Brooklyn and Matthew both recently got a job and want to start a savings account to earn interest on money they save. Brooklyn's paycheck for was for $625 net pay-after taxes. the bank her parents use offer savings account compounded monthly with an interest rate of 2.5%. Matthews paycheck was also for $446 net pay. his parents know of a savings account that earns 4% compounded quarterly.
a. use the compounding interest rate formula to identify who will have more money after two years (assuming no additional deposits or withdrawals are made)
b. use the Desmos graphing calculator to graph Brooklyn's equation and Matthew’s equation on the same graph. identify the points of intersection and interpret the results.
WHAT MISTAKES DID THE STUDENTS MAKE??
Answers
After two years, Brooklyn will have more money in her savings account than Matthew.
Brooklyn's savings account grows at a slower rate than Matthew's initially but eventually catches up and surpasses Matthew's account due to the higher interest rate and monthly compounding.
a.
[tex]A = P(1 + r/n)^{nt}[/tex]
where A is the final amount, P is the initial principal (or net pay), r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.
For Brooklyn saving account,
P = $625, r = 0.025, n = 12 (monthly compounding), and t = 2.
A = $625(1 + 0.025/12)^(12*2) = $686.71
For Matthew saving account,
P = $446, r = 0.04, n = 4 (quarterly compounding), and t = 2.
A = $446(1 + 0.04/4)^(4*2) = $506.84
b.
To graph Brooklyn's equation and Matthew's equation on the same graph, we can use the following equations:
Brooklyn's equation: A = 625(1 + 0.025/12)^(12t)
Matthew's equation: A = 446(1 + 0.04/4)^(4t)
Now,
The resulting graph will show the growth of each saving account over time.
The points of intersection on the graph represent the times when the two savings accounts have the same amount of money.
From the graph, we can see that the two accounts intersect at around 11 months and 23 months.
We can say that Brooklyn's savings account grows at a slower rate than Matthew's initially, but eventually catches up and surpasses Matthew's account due to the higher interest rate and monthly compounding.
Thus,
After two years, Brooklyn will have more money in her savings account than Matthew.
Brooklyn's savings account grows at a slower rate than Matthew's initially but eventually catches up and surpasses Matthew's account due to the higher interest rate and monthly compounding.
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Related Questions
Given X = [b a / 4 a] , Y = [c d / a b] , and Z= [a c / 16 b]
What is Y if X-2Y=Z?
[2 -4/ -6 -2]
[4 -8/ -12 -4]
[-4 8/ 12 4]
[12 0/ 12 -12]
Answers
Answer:
[2 -4/ -6 -2]
Step-by-step explanation:
To solve for Y, we need to rearrange the equation X-2Y=Z to isolate Y.
X - 2Y = Z
2Y = X - Z
Y = (X - Z)/2
Now we substitute the given matrices for X and Z, and solve for Y:
X =
[b a
4 a]
Z =
[a c
16 b]
X - Z =
[b-a a-c
-12 a-b]
Y = (X - Z)/2 =
[(b-a)/2 (a-c)/2
-6 (a-b)/2]
So the answer is Y = [ (b-a)/2, (a-c)/2 / -6, (a-b)/2 ].
Therefore, the answer is (a) [2 -4/ -6 -2].
The calculated value of the matrix Y is [tex]Y = \left[\begin{array}{cc}2&-4\\-2&-6&\end{array}\right][/tex]
Calculating the matrix YFrom the question, we have the following parameters that can be used in our computation:
The matrix definitions
Given that
X - 2Y = Z
So, we have
b - 2c = a
a - 2d = c
4 - 2a = 16
a - 2b = b
So, we have
4 - 2a = 16
-2a = 12
a = -6
Next, we have
a - 2b = b
-6 - 2b = b
3b = -6
b = -2
Next, we have
b - 2c = a
-2 - 2c = -6
-2c = -4
c = 2
Lastly. we have
a - 2d = c
-6 - 2d = 2
-2d = 8
d = -4
The matrix Y is given as
[tex]Y = \left[\begin{array}{cc}c&d\\b&a&\end{array}\right][/tex]
So, we have
[tex]Y = \left[\begin{array}{cc}2&-4\\-2&-6&\end{array}\right][/tex]
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Simplify the expression: 8y + 4 - 3y + 12
Answers
SOMEONE PLEASE HELP
The number of chips of different colors in Gail's bag is shown below
-2 blue chips
-4 pink chips
-8 white chips
Gail takes out a chip from the bag randomly without looking, She replaces the chip and then takes out another chip from the bag. What is the probability that Gail takes out a white chip in both draws?
Answers
Answer:
8 over 15 multiplied by 7 over 14 is equal to 56 over 210
8 over 15 plus 7 over 14 is equal to 217 over 210
8 over 15 plus 8 over 15 is equal to 16 over 15
8 over 15 multiplied by 8 over 15 is equal to 64 over 225
She's taking it out and then she replaces it
and so that means the denominator would stay 15 both times
and since it's a white chip in both draws, it would be 8/15 * 8/15
Después de analizar un conjunto de datos se encontró que la desviación estandar es igual a 9, se requiere conocer
ahora, el valor de la varianza
Answers
The variance of the data-set in this problem is given as follows:
81 units squared.
How to obtain the variance of the data-set?The standard deviation for the data-set in this problem is given as follows:
9 units.
The relation between the standard deviation and the variance is that the standard deviation is the square root of the variance, hence the variance is the square of the standard deviation.
Hence the variance of the data-set in this problem is given as follows:
(9 units)² = 81 units².
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When an object is dropped vertically from a platform, its height after
seconds can be estimated with the formula shown.
ℎ=ℎ0−162
ℎ
is the height of the object in feet.
ℎ0
is the initial height of the object in feet.
is the time in seconds after the drop.
Which equation and solution tells how long it takes the object to reach a height of 96
feet if its initial height is 208
feet?
Answers
An equation and solution that tells how long it takes the object to reach a height of 96 feet if its initial height is 208 feet is:
D. 96 = 208 - 16t²
t = √7
How to determine the time when the object would reach a height of 96 feet?Based on the information provided, we can logically deduce that the height (h) in feet, of this object above the ground is related to time by the following quadratic function:
h(t) = h₀ - 16t²
When the initial height is 208 feet and final height is 96 feet, the height function becomes;
h(t) = h₀ - 16t²
96 = 208 - 16t²
16t² = 208 - 96
16t² = 112
t² = 112/16
Time, t = √7 seconds.
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a certain forest covers an area of 1700km^(2). Suppose that each year this area descreases by 7.5%. What will the area be after 11 years?
Answers
Answer: y= 1700 (1- .0325) ^15= 1700(.9675) ^15=1700(.60920660)= 1035.65 km Hope this helps!
Step-by-step explanation:To calculate the area of the forest after 5 years, we need to use the formula:
A = A0 * (1 - r/100)^t
PLEASE MARK BRAINLIST
Need help solving this problem please help
Answers
The height of tree is given as follows:
40 ft.
How to obtain the height of the tree?The height of the tree is obtained applying the proportions in the context of this problem.
The proportions are applied as a rule of three can be formed between the heights and the shadows for both the tree and the person, as follows:
h/30 = 6/4.5
Applying cross multiplication, the value of h is obtained as follows:
4.5h = 30 x 6
4.5h = 180
h = 180/4.5
h = 40 ft.
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Joey's current monthly expenses include a rent payment of $1,100, a $178 car payment, and a combined minimum payment of $220 for his credit card debt. His current gross monthly income is $3,600. If Joey moves to a new apartment, what is the maximum monthly rent payment he can make and still maintain a DTI ratio of 36%?
a.
$702
b.
$898
c.
$922
d.
$960
Answers
Based on Joey's debt-to-income ratio, the maximum monthly rent payment he can make and still maintain the DTI ratio would be; b. $898.
WE are given that Joey has a DTI ratio of 36% which means that his maximum debt payment should be 36% of his income.
This amount would be:
= DTI x monthly income
= 36% x 3,600
= $1,296
Maximum monthly rent can be found as:
= Maximum monthly debt payment - Car payment - Credit card payment
= 1,296 - 178 - 220
= $898
In conclusion, option B is correct.
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What is the amount of your employer's contributions if the company matches 50% of the first 4% of your salary, and you make $72,000 a year?
O $1,440.00
O $1,000.00
O $2,880.00
O $36,000.00
Answers
4% of $72,000 is:
$72,000 x 0.04 = $2,880
50% of $2,880 is:
$2,880 x 0.5 = $1,440
Therefore, the employer's contribution would be $1,440.00. Option A is the correct answer.
4% of $72,000 is:
$72,000 x 0.04 = $2,880
50% of $2,880 is:
$2,880 x 0.5 = $1,440
Therefore, the employer's contribution would be $1,440.00. Option A is the correct answer.
An airplane company flies 39 airplanes daily. The CEO collects the following passenger counts for a random sample of airplanes from the fleet, as shown below. 123, 132, 158, 77, 158, 123, 132, 123, 158, 77 Assuming that the sample is representative of the entire fleet of airplanes, what would be the mean daily passenger count per plane?
Answers
Answer:
To find the mean daily passenger count per plane, we need to calculate the average of the passenger counts for the sample.
We can do this by adding up all the passenger counts and dividing by the number of planes in the sample:
(123 + 132 + 158 + 77 + 158 + 123 + 132 + 123 + 158 + 77) / 10
= 1259 / 10
= 125.9
Therefore, the mean daily passenger count per plane is approximately 125.9 passengers.
Step-by-step explanation:
In a jar of lollies there are 6 more orange lollies than green ones and there is only one red lolly. If there are 47 lollies in the jar, how many orange ones are there?
Answers
Answer:
Let's use "g" to represent the number of green lollies in the jar.
According to the problem, there are 6 more orange lollies than green ones, so the number of orange lollies is "g + 6".
We also know that there is only one red lolly.
The total number of lollies in the jar is 47, so:
g + (g + 6) + 1 = 47
Simplifying the equation:
2g + 7 = 47
Subtracting 7 from both sides:
2g = 40
Dividing by 2:
g = 20
So there are 20 green lollies in the jar.
And since there are 6 more orange lollies than green ones, there must be:
g + 6 = 20 + 6 = 26 orange lollies in the jar.
Step-by-step explanation:
Square with top and left sides labeled 1. The square is divided into 6 equal sections vertically and the first section is divided into 2 equal sections horizontally. The first of these sections is shaded.
Number line from 0 to 1. There are 5 large tick marks equally spaced between 0 and 1. There are 3 equally spaced smaller tick marks between every pair of large tick marks. The first of these smaller tick marks has a dot on it.
Question
Raj combined white sand with black sand to make 14 pound mixture of sand. Raj then put an equal amount of this sand mixture into each of 5 vases. All of Raj's sand mixture went into the vases.
How much sand was in each vase?
Responses
140 lb
1 over 40, , lb
120 lb
, 1 over 20, , lb
14 lb
1 fourth, , lb
45 lb
4 over 5, , lb
Answers
The amount of sand in each vase is 2.8 pounds by dividing the total amount by the number of vases.
Given that,
Raj combined white sand with black sand to make 14 pound mixture of sand.
Total amount of sand = 14 pounds
Number of vases to which sand is put = 5 vases
Amount of sand in each vase can be found by dividing the total amount by the number of vases.
Amount of sand in each vase = 14 / 5 = 2 4/5 pounds = 2.8 pounds
Hence the total amount of sand is 2.8 pounds.
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Please anwser this is all the points I have :)
Answers
Check the picture below.
so let's recall that the area of a circle is just πr² where r = radius, so since the sizes of each pizza are 10, 14, 18 and 22, that's simply their diameter, so that means they each have a radius half of that, or namely 5, 7, 9 and 11, as you see in the picture, so, hmmm which radius gives us the most area per the fraction provided, namely per slices provided?
[tex]\cfrac{4}{8}\pi 5^2\implies \cfrac{25\pi }{2} ~~ \approx ~~ 39.26~in^2 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{3}{8}\pi 7^2\implies \cfrac{147\pi }{8} ~~ \approx ~~ 57.73~in^2 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{2}{8}\pi 9^2\implies \cfrac{81\pi }{4}~~ \approx ~~ 63.62~in^2 ~~ \textit{\LARGE \checkmark} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1}{8}\pi 11^2\implies \cfrac{121\pi }{8}~~ \approx ~~ 47.52~in^2[/tex]
Answer: Large
Step-by-step explanation: Hope it helps Good luck!!!
Rectangle LMNP is similar to rectangle WXYZ.
The length of LM is 19 in, the area of rectangle LMNP is 140.6 in2, and the length of XY is 2.22 in.
What is the difference between the perimeters of the two rectangles?
A. 31.96 in
B. 36.96 in
C. 15.84 in
D. 41.96 in
Answers
The required, difference between the perimeters of the two rectangles is,
⇒ 46.03 in.
Since, rectangles LMNP and WXYZ are similar, their corresponding sides are proportional. Let's denote the scale factor as k.
Then, We get:
k = XY / LM
k = 2.22 / 19
To find the value of k, we can divide 2.22 by 19:
k ≈ 0.117
Hence, The area of rectangle LMNP is given as,
140.6 in².
We can use this to find the length of NP:
LM x NP = area of LMNP
19 x NP = 140.6
NP ≈ 7.4 in
Since, the sides of WXYZ are proportional to those of LMNP, we can find the length of YZ:
XY / YZ = LM / NP
2.22 / YZ = 19 / 7.4
YZ ≈ 1.167 in
Now we can calculate the perimeters of both rectangles:
Perimeter of LMNP = 2(LM + NP) = 2(19 + 7.4) = 52.8 in
Perimeter of WXYZ = 2(XY + YZ) = 2(2.22 +1.167) = 6.77in
Thus, The difference between the perimeters is:
52.8 - 6.77 = 46.03 in
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NO LINKS!!! URGENT HELP PLEASE!!!!
Please assist me with these problems.
Answers
Answers in bold
7. Not congruent
8. Congruent by the HL theorem
HL = hypotenuse leg
==========================================
Explanation for problem 7
The tickmarks on segments MA and AT tell us that these segments are congruent. Another pair of congruent segments would be AE = AE by the reflexive property.
Then angle EMA = angle ETA because of the similar arc markings for those angles.
We have these congruence facts:
MA = AT (side)AE = AE (side)angle EMA = angle ETA (angle)But recall that the "side side angle" rule isn't a valid congruence theorem. Search out "SSA ambiguous case" for more information.
We cannot use SAS because the angle is not between the sides mentioned.
Therefore, we don't have enough information to determine if the triangles are congruent or not. We can't say they are congruent, so the only thing we can do is say "not congruent" until more info comes along.
------------
Explanation for problem 8
We use the HL (hypotenuse leg) theorem. It works for right triangles only.
The congruent legs are segment ON = segment ON because of the reflexive property.
The congruent hypotenuses are MN = RO because of the tickmarks.
In short, the triangles are congruent by the HL theorem.
33% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut. Find the probability that the number who say cashews are their favorite nut is (a) exactly three, (b) at least four, and (c) at most two. If convenient, use technology to find the probabilities. Due Saturday night
Answers
The cumulative probability is
P(at most 2 ) = 0.187560896 [answer]
How to solvea)
Note that the probability of x successes out of n trials is
P(n, x) = nCx p^x (1 - p)^(n - x)
where
n = number of trials = 12
p = the probability of a success = 0.33
x = the number of successes = 3
Thus, the probability is
P ( 3 ) = 0.21509867 [answer]
***********
b)
Note that P(at least x) = 1 - P(at most x - 1).
Using a cumulative binomial distribution table or technology, matching
n = number of trials = 12
p = the probability of a success = 0.33
x = our critical value of successes = 4
Then the cumulative probability of P(at most x - 1) from a table/technology is
P(at most 3 ) = 0.402659566
Thus, the probability of at least 4 successes is
P(at least 4 ) = 0.597340434 [answer]
***************
c)
Using a cumulative binomial distribution table or technology, matching
n = number of trials = 12
p = the probability of a success = 0.33
x = the maximum number of successes = 2
Then the cumulative probability is
P(at most 2 ) = 0.187560896 [answer]
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Rewrite the following in the form log(c). log(5) + log(2)
Answers
Answer:
log(10)
Step-by-step explanation:
We can use the product property for logarithms:
log(a)+log(b)=log(ab)
In our case, a=5 and b=2. We can multiply a and b now to get the new number we're taking the logarithm of.
log(2)+log(5)=log(2×5)=log(10)
QUICK, I’LL MARK U BRAINLIEST!! Help me solve this problem!
Answers
Based on the information, bIda would owe $3700 at the end of 12 months.
Ida would owe $3808 at the end of 12 months.
How to calculate the interestThe formula will be:
I = P * r * t
I = 2500 * 0.04 * 12 = $1200
So, Ida would owe $2500 + $1200 = $3700 at the end of 12 months.
b. For option b, , the monthly interest rate is:
r = 0.01 * 4.33 = 0.0433
Using the same simple interest expression:
I = 2500 * 0.0433 * 12 = $1308
Ida would owe $2500 + $1308 = $3808 at the end of 12 months.
Therefore, option a is the better choice due to the fact she would owe less in total with a simple interest rate of 4% annually.
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What is the area of this polygon?
Answers
Answer:
78
Step-by-step explanation:
(5+8)×12/2=78
(5+8)×12/2=78
Thanks to an initiative to recruit top students, an administrator at a college claims that this year's entering
class must have a greater mean IQ score than that of entering classes from previous years. The
administrator tests a random sample of 17 of this year's entering students and finds that their mean IQ score
is 114, with a standard deviation of 15. The college records indicate that the mean IQ score for entering
students from previous years is 113.
Is there enough evidence to conclude, at the 0.05 level of significance, that the population mean IQ score, μ,
of this year's class is greater than that of previous years? To answer, assume that the IQ scores of this year's
entering class are approximately normally distributed.
Perform a one-tailed test. Then complete the parts below.
(If Rococcan consult a list of
Answers
Answer: The answer is B and im 100% correct
Step-by-step explanation:
the french club is holding a car wash fundraiser. They are going to charge $20 per car, and expect between 30 and 100 cars. Identify the independent and dependent quality in the situation, and find reasonable domain and range values
Answers
Correct option is,
A: number of cars; money raised; 30 to 100 cars; $600 to $2000 is the right option.
Since, An independent variable is a variable that represents a quantity that is being controlled in an experiment.
A dependent variable represents a quantity whose value depends on how the independent variable is controlled.
Now, In the given question;
The number of cars represents the independent variable while money raised represents independent variable .
Domain is the set of values the independent variable can take .
The number of cars 30 to 100 represents the Domain.
The range is corresponding y values .
The charge per car is $20.
Hence, Range = 30 x 20
=600
to Range = 100 x 20
= 2000.
Thus, Correct option is,
A: number of cars; money raised; 30 to 100 cars; $600 to $2000 is the right option.
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Complete question is,
The French club is holding a car wash fundraiser. They are going to charge $20 per car, and expect between 30 and 100 cars. Identify the independent and dependent quantity in the situation, and find reasonable domain and range values.
A: number of cars; money raised; 30 to 100 cars; $600 to $2000
B: money raised; number of cars; 30 to 100 cars; $600 to $2000
C: number of cars; money raised; $600 to $2000; 30 to 100 cars
D: money raised; number of cars; $600 to $2000; 30 to 100 cars
HELPPP DUE TOMORROW
Answers
Answer: 1/2 cup oats 2/3 cup flower
A wallet contains 34 notes, all of which are either $5 or $10 notes. If it amounts to $235, how many $10 notes are there?
Answers
According to the problem, we know that:
- x + y = 34 (since the wallet contains a total of 34 notes)
- 5x + 10y = 235 (since the total amount of money in the wallet is $235)
We can use the first equation to solve for x in terms of y:
x = 34 - y
Substituting this expression for x into the second equation, we get:
5(34 - y) + 10y = 235
Simplifying and solving for y, we get:
y = 15
Therefore, there are 15 $10 notes in the wallet.
Answer:
For this question, you can use the simultaneous equation to solve this problem.
Equation 1 reads: x + y = 34. (There are 34 notes in total.)
Equation 2: 5x + 10y = 235 (The notes are worth a total of $235.)
To find x in terms of y, we can apply equation 1:
x = 34 - y
When we use this expression to replace x in equation 2, we obtain:
5(34 - y) + 10y = 235
By condensing and figuring out y, we get at:
y = 15
There are 15 $10 bills in the wallet as a result.
full method please
-8+27÷(-3)-(-2)
Answers
The solution of the expression -8+27÷(-3)-(-2) is determined by applying the rule of BODMAS as -35.
What is the solution of the expression?
The solution of the expression is calculated by applying the following formula as shown below;
BODMAS;
B - stands for bracketO - stands for ofD - stands for divisionM - stands for multiplicationA - stands for AdditionS - stands for subtractionBased on the rule of BODMAS, we solve the bracket first, then division, before addition and subtraction.
-8+27÷(-3)-(-2) = -8+27÷ -1
-8+27÷ -1 = -8 - 27
-8 - 27 = - 35
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Find the indicated vector
Answers
Answer:
(d) 5i -j
Step-by-step explanation:
You want the value of the expression 2u -v where u=3i and v=i+j.
SubstitutionUse the given definitions of u and v, and simplify in the usual way.
2u -v = 2(3i) -(i+j)
= 6i -i -j . . . . . . . . . eliminate parentheses
= 5i -j
__
Additional comment
The unit vectors i and j can be treated as though they were variables. The usual properties of equality and (scalar) arithmetic apply.
Find the value of x 30 degrees and 50 degrees
Answers
Answer: I think its 1500x
Step-by-step explanation: I multiplied them both.
Hope it helped :D
Answer:
1500000000000
Step-by-step explanation:
i don't know how but the answer is pretty easy but I don't feel like it so yeah there's
11 zero s
Which function represents the graph of f(x) = -4 lxl after it is translated 3 units down?
A.g(x) = -4 lxl + 3
B. g(x) = -4 lxl - 3
C. g(x) = -4 lx + 3|
D. g(x) = -4 lx - 3l
Answers
Answer:
B
Step-by-step explanation:
When translating in the y-axis, we want to add or subtract our value outside of the function, or in this case, outside of the modulus.
We want to move 3 units down, or 3 units in the negative direction. Therefore, we take 3 away from the function.
Answer B.
Will give Brainliest and points.
A fair, 6-sided die is rolled 60 times. Predict how many times it will land on a number greater than 2.
60
40
20
two thirds
Answers
This is because 4/6 is = 40/60
At their practices, the volleyball team ran a total of 10 miles in 14 days. The tennis team ran a total of 8 miles in 7 days. Which team ran more miles per day?
Answers
Answer:
tennis team
Step-by-step explanation:
because they ran 8 miles is 7 days to get equal amount of days you multiply by 2 on both 8 miles and 7 days so they ran 16 miles in 14 days thats y tennisbteam ran more miles
Computer systems analysts
Database administrators
Computer software engineers,
systems software
Gaming and sports book writers
and runners
Environmental science and
protection technicians, including
health
Manicurists and pedicurists
Physical therapists
Physician assistants
504
650
119 154
350 449
18 24
36
78
47
100
220
29.0
28.6
28.2
28.0
28.0
27,6
27.1
146
34
99
5
10
22
47
18
Bachelor's degree
Bachelor's degree
Bachelor's degree
Short-term on-thi
Associate degree
Postsecondary vocational award
Master's degree
Master's degree
173
66
83
27.0
Based on the above table, what is the fastest growing listed occupation for those without a college degree?
a. Gaming and sports book writers and runners
b. Dental assistants
c. Marriage and family therapists
d. Manicurists and pedicurists
Answers
Based on the above table , the fastest growing listed occupation for those without a college degree is Gaming and sports book writers and runners.
Therefore option A is correct.
What is a college degree?The college degree is described as a qualification awarded to students after completing the requirements for a specific course of study of which the two most common types of degrees are the Bachelor of Arts and Bachelor of Science.
With reference to the table, the occupations that do not require a college degree are:
Gaming and sports book writers and runnersEnvironmental science and protection technicians, including healthManicurists and pedicuristsWe were able to conclude that Based on the above table , the fastest growing listed occupation for those without a college degree is Gaming and sports book writers and runners with a rate of 24.6%.
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