In 2012, the population of a city was 6.47 million. the exponential growth rate was 2.91% per year.
Answers
The population of the city after 5 years is approximately 7.94 million.
How to find the population of the city?Assuming that the population of the city grows exponentially, we can use the formula:
P(t) = \(P0 * e^(^r^t^)\)
Where:
- P(t) is the population after time t
- P0 is the initial population
- r is the annual growth rate expressed as a decimal
- t is the time elapsed in years
Using the given information:
- P0 = 6.47 million
- r = 2.91% = 0.0291
Let's calculate the population after 1 year:
\(P(1) = 6.47 million * e^(^0^.^0^2^9^1 ^* ^1^)\)
= 6.66 million (rounded to two decimal places)
So, the population of the city after one year is approximately 6.66 million.
We can also calculate the population after 5 years:
\(P(5) = 6.47 million * e^(^0^.^0^2^9^1 ^* ^5^)\)
= 7.94 million (rounded to two decimal places)
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Related Questions
somebody help me with this problem please
Answers
Answer:
Your answer is: Point T
Step-by-step explanation:
I hope this helps!
Have a peaceful day or night!
What is the half of 1.875 ? explain in detail ?
Answers
The half of the mentioned number after performing multiplication with 1/2 is 0.9375.
The half of 1.875 can be calculated by multiplying with (1/2). Half refers to two parts of one thing and hence it represented as the fraction 1/2. So, to find the half, we will multiply the mentioned number with 1/2.
Half value = 1.875 × 1/2
Now performing division and multiplication on Right Hand Side of the equation
Half value = 1.875/2
Half value = 0.9375
Thus, based on the division, the half of 1.875 is 0.9375.
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PLEASE HELP, i will give you brainliest
Answers
Answer:
55m²
Step-by-step explanation:
So for the two small triangles, I did 10x3 =30 and divided by 2 to get 15
For the two big triangles, did 10x8 and got 80/2 =40
To find area of a triangle, it's: base x height, then divided by 2.
(Yes that's not a kite, but I cut it in half)
\(\frac{4x}{5}+\frac{5x}{6}\)
Answers
To solve this issue, first we have to match the denominators, for this we have to take the LCM from the denominators 5.6, Then just solve the fraction normally, See:
\(\sf \dfrac{4x}{5}+\dfrac{5x}{6}\to LMC~(5,6)=30\\\\\\\sf =\dfrac{24x}{30}+\dfrac{25x}{30}\\\\\\\sf =\dfrac{24x+25x}{30}\\\\\\\boxed{\sf \frac{49x}{30}}\)
Okay?!![[tex]\frac{4x}{5}+\frac{5x}{6}[/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/f0zfaxrmj8q6xMIV6JvzX7QqBBF3pvHL.jpeg)
A spinner is divided into 11 equal sections numbered from 0 to 10. You spin the spinner once. What is P(not even)
Answers
I hope this helps
The probability of not getting an even number when spinning the spinner once is \(\frac{5}{11}\).
You want to know the probability of not getting an even number when spinning a spinner divided into 11 equal sections numbered from 0 to 10.
Step 1: Identify the even numbers in the given range (0 to 10). The even numbers are 0, 2, 4, 6, 8, and 10.
Step 2: Count the number of even numbers. There are 6 even numbers in the given range.
Step 3: Calculate the total number of possible outcomes when spinning the spinner. There are 11 possible outcomes (0 to 10).
Step 4: To find the probability of not getting an even number (P(not even)), subtract the number of even numbers from the total number of outcomes. This will give you the number of odd numbers: 11 - 6 = 5.
Step 5: Now, divide the number of odd numbers by the total number of outcomes to find the probability: P(not even) = 5/11.
So, the probability of not getting an even number when spinning the spinner once is \(\frac{5}{11}\).
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2/5 of Ashley's fruit are strawberries 1/4. of the strawberries are chocolate covered what fraction of Ashley's fruit covered strawberries? (your answer should be in simplest form)
Answers
We know that
• 2/5 are strawberries.
,• 1/4 of the strawberries are chocolate covered.
We have to find 1/4 of 2/5, let's multiply these fractions.
\(\frac{1}{4}\cdot\frac{2}{5}=\frac{2\cdot1}{4\cdot5}=\frac{2}{20}=\frac{1}{10}\)Therefore, 1/10 of the strawberries are covered.Jerome is a photographer. He earns $125 per hour
Answers
The graph of the data from the table is added as an attachment
Creating a graph of the data from the table.From the question, we have the following parameters that can be used in our computation:
Jerome is a photographer. He earns $125 per hour
This means that the equation of the function is
f(x) = 125x
Where x is the number of hours he works
Using the above as a guide, we have the following table of values
x f(x)
1 125
2 250
3 375
4 500
5 625
6 750
Next, we plot the graph from the table of values and the function f(x) = 125x
The graph of the function is added as an attachment
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The graph of part of linear function p is shown on the grid.
Which inequality best represents the domain of the part shown?
−7≤x<2
−7
−5≤p(x)<3
−5
Answers
Answer:
A
Step-by-step explanation:
The domain of a function is the span of x-values covered by the graph.
From the graph, we can see that it stretches from x=-7 to x=2.
However, note that at x=-7, the dot is closed (shaded in). In other words, x=-7 is in our domain.
On the other hand, at x=2, the dot is not shaded. So, x=2 is not included in our domain.
Therefore, our domain all are numbers between -7 and 2 including -7 (and not including 2).
As a compound inequality, this is:
\(-7\leq x<2\)
So, our answer is A.
Also note that we use x instead of p(x) because the domain relates to the x-variable. If we were to instead find the range, then we would use p(x).
If X-1 = 8, what justifies x - 1 = 16?
2
F Subtraction Property of Equality
G Division Property of Equality
H Transitive Property of Equality
J Multiplication Property of Equality
Answers
Answer:
I think G Division Property of Equality
Your teacher wants to use a point system to select the winning pet. She wants each pet to get a certain number of points for each 1st choice vote and a certain number of points for each 2nd choice vote.
Your teacher decides to use these rules for her point system:
Points need to be positive whole numbers
Points for a 1st choice vote have to be greater than or equal to the points for a 2nd choice vote.
Determine point values for the 1st and 2nd choice that would result in the turtle winning. Use words and numbers to explain how this point system results in the turtle winning
Answers
In the above case, the possible point system will be:
1st choice vote: 4 points
2nd choice vote: 2 points
What is the point system?In arranging for the turtle to win in this point framework, the point values relegated for 1st choice and 2nd choice votes have to be meet the taking after criteria:
The point got to be positive entire numbersThe point for a 1st choice vote need to be more noteworthy than or rise to to the focuses for a 2nd choice voteLets say:
1st choice vote: 4 points
2nd choice vote: 2 points
Thus by the use of these point values, the turtle would have the next chance of winning since 1st choice votes would be worth more point (4 point ) compared to 2nd choice votes (3 point ). This would push individuals to select the turtle as their 1st choice, because it would allow the turtle a better add up to point gains and increase its chances of winning.
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Please help, solve for x
Answers
Answer:
x=39°
Step-by-step explanation:
the tangent from the diameter is 90°
x+90+51=180 sum of interior angle of the triangle is 180
x=180-90-51=39°
A marine biologist dove 40ft below sea level to study the
coral and her drone is flying 20ft above sea level. What is
the distance between the marine biologist and the drone?
Answers
Answer:
60 feet
Step-by-step explanation:
every evening Jenna empties her pockets and puts her change in a jar. At the end of the week she counts her money. One week she had 38 coins, all of them being quarters and dimes. When she added them up she had a total of $6.95. Let d=number of dimes and q= number of quarters. How many dimes did Jenna have?
Answers
d = dimes
q = quarters
d+q = 38 coins
q=38-d
0.25q + 0.10d=6.95
0.25(38-d)+0.10d=6.95
9.5-0.25d+0.10d=6.95
-015d=-2.55
d=-2.55/-0.15 = 17
q=38-17 =21
21*0.25 =5.25
17*0.10 = 1.70
5.25+1.70 = 6.95
she had 21 quarters and 17 dimes
A company manufactures a certain over-the-counter drug. The company samples 80 pills and finds that the mean amount of drug in the pills is 325.5 mg with a standard deviation of 10.3 mg. Find the 90% confidence interval for the mean of all the pills.'
Answers
To find the 90% confidence interval for the mean amount of drug in all the pills manufactured by the company, we can use the following formula: CI = X ± Zα/2 * (σ/√n).
Where:
X = sample mean = 325.5 mg
σ = sample standard deviation = 10.3 mg
n = sample size = 80
Zα/2 = the critical value of the standard normal distribution corresponding to a 90% confidence level, which is 1.645.
Plugging in the values, we get:
CI = 325.5 ± 1.645 * (10.3/√80)
CI = 325.5 ± 2.38
CI = (323.12, 327.88)
Therefore, we can say with 90% confidence that the mean amount of drug in all the pills manufactured by the company is between 323.12 mg and 327.88 mg.
1. Calculate the standard error (SE) by dividing the standard deviation by the square root of the sample size:
SE = 10.3 mg / √80 ≈ 1.15 mg
2. Find the critical value (z) for a 90% confidence interval using a standard normal distribution table or calculator. In this case, the critical value is approximately 1.645.
3. Calculate the margin of error (ME) by multiplying the critical value (z) by the standard error (SE):
ME = 1.645 × 1.15 mg ≈ 1.89 mg
4. Determine the confidence interval by adding and subtracting the margin of error from the sample mean:
Lower Limit = 325.5 mg - 1.89 mg ≈ 323.61 mg
Upper Limit = 325.5 mg + 1.89 mg ≈ 327.39 mg
Thus, the 90% confidence interval for the mean amount of drug in all the pills manufactured by the company is approximately 323.61 mg to 327.39 mg.
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p.557(3-6 all): Similar Triangles and Indirect Measurement
I need helppp :/ please
Answers
Answer:
3. 200ft
4. 21ft
5. 37.5m
6. 4.2ft
Step-by-step explanation:
3. use proportions:
\(\frac{h}{50} = \frac{50}{12.5}\)
50(50) = 12.5h
h = 200ft
4.
\(\frac{h}{6} =\frac{7}{2}\)
6(7) = 2h
h = 21ft
5.
\(\frac{25}{8} =\frac{x}{12}\)
25(12) = 8x
x = 37.5m
6.
\(\frac{9}{15} =\frac{h}{7}\)
9(7) = 15h
h = 4.2ft
MEDICINE: Ahmad took 200 mg of a medication. The
function f(t) = 200e 0. 4+ can be used to determine the amount of
medication, f(t), still in his system after t hours. To the nearest hundredth,
after how much time will Ahmad have only 50 mg of medication left in his
system?
A 4. 37 hours
B 7. 47 hours
C
3. 47 hours
D
3. 74 hours
A BH
BO
Answers
If Ahmad took 200 mg of medication and the function \(f(t) = 200e^{-0.4t}\) can be used to determine the amount of medication, then He will have only 50 mg of medication left in his system after (c) 3.47 hours .
The Function that is used to determine the amount of medication, f(t), still in his system after t hours. is given as \(f(t) = 200e^{-0.4t}\) ,
we have to find the after how many hours there will be only 50 mg of medication left ;
we need to substitute f(t) as 50 ;
we get ;
⇒ \(50 = 200e^{-0.4t}\) ;
⇒ \(\frac{50}{200} =e^{-0.4t}\) ;
⇒ \(\frac{1}{4} =e^{-0.4t}\)
On solving further ,
we get ;
⇒ \(t=3.4657..\) hours ;
So , t≈ 3.47 hours .
Therefore , After 3.47 hours there will be 50 mg of medication left .
The given question is incomplete , the complete question is
Ahmad took 200 mg of a medication. The function \(f(t) = 200e^{-0.4t}\) can be used to determine the amount of medication, f(t), still in his system after t hours. To the nearest hundredth, after how much time will Ahmad have only 50 mg of medication left in his system ?
(a) 4.37 hours
(b) 7.47 hours
(c) 3.47 hours
(d) 3.74 hours
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What is the answer to the equation: 9x - 7= - 7
Answers
Answer:
9x
explanation:
you add the 7 to both sides
An archaeologist at a dig sets up a coordinate system using string. Two similar artifacts are found: one at position (1, 4) and the other at (5, 2). How far apart were the two artifacts? Round to the nearest whole number if necessary.
Answers
The distance between the two artifacts is approximately 4.47 units.
The problem statement provides two coordinates (1, 4) and (5, 2).
Here (1,4) and (5,2) are known as position (x1,y1) and position (x2,y2), respectively.
Let's find the distance between the two artifacts.
An archaeologist at a dig sets up a coordinate system using string.
wo similar artifacts are found: one at position (1, 4) and the other at (5, 2).
How far apart were the two artifacts? Round to the nearest whole number if necessary.
Distance between two points is given by,`\(d = sqrt((x2-x1)^2+(y2-y1)^2)`d\)(rounded to two decimal places)
\(= sqrt((5 - 1)\² + (2 - 4)\²)d \\\)
\(= sqrt((4)\² + (-2)\²)d\)
\(= sqrt(16 + 4)d\)
\(= sqrt(20)d = 4.47\)
Therefore, the distance between the two artifacts is 4.
The distance between the two artifacts, located at coordinates (1, 4) and (5, 2), can be calculated using the distance formula:
\(d = sqrt((x2 - x1)^2 + (y2 - y1)^2)\)
Plugging in the given values:
\(d = sqrt((5 - 1)^2 + (2 - 4)^2)d\)
\(= sqrt(4^2 + (-2)^2)d\)
\(= sqrt(16 + 4)d\)
\(= sqrt(20)\)
d ≈ 4.47 (rounded to two decimal places)
Therefore, the distance between the two artifacts is approximately 4.47 units.
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Square OPQR is inscribed in triangle ABC. The areas of △AOR, △BOP, △CRQ are 1, 3, and 1, respectively. What is the area of square OPQR?
Answers
Answer:
9 units²
Step-by-step explanation:
We know that ΔCRQ and ΔBOP are right triangles because RQ and OP are perpendicular to CB.
ΔAOR must also be a right triangle because ∠AOR = ∠OBP and ∠ARO = ∠RCQ.
Because of the Angle-Angle-Angle theorem, we know that ΔAOR ≅ ΔBOP ≅ ΔCRQ.
AR/AO = OP/PB
3(1/2)(AR)(AO) = (1/2)(OP)(PB)
PB = 6, OP = 3
3 x 3 = 9 units²
The area of square OPQR is 9 units².
Calculation of the area of square:Since
ΔCRQ and ΔBOP are right triangles since RQ and OP are perpendicular to CB.
Also,
ΔAOR must also be a right triangle due to ∠AOR = ∠OBP and ∠ARO = ∠RCQ.
So it can be like
AR/AO = OP/PB
3(1/2)(AR)(AO) = (1/2)(OP)(PB)
PB = 6, OP = 3
= 3 x 3
= 9 units²
hence, The area of square OPQR is 9 units².
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IN THE FIGURE BELOW LINES P AND Q ARE PARALLEL. WHAT DO YOU NOTICE
IREADY 50 POINTS!!!
Answers
Answer:
-> Supplementary
-> Add up to 180°
Explanation:
A straight line has a measurement of 180°. Supplementary angles are angles that, when added together, equal 180°.
Since angles 5 and 6 make up a straight line, we know they will add up to 180°.
An account is opened with a $600 deposit. The money sits for 15 years with 1 a 2.9% interest rate. When the money is withdrawn after 15 years, how much is available?
Answers
Answer:
$921.17 will be available in the bank account after 15 years.
Mickey drew a scale drawing of the room in his junior high building using the scale 1 centimeter (cm) - 1.5 meters (m). the office in his scale drawing measured 2.6 cm * 3.2 cm. what
are the actual dimensions of the office?
2.6 m x 3.2 m
1.7 m x 2.1 m
3.9 m x 4.8 m
4.1 m x 47 m
Answers
Answer:
3.9m x 4.8m
Step-by-step explanation:
1 cm = 1.5m
→ Multiply both sides by 2.6
2.6 cm = 3.9m
→ Multiply from the original statement, both sides by 3.2
3.2 cm = 4.8 m
→ Combine them
3.9m x 4.8m
I have no clue how to answer this?
Answers
The table shows the results of an experiment in which three coins were tossed.
What is the experimental probability that at least two of the coins will be heads? The theoretical probability?
Answers
The experimental probability that at least two heads would be gotten is 11 / 25.
The theoretical probability that at least two heads would be gotten is 1/2.
What are the probabilities?Probability calculates the odds that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Experimental probability is based on the result of an experiment that has been carried out multiples times.
Experimental probability = number of times at least two heads would be gotten / total number of tosses
( 5 + 6 + 6 + 5)/50 = 22/50 = 11 / 25
Theoretical probability = number of times at least two heads would be gotten / total number of possible outcomes
4 / 8 = 1/2
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Allie says that the expressions 4x - 2x +4 and 2(x + 2) are not equivalent because one expression
has a term that is subtracted and the other does not. Do you agree? Explain.
Yes,
the expressions are equivalent. The first expression, 4x - 2x +4, can be simplified to
which equals 2(x + 2).
(Use the operation symbols in the math palette as needed.)
Answers
Answer:
the espression are equivalent
Step-by-step explanation:
4x - 2x + 4 = 2 (x + 2)
2x + 4 = 2x + 4
the espression are equivalent
Determine the slope of a line that passes through (1,9) and (-2,3).
Answers
Answer:
the answer is m = 2
Step-by-step explanation:
Use Symbolab I use it all the time it gives correct answer and it gives good explanations (this isn't a sponsor I've just been using it since the 6th grade lol)
Find the equation of a line that passes through (1,7) and is parallel to the graph of y=2x+7. Write the equation in slope-intercept form, if possible.
Answers
Answer:
y=2x+5.................
Two dogs are running in a fenced park. One dog is following a path that can be modeled by the equation y=4. Another dog is following a path that can be modeled by the equation y=-x^2 +3. Well the dogs paths cross? Explain your answer.
Answers
Answer:
im not sure
Step-by-step explanation:
What is the slope intercept form of 2x+2y=10 (y=mx+b no extra words or comments)
Answers
Answer:
\(y=-x+5\)
Step-by-step explanation:
\(2x+2y=10\\2y=10-2x\\y=-2/2x+10/2\\y=-x+5\)
help asap if you can pls an thank u!!!!!!!
Answers
The value of angle S is 53°
What is exterior angle theorem?Exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of two remote interior angles.
With this theorem we can say that
7x+2 = 4x+13+19
collecting like terms
7x -4x = 13+19-2
3x = 30
divide both sides by 3
x = 30/3
x = 10
Since x = 10
angle S = 4x+13
angle S = 4(10) +13
= 40+13
= 53°
Therefore the measure of angle S is 53°
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