a population doubles in size every 15 years. assuming exponential growth, find the (a) annual growth rate (b) continuous growth rate
The annual growth rate is 4.73 %
The continuous growth rate is 4.62 %
What is exponential growth function ?
A process called exponential growth sees a rise in quantity over time. When a quantity's derivative, or instantaneous rate of change with respect to time, is proportionate to the quantity itself, this phenomenon takes place.
Let us assume:
The initial amount of 1, so results are 2.
Let x be the percent in decimal form
Growth rate per year:
[tex]1(1+x)^{15} = 2[/tex]
Take ln on both the sides
[tex]ln((1+x)^{15}) = ln(2)[/tex]
15*ln(1+x) =0 .693
ln(x+1) = 0.693/15
ln(x+1) = 0.04621
Take anti ln on both the sides
x+1 = 1.0473
x = 1.0473 - 1
x = .0473
x =4.73 % annual growth rate
Continuous growth rate:
[tex]1*e^{15x} = 2[/tex]
[tex]ln(e^{15x}) = ln(2)[/tex]
15x*ln(e) = ln(2)
ln(e) = 1
15x =0.693
x =0 .693/15
x = .0462
x = 4.62 %
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An environmental group conduct a tudy to meaure energy conumption in a large metropolitan city a meaured by the amount of gaoline purchaed. In a random ample of 17 vehicle owner on a particular day, they calculated a mean of 13. 62 gallon and a tandard deviation of 4. 68 gallon. What i the tandard error of the ample mean?
The random sample study's standard error, which measures the energy usage in a major metropolis, is 0.275.
How is the standard error calculated?The standard deviation among the sample means is typically the standard error of a sampling distribution. It fluctuates inversely with sample size, meaning that as sample size rises, the sampling distribution's standard error falls.The formula used to compute standard error is as follows:
standard error = standard deviation / √sample size
For the data given in question-
In a random sample of 17 car owners on a given day, the mean fuel consumption was 13.62 gallons, and the standard deviation was 4.68 gallons.Thus,
Standard error = 4.68 / 17
Standard error = 0.275
Thus, the standard error for the mean of the sample is found as 0.275.
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If x = 6, what y? Please help
Answer: I think the answer is 2
Step-by-step explanation:
The smaller of the two shapes is 12, and the larger of the two shapes is 16,
I found that the difference between the two is 4 (or 16 - 12 =4). If x = 6 and the difference is 4, then subtract 4 from 6 and the answer will come out to be 2
16-12=6-4
y=2
a research study reported that 10% of the people who are given a certain drug experience dizziness.if 15 people are selected at random, find the probability that none of them experience dizziness when given the drug.
Out of the 15 people the probability that none of the patients will experience dizziness is approximately 0.206 .
10% of the people experiences dizziness.
Probability that a random patient experiences dizziness = 0.1
Probability that the person does not experience dizziness = 0.9
Now this is in the form of a binomial distribution such that the probability is given by:
Sample = 15
P = 0.1
P' =0.9
Required probability :
= ¹⁵C₀ × P⁰ × P'¹⁵ (binomial distribution)
= 1 × 0.1⁰ × 0.9¹⁵
= 0.20589...
≈ 0.206
Hence the required probability is approximately 0.206 .
The binomial distribution is often used to predict the number of further successes in either a sample of size n drawn under replacement from either a population of size n.
If the sampling is carried out without replacement, the drawings are not independent, hence the resulting distribution is a hypergeometric one rather than a binomial one.
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To test the effectiveness of a liquid supplement that is supposed to help forgetful people with their memory, 400 college students are recruited for a study and divided into two groups. Group A with 250 students receives the supplement, while group B with 150 students receives some colored water. Neither group is told what they received. After several weeks, they are given a memory test. This study can best be described as: . a census a controlled placebo experiment a survey using quota sampling a survey using simple random sampling the placebo effect
This study can be best described as Controlled Placebo Experiment
What is a Controlled Placebo Experiment?
A controlled placebo experiment is a type of research method that is used to check the effectiveness of a drug in a patient. This is done by selecting a sample group, then randomly divide the two group into a placebo group (this are the group that will receive the drug treatment ) and the controlled group (these are the group that will receive a colored mixture that looks like the drug, but does not have any effect). Without the groups knowledge about the real drugs and the colored mixture, but are followed up and tested.
According to the given question:
This is a controlled placebo experiment, because 400 student has been chosen as the sample, and are divided into a placebo group and a controlled group, to check the effectiveness of a drug on their memory.
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In cooking class, Lupita and Jacob each make a mixture of basil and oregano. Lupita uses 2 tsp basil for every 3 tsp oregano. Jacob uses 4 tsp basil for every 5 tsp oregano. Lupita says the two mixtures will taste the same. Jacob says his will have a stronger basil taste than Lupita’s. Who is correct? Explain.
Using ratio and proportions, Jacob has mixture with stronger basil taste
Ratios and ProportionRatio can be defined as a comparison between two or more numbers that shows their sizes in relation to each other. A ratio often compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent.
Proportion can be defined as equality of two ratios. Two equivalent ratios are always in proportion. Proportion is an equation or statement that shows that the two ratios or fractions are equivalent.
In this case, we can compare the ratio and determine which will have a stronger basil taste.
Lupita mixed 2 tsp of basil for 3tsp of oregano
The ratio of basil to oregano = 2/3 = 0.67
Jacob mixed 4 tsp of basil for 5 tsp of oregano
The ratio of basil to oregano = 4/5 = 0.8
Comparing the ratios, Jacob ratio is higher compared to Lupita and makes Jacob have the strong basil taste.
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Help please!! I need this answer!!
Answer: Store B and C sell at a lower unit price.
Step-by-step explanation:
Store B: $3.48/3 = $1.16 per pound.
Store C: $3.80/4 = $0.95 per pound.
9. What is the distance between the coordinates (9, -2) and
(9,8)?
Answer:
10
Step-by-step explanation:
if u got up 10 from (9,-2) you will get to (9,8)
6y-5=7
what is y hdhfhdjshbdhdj
Answer: Y=2
Step-by-step explanation:
the residual is defined as the difference between the actual and predicted, or fitted values of the response variable. group of answer choices false true
The Residual is defined as the difference between the actual and predicted, or fitted values of the response variable. This statement is true.
Linear regression is a statistical tool that determines how well a straight line fits a set of paired data. The straight line that best fits that data is called the least squares regression line. This line can be used in a number of ways. One of these uses is to estimate the value of a response variable for a given value of an explanatory variable. Related to this idea is that of a residual.
Residuals are obtained by performing subtraction. All that we must do is to subtract the predicted value of y from the observed value of y for a particular x. The result is called a residual.
The formula for residuals is straightforward:
Residual = observed y – predicted y
It is important to note that the predicted value comes from our regression line. The observed value comes from our data set.
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for a list of five positive integers, none greater than 100, the mean is 1.5 times the mode. if 31, 58, 98, $x$ and $x$ are the five integers, what is the value of $x$?
The value of x from the given five integers is 34.
Here we have to find the value of x.
Data given:
Five positive number = 31, 58, 98, x, x
The mean is 1.5 times the mode.
Mean = (31 + 58 + 98 + x + x) / 5
= (187 + 2x) / 5
Mode = x
As the mean is 1.5 times the mode so from this we have:
mean = 1.5 × mode
(187 + 2x)/ 5 = 1.5x
187 + 2x = 7.5x
5.5x = 187
x = 34
Therefore the value of x is 34.
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can someone help me really quick
(please Explain how you know this is correct)
The answer is $12.50
You can see on the graph that if the weight is 20 pounds, it will cost $10. We are looking for how much it will cost to ship a 25 pound package. It can’t be $20.00 either.
hope this helps!
Give me Brainliest please!
the execution of the commandselect cname from customer where age < 30 and age > 40will produce the following number of rows:
The given command "select cname from customer where age < 30 and age > 40" will produce 4 rows according to the database table.
What is database?A database in computing is a structured collection of data that is electronically accessible and stored. Large databases are housed on computer clusters or cloud storage, whilst small databases can be kept on a file system. A database is a collection of data that has been organized to make it simple to maintain and update. Data records or files containing information, including as sales transactions, customer information, financial data, and product information, are often aggregated and stored in computer databases. A database is a planned gathering of data. They enable the manipulation and storage of data electronically. Data administration is made simple by databases. Let's use a database as an example. A database is used to store information about people, their phone numbers, and other contact information in an online telephone directory.
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find the dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius cm. what is the maximum volume?
The dimensions of a right circular cylinder of maximum volume are
[tex]5\sqrt{6}[/tex] and [tex]10\sqrt{3}[/tex].
Given the radius of sphere is 15 cm.
Let's assume radius of right circular cylinder = r
height of right circular cylinder = h.
Since the cylinder is inscribed in the sphere, their centers will coincide. As a result, the height is divided into two equal portions from the sphere's center. Therefore, we can apply Pythagoras' Theorem to get the cylinder's half-height in terms of radius.
[tex]R^2 = r^2 + (h/2)^2.[/tex]
[tex]r^2 = R^2 - h^2/4.[/tex]
Volume of cylinder = [tex]\pi*r^2*h.[/tex]
Now we can substitute value of [tex]r^2[/tex] in volume of cylinder.
V = [tex]\pi*( R^2 - h^2/4)*h[/tex]
taking R = 15 .
V = [tex]\pi*(225 - h^2/4)*h[/tex]
V = [tex]\pi*225*h - \pi*h^3/4[/tex]
For maximum volume we have to do derivative of volume = 0
derivative with respect to h.
V' = [tex]\pi*225 - 3*\pi*h^2/4[/tex]
V' = 0
[tex]\pi*225 - 3*\pi*h^2/4[/tex]= 0
[tex]3*h^2/4 = 225[/tex]
[tex]h^2 = 75*4.[/tex]
h = 10[tex]\sqrt{3}[/tex]
put the value of h in [tex]r^2 = 225 - h^2/4[/tex]
[tex]r^2[/tex] = 225 - (300/4)
[tex]r^2[/tex] = 150
r = [tex]\sqrt{150}[/tex]
r = 5[tex]\sqrt{6}[/tex].
So the dimensions of a right circular cylinder are 10[tex]\sqrt{3}[/tex] and 5[tex]\sqrt{6}[/tex].
Given Question is incomplete, Complete Question here:
find the dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 15 cm. what is the maximum volume?
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in a lecture hall containing 100 people, you consider whether or not there are three people in the room who share the same birthday. explain how to calculate this probability exactly, using the same assumptions as in our previous analysis.
The probability of three people who share the same birthday is 0.6459.
Let us consider that A₀ be the event that everyone in the room has a distinct birthday. Let Ai be the event that pairs of people share a birthday. Then the probability we are interested in is
P(at lest three people share a birthday) = 1 - P(A₀) - ∑ P(Ai)
where there are n people in the lecture hall.
First we note that P(A₀) is in the book and is
P(A₀) = (365Cn)n!/365^n.
Now we will compute P(Ai).
For i = 1,
P(A₁) = (365) × [tex]\frac{(nC2)(365-1Cn-2)(n-2)!}{365^{n} }[/tex]
For i = 2,
P(A₂) = [tex]\frac{(365C2)(nC2)(n-2C2)(365-2Cn-4)(n-4)!}{365^{n} }[/tex]
This generalizes for i pairs of people sharing i distinct birthdays
P(Ai) = (365Ci)πj=1toi(n-2j+2C2)(365-iCn-2i)(n-2i)!/([tex]365^{n}[/tex])
Substituting all values into the equation and putting in n = 100, we can compute a value for this probability.
Therefore we get,
P(at least 3 people share a birthday)0.6459.
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Which of these relations is a function?
The relation that is a function is the graph (d)
How to determine the function?From the question, we have the graphs to represent the given parameters that can be used in our computation
We are to find out which of them represents a function
For a graph to represent a function, the graph must pass the vertical line test
This means that a line drawn from the x-axis must touch the graph at most once
So, we draw these lines and attach the graphs (see attachment)
The graph that pass the vertical line test is graph d
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help plsssssssssssssss
Answer:
multiplication property of equality
if gallup wishes to use a 95% confidence interval, compute the minimum number of american adults that they need to survey to ensure that the error bound, under no circumstances, is more than 0.01 before conducting the experiment?
the minimum number of american adults that they need to survey to ensure that the error bound is 16,867 with sample size
The sample size of a study is the number of subjects or observations that are included.Two statistical properties are influenced by the sample size: 1) The accuracy of our estimates, and 2) The ability to draw conclusions from the study.
The minimum sample size required to get a 95% confidence interval with an error bound of 0.01 is 16,867. This can be calculated using the formula:
n = (1.96 / 0.01)2 = 16,867.
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If a building i 50 feet in diameter and you need 20 feet of clearance all the way around the building, how many feet of fence to you need to go around the building?
31.41 feet of fence to you need to go around the building.
What is circumference of a circle?
The measurement of the circle's boundaries is called as the circumference or perimeter of the circle. whereas the circumference of a circle determines the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it. The circle's radius is considered while calculating the circumference of the circle using the formula. As a result, in order to calculate the circle's perimeter, we must know the radius or diameter value.
The radius of the circle given is = 50/2 feet.
So the clearance of 20 feet will be there all way.
So total effective radius will be 25-20 5 feet.
the circumference is 2πr = 2*π*5 = 31.41 feet
Hence, 31.41 feet of fence to you need to go around the building.
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Morgan and her children went into a grocery store and she bought $10
worth of peaches and mangos. Each peach costs $1 and each mango
costs $2. She bought a total of 8 peaches and mangos altogether.
Graphically solve a system of equations in order to determine the
number of peaches, a, and the number of mangos, y, that Morgan
bought.
Answer:
The number of peaches and the number of mangos that Savannah bought
are 4 and 10 respectively.
The variable use to write the equation is x and it is the number of peaches
Savannah and her children bought
let
the number of peaches Savannah and her children bought = x
Therefore
the number of mangoes Savannah and her children bought = x + 6
The total worth of what they bought = $22
Therefore,
1.75x + 1.50(x + 6) = 22
1.75x + 1.50x + 9 = 22
3.25x + 9 = 22
3.25x = 22 - 9
3.25x = 13
x = 13 / 3.25
x = 4
Therefore,
number of peaches bought = 4
number of mangoes bought = 4 + 6 = 10
Step-by-step explanation:
Answer: 6 Peaches and 2 Mangos
Step-by-step explanation: If one peach is worth $1 and one mango is worth $2, to get $10 used you need to buy 6 peaches and 2 mangos since 2 + 2 = 4 and 6 + 4 = 10
a laboratory supply company produces graduated cylinders, each with an internal radius of 222 inches and an internal height between 7.757.757, point, 75 inches and 888 inches. what is one possible volume, rounded to the nearest cubic inch, of a graduated cylinder produced by this company?
One possible volume of a graduated cylinder produced by the company is 98 cubic inch.
The volume of a cube is defined as the total number of cubic units occupied by the cube completely. A cube is a three-dimensional solid figure, having 6 square faces. Volume is nothing but the total space occupied by an object. An object with a larger volume would occupy more space.
The volume of a cube can be found by multiplying the edge length three times. For instance, if the length of an edge of a cube is 4, the volume will be 4³. The formula to calculate the volume of a cube is given as,
Volume of a cube = s³, where 's' is the length of the side of the cube.
Given in the question:
Radius of cylinder = 2 inches.
Height of the cylinder = 7.75 to 8 inches.
We know that,
Volume of Cylinder = πr²
For minimum Volume 7.75 :
Volume = πr²× 7.75
= 3.14 × 4 × 7.75
= 97.34 cubic inches.
For maximum volume 8.00 inches
Volume = πr² × 8
= 3.14 × 4 × 8
= 100.81
Therefore, the possible volume could be between 97.34 cubic inches and 100.81 cubic inches.
Thus, the volume is 98 cubic inches.
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on your desk, there is a very special die with a prime number p of faces, and you throw this die once. show that no two events a and b can be independent unless either a or b is the whole sample space or the empty set.
We have proven that no two events a and b can be independent unless either a or b is the whole sample space or the empty set below.
A sample space can be defined as the set of all possible outcomes of any experiment.
We are already aware that the outcomes of this die are going to be (1,2,3,..p). If we have a pair of proper events A, B which are independent, this would mean that = A∩B={∅} (i)
This is a contradiction. So, now we suppose that = A∩B=C, for some proper event C (ii)
Using the values of (i) and (ii), we get -
= |C|p=P(A∩B)=P(A)P(B)=|A||B|p2.
= p|C|=|A||B|.
From this, we understand that neither A nor B are going to be full spaces and hence, no two events a and b are independent and 0<|A|<p and 0<|B|<p. Since |C| is also going to be less than 0 and p is prime, p divides either |A| or |B|. if p was not prime (say, p=4), then you would only need the factors of p to divide either |A|,|B|, so, it becomes necessary for p to be a prime number. Hence, proved.
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PLS HELP 50 pnts!!!!!!! giving brainliest!!! 1-4 (find the slope)
-attached pic
-unacceptable answers will result in 2 reports (2 warnings and the max is 3 then you will be banned)
Answer:
1) slope = 1/2 2) slope= -1 3)slope= 1/2 4) 5/4
Step-by-step explanation:
if you want y intercpt form
1) y=1/2x
2)y= -x-3
3) y= 1/2x-3.5
4) y= 5/4x - 1
Calculate the cfse for a d^3 system in an octahedral field in units of ∆_o. In other words, do not enter "∆_o" with your answer. For example, if your answer is −0. 8∆_o, then enter "−0. 8. "
The magnetic moment of an octahedral complex with CFSE=0.8Δo and weak field ligands can take the form of Q.
The Crystal Field Stabilization Energy for a (d3 metal in both forms must be determined in order to provide an answer. The chosen geometry will be the one with the greatest stabilization. The Crystal Field Stabilization Energy is therefore CFSE = -0.8 x 4/9 Δo = -0.355 Δo for tetrahedral d3.
The octahedral d7 complex [Co(CN)64-] is also CN—a strong field ligand. Because of its (t2g)6(eg)1 orbital occupancy, it possesses one unpaired electron. The CFSE in this instance is −(6)(25)ΔO+(1)(35)ΔO+P=−95ΔO+P.
The [Ti(H2O)6]3+ complex's crystal field stabilization energy (CFSE), measured in kJ/mol. The first absorption maximum for the transition, according to CFT, is at 20,3000 cm-1.
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The base of a triangle is four more than twice its height. If the area of the triangle is 43 square centimeters, find its base and height.
The height of the triangle is
centimeters.
(Simplify your answer. Type an exact answer, using radicals as needed.)
The height of the triangle would be 5.63 cm.
What is the area of the triangle?
For a given triangle of height 'h' and the base is 'b' then the area of the triangle is
A = 1/2 Base * Height
Given data:
Base of the triangle = 2*height of the triangle + 4
b = 2h + 4
Area = 43 square centimeters
By using the area of the triangle,
A = 1/2 *b * h
43 = 1/2(2h + 4)*h
86 = 2h²+4h
Simplifying this, we get
h² + 2h - 43 = 0
Solving this, we get
h = 5.63 and h = -7.63
Height cannot be a negative value so h = 5.63
Hence, the height of the triangle would be 5.63 cm.
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The money
m
(in £) Noah has to spend each week is his wage
w
(in £) subtract the tax
t
(in £) he pays on his income. Enter a formula for the money he can spend and enter how much he has to spend if he earns £160 a week and pays £55 in tax.
If Noah earns £160 a week and pays £55 in tax, he has £160 - £55 = £160-£55 = £105 to spend.
What is meant by subtraction?Subtraction is a mathematical procedure that includes subtracting one number from another. For example, if we have five apples and subtract three of them, we are left with two apples. Beginning with the bigger number and deducting the smaller number from it is how subtraction is done. Subtraction is denoted by the minus symbol (-). A difference is the outcome of a subtractive operation.
We may better grasp how to solve issues requiring the removal of one or more elements from a set by understanding the fundamental mathematical formula of subtraction. It is employed in many different scenarios, such as when we need to subtract incomes on a regular basis.
How to solve?
The formula for the money Noah has to spend each week is m = w - t.
£160 - £55 = £160 - £55 = £105
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a bathtub filled with 55 gallons of water is drained. the water drains at a rate of 5 gallons per minute. the function f(x)=-5x+55 represents the volume of water in the tub as it drains. how many minutes has passed if the tub still has more than 20 gallons of water remaining in it.
f-1(x)=1\5x-11
Step-by-step explanation:
samantha is considering job offers from two companies. company a offered her a starting salary of $48,000 with a $2100 raise at the end of each year. company b offered her a starting salary of $48,000 with a 3.7% raise at the end of each year.
Let f(t) represent Rosa's salary at Company A, t years after accepting a position at Company A, and let g(t) represent Rosa's salary at Company B t years after accepting a position at Company B.
Complete the table of values below:
t f(t) g(t)
0 50000 50000
1
2
3
The value of f(t) are 48000, 52200, 54300, 56400, and g(t) are 48000, 49776, 51617.71, and 53527.56.
She was given a starting wage of $48,000 from Company A, with annual raises of $2100.
The formula for Company A is
f(t) = 48000 + 2100t
She was given a starting wage of $48,000 from Company B, with an annual rise of 3.7%.
The formula for Company B is
g(t) = 48000 × [tex](1 + 0.037)^t[/tex]
The value of f(t) and g(t),
t ------- f(t) ------- g(t)
0 ----- 48000 ----- 48000
1 ------ 52200 ----- 49776
2 ----- 54300 ----- 51617.71
3 ----- 56400 ----- 53527.56
The graphical representation of both the linear equations of company A and company B.
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8(t+2) -3(t-4=6(t-7)+8
Answer: T-62
Step-by-step explanation: i think this is correct
The solution is, the value we get, t = 62.
What is simplification?Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
here, we have,
given that,
8(t+2) -3(t-4)=6(t-7)+8
or, 8t + 16 -3t +12 = 6t - 42 +8
or, 5t + 28 = 6t - 34
or, t = 62
Hence, The solution is, the value we get, t = 62.
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7x3/4=7 true or false
Answer:
false
Step-by-step explanation:
7*3 / 4 = 7
21 / 4 = 7
5.25 ≠ 7
Could you please give me brainliest? Thanks!