This is a multi-part question you will refer back to this and other finished parts to help answer this and future questions
In 2005 a town with a population of 10,000 finds that its population is declining by a rate of 0.3% per year. Find the following Johnny was asked how long it will take the population to reach 1/2 of the original population. He answered that it would never reach half, what is the incorrect assumptions Johnny made? (answer with a
Johnny was asked how long it will take the population to reach
complete sentence) Please help.
The assumption Johnny made is that, none of the residents of the town will live up to 230.7 years.
The given parameters are:
[tex]\mathbf{a =10000}[/tex] --- the initial population
[tex]\mathbf{r =0.3\%}[/tex] -- the declining rate
Population are always modelled using exponential function.
This is represented as:
[tex]\mathbf{y = a(1 - r)^x}[/tex]
Where y represents the population in x years.
So, we have:
[tex]\mathbf{y = 10000(1 - 0.3\%)^x}[/tex]
[tex]\mathbf{y = 10000(1 - 0.003)^x}[/tex]
[tex]\mathbf{y = 10000(0.997)^x}[/tex]
When the population reaches half, then y = 5000.
So, we have:
[tex]\mathbf{5000 = 10000(0.997)^x}[/tex]
Divide both sides by 10000
[tex]\mathbf{0.5 = 0.997^x}[/tex]
Take logarithm of both sides
[tex]\mathbf{log(0.5) = log(0.997)^x}[/tex]
Apply law of logarithm
[tex]\mathbf{log(0.5) = xlog(0.997)}[/tex]
Make x the subject
[tex]\mathbf{x = log(0.5) \div log(0.997)}[/tex]
[tex]\mathbf{x = 230.7}[/tex]
This means that the population will become half the original population in 230.7 years.
The assumption Johnny made is that, none of the residents of the town will live up to 230.7 years.
Read more about exponential function at:
https://brainly.com/question/11487261
Solve the simultaneous equations
3x - y = 5
-x + y = -1
Answer:
x= 2, y= 1
Step-by-step explanation:
3x -y= 5 -----(1)
-x +y= -1 -----(2)
(1) +(2):
3x -y -x +y= 5 -1
2x= 4
Divide both sides by 2:
x= 4 ÷2
x= 2
Substitute x= 2 into (2):
-2 +y= -1
y= -1 +2
y= 1
11. Consumer Math A store has apples on sale at $3.00 for 2 pounds.
a. How many pounds of apples can you buy for $9. Explain your answer
Answer:
6 pounds
Step-by-step explanation:
3$ for 2 pounds
9$ has three 3$
9 ÷ 3 = 3
Then multiply it to 2 pounds.
3 x 2 = 6
That's how we get the 6 pounds.
3. drinking 8 glasses of water a day is good for your health. if each glass of water is equivalent to 148 mL, how many liters of water you need to consume everyday.
Answer:
pap
Step-by-step explanation:
papi
Answer:
1184 mL (148×8)= 1.184 liters
marcus piano teacher wanted him to practice 1.5 hours before she saw him on friday afternoon he practiced 18 minutes on monday 23 minutes on tuesday 16 minutes on wednesday and 13 minutes on thursday. how long did he have to practice on friday morning to meet his goal? what fraction of an hour is that? pls help 15 if correct
he would have to practice 20 minutes on friday
18 + 23 + 16 + 13 = 70
1.5 hours = 90 minutes
90-70 = 20 minutes
2/9
Use point-slope form to write the equation of a line that passes through the point
(-6,3) with slope – 2.
Answer:
y = -2x - 9
Step-by-step explanation:
Slope = - 2
Using the slope = -2 and the point (-6, 3) substitute into y= mx + b and solve for "b"
y = mx + b
3 = -2(-6) + b
3 = 12 + b
3 - 12 = b
-9 = b
The equation of the line is y = -2x - 9
It takes Billy 40 minutes to drive to his friends house at his normal speed but it takes two hours if he drives 20 mph slower how far away is Billy's friends house
Answer:
Step-by-step explanation:
d/t=mph
Billy's friend's house is 20 miles away from him.
What is Speed?
The ratio of the distance travelled by an object to the time required to travel that distance.
Given that when Billy moves with his normal speed, it takes 40 min for him to reach his friend's house and if he slows his speed to 20 mph he takes 2 hours to reach the same distance.
We know, Speed = Distance/time
Let x be Billy's normal speed,
Therefore, 2x/3 = 2 (x - 20)
2x/3 = 2x - 40
x = 3x - 60
x = 30
Therefore, Billy's normal speed is 30 mph
Distance covered by him = 2 (30 - 20) = 20 mi
Hence, Billy's friend's house is 20 mi far.
For more references on speed, click;
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PLZ HELP ASAP! I'LL GIVE BRAINLIEST AND POINTS JUST HELP PLZ
plz no links
Divide these numbers in scientific notation.
(9.6*10^-8) divided by (3*10^-7)
Answer:
3.2 *10^-1
Step-by-step explanation:
Answer:
Step-by-step explanation:
[tex]\dfrac{9.6*10^{-8}}{3*10^{-7}}==\dfrac{9.6}{3}*10^{-8-[-7]}\\\\\\= 3.2*10^{-8+7}\\\\\\=3.2*10^{-1}[/tex]
-4/4 plus 160 percent plus 1/5
Answer:
-1 + (1.6) + 0.2
Step-by-step explanation:
-1 + 1.6 = 0.2 = 0.8
Answer:
-1 + (1.6) + 0.2
Step-by-step explanation:
-1 + 1.6 = 0.2 = 0.8
How many different pairs of 2-digit numbers multiply to give a 3-digit number with all digits the same? (A) 5 (B) 6 (C) 7 (D) 8 (E)S
Answer:
a
Step-by-step explanation:
po ang tamang sagon po
Plzzzz help meeeee plzzzz
Answer:
200
Step-by-step explanation:
Question is atttached below
Answer:
A. 20·60
Step-by-step explanation:
The product of force and distance is ...
[tex]F\cdot D=(20\text{ m})\cdot\dfrac{60\text{ kg$\cdot$m}}{\text{s}^2}=\dfrac{20\cdot60\text{ kg$\cdot$m$^2$}}{\text{s}^2}=\boxed{20\cdot60\text{ J}}[/tex]
The degree measure of each exterior angle of a regular octagon is represented by the expression 7x - 4. SOLVE FOR X.
Answer:
x = 4/7
Step-by-step explanation:
7x - 4
7x = 4
x = 4/7
what is? -6 = x + 6
this is one step equation addition / subtraction
[tex] \: \: \: \: \: [/tex]
x = - 12
refer to the attachment
refer to the attachmenthope it helps[tex]\sf \longmapsto-6 = x + 6[/tex]
Flip the equation[tex]\sf \longmapsto \: x+6=−6[/tex]
Subtract 6 from both sides[tex]\sf \longmapsto \: x+6−6=−6−6[/tex]
[tex]\sf \longmapsto \: x=−12[/tex]
[tex] \boxed{ \sf \: x=−12}[/tex]
what is the answer help
Answer:
$29.88
Step-by-step explanation:
$12.45 / 5
$2.95 each pound
2.95 * 12
29.88
cos135° =
A.√2/2
B.-√2/2
C.-1/2
we have cos135° = -√2/2
so B is the correct answer
ok done. Thank to me :>
A:B is equivalent to 11:5.
Answer:
yeeeeee
Step-by-step explanation:
Which term of the arithmetic sequence 1, 5, 9, 13, ... is 169?
It is the
th term.
Answer:
43rd term
Step-by-step explanation:
Arithmetic sequences are basically linear functions, so the same value is added every time. So, knowing that Asub1 is equal to one, and Asubn is equal to 169 we can take 169-1 and divide by our common difference. This is four as 5-1=4 and 9-5=4.
So, (169-1)/4=42.
This is however 42 terms after Asub1, so this would be the 43rd teen of the sequence!
(I’m having trouble with this question, it would be greatly appreciated if I could have some help, thank you)
What is the equation of a line that is parallel to – 2x + 3y = -6 and passes through the point (-2, 0)?
Answer:
y = 2/3x + 4/3
Step-by-step explanation:
you need to know the slope of the line -2x + 3y = -6 because parallel lines have the same slopes
let's put the equation in y=mx+b format (slope-intercept format)
-2x + 3y = -6
add 2x to each side to get:
3y = 2x - 6
divide each side by 3 to get:
y = 2/3x - 2
the equation now shows us the slope is 2/3 and the y-intercept is (0,-2)
now we use y=mx+b again and use the point (-2,0) and the m=2/3 to get the y-intercept ('b' value) of the equation that is parallel:
0 = 2/3(-2) + b
0 = -4/3 + b
b = 4/3
equation would be:
y = 2/3x + 4/3
an electrician has 4.1 meters of wire.How many strips of 7 tenths can be cut?and how much wire will be left over?
Rachel withdraws $19 from her bank account once each day for three days. What integer represents the change in the amount in the account? Find the integer that would represent the change in the amount in the account if Rachel deposits $19 into her bank account once each day for three days.
Answer:
How much did she start with tho???
Step-by-step explanation:
Find x. please help me!!
Answer:
I want to say B.
Step-by-step explanation:
Step 4: Plot the y-intercept.
Help me with this hw plzzz
this graph shows how much lisa earns babysitting compared with thge number of hours she works
Answer:
For every hour she earns 12$
Step-by-step explanation:
If your question looks like the picture, then the answer above is the right answer. If it's not, oh well, show the picture next time!
what is the correct way to label the entire line segment shown
Answer:Yea looks like you have it already C
Step-by-step explanation:
F(4p + 3) = 8 - 5(4p + 3)
=============================
[tex]\large\bold{Equation:}[/tex]
[tex]\large\sf{F(4p + 3) = 8 - 5(4p + 3)}[/tex][tex]\large\bold{Solution:}[/tex]
Let's solve for f
[tex]\large\sf{F(4p + 3) = 8 - 5(4p + 3)}[/tex]
1st step: Factor out variable f
[tex]\large\sf{F(4p+3)=−20p−7}[/tex]2nd step: Divide both sides by 4p+3
[tex]\large\sf{ \frac{F(4p + 3)}{4p + 3} = \frac{ - 20p - 7}{4p + 3} }[/tex][tex]\large\sf{F = \frac{ - 20p - 7}{4p + 3} }[/tex][tex]\large\bold{Answer:}[/tex]
[tex]\large\tt{F = \frac{ - 20p - 7}{4p + 3} }[/tex]===================================
How is it? Hope you appreciate and understand my answer. Have a great and nice day ahead!!
^^
Ping chooses four numbers.
The mode of these four numbers is 8, the range is 7 and the mean is 11.
Find Ping's four numbers.
What is the slope of a line that passes through the points (4, - 3) and (- 2, 9)
Answer:
-2
Step-by-step explanation:
slope = y2 - y1 / x2 - x1
= 9 - (-3) / -2 -4
= 12 / -6
= -2
Which one of the quotients is correct?
Answer:
B
Step-by-step explanation:
B is correct 24r11 one ................
If 'r' represents remainder then the correct answer is option A. The quotient is 24 & the remainder is 13.
Steps are in the attachment.
____
RainbowSalt2222 ☔