Answer:
Michelle's age = 16
Step-by-step explanation:
As we know,
Amount = [tex]P (1 + r)^{t}[/tex] where
P = Principal amount
r = rate of interest
t = time
Given ,
P = $1000
r = 4.5 % = [tex]\frac{4.5}{100} = 0.045[/tex]
Now,
Given that Amount reaches more than $2000
⇒[tex]P (1 + r)^{t}[/tex] > 2000
⇒[tex]1000(1 + 0.045)^{t}[/tex] > 2000
⇒[tex](1.045)^{t}[/tex] > 2
Now,
we put the value of t from 0 , 1, 2, ..... untill the above equation does not satisfy
Now,
for t = 0
[tex](1.045)^{0} = 1 \ngeq 2[/tex]
for t = 1
[tex](1.045)^{1} = 1.045 \ngeq 2[/tex]
for t = 2
[tex](1.045)^{2} = 1.092 \ngeq 2[/tex]
for t = 3
[tex](1.045)^{3} = 1.14 \ngeq 2[/tex]
for t = 4
[tex](1.045)^{4} = 1.19 \ngeq 2[/tex]
for t = 5
[tex](1.045)^{5} = 1.25 \ngeq 2[/tex]
for t = 6
[tex](1.045)^{6} = 1.30 \ngeq 2[/tex]
for t = 7
[tex](1.045)^{7} = 1.36 \ngeq 2[/tex]
for t = 8
[tex](1.045)^{8} = 1.42 \ngeq 2[/tex]
for t = 9
[tex](1.045)^{9} = 1.48 \ngeq 2[/tex]
for t = 10
[tex](1.045)^{10} = 1.55 \ngeq 2[/tex]
for t = 11
[tex](1.045)^{11} = 1.62 \ngeq 2[/tex]
for t = 12
[tex](1.045)^{12} = 1.69 \ngeq 2[/tex]
for t = 13
[tex](1.045)^{13} = 1.77 \ngeq 2[/tex]
for t = 14
[tex](1.045)^{14} = 1.85 \ngeq 2[/tex]
for t = 15
[tex](1.045)^{15} = 1.93 \ngeq 2[/tex]
for t = 16
[tex](1.045)^{16} = 2.02 > 2[/tex]
It satisfies at t= 16
∴ we get
Michelle's age = 16
10 points !!
Which expression is equivalent to this polynomial x^2+12
Answer:
expand x^2+12 --> results in AUse the graph of the polynomial
function to find the factored form of
its related polynomial. Assume it
has no constant factor
Answer:
The factored form of the polynomial is [tex]y = (x-2)\cdot (x+1)[/tex].
Step-by-step explanation:
According to the graph, we have a second order polynomial with a vertical axis of symmetry. The standard form of the polynomial is:
[tex]y = a\cdot x^{2}+b\cdot x + c[/tex] (1)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Coefficients.
We can obtain the solution of the polynomial by knowing three distinct points. From graph we know that the curve pass through the following three points: [tex](x_{1},y_{1}) = (-1, 0)[/tex], [tex](x_{2},y_{2}) = (0, -2)[/tex], [tex](x_{3},y_{3}) = (2,0)[/tex]. Three linear equations are constructed:
[tex]a^{2}-b+c = 0[/tex] (2)
[tex]c = -2[/tex] (3)
[tex]4\cdot a + 2\cdot b + c = 0[/tex] (4)
The solution of this system is [tex]a = 1[/tex], [tex]b = -1[/tex] and [tex]c = -2[/tex]. Then, the polynomial in standard form is [tex]y = x^{2}-x-2[/tex]. By factorization, we find that factored form is:
[tex]y = (x-2)\cdot (x+1)[/tex] (5)
A wedding dress was marked up 35% and is now selling for $270.00. What was the original price of the dress?
Answer:
365.50 dollars
Step-by-step explanation:
multiply 270 by 35% then add that to 270
Help me please!! I don’t know what a quadratic graph is and need help answering this question! ASAP
Answer:
C
Step-by-step explanation:
2. A nutritionist wants to collect data on how much caffeine the average American drinks per day. She has the following ideas for how she could obtain a sample:
a. Ask the first 20 adults who arrive at a grocery store after 10:00 a.m. about the average amount of caffeine they consume each day.
b. Every 30 minutes, ask the first adult who comes into a coffee shop about the average amount of caffeine they consume each day.
Answer:
B
Step-by-step explanation:
If you start to ask after 10:00 am, a lot of people isn't drinking caffeine. And, were trying to figure out the average.
how many real sixth roots does 1 have
Answer:
Im pretty sure it's 2, but Im not sure
Step-by-step explanation:
please please help with equations
Answer:
Clara: y=40x+ 50 Hector: y=35x+100To cost the same we need to set the equations equal to each other 40x+50=35x+1005x=50 --> x= 10hours I do exams and quizzes if your interested!The radius of a circle is 2 millimeters. What is the circle's area?
r=2 mm
Use 3.14 for .
sanare millin
Answer:
12.56 mm²
Step-by-step explanation:
[tex]A=\pi r^{2}[/tex]
Plug the given values into the area equation
[tex]A=3.14*2^{2}\\A=3.14*4\\A=12.56[/tex]
Therefore, the area of the circle is 12.56 mm².
I hope this helps!
find the missing side length of similar polygons
Answer:
23
Step-by-step explanation:
What is the measure of ∠XYZ? show your work
Answer:
i don't know..........,......
Which of the following equations represent exponential growth functions? Choose all that apply.
a) f (x)=4^x
b) f (x)=(1/4)^-x
c) f (x)=(2/3)^x
d) f (x)= (2.3)^x
e) f (x)=(.8)^x
Option:-
a) f(x) = 4^x is applicable
b) f(x) ={ (1/4)^-x = 4^x }is applicable
c.) f(x) = (2/3)^x is not applicable
d.) f(x) = (2.3)^x is applicable
e.) f(x) = (.8)^x is not applicable
Options (a), (b) and (d) are exponential growth functions.
What is Exponential function?An exponential decay is in the form:
y = abˣ
where y, x are variables, a is the initial value of y and b is the multiplier which is less than 1.
By the Exponential decay form,
An exponential decay is in the form: y = abˣ
(a) f (x)=4ˣ is applicable as 4>1
(b) f (x)=(1/4)⁻ˣ is applicable as (1/4)-1=4>1
(c) f (x)=(2/3)ˣ is not applicable because 2/3<1
d) f (x)= (2.3)ˣ is applicable as 2.3>1
e) f (x)=(.8)ˣ is not applicable, 0.8<1.
So options (a), (b) and (d) are applicable for exponential growth functions.
To learn more on exponential functions click:
https://brainly.com/question/15352175
#SPJ2
An Olympic runner set a record for the 100m event. The time was ten and sixty two hundredths seconds. Express the decimal form of the given time
please help me
Find the value of x *
A) 20
B) 10
C) 15
D) 25
Answer:
B. 10
Step-by-step explanation:
While doing construction O and P are joined then
OQ = OR
<QOR = 80°
<QPR = <QOR /2 ( INSCRIBED ANGLE IS HALF OF THE CENTRAL ANGLE STANDING ON SAME ARC)
<QPR = 80°/2
<QPR = 40°
SO
< QPO = X
<RPO = 30°
<QPO + <RPO = < QPR
X + 30° = 40°
X = 40° - 30°
X = 10°
hope it helps
In ΔMNO, n = 92 inches, ∠N=119° and ∠O=20°. Find the length of m, to the nearest 10th of an inch.
Answer:
Step-by-step explanation:
The length of the side of the triangle will be 69 inches.
What is the sine law?The Law of Sines The law of trigonometric functions, sine law, sine formula, or sinusoidal rule is a trigonometric equation that relates the sizes of any triangle's edges to the sines of its orientations.
The sine law in the triangle ΔMNO is given as,
n / sin N = m / sin M = o / sin O
The third angle is calculated as,
∠M + ∠N + ∠O = 180°
∠M + 119° + 20° = 180°
∠M = 41°
The length m is calculated as,
n / sin N = m / sin M
92 / sin 119° = m / sin 41°
m = 69 inches
The length of the side of the triangle will be 69 inches.
More about the sine law link is given below.
https://brainly.com/question/17289163
#SPJ3
Write the Linear Equation (y=mx+b) from the following table:
Answer:
y=3x+2
Step-by-step explanation:
y2 - y1 / x2 - x1
17-11 / 5-3 = 6/2 = 3
m = 3
17 = 3(5) + b
17 = 15 + b
b = 2
(please correct me if i did this wrong)
Mario is constructing a wall around a rectangular area which will cover a maximum of 60 square feet. The length of the wall will be 10
feet.
Which inequality represents all the possible widths in feet, w, that Mario can use to construct the rectangular
wall?

Answer:
[tex]W \le 6[/tex]
Step-by-step explanation:
Given
[tex]Area = 60ft^2\ (max)[/tex]
[tex]Length = 10ft[/tex]
Required
Represent the width as an inequality
First, we represent the area as an inequality.
[tex]Area = 60ft^2\ (max)[/tex]
max as used above means less than or equal to.
So, we have:
[tex]Area \le 60[/tex]
The area of a rectangle is:
[tex]Area = L * W[/tex]
So, we have:
[tex]L * W \le 60[/tex]
Substitute 10 for L
[tex]10 * W \le 60[/tex]
Divide both sides by 10
[tex]\frac{10 * W}{10} \le \frac{60}{10}[/tex]
[tex]W \le \frac{60}{10}[/tex]
[tex]W \le 6[/tex]
Rachel loves to read. Her favorite books are Dr Suess. For every 13 books Rachel owns 8 are Dr Suess books.
If Rachel had 32 Dr Suess books, how many books did she have in total?
Answer:
32
Step-by-step explanation:
graph the image of V (3,–7) after a rotation 180° clockwise around the origin.
Answer and Step-by-step explanation:
It is in the screenshot.
The point is (-3, 7), and would be noted as V'.
#teamtrees #WAP (Water And Plant)
Image of the point V is V' = (-3, 7) as shown in the graph below.
What is Coordinate Geometry?One of the most intriguing ideas in mathematics is called coordinate geometry. By using graphs with curves and lines, coordinate geometry (also known as the analytic geometry) explains how geometry and algebra are related. They can answer geometrical problems because it gives them geometrical aspects of algebra. In this area of geometry, a pair of ordered numbers is used to describe the location of points on a plane.
As per the given data:
Coordinates of point V = (3, -7)
Rotation to be given = 180° (clockwise)
For drawing the image of point V (3, -7):
Step 1: Draw a line passing through the origin and V (3, -7) extending through 2nd and 4th quadrant.
Step 2: Change sign of x and y coordinates as rotation is of 180° and mark the point in the 2nd quadrant.
Image of the point V is V' = (-3, 7) as shown in the graph below.
Hence, the image of the point V is V' = (-3, 7).
To learn more about Coordinate Geometry, click:
brainly.com/question/7869125
#SPJ2
A family purchased tickets to a museum and spent a total of $45.00. The family purchased 5 tickets. There was $1.50 processing fee for each ticket. What is the cost of one ticket without the processing fee?
Which lines in the diagram must be parallel?
(not drawn to scale)
514
1337
47°
q
S
Answer
47
Step-by-step explanation:
Leroy borrowed $1500 at an annual simple interest rate of 12%. He paid $270 in interest. For what time period did Leroy borrow the money? Remember, your answer will be in years!
Step-by-step explanation:
well..this is the answer..using..time formula
4x – y = 7 3y – 12x = –21
Answer:
y=4x-7 3(4x-7)-21x=-21 12x-21-12x=-21 -21=-21
Step-by-step explanation:
Graph the line with the given slope that passes through the given point
Slope=2;(-1,4)
Answer:
BStep-by-step explanation:
Point (-1, 4) it's point where x-coordinate is -1 and y-coordinate is 4
Graph in B is the only one passing through (-1, 4)
The equation of the line is y = 2x + 6. The graph is represented by B.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given that the slope of the line is 2 and the point through which it is passing is (-1,4).
The equation of the line will be calculated as,
y = mx + c
y = 2x + c
4 = -2 + c
c = 6
The equation will be written as,
y =2x + 6
The graph of the line is attached with the answer below.
To know more about an equation of the line follow
https://brainly.com/question/18831322
#SPJ5
when is season 3 of Jurassic Park camp Crutasus coming out TELL ME THE REAL ANSWER
Jurassic Park: Camp Cretaceous season 3 is planned to release anywhere from September to October of 2021.
Answer:
It depeands on where you live but it should be out in America on January 30, 2021
Step-by-step explanation:
Which expression is equivalent to 8(7m - 9p)?
Answer:
8(7m-9p) = 8(7m) - 8(9p)
= 56m - 72p
Let me know if this helps!
Answer:
56m-72p
Step-by-step explanation:
8(7m-9p) = 8*7p + 8*-9p = 56m-72p
solve the following equation
Which is the graph of y= -x-3?
Answer:
Graph a
Step-by-step explanation:
Answer:
the answer is A
Step-by-step explanation:
to start, I would use the slope intercept, in this case -3 which lets you know the slope meets the y axis at (0,-3) since you have that point, you count with the slope.
now slope is rise over run, therefore, it would be y over x and since the y in this case is 3, you'd go up three from your point. since x is 4, you'd go right four units from where you are. since A is the only graph that follows that, A would be correct.
what is the equation of the vertical line through (2, 3) hurry! 40 points
Step-by-step explanation: The equation of a vertical line can always be written as x = the x-coordinate of the given point.
So in this case, our equation is x = 2.
In the equation below, what value of bresults in an
equation with infinitely many solutions?
3(bx - 1) = -3 + 12x
Step-by-step explanation:
3bx-3 = -3+12x
3bx=-3+3+12x
3bx=12x
3bx/3=12x/3
bx=4x
bx/x=4x/x
b=4
HELP DUE IN 15 mins need help ASAP please!!!!!
idek but imma ask mah mate who's a maths genius or whateva to help out ig