room and board at state university is 2,584 dollars and tuition costs 704 dollars more than room and board, then the tuition fees is 1644 dollars
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Which number appears farther to the right on the number line?
a) -53/2
b) -1
c) -100
Answer:
-1
Step-by-step explanation:
-1 has the greatest value
find the area and circumference of each circle. Use pi in your answer (example: radius = 8, or diameter = 14).
The area of the circle is 64π square unit and the circumference is 16π units
Calculating area and circumference of a circleFrom the question, we are to find the area and circumference of the circle
The area of a circle is given by the formula,
A = πr²
Where A is the area
and r is the radius
Using the parameter, radius = 8
Then,
A = π × 8²
A = 64π square unit
Calculating the circumference
The circumference of a circle is given by the formula
C = 2πr
Where C is the circumference
and r is the radius
Thus,
C = 2 × π × 8
C = 16π units
Hence, the area of the circle is 64π square unit and the circumference is 16π units
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in a large population, 71% of the people have been vaccinated. if 5 people are randomly selected, what is the probability that at least one of them has been vaccinated?
The probability that AT LEAST ONE of them has been vaccinated is 0.9979.
Vaccination rate among the population: p = 0.71
Sample size = 5
Assume that X people have received vaccinations.
P(atleast one) = 1 - P (none)
By the binomial distribution, now,
P(none)= (⁵₀) 0.71° (1-0.71)⁵⁻⁰
= 1 × 1 (0.29)⁵
= 0.0021
So,
P(at least one) therefore equals 1 - P (none)
= 1 - 0.0021
= 0.9979
Therefore, the probability that AT LEAST ONE of them has been vaccinated is 0.9979
An explanation of probability theory?
Probability theory is a mathematical discipline that analyzes random encounters. A random event's outcome cannot be predicted before it occurs, but it could take any of several various forms. The end outcome is thought that it was determined by chance.
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Bob is interested in examining the relationship between the number of bedrooms in a home and its selling price. After downloading a valid data set from the internet, he calculates the correlation. The correlation value he calculates is only 0. 5. What does bob conclude?.
Bob after downloading the valid data set from the internet and calculating the correlation values as 0.5 concludes that as the number of bedrooms in a home increases its selling price also increases.
This happens because as there is an increased demand for the number of bedrooms in a home there should be enough supply in the market to fulfill the requirements. So, there should be a surplus of beds in the market and for that the selling price increases to maintain the surplus.
The law of Demand states that as the demand for a particular commodity or a product increases its price also increases. The above example of Bob gets verified according to the Law of Demand.
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Imagine that you are a teacher grading your students’ assignments. The following questions were turned in with incorrect answers. Trace through the process of solving them to discover where your students made a mistake in their order of operations. Which step of PEMDAS did they do out of order? Explain.
(6-2)^2+12-3^2
The correct answer is 19
student answer 97
The student did the subtraction step of PEMDAS out of order.
What is PEMDAS?PEMDAS is a rule regarding precedence of operations, given as follows, from highest to lowest precedence.
Parenthesis.Exponents.Multiplication/Division.Addition/Subtraction.In this problem, the expression is:
(6 - 2)² + 12 - 3².
The student reached an answer of 97 as follows:
(6 - 2)² + 9² = 4² + 9² = 16 + 81 = 97.
The student did the subtraction first, hence the student did the subtraction step of PEMDAS out of order.
The correct solution is:
(6 - 2)² + 12 - 3² -> Solve the Parenthesis.
4² + 12 - 3² -> Solve the Exponents.
16 + 12 - 9 -> Solve the Addition and Subtraction.
19.
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Find the LCM of
[tex]8 {a}^{2} {b}^{3} {f}^{4} [/tex]
and
[tex]3abg[/tex]
The LCM of 8a²b³f⁴ and 3abg is 24a²b³f⁴g.
What is defined by the term LCM?LCM is an abbreviation for "Least Common Multiple." The smallest multiple which two or even more numbers have in common is defined as the least common multiple.
Consider the following two integers: 2 and 3.2 multiples: 2, 4, 6, 8, 10, 12, 14....Multiples of three: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, and so on.The numbers 6, 12, and 18 are all common multiples of 2 and 3. The smallest number is six. As a result, the least common multiple of 2 and 3 is 6.The smallest number divisible both by numbers is the LCM of two numbers.Figuring the lowest common denominator (LCD) of 2 or even more fractions is a common application of LCM.
It is useful for adding, subtracting, as well as compare different or more fractions.
For the given question, the two numbers are given as; 8a²b³f⁴ and 3abg.
The least common multiple which will divide both the numbers are; all the values with their highest power.
LCM = 24a²b³f⁴g.
Thus, the LCM is found as 24a²b³f⁴g.
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Homework help please
Answer:
Step-by-step explanation:
180
1/3 ÷ 8 =
what s the answer
Answer:
0.0416¯
Step-by-step explanation:
after the 1 six is being repeated. Hope this helps! :)
25 points plus brainliest
Answer:
i think b
Step-by-step explanation:
Answer:
B. y = 2x + 8
Step-by-step explanation:
14x - 7y = 1
7y = 14x - 1
y = 2x - 1/7
If two lines are parallel, their slopes are equal.
With m = 2, x = -2, y = 4
y = mx + b
4 = 2(-2) + b
4 = -4 + b
b = 8
so y = 2x + 8
a traffic study has shown that the probability that 55 cars will pass over a small bridge in a 4-4-minute period is 0.16.0.16. what are the odds against exactly 55 cars passing over the bridge in that time?
REWRITE USING SET BUILDER NOTATION
a) the set of natural numbers less than 10
b) the set of integers greater than -7 but less than 7
c) the set of whole numbers greater than zero but less than or equal to 20
Answer:
See explanation
Step-by-step explanation:
n=number
a. { n ∈ N | n<10 } ==> N denotes natural numbers
b. { n ∈ Z | -7<n<7 } ==> Z denotes integers
c. {n ∈ W | 0<n<=20 } ==> W denotes whole numbers
The probability a d-link network server is down is 0.10. if you have three independent servers, what is the probability that at least one of them is operational?
The probability that at least one of them is operational is 0.999
Probability:
Probability means the possibility of happening the particular event. So, it can be written as the fraction of possible event by the total number of event.
Given,
The probability a D-Link network server is down is 0.10.
Here we need to find if you have three independent servers, what is the probability that at least one of them is operational.
Let D be an event that a D-Link network server is down.
It is given that the probability that a D-Link network server is down is
=> P(D) = 0.10
The number of independent servers
=> (n) = 3
The probability that none of the servers is working is
=>P(None) = P(D) x P(D) x P(D)
=> P(None) = 0.10 x 0.10 x 0.10
=> P(None) = 0.001
The probability that at least one of them is operational is given as
=> 1 - P(None)
=> 1 - 0.001
=> 0.999
Therefore, the probability that at least one of them is operational is 0.999.
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the air quality index, or aqi, measures how polluted the air is in your city and assigns a number based on the quality of the air. over 100 is "unhealthy".the following quadratic regression equation gives us an estimate of n, which is the number of days the aqi exceeded 100 a particular year. we will use this equation to estimate the number of days the aqi was over 100 in the year 1995.n
Final answer:
The estimated number of days the aqi was over 100 in the year 1995 is calculated as 135 days.
Is linear regression quadratic regression ?
Simple linear regression is expanded upon in quadratic regression. While quadratic regression has the drawback of requiring more data points to ensure that your data falls into the "U" shape, linear regression can be carried out with as few as two points (i.e., enough points to draw a straight line).
In situations where the second differences are constant, a quadratic model is adequate. We can ascertain the degree of the model for the data by identifying variations between the dependent values. The model will be linear if the initial difference has the same value. The model will be quadratic if the second difference has the same value as the first.
Explanation:
The air quality index, or aqi, calculates a number depending on how clean or dirty the air. Then it is estimate n, the number of days the aqi exceeded 100 in a specific year is evaluated and calculated as it is actually as 135 days on edge.
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Matt had 6 books to read. Each book has 11 pages. He has already read 60 pages. How many pages does he have left to read? The answer
Simplify an expression for the perimeter of the rectangle shown.
8.6x + 3
5.2
4
Write your answer with NO spaces:
The perimeter of the rectangle is P = (17.2x₊16.4).
Given that,
Length, l = 8.6x₊3
Width, b = 5.2
In the formula P=2l+2w, where l is the rectangle's length and w is its width, the perimeter P of a rectangle is determined. Using the formula A=l×w, where l is the length and w is the width, we can determine the area A of a rectangle.
We need to find the expression for the perimeter of the rectangle. The formula for the perimeter of the rectangle is given by :
P=2(l₊b)
Putting values of l and b in the above formula:
p = 2(8.6x ₊ 3 ₊ 5.2)
= 2(8.6x ₊ 8.2)
= 2(8.6x) ₊ 2(8.2)
= 17.2x ₊ 16.4
So, the required perimeter of the rectangle is 17.2x₊16.4.
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Pierce sold six gallons of paint for $75.78. What was the price per gallon of the paint?