Answer:
Basic Relationship
We will use the equation below to derive all the other forms:
(1) log(NN0)=rt
Where:
N0 (initial population) = The population at time t = 0.
N (future population) = The population at time t.
r (rate) = The rate of population change as a function of t (a 1% increase is expressed as 0.01).
This variable is called the Malthusian Parameter.
In population studies, r is usually taken to mean births minus deaths.
t (time) = The amount of time required to produce a growth in population proportional to N/N0.
Source: Wolfram Math World: Population Growth
Derived Forms
Here are the forms of equation (1) in terms of each of its variables:
(2) N=N0e(rt) (future population)
(3) N0=Ne(−rt) (present population)
(4) t=log(NN0)r (time)
(5) r=log(NN0)t (rate)
Note that e in the above equations is the base of natural logarithms, and log(x) refers to the natural logarithm of x.
Doubling time
At the present world population growth rate of 1.1% per year (Population Growth), how long will it take to double the world's population?
The appropriate equation for this case is (4) above, with the following arguments:
t=log(NN0)r=log(21)0.011=63.243 (years)
This equation shows that it will take about 63 years to double the world's population. If this prediction is borne out, there will be 14 billion people on Earth in 2074 (based on the 2011 population of 7 billion).
Rate of Increase
How many more people join us each day?
The base equation for this case is (2) above:
N=N0e(rt)
But because we want the increase per day, we will use this form:
Nd=N0e(rt)−
Find the AREA of the triangle below.
Answer:
212.5
Step-by-step explanation:
a=b*h/2
b=25
h=17
25*17 =425
425/2=212.5
a=212.5
You mow 1/3 of the lawn. Your sister mows 2/5 of the lawn. What fraction of the lawn is left to mow?
Answer: 4/15
Step-by-step explanation:
1/3+2/5 change it to 5/15+6/15=11/15 4/15 left of the lawn
SOMEONE, PLEASE SEND HELP
A bag has 8 green, 2 yellow, 6 blue, and 4 red marbles. What is the probability of selecting a green marble, keeping it, and then selecting another green marble?
4/25
1/400
1/380
14/95
Answer:1/400
Step-by-step explanation:
because you have to add
The problem is: 4 divided by 2 plus 5 squared
A) 49
B) 31
C) 27
D) 4 over 49
Answer:
C
Step-by-step explanation:
4/2 + 5(2)
4/2 + 25
2 + 25
c.) 27
james jogged around the track 0.68 hours at an average speed 28.9 miles per hour how far did he jog?
Answer:
Step-by-step explanation:
0.68hr(28.9mi/hr)=19.652mi
A triangle has side lengths of 6, 8, and 10. Is it a right triangle? Explain.
Answer:
yes
Step-by-step explanation:
Yes it is, assuming we decide to use the Pythagorean Theorem to find the hypotenuse (10) it'll be possible considering the formula is c²=√a²+b²
(c being the longest side of the triangle)
a= 6 and b= 8
Alex has 30,000 in his savings account that earns 10%
annually.
How much interest will he earn in one year?
Answer:
i dont know im so sorry
Step-by-step explanation:
i hope u find ur answer
A large school district is considering implementing a program that, if successful, would improve the reading scores of its students by 10 points. The current reading scores for the district are normally distributed with a mean of 25 and a standard deviation of 8. The administrators decide to test the new program in one school of 200 students. What is the standard deviation of the comparison distribution
Answer:
The standard deviation of the comparison distribution is 0.5657.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
In this question:
Standard deviation of the population is 8, sample of 200. So
[tex]s = \frac{8}{\sqrt{200}} = 0.5657[/tex]
The standard deviation of the comparison distribution is 0.5657.
Can someone help me
9514 1404 393
Answer:
vertical50°Step-by-step explanation:
Angles BGC and FGE share vertex G and are composed of opposite rays. This makes them vertical angles.
Angle BGC and CGD make up a right angle, so they are complementary. That makes angle BGC equal to 90° -40° = 50°.
Vertical angles have the same measure, so ∠FGE = 50°.
you buy a watch that cost 45.50. The tax rate is 9.5%. What is the final cost?
Answer:
$49.8225
Step-by-step explanation:
9.5%=0.095
45.50*0.095=4.3225
45.50+4.3225=49.8225
Which of the following sets of ordered pairs is a function?
Answer:
A
Step-by-step explanation:
for every input there's one output
Please help me asap this is my math homework
Answer:
3.5 would be the answer
Step-by-step explanation:
In the song, 7 pounds, 5 ounces was the median weight of the students at birth. Which of these is correct?
Answer: Half the students weighed less than 7 pounds, 5 ounces, and half the students weighed more.
Step-by-step explanation:
WHO WANT BRAINLYEST????????
PLs shw how to solve
Answer: 60
Step-by-step explanation: you have to do the base X height which is 12 x 10 and that gets you 120. Then you have to divide that by 2 and it will get you 60 :)
╔═.✵.══════════╗
A N S W E R
╚══════════.✵.═╝
☆ ☆ ☆
You multiply each number, so: 10 x 12 x 13
Which gives you the conclusion of 1560.
Hope this helped, love! ☆ ☆ ☆
find the surface area of a cylinder with the height of 10 inches and a base diameter of 6 in
Answer:
339.24
Step-by-step explanation:
To find the surface area, you will need to the the area of the base of the cylinder. To do that, use the formula A=pi (r)^2
The radius is half the diameter do r=3
3.14(3)^2 should give you about 28.27.
This is the area of the top and bottom of the cylinder.
Now, do 28.27x10=282.7 to find the height surface area.
282.7+28.27+28.27=Surface area.
SA= about 339.24
Find the value of −12 + 8 −(−9). Question 20 options: −13 −5 13 5
Answer:
D) 5
Step-by-step explanation:
-12 + 8 + 9 = 5
What is the surface area of the right rectangular prism?
Enter your answer in the box
ft?
2(lb+bh+hl)
2(6×3+3×4+4×6)
2(18+12+24)
2(54)
108cm^2
Answer:
108cm2
Step-by-step explanation:
hello! I am currently failing math class and if I don’t get it together I might have to repeat the grade! so I really need you help and if you have the answer let me know in the comments please !! <3 :)
question⬇️⬇️
Hannah ran 10 miles. how many feet is this ?
10 miles in feet is 52800ft.
1 mile in feet is 5280 and when multiplying by 10, you usually just add a zero at the end of the number which makes 5280 turn into 52800!
If this is incorrect please don't refrain to tell me and I'll correct my answer. Thank you.
Someone please help me find the area I’ll give brainliest
Answer:
The area of the rectangle? If so it's 240.
Simplify the following expression.
Answer:
x^(4/21)
Step-by-step explanation:
A virus has infected 400 people in the town and is spreading to 2.5% more people each day.
Write an exponential function to model this situation, then find the number of people that will be
infected in 10 days.
Answer:
3725 infected people in 10 days
Step-by-step explanation:
that is the answer
After experiencing a period of rapid increase beginning in 2005, the populations of swallows in two different national parks level off. The approximate populations are modeled here, where x is time, in years, since 2005. Find the rates of change in population for both parks between 2009 and 2014, and determine which park showed faster population growth during those years. HINT: It's not C. GRAPHS BELOW
A. Park B showed faster growth between 2009 and 2014, at an average rate of 100 swallows per year.
B. Park A showed faster growth between 2009 and 2014, at an average rate of 100 swallows per year.
C. Park A showed faster growth between 2009 and 2014, at an average rate of 120 swallows per year.
D. Park B showed faster growth between 2009 and 2014, at an average rate of 120 swallows per year.
Answer: D. Park B showed faster growth between 2009 and 2014, at an average rate of 120 swallows per year.
Step-by-step explanation:
I did the math
The Park B showed faster growth between 2009 and 2014, at an average rate of 100 swallows per year i.e. option A.
What is average rate?The average rate is defined as a measure of how much the function changed per unit, on average, over that interval.
We have,
x is time, in years, since 2005,
and,
f(c) is population in hundreds.
Now,
For Park A,
at x = 4 ,
Swallows Population = 2370
and,
at x = 9,
Swallows Population = 2870
So,
Average Rate [tex]=\frac{2870 - 2370}{10} = 50[/tex]
Now,
For Park B,
at x = 4,
Swallows Population = 2200
and,
at x = 9,
Swallows Population = 2800
So,
Average Rate [tex]=\frac{2800- 2200}{10} = 60[/tex]
So,
Difference in average rate = 60 - 50 = 10
From the average rate of of both park A and Park B,
We can see that,
Park B has faster growth rate of 100 per year.
Hence, we can say that the Park B showed faster growth between 2009 and 2014, at an average rate of 100 swallows per year i.e. option A.
To know more about average rate click here
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3.16 SAT scores: SAT scores (out of 2400) are distributed normally with a mean of 1490 and a standard deviation of 295. Suppose a school council awards a certificate of excellence to all students who score at least 1900 on the SAT, and suppose we pick one of the recognized students at random. What is the probability this student's score will be at least 2100
Answer:
0.2333 = 23.33% probability this student's score will be at least 2100.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution, and conditional probability.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
SAT scores (out of 2400) are distributed normally with a mean of 1490 and a standard deviation of 295.
This means that [tex]\mu = 1490, \sigma = 295[/tex]
In this question:
Event A: Student was recognized.
Event B: Student scored at least 2100.
Probability of a student being recognized:
Probability of scoring at least 1900, which is 1 subtracted by the pvalue of Z when X = 1900. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1900 - 1490}{295}[/tex]
[tex]Z = 1.39[/tex]
[tex]Z = 1.39[/tex] has a pvalue of 0.9177
1 - 0.9177 = 0.0823
This means that [tex]P(A) = 0.0823[/tex]
Probability of a student being recognized and scoring at least 2100:
Intersection between at least 1900 and at least 2100 is at least 2100, so this is 1 subtracted by the pvalue of Z when X = 2100.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2100 - 1490}{295}[/tex]
[tex]Z = 2.07[/tex]
[tex]Z = 2.07[/tex] has a pvalue of 0.9808
This means that [tex]P(A \cap B) = 1 - 0.9808 = 0.0192[/tex]
What is the probability this student's score will be at least 2100?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0192}{0.0823} = 0.2333[/tex]
0.2333 = 23.33% probability this student's score will be at least 2100.
How many 2/3 are in 5?
Answer:
7.5
Step-by-step explanation:
5/(2/3) = 7.5
Sales total : $155,000
Commission : 3.4%
How much is the commission?
Answer:
5,270
Step-by-step explanation:
155,000 x 3.4%
Answer:
5270
Step-by-step explanation:
multiply 155,000 by 3.4 and then divide it by 100
155,000 x 3.4=527,000
527,00 divided by 100 = 5270
I WILL GIVE BRAINLIEST.
Find the lateral surface area of a cylinder with a diameter of 21 inches and a height of 15 inches.
Answer:
Step-by-step explan
21
HELP ASAP PLS ANSWER THE QUESTION IN THE PIC I GIV BRAINLEST AND LOTS OF POINTS TO CORRECT ANSWER
The answer could be either
C or B
I need the answer for this one please
Answer:
Step-by-step explanation:
65
Solve the following equations for x
13−(2x+2)=2(x+2)+3x
Answer:
x = 7
Step-by-step explanation:
Distribute the 2 on the right and the -1 on the left: 13 - 2x - 2 = 2x + 4 + 3x
Combine like terms on each side of the equation: 11 - 2x = 5x + 4
Add 2x to both sides, and subtract 4 from each side: 7 = 7x
Divide both sides by 7: x = 7
What is the value of x?
If your answer is not an integer,
express it in simplest radical form.
Answer:
±8√2
Step-by-step explanation: