Mathematics College

The population of a city grew from 23,000 in 2010 to 25,000 in 2015.
a. What was the average rate of change during this time interval?
Type the answer in the box below.

Answers

Answer 1

The average rate of change during this time interval is 400 population per year

The average rate of change during this time interval is expressed as:

Rate of change = change in population/change in time

Change in population = 25000 - 23000

Change in population = 2000

Change in time = 2015 - 2010

Change in time = 5 years

Substitute into the formula;

Rate of change = 2000/5

Rate of change = 400

Hence the average rate of change during this time interval is 400 population per year

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Related Questions

NEED NOW PLEASE.....

Answers

i believe it’s b :)))

(x3 + 9x2 + 1)(3x2 + 4x − 4)

Answers

I don’t understand the question so I answer in two ways

Consider the following function.
f(x) = 1 + 5/x - 4/x2
(a) Find the vertical asymptote(s).
(b) Find the interval where the function is increasing.
Find the interval where the function is decreasing.
(c) Find the local maximum and minimum values.
(d) Find the interval where the function is concave up.
Find the interval where the function is concave down.
Find the inflection point.
(e) Use the information from parts (a)-(d) to sketch the graph of f.

Answers

Answer:

See below

Step-by-step explanation:

I assume the function is [tex]f(x)=1+\frac{5}{x}-\frac{4}{x^2}[/tex]

A) The vertical asymptotes are located where the denominator is equal to 0. Therefore, [tex]x=0[/tex] is the only vertical asymptote.

B) Set the first derivative equal to 0 and solve:

[tex]f(x)=1+\frac{5}{x}-\frac{4}{x^2}[/tex]

[tex]f'(x)=-\frac{5}{x^2}+\frac{8}{x^3}[/tex]

[tex]0=-\frac{5}{x^2}+\frac{8}{x^3}[/tex]

[tex]0=-5x+8[/tex]

[tex]5x=8[/tex]

[tex]x=\frac{8}{5}[/tex]

Now we test where the function is increasing and decreasing on each side. I will use 2 and 1 to test this:

[tex]f'(2)=-\frac{5}{2^2}+\frac{8}{2^3}=-\frac{5}{4}+\frac{8}{8}=-\frac{5}{4}+1=-\frac{1}{4}[/tex]

[tex]f'(1)=-\frac{5}{1^2}+\frac{8}{1^3}=-\frac{5}{1}+\frac{8}{1}=-5+8=3[/tex]

Therefore, the function increases on the interval [tex](0,\frac{8}{5})[/tex] and decreases on the interval [tex](-\infty,0),(\frac{8}{5},\infty)[/tex].

C) Since we determined that the slope is 0 when [tex]x=\frac{8}{5}[/tex] from the first derivative, plugging it into the original function tells us where the extrema are. Therefore, [tex]f(\frac{8}{5})=1+\frac{5}{\frac{8}{5}}-\frac{4}{\frac{8}{5}^2 }=\frac{41}{16}[/tex], meaning there's an extreme at the point [tex](\frac{8}{5},\frac{41}{16})[/tex], but is it a maximum or minimum? To answer that, we will plug in [tex]x=\frac{8}{5}[/tex] into the second derivative which is [tex]f''(x)=\frac{10}{x^3}-\frac{24}{x^4}[/tex]. If [tex]f''(x)>0[/tex], then it's a minimum. If [tex]f''(x)<0[/tex], then it's a maximum. If [tex]f''(x)=0[/tex], the test fails. So, [tex]f''(\frac{8}{5})=\frac{10}{\frac{8}{5}^3}-\frac{24}{\frac{8}{5}^4}=-\frac{625}{512}<0[/tex], which means [tex](\frac{8}{5},\frac{41}{16})[/tex] is a local maximum.

D) Now set the second derivative equal to 0 and solve:

[tex]f''(x)=\frac{10}{x^3}-\frac{24}{x^4}[/tex]

[tex]0=\frac{10}{x^3}-\frac{24}{x^4}[/tex]

[tex]0=10x-24[/tex]

[tex]-10x=-24[/tex]

[tex]x=\frac{24}{10}[/tex]

[tex]x=\frac{12}{5}[/tex]

We then test where [tex]f''(x)[/tex] is negative or positive by plugging in test values. I will use -1 and 3 to test this:

[tex]f''(-1)=\frac{10}{(-1)^3}-\frac{24}{(-1)^4}=-34<0[/tex], so the function is concave down on the interval [tex](-\infty,0)\cup(0,\frac{12}{5})[/tex]

[tex]f''(3)=\frac{10}{3^3}-\frac{24}{3^4}=\frac{2}{27}>0[/tex], so the function is concave up on the interval [tex](\frac{12}{5},\infty)[/tex]

The inflection point is where concavity changes, which can be determined by plugging in [tex]x=\frac{12}{5}[/tex] into the original function, which would be [tex]f(\frac{12}{5})=1+\frac{5}{\frac{12}{5}}+\frac{4}{\frac{12}{5}^2 }=\frac{43}{18}[/tex], or [tex](\frac{12}{5},\frac{43}{18})[/tex].

E) See attached graph

What is correct A, B or C

Answers

Answer:

A is the correct solution

Step-by-step explanation:

     3x³ + 4x² + 0x - 1  /  x - 2

             3      10    20

-2 | 3       4       0    -1

 -  (3      -6)

             10       0

      -     (10    -20)

                      20    -1

                 -   (20  -40)

                              39

3x² + 10x + 20 + 39/(x - 2)

Help help help help help help help math

Answers

Answer:

Angle 6

Step-by-step explanation:

They are both the same angle size

Answer:

Angle 1

Step-by-step explanation:

Refer to the attached picture

what percent of 75cm is 5cm​

Answers

Answer:

6.67%

Step-by-step explanation:

5 / 75 = 0.066667

(0.066667)(100) = 6.67%

20 kilograms increased by 25%

Answers

Answer:

25 kilograms

Step-by-step explanation:

emma is finding 7/2 x 2/5

Answers

Answer:

14/10

OR

7/5

Step-by-step explanation:

(7*2)/(2*5) = 14/10

(14/2) / (10/2) = 7/5

Answer:

Mixed fraction: 1 2/5

Decimal form: 1.4

Hope this helps :)

In a proposed business​ venture, a businesswoman estimates there is a ​65% chance she will make ​$57000 and a 35​% chance she will lose ​$67000. Determine her expected value.

Answers

Answer:

q

Step-by-step explanation:

Which of the following describes exponential decay?

A. The amount at a given time can be calculated by multiplying the previous amount
by a value greater than 1.

B. The amount at a given time can be calculated by multiplying the previous amount by a value less than 1.

C. The amount at a given time can be calculated by adding an amount to the previous amount.

D. The amount at a given time can be calculated by subtracting an amount from the previous amount.

Answers

So it should be A bit look it up just in case

The amount at a given time can be calculated by multiplying the previous amount by a value less than 1, which represents exponential decay. Hence, option B is the right choice.

What does linear function mean?

A quantity grows (or depreciates) linearly if it increases (or decreases) by the same amount per unit of time.

What does exponential function mean?

A quantity grows (or depreciates) exponentially if the increase (or decrease) in the amount is a multiple of the previous amount.

How to solve the question?

In the question, we are asked to identify the option that best describes an exponential decay.

We assess each option and try to identify the exponential decay among them.

A. The amount at a given time can be calculated by multiplying the previous amount by a value greater than 1: This is an exponential function as it is multiplied by the previous amount, but it shows exponential growth as the quantity multiplied is greater than 1.B. The amount at a given time can be calculated by multiplying the previous amount by a value less than 1: This is an exponential function as it is multiplied by the previous amount, and it shows exponential decay as the quantity multiplied is less than 1.C. The amount at a given time can be calculated by adding an amount to the previous amount: This is a linear function as a fixed quantity is added.D. The amount at a given time can be calculated by subtracting an amount from the previous amount: This is a linear function as a fixed quantity is subtracted.

Therefore, the amount at a given time can be calculated by multiplying the previous amount by a value less than 1, which represents exponential decay. Hence, option B is the right choice.

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What is the solution to the system of equations

Answers

Answer:

x = 5

y = -4

Step-by-step explanation:

Britney is trying out for the track team along with 24 other people nine people were running distance seven people were there to sprint three people are in the competition to throw Shotput and six people were there to polevault Britney was able to run a half a mile in six minutes and she finish seventh Place in the 100 m dash which of these pieces of data is discreet and which one is continuous

Answers

Answer:

The 6-minute half-mile time is continuous data; the number of people trying out for the team is discrete data.

Step-by-step explanation:

Emilio has 8 large bottles of soda and 12 large jugs of water. Emilio wants to set up identical tables and have no drinks left over. What is the greatest number of tables that he can set up?

Answers

Answer:

4

Step-by-step explanation:

Think about the ratio between the current number of large bottles of soda(8) and the current number of jugs of water (12)

By finding the GCF (Greatest Common Factor) of the two numbers, we can conclude that if both numbers were to be divided by the GCF, 4, we would get a 2:3 ratio.

For every 2 bottles of soda, 3 jugs of water will be placed. Keep doing this until we run out of both sources of liquid, in this case, 4 tables where we would use all the bottles of soda and the jugs of water.

Mrs. Harris treated her 1st period with donuts for averaging the highest on the midterm exam. She bought 25 donuts, By the end of the period, there were 3 donuts remaining. What is the percent decrease?

Answers

Answer:

88% decrease

Step-by-step explanation:

3 is only 12% of 25 so there was a 88% decrease

Response time is an important statistic for measuring the effectiveness of a fire department, and is measured as the difference between the time a fire station receives a call and the time the first piece of fire equipment leaves the station. The response times for fire departments in a large city are found to have an approximately Normal distribution, with a mean of 4.5 minutes and a standard deviation of 1.2 minutes. What percentage of fire station response times are under 3 minutes? Find the z-table here. 6.68% 10.56% 89.44% 93.32%

Answers

Answer:

mean = 4.5

SD = 1.2

Z value = (3-4.5)/1.2 = - 1.25

Percentage based on z value = 1 - pnorm(1.25) =  0.1056498 = 10.56498%

The response times under 3 minutes is 10.56%

What is Normal Distribution?

'Normal distribution is a continuous probability distribution wherein values lie in a symmetrical fashion mostly situated around the mean.'

According to the given problem,

mean = 4.5

SD = 1.2

Z value = [tex]\frac{3 - 4.5}{1.2}[/tex] = - 1.25

Percentage based on z value = 1 - pnorm(1.25)

                                                 =  0.1056498

                                                 = 10.56498%

Hence, we can conclude that the response time of fire station under 3 minutes is 10.56%.

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Consider the functions f(x) = 12^x and g(x)= -2(12)^x. Which transformations must be applied to function F to produce the graph of function g?

SELECT ALL CORRECT ANSWERS

Vertical stretch
Vertical Shift
Vertical Compression
Reflection over the x-axis
Horizontal Shift

Answers

Answer:

Step-by-step explanation:

g(x) = -2f(x)

Vertical stretch                       by virtue of the factor 2

Reflection over the x-axis      by virtue of the factor -1

The transformations which must be applied to function F to produce the graph of function g are vertical stretch and reflection over the x-axis.

To transform the function f(x)=12ˣ into the function  g(x)=−2(12)ˣ

Since g(x) is multiplied by -2 compared to f(x), this represents a vertical compression.

The absolute value of the multiplier indicates the degree of compression/stretch.

The negative sign in front of 2(12)ˣ in g(x) reflects the graph over the x-axis. This means that the graph of g(x) is reflected below the x-axis compared to f(x).

Hence, vertical stretch and reflection over the x-axis are the transformations which must be applied to function F to produce the graph of function g.

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Find the length of the second base of a trapezoid with one base measuring 12 feet,a height of 4,and an area of 58 square feet.

Answers

Answer:

Step-by-step explanation:

A = ½(b₁ + b₂)h

b₂ = 2A/h - b₁

b₂ = 2(58)/4 - 12

b₂ = 17 ft

What is the value of y in the solutions of the system of equations: 3x + 4y = 3 and 2x – 4y = 12?

Answers

Answer:

y = -3

Step-by-step explanation:

3x + 4y = 3

2x - 4y = 12

5x       = 15       Add the two equation together because the y terms are

                       opposite each other and goes out when you add the equations

x = 5

Substitute into the first equation and solve for y when x = 5

 3x + 4y = 3

3(5) + 4y = 3

 15 + 4y = 3

    4y = 3 - 15

    4y =  -12

      y = -3  

Explanation:
Step 1) Solve the second equation for
y
2
x
+
y
=
−
8
−
2
x
+
2
x
+
y
=
−
2
x
−
8
0
+
y
=
−
2
x
−
8
y
=
−
2
x
−
8
Step 2) Substitute
(
−
2
x
−
8
)
for
y
in the first equation and solve for
x
:
−
3
x
+
4
y
=
12
becomes:
−
3
x
+
4
(
−
2
x
−
8
)
=
12
−
3
x
+
(
4
×
−
2
x
)
+
(
4
×
−
8
)
=
12
−
3
x
+
(
−
8
x
)
+
(
−
32
)
=
12
−
3
x
−
8
x
−
32
=
12
(
−
3
−
8
)
x
−
32
=
12
−
11
x
−
32
=
12
−
11
x
−
32
+
32
=
12
+
32
−
11
x
−
0
=
44
−
11
x
=
44
−
11
x
−
11
=
44
−
11
−
11
x
−
11
=
−
4
x
=
−
4
Step 3) Substitute
−
4
for
x
in the solution to the second equation at the end of Step 1 and calculate
y
:
y
=
−
2
x
−
8
becomes:
y
=
(
−
2
×
−
4
)
−
8
y
=
8
−
8
y
=
0
The Solution Is:
x
=
−
4
and
y
=
0
Or
(
−
4
,
0
)

One mom has 3 children, and each child attends a different level of school. If the mom plans to pick her children up, what would be her total distance traveled if she starts at the high school, then goes to the elementary school, and finally the middle school? (Write your answer as a decimal rounded to the nearest tenths place). *

Answers

Answer: I need the map good sir please show it

Step-by-step explanation:

Write an equation involving absolute value or the graph

Answers

Answer:

Step-by-step explanation:

2 AND 4

Given the line segment AD. AD=24 BC=12,AB=CD Find AB ?

Answers

Answer:

I think its 6

Step-by-step explanation:

solve for m -7/9 m = 11/6

Answers

Answer:

19/18

Step-by-step explanation:

substitute the value of m(11/6) in m-7/9

which is equal to 11/6 -7/9 =19/18

All you have to do is just cross multiply and collect like terms

what is c3 - 1 when c = 4

Answers

The answer to your question is 11.
4x3=12-1=11
You just have to substitute
c3-1
4*3-1
12-1
=11

Mandy has 37 red markers and 24 green markers. She wants to place an equal number of markers on 4 tables. What is the greatest number of markers she could place on each table ? Explain please

Answers

Answer:

15 marker's

Step-by-step explanation:

37+24=61

61÷4=15.25

because she wants an even number of makers the answer is 15.

2. Which will help you answer, "To what power must a student raise the number 5 to have an answer of 625?"

Answers

Answer:

125

Step-by-step explanation:

The power of 4. Powers are numbers multiplied by themselves. 5 to the fourth power is really 5x5x5x5 which equals 625

Tell which value of the variable is the solution of the equation.
s−4.3=​0; s=4.3​, 4.4​, 4.5​, 4.6
Question content area bottom
Part 1
Which of the following is the solution of the​ equation?
A. 4.3
B. 4.5
C. 4.4
D. 4.6
E. No solution is given in the set of values

Answers

Answer:

a

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.shshs

Question Write an equation of the line passing through the point A(0, 3) that is perpendicular to the line y = −1/2x−6

Answers

Answer:

The equation would be y=2x+3 I am pretty sure

Step-by-step explanation:

This is because you take the slope which is 2 from the line y=-1/2x-6. To find the slope perpendicular to the line, you need to find the exact opposite of the slope: -1/2, and in this case, it would be 2.

(Ex: if it was -3/4, you would need to use a slope of 4/3 since it is the opposite)

Then you take that slope (2) and the point (0, 3) and put it into "y-y1=m(x-x1)"

y-y1=m(x-x1)

y-3=2(x-0)

-distribute the 2-

y-3=2x-0

-add 3 on both sides-

so equation would be y=2x+3

Not sure if this is all correct, but I hope it helps! :)

if h(x) =5 for the function h(x) =2x+1, what is the value of x?
12
11
2​

Answers

Answer:

2

Step-by-step explanation:

5=2x+1

5-1=2x

2x=4

x=2

Answer:

x = 2

Step-by-step explanation:

2x+1 = 5

    -1   -1

-------------

2x = 4

x = 2

hope this helps! :D

have a miraculous day, and brainliest is immensely appreciated!! <3

There are 30 students in a class and 18 of them at least have 1 pet. what fraction of the class has pets Give your answer in its simplest form

Answers

Answer:

3/5

Step-by-step explanation:

3/5 pet is the exact fraction of pet that each student will have.

18 pets out of 30 students

= total pets divided by total students that would be 18/30

Simplifying 18/30 would make

9/15 first and then 3/5

So 3/5 is the answer

Graph the solution set to this inequality. -2x+9_> 5x-12

Answers

x ≤  3 (closed dot going to the left)

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Pls I need help quickly!Mindy owns 20 pairs of shoes and every week she purchases two more pairs. How long will it take for her closet to have 50 pairs of shoes? The weight of 120 books is 36kg, find the weight per book what was the final major battle of the american revolution find the perimeter of the triangle A(4,-2) B(9,-2) C(9,10) what did William Prescott do A bag of mixed nuts has 18 almonds, 8 cashews, and 14 peanuts. If one nut is selected, what is the probability that a peanut is chosen?Provide the answer as a simplified fraction. PLEASE HELP ILL GIVE A HEART AND 5 STARS In Canada, just like in China, eating at McDonalds was a novelty for us. In the wake of post-Mao economic reforms, the belated introduction of the Golden Arches to China represented a whole ethos about what constituted the good life. Fast food might connote easy accessibility or overindulgence in the West, but McDonalds presented a different kind of comfort for my family and me. The cost of a burger was hardly a trivial thing for us at the time, and my parents didnt actually treat me to meals there all that often. When they did, we always got takeout so we could eat our burgers and fries around our Formica dining table, on our own plates. The hope was to have our fast food as slowly as we could. The Filet-O-Fish became my menu item of choice. Its virtues are too many to count; doing so would be futile. As McDonalds only seafood-based option, the Filet-O-Fishs semblance of relative health appealed to my parents. Luckily it was also McDonalds most delicious item. It played to my Chinese palate: While other McDonalds buns were toasted, the Filet-O-Fishs was steamed, much like the baozi2. From its honeyed starch to its tangy tartar and savory fillet, the taste of the Filet-O-Fish carries an ineffable umami-ness. At once sweet and sour, it reminds me of orange-chicken sauce: a plausibly Chinese flavor mass-produced in America. Eating one always felt transportive the equivalent of Prousts madeleine3 for my Chinese diasporic upbringing. The Filet-O-Fish is the gold standard of fast food for many Asian-Americans, as well as other minority American communities. Invented by an Ohio franchise owner in 1962, the first Filet-O-Fish was the answer to the problem of McDonalds falling sales on Fridays, when observant Catholics abstained from eating meat. Born from an attempt to market fast food to as many people as possible, the tasty little unit has since been further claimed by everyone from fish-loving Chinese-Americans to practicing Muslims to well, anyone with taste. By 1965 the sandwich had gone national. Its appeal is inscrutable, perhaps out of proportion to its paltry constituent parts. Consider the recognizably flaky fish patty, made from the ubiquitous Alaskan pollock. Pollock is everywhere, writes the marine fisheries biologist Kevin M. Bailey in the book Billion-Dollar Fish. It is the pure white meat in fish sticks bought at Walmart and Filet-O-Fish burgers ordered in McDonalds. But you wouldnt want the fish to be more interesting. The generic quality of pollocks fishiness common enough for various cuisines to lay claim to it is part of its allure. So maybe what makes the sandwich beloved isnt its taste at all, but the juxtaposition of its elements: A single fillet of fried fish, topped with a thin slice of American cheese and tartar sauce, all of it cradled in a bun whose impossible roundness suggests the triumph of industrial food production. As a child, I was under the fantasy that my obsession with such a strange sandwich was eccentric. When I went to McDonalds with friends who got Chicken McNuggets Happy Meals or cheeseburgers, ordering the Filet-O-Fish made me feel as if I was in on some sort of secret. After a few years in Montreal, my dad landed a good government job in Victoria, British Columbia. On our drive across Canada, we indulged in the prospect of my dads earning a real salary by eating at McDonalds almost daily, a whirlwind of Filet-O-Fish meals (for me) and hamburgers (for my parents). But my experience was shattered when I, fancying myself different, pointed out that my parents both loved hamburgers while I, a renegade, preferred the Filet-O-Fish. Well, I like the Filet-O-Fish most too, my mother put it candidly. But it is expensive, so we only buy it for you. These days, the sandwich is more expensive than ever; its also less beautiful than I remember. At some point, the Filet-O-Fish underwent rebranding: An ostentatious paper box replaced the modest blue wrapper, while what I remember being a full slice of cheese seems to have shrank by half. McDonalds insists that the cheese has always been half a slice so as not to overwhelm the fishiness of the fillet. Todays unboxing experience most often reveals limp cheese sagging off the patty, frequently stuck to the ill-advised box. Where is the madeleine of my youth? Nowadays, a good Filet-O-Fish is hard to find. Which of the following statements best encapsulates the authors line of reasoning in the passage?A....McDonalds presented a different kind of comfort for my family and me. (paragraph 2)B.By 1965 the sandwich had gone national. (paragraph 4)C.Its appeal is inscrutable, perhaps out of proportion to its paltry constituent parts. (paragraph 5)D.These days, the sandwich is more expensive than ever; its also less beautiful than I remember. (paragraph 7, sentence 1)E.Nowadays, a good Filet-O-Fish is hard to find. (paragraph 7, sentence 6) what is the constant for 1000z + 800y A shopkeeper orders a special brand of coffee powder to be delivered tohim. A packet of this coffee powder cost $2. These packets are packed intocontainers which cost $3 each. Each container can hold 30 packets. 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A boutique is offering a 25% discount on purchase made in cash. Calculate the cash price Janelle paid for articles totaled to $465.