Value of ring after four years with appreciation of 4 % each year is 4445.46
Solution:Given that
Tom bought his fiancée Marie a 3800 diamond engagement ring
Marie discovers that the value of the ring appreciates 4% each year
Need to determine value of ring after four years
Initial value of the ring = 3800
Appreciation of 4% in value means 4% increase
After 1 years , value increases by 4% which means
Value after 1 year = Initial value of the ring + 4% of Initial value of the ring
[tex]\begin{array}{l}{=3800+4 \% \text { of } 3800} \\\\ {=3800+\frac{4}{100} \times 3800=3952}\end{array}[/tex]
After 2 years, value increases by 4% of Value after 1 year which means
Value after 2 years = Value after 1 year + 4% of Value after 1 year
[tex]\begin{array}{l}{=3952+4 \% \text { of } 3952} \\\\ {=3952+\frac{4}{100} \times 3952=4110.08}\end{array}[/tex]
After 3 years, value increases by 4% of Value after 2 years which means
Value after 3 years = Value after 2 years + 4% of Value after 2 years
[tex]\begin{array}{l}{=4110.08+4 \% \text { of } 410.08} \\\\ {=4110.08+\frac{4}{100} \times 4110.08=4274.4832}\end{array}[/tex]
After 4 years , value increases by 4% of Value after 1 year which means
Value after 4 years = Value after 3 years + 4% of Value after 3 years
[tex]\begin{array}{l}{=4274.4832+4 \% \text { of } 4274.4832} \\\\ {=4274.4832+\frac{4}{100} \times 4274.4832=4,445.46}\end{array}[/tex]
Value of ring after four years with appreciation of 4 % each year is 4445.46
To calculate the future value of a ring appreciating at 4% each year for 4 years, compound interest formula is used. The ring's value after 4 years is approximately $4,445.46.
Explanation:The question refers to the calculation of the future value of an investment, which is a common problem in mathematics dealing with compound interest. Tom bought an engagement ring for $3,800, and its value appreciates at a rate of 4% each year. To find the value of the ring after 4 years, we use the formula for compound interest:
Future Value = Present Value x (1 + Rate of Interest)Number of Years
Step-By-Step Calculation
After applying the compound interest formula, the value of the ring after 4 years would be approximately $4,445.46.
the school office users r reams or white paper and 3 reams of blue paper every day use distributive property to write and simplify an expression for how much paper the school office uses in one day
Answer:
(500r + 1500) sheets per day.
Step-by-step explanation:
The school office uses r reams of white paper and 3 reams of blue paper every day.
Now, the total number of reams of paper that the school office uses every day will be (r + 3) reams.
Now, we know that 1 ream of paper is equivalent to 500 sheets of paper.
So, the school office uses a total 500(r + 3) sheets of paper every day.
Now, using the distributive property the total number of sheets will be = (500r + 1500) (Answer)
Answer:(500+1500)
Step-by-step explanation:
Find the measure of DF
Answer:
DF = 50Step-by-step explanation:
[tex]\bold{METHOD\ 1:}[/tex]
[tex]\triangle ABC\sim\triangle DE F\qquad(\text{similar tringles)}\\\\\text{Therefore corresponding sides are in proportion:}\\\\\dfrac{BA}{AC}=\dfrac{ED}{DF}\\\\\text{Substitute}\ BA=360,\ AC=600,\ ED=30\\\\\dfrac{360}{600}=\dfrac{30}{DF}\qquad\text{cross multiply}\\\\360DF=(600)(30)\\\\360DF=18000\qquad\text{divide both sides by 360}\\\\DF=50[/tex]
[tex]\bold{METHOD\ 2:}[/tex]
[tex]\text{Use the Pythagorean theorem:}\\\\leg^2+leg^2=hypotenuse^2\\\\\text{We have}\ leg=40,\ leg=30,\ hypotenuse=DF.\\\\\text{Substitute:}\\\\40^2+30^2=DF^2\\\\1600+900=DF^2\\\\2500=DF^2\to DF=\sqrt{2500}\\\\DF=50[/tex]
The measure of DF cannot be determined without additional context or a specific function. DF could imply distance in a physics scenario or represent an infinitesimal change in a function in calculus.
Explanation:The measurement of DF seems to be a question related to calculus and physics, specifically pertaining to infinitesimal changes and dynamics. In calculus, df represents an infinitesimally small change in a function, often a result of changing variables x and y. In a physics context, DF can be interpreted as the distance fallen in a typical free fall scenario under gravity, with an initial velocity. Unfortunately, without additional context or a specific function provided, the measure of DF cannot be accurately determined.
For example, in the context of electromagnetism, dF could represent the infinitesimal force on a wire carrying current in a magnetic field, according to the formula dF = i (dl) x B, where i represents current, dl represents an infinitesimal length of wire, and B represents the magnetic field.
The price of packs of bubble gum are listed in the table below.
Bubble Gum Prices
Size of Pack Price
5 pieces $0.35
10 pieces $0.75
12 pieces $1.00
15 pieces $1.35
Which size pack of bubble gum has the lowest unit rate?
Answer:
The first one
Step-by-step explanation:
0.35÷5=0.07
0.75÷10=0.075
1.00÷12=0.08
1.35÷15=0.09
What is the difference between calculations and patterns
Answer:
"Calculation" is a mathematical determination of finding the size or number of something while "pattern" is a sequence of elements that is being repeated in a predictable manner.
Step-by-step explanation:
Calculation- This process allows you to put elements together or transform them into a new result. It produces an obvious change.
For example: 7 x 6 = 42
The numbers 7 and 6 when multiplied produces 42.
Pattern- This process allows you to put the elements in an intelligible way. The elements are organized or repeated regularly.
For example: A, B, C, A, B, C, A, B, C
It is noticeable that the letters A, B and C are being repeated in the same way.
A 60-kilogram person stands on a compression spring. The spring constant is 2500 Newtons per meter What is the displacement of the spring?
A)0.00392M
B) 0.024m
C)0.1176m
D)0.2352M
The displacement [tex](\( \Delta x \))[/tex] of the compression spring when a 60-kilogram person stands on it, with a spring constant of 2500 N/m, is approximately -0.2352 meters. The negative sign indicates the direction of the displacement. Therefore, the correct answer is D.
To find the displacement [tex](\( \Delta x \))[/tex] of the spring, you can use Hooke's Law:
[tex]\[ F = -k \cdot \Delta x \][/tex]
Where:
- F is the force applied (weight in this case),
- k is the spring constant, and
- [tex]\( \Delta x \)[/tex] is the displacement of the spring.
Rearrange the formula to solve for [tex]\( \Delta x \)[/tex]:
[tex]\[ \Delta x = -\frac{F}{k} \][/tex]
Substitute the given values:
[tex]\[ \Delta x = -\frac{mg}{k} \]\[ \Delta x = -\frac{(60 \, \text{kg})(9.8 \, \text{m/s}^2)}{2500 \, \text{N/m}} \][/tex]
Calculate the result:
[tex]\[ \Delta x \approx -0.2352 \, \text{m} \][/tex]
The negative sign indicates that the displacement is in the opposite direction to the applied force. Therefore, the correct answer is:
D) [tex]\( -0.2352 \, \text{m} \)[/tex]
This set of ordered pairs defines a function. {(-49,7), (-56,8), (-63,9), (-70,10)} Which table represents the inverse of the function defined by the ordered pairs? A. x 7 8 9 10 y -49 -56 -63 -70 B. y -70 -63 -56 -49 x -10 -9 -8 -7 C. y 49 56 63 70 x -7 -8 -9 -10 D. x 7 8 9 10 y 49 56 63 70
Option A. x 7 8 9 10 y -49 -56 -63 -70 is the right answer.
Step-by-step explanation:
The inverse of a function means that the input becomes the output of the function and the output becomes input. When the function is given in the form of ordered pairs, the fiirst element of each ordered pair represents input and second element represents the output.
So, for given function: {(-49,7), (-56,8), (-63,9), (-70,10)}
The inverse will be:
{(7, -49), (8,-56), (9,-63), (10, -70)}
Hence,
Option A. x 7 8 9 10 y -49 -56 -63 -70 is the right answer.
Keywords: Function, Inverse
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Correct Answer:
X= 7, 8, 9, 10
Y= -49, -56, -63, -70
Max constructed a scale model of the Eiffel tower. The base area of the model is 0.25 square meters, while the base area of the actual Eiffel tower is 15,625 square meters
What is the scale factor of the model?
A) 1:625
B) 1:250
C)250:1
D)625:1
Answer:
1:250
Step-by-step explanation:
[tex]\sqrt{15625/0.25}[/tex]
=[tex]\sqrt{62500}[/tex]
=250
find the measure of the complement and supplement of 3y
Answer:
Step-by-step explanation:
x + y = 180
x = 3y + 8
3y+8 + y = 180
4y = 172
y = 43 degrees
x = 180-43 = 137 degrees
Eva and jin are new volunteers at the animal shelter . If they both volunteer the first of the month,in how many days will they volunteer on the same day again? Eva volunteers every 3 days and jin volunteers every 5 days
Answer:
In 15 days
Step-by-step explanation:
Eva Volunteers Every 3 Days:
So, Eva volunteers on:
3rd, 6th, 9th, 12th, 15th, 18th, 21st...and so on DAYS
Jin Volunteers Every 5 Days:
So, Jin volunteers on:
5th, 10th, 15th, 20th, 25th...and so on DAYS
So, we see NEXT which day they vounteer together. Looking at the list, we see that it is on 15th day. This is also the LCM (Least Common Multiple) of 3 and 5.
So, in 15 days, they volunteer on the same day again.
If Johnny has 22 biscuits and Lucy has 5 how many biscuits does Ruby have?
Answer:
Ummmmm none I guess
Step-by-step explanation:
rawr
Answer: 27
Step-by-step explanation: bc thats what some random persons teacher said.
What is the sum of a number and 5
Answer:
x+5
Step-by-step explanation:
x+5
-5/7 is greater than -4/5
Answer:
Yes.
Step-by-step explanation:
Forget about the negative sign for now.
Just compare 5/7 and 4/5 first.
Find the common denominator so it's easy to determine which one is bigger/larger.
5/7=25/35 and 4/5=28/35
From here, you can tell which one is bigger/larger, right?
Definitely, 25/35<28/35.
5/7<4/5, but don't forget the negative sign.
It's -5/7 compared to -4/5, so the answer is yes, -5/7>-4/5.
two numbers have these properties both numbers are greater than 6 the highest common factor is 6 the lowest common multiple is 60 find the two numbers
The two numbers that fulfill these properties are 12 and 30. They both have a highest common factor of 6 and a lowest common multiple of 60.
Explanation:The two numbers that fit the description provided both need to be greater than 6, have a highest common factor (HCF) of 6, and a lowest common multiple (LCM) of 60.
For two numbers to have an HCF of 6, they must be multiples of 6. Looking at multiples of 6 that are greater than 6, we have 12, 18, 24, 30 etc. Since the LCM must be 60, we aim to find two numbers that when multiplied would produce 60. This leads us to the pair 12 and 30.
12 and 30 have an HCF of 6 (because 12=2*2*3 and 30=2*3*5, so the HCF is 2*3=6), and 12 and 30 both have an LCM of 60. Therefore, the two numbers are 12 and 30.
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The two numbers that meet these criteria, are greater than 6 and the ones that have the highest common factor as 6 and lowest common multiple as 60, are 6 and 60.
Explanation:In this problem, we are asked to find two numbers that have the following properties: they are both greater than 6, their highest common factor(HCF) is 6 and their lowest common multiple(LCM) is 60. Since HCF is 6, it's logical to assume that the two numbers can be multiples of 6. As per hints given the highest common factor of two numbers is 6 and the lowest common multiple is 60, the numbers should be 6 and 60 as these are the only two numbers that satisfy all conditions.
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Simplify this equation 6√40 -2√90 +3√160
Answer:
BRAINLIEST PLZZZ
Step-by-step explanation:
Pull terms out from under the radical, assuming positive real numbers.
Exact Form:
18 √ 10
Decimal Form:
56.92099788
…
Sarah is 12 years old. Her sister, Emily, is 8 years less than 3 times Sarah's age. Write an expression for Emily's age in terms of Sarah's age, s.
Answer:
x= 3s -8
3 times Sarah's age is 3s hence the expression is as shown
Emily's age in terms of Sarah's age can be expressed by the algebraic expression '3s - 8', where 's' is Sarah's age.
Explanation:The student's question asks to express Emily's age in terms of Sarah's age, s. In the problem, it is stated that Emily is 8 years less than 3 times Sarah's age. This relationship can be expressed as an algebraic expression, where Emily's age, e, is equal to '3s - 8'. In this expression, 's' represents Sarah's age(12 years old in this case), '3s' means '3 times Sarah's age', and '- 8' represents '8 less than' the amount.
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✓ Express 9 inches of rain in 72 hours as a unit rate. *
The unit rate of 9 inches of rain in 72 hours is calculated by dividing the depth of the rainfall by the duration, resulting in a unit rate of 0.125 inches of rain per hour.
To express 9 inches of rain in 72 hours as a unit rate, you divide the total amount of rain by the total number of hours to find the rainfall intensity per hour. The calculation would go as follows:
Write down the total rainfall depth: 9 inches.
Write down the duration over which the rain occurred: 72 hours.
Divide the total rainfall depth by the duration to calculate the unit rate: 9 inches / 72 hours = 0.125 inches per hour.
So, the unit rate is 0.125 inches of rain per hour.
There are two numbers whose sum is 64. The larger number subtracted from 4 times the smaller number gives 31. Find the numbers.
There are two numbers whose sum is 64. The larger number subtracted from 4 times the smaller number gives 31. Then the numbers are 45 and 19
Solution:Given that, There are two numbers whose sum is 64.
Let the number be a and b in which a is bigger.
Then, a + b = 64 ------ eqn (1)
The larger number subtracted from 4 times the smaller number gives 31.
4 x b – a = 31
4b – a = 31 ----- eqn (2)
We have to find the numbers.
So, from eqn (2)
a = 4b – 31
Subatitute a in (1)
4b – 31 + b = 64
On solving we get
5b = 64 + 31
5b = 95
b = 19
So, b = 19, then eqn 1
a + 19 = 64
On simplification,
a = 64 – 19
a = 45
Hence, the two numbers are 45 and 19
How much water must be added to 1 liter of a 5% saline solution to get a 2% saline solution?
Answer:
- 1,5 liters
Step-by-step explanation:
If 1 liter has 5% of saline solution, we know that our solution has 2,5 times the salt we want it to have: [tex]\frac{5\%}{2\%} =2.5[/tex], which means that, in the liter of water, there is an amount of salt that is 1,5 greater than what is desired.Then, if we want to lower the concentration of salt, we just have to add water. How much water? 1.5 liters. Then, 5% of solution divided in 2.5 liters of water yields in a 2% solution.Answer:
The water must be added to 1 liter of a 5% saline solution to get a 2% saline solution is 1.5 litres
Explanation:
We assume that the quantity of water added to be x litres. The quantity of saline in the existing solution is 5% of 1litre = 0.05 litres, with the addition of water, the quantity of new solution becomes (1 + x) litres. As per the problem, the percentage of saline in new solution should be equal to 2%. Therefore,
[tex]\frac{0.05}{1+x} \times 100=2[/tex]
So, 5 = 2(1+x)
2x = 5 - 2
[tex]x=\frac{3}{2}=1.5[/tex]
So, 1.5 litres water should be added to make the 1litre 5% saline solution a 2% saline solution.
Which of the following represents the equation of the inverse of y=5x-20
The equation of the inverse of y = 5x - 20 is y = (x + 20)/5.
Explanation:To find the equation of the inverse of y = 5x - 20, we need to switch the x and y variables and solve for y. So the inverse equation will be x = 5y - 20. Now, let's isolate y by adding 20 to both sides: x + 20 = 5y. Next, divide both sides by 5: (x + 20)/5 = y. Therefore, the equation of the inverse is y = (x + 20)/5.
With a convenience sample, a population is broken up into different subgroups and then simple random samples are conducted within each of these subgroups.
A. True
B. False
Answer:
i would like to say the answer is FALSE
Step-by-step explanation:
What is the answer to 53
The solution is y=(7a+9b)÷8
Step-by-step explanation:
Given equation is;
[tex]\frac{2y-a}{3}=\frac{a+3b}{4}[/tex]
Multiplying both sides by 12;
[tex]12*\frac{2y-a}{3}=\frac{a+3b}{4}*12\\4(2y-a)=3(a+3b)\\8y-4a=3a+9b\\8y=3a+4a+9b\\8y=7a+9b[/tex]
Dividing both sides by 8;
[tex]\frac{8y}{8}=\frac{7a+9b}{8}\\y=\frac{7a+9b}{8}[/tex]
The solution is y=(7a+9b)÷8
Keywords: linear equations, variable
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Y=2x+5 rotate 90 degrees
Answer:
Don't know
Step-by-step explanation:
Which way? Clockwise or Counterclockwise?
2 divided by 1 6/7 in simplest form
Answer:
1 1/13
Step-by-step explanation:
2/1 6/7
2/ 13/7
2/1*7/13
14/13
1 1/13
The division of '2' by '1 6/7' involves the conversion of the mixed number to an improper fraction, after which it becomes '2 * 7/13'. This simplifies down to '14/13' or '1 1/13'.
Explanation:To calculate the division of '2' by '1 6/7', we first have to convert '1 6/7' to an improper fraction. '1 6/7' equals '13/7' when simplified. So, now the task is to divide '2' by '13/7'. In the division of fractions, we multiply the first fraction by the reciprocal of the second fraction. Thus, this becomes '2 * 7/13' (i.e. '2' over '1' times '7' over '13'). Multiplying the numerators together gives us '14', and multiplying the denominators together gives us '13'. Therefore, '2 divided by 1 6/7', in simplest form, is '14/13' or '1 1/13' when converted to a mixed number.
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Terrance bikes 3.6 miles to school in 18 minutes. Jaqueline bikes 5.4 miles to school in 30 minuets assuming each student rode at a constant speed , who is traveling at a faster speed
Answer:
jaqueline, because 3.6/18 =0.2 and 5.4/30=1.8
Step-by-step explanation:
Final answer:
Terrance is traveling at a faster speed of 12 mph compared to Jaqueline's 10.8 mph, after converting their biking times to hours and calculating the speed for each.
Explanation:
To determine who is traveling at a faster speed, we calculate the speed (rate) at which each student is biking. Speed is computed using the formula: speed = distance / time. For Terrance, who bikes 3.6 miles in 18 minutes, we must first convert minutes to hours, so 18 minutes is 0.3 hours (since 1 hour = 60 minutes). Thus, Terrance's speed is 3.6 miles / 0.3 hours = 12 miles per hour (mph).
For Jaqueline, who bikes 5.4 miles in 30 minutes, we also convert the minutes to hours to get 0.5 hours. Jaqueline's speed is 5.4 miles / 0.5 hours = 10.8 mph.
Comparing the two speeds, Terrance has a faster speed at 12 mph compared to Jaqueline's 10.8 mph.
what answer list all the common factors of 18 and 32
Answer:
Common factors of 18 & 32: 1, 2
Step-by-step explanation:
1 x 18 = 18
1 x 32 = 32
2 x 9 = 18
2 x 16 = 32
~
Which CANNOT be used in a proof?
A) Theorems
B) Postulates
C) Properties
D) Undefined terms
Leonard wants to save $100 in the next 2 months. He knows that in the
second month, he will be able to save $20 more than the first month.
How much should he save each month?
Answer:
$40,$60
Step-by-step explanation:
Let the money in the first month be x.
2x+20=100
x=40
find the distance between (20, -2) and (19, 5)
any help would be appreciated thx! ❤❤❤
Answer: 5 root 2
Step-by-step explanation:
using pyth. theorem
x^2= 1^2 +7^2
x^2 = 50
x = 5 root 2
Answer:
Square root of 50 approx. 7.07
Step-by-step explanation:
Do the distance formula, Which is d= sqrt of (xsub2-xsub1)squared + (ysub2-xsub1)Squared.
It would be d= sqrt of (19-20)^2 +(5-(-2))^2 = sqrt of 50
Divide the following polynomials. Then place the answer in the proper location on the grid. Write your answer in order of descending powers of y. Do not include parentheses in your answer.
(y3 - 4y2 + 7y - 6) ÷ (y - 2)
Answer:
this is the answer. hope it helps you
Here this is the answer, i hope this helps u have a great day ik this is late sorry...
NEVERMIND sorry this was the answer for another question, this is incorrect for this one.
A saleswoman earns 9% commission on all merchandise that she sells. Last month she sold $9000 worth of merchandise. How much commission (in dollars) did she earn last month
Answer:
$810
Step-by-step explanation:
you have to turn your commission into a decimal and then multiply it by the total amount and then you will get your answer
The saleswoman earned $810 in commission last month.
Explanation:To find the commission earned by the saleswoman, we need to calculate 9% of the total merchandise sold.
9% of $9000 = $9000 * 0.09 = $810.
Therefore, the saleswoman earned $810 in commission last month.