Answers
Problem 1
a = 2500 = starting amount
b = 1 + r = 1 + 0.035 = 1.035 = growth factor
The equation is [tex]y = 2500*1.035^x[/tex] as it is in the form [tex]y = a*b^x[/tex]
Plug in y = 5000 and solve for x.
[tex]y = 2500*1.035^x\\\\5000 = 2500*1.035^x\\\\1.035^x = 5000/2500\\\\1.035^x = 2\\\\\log(1.035^x) = \log(2)\\\\x\log(1.035) = \log(2)\\\\x = \log(2)/\log(1.035)\\\\x \approx 20.148792\\\\x \approx 21\\\\[/tex]
I rounded up to get over the hurdle. This is because plugging x = 20 will lead to y being smaller than $5000, so we must use x = 21.
Answers:The function is [tex]y = 2500*1.035^x[/tex]It takes about 21 years to reach $5000=========================================================
Problem 2
a = 4.22 = starting amount
b = 1 + r = 1 + 0.031 = 1.031 = growth factor
The equation goes from [tex]y = a*b^x[/tex] to [tex]y = 4.22*1.031^x[/tex]
Plug in y = 9.33 and solve for x.
[tex]y = 4.22*1.031^x\\\\9.33 = 4.22*1.031^x\\\\1.031^x = 9.33/4.22\\\\1.031^x \approx 2.21090047393365\\\\\log(1.031^x) \approx \log(2.21090047393365)\\\\x\log(1.031) \approx \log(2.21090047393365)\\\\x \approx \log(2.21090047393365)/\log(1.031)\\\\x \approx 25.9882262216245\\\\x \approx 26\\\\[/tex]
Answers:The function is [tex]y = 4.22*1.031^x[/tex]It takes about 26 years for the ticket to reach the price of $9.33=========================================================
Problem 3
a = 400 = initial value
b = 1 + r = 1 + 0.25 = 1.25 = growth factor
The template [tex]y = a*b^x[/tex] updates to [tex]y = 400*1.25^x[/tex]
Plug in y = 3000 and isolate x.
[tex]y = 400*1.25^x\\\\3000 = 400*1.25^x\\\\1.25^x = 3000/400\\\\1.25^x = 7.5\\\\\log(1.25^x) = \log(7.5)\\\\x\log(1.25) = \log(7.5)\\\\x = \log(7.5)/\log(1.25)\\\\x \approx 9.029627\\\\x \approx 10\\\\[/tex]
Like with the first problem, I rounded up to the nearest whole number. If you tried out x = 9, then y = 2980 approximately which is short of the goal of 3000. Trying x = 10 leads to y = 3725 approximately, which is now over the goal we're after.
Answers:The function is [tex]y = 400*1.25^x[/tex]It takes about 10 days for 3000 people to get infected.[tex]\\ \rm\Rrightarrow P=P_o(1+r)^t[/tex]
[tex]\\ \rm\Rrightarrow 5000=2500(1+0.035)^t[/tex]
[tex]\\ \rm\Rrightarrow 2=1.035^t[/tex]
[tex]\\ \rm\Rrightarrow log2=log1.035^t[/tex]
[tex]\\ \rm\Rrightarrow log2=tlog1.035[/tex]
[tex]\\ \rm\Rrightarrow t=\dfrac{log2}{log1.035}[/tex]
[tex]\\ \rm\Rrightarrow t=20.15[/tex]
We can't take 20 as it can cause depict in price .
So t=21years#2
[tex]\\ \rm\Rrightarrow 9.33=4.22(1+0.031)^t[/tex]
[tex]\\ \rm\Rrightarrow 9.33=4.22(1.031)^t[/tex]
[tex]\\ \rm\Rrightarrow 1.031^t=2.21[/tex]
[tex]\\ \rm\Rrightarrow log1.031^t=log2.21[/tex]
[tex]\\ \rm\Rrightarrow tlog1.031=log2.21[/tex]
[tex]\\ \rm\Rrightarrow t=\dfrac{log2.21}{log1.031}[/tex]
[tex]\\ \rm\Rrightarrow t=25.97\approx 26[/tex]
#3
[tex]\\ \rm\Rrightarrow 3000=400(1+0.25)^t[/tex]
[tex]\\ \rm\Rrightarrow 30/4=1.25^t[/tex]
[tex]\\ \rm\Rrightarrow 7.5=1.25^t[/tex]
[tex]\\ \rm\Rrightarrow log7.5=log1.25^t[/tex]
[tex]\\ \rm\Rrightarrow log7.5=tlog1.25[/tex]
[tex]\\ \rm\Rrightarrow t=\dfrac{log7.5}{log1.25}[/tex]
[tex]\\ \rm\Rrightarrow t=9.03[/tex]
Same like first case
t=10Related Questions
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
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
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%
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
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!
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
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
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
ASAP!!! Find the surface area of this net.
Answers
Answer:
240 cm
Step-by-step explanation:
18*12= 216
+
4*3*2= 24
216*24= 240
Find the vertex, axis of symmetry, and y-intercept of the quadratic function.
Answers
Answer:
Below in bold.
Step-by-step explanation:
f(x) = 1/2x^2 + 4x
Convert to vertex form:
f(x) = 1/2(x^2 + 8x)
= 1/2 [(x + 4)^2 - 16]
= 1/2(x + 4)^2 - 8 <------ Vertex form.
So the Vertex is at (-4, - 8).
Axis of symmetry is x = -4.
y -intercept (when x = 0) = 8-8 = 0.
Answer:
see explanation
Step-by-step explanation:
given a quadratic function in standard form
f(x) = ax² + bx + c ( a ≠ 0 ) , then
the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
f(x) = [tex]\frac{1}{2}[/tex] x² + 4x ← is in standard form
with a = [tex]\frac{1}{2}[/tex] , b = 4 , c = 0 , then
[tex]x_{vertex}[/tex] = - [tex]\frac{4}{1}[/tex] = - 4
substitute x = - 4 into f(x) for corresponding y- coordinate of vertex
f(- 4) = [tex]\frac{1}{2}[/tex] (- 4)² + 4(- 4) = [tex]\frac{1}{2}[/tex] × 16 - 16 = 8 - 16 = - 8
vertex = (- 4, - 8 )
the equation of the axis of symmetry is a vertical line passing through the vertex with equation
x = c ( c is the x- coordinate of the vertex ) , then equation of axis of symmetry is
x = - 4
to find the y- intercept substitute x = 0 into f(x)
f(0) = [tex]\frac{1}{2}[/tex] (0)² + 4(0) = 0 + 0 = 0
then y- intercept is 0
Make q subject of the formula 2(q+p) = 1+5q
Answers
Answer:
expand the equation
then make q the subject of the formal
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
Luis is going to purchase a new iPhone with a
case. He is looking at the iPhone 4, 4s and 5,
with an otterbox in either black, blue, or camo.
What are all of the different choices he has?
Answers
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:
what is the definition of accounting equation
Answers
Answer:
The accounting equation is a formula that shows the sum of a company’s liabilities and shareholders’ equity are equal to its total assets (Assets = Liabilities + Equity). The clear-cut relationship between a company’s liabilities, assets and equity are the backbone to double-entry bookkeeping. The source of a company’s accounting equation numbers is its balance sheet. Equity can be Shareholders’ Equity, Stockholders’ Equity, or Owner’s Equity.
Like other equations, if two terms of the basic accounting equation are known, you can solve for the third term. For example, Total Assets – Total Liabilities = Total Equity, or Total Assets – Total Equity = Total Liabilities. You move a term from the right side to the left side of the accounting equation by using a minus sign.
Names meaning the same as Balance Sheet are Statement of Financial Position or Statement of Financial Condition.
A restaurant surveys customers with the following results: 8 pizzas, 12 hamburgers, 14 pastas, and 6 steaks. What is the experimental probability of pizza?
Answers
Answer:
20%
Step-by-step explanation:
8 -> pizzas
12 -> hamburgers
14 -> pastas
6 -> steaks
40 = 8 + 12 + 14 + 6 -> total dishes
so the probability become from actual cases on total cases
so (8 / 40)
8/40 = 1/5 = 20/100 = 20%
linda recorded the number of minutes she practiced playing her violin for 10 days. The table shown represents the data she collected.
According to the data, what is the average amount of time Linda spent practicing per day?
Answers
Answer:
29.3
Step-by-step explanation:
its avarage just add everthink and : to 10
part 2 to previously asked question 100 points detailed answers please
Answers
#1 Calculate the Area: 11m 8m 5m
Answers
Answer:
24
Step-by-step explanation:
you have to add them
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]
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.
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.
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.
Pls ingore all of the questions below, but help me with the attached image
What is the only number that has the same number of letters as it's meaning? ...
What number doesn't have its own Roman numeral? ...
What is the only even prime number? ...
What is the smallest perfect number? ...
What is our current numerical system based on? ...
Is Pi a rational or irrational number?
Answers
Answer:
v=44
w=68
Step-by-step explanation:
in the diagram above K and I are equal therefore the angles are going to be the same that is why w = 68
for v
since we know two angles out of the three we will equate everything inside the triangle to 180° because that is the sum of angle on a triangle
v+68+68=180( sum of angle in a triangle)
v+136=180
subtract 136 from both sides
v= 44
Pls help me!!!!!!!!!!!
Answers
Answer:
x=55 degrees
Step-by-step explanation:
Because triangle is 180 degrees,
35+90+y=180
y=55
Answer:
x = 55 degrees
Step-by-step explanation:
The angles in a triangle add up to 180 degrees. We are already given 2/3 of the angles that make up the triangle.
The two given angles are 35 degrees and 90 degrees (we got the ninty from the right angle)
We can add these given angles together and subtract them by 180 to find the measure of the missing angle:
35 + 90 = 125
180 - 125 = 55 degrees
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.
HELP PLEASEEEEEEEEEEE
Answers
Answer:
c
Step-by-step explanation:
The youngest child in a family is 6 years old. The oldest
parent is 35 years old. What is the range of ages in.
the family?
Answers
Work Shown:
Range = Max - Min
Range = Oldest - Youngest
Range = 35 - 6
Range = 29
The range of 29 is the gap between the youngest person and the oldest.
