The approximate difference in the ages of the two cars, which depreciate to 60% of their respective original values, is 1.7 years.
Depreciation is to decrease in the value of a product in a period of time. This can be given as,
[tex]FV=P\left(1-\dfrac{r}{100}\right)^n[/tex]
Here, (P) is the price of the product, (r) is the rate of annual depreciation and (n) is the number of years.
Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of 10%.
Suppose the original price of the first car is x dollars. Thus, the depreciation price of the car is 0.6x. Let the number of year is [tex]n_1[/tex]. Thus, by the above formula for the first car,
[tex]0.6x=x\left(1-\dfrac{10}{100}\right)^{n_1}\\0.6=(1-0.1)^{n_1}\\0.6=(0.9)^{n_1}[/tex]
Take log both the sides as,
[tex]\log 0.6=\log (0.9)^{n_1}\\\log 0.6={n_1}\log (0.9)\\n_1=\dfrac{\log 0.6}{\log 0.9}\\n_1\approx4.85[/tex]
Now, the second car depreciates at an annual rate of 15%. Suppose the original price of the second car is y dollars.
Thus, the depreciation price of the car is 0.6y. Let the number of year is [tex]n_2[/tex]. Thus, by the above formula for the second car,
[tex]0.6y=y\left(1-\dfrac{15}{100}\right)^{n_2}\\0.6=(1-0.15)^{n_2}\\0.6=(0.85)^{n_2}[/tex]
Take log both the sides as,
[tex]\log 0.6=\log (0.85)^{n_2}\\\log 0.6={n_2}\log (0.85)\\n_2=\dfrac{\log 0.6}{\log 0.85}\\n_2\approx3.14[/tex]
The difference in the ages of the two cars is,
[tex]d=4.85-3.14\\d=1.71\rm years[/tex]
Thus, the approximate difference in the ages of the two cars, which depreciate to 60% of their respective original values, is 1.7 years.
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Use prime factors to determine the HFC of 90 and 126
Answer:
Step-by-step explanation:
Comment
The question means that you are to break both numbers down in to prime factors. When you do, what do the numbers have in common
90: 2 * 3 * 3 * 5
126: 2 * 3 * 3 * 7
The bolded numbers are the primes in common
Primes in common (answer): 2 * 3 * 3 = 18
Please help in answering these. The are five correct choices!
Answer:
True: B, C, D, F, G
False: A, E
Step-by-step explanation:
The false statements are false because we don't know anything about the measures of the sides of the red and blue triangles.
We do know that EF which is vector v is the hypotenuse of a 3-4-5 triangle, And that triangle ABC and triangle A'B'C' are exactly the same shape and size. And that one slid (translation) down at the exact angle and direction of vector v...so all the points, parts, sides, pieces of the triangle slid down in the same angle and direction.
HELP How many 1/4 cup servings of milk are in a 4-cup container? show your math
Answer:
16 servings
Step-by-step explanation:
ok so there are 4 of the 1/4 cups for each cup, knowing that we can take each cup times 4 so 4 times 4 equals 16.
A rectangle has a area of 50 cm squared if each sides lenght is doubled what is the new area.
Answer:
200 cm^2
Step-by-step explanation:
1. the side lengths are 10 and 5
2. double
3. 20*10 = 200
Complete the following statement.
20% of $55 = $____
Answer:
$11
Step-by-step explanation:
Let's take 20% and convert it into a decimal, which is .20. Multiply that percentage by $55 (.20 * 55) and you get $11, which is the answer.
6. Write the standard form of the line: y=2/5x-7
The standard form for a linear equation is: ax + by + c = 0
Once we move all the variables and constants to one side, we get the standard form for a linear equation
[tex]y = \frac{2}{5} x - 7\\y -\frac{2}{5}x = -7\\ y - \frac{2}{5}x + 7 = 0\\[/tex]
Hope that helps!
What is the rule of (2,5) (3,6) (4,7) (5,?)
Answer:
5,8
Step-by-step explanation:
Because each number goes up by one and has a pattern
A package of Oreos has 51 cookies. how many cookies would there be if there is 4 rows instead of 3 rows? Please Help!
Answer:
number of cookies in each row = 17
Step-by-step explanation:
Which of these is a proportional relationship?
A
Justin charges $1 for 1 cup of lemonade, $3 for 2 cups of lemonade and $4 for 3 cups of lemonade.
B
Jared charges $1 for 1 cup of lemonade, $2 for 2 cups of lemonade and $3.50 for 3 cups of lemonade.
C
Jasmyne charges $1 for 2 cups of lemonade, $2 for 4 cups of lemonade and $3 for 6 cups of lemonade.
D
Jessica charges $1 for 1 cup of lemonade and $2 for anyone who wants 2, 3 or 4 cups of lemonade.
BACK
(C) jasmyne is the one with the proportinal relationship
How do you solve this ?
Step-by-step explanation:
similR triangles
so
x/(x+16) = 20/32= 5/8
8x = 5x+80
3x = 80
x = 80/3
HEY, CAN SOMEONE PLEASE HELP WITH THIS QUESTION???
Answer:
five thousand one hundred and seventy nine
5/10 = n/40 HELP, WILL GIVE BRAINLIST IF PERFECT ANSWER
Answer:
n=20
Step-by-step explanation:
5/10 equals 1/2 when simplified since 5÷5=1 and 10÷5=2
Half of 40 equals 40÷2 = 20 so n=20
Another way to do it is
Since the denominator is multiplied by 4 to get to 40
We must multiply 5 by 4 to get the numerator:
5×4=20
So n=20
What is the slope of the line that passes through the points(1,−6) and(−2,−8)? Write your answer in simplest form.
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-8}-\stackrel{y1}{(-6)}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{1}}}\implies \cfrac{-8+6}{-3}\implies \cfrac{-2}{-3}\cfrac{2}{3}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{\cfrac{2}{3}}(x-\stackrel{x_1}{1})\implies y+6=\cfrac{2}{3}x-\cfrac{2}{3}[/tex]
hmmm now let's put that in standard form, that is
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex]\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y+6)~~ = ~~3\left( \cfrac{2}{3}x-\cfrac{2}{3} \right)}\implies 3y+18~~ = ~~2x-2 \\\\\\ 3y=2x-20\implies -2x+3y=-20\implies 2x-3y=20[/tex]
Nadia’s bookshelf contains 10 fiction books, two reference books, and five nonfiction books. What is the probability that she randomly picks up a reference book and then, without replacing it, picks up a nonfiction book? StartFraction 1 Over 289 EndFraction StartFraction 10 Over 289 EndFraction StartFraction 5 Over 136 EndFraction One-tenth.
The probability that Nadia randomly picks up a reference book and then, without replacing it, picks up a nonfiction book is 5/136.
We have,17 total number books out of which,10 are fiction books, 2 are reference books, 5 are non-fiction books.
What are combination and probability?The combination is the number of ways of selecting things.
Probability is to quantify the possibilities.
Number of ways in which a reference book can be picked = ²C₁
Probability of picking a reference book = ²C₁ / ¹⁷C₁ = 2/17
Now, the total number of books left on the bookshelf is 16
The number of ways in which a non-fiction book can be picked after a reference book is already picked up( no replacement) = ⁵C₁ / ¹⁶C₁ = 5/16
Total probability =multiplication of both the possibilities
Total probability =(2/17)×(5/16) = 5/136
Therefore, the probability that she randomly picks up a reference book and then, without replacing it, picks up a nonfiction book is 5/136
To get more about probability refer to the link,
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Answer:
C. 5/156
Step-by-step explanation:
Edge 2023
solve the inequallity for x
-3x + 6 > 48
Answer: x<-21
Step-by-step explanation: I worked on the problem and checked online. Your good! Hope this helps! ^w^
what is 1000+2.10. I hope everyone has a nice day!!!
The radius of the driving wheel of an engine is 1.75m. How many revolutions will it make in travelling 22 km? (clue: total distance covered - distance covered for 1 revolution = no of revolutions) *distance covered for 1 revolution means circumference of the wheel
Answer:
Given:
The radius of the driving wheel of an engine is 1.75mTo Find:
How many revolutions will it make in traveling 22 km.Solution:
First, we have to find the Circumference of the Wheel:
As, we know:
[tex] \bigstar \:{\boxed{ \rm{Circumference_{(Circle)} = 2 \pi r }}} \: \bigstar[/tex]
where,
pi (π) = 22/7 Radius (r) = 1.75mSo, the Circumference of wheel will be:
[tex]{\large{\rm{\dashrightarrow{Circumference_{(Wheel)} = 2 \times \frac{22}{7} \times 1.75 }}}} [/tex]
[tex]{\large{\rm{\dashrightarrow{Circumference_{(Wheel)} = \frac{2 \times 22}{7} \times 1.75}}}}[/tex]
[tex]{\large{\rm{\dashrightarrow{Circumference_{(Wheel)} = \frac{44}{7} \times 1.75 }}}}[/tex]
[tex]{\large{\rm{\dashrightarrow{Circumference_{(Wheel)} = \frac{44 \times 1.75}{7} }}}}[/tex]
[tex]{\large{\rm{\dashrightarrow{Circumference_{(Wheel)} = \frac{77}{7} }}}}[/tex]
[tex]{\large{\rm{\dashrightarrow{Circumference_{(Wheel)} ={ \boxed{ \rm{ \red{11m}}}}}}}}[/tex]
Hence, the circumference of the wheel is 11m.
Now, we have to convert distance covered km into m:
[tex]{\leadsto{\large{\rm{ \: Distance \: Covered = 22km}}}}[/tex]
[tex]{\leadsto{\large{\rm{ \: Distance \: Covered =(22 \times 1000)m }}}}[/tex]
[tex]{\leadsto{\large{\rm{ \: Distance \: Covered = {\boxed{\rm{\red{22000m}}}}}}}}[/tex]
Hence, the distance covered is 22000m.
Now, we have to find the number of revolution:
Given:
Circumference = 11m Distance Covered = 22000mAccording to the question by using the formula, we get:
[tex] \bigstar \: { \boxed{ \large{ \rm{Number \: of \: Revolution \: = \: \frac{Distance \: Covered}{Circumference }}}}}[/tex]
[tex]{ \large{ \longrightarrow{ \rm{Number \: of \: Revolution = \frac{22000}{11} }}}}[/tex]
[tex]{ \large{ \longrightarrow{ \rm{Number \: of \: Revolution = { \boxed{\red{2000}}}}}}}[/tex]
Thus, the revolution will it make in traveling 22km is 2000.£54 is split into a ratio of 5:4 how much does each person get?
Answer:
$30 and $24
Step-by-step explanation:
Hello! We can rewrite ratios as 5x:4x because essentially we can put x in for any value and it would still be the same ratio (10:8, 15:12). So we will put x there just to make it easier to understand.
You know that the ratio of 5x:4x adds up to 54. And, now that we have the x, we can do a nifty trick. We can add 5x and 4x to get 9x. Now we have 9x = 54. If we simplify this, we get x = 6.
Now that we have x = 6, we can plug in that value in the ratio 5x:4x. 5 * 6 = 30 and 4 * 6 is 24
And that is exactly your answer: 30 and 24 dollars respectively
If you want to test it, you can add the two numbers to see if it adds to the number you want it to. After that, you can put it in a ratio and simplify it to see if it simplifies down to the same ratio. In this case, the two numbers satisfy both conditions.
Let me know if you have any questions!
Paul wants to play quarterback, but that decision depends on who coaches for a given game. Coach Smith is coach 60 percent of the time, and Coach Brown is coach the other 40 percent. Coach Brown has faith in Paul, so he starts him at quarterback in 80 percent of the games he coaches. Coach Smith, though, isn't so sure, so he starts Paul at quarterback 40 percent of the time. What's the probability of Paul starting as quarterback for the next game?
Answer:
56/100
Sorry, I looked this up so someone else might need to show you the work.
But I got the answer
Help on this please
Answer:
D I think it's d I'm 90% confident
Answer:
D I think it's d I'm 90% confident
Step-by-step explanation:
What is the largest fraction 3/4 7/8 4/5/7/9 7/100
Bradley wants to carpet his hallway. The hallway is 4 feet wide and 10 feet long. How much carpeting does he need?
Answer:
49 feet long of carpeting
Step-by-step explanation:
10 feet × 4 feet = 40 feet
Please help meeeeeeereerreee
Answer:
c
Step-by-step explanation:
Answer:
Checking account
Step-by-step explanation:
pls give me brainlest <3
what is the domain and range?
f(x) = 2x^3 – 2
hope this answer helps
Can u mark this as brainliest
Find the area of the rhombus
9 in
12 in
A = [?] in?
=
Enter
Based on information given on rhombus' dimensions and the area formula of the rhombus, we conclude that the area of the figure is 54 square inches.
How to determine the area of a rhombusThe area of a rhombus (A), in square inches, is represented by a model in terms of the diagonals of the figure, which is described below:
A = 0.5 · d · D (1)
Where:
d - Small diagonal, in inches.D - Large diagonal, in inches.If we know that d = 9 in and D = 12 in, then the area of the rhombus is:
A = 0.5 · (9) · (12)
A = 54 in²
Based on information given on rhombus' dimensions and the area formula of the rhombus, we conclude that the area of the figure is 54 square inches.
Remark
The statement is incomplete. Complete statement is shown below:
Find the area of the rhombus with following dimensions:
Small diagonal - 9 in, large diagonal - 12 in
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Answer: 216 in²
Step-by-step explanation:
the area (A) of a rhombus is calculated as
A = × d₁ × d₂ (d₁ and d₂ are the lengths of the diagonals )
the diagonals of a rhombus bisect each other , then
d₁ = 12 + 12 = 24
d₂ = 9 + 9 = 18
then
A = × 24 × 18 = 12 × 18 = 216 in²
5 pumps are required to fill a tank in 90 minutes .how many pumps of the same type are used to fill the tank in 30 minutes
Answer: 15 pumps
More the number of pumps lesser is the time taken to fill the tank
Number of pumps ∝ 1/Time
n = k / t
[where k = constant]
In 1st case
5 = k / (1.5)
k = 7.5
In second case
n = k / t
= 7.5 / 0.5
= 15
∴ 15 pumps are used to fill the empty tank in half an hour.
I need help with my imagine math
Answer:
The answer is
Step-by-step explanation:
Similar : 2yd - 8yd, 6yd - 18yd
Not similar - Shape : 18yd - 6yd
Not similar - Ratio : 6yd - 3yd, 9yd - 18yd, 3yd - 1yd
Carla plans to invest $9,000 for 10 years. Better Bank offers a 10 year CD at an annual rate of 4% using simple interest. How much is the investment worth?.
If Carla plans to invest $9,000 for 10 years and Better Bank offers a 10 year CD at an annual rate of 4% using simple interest. then investment will be worth $12600 .
What is simple interest?
Simple interest is based on the principal amount of a loan or the first deposit in a savings account.
Given that Carla plans to invest $9,000 for 10 years. Better Bank offers a 10 year CD at an annual rate of 4% using simple interest.
We know
A= PRT+ P =P(RT+1)
Where
A = Final amount,
P = Principal amount=9000
R = Annual interest rate in decimal form=0.04
t = Time in years=10
Final amount can be calculated as
[tex]&A=\$ 9000(1+0.04 \times 10) \\\\&A=\$ 9000(1+0.4) \\\\&A=\$ 9000(1.4) \\\\&A=\$ 12600\\[/tex]
If Carla plans to invest $9,000 for 10 years and Better Bank offers a 10 year CD at an annual rate of 4% using simple interest. then investment will be worth $12600 .
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What is 45 divided by 70?
Answer:
0.6428571429
=
9/14
this is the answer
0.64 or 1.55
Step-by-step explanation:
What is the slope of the line?
-3x+5y=2x+3y
Choose 1 answer:
(Choice A)
A
-5/2
(Choice B)
1
(Choice C)
5/2
(Choice D)
-1
Answer:
☘ QUESTION☘What is the slope of the line?
-3x+5y=2x+3y
☘ ANSWER☘-3x+5y=2x+3y → 2y = 5x → y = (5/2)x.
There are infinitely many ordered pairs that satisfy -3x+5y=2x+3y.
Answer: C.5/2Step-by-step explanation:
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