Answers
Problem 4
a = 10800 = initial populationb = 1 + r = 1 + (-0.025) = 0.975 is the decay factorThe template of [tex]y = a*b^x[/tex] becomes [tex]y = 10800*0.975^x[/tex] to represent the exponential function.
x = number of years since 2002y = populationWe want to know when the population reaches half of 10800, so we want to know when the population is 10800/2 = 5400
Plug in y = 5400 and solve for x.
[tex]y = 10800*0.975^x\\\\5400 = 10800*0.975^x\\\\0.975^x = 5400/10800\\\\0.975^x = 0.5\\\\\log(0.975^x) = \log(0.5)\\\\x\log(0.975) = \log(0.5)\\\\x = \log(0.5)/\log(0.975)\\\\x \approx 27.377851\\\\x \approx 28\\\\[/tex]
I rounded up to the nearest whole number because x = 27 leads to y = 5452, which is not 5400 or smaller.
Luckily, x = 28 leads to y = 5315 which gets over the hurdle of being 5400 or smaller.
Add 28 years onto the starting year 2002 and we get to 2002+28 = 2030
The population reaches half of its original amount in the year 2030.
Answers:The exponential function is [tex]y = 10800*0.975^x[/tex]It takes 28 years to get to half the population. This occurs in the year 2030============================================================
Problem 5
a = 28750 = starting value for the carb = 1 + r = 1 + (-0.12) = 0.88 = decay factorIf the car loses 12% of its value each year, then it keeps the remaining 88%
Plug those values into [tex]y = a*b^x[/tex].
We find the equation is [tex]y = 28750*0.88^x[/tex] where,
x = number of years since 2012y = car's valueReplace y with 10,000 and solve for x.
[tex]y = 28750*0.88^x\\\\10000 = 28750*0.88^x\\\\0.88^x = 10000/28750\\\\0.88^x \approx 0.347826\\\\\log(0.88^x) \approx \log(0.347826)\\\\x\log(0.88) \approx \log(0.347826)\\\\x \approx \log(0.347826)/\log(0.88)\\\\x \approx 8.261168\\\\x \approx 9\\\\[/tex]
Like in the previous problem, we round up so we clear the hurdle.
Adding 9 years onto 2012 gets us to 2012+9 = 2021
Answers: The function is [tex]y = 28750*0.88^x[/tex]It takes about 9 years, and it occurs in the year 2021Answer:
Exponential Function
General form of an exponential function: [tex]y=ab^x[/tex]
where:
a is the initial value (y-intercept)b is the base (growth/decay factor) in decimal formx is the independent variabley is the dependent variableIf b > 1 then it is an increasing function
If 0 < b < 1 then it is a decreasing function
Question 4Given:
a = 10,800b = decrease of 2.5% = 0.975x = time (in years)y = populationAs the population is decreasing by 2.5% each year, the population will be 100% - 2.5% = 97.5% of the previous year. Therefore, the base is 0.975.
Final equation: [tex]\large \text{$ y=10800(0.975)^x $}[/tex]
Half of population: 10800 ÷ 2 = 5400
[tex]\large \begin{aligned}y & =5400\\\implies 10800(0.975)^x & =5400\\(0.975)^x & = \dfrac{5400}{10800}\\(0.975)^x & = 0.5\\\ln (0.975)^x & = \ln 0.5\\x \ln 0.975 & = \ln 0.5\\x & = \dfrac{\ln 0.5}{\ln 0.975}\\x & = 27.377785123\end{aligned}[/tex]
2002 + 27.37785... = 2029.37785...
Therefore, the population will reach half during 2029 (by 2030).
Question 5Given:
a = 28,750b = decrease of 12% = 0.88x = time (in years)y = value (in dollars)As the value is decreasing by 12% each year, the value will be 100% - 12% = 88% of the previous year. Therefore, the base is 0.88.
Final equation: [tex]\large \text {$ y=28750(0.88)^x $}[/tex]
Find when the car is worth $10,000:
[tex]\large \begin{aligned}y & = 10000\\\implies 28750(0.88)^x & = 10000\\(0.88)^x & = \frac{10000}{28750}\\(0.88)^x & = \frac{8}{23}\\\ln (0.88)^x & =\ln \left(\frac{8}{23}\right)\\x \ln (0.88) & =\ln \left(\frac{8}{23}\right)\\x & =\dfrac{\ln \left(\frac{8}{23}\right)}{\ln (0.88)}\\x & = 8.26116578\end{aligned}[/tex]
2012 + 8.26116578.. = 2020.26116578..
Therefore, the value of the car will reach $10,000 during 2020 (by 2021).
Related Questions
What is the area of a sector, if the radius is 12cm and the angle for the sector is 134°? Use π = 3.14
Answers
Given:
radius(R) = 12 units
arc = 134°
Find: area of sector
Plan: if you think about it, a sector area is a fractional part of the full area of the circle. It’s a pie piece.
A(circle) = π R^2
134° is 134°/360° = 67/180 That is 67/180 th of the full circle
area (S) = 67/180 (π R^2)
S = 67/180 (π )(12^2) = 67/180(144 π) = 54 π units^2 or
≈ 54(3.1416) ≈ 168.389 units^2
Double Check: ✅ ✅
Answer: 18 π units^2 or 168.39 units^2 approximately
Simplify this algebra expression:
6j-2j-2j+8+9+6e+5
Answers
Answer:
6j-2j-2j+8+9+6e+5
= 6j - 4j + 6e + 24
= 2j + 6e + 24
The number of students enrolled at a school varies from year to year. For the first eight years the school is open, the number of students enrolled is recorded in the table shown.
The equation of the least-squares regression line is
ŷ = 68.5 + 11.4x, where ŷ is the number of students enrolled and x is number of years the school has been open. Which shows the residual plot?
Answers
The residual plot will be the one showing the difference between the students that were expected to enroll and the real number of students who enroll.
What is a residual plot?A residual plot is one plot that shows the error or the residual.
What would be the data displayed in this case?In this case, the residual plot will show the difference between the students that were expected to enroll based on the equation given and the real number of students who enroll.
Note: This question is incomplete because the options are not given; due to this, the answer is based on general knowledge.
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Winona has to paint the entire surface of the barrel shown below.
What is the surface area of the barrel including the top and bottom? (Use 3.14 for !.)
_A 1,099 square feet _B 1,256 square feet
_C 1,570 square feet _D 2,198 square feet
Answers
Can i get a reaolve of that problem? Statics
Answers
Answer:
which question
Step-by-step explanation:
give us clarity please
What is the value of x in the equation 0.3x + 0.2 = 5?
Answers
[tex]~~~~0.3x +0.2 = 5\\\\\implies 3x+2 = 50~~~~~~;[\text{Multiply both sides by 10}]\\\\\implies 3x = 50 -2\\\\\implies 3x = 48\\\\\implies x = \dfrac{48}3\\\\\implies x = 16[/tex]
rico wants to know if his score in math test is higher than 80% of his classmates which measure of position should be used to determine this? is it quartiles or deciles?defend your answer.
Answers
Answer:
Decile
Step-by-step explanation:
Quartile only divides group into 4 => 25%, 50%, 75%, 100%
Decile divides group into 10 => 10%, 20%,..., 80%, 90%, 100%
Manuel borrowed money from credit union for 3 years and charged simple ingress at 2% annually and paid $24 in interest how much money did he borrow
Answers
Answer:
$400
Step-by-step explanation:
Hope the picture will help you........
24x-12 equivalent expressions
Answers
Answer:
24x-18+6
Step-by-step explanation:
24x-18+6, 6+-18=-12, 24x-12=24x-2
could someone help me rnnn?
Answers
Answer:
vertex = (0, -4)
equation of the parabola: [tex]y=3x^2-4[/tex]
Step-by-step explanation:
Given:
y-intercept of parabola: -4parabola passes through points: (-2, 8) and (1, -1)Vertex form of a parabola: [tex]y=a(x-h)^2+k[/tex]
(where (h, k) is the vertex and [tex]a[/tex] is some constant)
Substitute point (0, -4) into the equation:
[tex]\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}[/tex]
Substitute point (-2, 8) and [tex]ah^2+k=-4[/tex] into the equation:
[tex]\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}[/tex]
Substitute point (1, -1) and [tex]ah^2+k=-4[/tex] into the equation:
[tex]\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}[/tex]
Equate to find h:
[tex]\begin{aligned}\implies a(1+h) &=a(1-2h)\\1+h &=1-2h\\3h &=0\\h &=0\end{aligned}[/tex]
Substitute found value of h into one of the equations to find a:
[tex]\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}[/tex]
Substitute found values of h and a to find k:
[tex]\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}[/tex]
Therefore, the equation of the parabola in vertex form is:
[tex]\implies y=3(x-0)^2-4=3x^2-4[/tex]
So the vertex of the parabola is (0, -4)
It can be solved through some shortcut tricks of parabola
y intercept= (0,-4)It passes through (-2,8) and (1,-1)
The minimum equation of the parabola (as it's quadratic) for vertex at (0,0)
y=ax²whatever our required parabola be it's translated from the above one
So
ax²=yLet a be 0
current equation is y=x²So it has vertex as well as y inetrcept at (0,0)
For x=-2
y=(-2)²=4 (but its 8 in our translated one )For x=1
y=1It wasn't negative but in translation it's negative so something is subtracted
Take a =2 and subtract (-2)² i.e 4 as it's minimal value of y=x² where x≠y
For
(-2,8)
-2=2(4)-4=8-4=4No try a=3
-2=3(4)-4=12-4=8Yes satisfied
Take (1,-1)
-1=3(1)-4=3-4=-1Verified
The required equation is
y=3x²-4Jessamyn bought 3 notebooks that cost $2.25 each and a pen that cost $0.75. Sales tax on her purchases was
6%. What was the amount of the sales tax?
$0.54
$0.75
$0.18
$0.45
Answers
can I have some help graphing inequalities?
Answers
Answer:
x+5>11
x>11-5
x>6
So it should be equal to or bigger than 6
Solve for x first
x + 5 = 11
-5
x = 6
So, x is greater or equal to 6 and the symbol next to box is the right one to use.
There should be a shaded in circle at 6, pointing to the right.
( the length of the arrow doesn't matter, you could even extend it to 7, 8, 9 or 10)
Hope this helps!
Liberal arts Mathmatics 1 for CR Sem 2
Answers
Check the picture below.
Subtract the sum and difference identities for sin x to derive 1/2 [sin(x+y)+sin(x-y)]= cos x sin y
Answers
The required trigonometric identity is 1/2[sin(x + y) - sin(x - y)] = cosxsiny
To answer the question, we need to know what trigonometric identities are
What are trigonometric identities?Trigonometric identities are relationships between the trigonometic ratios.
Since we require cosxsiny
Given that
sin(x + y) = sinxcosy + cosxsiny and sin(x - y) = sinxcosy - cosxsinySo, subtracting both expressions, we have
sin(x + y) - sin(x - y) = sinxcosy + cosxsiny - (sinxcosy - cosxsiny)
= sinxcosy + cosxsiny - sinxcosy + cosxsiny
= sinxcosy - sinxcosy + cosxsiny + cosxsiny
= 0 + 2cosxsiny
= 2cosxsiny
sin(x + y) - sin(x - y) = 2cosxsiny
Dividing through by 2, we have
1/2[sin(x + y) - sin(x - y)] = cosxsiny
So, the required trigonometric identity is 1/2[sin(x + y) - sin(x - y)] = cosxsiny
Learn more about trigonometric identities here:
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help find the measure of the arc or angle indicated.
please provide work with your answer!
Answers
Answer:
The answer is a angle indicated to this answer
if is right mark me the brainliest if not don't worry please
calculate the area of a parallelogram pqrs if qr=5cm,rs=6cm qrs=118°
Answers
Check the picture below.
[tex]\cos(28^o)=\cfrac{h}{5}\implies 5\cos(28^o)=h \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a parallelogram}\\\\ A=bh~~ \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ b=6\\ h=5\cos(28^o) \end{cases}\implies A=6[5\cos(28^o)]\implies A\approx 26.49[/tex]
Make sure your calculator is in Degree mode.
Find the volume of this
Answers
The Answer would be: V≈ 376.99
a bamboo shoot is 20 inches tall at day 0 and grows 24 inches each day. which function(s) shown below can be used to determine height, f(n), of bamboo after n days
Answers
Answer:
f(n) = 20 + 24n
Step-by-step explanation:
In slope-intercept form, y = mx + b, where m is the slope and b is the y intercept, you need to input the values you are given. f(n) is your "y" here.
The tricky part here is finding "b". Well, at the start, the bamboo shoot is 20 inches tall, so if you think about it, the equation should start with 20, which will be your "b".
Finally, you must show how the bamboo shoot will grow taller by 24 inches each day. Days in this case will be "n", which is like "x" in the general slope-intercept equation, and 24 is your slope ("m"). This will be positive because the height is increasing.
y = 24x + 20 ⇒ f(n) = 20 + 24n
Answer:
Because it starts at 20, that will be your base number
We know it grows 24 in. per day, but we dont know how many, so then we use n
so 20 + 24n
Step-by-step explanation:
20 + 24n
What is the volume, in cubic meters, of a rectangular prism that has a length of 22 meters, a width of 4 meters, and a height of 8 meters?
Answers
Answer:
V =704 m^3
Step-by-step explanation:
Remark
The Volume of a cubical Prism = Length * Width * Height of L * w * h
Givens
L = 22 meters
w = 4 meters
h = 8 meters
Solution
V = L * w * h
V = 22 * 4 * 8
V = 704 m^3
What is the volume, in cubic meters, of a rectangular prism that has a length of 22 meters, a width of 4 meters, and a height of 8 meters?
Explanation -:In this question we are provided with the length, breadth and height of a rectangular prism. We are asked to calculate the volume of the rectangular prism.
We know,
[tex] \star \: \small\boxed{ \rm{ Volume_{(rectangular \: prism)} = L×B×H}}[/tex]
Where,
L stand for LengthB stand for BreadthH stand for HeightSubstituting the values we get
[tex] \small\sf{ Volume_{(rectangular \: prism)} = 22×4×8 = 704 m³}[/tex]
Hence, the volume of the rectangular prism is 704 m³.
Find the value of x.
Answers
Answer:
x=13
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
(2*x+14)-((3*x+1))=0
1.1 Solve : -x+13 = 0
Subtract 13 from both sides of the equation :
-x = -13
Multiply both sides of the equation by (-1) : x = 13
There are three marbles in a bag. One is red and two are black. What is the probability of picking a red marble first, putting it back in the bag and then picking a red marble? Use the following probability to find the answer.
Answers
Answer:
1/9
Step-by-step explanation:
1/3 x 1/3 = 1/9
What is the volume of the rectangular prism?
(not drawn to scale)
4 in.
7 in.
2 in.
A 100 in
B 15 in
C 28 in
D 56 in
Helppp
Answers
Answer:
D - 56
Step-by-step explanation:
Multiply the height, 4 inches, the length, 7 inches, and the width, 2 inches, to get 56.
part 2 to previously asked question 100 points detailed answers please
Answers
HELP PLEASEEEEEEEEEEE
Answers
Answer:
c
Step-by-step explanation:
In the early Iberian Peninsula both
Muslims and existed.
A. Catholics
B. Christians
C. Jews
Answers
Answer:
jews
Step-by-step explanation:
Answer:
Christians.
Step-by-step explanation:
how do i figure this out?
Answers
Answer:
(y+2) / y
Step-by-step explanation:
Just do what is says f(x ) = (y+2) / y
help pls i have 7 of these question 100 points there is a part 2 to this question i will be making another one 100 points as well. detailed answers are appreciated
Answers
Answer:
[tex]y=x[/tex][tex]y=x-2[/tex][tex]y=2x+10[/tex][tex]y=5x[/tex][tex]y=x+21[/tex]Whenever finding a rule, figure out what x+1 relates to in terms of y (aka the slope). Also, figure out the y-intercept (0,y)
Example:
x+1 = y+2.
Slope: 2 ÷ 1 = 2.
The y-intercept is (0,9)
This would make the rule y=2x+9
Answer:
1. y=x 2. y=x-2 3. y=2x+10 4. y=5x 5. y= x+21
Step-by-step explanation:
When solving the equation 4 (3x2 + 2) - 9 = 8x2 + 7, Emily
wrote 4 (3x + 2) = 8x2 + 16 as her first step. Which
property justifies Emily's first step?
A addition property of equality
B commutative property of addition
multiplication property of equality
distributive property of multiplication over addition
A
Answers
Answer:
A
Step-by-step explanation:
In this example, Emily is adding 9 to both sides of the equation. Doing so keeps the equation equal since the operation was done to both sides, so this must be the addition property of equality.
I have 2 questions, What is the smallest power of ten that exceeds 89,876,230,128,970?
Question 1 options:
A. 10^11
B. 10^14
C. 10^15
D. 10^12 What is the smallest power of 10 that exceeds? 981 44/61
Question 2 options:
A. 10^3
B. 10^4
C. cannot be found
D. 10^-2
Answers
Answer:
Question 1: Option B
Question 2: Option A
Step-by-step explanation:
Question #1:
Options are:
10¹¹ = 100000000000
10¹⁴ = 100000000000000
10¹⁵ = 1000000000000000
10¹² = 1000000000000
The power that exceeds the given quantity would be:
10¹⁴ ⇒ There are more digits.
Question #2:
We have the following expression:
981 44/51 = 61*981+44/61 = 981.72
We have to 10³ = 1000
So, the correct option is 10³
please i need help as fast a possiable
Answers
Agree
-(-7) would be positive 7 which is what is plotted.
Also the other two numbers are also plotted
Answer:
Agree with all three
Step-by-step explanation:
The points displayed on the numberline are -2, 1, and 7. The points given to you are -(-7), 1, and -2. Because -(-7) = 7, and 1 = 1, and -2 = -2. All three numbers given are ineed plotted on the numberline below.
