Answers
Answer:
Part B:
5) She will have $4445.244256 in 3 years
Part C:
1) She will have $8081.130039 in 10 years
2) He will have $13360.55059 in 8 years
Step-by-step explanation:
The formula of the compound interest is A = P [tex](1+\frac{r}{n})^{nt}[/tex], where
A is the new valueP is the initial amountr is the rate in decimaln is the number of the periodt is the time in yearsPart B:
5)
∵ P = $4250
∵ r = 1.5% = 1.5 ÷ 100 = 0.015
∵ n = 4 ⇒ Compounded quartly
∵ t = 3 years
→ Substitute them in the formula above
∴ A = 4250 [tex](1+\frac{0.015}{4})^{4(3)}[/tex]
∴ A = 4250 [tex](1.00375)^{12}[/tex]
∴ A = 4445.244256
∴ She will have $4445.244256 in 3 years
Part C:
1)
∵ Grace deposits $6000
∴ P = 6000
∵ The account is compounded semi-annually at 3%
∴ r = 3% = 3 ÷ 100 = 0.03
∴ n = 2 ⇒ compounded semi-annually
∵ The time is 10 years
∴ t = 10
→ Substitute them in the formula above
∴ A = 6000 [tex](1+\frac{0.03}{2})^{2(10)}[/tex]
∴ A = 6000 [tex](1.015)^{20}[/tex]
∴ A = 8081.130039
∴ She will have $8081.130039 in 10 years
2)
∵ Danial opens an account that is compounded semi-annually at 5%
∴ r = 5% = 5 ÷ 100 = 0.05
∴ n = 2 ⇒ compounded semi-annually
∵ He deposits $9000
∴ P = 9000
∵ The time is 8 years
∴ t = 8
→ Substitute them in the formula above
∴ A = 9000 [tex](1+\frac{0.05}{2})^{2(8)}[/tex]
∴ A = 9000 [tex](1.025)^{16}[/tex]
∴ A = 13360.55059
∴ He will have $13360.55059 in 8 years
Related Questions
about 99.7 of sixth grade students will have heights between inches and inches
Answers
51.1 and 64.9
Step-by-step explanation:
Answer: 55.1 and 64.9
On edge.
Step-by-step explanation:
Which one of the statements below is FALSE?
O Graphing is a method for solving a System of Equations.
Substitution is a method for solving a System of Equations.
Simplification is a method for solving a System of Equations.
Elimination is a method for solving a System of Equations.
Answers
Answer:
Simplification is a method for solving a system of equations
Step-by-step explanation:
-Graphing is a real way to solve a System of Equations
-Substitution is a real way to Solve Systems of Equations
-Elimination is a real way to solve Systems of Equations
so, Simplifcation can't be one
Take 2x-4y=6 and 4x+2y=17 for example.
They are both in standard form, so you could change them to y=mx+b and graph it. The intersection is the correct answer.
You can also solve one of the equations for y or x, and substitute that into the other equation, and solve for both x and y
or, you could add the two equations together and solve for x and y.
You can't simplify them.
The length of a rectangle is twice its width. Find its area, if its perimeter is 7 1/3 cm.
Answers
Answer:
241/81 cm^2
Step-by-step explanation:
[tex]2\: lenghts = wide\\\\lenght=x\\\\2x=wide\\\\Perimeter = 2(wide+lenght)\\\\P=2(2x+x)\\\\P=2(3x)\\\\P=7\frac{1}{3}\\\\\frac{22}{3}=6x\\\\x=\frac{22}{3*6}\\\\x=\frac{11}{9}\\\\width = 2x=2(\frac{11}{9})=\frac{22}{9}[/tex]
[tex]Area = lenght\times width\\\\Area = \frac{11}{9}\times\frac{22}{9}\\\\A=\frac{11*22}{9*9}\\\\A=\frac{242}{81}cm^2[/tex]
Answer:
[tex]2\frac{80}{81}[/tex] cm²
Step-by-step explanation:
A = lw
P = 2(l + w)
~~~~~~~~~~~
l = 2w
2(2w + w) = [tex]7\frac{1}{3}[/tex]
2(3w) = [tex]\frac{22}{3}[/tex]
3w = [tex]\frac{11}{3}[/tex]
w = [tex]\frac{11}{9}[/tex]
l = [tex]\frac{22}{9}[/tex]
A = [tex]\frac{22}{9}[/tex] × [tex]\frac{11}{9}[/tex] = [tex]\frac{242}{81}[/tex] = [tex]2\frac{80}{81}[/tex] cm²
1) There are about 20 million people in New York State, with a total land area of about 47,000 square miles.
What is the population density of New York State?
A. 0.0004 people per sq. mile
B. 426 people per sq. mile
C. 2,350 people per sq. mile
D. 940,000 people per sq. mile
Answers
Step-by-step explanation:
B. 426 people per square. mile
Let y 00 + by0 + 2y = 0 be the equation of a damped vibrating spring with mass m = 1, damping coefficient b > 0, and spring constant k = 2. (a) Convert this second order equation into a system of two first order equations. (b) Express the eigenvalues for this system in terms of b. (c) Describe the stability of the equilibrium solution ~0 for b > 2 √ 2. Justify your claim with information about the eigenvalues of the matrix for the system. (d) Connect the behavior of solutions near an equilibrium of this type with the spring mass system with damping coefficient b > 2 √ 2 and explain why your answer for part (c) is (or is not) what one should expect.
Answers
Answer:
Step-by-step explanation:
Given that:
The equation of the damped vibrating spring is y" + by' +2y = 0
(a) To convert this 2nd order equation to a system of two first-order equations;
let y₁ = y
y'₁ = y' = y₂
So;
y'₂ = y"₁ = -2y₁ -by₂
Thus; the system of the two first-order equation is:
y₁' = y₂
y₂' = -2y₁ - by₂
(b)
The eigenvalue of the system in terms of b is:
[tex]\left|\begin{array}{cc}- \lambda &1&-2\ & -b- \lambda \end{array}\right|=0[/tex]
[tex]-\lambda(-b - \lambda) + 2 = 0 \ \\ \\\lambda^2 +\lambda b + 2 = 0[/tex]
[tex]\lambda = \dfrac{-b \pm \sqrt{b^2 - 8}}{2}[/tex]
[tex]\lambda_1 = \dfrac{-b + \sqrt{b^2 -8}}{2} ; \ \lambda _2 = \dfrac{-b - \sqrt{b^2 -8}}{2}[/tex]
(c)
Suppose [tex]b > 2\sqrt{2}[/tex], then λ₂ < 0 and λ₁ < 0. Thus, the node is stable at equilibrium.
(d)
From λ² + λb + 2 = 0
If b = 3; we get
[tex]\lambda^2 + 3\lambda + 2 = 0 \\ \\ (\lambda + 1) ( \lambda + 2 ) = 0\\ \\ \lambda = -1 \ or \ \lambda = -2 \\ \\[/tex]
Now, the eigenvector relating to λ = -1 be:
[tex]v = \left[\begin{array}{ccc}+1&1\\-2&-2\\\end{array}\right] \left[\begin{array}{c}v_1\\v_2\\\end{array}\right] = \left[\begin{array}{c}0\\0\\\end{array}\right][/tex]
[tex]\sim v = \left[\begin{array}{ccc}1&1\\0&0\\\end{array}\right] \left[\begin{array}{c}v_1\\v_2\\\end{array}\right] = \left[\begin{array}{c}0\\0\\\end{array}\right][/tex]
Let v₂ = 1, v₁ = -1
[tex]v = \left[\begin{array}{c}-1\\1\\\end{array}\right][/tex]
Let Eigenvector relating to λ = -2 be:
[tex]m = \left[\begin{array}{ccc}2&1\\-2&-1\\\end{array}\right] \left[\begin{array}{c}m_1\\m_2\\\end{array}\right] = \left[\begin{array}{c}0\\0\\\end{array}\right][/tex]
[tex]\sim v = \left[\begin{array}{ccc}2&1\\0&0\\\end{array}\right] \left[\begin{array}{c}m_1\\m_2\\\end{array}\right] = \left[\begin{array}{c}0\\0\\\end{array}\right][/tex]
Let m₂ = 1, m₁ = -1/2
[tex]m = \left[\begin{array}{c}-1/2 \\1\\\end{array}\right][/tex]
∴
[tex]\left[\begin{array}{c}y_1\\y_2\\\end{array}\right]= C_1 e^{-t} \left[\begin{array}{c}-1\\1\\\end{array}\right] + C_2e^{-2t} \left[\begin{array}{c}-1/2\\1\\\end{array}\right][/tex]
So as t → ∞
[tex]\mathbf{ \left[\begin{array}{c}y_1\\y_2\\\end{array}\right]= \left[\begin{array}{c}0\\0\\\end{array}\right] \ \ so \ stable \ at \ node \ \infty }[/tex]
Anju's office uses paper cups shaped like cones to serve water. Each cup has a maximum diameter of 8 cm and a height of 10 cm. Anju fills the cup to of its height to prevent spills.
What is the approximate volume of water in Anju's cup?
Answers
Answer:
V = 167.55
Step-by-step explanation:
V = pir^2 h/3
V = pi(4)^2 (10/3)
The approximate volume of water in Anuj's cup is 42 cubic cm.
What is volume?Volume is a measure of capacity that an object holds.
Formula for finding the volume of cone
volume of cone = [tex]\frac{1}{3} \pi r^{2} h[/tex]
where,
r is the radius of cone
h is the height of cone
π = 3.14
According to the given question
paper cups are of the shape of cone.
and,
diameter = 8cm
⇒ radius = [tex]\frac{8}{2}[/tex] = 4cm
the approximate volume of water in cup = [tex]\frac{1}{3} \pi r^{2} h[/tex]
=[tex]\frac{1}{3}[/tex]×[tex]2^{2}[/tex]×π×10
=[tex]\frac{1}{3}[/tex]×4×3.14×10
= 41.86 = 42 cubic cm.
Hence, the approximate volume of water in Anuj's cup is 42 cubic cm.
Learn more about the volume of cone here:
https://brainly.com/question/1984638
#SPJ2
Evaluate each expression for g = -7 and h = 3 and match it to its value.
1. gh
2. g2 - h
3. g + h2
4. g + h
5. h - g
6. g - h
Answers
Answer:
The values of given expressions are:
1. gh = -21
2. g^2 - h = 46
3. g + h^2 = 2
4. g + h = -4
5. h - g = 10
6. g - h = -10
Step-by-step explanation:
Given values of g and h are:
g = -7
h = 3
1. gh
The two numbers are being multiplied
Putting the values
[tex]gh = (-7)(3) = -21[/tex]
2. g^2-h
Putting the values
[tex]=(-7)^2-3\\=49-3\\=46[/tex]
3. g+h^2
Putting the values
[tex]= -7 + (3)^2\\=-7+9\\=2[/tex]
4. g+h
Putting the values
[tex]= -7+3\\=-4[/tex]
5. h-g
Putting the values
[tex]= 3 - (-7)\\=3+7\\=10[/tex]
6. g-h
Putting values
[tex]=-7-3\\=-10[/tex]
Hence,
The values of given expressions are:
1. gh = -21
2. g^2 - h = 46
3. g + h^2 = 2
4. g + h = -4
5. h - g = 10
6. g - h = -10
Answer:
1) - 21
2) 46
3) 2
4) -4
5) 10
6) -10
Step-by-step explanation:
g = -7h = 3[tex]1)gh = - 7(3) \\ \: \: \: \: \: \: = - 21[/tex]
[tex]2){g}^{2} - h = ( - 7 {)}^{2} - 3 \\ \: \: \: \: \: \: \: \: \: \: \: = 49 - 3 \\ \: \: \: = 46[/tex]
[tex]3)g + {h}^{2} = - 7 + {3}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - 7 + 9 \\ \: \: \: \: = 2[/tex]
[tex]4)g + h = - 7 + 3 \\ \: \: \: \: \: \: \: = - 4[/tex]
[tex]5)h - g = 3 - ( - 7) \\ \: \: = 10[/tex]
[tex]6)g - h = - 7 - 3 \\ \: \: \: \: \: \: \: \: \: \: = - 10[/tex]
Identify the slope in this equation -y = -5x + 9
Answers
Answer:
-5
Step-by-step explanation:
The equation given is written in slope-intercept form (y = mx + b). In this form, 'm' represents the slope of a line and 'b' represents the y-intercept of the line. Since the equation asks for the slope, we can simply look at the value of 'm' in the equation. Then, we will find the slope.
slope - intercept form
y = mx + b
given equation
-y = -5x + 9
values
m = slope = -5
b = y-intercept = 9
Your friend finds the measure of the exterior angle shown. Is your friend correct?
Answers
Answer:
will i think that's true
Step-by-step explanation:
I hope this helps you
Answer:
I think that it is yes
Step-by-step explanation:
Hope this helped have an amazing day!
At a football match, 10 men bought either a pie or a cup of
coffee. A pie costs 60p and a coffee costs 50p. The total
amount spent on pies and cups of coffee was £5.80. How many
of each must have been bought? (show all your working)
Answers
Answer:
8 pies and 2 coffees
Step-by-step explanation:
10 men bought pie or a cup of coffee.
x=pie
y=coffee
x+y=10
0.6x+0.5y=5.8
0.6x+0.6y=6
0.1y=0.2
y=2
x=8
Hope this helps plz hit the crown :D
4x-3y=24 in slope-intercept form
Answers
Answer:
y=(4/3)x-8
Step-by-step explanation:
Slope-intercept form: y=mx+b
4x-3y=24
3y=4x-24 (isolating the 3y)
y=(4/3)x-8 (dividing both sides by 3)
Hope this helps!
Mal runs around a track at a constant speed of 750 meters in 30 minutes how many meters per minute is that?
Answers
Answer:
25 meters per second
Step-by-step explanation:
Divide to find m/s.
750 / 30 = 25
Check in necessary.
25 * 30 = 750
Answer:
25 per sec
Step-by-step explanation:
Can some one help me understand this?
Answers
Answer:
0 cavities
minimum is 0 cavities. there are people having 0 cavities. see the graph.
hope it helps!
Answer:
0
Step-by-step explanation:
The minimum is the smallest value in the dataset. The smallest number of cavities is 0.
please give thanks by clicking the heart button! :)
plees 555+555 and 6 541,5-5 410,6
Answers
Answer:
what is this......................
what are coordinates of point j?
Answers
Answer:
(7,4)
Step-by-step explanation:
The x always goes first and the y goes second
Answer:
7,4
Step-by-step explanation:
x,y
You have 15 marbles in a bag; 5 are red. If you pull out five marbles in a row and don't put
them back in, what are your chances of pulling all 5 red marbles? Decimal answer please.
Answers
Step-by-step explanation:
0.33 so says my mother bc she divide
Answer:
The probability of drawing a different marble is 0.25. The probability of drawing a red marble = 0.5
I do not know if this is correct please forgive me if I am wrong.
If I am right hope this helps!
Find the slope of the line that passes through the points given in the table.
х у
-3 | 0
2 | 2
7 | 4
12 | 6
Answers
Answer:
2/5
Step-by-step explanation:
(2,2) and (7,4) 4-2/7-2=2/5
Pls help with the math!! It would mean a lot if you could print it out and do it! Tyyyyyy WILL MARK BRAINLIST!
Answers
Answer:
Step-by-step explanation:
Answer:
mark the answer below as brainliest x
Step-by-step explanation:
(5 + 3i) + (2 - 81)
(Plz help)
Answers
Answer:
-74+3i
Step-by-step explanation:
Answer:
Step-by-step explanation:
(5 + 3i) + (2 - 81)
5 + 3i + 2 - 81
74 + 3i
A parabola has the focus at (4, 6) and the directrix y = –6. Which equation represents this parabola?
(x – 4)2 = 24y
(x – 4)2 = StartFraction 1 Over 24 EndFractiony
(x – 4)2 = –24y
(x – 4)2 = Negative StartFraction 1 Over 24 EndFractiony
Answers
Answer:
Step-by-step explanation:
If you graph both the focus and the directrix you will see that the directrix is below the focus...12 units below to be exact. The focus is on the vertical line x = 4, so the vertex also has an x coordinate (which is actually h since h and k represent the vertex) of 4. The vertex is exactly halfway between the focus and the directrix, so that means that the vertex is at (4, 0). h = 4, k = 0. The standard form for this parabola (we know it opens upwards since the parabola ALWAYS wraps itself around the focus and is directed away from the directrix) is:
[tex](x-h)^2=4p(y-k)[/tex]
p is the number of units between the focus and the vertex, or the vertex and the directrix (which is the same number of units since the vertex is smack dab in the middle of them!). That means that p = 6. Filling in 6 for p, 4 for h, and 0 for k we have:
[tex](x-4)^2=4(6)(y-0)[/tex] and simplify to
[tex](x-4)^2=24y[/tex] which is the first choice you're given.
The equation that shows the parabola when parabola has the focus at (4, 6) and the directrix y = –6 should be considered as the (x – 4)2 = 24y.
What is a parabola?In terms of mathematics, a parabola represent the plane curve in which there is the mirror-symmetrical and should be made of U-shaped.
Since there has the focus at (4, 6) and the directrix y = –6
So the first equation should be considered.
Learn more about parabola here: https://brainly.com/question/8063993
An exponential function in the form y = ab^x goes through the points (3, 10.125) and (6, 34.2). Find a to the
nearest integer and b to the nearest tenth, then find f (10) to the nearest integer.
Answers
Answer:
[tex]f(10) = 173[/tex]
Step-by-step explanation:
Given
Exponential Function
[tex](x_1,y_1) = (3,10.125)[/tex]
[tex](x_2,y_2) = (6,34.2)[/tex]
Required
Determine f(10)
We have that
[tex]y = ab^x[/tex]
First, we need to solve for the values of a and b
For [tex](x_1,y_1) = (3,10.125)[/tex]
[tex]10.125 = ab^3[/tex] --- (1)
For [tex](x_2,y_2) = (6,34.2)[/tex]
[tex]34.2 = ab^6[/tex] ---- (2)
Divide (2) by (1)
[tex]\frac{34.2}{10.125} = \frac{ab^6}{ab^3}[/tex]
[tex]\frac{34.2}{10.125} = \frac{b^6}{b^3}[/tex]
[tex]3.38= b^{6-3}[/tex]
[tex]3.38= b^{3}[/tex]
Take cube root of both sides
[tex]b = \sqrt[3]{3.38}[/tex]
[tex]b = 1.5[/tex]
Substitute 1.5 for b in [tex]10.125 = ab^3[/tex]
[tex]10.125 = a * 1.5^3[/tex]
[tex]10.125 = a * 3.375[/tex]
Solve for a
[tex]a = \frac{10.125}{3.375}[/tex]
[tex]a = 3[/tex]
To solve for f(10).
This implies that x = 10
So, we have:
[tex]y = ab^x[/tex] which becomes
[tex]y = 3 * 1.5^{10[/tex]
[tex]y = 3 * 57.6650390625[/tex]
[tex]y = 172.995117188[/tex]
[tex]y = 173[/tex] -- approximated
Hence:
[tex]f(10) = 173[/tex]
Sam got a job mowing lawns earning $20 for every lawn he mows, m Represents this situation by filing in the table below, creating a graph, and writing an expression. Then determine how much Sam will earn for mowing 22 lawns, justifying/showing how much you got your answer
Answers
You would multiply each number by 20
Step-by-step explanation:
It says that right there
what’s the slope?
a line has the given equation 8x-6y=24
Answers
Answer:
-1.333333
Step-by-step explanation:
:)
have a very nice day
-6y = 24 -8x
y = -4 + 4/3x
Slope: 4/3 = 1.333
Distribute 2(-3x + 5)
Answers
Answer:
= −6x+10
Step-by-step explanation:
Answer:
-6x+10
Step-by-step explanation:
Multiply the 2 by each figure in the parenthesis. So, it becomes the sum of (2)-3x and 2(5), which is -6x+10.
i will give brainliest<3
Answers
I multiplied 38,000 by .06
Chris bought c tickets to a movie for $8 each. Michele bought m tickets to a movie for $8 each. Which expression can be used to find the total amount Chris and Michele spent for these tickets?
Answers
Answer:
8c+8m
Step-by-step explanation:
c tickets are $8 a piece and m tickets are also $8 a piece. as an expression, the equation is not completed and cannot be completed until we know the value of the missing variables. to find the total, you must add the total amount of tickets Chris bought for 8 dollars and add that to the total of tickets Michele bought for 8 dollars
solve for x and y :
9 + 12i = 3x + 4yi
Answers
Answer:
27
Step-by-step explanation:
A department store is having a holiday sale. Mr. Smith bought a couch
that had a regular price of $500. He received a $150 discount. What was
the percentage of the discount that Mr. Smith received?
Answers
Answer:
Step-by-step explanation:
500×30=15000
Tim has 39 pairs of headphones and 13 music players. Tim wants to sell all of the headphones and music players in identical packages.
What is the greatest number of packages Tim can make?
Answers
Answer:
he can make 4 packages hope this helps
can u pls help me with this question
Answers
Answer:
Please check the explanation.
Step-by-step explanation:
We know that when 'y' varies directly with 'x', the equation becomes
y ∝ x
y = kx
where 'k' is called the constant of proportionality.
From the table, it is clear that 'y' varies directly with 'x'
Let us check the value of k for all the points
k = y/x
For the point (130, 9.10)
k = 9.10 / 130 = 0.07For the point (145, 10.15)
k = y/x = 10.15 / 145 = 0.07For the point (150, 10.50)
k = y/x = 10.50 / 150 = 0.07For the point (185, 12.95)
k = y/x = 12.95 / 185 = 0.07Thus, the value of proportionality constant is same.
i.e. k = 0.07
Determining the cost of 21 feet of the wire
And need 21 feet of the wire.21 feet = 252 inch
Using the equation
y = kx
where y represents the cost and x represents the length in inchesThus, the cost of 252-inch wire will be:
y = kx
substituting k = 0.07, and x = 252
y = 0.07 × 252
y = 17.64 Dollars
Thus, the cost of 21 feet wire will be: 17.64 Dollars
Determining the cost of 15 yards of the wire
Emily needs 15 yards of the wire.15 yards = 540 inches
Using the equation
y = kx
where y represents the cost and x represents the length in inchesThus, the cost of 15 yards of wire will be:
y = kx
substituting k = 0.07, and x = 540
y = 0.07 × 540
y = 37.8 Dollars
Thus, the cost of 15 yards of wire will be: 37.8 Dollars