a. A function that models the population of the city's years after 2010 is:
f(x) = 50,000 * (1 + 0.05)^(x-2010)
where x is the number of years after 2010.
b. The population of the city in 2017 (7 years after 2010) is:
f(2017) = 50,000 * (1 + 0.05)^7
= 65,128
c. The population of the city in 2020 (10 years after 2010) is:
f(2020) = 50,000 * (1 + 0.05)^10
= 76,923.1
The population of the city in 2030 (20 years after 2010) is:
f(2030) = 50,000 * (1 + 0.05)^20
= 129,382
d. The population in 2020 is 76,923.1, and the population in 2010 is 50,000, so the population grows by:
= 76,923.1 / 50,000
= 1.53846
The population in 2030 is 129,382, and the population in 2020 is 76,923.1, so the population grows by:
= 129,382 / 76,923.1
= 1.6859
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A stack of 200 file folders is 5. 125 inches tall. A. Elena guesses that each file folder is 0. 035 inches thick. Explain how you know that Elena’s answer is not correct
To know whether Elena is correct or not, you need to find out the height of each stack of file folder.
Assume that all 200 files have the same height.
Let the height of each file folder be m inches.
So, by unitary method the height of each file folder would be,
m = Total height of stack / Number of file folders
here, the total height of stack = 5.125 inches
And the number of file folders = 200
So, m = 5.125 / 200
m = 0.0256 inches
But Elena guesses that each file folder is 0. 035 inches thick.
This means, Elena is wrong as the answer Elena gave is too large than the actual answer.
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Yesterday, Camille's Snack Shack went through 1/4 of a bottle of ketchup. If they used 2/3 as much mustard as ketchup, how many bottles of mustard did they go through?
The number of bottles of mustard they went through is given by the equation A = 1/6 of the bottle
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of bottles of mustard be represented as A
Now , the equation will be
The amount of ketchup used by Camille's Snack Shack = ( 1/4 ) of the bottle
Now , the amount of bottle of mustard used = ( 2/3 ) of the bottle of ketchup
Substituting the values in the equation , we get
The number of bottles of mustard used A = ( 2/3 ) of ( 1/4 ) of the bottle
On simplifying the equation , we get
The number of bottles of mustard used A = ( 2/3 ) x ( 1/4 )
The number of bottles of mustard used A = ( 1/6 ) of the bottle
Therefore , the value of A is 1/6
Hence , the number of bottles is 1/6
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To be able to walk to the center $C$ of a circular fountain, a repair crew places a 16-foot plank from $A$ to $B$ and then a 10-foot plank from $D$ to $C$, where $D$ is the midpoint of $\overline{AB}$ . What is the area of the circular base of the fountain
The area of the circular base of the fountain is 179 square feet.
What is the area of the circular base ?A circle's area is equal to its radius, r, squared, then multiplied by the mathematical constant pi: A = pi x r2.
A cylinder has two bases that are two congruent circles at the top and bottom. The radius r of a cylinder is only the radius of the circular bases, and the height h of a cylinder is the perpendicular distance between these bases.
Combined area of the walkway and fountain: (3.14)112=379.94 ft2.
Fountain area: (3.14)8*2=200.96 feet
Walkway area: 379.94-200.96=178.98 square feet, which is also rounded to 179 square feet.
The area of the circular base of the fountain is 179 square feet.
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(a) On the axes provided, sketch a slope field for the given differential equation at the 9 points indicated.
A slope field for the given differential equation dy/dx = xy/2 at the 9 points indicated is shown below.
We know that a slope field represents the slope of a differential equation at certain vertical and horizontal intervals on the coordinate plane.
First we construct a table which contains the values of slope.
Consider given differential equation dy/dx = xy/2
where -1 ≤ x ≤ 1,
1 ≤ y ≤ 3
Let the slope be m
so, dy/dx = m
For x = -1, y = 1
m = (-1 × 1)/2
= -1/2
For x = -1, y = 2
m = (-1 × 2)/2
= -1
For x = -1, y = 3
m = (-1 × 3)/2
= -3/2
For x = 0, y = 1
m = (0 × 1)/2
= 0
For x = 0, y =2
m = (0 × 2)/2
= 0
For x = 0, y = 3
m = (0 × 1)/2
= 0
For x = 1, y = 1
m = (1 × 1)/2
= 1/2
For x = 1, y = 2
m = (1 × 2)/2
= 1
For x = 1, y = 3
m = (1 × 3)/2
= 3/2
So, the table is:
x/y 1 2 3
-1 -1/2 -1 -3/2
0 0 0 0
1 1/2 1 3/2
Therefore, the slope field is as shown below.
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Alice, Bob, Charles and Darwin are sharing an orange. Bob got twice as many slices as Charles,
Charles got 5 times less slices than Darwin, and Darwin got 8 slices more than Charles. Find the
number of slices in the orange given that Alice got only the peel.
(A) 10 (B) 12 (C) 14 (D) 15 (E) 16
Answer:
E
Step-by-step explanation:
Let
A = # of slices Alice got
B = # of slices Bob got
C = # of slices Charles got
D = # of slices Darwin got
First, write equations based on given information:
A = 0
B = 2C
5C = D
D = C + 8
5C = D -> D = 5C
Now that we have two equations for D, we can set them equal to each other:
5C = C + 8
4C = 8
C = 2
Now just plug in the rest:
A = 0
B = 2(2) = 4
C = 2
D = 2 + 8 = 10
Add all solutions together to get (E) 16 slices
Can someone tell me how to do this?
solve 4x + 3 = 11
x = ?
Answer:
x = 2
Step-by-step explanation:
4x + 3 = 11
(4x + 3) - 3 = 11 - 3
4x = 8
4x/4 = 8/4
x = 2
As you can see, to isolate x, we must do the opposite operations to both sides.
How many possible real solutions are there?
The number of real solution varies according to the degree of the equation and the nature of the equation, The answer is dependent on degree and nature.
What do you mean by a solution?In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.
What are ideal and real solutions?In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.
example:
A linear equation (degree 1) has one real solution.
A quadratic equation (degree 2) can have either two real solutions, one real solution or no real solutions, as it depends on the discriminant of the equation, as I explained in my previous answer.
A cubic equation (degree 3) can have one to three real solutions, depending on the coefficients of the equation.
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Find 1)
4 integral 0 f(x) dx
if f(x) = 2 for x < 2
= x for x ? 2
Answer:
X = 1 and below
Step-by-step explanation:
since X is less than 2.
the value of X will be 1 and below.
2/3(6x-1/6) + 3x simplify the expression
Answer:
[tex]21x \: - \frac{1}{3} \\ 3[/tex]
Choose three true statements about the angles of the figure
1: Z1 and the 55* angle are adjacent
2: mZ1=55* because Z1 and the 55* angle are vertical angles
3: mZ2=125* because Z2 and the 55* angle are supplementary
4: mZ2 cannot be determined from the information
5: mZ1=180*-55*
6: mZ2=180*-55*-45*
Three true statements about the angles of the given figure are,
1. angle 1 and the 55 degree angle are adjacent.
5. angle 1 = 180 degree - 55 degree
6. angle 2 = 180 degree - 55 degree - 45 degree.
How are complementary angles defined?Complementary angles are two angles whose measures add up to 90 degrees. For example, an angle of 45 degrees and an angle of 45 degrees are complementary. When two angles are complementary, they form a right angle. The symbol for complementary angles is ∠A + ∠B = 90°.
What is the difference between acute angles and obtuse angles?Acute angles are angles whose measure is less than 90 degrees. They are sharp angles that are less than a right angle. On the other hand, obtuse angles are angles whose measure is greater than 90 degrees. They are angles that are greater than a right angle and less than 180 degrees. In other words, obtuse angles are angles that are wider than a right angle but less than a straight angle.
Analysing all the statements given in the question,the corrrect options are
Option 1, since angle 1 and 55 degree share the same vertex.
Option 5, since the sum of angle 1 and 55 degree is 180 degrees being supplementary angles.
Option 6, since the sum of all the interior angles of a triangle is 180 degrees.
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Question Progress
Here are some temperatures.
Ottawa
New York
Oslo
Moscow
-9.5 °C
-11.6 °C
-4.3 °C
-7.9 °C
a) Which place has the highest temperature?
b) What is the difference in temperature between Ottawa and Oslo?
The temperature in Moscow falls by 3.1°C.
c) What is the new temperature in Moscow?
The place with the highest temperature is Oslo.
The difference between the temperature in Ottawa and Oslo is 5.2 degrees Celsius .
The new temperature in Moscow is 11 degrees Celsius .
How to find the temperature ?When temperatures are in the negatives, the higher temperature would be the smaller number. Oslo therefore has the highest temperature at - 4.3 °C.
The difference between the temperature in Ottawa and Oslo can be found by subtracting the temperatures:
= - 4 . 3 - ( - 9 . 5 )
= - 4.3 + 9 .5
= 5. 2 degrees Celsius
The new temperature in Moscow is:
= - 7.9 - 3.1
= 11 degrees Celsius
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where h is the height of the car in metres, t is the time that has elapsed in minutes and a, b and c are constants.
Find values for a, b and c that will effectively model your motion on the big wheel.
The graph of the variation of the height of a person on the Ferris wheel with time, created with MS Excel is attached
The values of the constants in the sinusoidal function, h = a + b·(c·t) are;
a = 30
b = -20
c = π/1.5
What is a sinusoidal function?A sinusoidal function is a periodic, oscillatory function, that is based on the sine (or cosine) trigonometric ratios.
The diameter of the Ferris wheel = 40 m
The location of the axle above the ground = 30 m
The time it takes to make a complete a rotation = 3 minutes
The formula for modelling the elevation or height, h, of a person above the ground is presented as follows;
h = a + b·cos(c·t)
The details in the question is that at time, t = 0, the person enters the wheel at the lowest point.
Therefore;
At t = 0, h = 30 - 40/2 = 10
h = 10 = a + b·cos(c × 0) = a + b·cos(0) = a + b
a + b = 10
Whereby the height of the axis of the wheel above the ground is a constant, for visibility in the analysis, let the constant a represent the constant height of the axis from the ground, we get;
a = 30
a + b = 10, therefore;
b = 10 - a
b = 10 - 30 = -20
b = -20
At t = 1.5 minutes, the location on the wheel the person enters is at the maximum height on the wheel = 30 + 20 = 50
50 = a + b·cos(1.5·c)
50 = 30 - 20 × cos(1.5·c)
20 × cos(1.5·c) = 30 - 50 = -20
cos(1.5·c) = -1
cos(π) = -1
Therefore; 1.5·c = π
c = π/1.5
The equation is therefore;
h = 30 - 20·cos((π/1.5)·t)
a = 30, b = -20, c = π/1.5
Please find attached a graph showing the variation of height with time of the motion on a Ferris created with MS Excel
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What is the Pythagorean theorem rounding of 16 and 18
The Pythagorean theorem rounding of 16 and 18 would be = 24 (approximately)
What is Pythagorean theorem?Pythagorean theorem is defined as the theorem that expresses the relationship that exists between the three side of a right angle triangle.
The relationship states that the square of the longest side is equal to the sum of the square of the other two sides.
That is, c² = a² + b²
Where, a = 16
b = 18
c² = 16²+18²
c² = 256 + 324
c² = 580
C =√580
C = 24.1
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I NEED HELP PLS PSSSSSSSSSSSSSSS
Answer:
240
Step-by-step explanation:
The total overall profit of all the weekdays is 1200. The question asks for the average. 1200 divided by 5 is 240. the average is 240 dollars per weekday
Answer:
278
Step-by-step explanation:
average = sum/count
count = 7 (7 days)
monday = 150
tuesday = 250
wednesday = 200
thursday = 250
friday = 350
saturday = 450
sunday = 300
sum = 150 + 250 + 200 + 250 + 350 + 450 + 300 = 1950
mean = 1950/7 = 278.571428571 ≈ 278
Select the correct answer from each drop-down menu. the function has been transformed, resulting in function h. to create function h, function f was translated 2 units , translated 4 units , and reflected across the _______.
Across the y-axis, translated 2 units to the right and four units to the left, the new function is now h(x) = -(x + 2)3 - 4
Step (i): The type of transformation change of the function
a) The translated left "c" units are x - c;
b) The translated right "c" units are x + c
Step (ii) The given function is translated "2" units right side, then the new function is
h(x) = (x + 2 )3followed by the translated "4" units left sides and reflected across the y-axis.
Now the new function is h(x).
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What is the solution to the equation 9 W 4 )- 7w 5 3w 2?
The solution to w in the equation 9(w - 4) - 7w = 5(3w - 2) is w = -2.
Now, According to the question:
The given Equation:
9(w-4)-7w=5(3w-2)
To solve for w we first need to simplify our equation, removing any brackets and adding together similar terms. This gives us:
9(w-4)-7w=5(3w-2)
9w - 36 -7w = 15w - 10
2w - 36 = 15w - 10
Next, we subtract 2w from both sides to have all the variables on one side of our equation, then we add 10 to both sides to move the numerical values to one side.
2w - 36 = 15w - 10
2w -2w - 36 = 15w - 2w - 10
-36 = 13w - 10
-36 + 10 = 13w - 10 + 10
-26 = 13w
Finally, we divide both sides by 13 to find the value of w.
w = -2
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The complete question is this :
What is the solution to the equation of 9(w - 4) - 7w = 5(3w - 2).
A truck uses 2.5 litres of fuel to travel 8 kilometres.
a How far will the truck travel on 1 litre of fuel?
b How far will the truck travel on 120 litres of fuel?
Answer:
a：20 km
b：384
Step-by-step explanation:
a：
[tex] \frac{2.5}{ 8} = \frac{1}{x} [/tex]
[tex]x = 20[/tex]
b：
[tex] \frac{2.5}{8} = \frac{120}{y} [/tex]
[tex]y = 384[/tex]
400 families were surveyed. It was found that 90% had a TV set and 60% had a computer. Every family had at least one of these items. One of these families is randomly selected, and it is found that it has a computer. Find the probability that it also has a TV set.
A random selection of one of the families is made, and a computer is discovered there. P(computer AND TV) = 5/6.
How to find the Calculation?We surveyed 400 households. 60% of people had computers, while 90% of them had TVs.
These were something that every family owned at least one of.
A random selection of one of the families is made, and a computer is discovered there.
Check to see if there is a TV there as well.
union: # with computer, # with TV, - # with both, # with both
400 = 360 + 240 - # with both # with both = 200 / 400 = 0.9 * 400 + 0.6 * 400
P(computer AND TV) = 200/400 = 1/2 ——-
P(TV | computer) + P(TV and computer) / P(computer) = 0.5/0.6 = 5/6
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Write an algebraic expression that represents five less than the product of a number and six
Answer:
6n-5
Step-by-step explanation:
let 'n' equal 'a number'
the equation above means you are multiplying 6 and that number, then reducing it by 5
20x+85y=120 rate of change
Answer:
-4/17
Step-by-step explanation:
You want the slope of the line described by the equation 20x +85y = 120.
Slope
Putting the equation in slope-intercept form by solving for y gives ...
20x +85y = 120
85y = -20x +120
y = -20/85x +120/85
y = -4/17x +24/17
The slope is the coefficient of x: -4/17.
The rate of change is -4/17.
Can I join Wikipedia?
Yes , you can join Wikipedia as a creator who can help maintain the platform and update the content from time to time. There are also different types of job roles which you can find for Wikipedia .
You can also simply just create an account and start contributing as a member of Wikipedia.
For this the first step would be to select an appropriate username, which will be unique , as this will be used to identify and differentiate you from others. Then you can start contributing to Wikipedia and other Wikimedia projects.
Communicate with other editors via your own talk page. You can also opt in to exchanging emails with other users and thus increase your community.
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Please HURRY!!!
Which of the following must be true
5. Jamal got a job working on an assembly line in a toy factory. On the 20th day of work, he
assembled 137 toys. He noticed that since he started, every day he assembled 3 more
toys than the day before. How many toys did Jamal assemble altogether during his first
20 days?
(Arithmetic sequence)——
2170 toys Jamal assemble altogether during his first 20 days.
What is the arithmetic sequence?
A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms.
Here, we have
Given: Jamal got a job working on an assembly line in a toy factory. On the 20th day of work, he assembled 137 toys. He noticed that since he started, every day he assembled 3 more toys than the day before.
We have to find how many toys did Jamal assemble altogether during his first 20 days.
We apply the arithmetic sequence formula and we get
tₙ = t₁ + (n-1)d
137 = t₁ + (20-1)(3)
t₁ = 80
To calculate the total number of toys that Jamal assemble in his first 20 days,
S₂₀ = (20/2)(2×80 + (20-1)(3))
S₂₀ = 2170
Hence, 2170 toys Jamal assemble altogether during his first 20 days.
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What are two ways to write m2 in word form?
Answer:
not sure if I understand but I believe you are talking about writing it down
In any version of Microsoft Word, type m2, then highlight the 2. Now press and hold Ctrl and Shift, then press the + key and it will be changed to superscript and will look like this: m2
Find the equation of the line. Write the answer in standard form.
Answer:
1.Given points are:-
(1,2)=(x1/,y1)
(3,4)=(x2,y2)
Now,from two point formula,
y-y1=(y2-y1)/(X2-X1)×(X-X1)
or,y-2=(4-2)/(3-1)×(X-1)
or,y-2=2/2×(X-1)
or,y-2=1(X-1)
or,y-2=X-1
or, X -1-y+2=0
or,X-y+1=0 is the req. eqn in standard form
2.Given points are:-
(2,5)=(x1, y1)
(3,7)=(x2,y2)
Now, from two point formula,
y-5=(7-5)/(3-2)×(X-2)
or,y-5=2/1×(X-2)
or,y-5=2(X-2)
or,y-5=2X-4
or,2X-y-4+5=0
or,2x-y+1=0 is the req. eqn in standard form.
c.do similarly
and*mark me brainliest
Answer:
see explanation
Step-by-step explanation:
the equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
First obtain the equations in slope- intercept form
y = mx + c ( m is the slope and c the y- intercept )
(1)
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 2 ) and (x₂, y₂ ) = (3, 4 )
m = [tex]\frac{4-2}{3-1}[/tex] = [tex]\frac{2}{2}[/tex] = 1 , then
y = x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (3, 4 ) , then
4 = 3 + c ⇒ c = 4 - 3 = 1
y = x + 1 ( subtract y from both sides )
0 = x - y + 1 ( subtract 1 from both sides
- 1 = x - y , that is
x - y = - 1 ← in standard form
Use the same procedure for the next 2 questions
(2)
(x₁, y₁ ) = (2, 5 ) and (x₂, y₂ ) = (3, 7 )
m = [tex]\frac{7-5}{3-2}[/tex] = [tex]\frac{2}{1}[/tex] = 2 , then
y = 2x + c ← is the partial equation
using the point (2, 5 ) to find c
5 = 2(2) + c = 4 + c ( subtract 4 from both sides )
1 = c
y = 2x + 1 ( subtract y from both sides )
0 = 2x - y + 1 ( subtract 1 from both sides )
- 1 = 2x - y , that is
2x - y = - 1 ← in standard form
(3)
(x₁, y₁ ) = (5, 2 ) and (x₂, y₂ ) = (3, 12 )
m = [tex]\frac{12-2}{3-5}[/tex] = [tex]\frac{10}{-2}[/tex] = - 5 , then
y = - 5x + c
using the point (5, 2 ) to find c
2 = - 5(5) + c = - 25 + c ( add 25 to both sides )
27 = c
y = - 5x + 27 ( add 5x to both sides )
5x + y = 27 ← in standard form
what meat is the most expensive per pound?
Answer:
B
Step-by-step explanation:
14.50 / 1.75 = 8.3
26.25 / 2.5 = 10.5
3/8 * 2 = 0.75 .... 5.5 * 2 = 11 (no need to continue)
A regular pentagon is a pentagon with five sides of the same length. If the length of one side of the pentagon is represented by 2X -1, what expression would represent the perimeter of this pentagon
Step-by-step explanation:
one side : 2x - 1
so, 5 sides (the perimeter is the sum of all sides) :
5 × (2x - 1) = 10x - 5
What is the longest triangle side called?
Answer:
The Hypotenuse
Step-by-step explanation:
The Hypotenuse is the longest side of a Triangle.
Natalia paid a total of 38.95 for 3 pizzas and a salad. The price of each pizza was p dollars. And the price of the salad was 11.98 what is the cost of 1 pizza
Answer:
The cost for 1 pizza is $8.99
Step-by-step explanation:
We know
Natalia paid a total of 38.95 for 3 pizzas and a salad
A salad = $11.98
We first find the total cost of 3 pizzas by
38.95 - 11.98 = $26.97
$26.97 is the cost for 3 pizzas; to find the cost of 1 pizza, we take
26.97 divided by 3 = $8.99
So, the cost for 1 pizza is $8.99
Answer:
The cost of 1 pizza is $8.99.
Step-by-step explanation:
Let
[tex]t[/tex] = total price
[tex]p[/tex] = pizzas
[tex]s[/tex] = salads
Natalia bought 3 pizzas and 1 salad
[tex]38.95=3p+1s[/tex]
We are given the price of the salad.
[tex]38.95=3p+11.98[/tex]
Now we can find the cost of 1 pizza.
Lets solve for [tex]p[/tex].
Subtract 11.98 from both sides of the equation.
[tex]26.97=3p[/tex]
Divide both sides of the equation by 3.
[tex]p=\frac{26.97}{3}\\p=8.99[/tex]
the swim team trains 4 days every week. Mon, Tues, and Thurs, the swim tea spends 1/2h in the gym followed by 1 1/4 in the pool. On Saturday there is no gym work but double the swim team time. how many hours per week does the team train?
The number of hours that the team trians per week is 17 hours.
How to illustrate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
Since the the swim tea spends 1/2h in the gym followed by 1 1/4 in the pool. On Saturday there is no gym work but double the swim team time. The number of hours will be:
( 1 1/4 + 1/2 + 2 1/2) × 4
= 4.25 × 4
= 17 hours.
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