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
I need help with this ASAP !! I’m failing !!!
Answer:
c=130,b=50
Step-by-step explanation:
[tex]c = 180 - 50 = 130[/tex]
[tex]b = 180 - 130 = 50[/tex]
i think this is the answer
Intro:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
<b and 50° are vertical angles so that means they are congruent. So that means <b is 50.
<c and 50° are supplementary angles which means when you add them you should get 180. So if do 180 - 50 we will get 130. So that means <c is 130°.
If a polygon is a pentagon, then it has 5 sides hypothesis conclusion
Answer:
Hypothesis
Step-by-step explanation:
a polygon has five sides Conclusion: it is a pentagon If a polygon has five sides, then it is a pentagon.
hope this helps
HELP ME PLEASE I ALREADY GRAPHED IT BUT PLEASE ANSWER THE QUESTION BELOW
Answer:
32ed
Step-by-step explanation:
2x + 7 = 13
Please help
Answer:
x=3
Step-by-step explanation:
Hope this helps u..
Round 24.9652 to
1 decimal Place
Answer:
2.5 one decimal rounding off means to make it to one decimal place.the no is 24.9652 if you want to round of then you have to put decimal after 2 only then it will be one decimal place .this is because when we see a number after the point greater than 5 then we add 1 to the right side .now if we add 1 to the right side of 24.9652 by rounding off and making it to one decimal place then it will be 2.5.
How many pounds are in 80 kilograms? Round your answer to the nearest whole number. Note: There are approximately 2.2lbs in a kg.
Answer:
176.37 orrrr 176
Step-by-step explanation:
Answer:
176 pounds
Step-by-step explanation:
Which of the following is equal to the opposite of −45?
−|45|
−|−45|
−(−45)
−45
Which of the following statements does not represent the same value as the others?
the absolute value of 9
the absolute value of negative 9
the opposite of 9
the distance between 0 and −9
All of the following are true statements except _____.
|−93| = −93
|−93| = 93
−|93| = −93
|93| = 93
If you move from zero to 15 on the number line, you are representing all of the following except _____.
the absolute value of 15
the distance between zero and 15
the opposite of −15
the opposite of 15
All of the following expressions are equal to N except _____.
−(− N )
− N
| N |
|− N |
Answer:
The first one
Step-by-step explanation:
Martha earns $24 in four hours. How much would she
earn in 10 hours?
Answer:
$60
Step-by-step explanation:
24/4=6
6*10=60
Answer:
$60
Step-by-step explanation:
24 ÷ 4 = 6
6 × 10 = 24
she makes $6 an hour. $60 in ten hours.
What is m<KNL?
Enter your answer in the box
The measurement of ∠KNL is 102°
First, you must set up an equation to find x.
[tex]5x+2=[3(x+14)[/tex]
Then, you must simplify both sides of the equation.
[tex]5x+2=3x+42[/tex]
Next, subtract 3x on both sides.
[tex]2x+2=42[/tex]
Then, subtract 2 on each side.
[tex]2x=40[/tex]
Next, divide 2 on each side.
[tex]x=20[/tex]
Now that we have the value of x, we can substitute it in for angle KNL.
[tex][3(20+14)][/tex]
[tex][3(34)][/tex]
[tex]102[/tex]
[tex]102[/tex]°
Which point represents the opposite of –2?
A number line going from negative 5 to positive 5. Point A is at negative 2, point B is between negative 1 and 0, point C is between 0 and 1, and point D is at 2.
A
B
C
D
Answer:
Point D
Point D is at 2, the absolute value of -2.
2 is the opposite of -2, and D is at 2.
So, the answer must be option D.
Hope this helps!
Answer:
d
Step-by-step explanation:
what is the rectangular prism of 2 units and 7 1/3
Answer:
it could be 14 2/6 units squared
Step-by-step explanation:
idkI don’t know but for area is units squared and for volume it has units cubed
Convert 2 days into months. Round your answer to the nearest hundredth.
Answer:
0.0657534
Step-by-step explanation:
divide 2 by 30.417
3. Determine if the graph below is a function.
Explain your reasoning.
Answer:
A function defines one variable in terms of another. The statement "y is a function of x" (denoted y = y(x)) means that y varies according to whatever value x takes on. A causal relationship is often implied (i.e. "x causes y"), but does not *necessarily* exist.
Step-by-step explanation:
Plz help i only need c im confused lol 6th grade history
Answer:
War
Step-by-step explanation:
Criminals
Kumar is opening a lemonade stand. He spent $4.50 to build the stand and $2.50 for lemons and sugar. He has enough ingredients to make 20 glasses of lemonade. How much should he charge for one glass of lemonade to cover his expenses and make $10 in profit?
Round to the nearest cent.
Timed test
Answer:
profit = revenue - cost
10 = 20x - (4.5 + 2.5)
10 = 20x - 7
10 + 7 = 20x
17 = 20x
17/20 = x
0.85 = x
check...
profit = revenue - cost
10 = 20(0.85) - 7
10 = 17 - 7
10 = 10 (correct)
so he would have to sell each cup at 0.85 ccents to make a profit of $ 10
Step-by-step explanation:
Answer:
I cant find the next one hehrh
7) Order the numbers from least to greatest.
A. 6.66
B. 6.07
C. 7
D. 6.32
the Answear is B,D,A,C
point Q was rotated about the origin (0,0) by 180
Answer:B
Step-by-step explanation:
The coordinates of the image of the rotation of the point Q is:
Q' = (4, 2)
What is the image of the rotation?
We can see that the original coordinates of point Q are (-4, 0).
If we apply a rotation of 180° about the point (0, 0), it is equivalent to a reflection around the y-axis.
It only changes the sign of the x-component.
Then the image of the rotation is:
Q' = (4, 0)
If you want to learn more about rotations:
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a pizzeria had 4 cans of tomato sauce how many pizzas could they make with the cans if each pizza took one fourth of a can
Answer:
16 pizzas.
Step-by-step explanation:
That is 4 divided by 1/4
= 4 * 4/1
= 16.
Answer:
16
Step-by-step explanation:
There are 4 pizzas per can and you have 4 cans.
4 x 4 = 16
A dentist sees a patient every 20 minutes. He works an average of 60 hours per week. How many patients does he see in a year. He takes 3 weeks vacation. Round your answer down.
Answer:
1040
Step-by-step explanation:
Find area of the figure :)
768 square meters.
We can break it down into two shapes, a rectangle and a triangle.
Rectangle:
[tex]a = b \times h[/tex]
[tex]a = (48) \times (11)[/tex]
[tex]a = 528m^{2} [/tex]
Triangle:
[tex]a = \frac{b \times h}{2} [/tex]
[tex]a = \frac{(48) \times (10)}{2} [/tex]
[tex]a = \frac{480}{2} [/tex]
[tex]a = 240m^{2} [/tex]
Add them together:
[tex]528m^{2} + 240m^{2} = 768m^{2} [/tex]
A math class consists of 26 students, 14 women, 10 men, and 2 non-binary. Two students are selected at random to participate in a probability experiment. Compute the probability that:
Answer:
there's a higher probability for females
ANSWER ONE PLS :(
Beyonce’s fish tank holds 180 gallons of water and is leaking at a rate of 8 gallons per day. Jay Z’s fish tank holds 160 gallons of water and is leaking at a rate of 6 gallons per day. At how many days will the two fish tanks have the same amount of water in them?
Justin Bieber’s sand castle is 180cm tall but the wind is blowing away sand at a rate of 8cm per minute. Taylor Swift’s sand castle is 160cm tall and she it adding sand to it at a rate of 6cm per minute. After how many minutes will their sand castles be the same height?
Answers:
1) 160 + 8x = 180 + 6x
2) 160 + 6x = 180 - 8x
The fish tank problem:
x = # of days
180 - 8x = 160 - 6x
Add 8x to both sides and subtract 160 from both sides.
20 = 2x
Divide both sides by 2
10 = x
It will take 10 days for the fish tanks to have the same amount of water in them.
The sand castle problem:
x = # of minutes.
180 - 8x = 160 + 6x
Add 8x to both sides and subtract 160 from both sides.
20 = 14x
Divide both sides by 14
x = 10/7 mins
After 10/7 mins their sand castles will be the same height
Which coordinate pair is a solution of the linear
equation below?
-X + 3y = 21
Click on the correct answer.
(3,-8)
(-3,8)
(3,8)
Answer:
slope is 4/3 and y intercept is -7
Step-by-step explanation:
3y+21=4x.........now subtract 21 from each side
3y=4x-21......now divide all terms by 3
y=%284%2F3%29x-7......there ya go ...slope is 4/3 and y intercept is -7
Answer:
B (-3,8)
Step-by-step explanation:
awnser A is incorrect because if you switch out the x for 3 and the y for -8. The equation would look like -3+3×(-8)=21. and after multiplying 3×-8 which equals -24. The equation turns into -3+(-24)=21 . And after adding -3 and -24 you get -27=21
awnser B is correct because if you switch out the x for -3 and the y for 8. The equation would look like -3+3×8=21. After multiplying 3×8 which equals 24. The equation turns into -3+24=21. And after adding -3and 24 which is pretty much subtracting you get 21=21.
Best apologies if incorrect
If the points P(5,2),Q(0,7) and R(-5,2) are drawn on coordinate plane,where must point S be located so that figure PQRS is square.
Answer:
(0, -7) i think
hope this helps :3
sorry if im wrong
the measure of an angle is 79.7 what is the measure of its complementary angle
Answer:
10.3
Step-by-step explanation:
Answer:
10.3°
Step-by-step explanation:
complementary angles are angles that sum up to 90°.
Therefore the complement of 79.7
= 90-79.7
=10.3°
According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. [Round your answers to three decimal places, for example: 0.123]
Compute the probability that a randomly selected peanut M&M is not yellow.
Compute the probability that a randomly selected peanut M&M is brown or red.
Compute the probability that three randomly selected peanut M&M’s are all brown.
If you randomly select three peanut M&M’s, compute that probability that none of them are blue.
If you randomly select three peanut M&M’s, compute that probability that at least one of them is blue.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
P(brown) = 12% = 0.12
P(Yellow) = 15% = 0.15
P(Red) = 12% = 0.12
P(blue) = 23% = 0.23
P(orange) = 23% = 0.23
P(green) = 15% = 0.15
A.) Compute the probability that a randomly selected peanut M&M is not yellow.
P(not yellow) = P(Yellow)' = 1 - P(Yellow) = 1 - 0.15 = 0.85
B.) Compute the probability that a randomly selected peanut M&M is brown or red.
P(Brown) or P(Red) :
0.12 + 0.12 = 0.24
C.) Compute the probability that three randomly selected peanut M&M’s are all brown.
P(brown) * P(brown) * P(brown)
0.12 * 0.12 * 0.12 =0.001728
D.) If you randomly select three peanut M&M’s, compute that probability that none of them are blue.
P(3 blue)' = 1 - P(3 blue)
P(3 blue) = 0.23 * 0.23 * 0.23 = 0.012167
1 - P(3 blue) = 1 - 0.012167 = 0.987833
If you randomly select three peanut M&M’s, compute that probability that at least one of them is blue.
P(1 blue) + p(2 blue) + p(3 blue)
(0.23) + (0.23*0.23) + (0.23*0.23*0.23)
0.23 + 0.0529 + 0.012167
= 0.295067
what are the steps we should follow to solve and equation
Use substitution to solve the following systems of equations:
-3x -4y = 2
5x + 5y = -5
O (4,3)
O (-3, 2)
O (3, 2)
O (-2, 1)
Ellie the elephant has some peanuts. She eats up 49 peanuts. Now Ellie the elephant has 31 peanuts. How many peanuts did she have before?
Answer:
80
Step-by-step explanation:
do: 49+31=Your answer
Ellie had 80 peanuts before she ate 49 of them.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let x be the number of peanuts Ellie had before she ate 49 of them.
After eating 49 peanuts, Ellie has 31 peanuts left, so we can write an equation:
x - 49 = 31
To solve for x, we add 49 to both sides of the equation:
x - 49 + 49 = 31 + 49
Simplifying, we get:
x = 80
Therefore, Ellie had 80 peanuts before she ate 49 of them.
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