Answer:
The correct option is a. Amy’s balance would be greater than Hank’s in the end.
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question as follows:
Amy invested $500 per month in a 401k that earned 6% annual return for 40 years. Hank invested $1,000 per month in a 401k that also earned 6% annual return, but for 20 years. Which of the following would be true?
a. Amy’s balance would be greater than Hank’s in the end.
b. Amy’s balance is $5,142 and Hank’s balance is $3,207.
c. Hank’s balance would be greater than Amy’s in the end.
d. The investment and balance would be the same.
e. None of these are true
The explanation to the answer is now given as follows:
The balance in the end for each can be determined using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:
FV = M * (((1 + r)^n - 1) / r) ................................. (1)
Where;
For Amy:
FV = Future value or balance in the end = ?
M = Monthly investment = $500
r = Monthly interest rate = 6% / 12 = 0.06 / 12 = 0.005
n = number of months the investment will be made = 40 years * 12 months = 480
Substituting the values into equation (1), we have:
FV = $500 * (((1 + 0.005)^480 - 1) / 0.005)
FV = $500 * 1,991.49
FV = $995,745.37
Therefore, Amy’s balance would be $995,745.37 in the end.
For Hank:
FV = Future value or balance in the end = ?
M = Monthly investment = $1,000
r = Monthly interest rate = 6% / 12 = 0.06 / 12 = 0.005
n = number of months the investment will be made = 20 years * 12 months = 240
Substituting the values into equation (1), we have:
FV = $1,000 * (((1 + 0.005)^240 - 1) / 0.005)
FV = $1,000 * 462.04
FV = $462,040.90
Therefore, Hank’s balance would be $462,040.90 in the end.
Conclusion
Since Amy’s balance of $995,745.37 is greater than Hank’s balance $462,040.90, it therefore implies that the correct option is a. Amy’s balance would be greater than Hank’s in the end.
Find two positive integers such that their sum is 10, and minimize and maximize the sum of their squares.
Two numbers whose sum is 10 is required.
The answer is
Minimum: 5, 5
Maximum: 9, 1
Let [tex]x[/tex] and [tex]y[/tex] be two numbers
[tex]x+y=10\\\Rightarrow y=10-x[/tex]
The sum of the squares would be
[tex]x^2+y^2=x^2+(10-x)^2\\ =2x^2-20x+100[/tex]
[tex]f(x)=2x^2-20x+100[/tex]
Differentiating with respect with x
[tex]f'(x)=4x-20[/tex]
Equating with zero
[tex]4x-20=0\\\Rightarrow x=\dfrac{20}{4}\\\Rightarrow x=5[/tex]
Double derivative of f(x)
[tex]f''(x)=4[/tex]
[tex]f''(x)>0[/tex]
So, at [tex]x = 5[/tex] the value of the function is minimum.
Therefore, at [tex]x=5[/tex] and [tex]y=10-5=5[/tex] the function has minimum value of [tex]5^2+5^2=50[/tex]
For the finding the maximum values of [tex]x[/tex] and [tex]y[/tex] we have to use trial and error method
[tex]9^2+1^2=82[/tex]
[tex]8^2+2^2=68[/tex]
[tex]7^2+3^2=58[/tex]
[tex]6^2+4^2=52[/tex]
0 and 10 will not be considered as 0 is neither positive nor negative.
So, the maximum value of the numbers is 9 and 1 and the maximum value of the function is 82.
Learn more:
https://brainly.com/question/1625850?referrer=searchResults
what are vowels in numbers
hi! i'm not really sure if i comprehend this question clearly, but if you're talking about the vowels in the word "numbers"...
Answer:
the letter "u" and "e"
Step-by-step explanation:
vowels in english are: a, e, i, o, u
hope this helped but if you have any others questions, please feel free to let me know!
Pls help i need to get this done or i will get grounded for a week
Answer: the answer is 3
Step-by-step explanation:
Isolate the x so in other words do the opposite, then you have your answer.
Answer:
D
Step-by-step explanation:
BRUH ALL IT SAYS IS "IT HAS ADDITION" HOW CAN YOU NOT SEE THAT I-
1.)How many people chose superman or thor?
2.) How many people chose Thor than The Hulk?
3.) How many more people chose Thor than Batman?
Answer:
40% chose superman or thor
8% chose thor more than hulk
And 12% chose batman than Thor
Answer:
1) 40% of people chose Superman or Thor
2) 8% more people chose Thor than The Hulk
3) 15% more people chose Thor than Batman
Step-by-step explanation:
29 + 11 + 13 + 13 + 21 = 86
100 - 86 = 14
Batman: 14%
29 + 11 = 40
29 - 21 = 8
29 - 14 = 15
someone please help me i am so bad with point slope stuff
Write the equation of the line that passes through the points (2,−6) and (6,-6).
Write the equation of the line that passes through the points (9,8)and (6,3).
Write the equation of the line that passes through the points (-9,-4) and (-9,-4).
What is the equation of the line that passes through the point (−8,5) and has a slope of 0?
What is the slope of the line that passes through the points (-2, 7)and (2, -5).
What is the slope of the line that passes through the points (6, -5)and (6, -8).
Answer:
1.) y = -6
2.) y = 5/3x - 7
3.) y = 5
4.) y = -3x + 1
5.) x = -3
Step-by-step explanation:
So the equation you want to use is this: [tex]\frac{y2-y1}{x2-x1}[/tex]
1.) Plug in
[tex]\frac{-6 - (-6)}{6 - 2} \\\\\frac{0}{4} = 0\\[/tex]
This line is zero slope to find the y-intercept get one of you points and plug them and the slope into this equation y = mx+ b. We will use (2,-6)
-6 = 0(2) + b (b represents y-intercept) (0*2=0)
-6 = b
So the equation is y = -6
2.) Do the same thing.
[tex]\frac{3-8}{6-9} \\\\\frac{-5}{-3} =\frac{5}{3}[/tex]
It's positive because when you divide a negative by a negative you get a positive. Plug in a point (6, 3) y = mx + b (b represents y-intercept)
3 = 5/3(6) + b (5/3*6 = 10)
3 = 10 + b (subtract 10 on both sides)
-7 = b
y = 5/3x - 7
3.) For this one you are just going to point slope form. y - y1 = m(x - x1)
Plug in
y - 5 = 0(x - (-8))
y - 5 = 0 (add 5 to both sides)
y = 5
4.) Do [tex]\frac{y2 - y1}{x2 - x1}[/tex] for this one
Plug in
[tex]\frac{-5 - 7}{2 - (-2)} \\\\\frac{-12}{4} = -3[/tex]
So the slope is -3. Plug into y = mx + b with the point (2, -5)
-5 = -3(2) + b (b represents y-intercept)
-5 = -6 + b (add 6 to both sides)
1 = b
The equation is y = -3x + 1
5.) Do the same thing as #4
[tex]\frac{-8 - (-5)}{6 - 6} \\\\\frac{-3}{0}[/tex]
This slope is undefined
Since you can't divide by 0 the equation would be
x = -3
Hope this helps ya!!
write an equation that passes through points (-6,1) (4,3)
[tex]y=mx+b[/tex]
First, we find the slope.
[tex]m=\frac{y_2-y_1}{x_2-x_1} \\m=\frac{3-1}{4+6} \\m=\frac{2}{10}\\m=\frac{1}{5}[/tex]
Second, we know the slope. Substitute any ordered pairs that are given in the equation.
[tex]y=mx+b\\y=\frac{1}{5}x+b\\[/tex]
I'll use the ordered pairs (4,3) as I substitute x = 4 and y = 3.
[tex]3=\frac{1}{5}(4)+b\\3=\frac{4}{5}+b\\15=4+5b\\15-4=5b\\11=5b\\\frac{11}{5}=b[/tex]
Therefore, the equation is [tex]y=\frac{1}{5}x+\frac{11}{5}[/tex]
I WILL MARK BRAINIEST
Answer:
m<4= 60
m<1=60
m<3=30
Step-by-step explanation:
I'd like to explain but I would be very difficult to do with out being in person
Answer:
m1 = 60°
m2 = 90°
m3 = 30°
m4 = 60°
Step-by-step explanation:
m<5 + m<4 = 180° ( on a straight line)
120° + m<4 = 180°
m<4 = 60°
m<2 = m<3 + m<4
90° = m<3 + 60° ( on a straight line)
m<3 = 90° - 60°
m<3 = 30°
m<1 + m<2 + m<3 = 180°
m<1 = 180 - 90 -30
m<1 = 60°
If f(x) and g(x) are quadratic functions but (f + g)(x) produces the graph below, which statement must be true?
Answer:
That the graph of (f+g)(x) is a parent graph of f(x) and g(x)
Answer:
A. The leading coefficients of f(x) and g(x) are opposite
Step-by-step explanation:
Andrea has 8 books on her summer reading list . She has read 5 out of the 8 books.what percent does she have left to read! Pls help ASAP!!
Answer:
3 percent because 8-5=3
Step-by-step explanation:
Answer:
37.5%
Step-by-step explanation:
(please answer)
If f(x) = (x + 3) - 2, which of the following is the value of f(-3)?
Answer:
f(3)= 4
Step-by-step explanation:
x= -3=0
x= 3
f(3)=(3+3)-2
f(3)= 6-2
f(3)= 4
a spring stretches to 18 cm with a 70 g weight attachment to the end. with a 100 g attached, it stretches to 24 cm . which equation models the distance y the spring stretches with weight x attached to it?
Answer:
Yes it is y=1/5x+4
Step-by-step explanation:
Why is this the answer can u show work please
Giving extra points
Brooke already owns 4 necklaces, and additional necklaces are priced at 2 for a dollar. With $2 to spend on new necklaces, how many total necklaces can Brooke own? Write and solve an equation to find the answer.
4+1+1=6
Step-by-step explanation:
she already has 4 necklaces so than she got 2 for a dollar so that equals 6.
A six sided cube is rolled. What is the probability of getting a 3 and then a 4, givrn the first number rolled was 3.
Answer:
1/6
Step-by-step explanation:
Use conditional probability:
P(A given B) = P(A and B) / P(B)
P(4 given 3) = P(4 and 3) / P(3)
P(4 given 3) = (1/36) / (1/6)
P(4 given 3) = 1/6
rewrite the function f(x)=-3(x+3)^2-13
in the form f(x)=ax^2+bx+c
Answer:
-3x^2-18x-40
Step-by-step explanation:
(x+3)^2: x^2+6x+9
= -3(x^2+6x+9)-13
Expand:
-3(x^2+6x+9): -3x^2-18x-27
= -3x^2-18x-27-13
Final Answer: -3x^2-18x-40
Answer:
-3x^2-18x-40
Step-by-step explanation:
-3(x+3)^2-13
-3(x^2+6x+9)-13
-3x^2-18x-27-13
-3x^2-18x-40
Which function describes this graph ?
What is the value of x?
Answer:
I believe it is x+3..
Step-by-step explanation:
Answer:
x = 5
which agrees with the first answer option listed
Step-by-step explanation:
Use the proportionality associated with similar triangles, considering that the larger triangle has sides:
x + (x+5) = 2 x + 5
and
(x+1) + (x-2) = 2 x - 1
and the smaller triangle:
x and (x-2)
The we build the following proportionality:
(2 x + 5) / x = (2 x - 1) / (x - 2)
cross multiply to eliminate denominators:
(2 x + 5) (x - 2) = x (2 x - 1)
operate:
2 x^2 - 4 x + 5 x -10 = 2 x^2 - x
combine like terms:
2 x^2 + x -10 = 2 x^2 - x
subtract 2 x^2 from both sides:
x - 10 = - x
add x to both sides:
2 x -10 = 0
add 10 to both sides
2 x= 10
divide both sides by 2:
x = 5
which agrees with the first answer option listed
Basketball shoes are on sale for 22% off. What is the regular price if the sale price is $42?
Answer:
x =53.85
Step-by-step explanation:
Let x be the original price
If the price is 22% of, you will pay 100% -22% = 78%
x * 78% = 42
Change to decimal form
.78x = 42
Divide each side by .78
.78x/.78 = 42/.78
Rounding to the nearest cent
x =53.85
Jerry read a 200 page book in 10 hours. At that rate, how long will it take him to read a 320 page book?
16 hours
18 hours
24 hours
32 hours
A model of a park was built on a scale of 1.5 cm to 50 m. If the distance between two trees in the park is 150m, what is this distance on the model? *
0.5 cm
4.5 cm
75 cm
225 cm
The practice range at a golf course charges $4.00 for a bucket of 40 golf balls. At this rate, how much will a bucket of 100 golf balls cost? *
$10.00
$10.50
$13.50
$16.00
Step-by-step explanation:
1. 200 = 10h
320 =
320x10 / 200
= 16h
2. 1.5 = 50m
x = 150 m
150x1.5 / 50
= 4.5cm
3. 4$ = 40balls
x = 100balls
100x4 / 40
= $10
2. The electrical resistance R of a wire varies inversely with the square of its diameter d. If a wire with a
diameter of 3 millimeters has a resistance of 0.4 ohm, find the resistance of a wire having the same
length and a diameter of 8 millimeters.
Simplify: –6(2x – 5)
–12x – 30
–12x + 30
12x – 30
12x + 30
Answer: -12x + 30
Step-by-step explanation:
Answer:
the answer is b
Step-by-step explanation:
-6(2x-5)
-6(2x+5)
-6(2x) + 6(5)
-12x +30
Please help it’s due
1 = 70
2 = 20
3 = 70
4 = 20
5 =110
Function and Linear question look at the image
I will give brainliest if correct
Two cars head toward each other from opposite ends of a freeway 2286 miles long. If the speed of the first car is 68 miles per hour and the speed of the second car is 59 miles per hour, how long will it take before the cars pass each other? hours
Answer:
Step-by-step explanation:
multiply 68*59
A large container for water weighs 21 pounds. If a gallon of water weighs 8.34 pounds, what is an equation that relates the weight of the
water and the container, W. in pounds and the amount of water, A, in gallons? (1 point)
W
Answer:
The equation that relates the weight of the water and the container in pounds and the amount of water in gallons is [tex]A = \frac{W}{8.34}[/tex].
Step-by-step explanation:
From Physics we understand that conversions are represented by the following linear equation:
[tex]u' = r\cdot u[/tex] (1)
Where:
[tex]u[/tex] - Original value, measured in original unit. (pounds)
[tex]r[/tex] - Conversion value, measured in final unit per original unit. (gallons per pound)
[tex]u'[/tex] - Final value, measured in final unit. (gallons)
If we know that [tex]u' = A[/tex], [tex]u = W[/tex] and [tex]r = \frac{1}{8.34} \,\frac{gal}{lbm}[/tex], then the equation is:
[tex]A = \frac{W}{8.34}[/tex]
The equation that relates the weight of the water and the container in pounds and the amount of water in gallons is [tex]A = \frac{W}{8.34}[/tex].
Five years ago, John’s age was half of the age he will be in 8 years. How old is he now? Show your steps.
Answer:
John is 18 years old at this point in time.
Step-by-step explanation:
This question is basic algebra. The equation you will need to write to solve it is (x-5) = (x+8)/2. When you solve this equation, the answer comes out to 18.
valor de x de (5x-20) 85
I really need help on this one too please!
Answer:
53 degrees
Step-by-step explanation:
a complementary angle is 90 degrees and it's split, if one is 47 degrees, you do 90-47 which equals 53
What is the standard form of y –7 = – 23 (x + 1)
Answer:
23x+y=-16
Step-by-step explanation:
Pls help i dont get i t
The store is selling 6 oranges for $ 1.80. How much will it cost to buy 16 orange .Show work .
Answer:
$4.80
Step-by-step explanation:
6 oranges for 1.80
sp 6 divided by 1.80 comes out to 0.3 per orange
0.3 times 16 comes out to 4.80
therefor $4.80
Answer:
$4.80
Step-by-step explanation:
1.80/6=0.3
0.3=$0.30 for each orange
16×0.3=4.8
4.8=$4.80 for 16 oranges