Answer:36 i think
Step-by-step explanation:
The population of a community is known to increase at a rate proportional to the number of people present at time t. The initial population P0 has doubled in 5 years. Suppose it is known that the population is 9,000 after 3 years.
Required:
a, What was the initial population P0?
b. How fast is the population growing at t = 10?
Step-by-step explanation:
Let the initial population of a community be P0 and the population after time t is P(t).
If the population of a community is known to increase at a rate proportional to the number of people present at time t, this is expressed as:
[tex]P(t) = P_0e^{kt}[/tex]
at t = 5 years, P(t) = 2P0
substitute:
[tex]2P_0 = P_0e^{5k}\\2 = e^{5k}\\ln2 = lne^{5k}\\ln2 = 5k\\k = \frac{ln2}{5}\\k = 0.1386[/tex]
If the population is 9,000 after 3 years
at t = 3, P(t) = 9000
a) Substitute into the formula to get P0
[tex]9000 = P_0e^{0.1386\times 3}\\9000 = P_0e^{0.4158}\\9000 = 1.5156P_0\\P_0 = \frac{9000}{1.5156}\\ P_0 = 5938.24[/tex]
Hence the initial population is approximately 5938.
b) In order to know how fast the population growing at t = 10, we will substitute t = 10 into the formula as shown:
[tex]P(10) = 5938.24e^{0.1386(10)}\\P(10) = 5938.24e^{1.386}\\P(10) = 5938.24(3.9988)\\P(10) = 23,745.97[/tex]
Hence the population of the community after 10 years is approximately 23,746
One-half of a number x is equal to the sum of two and
the same number & . Find the value of x.
Answer:
x=-4
Step-by-step explanation:
This is the equation you can write (assuming you meant "the same number x"):
1/2x=2+x
x=4+2x
-x=4
x=-4
Mrs. Olen wants to join a gym. Francis Lewis Gym charges a new member fee of $150 plus $10 each month. Clintonville Gym charges a new member fee of $50 plus $35 each month.
Answer:Step-by-step explanation:
a. Let x = number of months
Amount charged by Francis Lewis Gym = 150 + 10x
Amount charged by Clintonville Gym = 50 + 35x
Set each expression equal to the other to generate an equation to use in finding the number of months for which the cost of membership will be the same at both months
150 + 10x = 50 + 35x
Collect like terms
150 - 50 = -10x + 35x
100 = 25x
Divide both sides by 25
100/25 = x
4 = x
Answer: 4 months
b. Substitute x = 2 into each if the expression of the amount charged by each gym. The one that gives the lowest amount should be the one Mrs. Open should should join.
Amount charged by Francis Lewis Gym = 150 + 10x
= 150 + 10(2)
= 150 + 20
= $170
Amount charged by Clintonville Gym = 50 + 35x
= 50 + 35(2)
= 50 + 70
= $120
She should join the Clintonville Gym if she plans to join a gym for 2 months.
Answer: Clintonville Gym
The sum of three consecutive odd integers is 18 less than five times the middle number fimd the three integers
Answer:
7, 9, 11
Step-by-step explanation:
x+x+2+x+4=5(x+2)-18
3x+6=5x+10-18
3x+6=5x+-8
3x=5x+-14
-2x=-14
x=7
two times a number is four times that number minus a negative eighteen
Answer:
-9
Step-by-step explanation:
the number is x
2x = 4x - - 18
2x = 4x + 18
-2x = 18
x = -9
Answer:
-9
Step-by-step explanation:
Let's solve your equation step-by-step.
2x=4x−(−18)
Step 1: Simplify both sides of the equation.
2x=4x+18
Step 2: Subtract 4x from both sides.
2x−4x=4x+18−4x
−2x=18
Step 3: Divide both sides by -2.
−2x/−2
= 18 /−2 x
=−9
Complete the equation of the line whose y-intercept is (0,6) and slope is 3
Answer:
y= 3x+6
Step-by-step explanation:
the equation to use for this problem is y= mx+b
m is the slope (3) and b is the y-intercept (0,6)
let's plug those numbers into the equation.
y= 3x+6
Hope this helps!
Help please!!!!!! I can’t figure it out.
Answer:
A.) parallel
Step-by-step explanation:
they are on opposite sides, and will never touch.
Hope I helped!! :)
PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE i'll give you brainliest
When a piece of metal is subject to below zero temperatures, shrinking will normally take place. If the diameter of a steel rod shrinks from 0.02 meters to 0.015 meters, what is the percentage decrease in the diameter?
1.333...percent
Hope it helps
In an inequality, -2.5 is the lesser number. What is the position of the other number on the horizontal number line in relation to -2.5?
Answer:
It would be to the right of -2.5.
Step-by-step explanation:
Help plz I need it ASAP give poinys
Answer:
1 4/5
Step-by-step explanation:
Download photogmath
Answer:
1 7/8
Step-by-step explanation:
9÷4 4/5
=9÷24
=9/1×5/24
=
9×5
-----------
1×24
=45/2
15/8=1 7/8
if 1 apple cost 3 dollars how much would 5 cost?
Answer:
It would be 15
Step-by-step explanation:
because 5x3 equals 15.
Answer:
15 dollars
Step-by-step explanation:
because you have to multiply how many apples there are to how much each one cost. So the answer would be 5 x 3 equals 15 dollars
Y = 3x + 4 Y = 3x + 7
Answer:
y-7/ 12y+3
Step-by-step explanation:
A delivery person uses a service elevator to bring boxes of books up to an office. The delivery person weighs
170 lb and each box of books weighs 60 lb. The maximum capacity of the elevator is 1300 lb. How many boxes
of books can the delivery person bring up at one time?
Answer:
18 at most.
Step-by-step explanation:
I got this wrong can someone, please help me with this.
You found the correct slope for Line 1, but Line 2 has a slope of (3 - 2)/(6-3) = 1/3.
If 2 lines are parallel, their slopes are the same; perpendicular and their slopes are opposite reciprocals (change the sign of the first slope, then divide 1 by it and you get the perpendicular line's slope). 1/3 is NOT the opposite reciprocal of 3 (because they have the same sign) and 1/3 is NOT equal to 3, so that makes the answer neither.
The slope for Line 3 is (3 - 1)/(1 - (-1)) = 2/2 = 1
The slope of Line 4 is (1 - (-1))/(4 - 2) = 2/2 = 1
1 = 1, so these lines are parallel
Pleas help I am brainliesting and explain please
Answer:
-2.63 is bigger
Step-by-step explanation:
-2 5/7 is the same as -2.71428571428...
and when you compare a negative the smaller number is always greater than the bigger number because it is negative.
What is the product of 5/11 and 3/4
Answer:
15/ 44
Step-by-step explanation:
just multiply across
5 x 3 = 15
11 x 4 = 44
= 15/44
Answer:
[tex]\frac{15}{44}[/tex]
I hope this helps!
c is opposite___
AC
AC and BC
Answer:a=bc
Step-by-step explanation:
over evaluate function
Answer:
C. hope it helps :)
Step-by-step explanation:
What is the additive inverse of the polynomial
9xy² + 6x²y -5x
Answer:
-9xy² - 6x²y + 5x
Step-by-step explanation:
The additive inverse of a polynomial is simply defined as the same polynomial but the difference is that the signs attached to each of the terms will change. This means that positive sign will change to negative while negative sign will change to positive.
Now, we are given the polynomial;
9xy² + 6x²y - 5x
Thus, from earlier description, additive inverse of this polynomial is;
-9xy² - 6x²y + 5x
A store owner discounted some canoes from $76 to $38. What is the discount, as a percentage?
Answer:
50.00%
Step-by-step explanation:
The volume of air in a balloon is represented by the function v(n) = nr), where r is the radius of the balloon, in
inches. The radius increases with time, in seconds, by the function r(t) = 4,2. Which statements are true?
Answer:
When V is composed with r, the composite function is [tex]\frac{1}{48} \pi t^{6}[/tex]
When Vr6 shows that the volume is 9724. When the radius is increased to 6 inches.
Step-by-step explanation:
Volume is determined by [tex]cm^{3}[/tex] if the balloon is filled with air its volume will be increased and the composite function will represent the volume of the balloon. The radius of the balloon will rise in seconds. If t seconds are consumed to reach to a radius of 6 inches then the pie function is used to determine the volume.
Which statement best describes the graph of 2c - 5y=-25 and the graph of y= +5?
Answer:
To easily compare the two linear equations just by looking at the equation, let's rearrange this into the slope-intercept formula: y = mx + b, where m is the slope and b is the y-intercept.
2x - 5y = -25
(-5y = -25x - 2x)-1
5y = 25/5 +2x/5
y = (2/5)x + 5
Thus, the slope is 2/5 and the y-intercept is 5.
y=52x + 5
The slope is 52 and the y-intercept is 5.
Thus, we can say that the two linear equations have the same y-intercept. This is the point in the y=-axis in which the two lines intersect. They must intersect at (0,5).
Step-by-step explanation:
What is the value of x?
A) 42
B)48
C)138
D)158
Answer:
138 I think
Step-by-step explanation:
math go brrr
Perform the indicated operation
3/4 divided by 1/3
Answer:
2 1/4
Step-by-step explanation:
3/4 ÷ 1/3 = ?
(to divide fractions faster you flip the second fraction so:)
3/4 x 3/1 = 2 1/4
A part manufactured by plastic injection molding has a historical mean of 100 and a historical standard deviation of 8. Find the value of the mean thickness required to make the probability of exceeding 101 less than 8%.
Answer:
The probability of thickness exceeding 101 is 0.4483.
Step-by-step explanation:
Let X denote the thickness of the part manufactured by plastic injection molding.
Assume that X follows a normal distribution with mean, μ = 100 and standard deviation, σ = 8.
Compute the probability of thickness exceeding 101 as follows:
[tex]P(X>101)=P(\frac{X-\mu}{\sigma}>\frac{101-100}{8})[/tex]
[tex]=P(Z>0.125)\\\\=1-P(Z<0.125)\\\\=1-0.55172\\\\=0.44828\\\\\approx 0.4483[/tex]
Thus, the probability of thickness exceeding 101 is 0.4483.
Help plz Easy math I know the answer isn’t A
Answer: B
Step-by-step explanation: It is greater or equal to -6 and less than or equal to 5.
Find the focus and directrix of the parabola with the given equation. y^2-4x=0
Answer:
directrix: x=-1
focus: (1,0)
Step-by-step explanation:
The average customer for a certain utility company pays $120 per month for utilities. The company plans to decrease utility bills by 3% each year for the next five years. Which of the following can be used to determine the total amount an average customer will pay for utilities during the next five years? an arithmetic series a geometric series a series that is neither arithmetic nor geometric a series that is both arithmetic and geometric
an arithmetic series
a geometric series
a series that is neither arithmetic nor geometric
a series that is both arithmetic and geometric
Answer:
a geometric series
Step-by-step explanation:
Help! Whats the answer
Answer:
its c
Step-by-step explanation:
Please help me and answer that ??
Answer: A. 7/21 = 1/x
Step-by-step explanation: 7/21 = 1/3 so x would be 3.
please help
Which values of k would cause this system of equations to have no solution? Check all that apply.
6x + 4y = 14,
3x + 2y = k
-2
5
7
10
21
Answer:
a , b , d , e
Step-by-step explanation: