The table below gives the population of a town (in thousands) from 2000 to 2008. What was the average rate of change of population between 2002 and 2004, and between 2002 and 2006?
Answers
The average rate of change in population is -35 between 2002 and 2004, and -2.5 between 2002 and 2006 which represents the decrease in the population.
What is Lagrange mean value theorem?Lagrange mean value theorem states that, if a function f is continuous over the closed interval [a, b] and differentiable over the open interval (a, b), then there must be at least one point c in the interval (a, b) where the slope of the tangent at the point c is equal to the slope of the tangent through the curve's endpoints, resulting in the expression f'(c) = {F(b) -F(a)}/(b-a)
As per the given data in the table, the required solution would be below
The average rate of change in population between 2002 and 2004 as:
⇒ (76-83)/(2004-2002)
⇒ -7/2
⇒ -3.5
The average rate of change in population between 2002 and 2006
⇒ (78-83)/(2006-2002)
⇒ -5/2
⇒ -2.5
This represents the decrease in the population.
Therefore, the average rate of change in population is -35 between 2002 and 2004, and -2.5 between 2002 and 2006.
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Related Questions
HELP PLEASE !!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
The equation of the line perpendicular to y = - (2 / 3) · x and the point (4, - 8) is y = (3 / 2) · x - 14.
How to determine the equation of a perpendicular line
Mathematically speaking, lines are represented by equations of the form y = m · x + b, where m and b are the slope and the intercept of the line. Additionally, two lines are perpendicular to each if the product of their slopes is equal to - 1.
First, we determine the slope of the perpendicular line:
m' = - 1 / m
m' = - 1 / (- 2 / 3)
m' = 3 / 2
Second, the intercept of the perpendicular line is:
b = y - m · x
b = - 8 - (3 / 2) · 4
b = - 8 - 6
b = - 14
Then, the equation of the perpendicular line is y = (3 / 2) · x - 14.
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Raffle tickets are being sold for a fundraiser. The function a(n) relates theamount of money raised to the number of tickets sold, n.It takes as input the number of tickets sold and returns as output the amountof money raisedan) = 4n - 20Which equation represents the inverse function n(a), which takes the moneyraised as input and returns the number of tickets sold as output?O A. n(e) -47,20O B. n(e) – +20OC. n() - 0-20OD. n(a) -3 -20
Answers
A
Since The equation is
[tex]a(n)\text{ = 4n-20}[/tex]To find its inverse we have to proceed to some steps
a= 4n-20
1) Swap a for n, in this case,
n=4a-20
2) Isolate n on the left side by subtracting 4a on both sides:
n -4a =4a-4a -20
n-4a=-20
3) Subtract n on both sides
a-a-4n =-20-a
-4n=-20 -a
4) Multiply it by -1
4n = 20 + a
5) Divide by 4, there you have it. The inverse function:
[tex]n(a)=\frac{20+a}{4}[/tex]To find its in
Determine whether the triangles are similar. If so, what are the similarity statement and the postulate or theorem used? (image attached)thank you ! :)
Answers
ANSWER
ΔOMN ~ ΔOJK; SAS
EXPLANATION
As we can observe in the diagram, the triangles share angle O and we have information about the sides forming that angle, so the postulate to use, in case they are similar, is SAS.
If two triangles are similar, then the ratio between corresponding sides is constant.
Let's assume that the similar triangles are triangle OMN and triangle OJK. Then, the previous statement is,
[tex]\frac{OM}{OJ}=\frac{MN}{JK}=\frac{ON}{OK}[/tex]Replace the side lengths for the first and last ratios - since we don't know the lengths of sides MN and JK,
[tex]\begin{gathered} \frac{30+10}{30}=\frac{3+1}{3} \\ \\ \frac{40}{30}=\frac{4}{3} \\ \\ \frac{4}{3}=\frac{4}{3} \end{gathered}[/tex]The ratio between corresponding sides is constant, 4/3. Hence, triangles OMN and OJK are similar, by SAS.
David left $300 in an account that earns 5% on the money he originally deposited. When he collected his interest, he had earned $60 in interest. How long did he leave the money in the account?
Answers
The time that David left the money in the account would be = 4 years
What is an earned interest?An earned interest is the amount of money that is regularly paid to an individual who invested a specific amount of money for a stipulated period of time.
The principal amount(p)= $300
The time (T)= X
The rate of interest yield (R)= 5 %
Simple interest( SI)= $ 60
Using the formula;
SI = P×T×R/100
Make T the subject of formula;
T = SI×100/P*R
T= 60×100/300×5
T= 6000/1500
T = 4 years.
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PLEASE HELP!!!
Explain how the cosine of an angle in the second quadrant differs from the cosine of its reference angle in the unit circle.
Answers
Answer:
the second quadrant is negative but the reference angle is exactly the same but positive
Step-by-step explanation:
looking at 150 on the unit circle in the second quadrant you will see the cosine is negative square root 3 divided by 2 but the reference angle is 30 degrees and when we look at the cosine of that which is the x value of what we see it is positive square root of 3 divided by 2
Hi I have tried calling but I can’t do anything
Answers
For the given functions, we will find the first derivative of each function
Note:
a, and b are constants
y, f, and g are functions
2) y = (a+bf)/g
We will use the quotient rule to find y' as follows:
[tex]y^{\prime}=\frac{g*b\frac{df}{dx}-(a+bf)\frac{dg}{dx}}{g^2}[/tex]=============================================================
3) y = (x+f)/g
We will use the quotient rule to find y' as follows:
[tex]y^{\prime}=\frac{g(1+\frac{df}{dx})-(x+f)\frac{dg}{dx}}{g^2}[/tex]==========================================================
4) y = (x+f)³
We will use the exponent rule to find the derivative as follows:
[tex]y^{\prime}=3(x+f)^2(1+\frac{df}{dx})[/tex]===========================================================
5) y = ax² + bg² + f
so, y' will be as follows:
[tex]y^{\prime}=2ax+2bg\frac{dg}{dx}+\frac{df}{dx}[/tex]==========================================================
The measures of the angles of a triangle are shown in the figure below. Solve for x.
(8x-18)°
40°
110°
Answers
The value of the variable x associated to the triangle is equal to 6.
What is the variable associated to internal angles of a triangle?
Triangles are figures with three sides and three internal angles. According to Euclidean geometry, the sum of the measures of the internal angles is equal to 180° and we must solve the following equation for x:
(8 · x - 18) + 40 + 110 = 180
(8 · x - 18) + 150 = 180
(8 · x - 18) = 30
8 · x = 48
x = 6
The triangle has internal angles of 30°, 40° and 110° and the value of variable x is 6.
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The graph shows the linear parent function.Y5-55----Which statement best describes the function?
Answers
From the picture, we have the graph of the linear parent function f(x) = x.
We have the following statements as descriptions of the function:
A. The function is negative when x < 0.
From the graph, we see that the function takes negative values for x < 0. This statement is true.
B. The function is negative when x < 0 and also when x > 0.
The first part of this statement is true, but the second is not because that we see that the function takes positives values for x > 0. So this statement is false.
C. The function is never negative.
If we see the graph, the function is negative when x < 0. So this statement is false.
D. The function is negative when x > 0.
Again, seeing the graph we note that the function takes positive values for x > 0. So this statement is false.
So the only statement that it is true, is option A.
rewrite 13% into equivalent fraction
Answers
The number 13% as an equivalent fraction is 13/100
How to rewrite the percentage into equivalent fraction?From the question, the given parameter is
13%
This above number is a percentage or percentile
So, we have
Percentage = 13%
Next, we multiply the percentage by 1
So, we have
Percentage = 13% x 1
Express 1 as 100/100
So, we have
Percentage = 13% x 100/100
Evaluate the product of 13% and 100
So, we have
Percentage = 13/100
Rewrite as
Fraction = 13/100
The fraction cannot be further simplified
Hence, the equivalent fraction of 13% is 13/100
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You volunteer at a nursing home for 3 hours a day. You volunteered 6 hours last week and 12 hours this week. How many days did you volunteer?
Answers
Answer: 6 days
a bucket contains 15 blue pens 35 black pins and 40 Red Pins. You pick one pin at random find the theoretical probabilities below . Express your answer as a percent to the nearest whole number p(black)=???p(blue or black)=???
Answers
The number of blue pen is 15
The number of black pens is 35
The number of red pens is 40
The total number of pens in the bucket = Blue pens + black pens + red pens
The total number of pens = 15 + 35 + 40
= 90
Therefore, the total number of pens in the bucket = 90 pens
The probability that black pen is picked is
Probablity = possible outcomes/ total outcomes
P(black) = 35 / 90 x 100%
P(black) = 0.3888 x 100%
P(black) = 38.88%
P(black) = 39%
P(blue or black)
If its pick at random without replacement then
If the first pick is blue, then the total number of pen in the bucket remains 89
For the first pick will be 15/90
Since the remaining pens is 89, then the second pick is
35/89
Then we have
15/90 + 35/89
LCM is 8010
8010 x 15 / 90 + 35 x 8010 /89 / 8010
89 x 15 + 35 x 90 / 8010
P(blue / black) = 1335 + 3150 / 8010
P(blue or black) = 4485 / 8010
P(blue or black) = 0.559 x 100%
P(blue or black) = 55.9%
P(blue or black) = 56%
A 20-foot support post leans against a wall, making a 70° angle with the ground. To the nearest tenth of a foot, how far is the base of the post from the wall?
Answers
The following problem can be well explained by the diagram shown below:
Hence by the trigonometry of the figure use the trigonometric ratio of cos to get:
[tex]\begin{gathered} \cos 70=\frac{BC}{AC}=\frac{x}{20} \\ x=20\cos 70 \\ x=6.8404\approx6.8 \end{gathered}[/tex]Hence the support is 6.8 feet away from the wall.
Option A is correct.
Joshua opened a bank account with some money he had saved. During the month, he made deposits of $25 and $40, and he made withdrawals of $15 and
$35. At the end of the month, he had $170 in his account. How much money did he have when he opened the account?
A $285
B $155
C $55
D $15
Answers
Initially, Joshua had $155 in his account.
How to find the initial amount?Deposits of $25 and $40
Withdrawals = $15, $35
At the end of the month, he had $170 in his account.
Solution:
Let x be the amount of money he had initially.
Then,
x + 25 + 40 - 15 -35 = 170
x + 65 - 50 = 170
x = 170 + 50 - 65
x = 220 - 65
x = 155
Therefore, initially, he had $155 in his account.
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the average daily rainfall is typically 5/8 of an inch. Last year, the average daily rainfall
was only 3/8 of an inch. What percent of the typical average daily rainfall fell last year in Green Valley?
Answers
Suppose that the functions s and t are defined for all real numbers x as follows.
s(x)=x-3
t(x) = 3x+4
Write the expressions for (s•t) (x) and (s-t) (x) and evaluate (s+t) (-2).
Answers
7 is the value of function s and t .
What is function explain?
A relation between a set of inputs and a set of allowable outputs is called a function, and it has the property that every input is associated to exactly one output. When every element in set A has one end and only one image in set B, then the mapping from set A to set B is a function. Let A & B be any two non-empty sets.Four main categories can be used to classify the many sorts of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element.s(x)= x-3
t(x) = 3x+4
(s•t) = ( x -3 ) ( 3x + 4 )
= ( 3x² + 4x - 3x² - 12 )
= 4x - 12
(s-t) (x) = ( x-3 ) - ( 3x+4 )
= x-3 - 3x + 4
= -2x + 1
(s + t) (-2) = x-3 + 3x+4
= 4x + 1
(s + t) (-2) = 4 * - 2 + 1
= 8 - 1 = 7
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Refer to this diagram for the next five statements. Write the correct postulate, theorem, property, or definition that justifies the statement below the diagram.
Given: ∠MRS ≅ ∠MRO
m∠MRO + m∠MRS = m∠SRO
Answers
This statement is justified by the angle addition postulate.
I need help with my math
Answers
Callan hikes at the rate of 3 miles per hour, that means, the table of values of values would be completed as follows;
Hours, x Miles, y
1 3
3 9
5 15
The ordered pair above is derived by multiplying every hour by 3 to arrive at the number of miles.
The graph is now shown as;
A local hamburger shop sold a combined total of 598 hamburgers and cheeseburgers on Wednesday. There were 52 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Wednesday?
Answers
In the local hamburger shop the total number of hamburgers sold on Wednesday , based on the given data is :
325 hamburgers.
Explanation:A General Rule for Equation Solving
Remove parentheses and combine like terms to simplify each side of the equation.To isolate the variable term on one side of the equation, use addition or subtraction.To find the variable, use multiplication or division.here form a equation based on given data ;
let , Hamburgers be = x
let, Cheeseburgers be = y
here , No. of burgers (hamburgers and cheeseburgers )sold = 598
here,
x + y = 598 =>(1)
y = x - 52 => (2)
solving 2 equations ,
x + ( x - 52 ) = 598
x + x - 52 = 598
2x = 598 + 52
x = 650 /2
x = 325
on Wednesday 325 hamburgers were sold.
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Question 2 of 25The coach of a college basketball team categorizes the number of pointsscored by the team in each game, with the categories being 51 - 57, 58 - 64,65 - 71, and 72 or more. If the following data represent the numbers ofpoints scored in the last 10 games, how many games were in the 51 - 57category?51, 70, 63, 59, 56, 75, 60, 55, 67, 64O A1B. 2O c. 4O D. 3
Answers
In the table, we can see that the highest number corresponds to the cats who failed. Then, if a comparative bar chart represents the data, the bar representing the number of cats that failed will be the tallest.
AnswerA. Cats who failed
if g(x) = 1/2|x|-6 and h(x)=x-4 Which expression is equivalent to h(g(x))?
1/2|x| - 2
1/2|x-4| -6
1/2|x|-10
1/2|x-10|
Answers
h(g(x)) is equivalent to the expression 1/2|x|-10
What will the expression be?Given g(x) = 1/2|x|-6 and h(x) = x-4
h(g(x)) = h(1/2|x|-6)
Put the value of g(x) in the expression
Now, evaluate the expression using the definition of h(x) by replacing x in x-4 with 1/2|x|-6:
h(g(x)) = 1/2|x|-6 - 4 = 1/2|x|-10
Since h(g(x)) = 1/2|x|-10. Therefore, 1/2|x|-10 is the expression equivalent to h(g(x)) so the third option is the answer.
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HELP PLSSS
(Attached to image)
Answers
The inequality is lies between the 5.26 < 5.71
The correct option is (a)
Given,
From the figure,
To see the number line and determine the which of the expression is true.
What is Inequality?
Inequality is defined as an equation that does not contain an equal sign.
Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The number line goes from 5.0 to 6.0 with 9 labeled marks in between.
Each mark increases by point one
There are five labeled points.
A point labeled 5.04 is between 5.0 and 5.1.
A point labeled 5.26 is between 5.2 and 5.3.
A point labeled 5.4 is at the mark labeled 5.4
A point labeled 5.520 is between 5.5 and 5.6.
A point labeled 5.71 is between 5.7 and 5.8.
Then the ascending order of the number line will be :
5.04 < 5.26 < 5.4 < 5.52 < 5.71
Hence, The correct option is (a)i.e., 5.26 < 5.71
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whats the gcf of 96 and 40
Answers
Answer:
8
Step-by-step explanation:
Find the prime factorization of 40
40 = 2 × 2 × 2 × 5
Find the prime factorization of 96
96 = 2 × 2 × 2 × 2 × 2 × 3
To find the GCF, multiply all the prime factors common to both numbers:
Therefore, GCF = 2 × 2 × 2
GCF = 8
Answer:
8
Step-by-step explanation:
8 is the greatest number that 40 and 96 divides into
Is -7. a rational number
Answers
A rational number can be represented by dividing two integers.
So, it can be represented as a ratio of 2 integers.
-7 = -7/1
-7 is a rational number
Explain how travelling to a ski resort to go skiing could influence travel time
Answers
A ski trip requires a lot of planning.You must choose your travel dates, choose the ideal location, identify the best ski resorts for your family in the area, book lodging, purchase lift tickets, schedule lessons, consider your equipment and clothing needs, and possibly book flights or a rental car.
Describe the possible effects that traveling to a ski resort might have on travel time?
Beyond making reservations, there are more actions to be taken.Making decisions, locating the best offers, and making reservations take time.While some tasks should be completed in advance, others can wait till later.Before heading to the slopes, use this helpful planning timeline to help you save some green (and your sanity). Planning is more necessary when skiing with children as it differs from skiing alone.When there was an incredible snowstorm, I remember those last-minute college ski excursions that somehow came together, allowing me to jump in an SUV with someone else and crash on their lily pad with them and 10 to 20 other pals.I have happy recollections of those ski holidays when I was a younger frog. Perhaps I have forgotten the sleepless nights spent in the company of snorers and surviving on sugar and coffee, but those things were unavoidableBut now, on our mountainous excursions, Leap, my husband, who is learning to ski, and two tadpoles are also hopping along.The majority of our preferred ski resorts involve travel by plane, which is difficult to arrange at the last minute due to our tight schedules.In addition, it appears that my standards and working hours have changed, and now I no longer consider sleeping on a couch or the floor with complete strangers to be a vacation. As a result, I must think carefully and plan ahead for my ski trips in order to accommodate a family with a toddler, a tween, and adults.You should begin planning your ski vacation up to a year in advance.Choose the ski region or areas you want to go to.For instance, focus on a specific area; perhaps you want to look into the Denver region, Lake Tahoe, or Utah.Find the finest ski resort for your family by researching ski resorts in those areas.Check out mountain statistics and trail maps to determine if there are any runs that your family will enjoy.In comparison to other resorts, you might notice that one has more terrain for beginner to intermediate skiers. When there aren't any lift tickets or lessons available, it might be difficult to compare pricing during the off-season. To illustrate, imagine that you decide to go skiing in Colorado the next winter a year in advance.To help you plan and get an idea of costs so you can budget, look at the prices of different resorts in the area during peak and off-peak seasons on their websites more than a year in advance. You can also compare the costs of different resorts in the area at both peak and off-peak times.You may discover that Keystone and Breckenridge are more affordable while still providing excellent family-friendly amenities than places like Vail and Beaver Creek.To learn more about ski resort refer
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An aeroplane flies between two cities that are 8100 km apart.
The aeroplane takes 9 hours to complete the journey.
Calculate the average speed of the aeroplane, in km/h.
Answers
Answer:
7,290,000.answer
Step-by-step explanation:
1 km= 100000 m
1 hour = 60 minute
8100 km = 810000 m
9 hour=540 minute
60/540.00 cancel
6/54 will be than cut 6×9=54
SO,multiply 810000×9 = 7,290,000
Answer:
The answer is 7,290,00
Step-by-step explanation:
1 km= 100000 m
1 hour = 60 min
8100 km = 810000 m
9 hour=540 min
60/540.00 cancel
6/54 will be than cut 6×9=54
so ,multiply 810000×9 = 7,290,000
I will need help with this math problem it has three parts to it
Answers
a)The smaller break even quantity is 10
b)The quantity that must be sold to maximize the profit= 14.25
c)The maximum profit = $36.13
STEP - BY - STEP EXPLANATION
What to find?
• The smaller break even quantity is
,• The quantity that must be sold to maximize the profit
,• The maximum profit.
Given:
C(x)= 13x + 370
R(x)=70x - 2x²
a) At the break even quantity, the revenue = cost, that is no profit and no loss.
R(x) = C(x)
So that we have;
70x - 2x² = 13x + 370
Re-arrange.
-2x² + 70x - 13x - 370 =0
-2x² +57x - 370 =0
2x² - 57x + 370 = 0
We can now solve the quadratic equation above.
Using the qudaratic formula
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]a=2 b=-57 c=370
Substitute the values into the formula and evaluate.
[tex]x=\frac{-(-57)\pm\sqrt[]{(-57)^2-4(2)(370)}}{2(2)}[/tex][tex]x=\frac{57\pm17}{4}[/tex][tex]Either\text{ x=}\frac{57+17}{4}=\frac{74}{4}=\frac{37}{2}[/tex]Or
[tex]x=\frac{57-17}{4}=\frac{40}{4}=10[/tex]x = 37/2 or x=10
We take the smaller value.
Hence, x=10
Therefore, the smaller break even quantity is 10.
b)To find the quantity that will maximize the profit, find the profit function.
p(x) = R(x) - C(x)
P(x) = 70x - 2x² - (13x +370)
= 70x - 2x² - 13x - 370
P(x) =-2x² + 57x - 370
Equate to zero
-2x² + 57x - 370 = 0
2x² - 57x + 370 =0
The maximum is at x = -b/2a
b= -57 and a=2
Substitute the values
x= - (-57) /2(2)
x= 57 /4
x= 14.25
c) To find the maximum profit, simply substitute x=14.25 into the profit function and simplify.
That is;
P(x) =-2x² + 57x - 370
P(14.25) =-2(14.25)² + 57(14.25) - 370
= -406.125 + 812.25 - 370
= 36.125
≈ 36.13
Hence, the maximum profit is $36.13
Carrots costs $0.99 per pound. Broccoli costs $1.50 per pound. Jack buys 3.5 pounds of carrots and 1.25 pounds of broccoli. What is Jack’s total bill?
Answers
Answer: his total bill is 7.24
Step-by-step explanation:
help help help help help help help
Answers
-6=-2/3z
-6*3/2=-9
Z=-9
Would you please check this answer for me? Use elimnation to solve the system of equations:2x+2y=162x+3y=14My answer: (10, - 2)
Answers
Equation
[tex]\begin{gathered} 2x+2y=16 \\ 2x+3y=14 \\ \end{gathered}[/tex]Let's multiply -1 by Eq 1
[tex]\begin{gathered} -2x-2y=-16 \\ 2x+3y=14 \\ 2x-2x+3y-2y=-16+14 \\ y=-2 \end{gathered}[/tex]Now for x
[tex]\begin{gathered} 2x+2y=16 \\ x=\frac{16-2y}{2} \\ x=\frac{16-2\cdot(-2)}{2} \\ x=\frac{16+4}{2} \\ x=\frac{20}{2} \\ x=10 \end{gathered}[/tex]The answer would be (10, -2)
rectangle perimeter ; 36 unitswidth; xlength ; 4x - 2solve for x
Answers
Perimeter = 36 units
width = x
length = 4x - 2
Equation of perimeter = 2width + 2length
Substitution
36 = 2(x) + 2(4x - 2)
Expanding
36 = 2x + 8x - 4
36 = 10x - 4
36 + 4 = 10x
40 = 10x
x = 40/10
x = 4