The population in 20 years is 719 people.
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
According to the question
[tex]\frac{dP}{dt} = kP[/tex] where P is population at any time
solving equation,
[tex]\int[/tex][tex]\frac{dP}{dt} =\\[/tex] [tex]\int kP[/tex]
[tex]lnP=kt+C[/tex] -(1)
Applying the conditions,
at t=0, P = 500
[tex]ln500=C[/tex] -(2)
at t=10, P= 600
putting it in equation gives
[tex]ln(600) = k(10)+ln(500)[/tex]
ln(6/5) = k(10)
[tex]k = \frac{ln(6/5)}{10}[/tex]
at t=20 , P= ?
[tex]lnP=(\frac{ln(6/5)}{10})20 + ln500[/tex]
[tex]lnP=({ln(6/5)}{2 + ln500[/tex]
On putting the values of ln(6/5) , ln(500)
[tex]lnP=0.182(2) + 6.214[/tex]
[tex]P = e^{6.578}[/tex]
P = 719.099
On rounding off
P ≈ 719 people
Thus the population in 20 years is 719 people.
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The sides of this rectangle are marked off in centimeters. If the rectangle is enlarged proportionally so that the longer side is 35 cm, how long will the shorter side be?
Answer:
10
Step-by-step explanation:
proportion
35 ÷ 7 = 5
2 x 5 = 10
Tim drives a average speed og 80km per hhour for 3 hours 45 minutes work out how many kilometers tim drives
The distance Tim drives is 300 kilometers
Average speed= 80 km
Time= 3 hours 45 minutes (15/4 hours)
Distance= Average speed/time
= 80 × 15/4
= 1200/4
= 300 kilometers
Hence the distance Tim drives is 300 kilometres
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Someone gotta help me out, it’s geometry and I’m in a hurry and I can’t figure this out. Someone help pls :(
Equilateral Triangle: All 3 sides of a Triangle are equal in length
Isosceles Triangle: Two sides of Triangle are equal in length
Scalene: Triangle has different side lengths
So, for example, when you see Q1, you estimate the length of each side and think it is Scalene Triangle because all of its sides are of different length. (You can also use a ruler to find out the side lengths if it can be used for scale)
Q2, you can say that the side lengths AC and BC look similar, so it is an Isosceles Triangle
Q6, when you look at the side lengths, you can tell it is an equilateral Triangle because all the sides are equal in length
You can try the rest and check for yourself. If you still have any doubts, you could ask me. I hope this information helps you.
What is the equation for the cones volume?
Answer: D
Step-by-step explanation:
[tex]V=\frac{1}{3}\pi r^{2} h[/tex] is the general formula for the volume of a cone with radius r and height h.
Substituting in s for both r and h, [tex]V=\frac{1}{3}\pi s^{3}[/tex].
Given ƒ(x) = x + 10 and g(x) = x2 + 5x - 1, find ƒ(3) + g(5).
True or false: Exponential growth depends on the per capita growth rate (rmax) of a population gradually increasing over time.
FALSE
Exponential growth is a pattern of data that shows sharper increases over time. In finance, compounding creates exponential returns. Savings accounts with a compounding interest rate can show exponential growth.
One of the best examples of exponential growth is observed in bacteria. It takes bacteria roughly an hour to reproduce through prokaryotic fission. If we placed 100 bacteria in an environment and recorded the population size each hour, we would observe exponential growth
First, population size is influenced by the per capita population growth rate, which is the rate at which the population size changes per individual in the population. This growth rate is determined by the birth, death, emigration, and migration rates in the population.
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Exponential growth depends on the per capita growth rate (rmax) of a population gradually increasing over time.
The given statement is false.
Exponential growth is a continuous boom or lower in a populace in which the price of change is proportional to the range of people at any given time.
It is growth that maintains acceleration with time and is a J-shaped curve. The intrinsic price of an increase in a populace is calculated by including the dying rate and the birth price.
Divide both sides by N and you get the growth rate per number of individuals ("per capita"): Because r = rmax [1-(N/K)] in the logistic model, we can substitute r: Thus, r equals the per capita growth rate.
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Given that
5x:9=8:3
Calculate the value of x
Give your answer in its simplest form.
Answer:
24/5
Step-by-step explanation:
5x : 9
(8 : 3)×3
5x : 9
24 : 9
5x = 24
x = 24/5 = 4/4/5
Hello!
5x : 9 = 8 : 3
5x × 3 = 8 × 9
15x = 72
5x = 24
x = 24/5
x = 4.8
∴ The value of x is 4.8.
What is the probability that a standard number cube will show a two or four when it is rolled?
Determine the point of intersection of the lines x+y=4 and 2x+3y=12 algebraically
Answer:
this is just a system of equations
x+y=4
2x+3y=12
x=-y+4
plug in
2(-y+4)+3y=12
-2y+8+3y=12
y+8=12
y=4
plug in
x+4=4
x=0
(0,4)
Hope This Helps!!!
Answer:
(0,4)
Step-by-step explanation:
find x by subtracting y from both sides
A fast food restaurant executive wishes to know how many fast food meals adults eat each week. They want to construct a 90% confidence interval for the mean and are assuming that the population standard deviation for the number of fast food meals consumed each week is 1.4. The study found that for a sample of 1271 adults the mean number of fast food meals consumed per week is 3. Construct the desired confidence interval. Round your answers to one decimal place.
The confidence interval which shows 90% confidence level for the mean and assumed standard deviation is (2.94 meals, 3.0565 meals).
Given standard deviation=1.4. Sample size =1271, mean=3.
We have to find the confidence interval for 90% confidence level.
We have to find out α level that is the subtraction of 1 by the confidence interval divided by 2.
α=(1-0.90)/2
=0.05
Now we have to find z in the z table as such z has a p value of 1-α so it is z with p value of 1-0.05=0.95
Z=1.44 from z table.
Now find M as such that
M=z* st/[tex]\sqrt{n}[/tex]
where st is standard deviation ,n is sample size.
M=1.44*1.4/[tex]\sqrt{1271}[/tex]
=1.44*1.4/35.65
=2.016/35.65
=0.0565
Lower end= mean -M
=3-0.0565
=2.94
Upper end=Mean+ M
=3+0.0565
=3.0565
Hence the confidence interval showing 90% confidence level is (2.94,3.0565).
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If m=5 and n = 2, find the value of 3mn
Answer:
30
Step-by-step explanation:
3mn=3x5x2=30
Algebra 2 - Composition Functions
#4-6: let f(x)= 5x^3-2x and g(x)= 3x^3. Perform the indicated operation.
[tex]f(x) = 5x {}^{3} - 2x \\ g(x) = 3x {}^{3} [/tex]
4)[tex] \frac{f(x)}{g(x)} = \frac{5x {}^{3} - 2x }{3x {}^{3} } = \frac{x(5x {}^{2} - 2)}{3x {}^{3} } = \frac{5x {}^{2} - 2}{3x^2} [/tex]
5)[tex]f(g(x)) = 5( 3x {}^{3} ) {}^{3 } - 2(3x {}^{3} ) \\ f(g(x)) = 135x {}^{9} - 6x {}^{3} [/tex]
6)[tex]g(f(x)) = 3(5x {}^{3} - 2x) {}^{3} \\ g(f(x)) = 3(125x {}^{9} - 150x {}^{7} + 60x {}^{5} - 8x {}^{3} ) \\ g(f(x) )= 375x {}^{9} - 450x {}^{7} + 180x {}^{5} - 24x {}^{3} [/tex]
In your own words, describe the difference between correlation and causation. Give an example (not given in the content) of two variables that might be positively or negatively correlated.
The difference between causation and correlation is that, Causation is characterized by cause-and-effect while correlation establishes a probable relationship.
What is the difference between Causation and correlation?While Causation is characterized by a situation in which an action certainly causes an outcome and hence, is described as a cause-and-effect relationship, Correlation on the other hand only establishes a relationship between the two events and doesn't necessarily ascertain the occurrence of the other event .
An example of two variables which may be correlated is; the height and weight of an individual in which case it is generally perceived that taller people are heavier.
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If g stands for a whole number, find the first three possible values of g2 + 3.
3, 4, 7
1, 4, 7
3, 5, 7
0, 4, 7
The first three values of g² + 3 are 3, 4, 7. The correct option is the first option 3, 4, 7
Evaluating an expressionFrom the question, we are to determine the first three possible values of g² + 3
From the given information,
g stands for a whole number
∴ The first three values of g are 0, 1, 2
When g = 0
g² + 3 becomes
0² + 3
= 0 + 3
= 3
When g = 1
g² + 3 becomes
1² + 3
= 1 + 3
= 4
When g = 2
g² + 3 becomes
2² + 3
= 4 + 3
= 7
Hence, the first three values of g² + 3 are 3, 4, 7. The correct option is the first option 3, 4, 7.
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Solve each triangle. Round answers to the nearest tenth.
Answer:
Step-by-step explanation:
a = 12 mi
b ≈ 14.0 mi
c = 7 mi
m∠A ≈ 59.0 °
m∠B ≈ 91°
m∠C ≈ 30.0 °
The lengths of the triangle are:
a = 12 mi
b ≈ 14.0 mi
c = 7 mi
And the angles of the triangle are :
m∠A ≈ 59.0°
m∠B ≈ 91°
m∠C ≈ 30.0°
What are the angles in a triangle?
Every triangle has interior angles that total 180.
Angles in a triangle are the total (sum) of the angles at each of its three vertices.
Given, in a triangle ∠B is = 91°
length of c = 7 mi
a = 12 mi
We need to find the missing angles and side length of b.
⇒ b² = a² ₊ c² ₋ 2accosB
⇒ b/sinB = a/sinA = c/sinC
b² = 12² ₊ 7² ₋ 2(12)(7)cos91°
b² = 144 ₊ 49 ₋ 2(84)cos91°
b² = 193 ₋ 168 cos 91°
b² = 195.856
b=√195.856
b = 14.0 mi
⇒14.0/sin91° = 12/sinA
⇒ sinA = 12sin91°/14.0
sin A = 0.857
A = arcsin(0.857)
A = 59.0°
∴ C = 180° ₋ (sum of two angles in a triangle)
C = 180 ₋ (91° ₊ 59°)
C = 180 ₋ 150°
C = 30°
Hence we get the angles in the triangle as m∠A = 59.0°, m∠B = 91° and m∠C = 30°
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idenify the numbers that are located below -3.5 on a vertical number line
A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. The numbers that are located below -3.5 on a vertical number line are (-∞,-3.5).
What is a number line?A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. It’s not a ruler, so the space between each number doesn’t matter, but the numbers included on the line determine how it’s meant to be used.
The numbers that are located below -3.5 on a vertical number line are all the numbers that are less than -3.5. The numbers that are located below -3.5 on a vertical number line are (-∞,-3.5).
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SOMEONE PLS HELP, ITS GEOMETRY, ITS URGENT ASAP PLS
Answer:
for st1: It's Given
For St2: Definition
For St3: Dividing BE as BF and FE or You can write From Figure:
For St4: You can write From st3
for st5: From St 4
For St7 : They are congruent by SSS axiom
prove that sin4a+2sin2acos2a+cos4a=1
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex] \qquad❖ \: \sf \: \sin {}^{4} ( \alpha) + 2 \sin {}^{2} ( \alpha) \cos {}^{2} ( \alpha) + { \cos {}^{4} ( \alpha) }^{} [/tex]
[tex] \qquad❖ \: \sf \:( \sin {}^{2} ( \alpha) ) {}^{2} + 2( \sin {}^{2} ( \alpha))( \cos {}^{2} ( \alpha)) + {( \cos {}^{2} ( \alpha)) }^{} [/tex]
( use identity a² + 2ab + b² = (a + b)² )
[tex] \qquad❖ \: \sf \:( {\sin {}^{2}( { \alpha}) + \cos {}^{2} ( \alpha)) }^{2} [/tex]
( sin² x + cos ² x = 1 )
[tex] \qquad❖ \: \sf \: {1}^{2} [/tex]
[tex] \qquad❖ \: \sf \: {1}^{} [/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
Value of that expression is 1
What is the shaded portion of the figure?
Answer:
D
Step-by-step explanation:
Area of Part of a Circle = (θ/360)[tex]\pi r^{2}[/tex]
We first find the area of CAB first.
Radius of CAB = AB = 6cm
θ = 112
Area of CAB = [tex]\frac{112}{360} \pi (6)^{2} \\=\frac{56}{5} \pi cm^{2}[/tex]
Next we will find the area of FAE.
Radius of FAE = AE = 4cm
Area of FAE = [tex]\frac{112}{360} \pi (4)^{2} \\=\frac{224}{45} \pi cm^{2}[/tex]
Lastly,
Area of Shaded Region = Area of CAB - Area of FAE
= [tex]\frac{56}{5} \pi -\frac{224}{45}\pi \\=\frac{56}{9} \pi cm^{2}[/tex]
Therefore the answer is D.
Bobby is a freshman in high school and he just received $500 for graduation from middle school from his grandparents. he wants to save his $500 for college in 4 years if he deposits his $500 into a simple interest savings account for the next 4 years that has a rate of 2.85%. how much will he have in his account after 4 years?
Bobby will have $557 in his account after 4 years.
What is simple interest?Simple interest is calculated based on a loan's principal or the initial deposit into a savings account.
Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.
Simple interest = (principal amount×Rate of interest×time-period)/100
The principal amount deposited was $500.
The rate of interest given by the bank is 2.85%.
The duration of deposit is 4 years.
Simple interest = (500×2.85×4)/100
= 57
Simple interest given by the bank after 4 years is $57.
The total sum of money Bobby will have in his bank is $500 + $57 = $557.
Therefore, after 4 years Bobby will have $557 in his account.
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The following expression gives an approximate value of the total average credit card debt in a u.s. household (in dollars) t years after 1995. 404t+5190 use this expression to predict what the total average credit card debt was or will be in the year 1998. answer: in the year 1998, the total average credit card debt for a u.s. household will be (or was) dollars.
The total average credit card debt for a U.S household will be $9292.
How much is considered a lot of credit card debt?If your total balance is more than 30% of the total credit limit, you may be in too much debt. Some experts consider it best to keep credit utilization between 1% and 10%, while anything between 11% and 30% is typically considered good.
We are given that an expression which gives an approximate value of the total average credit card debt in a U.S. household (in dollars )t years after 1995
We have to find the total average credit card debt will be in the year 2004.
Number of years =2004-1995=9
t=9 years
Substitute the value of t in the given expression
Then , total average credit card debt in a U.S household will be in the year
Debt(t)=418t+5530
Debt(9)=418 * 9+5530= $9292 in 2004
Hence, in the year 2004, the total average credit card debt for a U.S household will be $9292.
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factorise fully
-x-5
The fully factorized version of -x-5 is [tex]-1 \times (x+5)[/tex].
What is Factorization?
Usually, factorization or factoring means writing a number (or another mathematical object) as a product of minor or more uncomplicated objects of the same kind.
Given -x-5 is a linear expression.
For factorizing, first, make the coefficient of x positive. For this take -1 common.
⇒ -x-5 = [tex]-1\times(x+5)[/tex]
Now take the greatest common divisor (gcd) of absolute values of coefficients in x+5.
⇒ gcd(1,5) = 1.
Now take gcd 1 common in the expression.
⇒ [tex]-1\times1\times(x+5)[/tex]
⇒ [tex]-1\times(x+5)[/tex].
∴ The fully factorized version of -x-5 is [tex]-1\times(x+5)[/tex].
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A cone has a slant height of a 26 cm and a radius of 10 cm what is the height of the cone
The height of the cone is 24 cm.
How is the slant height calculated?The distance along the curved surface, measured from the edge at the top to a point on the circumference of the circle at the base, is known as the slant height of an object (such as a cone or pyramid). In other words, the slant height, represented either as s or l, is the shortest distance that may be traveled along the surface of the solid.
Slant height(l)=26cm
Radius(r)=10cm
It is known that, [tex]l^{2}=r^{2}+h^{2}[/tex]
Here, h is the height of the cone.
On substituting the values,
[tex]26^{2}= 10^{2}+h^{2}[/tex]
[tex]\\676=100+h^{2}\\[/tex]
[tex]h^{2}=676-100\\[/tex]
[tex]h^{2}=576\\[/tex]
[tex]h=\sqrt{576}\\[/tex]
h=24
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CAN SOMEONE PLEASE HELP m4A=33°, a=6, b=11. Find m&B to the nearest degree.
Answer:
B = 87
Step-by-step explanation:
The Attached Pic includes Sine Law which can be used in any Triangle
So for our Question
we have A=33 , a=6 , b=11
by Applying Sine Law
[tex]\frac{sin(A)}{a} =\frac{sin(B)}{b}[/tex]
Then
[tex]sin(B)=\frac{b*sin(A)}{a} =\frac{11sin(33)}{6}=0.9985\\ B=sin^{-1}( 0.9985)=87[/tex]
If DAB = CBA,
DAB = 35° and CBA = 8x + 3
X= ?
Answer:
35= 8x + 3
35 - 3 = 8x
32 = 8x
32/8= 8x/8
x = 4
Which statement best defines perpendicular lines?
A.
lines that share a point
B.
lines that intersect and form right angles
C.
lines that lie in the same plane and do not intersect
D.
lines that lie in the same plane
Reset Next
Perpendicular lines are lines that intersect and form right angles
What is a line?A line is defined as the shortest distance between two points. Its equation is written in slope-intercept form as y = mx + b
Perpendicular lines on the other hand are lines that meet at a point to form a right angle. Hence we can conclude that perpendicular lines are lines that intersect and form right angles
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Step-by-step explanation:
help! I need help, pls show work!
Let us first define what any of these terms mean.
The mean is found by adding all the numbers in the set, and dividing the sum by how many numbers are found in the set.
> Given set {5, 12, 6, 3, 8, 16, 8, 6}, the sum of the numbers is 5 + 12 + 6 + 3 + 8 + 16 + 8 + 6 = 64. 64 ÷ 2 = 32. Thus, the mean is 32.
The median is found by finding the number in the middle of the set, and dividing it by 2. This is easy in odd numbers as there is only one number in the middle that is the same amount of numbers left and right proportionally. However, in even numbers, there are two middles to be proportional. If it as an even number, then add the 2 middles together, and divide by 2.
> Given set {5, 12, 6, 3, 8, 16, 8, 6}, this set has an even number of numbers in the set. Thus, the middles are 3 and 8. 3 + 8 = 11, and 11 ÷ 2 = 5.5. Thus, the median is 5.5.
The mode is the number that most frequently appears in the set. In this case, we have 2 frequent numbers. That is 6 and 8. They both appear 2 times separately. Thus, 6 and 8 are the modes of this set.
The range is the difference (i.e subtraction) between the largest number on the set and the smallest number on the set.
> Given set {5, 12, 6, 3, 8, 16, 8, 6}, the range is 16-3 or 13. Thus, the range is 13.
Now that we have the definitions, we can compute the other set very easily.
> Given set {2, 7, 4, 11, 12, 4, 6}, the mean is 18.
> Given set {2, 7, 4, 11, 12, 4, 6}, the median is 5.5.
> Given set {2, 7, 4, 11, 12, 4, 6}, the mode is 4.
> Given set {2, 7, 4, 11, 12, 4, 6}, the range is 10.
Hope it helped!
Choose the term that best fills in the blank to complete the statement.
A dilation is a transformation that maps every point on a line segment to a point on a parallel line segment. The image has a length that is determined by the preimage and a scale factor, which is a fixed _[blank]_ of the original segment's length.
a. Distance
b. Length
c. Multiple
d. Width
Answer:
d
Step-by-step explanation:
becoz u already answered it lloll
can someone please help mee ( will give brainliest 20 points!!!)
Answer:
1. can't answer, can only approximate
2. when f(x) = 2, x = -1
Step-by-step explanation:
We can't evaluate f(2) because we don't have f(x), if we did, we would plug in 2 for x.
On the other hand, solve f(x) = 2 asks for what x is equal to when f(x) = 2, f(x) is just the value on the y axis in relationship with x (in short terms, the value on the y axis).
So looking at the graph, we cam see that when x = -1, f(x) = 2.
3 bells ring at an interval of 4,7 and 14 mins.all three bells rang at 6am, when will the three bells ring together next