Help please with this
The population of a certain community is known to increase at a rate proportional to the number of people present at time t. If the population has doubled in 5 years, how long will it take to triple?
Answer:
[tex]t=7.85 years[/tex]
Step-by-step explanation:
We can write this rate as an ordinary differential equation.
[tex]\frac{dP}{dt}=aP[/tex]
Where a is proportional constant, P the population variable, and t the time.
[tex]\frac{dP}{P}=adt[/tex]
Integrating each side of the equation.
[tex]\int \frac{dP}{P}=\int adt[/tex]
[tex]ln(P)=at+c[/tex]
[tex]P=e^{at+c}[/tex]
[tex]P=e^{c}e^{at}=Ce^{at}[/tex]
To find C we need to use the initial condiction, it means evaluae P at t=0.
[tex]P_{0}=Ce^{0}=C[/tex]
[tex]P=P_{0}e^{at}[/tex]
Now, we use the sentence the population has doubled in 5 years.
[tex]2P_{0}=P_{0}e^{a5}[/tex]
We can find "a" in this condition.
[tex]2=e^{a5}[/tex]
[tex]ln(2)=a5[/tex]
[tex]a=\frac{ln(2)}{5}[/tex]
[tex]a=0.14[/tex]
Finally, let's find how long will it take to triple.
[tex]3P_{0}=P_{0}e^{0.14t}[/tex]
[tex]3=e^{0.14t}[/tex]
[tex]t=\frac{ln(3)}{0.14}[/tex]
[tex]t=7.85 years[/tex]
I hope it helps you!
CJ walks 8 miles in 3 hours. at what unit rate does CJ walk? Please only answer is you understand the question
Answer:
B
Step-by-step explanation:
I had this on my previous test, lol
Is the following table proportional or non-proportional?
Answer: Proportional
Step-by-step explanation: 8 goes into 36, 2 goes into 24, and 5 goes into 10
Please help me answer this :)
Explain your answer
Will give brainiest ! Oh
Answer:
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Because the points are going up by 10 :)
11
10
8
7
6
4
2
1
-12-11-10-9-8
6-548-21
1 2 3 4 5 6 7 8 9 10 12
-3
4
-5
6
7
8
- 10
- 12
Answer: -502
Step-by-step explanation: I think
Answer:-502
Step-by-step explanation:
hope this helps
have a great day!
Solve the inequality -15k>-120
Answer:
-15k<-120
Step-by-step explanation:
15k isbigger than -120 but less close to 0 as 15k is
Two pounds of grapes cost $6. How much does it cost for 5 pounds of grapes
Answer:
if we take the total cost of the grapes, and divide by the number of pounds of grapes we can conclude that each pound of grapes costs $3. so 5 pounds of grapes multiplied by $3 per pound, gives us $15 for 5 pounds of grapes.
Answer:
$15
Step-by-step explanation:
If 2 pounds of grapes cost $6, then one pound of grapes would be $3, because 6 divided by 2 (because there is two pounds) would equal 3. 5 pounds of grapes would cost $15 because 3+3+3+3+3 (or 5 x 3) is equal to 15.
The sum of -5, -9, and 10 is _______.
A. 14
B. -14
C. 4
D. -4
Answer:
D. -4
Step-by-step explanation:
-5 + -9 = -14
-14 + 10 = -4
Answer:
the sum of -5, -9, and 10 is -4
Step-by-step explanation:
add all of them together
PLEASE ANSWER ASAP FOR BRANLEST!!!!!!!!!!!!!!!
Solve this equation and show your work step by step using PEMDAS
3y + 6 = 30
Answer:
3y+6=30
-6
3y=24
divde by 3
y=8
:)
3.
5y + 3y for y = 2
Answer:
16
Step-by-step explanation:
You plug in the value of y into the expression:
5(2) + 3(2)
10 + 6 = 16
What the answer? plzzz help be serious
Answer:
It’s the 3 one
Step-by-step explanation:
A carpenter is installing linoleum for the floor. It costs $2.50 to install a square meter of linoleum. How much will it cost to install linoleum for the entire room?
=========================================================
Explanation:
We need to find the total area first.
Break the figure into 2 parts. The part on the left is a rectangle, and the portion on the right side is a nonrectangular parallelogram.
The rectangle's area is 25*20 = 500 square meters.
The parallelogram's area is 18*10 = 180 square meters.
The formula to find the area of each is base*height
The total area of the entire figure is 500+180 = 680 square meters.
Since 1 square meter of linoleum costs $2.50, this means 680 square meters cost 680*2.50 = 1700 dollars.
Farmer Bill sold potatoes at the farm market. He sold a quarter to the first person, 4/9 of what was left to the second person, and the third buyer bought 4/5 of what was left and the last 10 lb. How many pounds of potatoes did farmer Bill sell?
Answer:
Farmer Bill sold 120 lb of potatoes
Step-by-step explanation:
Suppose farmer Bill had x lb of potatoes. He sold a quarter to the first person. A quarter is written as (1/4)x. After that, Bill had x-(1/4)x = (3/4)x.
Then he sold 4/9 of what was left to the second person, thus it was left 1-4/9=5/9 of the remaining potatoes. Multiplying both factors:
[tex]\frac{5}{9}*\frac{3}{4}x=\frac{5}{12}x[/tex]
This is the remaining portion of the potatoes.
Finally, he sold 4/5 of it and the last 10 lb. This means 1 - 4/5 = 1/5 of the remaining is equivalent to 10 lb:
[tex]\frac{1}{5}*\frac{5}{12}x=\frac{1}{12}x[/tex]
Thus:
[tex]\frac{1}{12}x=10[/tex]
x = 120 lb
Farmer Bill sold 120 lb of potatoes
The Farmer will sold 120 lb of potatoes.
Let us consider that farmer have x lb of potatoes.
He sold a quarter to the first person, that is [tex]\frac{x}{4}[/tex]
Potatoes left,[tex]=x-\frac{x}{4} =\frac{3x}{4}[/tex]
4/9 of what was left to the second person,
Potatoes sell to second person is, [tex]\frac{3x}{4} *\frac{4}{9} =\frac{x}{3}[/tex]
the third buyer bought 4/5 of what was left
that is, [tex]\frac{4}{5}*(\frac{3x}{4} -\frac{x}{3} ) =\frac{x}{3}[/tex]
Potatoes left [tex]=\frac{5x}{12} -\frac{x}{3} =\frac{x}{12}[/tex]
Since, Potatoes left = 10 lb
So, [tex]\frac{x}{12} =10\\\\x=12*10=120[/tex]
Thus, The Farmer will sold 120 lb of potatoes.
Learn more:
https://brainly.com/question/2785554
if h(x)=0 then does h([tex]x^{2}[/tex])= 0
TRUE or FALSE?
Answer:
true
Step-by-step explanation:
6x+4 divided by 2=8
You don’t have to explain... just answer
Trevor is making 2/3 of a recipe for chicken noodle soup. He adds ½ cup of chopped celery. The equation 2/3 c = 1/2 can be used to find the number of cups c of chopped celery in the original recipe. How many cups of chopped celery does the original recipe call for?
Answer:
Cups of chopped celery in original recipe = [tex]\frac{3}{4}\ cups[/tex]
Step-by-step explanation:
Given that:
Trevor is making 2/3 of a recipe
Number of cups of chopped celery used = 1/2 cup
The following equation can be used to find the original number of cups of chopped celery used in recipe.
[tex]\frac{2}{3}c=\frac{1}{2}[/tex]
Multiplying both sides by 3/2
[tex]\frac{3}{2}*\frac{2}{3}c=\frac{1}{2}*\frac{3}{2}\\\\c= \frac{3}{4}\\[/tex]
Hence,
Cups of chopped celery in original recipe = [tex]\frac{3}{4}\ cups[/tex]
Please help this is due in tomorrow you dont have to answer all questions
Answer:
1 is multiplication
2 is division
3 is parentheses
4 is exponents
5 is parentheses
6 is exponents
7 is G.
8 is F.
9 is H.
10 is A.
11 is C.
12 is E.
13 is D.
14 is B.
Step-by-step explanation:
PEMDAS
parentheses
exponents
multiplication
division
addition
subtraction
do it in that order. but multiplication and division are on the same level so whichever comes firsts gets solved first and addition and subtraction are on the same level so whichever that come first gets solved first
PLEASE ANSWER ASAP FOR BRANLEST!!!!!!!!!!!!!!!
Solve the equation
9 = -8s - 7
what is s?
Answer:
s=2
Step-by-step explanation:
9 = -8s - 7
16=8s
s=2
Answe
the answer -2
Step-by-step explanation:
I Got it right thats how i know
Given z1 = 2 +StartRoot 3 EndRoot i and z2 = 1 – StartRoot 3 EndRoot i, what is the sum of z1 and z2?
1
3
3 + 2StartRoot 3 EndRoot i
–1 – 2StartRoot 3 EndRoot i
Answer:
its b.3
Step-by-step explanation: I did it in on edge and got it right
Answer:
It's a 3
Step-by-step explanation:
Mario said so
is 9 a irrational number
Answer:
No.
9 Is rational.
Step-by-step explanation:
I'm 100% sure.
What is the value of -b/(2a) in the given function below?
h(x)= -4x^2 -8x + 5
A. 2
B. -2
C. -1
D. 1
Aubrey's coach asks her to bring 5 liters of water to practice.
How many 500-milliliter bottles does Aubrey need to buy to have
exactly enough water?
500
A. 1 bottle
b. 5 bottles
c. 10 bottles
d. 15 bottles
Answer:
C
Step-by-step explanation:
This is because a liter is 1000 milliliters, so multiplying the amount of liters to the milliliters you would get 5000, you would then divide that by 500 since a bottle would contain that much, giving you 10 bottles
Find |x| when x = 15 and x = – 15.
Answer:15
Step-by-step explanation:trust me
Answer:
The absolute of x would be 15
Question???
-9 - (-4) =
Answer:
-5
Step-by-step explanation:
Answer:
-5
Please mark as brainliest if this helped you the most, thanks if you do and have a good day/night!
1. Given that cosθ≈0.646 where θ is in quadrant IV, find the values of sinθ and tanθ to the nearest thousandth
a. sinθ=−0.763; tanθ=−1.181
b. sinθ=−0.763; tanθ=−0.847
c. sinθ=0.763; tanθ=0.847
d. sinθ=0.763; tanθ=1.181
2. Terran’s running rate is 4 miles per hour faster than her walking rate. She can run 21 miles in the same amount of time it takes her to walk 9 miles. What are her walking and running rates in miles per hour? Write and solve a rational equation to answer the question. Let x be Terran’s walking rate
a. 21/x+4=9/x; Terran walks at 2 miles per hour and runs at 6 miles per hour.
b. 21/x=9/x−4; Terran walks at 7 miles per hour and runs at 10 miles per hour.
c. 21/x=9/x−4; Terran walks at 4 miles per hour and runs at 8 miles per hour.
d. 21/x+4=9/x; Terran walks at 3 miles per hour and runs at 7 miles per hour.
Answer:
d.) sinθ=0.763; tanθ=1.181
c. 21/x=9/x−4; Terran walks at 4 miles per hour and runs at 8 miles per hour.
Step-by-step explanation:
Given that:
θ is in the IV quadrant (All is positive) that is sin, cos and tan are all positive.
Cosθ = 0.646
Θ = Cos^-1(0.646)
θ = 49.75930
Hence,
Tanθ = tan(49.75930) = 1.1816365 = 1.182
Sinθ = sin(49.75930) = 0.7633373 = 0.763
2.)
Let
Walking rate = x mph
Running rate = x + 4 mph
21 miles run time = 9 miles walk time
Recall :
Time = distance / speed or rate
21 / (x + 4) = 9 / x
Cross multiply :
21 * x = 9(x + 4)
21x = 9x + 36
21x - 9x = 36
12x = 36
x = 36 /12
x = 4 mph = walking rate
Running rate = x + 4 = 4 + 4 = 8 mph
Amy's family drove to Lucky Land Fun Park for the day. Her dad and mom
shared the driving. Amy's dad drove 3 miles for every 5 miles her mom
drove. If Amy's mom drove 32 more miles than her dad, how many miles
did they drive altogether? (Draw a tape diagram to help you). *
Answer:
128 miles
Step-by-step explanation:
The number of miles Amy's parents drove altogether is 128 miles.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Amy's dad drove 3 miles for every 5 miles her mom
drove.
So, the ratio is 3:5
Amy's mom drove 32 more miles than her dad
Let number mile Amy's father drove be x and then the number of miles Amy's mom drove will be x+32
Here, x/(x+32) =3/5
5x=3(x+32)
5x=3x+96
2x=96
x=48
So, x+32=80
Then, total distance is 80+48=128 miles
Therefore, the number of miles Amy's parents drove altogether is 128 miles.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ2
If the variance of a data set if 6.25 what is the standard deviation
Answer:
Variance= (Standard deviation)^2=
✓6.25=Standard deviation
✓(625/100)= Standard deviation
25/10= Standard deviation
2.5= Standard deviation
Step-by-step explanation:
A value meal package at Ron's Subs consists of a drink, a sandwich, and a bag of chips. There are 5 types of drinks to choose from, 6 types of sandwiches, and 3 types of chips. How many different value meal packages are possible
Answer: 90 different meal packages.
Step-by-step explanation:
Given data:
Types of drinks available = 5
Types of sandwiches available = 6
Types of chips available = 3.
Solution:
No of meal packages possible for this combination
= 6*5*3
= 90
A total of 90 different meal packages would be gotten:
2% of what number is 1
Answer:
50
Step-by-step explanation: