The populations of 2 cities grow according to the exponential functions. Pi(t) = 120 e 0.011 t P2(t)= 125 e 0.007 t Where, P₁ and P2 are the populations (in thousands) of cities A and B respectively. t is the time in years such that t is positive and t = 0 corresponds to the year 2004. When were the populations of the two cities equal and what were their populations?
Answers
Hello,
I hope you and your family are doing well!
To find when the populations of the two cities are equal, we can set P1(t) = P2(t) and solve for t:
120 e 0.011 t = 125 e 0.007 t
Dividing both sides by e 0.007 t:
120 = 125 * (e 0.011 t / e 0.007 t)
Using the property that e^(a+b) = e^a * e^b, we have:
120 = 125 * e^(0.011 t - 0.007 t)
120 = 125 * e^(0.004 t)
Dividing both sides by 125:
1.2 = e^(0.004 t)
Taking the natural logarithm of both sides:
ln 1.2 = ln e^(0.004 t)
ln 1.2 = 0.004 t
t = ln 1.2 / 0.004
t = approximately 8.44 years
Therefore, the populations of the two cities were equal approximately 8.44 years after 2004, or in the year 2012. To find the population of the two cities at this point in time, we can substitute t = 8.44 into either of the exponential functions:
P1(8.44) = 120 e 0.011 * 8.44 = approximately 123.88 thousand
P2(8.44) = 125 e 0.007 * 8.44 = approximately 123.88 thousand
Therefore, the populations of the two cities were equal to approximately 123.88 thousand when they were equal.
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Related Questions
Ryan is riding a bicycle whose wheels are 28 inches in diameter. If the wheels rotate at 130 rpm, find the angular speed in radians per second in which he is traveling.
Answers
The angular speed in radians per second in which he is traveling is 60.2pi inch/sec.
What is the relation of speed and distance?
Speed describes how accelerated something or somebody is moving. If you know the distance traveled and the time it took, we can calculate the average speed of an object.
The speed formula is speed = distance / time.
Given that;
The diameter of bicycle wheel= 28inches
Rpm of wheel = 130rpm
Now,
Angular speed ω = 2pi*N/60 radian per second.
=2*pi*130/60
=260pi/60
=4.3pi radian per second
Speed of bicycle V = r*ω
V=14*4.3pi
V=60.2pi inch/sec
Therefore, the angular speed of ryan by the data is 60.2pi inch/sec.
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AB||CD. Find the measure of
Answers
Answer:
135 degrees
Step-by-step explanation:
3x+15 = 5x - 5 because of the alternate interior angles theorem.
20 = 2x
x = 10
3(10) + 15 = 30+15 = 45
Remember that a line has a measure of 180 degrees. So we can just subtract the angle we found from 180 degrees to get BFG.
180-45 = 135.
A manufacturing company finds that they can sell 250 items at $3.50 per item and 350 items at $2.50 per item.
If the relationship between the number of items sold a and the price per item p is a linear one:
Find a formula that gives a in terms of p: x =
Now use the formula to find the number of items they will sell if the price per item is $1.50.
They will sell…
items if the price is $1.50.
Answers
Answer:
a = 600 -100pa = 450 for p = 1.50Step-by-step explanation:
You want the formula that represents (p, a) = (3.50, 250) and (2.50, 350) as a linear function. Then you want the value of 'a' for p = 1.50.
SlopeWe can see from the ordered pairs that 'a' goes up by 100 when p goes down by 1.00. The slope is ...
m = ∆a/∆p = 100/(-1) = -100
InterceptThe y-intercept (b) can be found by solving the slope-intercept equation for b:
y = mx +b
b = y - mx
For (x, y) = (3.50, 250), the value of 'b' is ...
b = 250 -(-100)(3.50) = 600
EquationThe slope-intercept equation for 'a' in terms of p is ...
a = -100p +600
Evaluation
The value of 'a' for p = 1.50 is ...
a = -100(1.50) +600
a = 450
They will sell 450 items if the price per item is $1.50.
Having trouble finding Z.
Answers
z would be 115. you know that one angle is 65, so you'd subract 65 from 180, leaving you with an answer of 115. please mark brainliest and have a great day.
A coin is tossed twice. Let
E
be the event "the first toss shows heads" and
F
the event "the second toss shows heads".
(a) Are the events
E
and
F
independent?
Input Yes or No:
(b) Find the probability of showing heads on both tosses. Write your answer as a reduced fraction.
Answer:
Answers
Answer:
(a) Yes, E and F are independent events.
(b) P(E and F) = P(E)P(F) = (1/2)(1/2) = 1/4
Aashna thinks that the largest place value that 82.3 and 11.45 have in common is the tens place. Jake thinks that the largest place value they have in common is the tenths place.
Answers
Rachel, a 45-year-old female, bought a $120,000, 20-year life insurance policy through her employer. Rachel is paid biweekly.
How much is deducted from each of her paychecks for life insurance?
$63.14
$68.40
$81.05
$87.80
Answers
Answer: the answer is $63.14.
Step-by-step explanation:
I took the test and got it correct.
Answer:
$63.14
Explanation:
I got it right on the test
Please someone tell me the answer with work please please
Answers
The volume of the solid of revolution formed by revolving the region bounded by f(x) = -3x² + 8 and g(x) = 3x² + 2 about the x-axis is 16π cubic units.
To find the volume of the solid of revolution formed by revolving the region bounded by the curves f(x) = -3x² + 8 and g(x) = 3x² + 2 about the x-axis, we can use the method of cylindrical shells and integrate.
First, let's find the points of intersection between the two curves by setting them equal to each other:
-3x² + 8 = 3x² + 2
Rearranging the equation, we get:
6x² = 6
x² = 1
x = ±1
So, the curves intersect at x = -1 and x = 1.
To calculate the volume, we'll integrate along the x-axis from x = -1 to x = 1. The volume of each cylindrical shell can be determined by multiplying the circumference (2πy) by the height (dx), where y represents the distance from the axis of revolution to the curve at a given x-value.
The radius of the cylindrical shell, y, can be obtained by subtracting the lower curve (f(x)) from the upper curve (g(x)). Therefore, y = (3x² + 2) - (-3x² + 8) = 6x² - 6.
The integral to compute the volume of the solid can be expressed as:
V = ∫[from -1 to 1] 2π(6x² - 6) dx
V = 2π ∫[from -1 to 1] (6x² - 6) dx
Simplifying and evaluating the integral, we get:
V = 2π [2x³ - 6x] [from -1 to 1]
V = 2π [(2(1)³ - 6(1)) - (2(-1)³ - 6(-1))]
V = 2π [2 - 6 - (-2 + 6)]
V = 2π [8]
V = 16π
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Find the slope of the line
A. -4
B. -1/4
C. 1/4
D. 4
Answers
Answer:
C. 1/4
hopes this helped
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below
\((\stackrel{x_1}{-8}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{3}-\stackrel{y1}{(-1)}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{(-8)}}} \implies \cfrac{3 +1}{8 +8} \implies \cfrac{ 4 }{ 16 } \implies \cfrac{1 }{ 4 }\)
The concept of hope is nothing more than giving up. A word that holds no true meaning.
Answers
Answer:
lol fr
Step-by-step explanation:
Answer:
Big pp
Step-by-step explanation:
The baseball player threw the ball 30 feet to his teammate. How far would the throw be if measured in yards?
Answers
Answer:
10
Step-by-step explanation:
to convert to yard from feet you have to divide by 3
30/3-10 so he through the ball 10 yards
have a great day :D
An office pays its 8 clerical workers $205 per week, 4 secretaries $301 per week, and the office manager $481 per week. What is the total paid out to all employees every week?
Answers
Answer:
8 x 205= 1640
4 x 301=1204
1 x 481= 481
481+1204+1640
= $3325 every week
Closeness of a measurement to the actual value of the dimension being measured. For example, a measurement of 1.99999 cm for an object that is 2 cm wide has a high level of accuracy? a.precision b.conversion factor c.quantify d.accuracy?
a. precision
b. conversion factor
c. quantify
d. accuracy
Answers
Answer:
d. accuracy
Step-by-step explanation:
In measurements, accuracy is a term that is used to describe the closeness of a measured value to the actual or true value. While precision describes how close different measured values are to each other.
Thus when a measured value is accurate, it implies that the value is very close or almost equal to the true value. The correct answer to the question is is option D.
Apply the distributive
property to write
equivalent expressions in
expanded form.
4(h+6) 7(3h + 3)
Answers
Answer:
25h + 45
Step-by-step explanation:
4(h+6) 7(3h+3)
4h + 24 21h + 21
25h + 45
PLEASE ANSWER THIS IS DUE TODAY PLS
The _________ 8.92 and 6.7 is about 16.
1. sum of
2.Difference between
Answers
Answer:
sum of
Step-by-step explanation:
sum of = adding
What theorem shows that TPN ≅ TQM?
Triangles T Q M and T P N which share vertex T. Side T A in the first triangle is congruent to side T P in the second triangle. Side T M in the first triangle is congruent to side T N in the second. The angles at vertex T are vertical angles and are included between the two pairs of congruent sides.
Group of answer choices
AAS
ASA
SAS
SSS
Answers
Note: Consider the side of first triangle is TQ instead of TA.
Given:
Triangles TQM and TPN which share vertex T.
\(TQ\cong TP,TM\cong TN\)
To find:
The theorem which shows that \(\Delta TPN\cong TQM\).
Solution:
In triangle TQM and TPN,
\(TQ\cong TP\) [Given]
\(\angle QTM\cong \angle PTN\) [Given]
\(TM\cong TN\) [Given]
Since two sides and their including angle are congruent in both triangles, therefore both triangles are congruent by SAS postulate.
\(\Delta TPN\cong TQM\) [SAS]
Therefore, the correct option is C.
what is the formula for the rate of interest of an investment compounded monthly?
Answers
Answer:
CI = Amount - Principal
CI = P (1+(r/12))121 - P
P= principal amount
r= interest rate
t= time
Step-by-step explanation:
The compound interest each month is calculated using the monthly compound interest method. Return on credit is another name for compound interest. Simple interest and compound interest are identical in the initial amount of time, however the variation starts with the following phase. It is characterized as interest on interest because starting with the second intermission, it is also computed on the revenue that was thus generated on the prior time frame.
The interest is accrued directly to the principle every month using a method called monthly compounding principal, often termed as interest-on-interest equation. The ultimate sum minus the principle sum is known as total compound interest.
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HELP!!
Calculate the residuals for your scatterplot in step 2d.
Answers
In statistics, a residual is defined as the difference between the predicted value of an outcome variable and the observed value of that variable. Residuals are used to evaluate how well a regression model fits the data.In order to calculate the residuals for a scatterplot, follow these steps:
Step 1: Plot the data on a scatterplot.
Step 2: Perform a regression analysis on the data to find the equation of the regression line. This equation should take the form y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.
Step 3: Using the equation of the regression line, calculate the predicted value of y for each data point in the scatterplot.
Step 4: Subtract each predicted value of y from the actual value of y for each data point in the scatterplot. This difference is the residual for that data point.
Step 5: Plot the residuals on a new scatterplot. The x-axis of this scatterplot should be the independent variable, and the y-axis should be the residual values.
Step6: This scatterplot is called a residual plot.Residuals are useful for identifying patterns in data that the regression model fails to capture. If the residuals are randomly scattered around the horizontal axis, then the regression model is a good fit for the data. If there are clear patterns in the residual plot, then the regression model may not be a good fit for the data and further analysis is required.
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You want to open a checking account at your local bank which offers two options. A standard checking account charges $6 each month plus $.25 for each check written. A select checking account charges $4.50 each month plus $.50 for each check written. Which system of equations can be used to determine the number x of checks that must be written in a month in order for the total charges y for the two checking accounts to be the same?
Answers
Answer:
The total charges for the two checking accounts will be the same after 6 checks written.
Step-by-step explanation:
Since I want to open a checking account at my local bank which offers two options, a standard checking account that charges $ 6 each month plus $ 0.25 for each check written, and a select checking account that charges $ 4.50 each month plus $ 0.50 for each check written, to determine which system of equations can be used to determine the number X of checks that must be written in a month in order for the total charges Y for the two checking accounts to be the same, the following calculation must be performed:
6 + 0.25X = Y
4.5 + 0.5X = Y
6 + 0.25x5 = Y
4.5 + 0.5x5 = Y
6 + 1.25 = Y = 7.25
4.5 + 2.50 = 7
6 + 0.25x6 = Y
4.5 + 0.5x6 = Y
6 + 1.50 = Y = 7.50
4.5 + 3 = 7.50
Therefore, the total charges for the two checking accounts will be the same after 6 checks written.
Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
Answers
Answer:c
Step-by-step explanation:
Answer:
On Edge the answer is C i think
Use the following predicates when describing an object: Green, Blue, Red, Rectangle, Oval, Diamond, Border For example: Green(H) = True because object H is green Border(H) = False because object H has no border Problem 6 [21 points] For each statement below, write the contrapositive, the converse and the inverse using english (no logical operators needed). Tell which of the four statements (the three you wrote, in addition to the original statement) is true or false. If a statement is false, provide a counter-example. (example) Original Conditional Statement (P - Q): If an object is green, then it is a rectangle. False. Object H is green but it is also not a rectangle. Contrapositive (not Q - not P): If an object is not a rectangle then it is not green. False. Object H is not a rectangle but it is also green. Converse (Q - P) If an object is a rectangle then it is green. False. Object P is a rectangle but it is also not green. Inverse (not p → not q) If an object is not green then it is not a rectangle. False. Object P is not green but it is also a rectangle. (a) If an object is red, then it has a border. (b) If an object is a rectangle, then it is red and has a border. (c) If an object is red or blue then it has a border.
Answers
(a)Contrapositive: If an object does not have a border, then it is not red.
Converse: If an object has a border, then it is red.
Inverse: If an object is not red, then it does not have a border.
(b)Contrapositive: If an object is not red or does not have a border, then it is not a rectangle.
Converse: If an object is a rectangle, then it is red and has a border.
Inverse: If an object is not red or does not have a border, then it is not a rectangle.
(c)Contrapositive: If an object does not have a border, then it is not red or blue.
Converse: If an object is red or blue, then it has a border.
Inverse: If an object does not have a border, then it is not red or blue.
a) Original Conditional Statement (P - Q): If an object is red, then it has a border.
Contrapositive (not Q - not P): If an object does not have a border, then it is not red.
Converse (Q - P) If an object has a border then it is red.
Inverse (not p → not q) If an object is not red then it does not have a border.
The contrapositive is true, while the converse and inverse are false. For example, object H may have a border but not be red.
b) Original Conditional Statement (P - Q): If an object is a rectangle, then it is red and has a border.
Contrapositive (not Q - not P): If an object is not red and does not have a border, then it is not a rectangle.
Converse (Q - P) If an object is red and has a border, then it is a rectangle.
Inverse (not p → not q) If an object is not a rectangle then it is not red or does not have a border.
The contrapositive is true, while the converse and inverse are false. For example, object H may be red and have a border but not be a rectangle.
c) Original Conditional Statement (P - Q): If an object is red or blue, then it has a border.
Contrapositive (not Q - not P): If an object does not have a border, then it is not red or blue.
Converse (Q - P) If an object has a border then it is red or blue.
Inverse (not p → not q) If an object is not red or blue then it does not have a border.
The contrapositive and converse are true, while the inverse is false. For example, object H may have a border but not be red or blue.
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You buy 5 pounds of potatoes for $35. How much does one pound cost?
Answers
Answer:
2.5
Step-by-step explanation:
Answer: $7
Step-by-step explanation: 35 divided by 5= 7 so $7
The research question is: Do the data provide evidence that the treatments affect the mean LDL level in this population
Answers
Answer:
hello your question is incomplete attached below is the complete question
answer : The population mean LDL level after six months is same for all four treatments
Step-by-step explanation:
A null hypothesis represents a no difference in the question. therefore the correct option is The population mean LDL level after six months is same for all four treatments
Given: x + y = 10.
If x = -21, what is y?
31
11
-31
Answers
It wouldn’t be 11 because x is -21, so 11 + -21 would be -10.
It wouldn’t be -31 because that would make -52.
So, clearly your answer would be 31.
Please do me a favor and mark this as Brainliest! :))
Answer:
y is 31
Step-by-step explanation:
we need to substitute first
x + y = 10
x= -21 so...
-21 + y = 10
now we need to add 21 on both sides of the equation, we are adding because 21 because we want that 21 gone, and it's the oppisite of subtracting
-21 + 21 + y = 10 + 21
0 + y = 10 + 21
y= 31
Check:
x+y=10
-21 + 31= 10
10 = 10 correct!
Hope this helped!
Solve for x.
−2x−1+3x=7
x=−2
x=−1
x = 6
x = 8
Answers
Answer:
x=8 is the answer. x-1=7 => x=7+1= 8
please help quick!!!
Answers
what is the image point of (0,8) after a translation right 3 units and down 5 units
Answers
Answer:
(3,3) because (0+3, 8-3)
Which number(s) have a 5 that is 10 times the value of the 13,725 in ?
Answers
Answer:
I will give you three, but the answer is the number that has a 50
Step-by-step explanation:
52
654
7657
50 is the numbers that have a 5 in 10 times the value of the 13,725.
What is place value?Place value is the value of each digit in a number.
For example, the 5 in 350 represents 5 tens, or 50; however the 5 in 5006 represents 5 thousands, or 5000.
Now the given number is,
13,725
10 times of the number is givens as,
13,725*10
or, 137,250
here place value of 5 in 137,250 is 5 tens or 50.
Therefore, 50 is the numbers that have a 5 in 10 times the value of the 13,725.
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Pls hurry and help Solve.
Find the perimeter of a park that measures 7 miles by 9/10 miles.
A. 15 4/5 miles^2
B. 6 3/10 miles^2
C. 6 3/10 miles
D. 15 4/5 miles
Answers
Answer:
Find the perimeter of a park that measures 7 miles by 910 miles. Get the answers you need, now! ... Advertisement tasha005111 is waiting for your help. Add your answer and earn points. kaylapoo34 kaylapoo34 Answer: the answer is 130. Step-by-step explanation: ... 15 Niles and Bob sailed at the same time for the same length of time.
Step-by-step explanation:
Answer:B
Step-by-step explanation:
HELP ME PLEASEEEEEEEEEEEEE
Answers
Answer:
A
Step-by-step explanation:
Lets treat this linear inequality as a linear equation first and simplify it and "solve" for x.
-3x+12 ≤ 15
Subtract 12 on both sides
-3x≤3
Now divide -3 on both sides. However, don't fall into the trap many fall into. When dividing or multiplying an inequality by a negative number, you must switch the sign direction.
x≥-1