Answers
Answer:
See below ~
Step-by-step explanation:
What is the rat population in 1993?⇒ Number of years since = 0 ⇒ t = 0
⇒ Apply in the formula
⇒ n(0) = 73e^(0.02 × 0)
⇒ n(0) = 73e⁰
⇒ n(0) = 73,000,000 rats
=============================================================
What does the model predict the rat population was in the year 2009?⇒ Number of years since 1993 : 2009 - 1993 = 16 ⇒ t = 16
⇒ Applying in the formula
⇒ n(16) = 73e^(0.02 × 16)
⇒ n(16) = 73e^(0.32)
⇒ n(16) = 73 × 1.37712776 × 10⁶
⇒ n(16) = 100.530326 x 10⁶
⇒ n(16) = 100,530,326 rats
Answer:
Given function:
[tex]\large \text{$ n(t)=73e^{0.02t} $}[/tex]
where:
t is the number of years since 1993n(t) is the rat population measured in millionsTo calculate the rat population in 1993, substitute [tex]t = 0[/tex] into the function:
[tex]\large \begin{aligned}\implies n(0) & =73e^{0.02(0)}\\& = 73 \cdot 1\\& = 73 \sf \: million\end{aligned}[/tex]
To calculate a prediction of the rat population in 2009, first determine the value of t by subtracting the initial year of 1993 from the given year of 2009:
[tex]\large \text{$ \implies t=2009-1993=16 $}[/tex]
Substituting the found value of t into the function to find the predicted number of rats in 2009:
[tex]\large \begin{aligned}\implies n(16) & =73e^{0.02(16)}\\& = 73e^{0.32}\\& = 100.5303268...\\ & = 100.5 \sf \: million\:(1\:dp)\end{aligned}[/tex]
Related Questions
(2x-2) (x+5) what does x =
Answers
Answer:
a
x
2
+
b
x
+
c
=
0
the two roots of the equation take the form
x
1
,
2
=
−
b
±
√
b
2
−
4
a
c
2
a
So, start by adding
−
5
to both sides of the equation to get
2
x
2
+
x
−
5
=
5
−
5
2
x
2
+
x
−
5
=
0
Notice that you have
a
=
2
,
b
=
1
, and
c
=
−
5
. This means that the two solutions will be
x
1
,
2
=
−
1
±
√
1
2
−
4
⋅
2
⋅
(
−
5
)
2
⋅
2
x
1
,
2
=
−
1
±
√
41
4
You can simplify this if you want to get
x
1
=
−
1
+
√
41
4
≅
1.35078
and
x
2
=
−
1
−
√
41
4
≅
−
1.85078
Answer:
(2x-2)=
+2 =+2
(2x)=2
----------
2
x= 1
-----------------------------------------------
(x+5)=
-5=-5
x= -5
Step-by-step explanation:
You just need to separate the variable from the numbers
The data below represent a demand schedule.
Product Price: $30, $25, $20, $15, $10
Quantity Demanded: 5, 15, 25, 35, 45
Using the midpoint approach, determine the price elasticity of demand between each of the following prices:
A. Between P1 = $30 & P2 = $25, Ed=?
B. Between P1 = $25 & P2 = $20, Ed=?
C. Between P1 = $20 & P2 = $15, Ed=?
D. Between P1 = $15 & P2 = $10, Ed=?
Round your answers to two decimal places. Enter your answers as a positive value (absolute value).
Answers
By using the midpoint approach, the price elasticity of demand between each of the given prices are:
5.502.251.170.63What is the price elasticity of demand?The price elasticity of demand measures the responsiveness of the quantity demanded by a consumer with respect to a specific change in price of the product, all things being equal (ceteris paribus).
By using the midpoint approach, the price elasticity of demand between each of the given prices is given by:
Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]
Price elasticity of demand = (15 - 5)/[(15 + 5)/2]/(25 - 30)/[(25 + 30)/2]
Price elasticity of demand = 1/-0.1818
Price elasticity of demand = 5.50.
Part B.Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]
Price elasticity of demand = (25 - 15)/[(25 + 15)/2]/(20 - 25)/[(20 + 25)/2]
Price elasticity of demand = 0.5/-0.2222
Price elasticity of demand = 2.25.
Part C.Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]
Price elasticity of demand = (35 - 25)/[(35 + 25)/2]/(15 - 20)/[(15 + 20)/2]
Price elasticity of demand = 0.33/-0.2857
Price elasticity of demand = 1.17.
Part D.Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]
Price elasticity of demand = (45 - 35)/[(45 + 35)/2]/(10 - 15)/[(10 + 15)/2]
Price elasticity of demand = 0.25/-0.4
Price elasticity of demand = 0.63.
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HELP WITH THIS MATH QUESTION!!! I DONT KNOW HOW TO DO THIS
Answers
The similarity relationship is AC / EC = AB / ED.
The length of AB is 157.50m.
What is the length of AB?When two triangles are similar, the ratio of the known sides of the triangles can be used to determine the length of the side of the unknown length.
The similarity relationship is : AC / EC = AB / ED
AC = 160 + 50 = 210
210 / 160 = AB / 120
AB = (210 X 120) / 160 = 157.50
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I want to buy a car for $17,500 and I make 13 an hour roughly how long would it take me to reach my goal? & how many hours would i have to work ?
Answers
Answer:
1347 hours
Step-by-step explanation:
Assuming the income is net income (total after taxes etc.):
Cost of car = $17,500Net income = $13 per hourTo calculate the number of hours to be worked to save enough to buy the car, divide the cost of the car by hourly net income:
[tex]\begin{aligned}\implies \textsf{Number of hours to work} & = \dfrac{\textsf{Cost of car}}{\textsf{hourly net income}}\\\\& = \sf \dfrac{17500}{13}\\\\& = \sf 1346.1538...\end{aligned}[/tex]
We have to round the number up to 1347 hours, as only $17,498 will be saved if 1346 hours are worked.
The average working week is approximately 40 hours, therefore to calculate how many weeks it would take to earn enough money to purchase the car, divide the number of hours by 40:
⇒ 1347 ÷ 40 = 33.675
So it would take 34 weeks, working an average of 40 hours a week and not spending any of the money earned, to save enough to purchase the car.
Total hours
Cost/Earnings17500/131346.15Round to the next whole instead of nearest whole to avoid depicit
1347 hours you have to work atleastIn most of the countries the average working hours per week is
45 hoursTotal weeks
1347/4529.930weeks you have to work if you don't spend any money of itWhat is the value of x???
Answers
The given polygon isa pentagon and the sum of its exterior angle is 360°. The value of x from the given polygon is 8
Sum of the exterior angle of a polygonThe given polygon isa pentagon and the sum of its exterior angle is 360°.
Take the sum of the angles and equate to 360° as shown;
77 + 66 + 62+ 59 + 12x = 360°
264 + 12x = 360
12x = 96
x = 8
Hence the value of x from the given polygon is 8
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HELP WITH THE RIGHT ASNWER FOR BRAINLIEST!!!!
Graph the line with slope 3 passing through the point (2,1).
Answers
Worth 30 points! Select the correct answer.
What is the value of x in the triangle? (file is attached below)
Answers
Answer:
A
Step-by-step explanation:
tan60=opp/adj
tan60=15/x
15tan60=x
25.98=x (when you calculate 15 root 3 it is the same number)
Help please i need it
Answers
Answer:
4 pints
Step-by-step explanation:
1(2 1/2) + 2(4) + 1(5 1/2) =5/2 + 8 + 11/2 =16/2 + 88 + 816/28/24Therefore each can would contain 8/2 = 4 pints
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Please feel free to comment, ask questions, give feedback, or correct me if I am wrong!
Have a great day!
:)
A cylinder has a base radius of 9 feet and a height of 4 feet. What is its volume in
cubic feet, to the nearest tenths place?
Answers
The volume of the cylinder will be equal to 1017.87 cubic feet.
What is volume?Volume is defined as the space occupied by any object in the three-Dimensions. For the cylinder, the volume will be calculated by radius and the height of the cylinder.
Given that:-
The volume of the cylinder will be calculated by using the formulas below:-
V = πr²h
V = π ( 9 )² 4
V = 1017.87 cubic feet.
Therefore the volume of the cylinder will be equal to 1017.87 cubic feet.
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If f(n) = 2n^2 + 2 and g(n) = n + 1, what is (f -g)(n) when n = -1?
Answers
2n^2+2-n-1 => 2n^2-n+1
now we replace n with -1
2(-1)^2-(-1)+1 => 2+2=4
"4" is teh final answer
Two dice are rolled. Event A is that the sum of the numbers is 7 or 11. Event B is that the sum of the numbers is 11 or 12. Find the probability of Event A or B(A union B)
Answers
Answer:
the probability is %25 percent :P
Step-by-step explanation:
If one student is chosen at random, Find the probability that the student was NOT a female that got a "C"
--------- A // B // C // Total
Male: 10 // 8 // 15 // 33
Female: 7 // 9 // 17 // 33
Total: 17 // 17 // 32 //66
Answers
The probability that the student was NOT a female that got a "C" is 15 / 32.
What is the probability?
Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that the student was NOT a female that got a "C" = number of males that got a C / total number of people that got a C = 15 / 32.
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If p+q = - 2, show that p^3 + q^3 +8 =6pq
Answers
Answer:
Step-by-step explanation:
Algebraic Identities:Identity used: (a +b)³ = a³ + b³ + 3ab(a +b)
p + q = -2 ------------------(I)
Both sides take cube,
(p +q)³ = (-2)³
a = p and b =q
p³ + q³ + 3pq(p +q) = -8
p³ + q³ + 3pq*(-2) = - 8 {From (I)}
p³ + q³ - 6pq = -8
p³ + q³ = -8 + 6pq
p³ + q³ + 8 = 6pq
Hence, proved.
If F(x) = x-3, which of the following is the inverse of F(x)?
O A. F1(x) = x+ 3
B. F¹(x) = 3x
OC. F¹(x) = x-3
OD. F¹(x) = 3-x
Answers
Answer:
3-x is the inverse of f(x)=x-3
HELP PLS! A kiddie pool is 9 feet long and 6 feet wide. Surrounding wach side of the kiddie pool is a cement walkway of uniform width. The combined area of the pool and walk way is 108 ft^2. Find the width of the walkway
Answers
Answer:
wait I will edit and answer it in a few minutes
What is the value of x? 2 3 6 7
Answers
Answer:
6
Step-by-step explanation:
Answer:
2 or A
Step-by-step explanation:
Correct on edge22
EASY 5TH GRADE QUESTION. WILL GIVE BRAINLIEST
How would you read the number -30?
Answers
Answer:
Negative thirty
Step-by-step explanation:
-6 3/5 - (-7 4/15) + 2 1/5
Answers
The answer to your question would be 43/15 or 2.866 and ongoing.
Find the amount of simple interest on a loan of $2,500 at 4.44% interest for 12.75 months. (Round to the nearest cent)
Answers
2500* 4.44 / 100 = 111 iterest per month
Question 6 of 10 In order to solve the following system of equations by addition, which of the following could you do before adding the equations so that one variable will be eliminated when you add them? 2x - 4y = 5 6x - 3y=10 A. Multiply the top equation by -2. B. Multiply the top equation by -3 and the bottom equation by 2. C. Multiply the top equation by 3 and the bottom equation by 4. D. Multiply the top equation by -3. SUBMIT
???
Answers
Multiply the top equation by -3 and then adding both the equations one variable will be eliminated. So the correct answer is option D.
What is an equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
We are having two equations:-
2x - 4y = 5
6x - 3y=10
When we multiply the first equation by -3 the equation will become as follows:-
-6x + 12y = - 15
6x - 3y = 10
By adding both the equations one variable will be eliminated:-
9y = - 5
Therefore Multiply the top equation by -3 and then add both the equations one variable will be eliminated. So the correct answer is option D.
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The graph of which of the following equations has a slope of -and an x-intercept of
(-6,0)?
A y=-x-6
B. y = − ½ x − 3
-
C. y = -x +3
D. y = -x +6
Answers
The answer is A
[tex]y = - x - 6 \\ 0 = - x - 6 \\ x = - 6[/tex]
so x intercept : (-6,0)
and slope is negative
Hope it helps
Please give brainliest
The equation of line which a slope is -1 and an x-intercept of (-6,0) will be;
⇒ y = - x - 6
What is Equation of line?The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The slope of the line = - 1
And, The x-intercept = (- 6, 0)
Now,
Let the equation of line;
⇒ y = - x - 6
Slope (m) = dy/dx = - 1
And, The x - intercept is find as;
Put y = 0;
⇒ y = - x - 6
⇒ 0 = - x - 6
⇒ x = - 6
Thus, The correct equation is,
⇒ y = - x - 6
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Solve this system of equations by using the substitution method. y=2x-5 6x+7=y
Answers
Answer:
[tex]x = - 3 \: and \: y = - 11[/tex]
Step-by-step explanation:
L
[tex]since \: y = 2x - 5(equation \: 1) \: \\ [/tex]
[tex]substitute \: for \: y \: in \: equation \: 2 \: (6x + 7 = y)[/tex]
[tex]6x + 7 = y \\ 6x + 7 = 2x - 5 \\ collect \: like \: terms \\ 6x - 2x = - 5 - 7 \\ 4x = - 12 \\ x = \frac{ - 12}{4} \\ x = - 3[/tex]
[tex]substitute \: for \: x in \: equation \: 1[/tex]
[tex]y = 2x - 5 \\ y = 2( - 3) - 5 \\ y = - 6 - 5 \\ y = - 11[/tex]
Answer:
[tex]y = 2.x = \frac{1}{11} [/tex]
Step-by-step explanation:[tex] \binom{x - 56x + 7 = y}{y = 2} [/tex]
_______________________
1. Substitute y = 2 :
[tex](x - 56x + 7 = 2)[/tex]
2. Simplify :
[tex]( - 55x + 7 = 2)[/tex]
3. Isolate x for [tex]( - 55x + 7 = 2) : x = \frac{1}{11} [/tex]
4. The solution of the system of equations are :
[tex]y = 2.x = \frac{1}{11} [/tex]
What are the zeros of the quadratic function f(x)=8^2-16-15
Answers
Answer:
C)
Step-by-step explanation:
f(x)=[tex]8x^{2} -16x-15[/tex]
[tex]8x^{2} -16x-15=0[/tex]
[tex]x=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex] , a=8, b= - 16, c= - 15
[tex]x=\frac{-(-16)+-\sqrt{(-16)^2-4*8*(-15)} }{2*8} = \frac{16+-\sqrt{736} }{16} =\frac{16+-4\sqrt{46} }{16} = 1 +- \frac{\sqrt{46} }{4} = 1+- \frac{\sqrt{23} \sqrt{2}}{2\sqrt{2} \sqrt{2} } =1+-\frac{\sqrt{23} }{2\sqrt{2} } = 1+-\frac{\sqrt{23} }{\sqrt{8} }[/tex]
Write the converse of the statement
below.
If it is 9 a.m., then I am awake.
Answers
Answer:
if I am awake then it is 9 am.
Step-by-step explanation:
if p then q the converse is if q then p.
A tower, 50 feet high, is secured with a guy wire anchored 8
feet from the base of the tower. What angle will the guy wire
make with the ground?
Answers
The tangent of an angle is the ratio of perpendicular to the base. The angle will the guy wire makes with the ground will be 80.91°.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
A tower, 50 feet high, is secured with a guy wire anchored 8 feet from the base of the tower.
The angle will the guy wire makes with the ground will be given by the tangent.
The tangent of an angle is the ratio of perpendicular to the base.
Then we have
tan θ = 50/8
tan θ = 6.25
θ = tan ⁻¹ (6.25)
θ = 80.9097
θ ≅ 80.91°
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Triangle ABC = Triangle ADF, AD = 18, BC = 17, DF= [?]
Answers
The value of the length DF is 17
How to determine the length DF?The statement Triangle ABC = Triangle ADF means that the triangles ABC and ADF are congruent triangles.
So, we have:
AB = AD
AC = A F
BC = DF
Given that BC = 17;
The equation BC = DF becomes
17 = DF
Rewrite as:
DF = 17
Hence, the value of the length DF is 17
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How do u solve the pythagorean theorem to find out if they right trangles
Answers
To solve the theorem, we will take the square of the longest side of a right triangle and equate to the sum of the squares of the other two sides
What is Pythagoras theoremPythagoras theorem states that the square of the longest side of a right triangle is equal to the sum of the squares of the other two sides
For instance, let;
c be the longest sidea and b be the other two sidesAccording to the theorem above, mathematically;
c² = a² + b²
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belle walks 7/10 mile each morning, and 1, 4/10 miles each evening.
how many miles does she walk in 5 days
Answers
Answer:
10.5 miles.
Step-by-step explanation:
If she walks 7/10 of a mile each morning, and 1, 4/10 of a mile each day, Belle walks a total of 2 1/10 of a mile each day (2.1) miles each day)
We can just multiply the amount of miles per day by 5, (2.1 x 5) and we get 10.5 miles total.
Answer:
10 1/2
Step-by-step explanation:
divide 7/10 which is 0.7 then multiply that by 5 which is 3.5
then divide 4/10 which is 0.4 then multiply that by 5 which is 2, but add 5 which is 7.
then combine all of that together which is 3.5+7= 10.5
then convert that into a fraction which is 10 1/2
A continuous random variable X has cdf F(x)=x² b (a) Determine the constants a and b. for a < 0, for 0 < x < 1, for x > 1.
Answers
Any proper CDF [tex]F(x)[/tex] has the properties
• [tex]\displaystyle \lim_{x\to-\infty} F(x) = 0[/tex]
• [tex]\displaystyle \lim_{x\to+\infty} F(x) = 1[/tex]
so we have to have a = 0 and b = 1.
This follows from the definitions of PDFs and CDFs. The PDF must satisfy
[tex]\displaystyle \int_{-\infty}^\infty f(x) \, dx = 1[/tex]
and so
[tex]\displaystyle \lim_{x\to-\infty} F(x) = \int_{-\infty}^{-\infty} f(t) \, dt = 0 \implies a = 0[/tex]
[tex]\displaystyle \lim_{x\to+\infty} F(x) = \int_{-\infty}^\infty f(t) \, dt = 1 \implies b = 1[/tex]
i needs help with it please
Answers
The triangle are similar because they satisfy the AAA postulate : Triangle ABC ~ Triangle PQR ( AAA similarity postulate )
Meaning of congruent trianglesA triangle can be defined as a plain shape that has three sides and three angles.
Congruent triangles are triangles that satisfy one or more congruence postulates or laws. The triangles could either be similar based on their angles or sides or angles and side being similar.
In conclusion, The triangle are similar because they satisfy the AAA postulate : Triangle ABC ~ Triangle PQR ( AAA similarity postulate )
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