Answer:
p=c(1+r)^t so the population will be 4679.43424 or rounded to 4679
Step-by-step explanation:
p=c(1+r)^t
p=4,000(1+.04)^t
p=4,000(1.04)^t
p=4,000(1.04)^4
p=4679.43424
p= the population you are solving for
c= the initial amount of the population
(1+r)= the rate of change
t= the period of time
The exponential equation that represents the population of the town in terms of the number of years : [tex]p=4000 (1+0.4)^{t}[/tex]
What is an exponential equation?An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable.
It is similar to the amount received after investing a certain amount compounded annually.
Given,
Initial population = 4000
Rate of increase = 4%
Let current population be p.
Let number of years passed be t.
The exponential equation will be: [tex]p=4000 (1+0.4)^{t}[/tex]
(The population of the town has grown exponentially. This means that:
Initial population = 4000
Population in year I = 4000 + 4% of 4000 = 4000(1 + 0.4)
Population in year II = 4000 + 4% of 4000(1 + 0.4) = 4000(1 + 0.4)(1+0.4)
and this goes on.)
Learn more about exponential equation here
https://brainly.com/question/23729449
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Find the volume (in cubic feet) of a cylindrical column with a diameter of 6 feet and a height of 28 feet. (Round your answer to one decimal place.)
Answer:
[tex]791.7\:\mathrm{ft^3}[/tex]
Step-by-step explanation:
The volume of a cylinder with radius [tex]r[/tex] and height [tex]h[/tex] is given by [tex]A_{cyl}=r^2h\pi[/tex].
By definition, all radii of a circle are exactly half of all diameters of the circle. Therefore, if the diameter of the circular base of the cylinder is 6 feet, the radius of it must be [tex]6\div 2=3\text{ feet}[/tex].
Now we can substitute [tex]r=3[/tex] and [tex]h=28[/tex] into our formula [tex]A_{cyl}=r^2h\pi[/tex]:
[tex]A=3^2\cdot 28\cdot \pi,\\A=9\cdot28\cdot \pi,\\A=791.681348705\approx \boxed{791.7\:\mathrm{ft^3}}[/tex]
convert the fraction 3/8 to a decimal WITHOUT the use of a calculator. Show your method clearly. SHOW ALL STEPS!
here you go it's too easy
Step-by-step explanation:
Explanation is in the attachment .
Hope it is helpful to you ❣️☪️❇️
Help asap! Lia can rent a van for either $90 per day with unlimited mileage or $50 per day with 250 free miles and an extra 25¢ for each mile over 250. For what number of miles traveled in one day would the unlimited mileage plan save Lia money? (Show work)
Answer:
The unlimited mileage plan would save money for Lia from 410 miles onwards.
Step-by-step explanation:
Since Lia can rent a van for either $ 90 per day with unlimited mileage or $ 50 per day with 250 free miles and an extra 25 ¢ for each mile over 250, to determine for what number of miles traveled in one day would the unlimited mileage plan save Lia money, the following calculation must be performed:
90.25 - 50 = 40.25
40.25 / 0.25 = 161
161 + 250 = 411
Therefore, the unlimited mileage plan would save money for Lia from 410 miles onwards.
Find the domain.
p(x) = x^2+ 2
Answer:
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
( − ∞ , ∞ )
Set-Builder Notation:
{ x | x ∈ R }
Step-by-step explanation:
hope that helps bigger terms
F(x) =-2x-4 find x if f(x)=14
Answer:
14=-2x-4
18=-2x
x=-9
Hope This Helps!!!
is there a formula for this?
help asap!!
Answer:
yes
Step-by-step explanation:
the answer is c well thats what my teacher said
Answer:
B
Step-by-step explanation:
using sine rule
[tex] \frac{y}{sin \: 45} = \frac{5}{sin \: 45} \\ y = 5[/tex]
using sin rule
[tex] \frac{x}{sin \: 90} = \frac{5}{sin \: 45} \\ \\ 5sin90 = xsin45 \\ \\ x = \frac{5 \: sin \: 90}{sin \: 45} \\ x = \frac{5}{0.7071} \\ x = 7.071[/tex]
x=5√2
15/4 : 5/12 =
tolong dijawab ya :)
Answer:
3/1 : 1/3
Step-by-step explanation:
Just simplify it.
Solve the system of equations using the elimination method 5x+10y = 3
10x + 20y = 8
Answer:
No solution
Step-by-step explanation:
5x+10y=3 equation 1
10x+20y=8 equation 2
-2(5x+10y)=-2(3) multiply equation 1 by -2 to eliminate x
-10x-20y=-6 equation 1 multiplied by -2
10x+20y=8 equation 2
0 + 0 =2. Add above equations
0 =2
no solution
divide 64.050÷0.12. need whole process
Answer:
533.75
Step-by-step explanation:
Given the expression;
64.050÷0.12
Express first as a fraction
64.050 = 64050/1000
0.12 = 12/100
Divide both fractions
= 64050/1000÷12/100
= 64050/1000 *100/12
= 64050/10 * 1/12
= 64050/120
= 533.75
Hence the required answer is 533.75
Graph g(x)=-8|x |+1.
Answer:
[tex] g(x)=-8|x |+1. = 9552815 \geqslant 6[/tex]
The club will use the majority criterion method to determine the final winner. However, while finalizing the votes, a member of the club discovers that Mason did not meet the original criteria to be considered for the vacation package, because he is a county deputy, not a city police person, so Mason is eliminated from the votes. Who actually will win the tickets? Is the irrelevant alternative criterion supported in this case?
Answer and Explanation:
The irrelevant alternative criterion states that if two candidates A and B contest for an election and candidate B is preferred to candidate A then any other candidate X should not cause candidate A to win the election.
In this case if Mason was candidate A, then candidate B should still win by the majority criterion method and the irrelevant alternative criterion would still be supported. However if he is candidate B then the irrelevant alternative criterion is not supported.
In a family of 3 children, what is the probability that there will be exactly 2 boys assuming that the sexes are equally likely to occur in each birth
Answer:
There is a 60.00 percent probability of a particular outcome and 40.00 percent probability of another outcome.
The original price of a set lunch was 30 dollars. It is now sold at a 20%
discount. There is an extra discount of 10% for students. How much
should a student pay to order a set lunch?
Follow the process of completing the square
to solve 2x2 + 8x - 12 = 0.
After adding B2 to both sides of the equation in step 4, what is the constant on the right side of the equation?
2x^2 + 8x - 12 = 0..divide by 2
x^2 + 4x - 6 = 0
x^2 + 4x = 6...add 4 to both sides of the equation
x^2 + 4x + 4 = 6 + 4
(x + 2)^2 = 10....<== ur constant is 10
x + 2 = (+-)sqrt 10
x = -2 (+ - ) sqrt 10
x = -2 + sqrt 10
x = -2 - sqrt 10
if side of square is 4.05 find its area
Answer:
A
≈
16.4
please give brain listA cardboard box without a lid is to have a volume of 4,000 cm3. Find the dimensions that minimize the amount of cardboard used. (Let x, y, and z be the dimensions of the cardboard box.)
4 pts
>
Question 2
The total number of students enrolled in MATH 123 this semester is 5,780.
If it increases by 0.28% for the next semester, what will be the enrollment
next semester? Round to a whole person.
4 pts
Question 3
Answer:
17
Step-by-step explanation:
So, this is a percentage problem.
Start off by finding how many students 0.28% is:
If 100% = 5780
0.01% = 0.578
Now:
0.01% = 0.578
0.28% = 16.184
The exercise tells you to round for a whole person, so 16.184 turns 17
And that's the answer!
is y=3x^2-x-1 a function
Answer: Yes it is a function.
This is because any x input leads to exactly one y output.
The graph passes the vertical line test. It is impossible to draw a single vertical line through more than one point on the parabolic curve.
In how many ways could nine people be divided into two groups of two people and one group of five people?
Nine people could be divided into two groups of two people and one group of five people ways.
(Type a whole number.)
Answer:
your can only divide then up in that specific sequence one time
Please answer & number. Thank you! <33
Answer:
2）=2
4）=3
5）=5
8）=-1
Step-by-step explanation:
just divide the number by the number with variable
When P(x) is divided by (x - 1) and (x + 3), the remainders are 4 and 104 respectively. When P(x) is divided by x² - x + 1 the quotient is x² + x + 3 and the remainder is of the form ax + b. Find the remainder.
Answer:
The remainder is 3x - 4
Step-by-step explanation:
[Remember] [tex]\frac{Dividend}{Divisor} = Quotient + \frac{Remainder}{Divisor}[/tex]
So, [tex]Dividend = (Quotient)(Divisor) + Remainder[/tex]
In this case our dividend is always P(x).
Part 1
When the divisor is [tex](x - 1)[/tex], the remainder is [tex]4[/tex], so we can say [tex]P(x) = (Quotient)(x - 1) + 4[/tex]
In order to get rid of "Quotient" from our equation, we must multiply it by 0, so [tex](x - 1) = 0[/tex]
When solving for [tex]x[/tex], we get
[tex]x - 1 = 0\\x - 1 + 1 = 0 + 1\\x = 1[/tex]
When [tex]x = 1[/tex],
[tex]P(x) = (Quotient)(x - 1) + 4\\P(1) = (Quotient)(1 - 1) + 4\\P(1) = (Quotient)(0) + 4\\P(1) = 0 + 4\\P(1) = 4[/tex]
--------------------------------------------------------------------------------------------------------------
Part 2
When the divisor is [tex](x + 3)[/tex], the remainder is [tex]104[/tex], so we can say [tex]P(x) = (Quotient)(x + 3) + 104[/tex]
In order to get rid of "Quotient" from our equation, we must multiply it by 0, so [tex](x + 3) = 0[/tex]
When solving for [tex]x[/tex], we get
[tex]x + 3 = 0\\x + 3 - 3 = 0 - 3\\x = -3[/tex]
When [tex]x = -3[/tex],
[tex]P(x) = (Quotient)(x + 3) + 104\\P(-3) = (Quotient)(-3 + 3) + 104\\P(-3) = (Quotient)(0) + 104\\P(-3) = 0 + 104\\P(-3) = 104[/tex]
--------------------------------------------------------------------------------------------------------------
Part 3
When the divisor is [tex](x^2 - x + 1)[/tex], the quotient is [tex](x^2 + x + 3)[/tex], and the remainder is [tex](ax + b)[/tex], so we can say [tex]P(x) = (x^2 + x + 3)(x^2 - x + 1) + (ax + b)[/tex]
From Part 1, we know that [tex]P(1) = 4[/tex] , so we can substitute [tex]x = 1[/tex] and [tex]P(x) = 4[/tex] into [tex]P(x) = (x^2 + x + 3)(x^2 - x + 1) + (ax + b)[/tex]
When we do, we get:
[tex]4 = (1^2 + 1 + 3)(1^2 - 1 + 1) + a(1) + b\\4 = (1 + 1 + 3)(1 - 1 + 1) + a + b\\4 = (5)(1) + a + b\\4 = 5 + a + b\\4 - 5 = 5 - 5 + a + b\\-1 = a + b\\a + b = -1[/tex]
We will call [tex]a + b = -1[/tex] equation 1
From Part 2, we know that [tex]P(-3) = 104[/tex], so we can substitute [tex]x = -3[/tex] and [tex]P(x) = 104[/tex] into [tex]P(x) = (x^2 + x + 3)(x^2 - x + 1) + (ax + b)[/tex]
When we do, we get:
[tex]104 = ((-3)^2 + (-3) + 3)((-3)^2 - (-3) + 1) + a(-3) + b\\104 = (9 - 3 + 3)(9 + 3 + 1) - 3a + b\\104 = (9)(13) - 3a + b\\104 = 117 - 3a + b\\104 - 117 = 117 - 117 - 3a + b\\-13 = -3a + b\\(-13)(-1) = (-3a + b)(-1)\\13 = 3a - b\\3a - b = 13[/tex]
We will call [tex]3a - b = 13[/tex] equation 2
Now we can create a system of equations using equation 1 and equation 2
[tex]\left \{ {{a + b = -1} \atop {3a - b = 13}} \right.[/tex]
By adding both equations' right-hand sides together and both equations' left-hand sides together, we can eliminate [tex]b[/tex] and solve for [tex]a[/tex]
So equation 1 + equation 2:
[tex](a + b) + (3a - b) = -1 + 13\\a + b + 3a - b = -1 + 13\\a + 3a + b - b = -1 + 13\\4a = 12\\a = 3[/tex]
Now we can substitute [tex]a = 3[/tex] into either one of the equations, however, since equation 1 has less operations to deal with, we will use equation 1.
So substituting [tex]a = 3[/tex] into equation 1:
[tex]3 + b = -1\\3 - 3 + b = -1 - 3\\b = -4[/tex]
Now that we have both of the values for [tex]a[/tex] and [tex]b[/tex], we can substitute them into the expression for the remainder.
So substituting [tex]a = 3[/tex] and [tex]b = -4[/tex] into [tex]ax + b[/tex]:
[tex]ax + b\\= (3)x + (-4)\\= 3x - 4[/tex]
Therefore, the remainder is [tex]3x - 4[/tex].
Which of the following statements are true?
Answer:
D
Step-by-step explanation:
i think it's correct if not I'm sorry
I need help with this, please.
Answer:
it can not cleared clear but it can not cleared
Solve the equation 2sin^2(x) = 1 for x ∈ [-π,π], expressing all solutions as exact values. please help its urgent !!
Answer:
2sin.2(x) sd s
Step-by-step explanation:
Create a circle such that its center is point A and B is a point on the circle.
Answer:
The center of a circle is the point in the circle which is equidistant to all the edges of thr circle. The point a is the center, while point b is an arbitrary point in the circle. Find attachment for the diagram.
The amount of snowfall falling in a certain mountain range is normally distributed with a average of 170 inches, and a standard deviation of 20 inches. What is the probability a randomly selected year will have an average snofall above 200 inches
Answer:
0.0668 = 6.68% probability a randomly selected year will have an average snowfall above 200 inches.
Step-by-step explanation:
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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Normally distributed with a average of 170 inches, and a standard deviation of 20 inches.
This means that [tex]\mu = 170, \sigma = 20[/tex]
What is the probability a randomly selected year will have an average snowfall above 200 inches?
This is 1 subtracted by the p-value of Z when X = 200. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{200 - 170}{20}[/tex]
[tex]Z = 1.5[/tex]
[tex]Z = 1.5[/tex] has a p-value of 0.9332.
1 - 0.9332 = 0.0668
0.0668 = 6.68% probability a randomly selected year will have an average snowfall above 200 inches.
Which expression is equivalent to…
Answer:
D
Step-by-step explanation:
if cosA=3√2/5,then show that cos2A=11/25
Answer:
Step-by-step explanation:
Cos 2A = 2Cos² A - 1
[tex]= 2*(\frac{3\sqrt{2}}{5})^{2}-1\\\\=2*(\frac{3^{2}*(\sqrt{2})^{2}}{5^{2}})-1\\\\=2*\frac{9*2}{25} - 1\\\\=\frac{36}{25}-1\\\\=\frac{36}{25}-\frac{25}{25}\\\\=\frac{11}{25}[/tex]
Whoever helps me with this question I will give them brainliest
Hi there I hope you are having a great day :) I am pretty sure that you do 280 degrees around angle so i would say you would add 63 + 73 + 83 = 219 then you would take away it 280 - 219 = 61 so y must equal to 61 this is because we can see a z shape and a z shape adds up to 280.
Hopefully that helps you.
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So a Quadratic function,A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero
