Answer:
She'll have $661 in the account in 2022.
Step-by-step explanation:
Compound interest:
The amount of money earned in compound interest after t years is given by the following equation:
[tex]A(t) = A(0)(1+r)^t[/tex]
In which A(0) is the initial amount and r is the interest rate, as a decimal.
Rachael started off with $400. It earns 3% interest each year.
This means that [tex]A(0) = 400, r = 0.03[/tex]
So
[tex]A(t) = A(0)(1+r)^t[/tex]
[tex]A(t) = 400(1+0.03)^t[/tex]
[tex]A(t) = 400(1.03)^t[/tex]
She wants to know how much money she'll have in the account in 2022.
17 years after 2005, which means that this is A(17). So
[tex]A(17) = 400(1.03)^{17} = 661[/tex]
She'll have $661 in the account in 2022.
please help me if you know the answer
On a quiz you answer 7 out of 10 correctly. Did you reach your goal of getting
80% or better? *
Answer:
NO you only got 70 percent
Step-by-step explanation:
PLEASE HELP!!! use the pic to understand the question
Answer:
this is confusing. I'll try my best to sort it out for you. I'll tap in once I figure it out
find the y - intercept of the graph
Answer:
Step-by-step explanation:
yes that is correct!-2
A lighthouse is located on an island 33 miles from the closest point on a straight shoreline. If the lighthouse light rotates clockwise at a constant rate of 99 revolutions per minute, how fast does the beam of light move towards the point on the shore closest to the island when it is 5252 miles from that point
Question:
A lighthouse is located on an island 3 miles from the closest point on a straight shoreline. If the lighthouse light rotates clockwise at a constant rate of 9 revolutions per minute, how fast does the beam of light move towards the point on the shore closest to the island when it is 52 miles from that point
Answer:
The beam of light moves at [tex]16278\pi[/tex] miles/min
Step-by-step explanation:
This question is illustrated with the attached image
Taking the instructions in the question, one at a time.
A revolution of 9 per minute implies that:
[tex]\frac{d\theta}{dt} = \frac{9 * 2\pi\ rad}{1\ min}[/tex]
[tex]\frac{d\theta}{dt} = 18\pi \frac{rad}{min}[/tex]
Take tan of the angle in the attachment:
[tex]tan(\theta) =\frac{52}{3}[/tex]
Differentiate both sides with respect to time
[tex]\frac{d\ tan(\theta)}{dt} =\frac{52}{3} * \frac{dx}{dt}[/tex]
Rewrite as:
[tex]\frac{d\ tan(\theta)}{d\theta} * \frac{d\theta}{dt} =\frac{52}{3} * \frac{dx}{dt}[/tex]
In calculus:
[tex]sec^2(\theta) =\frac{d\ tan(\theta)}{d\theta}[/tex] -- Chain rule
So:
[tex]sec^2(\theta) *\frac{d\theta}{dt} =\frac{52}{3} * \frac{dx}{dt}[/tex]
In trigonometry:
[tex]sec^2(\theta) = tan^2(\theta) + 1[/tex]
So:
[tex](tan^2(\theta) + 1)\frac{d\theta}{dt} =\frac{52}{3} * \frac{dx}{dt}[/tex]
Recall that:
[tex]tan(\theta) =\frac{x}{3}[/tex]
[tex]((\frac{52}{3})^2 + 1)\frac{d\theta}{dt} =\frac{1}{3} * \frac{dx}{dt}[/tex]
[tex](\frac{52^2}{9} + 1)\frac{d\theta}{dt} =\frac{1}{3} * \frac{dx}{dt}[/tex]
[tex](\frac{2704}{9} + 1)\frac{d\theta}{dt} =\frac{1}{3} * \frac{dx}{dt}[/tex]
[tex](\frac{2704+9}{9})\frac{d\theta}{dt} =\frac{1}{3} * \frac{dx}{dt}[/tex]
[tex](\frac{2713}{9})\frac{d\theta}{dt} =\frac{1}{3} * \frac{dx}{dt}[/tex]
Recall that: [tex]\frac{d\theta}{dt} = 18\pi \frac{rad}{min}[/tex]
[tex](\frac{2713}{9}) * 18\pi =\frac{1}{3} * \frac{dx}{dt}[/tex]
[tex]2713 * 2\pi =\frac{1}{3} * \frac{dx}{dt}[/tex]
Multiply both sides by 3
[tex]3 * 2713 * 2\pi =\frac{1}{3} * \frac{dx}{dt} * 3[/tex]
[tex]3 * 2713 * 2\pi =\frac{dx}{dt}[/tex]
[tex]16278\pi =\frac{dx}{dt}[/tex]
[tex]\frac{dx}{dt} = 16278\pi[/tex] miles/min
Hence:
The beam of light moves at [tex]16278\pi[/tex] miles/min
Jason buys a plot of land that is 2/5 of an acre in size. Ava buys a
plot of land that is 2/8 of an acre in size. Whose plot of land is
smaller?
Answer:
Ava's
Step-by-step explanation:
To find whose plot of land is smaller, compare the sizes of their plots.
Jason's is 2/5 of an acre, while Ava's is 2/8 of an acre.
Because they have the same numerator, we can look at the denominator to see which is smaller.
The number with the larger denominator will be smaller. So, this means 2/8 is smaller than 2/5.
So, Ava's plot of land is smaller
What is the value of x
15x + 1=46
Help plz
I will give brainliest
Answer:
3
Step-by-step explanation:
Answer:
The answer to this question is X=3
Step-by-step explanation:
15x3=45
45+1=46
Hope my answer helps you!!!
True or false?is the point(16,4) included in this function: Y=2x or Y=x2 or y= x+12 or y=x-12
Answer:
True
Step-by-step explanation:
It is true because the graph of [tex]y=x-12[/tex] passes through the point [tex](16,4)[/tex]
x = 16
y = 4
Substitute
4 = 16 - 12
4 = 4
Therefore, the answer is true.
45 is what percentage of 150? A. 0.3% B. 3% C. 30% D. 35%
Answer:
C. 30%
Have a great day! Good luck.
Answer:
C. 30%
Step-by-step explanation:
All you have to do is 45/150 to get the answer. Simplify that and get 3/10 which is also equal to 30%.
Hope this helps you
subject : bible:
What two words summarize Romans 10:9-10?
sacrifice
work
believe
confess
justify
Answer:
confess and believe are the two main words.
Step-by-step explanation:
Just got this right :')
A parking lot in the shape of a trapezoid has an area of 126 square meters. The length of one base is 8 meters, and the length of the other base is 10 meters. What is the width of the parking lot?
Group of answer choices
7 meters
14 meters
10 meters
28 meters
Answer:
14
Step-by-step explanation:
126/9=14
does a trapezoid have exactly one pair of parallel sides always?
Please help I will give you brainliest
The school park has a circular pond with a radius of 4 yards. What is the pond's diameter?
Answer:
The diameter of the pond is 8.
Step-by-step explanation:
Diameter formula d = 2r
So d = [tex]2*4[/tex]
d = 8
Answer:
the answer is 8
Step-by-step explanation:
so 4r x 2=8d
or
2(4r)=8d
Explain the inequality -4 C > -9C describes how the temperatures are related
NO SPEAK ENGLISH SORRYYYY
The inequality explains the value of -4°C is greater than -9°C
What is inequality?It is known as inequality when both sides of a mathematical statement contain mathematical signs that are either less than or larger than one another.
It is given that,
-4°C > -9°C
We utilize the "Greater than or equal to" sign in linear inequalities when the value of a variable is greater than or equal to a certain value. The "greater than" symbol (>), which has a sleeping line beneath it, is used to denote it. It is represented by the character (≥).
Thus, the inequality explains the value of -4°C is greater than -9°C.
Learn more about inequality here:
brainly.com/question/19491153
#SPJ2
Let's assume our class is truly representative of the population at large. (a) Calculate the probability of having three right handed people in a sample of 10. Do this using R. (b) repeat, but this time calculate the probability of 3 or less right handed people in a sample of 10.n=17 right handed= 15 left handed=2
Answer:
0.1171875;
0.171875
Step-by-step explanation:
It is either a person is right handed or left handed
P(right handed) = 1/2
Probability of having 3 right handed people in a sample of 10 ;
P(x =x) = nCx * p^x * (1 - p)^(n - x)
P(x = 3) = 10C3 * 0.5^3 * 0.5^7
P(x = 3) = 120 * 0.125 * 0.0078125
P(x = 3) = 0.1171875
Using R ;
P(x ≤ 3)
We can obtain these from R using ;
pbinom( r, n, p)
pbinom(3, 10, 0.5) = 0.171875
The graph of a line and an exponential can intersect twice, once or not at all. Describe the possible number of intersections for each of following pairs of graphs. Your solution to each part should include all possibilities and a quickly sketched example of each one. Part 2; (SHOW WORK)
c. A parabola and a circle
d. A parabola and the hyperbola y = 1/x
Answer:
c) parabola and circle: 0, 1, 2, 3, 4 times
d) parabola and hyperbola: 1, 2, 3 times
Step-by-step explanation:
c. A parabola can miss a circle, be tangent to it in 1 or 2 places, intersect it 2 places and be tangent at a 3rd, or intersect in 4 places.
__
d. A parabola must intersect a hyperbola in at least one place, but cannot intersect in more than 3 places. If the parabola is tangent to the hyperbola, the number of intersections will be 2.
If the parabola or the hyperbola are "off-axis", then the number of intersections may be 0 or 4 as well. Those cases seem to be excluded in this problem statement.
5 more than a number m equals 8
Answer: m=3
Step-by-step explanation:
This could be written as m+5=8
You would then do the inverse to 'undo' the equation. So instead of adding 5 you would take away 5 from 8.
8-5=3
Hope this helps :)
if f(x)=5x-7,what isf(3)?
Answer:
Explanation:
f ( − 3 ) basically means substitute − 3 for x in the function − 5 x
f
(
−
3
)
=
−
5
(
−
3
)
−
7
f
(
−
3
)
=
15
−
7
f
(
−
3
)
=8
Step-by-step explanation:
Which statement about the area of a right triangle is true?
F :The area formula for a right triangle is the base times the height because a rectangle can be
divided into two right triangles.
G: The area formula for a right triangle is the base times the height because a right triangle
can be divided into two rectangles.
H: The area formula for a right triangle is one-half of the base times the height because a
rectangle can be divided into two right triangles.
J: The area formula for a right triangle is one-half of the base times the height because a right
triangle can be divided into two rectangles.
Answer:
H
Step-by-step explanation:
This is because a rectangle can be divided into two triangles.
what is 1 times 89what is 1 * 17
Answer:
1 times 89 = 89 lol 1 x 7= 7
Step-by-step explanation:
hope this helps lol
Identifica el cuadrante en el cual se encuentra el ángulo 2.200
Answer:your
Step-by-step explanation:
mom
1. How many times greater is the value of the 6 in 9,638 than the value of the 6 in 3,968?
(2 points)
Enter your answer
Answer:
100 times
Step-by-step explanation:
doesn't matter if the number is in the same place value so, the answer is 100 times.
Which choices are equivalent to the expression below? √-9
Answer:
Step-by-step explanation:
coach Emanuel is trying to lose weight. the stars 2017 weighing 296 pounds. if he plans to burn enough calories to lose 3 pounds per week, then how many weeks will pass before Couch Emanuel is at most 251 pounds
Thank you to whoever answers this :)
Answer:
13 weeks because he loses 3 pounds per week
Step-by-step explanation:
269-251=39
39 divided by 3 = 13
13 weeks is your answer!
please mark brainliest please!!!
Sammy counts the number of people in one section of the school auditorium. He counts 18 female students, 16 male students, and 6 teachers. There are720 people in the auditorium. Consider the probability of selecting one person at random from the auditorium.
Which of these statements are true? Choose all that apply.
I can't see the statements
PLEASE PLEASE PLEASE HELP ME!
Answer:
I dont see the question...
Step-by-step explanation:
20 PTS HELP PLEASE !!!!!!
The graph of linear function k passes through the points (-3, 0) and (1, 8).
Which statement must be true?
what’s the answer?
Answer:
-3,0
Step-by-step explanation:
What is 22/35 as a percent
Answer:
62.857142857143%
Step-by-step explanation: