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The formula for the question below is A=Pe^rt
Answers
=======================================================
Work Shown:
P = 1000 is the amount deposited
We want this value to double to A = 2000 which is the amount in the account at time t (in years).
r = 0.03 represents the interest rate in decimal form.
The value of t is unknown but we can solve for it like so
[tex]A = Pe^{rt}\\\\2000 = 1000e^{0.03t}\\\\2 = e^{0.03t}\\\\\ln(2) = \ln\left(e^{0.03t}\right)\\\\\ln(2) = 0.03t\ln\left(e\right)\\\\\ln(2) = 0.03t*1\\\\\ln(2) = 0.03t\\\\[/tex]
[tex]0.03t = \ln(2)\\\\t = \frac{\ln(2)}{0.03}\\\\t \approx 23.1049060186649\\\\t \approx 23\\\\[/tex]
It will take about 23 years for the amount to double.
As a check,
[tex]A = 1000e^{0.03t}\\\\A \approx 1000e^{0.03*23.104906}\\\\A \approx 1,999.9999988806\\\\A \approx 2000\\\\[/tex]
which helps show that after roughly 23 years, we'll have about 2000 dollars in the account.
------------
Side note: Use of the rule of 72 leads to 72/3 = 24. The '3' is from the 3% interest rate. So the rule of 72 says it will take about 24 years for the amount to double. This isn't too far off from the 23 answer we got.
Related Questions
The table shows data collected on the relationship between time spent playing video games and time spent with family. The line of best fit for the data is ý = -0.3694.5.
Video Games (Minutes) Time with Family (Minutes)
40 80
55 75
70 69
85 64
A) According to the line of best fit, the predicted number of minutes spent with family for someone who spent 36 minutes playing video games is 81.54.
B) Is it reasonable to use this line of best fit to make the above prediction?
1) The estimate, a predicted time of 81.54 minutes, is reliable but unreasonable.
2) The estimate, a predicted time of 81.54 minutes, is unreliable but reasonable.
3) The estimate, a predicted time of 81.54 minutes, is both unreliable and unreasonable.
4) The estimate, a predicted time of 81.54 minutes, is both reliable and reasonable.
Answers
Complete question :
The table shows data collected on the relationship between time spent playing video games and time spent with family. The line of best fit for the data is ý = -0.36x + 94.5.
Video Games (Minutes) Time with Family (Minutes)
40 80
55 75
70 69
85 64
A) According to the line of best fit, the predicted number of minutes spent with family for someone who spent 36 minutes playing video games is 81.54.
B) Is it reasonable to use this line of best fit to make the above prediction?
Answer:
81. 54
4) The estimate, a predicted time of 81.54 minutes, is both reliable and reasonable.
Step-by-step explanation:
Given that :
The equation of best fit is defined as :
ý = -0.36x + 94.5.
A.) Predicted number of minutes spent with family (y) for someone who spends 36 minutes playing games (x) will be :
x = 36
From the model :
ý = -0.36(36) + 94.5
y = - 12.96 + 94.5
y = 81.54
Hence.nunber of minutes spent with family = 81.54 minutes.
B.) The correlation Coefficient for the model is - 0.9993, which indicates a very strong negative relationship between both variables. Hence, using this fact, we can conclude that the prediction is reliable. From the data also, spending 36 minutes playing games means such individual will have more time than someone who plays games for 40 minutes, hence, the prediction is also reasonable.
An envelope is 60 centimeters wide. About how many inches wide is the envelope? (1 inch ≈ 2.5 centimeters)
Answers
Answer:
60/2.5 = 24 cm
Step-by-step explanation:
if you are satisfied with the results then plz make me genius
Answer:
The answer is 24 inches.
Step-by-step explanation:
Given:
1 inch = 2.5 cm
or, 1 cm = 1/2.5 inch............... eqn (i)
Now,
Wideness of envelope = 60 cm
= 60 (1/2.5) inches [From eqn (i)]
= 60/2.5 inches
= 24 inches Ans
Help me please I don’t know it
Answers
How to solve
3sin^2x-5sinx-2
Answers
Become one with the lord
Read the bible
Too many sins
Ask the lord for forgiveness
Thats how you solve you answer
Explanation
Listed above
Bababoey
The governor of state A earns $48,980 more than the governor of state B. If the total of their salaries is $289,660, find the salaries of each
Answers
Answer:
Governor of State B: $120,340; Governor of State A: $169,320
Step-by-step explanation:
For the sake of this problem, let's set the salary of State B's governor as x. That would make the salary of State A's governor equal to x+48980. The following lists out how to solve this problem.
Governor B salary + Governor A salary = $48980
x+x+48980=289660
2x+48980=289660
2x=240680
x=120340
120340+48980=169320
Let y = salary for governor of state B
Then x = y + 48980, since gov. of state A earns this much more than governor of state B.
Therefore we have x + y = 289660. Substitute for x.
(y + 48980) + y = 289660
2y + 48980 = 289660
2y = 240680
y = $120340, which is salary for governor B.
Now we substitute y into x = y + 48980
x = 120340 + 48980
x = $169320, which is salary for governor A.
Solve the equation
5x - ( 4x - 1) = 2
a. 1/9
b. - 1
c. - 1/9
d. 1
from the choices provided
Answers
Answer:
5x-4x+1=2
5x-4x=2-1
x=1ans
Answer:
D. 1
Step-by-step explanation:
Question 1 -What number in the equation below would be the coefficient?
- 4x
7 = 5
4
-7
O 5
O none of the above
Answers
Answer:
4
Step-by-step explanation:
coefficient is the number next to the variable.
what is 62 ÷ 3186 I need to know?
Answers
Answer:
0.02
Step-by-step explanation:
Help pls I'm really busy and if I get ur help you will make my whole day :(
Answers
Answer:
1.) 7 ft = 84 in 2.) 100 yd= 300 ft 3.) 96 oz= 6 lbs 4.) 32 fl oz= 4 c 5.) 48 oz 6.) 80,000 lbs
Step-by-step explanation:
You have to use conversation rates.
1. 84
2. 300
3. 6
4. 4
5. 48
6. 80,000
Step-by-step explanation: I hope this made your day ツ
I WILL GIVE BRAINLIEST TO RIGHT ANSWER: The length of a bridge on a map is 1.5 cm. What is the actual length of the bridge in meters if the map is drawn at a scale of 1 : 40,000.
Answers
Answer: 600 m
Step-by-step explanation:
Imagine we have measured a distance as 1.5 cm on this map, and we want to find out how far this is in real life.
To work out the distance in real life, we need to multiply this length by 40,000.
This gives 1.5 cm × 40,000 = 60,000 cm which is 600 m or 0.6 km.
Sol b : Alternatively, we could have just remembered that each 1 cm on the map is 0.4 km in real life.
Hence, 1.5 cm on the map must be 1.5 × 0.4 km = 0.6 km in real life.
Nolan is a songwriter who collects royalties on his songs whenever they are played in
a commercial or a movie. Nolan will earn $50 every time one of his songs is played in
a commercial and he will earn $100 every time one of his songs is played in a movie.
How much would Nolan earn if his songs were played in 10 commercials and 5
movies? How much would Nolan earn if his songs were played in x commercials and
y movies?
Answers
Answer:
500$+500$=1000$
Step-by-step explanation:
for songs=50×10=500$
for movie=5×100=500$
total=500$+500$=1000$
50x+100y
hope it helps:)
The answer to this questiob
Answers
y intercept = 2
equation : y= 3/4x+2
Answer: slope = 3/4
y intercept = 2
equation : y= 3/4x+2
Step-by-step explanation:
5) The sales tax in the town where Amanda lives is 5%. Amanda paid $35
in sales tax on a new stereo. What was the price of the stereo?*
O a. $14.29
O b. $1.75
O c. $700
O d. $3,500
Answers
Answer:
$700
Step-by-step explanation:
Given that,
The sales tax in the town where Amanda lives is 5%.
Amanda paid $35 in sales tax on a new stereo.
We need to find the price of the stereo. Let it is x. Using the formula for percentage as follows :
[tex]\%=\dfrac{\text{sales tax}}{\text{total}}\times 100\\\\5\%=\dfrac{35}{x}\times 100\%\\\\x=\dfrac{35\times 100\%}{5\%}\\\\=\$700[/tex]
So, the price of the stereo is $700. Hence, the correct option is(c).
1. 4/5 - 1/6
2. 3/10 - (-1/4)
3. -2/3 + (3/4 + 5/3)
Answers
2. Answer: 11/20 or 0.55
3. Answer: 7/4 or 1 3/4 or 1.75
2.11/20
3.7/4
For the frieze pattern to the right , describe all transformations that map the pattern onto itself.
Select all that apply
A. Reflection across one or more horizontal lines
B. Reflection across one or more vertical lines
C. Glide reflection
D. Rotation
E. Translation
Answers
All transformations that map the pattern onto itself are; a horizontal translation and a reflection across a vertical line.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).
All these translations have predetermined rules that we apply to the figures.
The congruence of a triangle can be obtain through Rotation; Translation; or Reflection.
For this particular strip pattern onto itself, can be obtained by a horizontal translation and a reflection across a vertical line
All transformations that map the pattern onto itself are; a horizontal translation and a reflection across a vertical line.
Learn more about reflection here;
https://brainly.com/question/28186407
#SPJ2
The y-intercept of 2x - y = 6 is -6.
O False
True
Answers
Answer:
It is true
Step-by-step explanation:
Convert to slope-intercept form:
2x-y=6
-y=6-2x
y=-6+2x
y=2x-6
Since y=mx+b is the form we want, then b=-6, making the statement true.
Answer:
true
Step-by-step explanation:
you switch the 2x to the other side to get -y = 2x + 6
then you multiply everything by -1 to get y = -2x-6
-6 is the y int
- {(-2, 6), (2.0), (3,6), (4, -1), (5,3)} is it a function
Answers
what additional information could be used to prove ABC MQR using SAS?
Answers
Answer:
To prove that ΔABC ≅ ΔMQR using SAS, we show that two sides with the intersection angle are congruent.
From the diagram, it is shown that CA is congruent to RM.
From the first option, given that m∠A = 64° and AB = MQ = 31 cm, then we have CA = RM, AB = MQ, and CAB = RMQ (i.e. m∠A = m∠M = 64°).
This shows that the first option is correct.
From the second option, given that CB = MQ = 29 cm, then we have CA = RM, CB = MQ, but ACB is not congruent to RMQ.
Thus the second option in not correct.
From the third option, m∠Q = 56° and CB ≅ RQ, then we have CA = RM, CB = RQ, ACB = 60°, but we do not know the value of MRQ.
Thus the third option is not correct.
From the fourth option, m∠R = 60° and AB ≅ MQ, then we have CA = RM, AB = MQ, RMQ = 64°, but we do not know the value of CAB.
Thus the fourth option is not correct.
From the fifth option, AB = QR = 31 cm, then we have CA = RM, AB = QR, but we do not know the value of CAB or MRQ.
Thus, the fifth option is not correct.
Therefore, the additional information that could be used to prove ΔABC ≅ ΔMQR using SAS is m∠A = 64° and AB = MQ = 31 cm
The additional information could be used to prove ABC≅MQR using SAS will be m∠R = 60° and AB≅MQ. Option D is correct.
What are the conditions of the congruent triangle?Triangles that are equivalent in terms of size and form are known as congruent triangles.
The conditions for ABC≅MQR are;
m∠R = 60°
AB≅MQ
Using the new data, it is possible to demonstrate that m∠R = 60° and AB is equal to the MQ will result in ABC≅MQR using SAS.
Hence option D is correct.
To learn more about the congruent triangle refer;
https://brainly.com/question/12413243
#SPJ2
Which of the following expressions is the inverse of the function y = 3x + 4?
Answers
Answer:
Reverse the x and y:
x = 3y + 4.
Now subtract 4 from both sides:
x - 4 = 3y
Divide both sides by 3:
1/3 x - 4/3 = y
Which of the
the
following fractions is the largest
11/16 , 3/5 , 7/10 , 13/18
Answers
Answer:
11/16, 3/5, 7/10
Step-by-step explanation:
What is the slope of the graph of y = 14x + 19?
Answers
is Water is stored in response to changing demand a cause or effect
Answers
the answer is effect
Answer:
this a effect you can change the change the water
solve your answer in the simplest form or as a mixed number.
5 7/9 + 4 5/6
Answers
Answer:
10 11/18
Step-by-step explanation:
5 42/54 4 45/54
9 87/54
10 33/54
10 11/18
pleas give me a brainliest if this helped
Answer:
The answer is [tex]10\frac{11}{18}[/tex]
Step-by-step explanation:
Given fractions are:
[tex]5\frac{7}{9} + 4\frac{5}{6}[/tex]
The given fractions are mixed fractions whose sum has to be found. In order to do this, the mixed fractions are first converted into proper fractions then the LCM is taken to find the sum.
So,
Converting the fractions into proper fractions
[tex]=\frac{52}{9} + \frac{29}{6}[/tex]
Taking LCM
[tex]=\frac{104+87}{18}\\=\frac{191}{18}[/tex]
Converting into mixed fraction
[tex]=10\frac{11}{18}[/tex]
Hence,
The answer is [tex]10\frac{11}{18}[/tex]
From midnight to 11:00 am, the temperature dropped 1.1°C each hour. If the temperature at 11:00 am was -16.1°C, what was the temperature at midnight?
Answers
Answer:
-41.4°C
Step-by-step explanation:
1.1 * 23 = 25.3
16.1 + 25.3 = 41.4
(I prefer working with positive numbers and just switch the sign at the end)
Hope this helped.
-Pepsi
The temperature at midnight was approximately -28.2°C, here the temperature dropped by 1.1°C each hour.
From midnight to 11:00 am, there are a total of 11 hours (since 11:00 am is 11 hours after midnight).
Given that the temperature dropped 1.1°C each hour, the total temperature drop is 1.1°C/hour × 11 hours = 12.1°C.
To find the temperature at midnight, we subtract the total temperature drop from the temperature at 11:00 am:
Temperature at midnight = Temperature at 11:00 am - Total temperature drop
= -16.1°C - 12.1°C
= -28.2°C
Therefore, the temperature at midnight was approximately -28.2°C.
Learn more about the temperature here:
https://brainly.com/question/28516935
#SPJ4
Andre divides some stickers evenly among 5 people. Each person receives 8 stickers with none left over. Which equation can be used to determine the
number of stickers, s, Andre had?
Answers
Answer:
multiplication
Step-by-step explanation:
5x8=40
Answer:
If you mean which equation with variables can be used it is s/5 = 8
Step-by-step explanation:
Which statement about graphs and their inverse is true?
Answers
WILL GIVE POINTS!! Must answer!
What is the range in interval notation?
Answers
Answer:I think it’s option 2, light blue
Step-by-step explanation:
Cube the following number
A. 1
B. 2
C. 4
D. 8
Answers
Answer: 1, 8, 64, 512
Step-by-step explanation:
1^3 = 1 * 1 * 1 = 1
2^3 = 2 * 2 * 2 = 8
4^3 = 4 * 4 * 4 = 64
8^3 = 8 * 8 * 8 = 512
When you expand 2 (6x + 12), you get an answer of 12x + 24. How many other ways can
you use brackets so you get the answer of 12x + 24 when you expand them?
Answers
Answer:
There is no other way you can expand the brackets
Step-by-step explanation:
HELP!!!!!!!!!!
The perimeter of a rectangle is 44 inches. If the width of the rectangle is 10 inches, what is the length?
A.
12 inches
B.
22 inches
C.
34 inches
D.
24 inches
Answers
P .= 2L + 2W at W= 10, P= 44
44 = 2L + 2 (10)
44 = 2L + 20
44-20 = 2L
24 = 2L
L= 24/2
L= 12cm