Answer:
City A and city B will have equal population 25years after 1990
Step-by-step explanation:
Given
Let
[tex]t \to[/tex] years after 1990
[tex]A_t \to[/tex] population function of city A
[tex]B_t \to[/tex] population function of city B
City A
[tex]A_0 = 10000[/tex] ---- initial population (1990)
[tex]r_A =3\%[/tex] --- rate
City B
[tex]B_{10} = \frac{1}{2} * A_{10}[/tex] ----- t = 10 in 2000
[tex]A_{20} = B_{20} * (1 + 20\%)[/tex] ---- t = 20 in 2010
Required
When they will have the same population
Both functions follow exponential function.
So, we have:
[tex]A_t = A_0 * (1 + r_A)^t[/tex]
[tex]B_t = B_0 * (1 + r_B)^t[/tex]
Calculate the population of city A in 2000 (t = 10)
[tex]A_t = A_0 * (1 + r_A)^t[/tex]
[tex]A_{10} = 10000 * (1 + 3\%)^{10}[/tex]
[tex]A_{10} = 10000 * (1 + 0.03)^{10}[/tex]
[tex]A_{10} = 10000 * (1.03)^{10}[/tex]
[tex]A_{10} = 13439.16[/tex]
Calculate the population of city A in 2010 (t = 20)
[tex]A_t = A_0 * (1 + r_A)^t[/tex]
[tex]A_{20} = 10000 * (1 + 3\%)^{20}[/tex]
[tex]A_{20} = 10000 * (1 + 0.03)^{20}[/tex]
[tex]A_{20} = 10000 * (1.03)^{20}[/tex]
[tex]A_{20} = 18061.11[/tex]
From the question, we have:
[tex]B_{10} = \frac{1}{2} * A_{10}[/tex] and [tex]A_{20} = B_{20} * (1 + 20\%)[/tex]
[tex]B_{10} = \frac{1}{2} * A_{10}[/tex]
[tex]B_{10} = \frac{1}{2} * 13439.16[/tex]
[tex]B_{10} = 6719.58[/tex]
[tex]A_{20} = B_{20} * (1 + 20\%)[/tex]
[tex]18061.11 = B_{20} * (1 + 20\%)[/tex]
[tex]18061.11 = B_{20} * (1 + 0.20)[/tex]
[tex]18061.11 = B_{20} * (1.20)[/tex]
Solve for B20
[tex]B_{20} = \frac{18061.11}{1.20}[/tex]
[tex]B_{20} = 15050.93[/tex]
[tex]B_{10} = 6719.58[/tex] and [tex]B_{20} = 15050.93[/tex] can be used to determine the function of city B
[tex]B_t = B_0 * (1 + r_B)^t[/tex]
For: [tex]B_{10} = 6719.58[/tex]
We have:
[tex]B_{10} = B_0 * (1 + r_B)^{10}[/tex]
[tex]B_0 * (1 + r_B)^{10} = 6719.58[/tex]
For: [tex]B_{20} = 15050.93[/tex]
We have:
[tex]B_{20} = B_0 * (1 + r_B)^{20}[/tex]
[tex]B_0 * (1 + r_B)^{20} = 15050.93[/tex]
Divide [tex]B_0 * (1 + r_B)^{20} = 15050.93[/tex] by [tex]B_0 * (1 + r_B)^{10} = 6719.58[/tex]
[tex]\frac{B_0 * (1 + r_B)^{20}}{B_0 * (1 + r_B)^{10}} = \frac{15050.93}{6719.58}[/tex]
[tex]\frac{(1 + r_B)^{20}}{(1 + r_B)^{10}} = 2.2399[/tex]
Apply law of indices
[tex](1 + r_B)^{20-10} = 2.2399[/tex]
[tex](1 + r_B)^{10} = 2.2399[/tex] --- (1)
Take 10th root of both sides
[tex]1 + r_B = \sqrt[10]{2.2399}[/tex]
[tex]1 + r_B = 1.08[/tex]
Subtract 1 from both sides
[tex]r_B = 0.08[/tex]
To calculate [tex]B_0[/tex], we have:
[tex]B_0 * (1 + r_B)^{10} = 6719.58[/tex]
Recall that: [tex](1 + r_B)^{10} = 2.2399[/tex]
So:
[tex]B_0 * 2.2399 = 6719.58[/tex]
[tex]B_0 = \frac{6719.58}{2.2399}[/tex]
[tex]B_0 = 3000[/tex]
Hence:
[tex]B_t = B_0 * (1 + r_B)^t[/tex]
[tex]B_t = 3000 * (1 + 0.08)^t[/tex]
[tex]B_t = 3000 * (1.08)^t[/tex]
The question requires that we solve for t when:
[tex]A_t = B_t[/tex]
Where:
[tex]A_t = A_0 * (1 + r_A)^t[/tex]
[tex]A_t = 10000 * (1 + 3\%)^t[/tex]
[tex]A_t = 10000 * (1 + 0.03)^t[/tex]
[tex]A_t = 10000 * (1.03)^t[/tex]
and
[tex]B_t = 3000 * (1.08)^t[/tex]
[tex]A_t = B_t[/tex] becomes
[tex]10000 * (1.03)^t = 3000 * (1.08)^t[/tex]
Divide both sides by 10000
[tex](1.03)^t = 0.3 * (1.08)^t[/tex]
Divide both sides by [tex](1.08)^t[/tex]
[tex](\frac{1.03}{1.08})^t = 0.3[/tex]
[tex](0.9537)^t = 0.3[/tex]
Take natural logarithm of both sides
[tex]\ln(0.9537)^t = \ln(0.3)[/tex]
Rewrite as:
[tex]t\cdot\ln(0.9537) = \ln(0.3)[/tex]
Solve for t
[tex]t = \frac{\ln(0.3)}{ln(0.9537)}[/tex]
[tex]t = 25.397[/tex]
Approximate
[tex]t = 25[/tex]
What is Limit of (3 x minus 3) Superscript five-halves Baseline as x approaches 4
Answer:
d 243
Step-by-step explanation:
The solution of given function is 243
What is limit of function?
A limit defined as the value which a function approaches as that function's inputs get closer and closer to some number
[tex]lim\ (3x-3)^\frac{5}{2} \\x\to 4[/tex]
[tex](3(4)-3)^\frac{5}{2}[/tex]
[tex](12-3)^\frac{5}{2}[/tex]
[tex](9)^\frac{5}{2}[/tex]
[tex](3^2)^\frac{5}{2}[/tex]
[tex]3^5[/tex]
243
Hence, the solution of given function is 243
Learn more about limit of function
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g^2+2g-48=0
g=
Use a comma to separate answers as needed
Answer:
g = -8, 6
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
QuadraticsFactoringMultiple RootsStep-by-step explanation:
Step 1: Define
Identify
g² + 2g - 48 = 0
Step 2: Solve for g
Factor: (g + 8)(g - 6) = 0Find roots: g = -8, 6What is the proof the outcome (not A)?
9514 1404 393
Answer:
B
Step-by-step explanation:
If the probability of event "A" is 'p', then the probability of the event "not A" is
P(not A) = 1 - P(A) = 1 - p
For p=0.5, this is ...
P(not A) = 1 -0.5 = 0.5 . . . . . matches choice B
Answer:
○B. 0.5 is the proof the outcome (not A).
what are the integers from 6 to 25
[tex]\huge\boxed{Answer\hookleftarrow}[/tex]
Answer:
✐ The integers from 6 to 25 are ⎆ [tex]\large\bold{7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22,23, 24}[/tex]
Step-by-step explanation:
Natural numbers are numbers that are greater than 0 (all numbers starting from positive 1). All natural numbers are integers. So, in this case ⎇ integers = natural numbers (note :- only in this case)
Look Below. (Will give brianliest)
Answer:
what is your question friend? :)
It takes Alice 90 minutes to put a futon frame together, and it takes Maya 60 minutes to put the same
type of frame together. If they worked together, how long would it take to put a frame together?
Answer:
36 minutes
Step-by-step explanation:
The equation to determine the time together is
1/a + 1/b = 1/c where a and b are the times alone and c is the time together
1/90 + 1/ 60 = 1/c
Multiply each side by 180c to clear the fractions
180c( 1/90 + 1/ 60 = 1/c)
2c + 3c = 180
5c = 180
Divide each side by 5
5c/5 = 180/5
c =36
If the measure of arc CB is 8/3 units, what is the measure of CAB?
Question:
If the measure of arc CB is [tex]\frac{8}{3} \pi[/tex] units, what is the measure of ∠CAB?
Answer:
120°
Step-by-step explanation:
The figure has been attached to this response.
The figure shows a circle centered at A and has a radius of 4 units.
Also, the length of the arc CB (as given in the question) is [tex]\frac{8}{3} \pi[/tex] units.
The length L of an arc is given by;
L = [tex]\frac{\beta }{360} * 2\pi * r[/tex] -----------------(i)
Where;
β = angle subtended by the arc at the center of the circle and measured in degrees
r = radius of the circle
From the question;
β = ∠CAB
r = 4 units
L = [tex]\frac{8}{3} \pi[/tex]
Substitute these values into equation (i) as follows;
[tex]\frac{8}{3} \pi[/tex] = [tex]\frac{\beta }{360} * 2\pi * 4[/tex]
=> [tex]\frac{8}{3} \pi[/tex] = [tex]\frac{\beta }{360} * 8\pi[/tex]
Cancel 8[tex]\pi[/tex] on both sides
[tex]\frac{1}{3}[/tex] = [tex]\frac{\beta }{360}[/tex]
Cross multiply
3 x β = 360 x 1
3β = 360
Divide both sides by 3
[tex]\frac{3\beta }{3} = \frac{360}{3}[/tex]
β = 120°
Therefore, the measure of ∠CAB is 120°
The sum of two numbers is 45 and their difference is 7. Find the numbers. *
the sum of two numbers that is 45 and their difference is 7 it is 39 and 6 more like 39+6
What are the x- and y-intercepts for the graph of 3x + y = 15?
x-intercept = −3
y-intercept = 15
x-intercept = 3
y-intercept = 1
x-intercept = −3
y-intercept = 1
x-intercept = 5
y-intercept = 15
Answer:
x-intercept = 5
y-intercept = 15
Step-by-step explanation:
Change the equation to slope-intercept form: y = -3x + 15
You have the y-intercept in that equation already, so you know it's 15. To find the x-intercept, substitute 0 in for y and solve algebraically.
0 = -3x + 15
-15 = -3x
5=x
Evaluate this expression for x=-5 and y=-5
Answer:
[tex]x - 2y=5[/tex]
Step-by-step explanation:
Given
[tex]x = -5; y=-5[/tex]
[tex]x - 2y[/tex] --- missing from question
Required
Evaluate
We have:
[tex]x - 2y[/tex]
Substitute for x and y
[tex]x - 2y=-5 - 2*-5[/tex]
[tex]x - 2y=-5 +10[/tex]
[tex]x - 2y=5[/tex]
Help please!
Fully factorise
Answer:
a.8y³-6y
taking common
2y(4y²-3)
is a required answer
b.
3x²-20x+12
doing middle term factorization
3x²-18x-2x+12
3x(x-6)-2(x-6)
(x-6)(3x-2)
is a required answer .
which of these expressions is equivalent to to 7(x+3)
On expanding the expression, we get - 7x + 21.
We have the following expression -
f(x) = 7(x + 3)
We have to write its equivalent expression.
Expand : f(x) = [tex]$\pi (\sqrt{x} + 5)[/tex]Expanding we get -
f(x) = [tex]$\pi \sqrt{x} + 5\pi[/tex]
According to the question, we have -
7(x + 3)
On expanding, we get -
7(x + 3) = 7x + 21
Hence, on expanding the expression, we get - 7x + 21.
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An ice cream shop finds that its weekly profit P (measured in dollars) as a function of the price x (measured in dollars) it charges per ice cream cone is given by the function k, defined by k(x) = 125x^2 +670x 125 where P= k(x).
Required:
a. Determine the maximum weekly profit and the price of an ice cream cone that produces that maximum profit
b. The cost of the ice cream cone is too low then the ice cream shop will not make a profit. Determine what the ice cream shop needs to charge in order to break even
c. The profit function for Cold & Creamy (another ice cream shop) is defined by the function g where gx)- k(x-2). Does the function g have at the same maximum value as k?
Answer:
The answer is below
Step-by-step explanation:
Given that k(x) = -125x² +670x - 125, where x is the charge per cone and P = k(x) is the weekly profit
a) The maximum profit is at P'(x) = 0. Therefore we have to find the derivative of the profit equation and equate it to 0.
P'(x) = k'(x) = 0
k'(x) = -250x + 670 = 0
-250x + 670 = 0
250x = 670
x = $2.68
P = k(2.68) = -125(2.68²) + 670(2.68) - 125 = $772.8
Hence the maximum profit is $772.8 when the price of each ice cream cone is $2.68
b) At break even, the profit is 0. Hence P= k(x) = 0
-125x² + 670x - 125 = 0
x = 5.17 or x = 0.19
Therefore to break even, the price of the ice cream cone needs to be $0.19 or $5.17
c) g(x) = k(x - 2)
g(x) = -125(x - 2)² + 670 (x -2) - 125
Maximum profit is at g'(x) = 0
g'(x) = -250(x-2) + 670
-250(x-2) + 670 = 0
-250x + 500 + 670 = 0
250x = 1170
x = 4.68
g(4.68) = -125(4.68 - 2)² + 670(4.68 -2) - 125 = $772.8
Therefore function g has the same maximum value as function k
A computer store buys a computer system at a cost of $450.20. The selling price was first at $710, but then the store
advertised a 30% markdown on the system. What is the current sale price? What is the percent mark up on the current sale
price?
Answer:
i believe it is 497 after the 30% mark down
Step-by-step explanation:
i subtracted 30% from 710
5(x+2)-4 = 13-7(x+1)
Answer:
0
Step-by-step explanation:
5x+10-4=13-7x-7
5x+6=6-7x
5x+0= -7x
0=-12x
Divide and u get x=0
For brainlest pls ……..
Answer:
4.5 cm²
Step-by-step explanation:
The given shape is a parallelogram , and the area of a parallelogram is ,
Area :-
1/2 * b * hSo , that,
=> A = 1/2 * 2.5 * 1.8
=> A = 4.5 cm²
Answer:
A = 4.5 m²
Step-by-step explanation:
The area (A) of a parallelogram is calculated as
A = bh ( b is the base and h the perpendicular height )
Here b = 2.5 and h = 1.8 , then
A = 2.5 × 1.8 = 4.5 m²
explanation would really help
Answer:
35
Step-by-step explanation:
the whole line is 49 and line DB is 30.
minus 16 from 30 so 30-16=14
then you minus line CB from EB so 49-14=35
that makes line EC 35
x[tex]x^{2}-8x+14=2x-7[/tex]
Answer:
[tex]x = 3\ or\ x = 7[/tex]
Step-by-step explanation:
Given
[tex]x^{2}-8x+14=2x-7[/tex]
Required
Solve
Equate to 0
[tex]x^{2}-8x-2x+14+7=0[/tex]
[tex]x^{2}-10x+21=0[/tex]
Expand
[tex]x^{2}-7x-3x+21=0[/tex]
Factorize
[tex]x(x-7)-3(x-7)=0[/tex]
Factor out x - 7
[tex](x-3)(x-7)=0[/tex]
Split
[tex]x - 3 = 0\ \ x - 7 = 0[/tex]
Solve
[tex]x = 3\ or\ x = 7[/tex]
line segment GJ is a diameter of circle L.Angle K measures (4x+6)°
what is the value of x?
21
24
32
44
Answer:
A. 21
Step-by-step explanation:
Recall: inscribed angle in a semicircle equals 90°
m<K is an inscribed angle in a semicircle = (4x + 6)°
Therefore,
4x + 6 = 90°
Solve for x. Subtract both sides by 6
4x + 6 - 6 = 90 - 6
4x = 84
Divide both sides by 4
4x/4 = 84/4
x = 21
a + b = 300 pls help i cant find out the answer
Answer:
a= 250
b= 50
250 + 50 = 300
Step-by-step explanation:
There's many solutions but this was the first one I could come up with.
Answer:
my opinion is seince a+b=300 then the sqaure of 300= 17.3?
Step-by-step explanation:
6 1/8 qt = ___ c please help
Answer:
24 1/2 cups
Step-by-step explanation:
we can change 6 1/8 into 49/4
there are 2 cups in 1 quart
now we can set up a proportion:
2÷1 = 'c'÷ 49/4
cross-multiply to get:
49/4 × 2 = c
49/2 = c
c = 24.5
Find the slope thanks
Find the 66th term of the arithmetic sequence -28,-45,-62
Answer:
Using the formula
an = a of 1 + (n-1)(d)
an = -28 + (n-1)(-17)
simplify
an = -17n - 11
Now that we have the formula, we just plug in 66 for n
a66 = -17(66) - 11
a66 = -1133
Which point on the x-axis lies on the line that passes through point P and is perpendicular to line MN?
Answer:
What is 1/3 of 814
Step-by-step explanation:
What is 1/3 of 814
Answer: I think C
Step-by-step explanation:
Steve earns extra money babysitting. He charges $37.00 for 4 hours and $64.75 for 7 hours. Let x represent the number of hours Steve babysits and y represent the amount he charges
Answer:$6.25
Step-by-step explanation:we have that
x------------------> represent the number of hours Steven babysits
y----------------- > represent the amount he charges
for x=6 hours
y=$37.50 ----------------> y/x=37.5/6=6.25
for x=8 hours
y=$50---------------------> y/x=50/8=6.25
therefore
y=6.25x
Determine the number of solutions for the system 2x+3y=5 and -9y=6x-15
9514 1404 393
Answer:
infinite number of solutions
Step-by-step explanation:
The two equations describe the same line.
Adding 9y+15 to the second equation makes it be ...
15 = 6x +9y
Dividing that by 3 gives you ...
5 = 2x +3y . . . . . . identical to the first equation
The lines intersect at every point, so there are an infinite number of solutions.
what is an algebraic expression for the quotient w and 7?
Answer:
the quotient of w and 7
is it correct?
Step-by-step explanation:
PLEASE LOOK BELOW!!! (Will give Brainliest)
No links and pls explain!!!!
Answer:
20 = x
Step-by-step explanation:
All interiror angles in this triangle will equal 180
Set your formula up as 180 = x+5+7x-5+x then solve for x
180 = x+5+7x-5+x
180 = x + 7x + x +5 - 5
180 - 5 + 5 = 9x
180 = 9x
180 / 9 = x
20 = x
You can check your result by pluging in 20 for all x
180 = 20+5+7*20-5+20
180 = 180
Someone help me please
Square root of 121
4/8 =?/2 please answer
Answer:
? = 1
Step-by-step explanation:
4/8 = ?/2
Change the ? into a variable so it's easier to calculate:
Variable x = ?
4/8 = x/2
Cross multiply:
4 × 2 = 8 × x
8 = 8x
Divide both sides by 8 to isolate the variable:
1 = x
Check your work:
4/8 = 1/2
4 × 2 = 8 × 1
8 = 8
Correct!