Jack has a saving account of value $65,550 at the start. The saving account has an interest rate of 3% that is compounded every six months. How long will it take Jack to have $100,000 in his account?
Given:
Principal value = $65,550
Rate of interest = 3% compounded every six month
To find:
The taken to have $100,000 in Jack's account.
Solution:
The formula for amount is
[tex]A=P(1+\dfrac{r}{n})^{nt}[/tex]
where, P is principal, r is rate of interest, n is number of times interest compounded in an year, t is time in number of years.
Interest compounded every six month. It means, interest compounded 2 times in an year.
Substitute A=100000, r=0.03 and n=2 in the above formula.
[tex]100000=65550(1+\dfrac{0.03}{2})^{2t}[/tex]
[tex]\dfrac{100000}{65550}=(1+0.015)^{2t}[/tex]
[tex]1.525553=(1.015)^{2t}[/tex]
Taking log on both sides.
[tex]\log (1.525553)=\log (1.015)^{2t}[/tex]
[tex]\log (1.525553)=2t\log (1.015)[/tex]
[tex]\dfrac{\log (1.525553)}{2\log (1.015)}=t[/tex]
[tex]t=14.1838928[/tex]
[tex]t\approx 14.18[/tex]
Therefore, after 14.18 year the amount will reach at $100,000 or we can say that in 15th year the amount will reach at $100,000.
Homer is 30 feet below sea level and Marge is 45 feet above sea level. Bart’s elevation is at the exact midpoint of those two values. What is the expression that model this problem, and which is Bart’s elevation?
Answer:
14.5 feet
Step-by-step explanation:
the midpoint is halfway from 30 to 45 so be(bart elevation) b.e = 45 - 30 / 2
7.5 m above sea level
__________________________________________________________
Step-by-step explanation:We are given:
The elevation of Homer = -30 feet [30 feet below sea level]
The elevation of Marge = +45 feet [45 feet above sea level]
The elevation of Bart is at the exact mid-point of the elevations of Homer and Marge
The elevation of Bart:
We are given that the elevation of Bart is at the exact mid-point of the elevations of Homer and Marge
So, Half the distance between the elevation of Homer and Marge is the elevation of Bart
Elevation of Bart (with respect to the elevation of Homer) =
(elevation of Marge - Elevation of Homer) / 2
replacing the variables with the suitable values:
(+45 - (-30))/2
(45 + 30) / 2
75 / 2
Elevation of Bart (w.r.t. Homer) = 37.5 feet
Since this is the elevation of Bart with respect to Homer, we can say that Bart is 37.5 m above Homer
So, we can say that:
Elevation of Bart (w.r.t Homer) = Elevation of Bart - Elevation of Homer
replacing the values
37.5 = Elevation of Bart -(-30)
37.5 = Elevation of Bart + 30
Elevation of Bart = 7.5 m above sea level [subtracting 30 from both sides]
What is 48 square feet in square meters
Answer: 4.45935
Step-by-step explanation: 1 Square foot (sqft) is equal to 0.09290304 square meter (sqm). For example, to convert 100 square feet to square meters, multiply 100 by 0.09290304, that makes 9.290304 sqm is 100 sqft. Hope this helps.
What is an equation of the line that passes through the points (0, -2) and (-5, 4)?
Put your answer in fully reduced form.
Answer:
I have no idea
Step-by-step explanation:
Answer: y= -6/5x-2
Step-by-step explanation:
That’s wut it said
This table shows a linear relationship. x 5 6 7 8 9 y 33 39 45 51 57 Based on the information in this table, which equation can be used to model the relationship between x and y? A y = 3x + 6 B y = 6x + 3 C y = 3x D y = 6x
Answer:
B. y = 6x + 3Step-by-step explanation:
Given
x = {5, 6, 7, 8, 9} andy = {33, 39, 45, 51, 57}The equation in slope- intercept form:
y = mx + bUsing two pairs of coordinates (5, 33), (6, 39), we will find the slope:
m = (39 - 33)/(6 - 5) = 6/1 = 6Using one point (5, 33) to find the y-intercept:
33 = 6*5 + b ⇒ b = 33 - 30 ⇒ b = 3The equation is:
y = 6x + 3Correct option is B
is -3/4 rational or irrational?
is the square root of 2 rational or irrational?
is 2π rational or irrational?
is 3.75 rational or irrational?
is 2 1/8 rational or irrational?
Find the distance of a line given the following points. R(3, 1), W(-1, -2)
Answer:
[tex]\sqrt{13}[/tex]
Step-by-step explanation:
we can solve this using the distance formula: [tex]\sqrt{(x_{2}-x_1)^{2} + (y_{2}-y_1)^{2}}[/tex]
[tex]x_1, y_1[/tex] is (3, 1)
[tex]x_2, y_2[/tex] is (-1, -2)
[tex]\sqrt{(1-3)^2 + (-2-1)^2}[/tex]
which simplifies to: [tex]\sqrt{(-2)^2 + (-3)^2}[/tex]
then: [tex]\sqrt{2^2 + 3^2}[/tex] or: [tex]\sqrt{4+9}[/tex]
your final answer is: [tex]\sqrt{13}[/tex] or about 3.61
Write an equation in slope intercept form and in standard form for the line passing through (4,9) and perpendicular to x=-6
Answer:
Input work is the work done on a machine as the input force acts through the input distance. This is in contrast to output work which is a force that is applied by the body or system to something else. Output work is the work done by a machine as the output force acts through the output distance.Jan 15, 2020 hwgsvsd d jxvsd
dvsud sgsgs hsysvdudbd dvyd dhsgtsjd vsytwgsud gsyfwuyebdbhys. dusgcejd b
What is an equation of the line that passes through the points (4,1) and (8,-3)?
PLZZ HELPP MEE!!
Answer:
y=-x+5
Step-by-step explanation:
(4,1)
(8,-3)
1)a slope of a line is (y2-y1)/(x2-x1)
so (-3-1)/(8-4)
-4/4=>m=-1
2)to find y-int replace any points in the equation by x and y
so 1=-1(4)+b
1=-4+b
1+4=b
so b= 5
therefore the equation is y=-x+5 so d
⚠️⚠️⚠️⚠️NEED HELP MARKING PEOPLE AS BRAINLIST!
I believe its a reflection
Sorry if im wrong
Simplify each term. please help!! 30 points + brainliest :)
1. -(-3y)³
2. (2c)⁵
3. (-2m)⁴
4. (4g)³
5. (7j)²
6. (-5z)⁵
Answer:
1. 27y^3
2. 32c^5
3. 16m^4
4. 64g^3
5. 49j^2
6. -3125z^5
Step-by-step explanation:
Can you help answer my question too, please?
I have $100 and I want to buy tshirt that cost $10 and sweatshirts that cost $20 how many tshirts and sweatshirts can I buy
Answer:
10 tshirts or 5 sweatshirts
Step-by-step explanation:
One t-shirt + one sweatshirt = $30.
We know that $100 ÷ $30 = 3 times with $10 left over.
This leads to the conclusion that you can buy 4 t-shirts and 3 sweatshirts.
Find the value of K. The diagram is not to scale. Explain your answer.
Answer:
639 lo hago para conseguir puntos ;V
Step-by-step explanation:
When rounded to the nearest thousands an elephant weight is 5,000 pounds. What is the least amount the elephant could weigh? I need step by step instructions please.
Answer:
Step-by-step explanation:
It depends on what you have been told about rounding when a 5 is involved.
If you can round if the answer is 4500, then that would be your answer. If you have some complicated method of dealing with the 5 (involving odd or even numbers) the elephant's minimum weight will be different.
I would go with 4500.
Sarah has saved 254 pound coins. She puts the pound coins into bags.
There are 20 pound coins in each full bag of coins. Sarah is going to take all her full bags of coins to the bank.
She can only take up to 5 full bags of coins to the bank each day.
Sarah wants to go to the bank on as few days as possible.
On how many days will Sarah need to go to the bank?
Answer:
Step-by-step explanation:
So for the fewest days it would be 3 days. The reason for that is because she has 254 pound coins. And she can inly take 5 bags to the bank a day, all of those 5 bags have 100 pound coins in them. If she take 2 days and get 200 pound coins to the bank. Then on the third day she would only have to bring three bags. So your answer for the fewest days possible is three days!
Hope it helps
A pharmacologist measured the concentration of dopamine in the brains of several rats. The mean concentration was 1,269 ng/gm and the standard deviation was 145 ng/gm.4 What was the standard error of the mean if:_______.(a) 8 rats were measured?
(b) 30 rats were measured?
Answer:
51.265242 ng/gm ; 26.473257 ng/gm
Step-by-step explanation:
The standard error of the mean = standard deviation / √sample size
Given that:
mean concentration = 1,269 ng/gm
Standard deviation (s) = 145 ng/gm
Standard Error if 8 rats were measured :
Sample size (n) = 8
Standard Error = s / √n
Standard Error = 145 / √8
Standard Error = 145 / 2.8284271
Standard Error = 51.265242 ng/gm
If 30 rats were measured :
Standard Error = 145 / √30
Standard Error = 145 / 5.4772255
Standard Error = 26.473257 ng/gm
In how many ways can you arrange the books A, B, C, and D on a bookshelf if books A and C must remain neighboring?
p=3y/q solve for y make sure to add steps pls
Answer:
Solving for y gives:
[tex]y = \frac{pq}{3}[/tex]
Step-by-step explanation:
Linear equations are the equations that are degree one equations. When it is asked to solve an equation for a specific variable that means that the specified variable has to be isolated on one side of the equation i.e. in the given question solving for y means isolating y on one side of the equation.
Given equation is:
[tex]p = \frac{3y}{q}[/tex]
Multiplication property of equality(Multiplying both sides by q)
[tex]p*q = \frac{3y}{q} * q\\pq = 3y[/tex]
Division property of equality(Dividing both sides by 3)
[tex]\frac{pq}{3} = \frac{3y}{3}\\\frac{pq}{3} = y[/tex]
Hence,
Solving for y gives:
[tex]y = \frac{pq}{3}[/tex]
A.4
B.3
C.6
D.5........ please help
Answer:
The answer is
A. 4
Step-by-step explanation:
A 3 m - 3 B 3 m + -5 C m + 1 D 3 m + 13
Answer:
It's A
Step-by-step explanation:
help please!!!!! (QUESTION #3)!!!!!!!
Una parte de 25 000 dólares se invierte al 10% de interés, otra parte al 12 % y el resto al 16%. El ingreso anual total de las tres inversiones es de 3200 dólares. Además, el ingreso de la inversión al 16% es igual al ingreso de las otras dos inversiones combinadas. ¿Cuánto se invirtió a cada tasa de interés?
Answer:
$5000 at 10%, $10000 at 12% and 10000 at 16%Step-by-step explanation:
One part of $ 25,000 is invested at 10% interest, another part at 12%, and the rest at 16%. The total annual income from the three investments is $ 3,200. Also, the income from the investment at 16% is equal to the income from the other two investments combined. How much was invested at each interest rate?==================
Let the parts be x, y and z
As per given we get below system of equations:
x + y + z = 250000.1x + 0.12y + 0.16z = 32000.1x + 0.2y = 0.16zSubstitute 0.1x + 0.2y in the second equation:
0.16z + 0.16z = 32000.32z = 3200z = 3200/0.32z = 10000Now we have:
x + y + 10000 = 25000 ⇒ x + y = 15000and
0.1x + 0.12y + 0.16*10000 = 3200 ⇒ 0.1x + 0.12y = 1600Multiply the second equation and then subtract the first one:
10(0.1x + 0.12y) = 10(1600) ⇒ x + 1.2y = 16000x + 1.2y - (x + y) = 16000 - 150000.2y = 1000y = 10000Then
x = 15000 - 10000 = 5000So the parts are:
$5000 at 10%, $10000 at 12% and 10000 at 16%I NEED HELP! Please.
Answer:
z = 12
Step-by-step explanation:
Answer:
Step-by-step explanation:
4z - 4 = 3z + 8
z = 12
Write a like term to: -5y
Answer:
-7y
Step-by-step explanation:
As long as the variable and exponent is the same, they are like terms
Answer: 68y
There are infinitely many ways to answer this. All you need to do is pick your favorite number and then stick y at the end of it. The terms -5y and 68y are like terms because they have the same variable attached.
You can think of 68y-5y as having 68 yoyos and then subtracting off 5 yoyos to get 63 yoyos when all is said and done. In terms of algebra, we would write 68y-5y = 63y.
the ratio 60 miles per hour is an example of a because it has two measurements having different units of measure
Answer:
180
Step-by-step explanation:
Answer: ejejejwjfmfmdnc
Step-by-step explanation:
PLS HELP ME FAST WILL GIVE POINTS
Triangle PQR is transformed to triangle P′Q′R′. Triangle PQR has vertices P(9, 0), Q(6, 3), and R(−3, −6). Triangle P′Q′R′ has vertices P′(3, 0), Q′(2, 1), and R′(−1, −2). Plot triangles PQR and P′Q′R′ on your own coordinate grid.
Part A: What is the scale factor of the dilation that transforms triangle PQR to triangle P′Q′R′? Explain your answer. (4 points)
Part B: Write the coordinates of triangle P′′Q′′R′′ obtained after P′Q′R′ is reflected about the y-axis. (4 points)
Part C: Are the two triangles PQR and P′'Q′'R′' congruent? Explain your answer. (2 points)
Answer:
The scale factor of the dilation that transforms the triangle is 1/3
Step-by-step explanation:
9x1/3 is 3. 6x1/3 is 2, etc.
Which of the restricted domains will produce an inverse function for tangent ?
X=-pi, x= pi
X=-pi/2, x=pi/2
X=0, x=pi/2
X=0, x=2pi
Answer: B) x=-pi/2 , x=pi/2
Step-by-step explanation:
Just did it!
Answer:
B
Step-by-step explanation:
Edge 2020
Which equation represents a linear function?
Group of answer choices
y – 5 = x(–x + 2)
y – 5 = x – 20
y(x – 1) = 9
y(y – 1) = x + 25
help pls
What is the solution to this system of equations?
x = 12 − y
2x + 3y = 29
Answer:
Step-by-step explanation:
Megan makes and sell slime online.
Answer:
44 containers