Using proportions, it is found that:
A. The vegetables weigh 66 pounds.
B. 0.5 pints are dispensed after 25 seconds.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
4 and 1/8 pounds is equivalent to 4.125 pounds. Since each pound has 16 ounces, the weight of the vegetable is of:
W = 16 x 4.125 = 66 pounds.
Every second, 0.16 gallons are dispensed. Hence the amount dispensed in 25 seconds is:
A = 25 x 0.16 = 4 gallons.
Each gallon has 8 pints, hence the number of pints dispensed is:
4/8 = 0.5 pints.
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A
(5x − 3)°
B
E
(7x+15)°
D
(6y + 7)°
C
Answer:
The value of x = 14 ...
The value of ∠AED = ( 7x + 15) = 7(14) + 15 = 113
The value of ∠AEB = 5x-3 = 5(14) -3 = 67
Step-by-step explanation:
=> ∠BEC = ∠AED { vertically opposite angles }
∠AED = (7x + 15)°
=> ∠AEB + ∠BEC = 180° { linear pair }
=> ( 5x-3) + ( 7x+15) = 180°
=> 5x -3 + 7x + 15 = 180°
=> 12x + 12 = 180°
=> 12( x +1 ) = 180°
=> x+1 = 180/12
=> x +1 = 15
=> x = 15-1
=> x = 14
The voice onset time (vot) for the sound /da/ is 17 ms, and the vot for the sound /ta/ is 91 msec. When a computer produces a sound with a vot of 65 ms, listeners are likely to report hearing?
The the /ta/ sound is the sound which listeners are likely to report hearing. The option B is correct option.
According to the statement
we have given that the The voice onset time (vot) for the sound /da/ is 17 ms, and the vot for the sound /ta/ is 91 msec. and we have to find the sound which listeners are likely to report hearing.
So, For this purpose, we know that the
Traffic announcement (TA) refers to the broadcasting of a specific type of traffic report on the Radio Data System. It is generally used by motorists, to assist with route planning, and for the avoidance of traffic congestion.
And according to this and the voice onset time is
The brief instant that elapses between the initial movement of the speech organs as one begins to articulate a voiced speech sound and the vibration of the vocal cord.
And according to this
the /ta/ sound is the sound which is the like by the listeners are likely to report hearing.
So, The the /ta/ sound is the sound which listeners are likely to report hearing. The option B is correct option.
Disclaimer: This question was incomplete. Please find the full content below.
Question:
The voice onset time (VOT) for the sound /da/ is 17 ms, and the VOT for the sound /ta/ is 91 msec. When a computer produces a sound with a VOT of 65 msec, listeners are likely to report hearing
a. the /da/ sound
b. the /ta/ sound
c. the /ja/ sound
d. a combination of /ta/ and /da/
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If a consumer purchases a combination of commodities x and y such that mux/px = 30 and muy/py = 40, to maximize utility, the consumers should buy.
If [tex]MU_{x}/P_{x}[/tex]=30 and [tex]MU_{y} /P_{y}[/tex]=40 then the consumer should buy the commodity y to maximise utility.
Given that [tex]MU_{x}/P_{x}[/tex]=30 and [tex]MU_{y} /P_{y}[/tex]=40 of commodities x and y.
Marginal utility is the additional utility that a consumer gets from consuming additional units of commodity. For maximising the utility of the consumer,the ratio of marginal utilities must be equal to the ratio of the products.
There can be two situations in our case:
Because [tex]MU_{x}/P_{x}[/tex]<[tex]MU_{y} /P_{y}[/tex]
So to equalise the ratio we need to reduce [tex]MU_{y} /P_{y}[/tex]. To reduce the utility of y the consumer needs to increase the consumption of y because as the consumption of commodity y increase it decreases the utility of commodity y.
Hence if [tex]MU_{x}/P_{x}[/tex]=30 and [tex]MU_{y} /P_{y}[/tex]=40 then the consumer should buy the commodity y to maximise utility.
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A bus moves away from a bus stop in a straight line. it moves 10 meters by the end of the 1st second, 20 meters by the end of the 2nd second, and 30 meters by the end of the 3rd second. how many meters away is the bus from the bus stop after 10 seconds? a. 100 c. 120 b. 110 d. 190 please select the best answer from the choices provided a b c d
10 meters away is the bus from the bus stop after 10 seconds.
What is arithmetic sequence?A series of integers in which the difference between succeeding words is always the same is referred to as an arithmetic sequence or arithmetic progression. For instance, the difference in the arithmetic series 1, 5, 9, 13, 17,... is always 4. The common difference is what we refer to as.
According to the given information:A bus moves away from bus stop in a straight line. After 1 second it was 10 meters away, after 2 seconds it was 20 meters and after 3 seconds it was 30 meters away.
In this way bus forms an arithmetic sequence
10, 20, 30, 40........up to 10 terms.
nth term of an arithmetic sequence is represented by
[tex]T_{n}[/tex] = a+ (n - 1)d
Here a = 10 and d = common difference = 10
Therefore 10th term = 10 + (10-1)10
= 10 + 90
= 100
Therefore after 10 seconds bus will be 10 meters away from the bus stop.
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What is the missing factor in this factor tree? 30 2x?
Answer:
15?
Step-by-step explanation:
2×15=30 i am not fully sure but this should be it
Can anyone help me with this!
Answer:
The answer is B.
[tex] \frac{1025}{4} [/tex]
Step-by-step explanation:
Greetings ![tex] \frac{x {}^{6} - x}{4y} ...substitute \: x = - 4 \: and \: y = 4 \\ \frac{( - 4) {}^{6} - (- 4) }{4(4)} ...apply \: exponent \: rule \\ \frac{4096 + 4}{16} = \frac{4100}{16} = \frac{1025}{4} [/tex]
(-4)^6 - - 4 / 4 x 4
4096 + 4 / 16
4100/16
= 1025/4
So, answer is B. 1025/4
Hope this helps!
The probability that a rental car will be stolen is. 4. if 3500 cars are rented, what is the approximate poisson probability that 2 or fewer will be stolen?
Using the Poisson distribution, there is a 0.8335 = 83.35% probability that 2 or fewer will be stolen.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successese = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval.The probability that a rental car will be stolen is 0.0004, hence, for 3500 cars, the mean is:
[tex]\mu = 3500 \times 0.0004 = 1.4[/tex]
The probability that 2 or fewer cars will be stolen is:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-1.4}1.4^{0}}{(0)!} = 0.2466[/tex]
[tex]P(X = 1) = \frac{e^{-1.4}1.4^{1}}{(1)!} = 0.3452[/tex]
[tex]P(X = 2) = \frac{e^{-1.4}1.4^{2}}{(2)!} = 0.2417[/tex]
Then:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2466 + 0.3452 + 0.2417 = 0.8335[/tex]
0.8335 = 83.35% probability that 2 or fewer will be stolen.
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An object is launched at an upward velocity of 96 feet per second from the top of a building 160 feet above the ground. Use the vertical motion model h = - 16t² + vt + c where h is the ending height of the object, c is the initial height, in feet, of the object, t is the time in seconds, and v is the velocity of the object. How long will it take the object to reach the maximum height and what is the maximum height? Fill in the blanks with the appropriate values.
[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&96\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&160\\ \qquad \textit{of the object}\\ h=\textit{object's height}&h\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ h(t)=-16t^2+96t+160[/tex]
Check the picture below.
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-16}x^2\stackrel{\stackrel{b}{\downarrow }}{+96}x\stackrel{\stackrel{c}{\downarrow }}{+160} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 96}{2(-16)}~~~~ ,~~~~ 160-\cfrac{ (96)^2}{4(-16)}\right) \implies \left( - \cfrac{ 96 }{ -32 }~~,~~160 - \cfrac{ 9216 }{ -64 } \right)[/tex]
[tex](3~~,~~160 + 144)\implies \underset{~\hfill feet}{\stackrel{seconds~\hfill }{(\stackrel{\downarrow }{3}~~,~~\underset{\uparrow }{304})}}[/tex]
At the end of the soccer season, the player who scored the most goals had 8 more goals than the player who had the second most goals. The player who had the second most goals had 15 more goals than the third player. The total number of goals scored by all three of the players was 98. Determine the number of goals scored by the player with the most goals. Show your working out.
Step-by-step explanation:
x = the number of goals of the top scorer.
y = the number of goals of the second top scorer.
z = the number of goals of the third top scorer.
x + y + z = 98
x = y + 8
y = z + 15
using the third in the second equation we get
x = z + 15 + 8 = z + 23
and now using this and the third equation in the first equation gives us
z + 23 + z + 15 + z = 98
3z + 38 = 98
3z = 60
z = 20
y = z + 15 = 20 + 15 = 35
x = y + 8 = 35 + 8 = 43
the player with the most goals scored 43 goals.
A company, ABC, wants to produce Graphing Calculators. The equipment rental costs are $150 per month and the parts for the calculators cost $1.50 per calculator.
a. Create a function that models this situation:
The total cost that company ABC uses to produce x graphing calculators in a month is given by y = 1.5x + 150
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The standard form of a linear function is:
y = mx + b
Where m is the rate of change and b is the initial value of y.
Let y represent the total cost of producing x calculators in a month, hence:
y = 1.5x + 150
The total cost that company ABC uses to produce x graphing calculators in a month is given by y = 1.5x + 150
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A gallon of Moo Milk costs 5.12$
What is the price, in dollars, of an 8 ounce glass of Moo Milk?
Answer:
$0.32
Step-by-step explanation:
8 ounces is 1/16 of a gallon so
5.12*(1/16) = 0.32
Answer:
32 cents (0.32 dollars)
Step-by-step explanation:
One gallon contains 128 ounces
Calculate the cost of each ounce:
[tex]\frac{5.12}{128} =0.04[/tex]
costs 4 cents an ounce
Calculate the cost of 8 ounces:
[tex](8)(4)=32[/tex]
Hope this helps
Saul walks dogs to earn extra money. He
earned $220 last week by walking 16 dogs.
Write and solve an equation to determine
how much he charges to walk each dog
each week.
Answer:
the answer is 13.75
Step-by-step explanation:
So how here is the solutionSaul earned 220 of 16 dogs so
when you divide 220 with 16 the answer be 13.75
[tex]220 \div 16[/tex]
[tex]13.75[/tex]
So let's checkwhen you multiply 13.75 by 16 the answer be 220
[tex]13.75 \times 16 \\ 220[/tex]
please mark as brainlist I only want 2 more please
May it helpful to you
thank you
Point M is the midpoint of AB. Find BM.
since we know that M is the midpoint of the AB segment, that simply means that the two halves it makes are congruent, namely AM = BM.
[tex]\stackrel{AM}{4x+13}~~ = ~~\stackrel{BM}{3x+17}\implies x+13=17\implies x=4~\hfill \stackrel{3(4)~~ + ~~17}{BM=29}[/tex]
The required length of the side BM is 29.
What is algebra?Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.
In the given question,
Point M is the midpoint of line AB.
AM = 4x + 13,
and BM = 3x + 17
To find the length of MB, use midpoint property.
Since, Point M is the midpoint of AB,
Therefore, AM = MB
4x + 13 = 3x + 17
4x - 3x = 17 - 13
x = 4
The length of MB = 3x + 17 = 3 × 4 + 17 = 12 + 17 = 29.
The length of MB, where M is midpoint of AB, is 29.
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Mean: about 25.1
Standard deviation: about 2.4
What is the z-score of the value 29,rounded to the nearest tenth
The z-score to the normal distribution table is 1.625
z-score of distribution tableThe standard score is the number of standard deviations by which the value of a raw score is above or below the mean value of what is being observed or measured.
The formula for calculating the z-score is expressed as;
z = x-μ/σ
where
μ is the mean of the data
σ is the standard deviation
x is the value
Given the parameters
μ = 25.1
σ = 2.4
x = 29
Substitute the given parameters
z = 29-25.1/2.4
z = 3.9/2.4
z = 1.625
Hence the z-score to the normal distribution table is 1.625
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What fraction of a clockwise revolution does the hour hand of a clock turn through, when it goes from a) 5 to 11? b)2 to 8? c)10 to 1?
Answer: 1/2, 1/2, 1/4
Step-by-step explanation:
To find the fraction that the hour hand turns of a clockwise revolution, we have to find how long it is going then divide by 12
Ex. a) 11 - 5 = 6, 6/12 = 1/2 so the hour hand turns by 1/2 of a clockwise revolution
b) 8 - 2 = 6, 6/12 = 1/2 so the hour hand turns by 1/2 of a clockwise revolution
c) For this, we have to convert 1 into 13 as 1 - 10 is a negative number
13 - 10 = 3, 3/12 = 1/4 so the hour hand turns by 1/4 of a clockwise revolution
The answers are :
a) 1/2
b) 1/2
c) 1/4
To find the fraction of a clockwise revolution, take the ratio between hours covered and hours covered in one revolution.
a)
Hours covered between 5 and 11 ⇒ 11 - 5 = 6Hours covered in 1 revolution ⇒ 126/12 = 1/2b)
Hours covered between 2 and 8 ⇒ 8 - 2 = 6Hours covered in 1 revolution ⇒ 126/12 = 1/2c)
Hours covered between 10 and 1 ⇒ 13 - 10 = 3 (∴ 12 + 1 = 13)Hours covered in 1 revolution ⇒ 123/12 = 1/4A machine pumps 2.1 gallons of water every 1.6 minutes. How many gallons is pumped per minutes?
Answer: 1.3125 gallons
Step-by-step explanation: The machine pumps 2.1 gallons of water every 1.6 minutes. 1.6 minutes is 1.6x more than 1 minute. So, we have to divide 1.6 by 1.6. Next, we have to divide 2.1 by 1.6. We can make this a bit easier by multiplying both of them by 10 to get 21/16 which is 1.3125.
Answer:
1.3125 gallons
Step-by-step explanation:
Using the given information, we can set up a proportion;
[tex]\frac{2.1gallons}{1.6minutes} = \frac{xgallons}{1minute}[/tex]
Now, we can cross multiply to solve for x.
2.1 = 1.6x
x = 1.3125 gallons
check ple im not sure its right
Answer:
8
Step-by-step explanation:
You are correct The distance from -6 to 2 is 8.
please answer these questions
Answer:12
Step-by-step explanation:
Answer:
8. -3, 16
9. -3, 4.5
Step-by-step explanation:
See attached worksheet.
The number of patients treated at Dr. Frank's dentist office each day was recorded for ten days: 13, 9, 7, 8, 2, 4, 22, 12, 5, 0. Using the given data, find the mean for this sample.
The mean of the sample from number of patients treated at Dr. Frank's dentist office each day for ten days is 8.2
MeanGiven data:
13, 9, 7, 8, 2, 4, 22, 12, 5, 0.
Mean of the sample = Total number of patients treated / number of days
= (13 + 9 + 7 + 8 + 2 + 4 + 22 + 12 + 5 + 0) / 10
= 82/10
= 8.2
Therefore, the mean of the sample is 8.2
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What steps may be necessary to predict data not included in a data set using a scatter plot and line of best fit? Select all that apply.
Answer:
Step-by-step explanation:
3. A line of best fit can be roughly determined using an eyeball method by drawing a straight line on a scatter plot so that the number of points above the line and below the line is about equal (and the line passes through as many points as possible). This will help me to see weather or not it is positive or negative.3
43% of a sample of 100 visitors to a national park believes that additional funds should be used to preserve endangered species. what is the margin of sampling error for a 95% confidence interval?
The margin of sampling error for a 95% confidence interval is 9.7%
How to find the Margin of Error?The formula for margin of error here is;
E = z√(p(1 - p)/N)
where;
n is sample size
z is the z score
p is the sample proportion
z-score for a 95% confidence interval from tables is 1.96.
We are given;
p = 43% = 0.43
n = 100
Thus;
E = 1.96√(0.43(1 - 0.43)/100)
E = 0.097 = 9.7%
Thus, we can conclude that the margin of sampling error for a 95% confidence interval is 9.7%
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30 points.
Please quick help
Using translation concepts, the expression for h(x) is given as follows:
[tex]h(x) = \sqrt{x + 4} - 1[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
For this problem, the parent function is:
[tex]f(x) = \sqrt{x}[/tex]
For the translations, we have that:
It was shifted 4 units right, hence x -> x + 4.It was shifted 1 unit down, hence y -> y - 1.Then the expression for h(x) is given as follows:
[tex]h(x) = \sqrt{x + 4} - 1[/tex]
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Select the correct answer. which function has a phase shift of to the right? a. b. c. d.
The function y = 2sin has a phase shift of pi/2 to the right (2x - pi).
What is a trigonometric function?An angle or angle function (such as the sine, cosine, tangent, cotangent, secant, or cosecant) is most simply defined in terms of the ratios of pairs of sides of a right-angled triangle.The inverse of a trigonometric function (such as arcsine, arccosine, or arctangent).To find the function which has a phase shift to the right:
The function has a phase shift of pi/2 to the right.
By definition, you have the phase shift is:
asin(bx+c)Phase shift = -c/bWhen you substitute the values from the function [tex]y=2sin(2x-\pi )[/tex], where [tex]c=-\pi[/tex] and [tex]b=2[/tex], you obtain:
Phase shift = [tex]-(-\pi )/2[/tex]Phase shift = [tex]\pi /2[/tex]Therefore, the function y = 2sin has a phase shift of pi/2 to the right (2x-pi).
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The complete question is given below:
Which function has a phase shift of pi/2 to the right?
Which of these is a simplified form of the equation 7y 8 = 9 3y 2y? 7y = 6 2y = 1 12y = 17 5y = 17
The simplified equation of 7y + 8 = 9 + 3y + 2y is 2y = 1
How to simplify an equation?The equation can be simplified as follows:
7y + 8 = 9 + 3y + 2y
We have to combine like terms
Hence,
7y + 8 = 9 + 3y + 2y
7y + 8 = 9 + 5y
subtract 5y from both sides
7y - 5y + 8 = 9 + 5y - 5y
2y + 8 = 9
Let's subtract 8 from both sides
2y + 8 - 8 = 9 - 8
2y = 1
Therefore, the simplified equation of 7y + 8 = 9 + 3y + 2y is 2y = 1
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Write the following as an inequality:
x is less than or equal to negative 3 or greater than or equal to 4
The become in the inequality form is -3≥x≥4.
According to the statement
we have given that the statement and we have to write this condition in the form of the inequality.
So, we know that the
Inequality, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
It is represented with the grater than or less than or equal to signs.
so, the given statement is
x is less than or equal to negative 3 or greater than or equal to 4
and we have to write in the inequality condition so,
we have to write it but before this break the statement like
x is less than or equal to negative 3
And
x is greater than or equal to 4.
So,
-3≥x≥4.
So, The become in the inequality form is -3≥x≥4.
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Determine the convergence or divergence of the sequence with the given nth term. if the sequence converges, find its limit. (if the quantity diverges, enter diverges. ) an = 21/n
The given sequence [tex]2^{\frac{1}{n} }[/tex] converges with limit 1.
According to the given question.
We have a sequence,
[tex]a_{n} = 2^{\frac{1}{n} }[/tex]
Since, we know that
The sequence of real numbers [tex]S_{n}[/tex], where n goes from 1 to infinity has a limit L, the the sequence is convergent to L. If the sequence doesn't have limit then it is divergent.
The nth root function is strictly increasing for positive real values.
Therefore,
[tex]1^{\frac{1}{n} } \leq 2^{\frac{1}{n} } \leq n^{\frac{1}{n} }[/tex] [tex]\forall \ n\geq 2[/tex]
Also,
[tex]\lim_{n \to \infty} n^{\frac{1}{n} } = 1[/tex]
[tex]\implies \lim_{n \to \infty} 1^{\frac{1}{n} } =1[/tex] ( by squeeze theorem)
Thereofore,
[tex]\lim_{n \to \infty}2^{\frac{1}{n} } =1[/tex]
So, the given sequecence has a limit i.e. 1. Which means [tex]2^{\frac{1}{n} }[/tex] is a convergent sequence.
Hence, the given sequence [tex]2^{\frac{1}{n} }[/tex] converges with limit 1.
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Find the taylor series for f(x) centered at the given value of a. [assume that f has a power series expansion. do not show that rn(x) → 0. ] f(x) = 8/x, a = −4
The taylor series for the f(x)=8/x centered at the given value of a=-4 is -2+2(x+4)/1!-24/16 [tex](x+4)^{2}[/tex]/2!+...........
Given a function f(x)=9/x,a=-4.
We are required to find the taylor series for the function f(x)=8/x centered at the given value of a and a=-4.
The taylor series of a function f(x)=[tex]f(a)+f^{1}(a)(x-a)/1!+ f^{11}(a)(x-a)^{2} /2! +f^{111}(a)(x-a)a^{3}/3!+..........[/tex]
Where the terms in f prime [tex]f^{1}[/tex](a) represent the derivatives of x valued at a.
For the given function.f(x)=8/x and a=-4.
So,f(a)=f(-4)=8/(-4)=-2.
[tex]f^{1}[/tex](a)=[tex]f^{1}[/tex](-4)=-8/([tex]-4)^{2}[/tex]
=-8/16
=-1/2
The series of f(x) is as under:
f(x)=f(-4)+[tex]f^{1}(-4)(x+4)/1!+ f^{11}(-4)(x+4)^{2}/2!.............[/tex]
[tex]=8/(-4)-8/(-4)^{2} (-4)(x+4)/1!+ 24/(-4)^{3} (-4)(x+4)^{2}/2!.............[/tex]
=-2+2(x+4)/1!-24/16 [tex](x+4)^{2}[/tex]/2!+...........
Hence the taylor series for the f(x)=8/x centered at the given value of a=-4 is -2+2(x+4)/1!-24/16 [tex](x+4)^{2}[/tex]/2!+...........
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Two airplanes leave an airport at the same time and travel in opposite directions. One plane travels 66 kmh faster than the other. If the two planes are 10,716 kilometers apart after 6 hours, what is the rate of each plane
Answer:
The rate of planes: 926 km/h and 860 km/h
=========================
GivenTwo planes travel in opposite directions,One plane travels 66 km/h faster than the other,The distance between the two planes after 6 hours is 10716 km.To findThe rate of of each planeSolution
The distance traveled by two planes in an hour is:
10716/6 = 1786 km/hLet the rate of one plane be x, then the other plane's rate is x - 66.
The sum of two rates is the distance traveled in one hour:
x + x - 66 = 17862x - 66 = 17862x = 1786 + 662x = 1852x = 1852/2x = 926So the rate of one plane is 926 km/h and of the other plane is:
926 - 66 = 860 km/hFundamentally, pressure is defined as force per unit area. what is the source of the force in a gas sample?
The source of the force in the gas sample is; The force is composed of the sum of the collisions only between the gas molecules and the container
What is the relationship between Force and Pressure?We are given that;
Pressure = Force /Area
Now, for any gas sample, force is defined as basically the force exerted by the gas molecules when they strike the surface and bounce back inside the container where they are located.
Now, from the definition above we can conclude that the source of the force in the gas sample will be The force is composed of the sum of the collisions only between the gas molecules and the container
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The exponential model A = 999.8 0.002t describes the population, A, of a country' in millions, t years after 2003. Use
the model to determine when the population of the country will be 1051 million?
The population of the country will be 1051 million in 2014
How to model the population of the country?The exponential model that describes the population of a country' in millions, t years after 2003 is given as:
A = 999.8 e0.002t
Rewrite the function properly as:
A = 999.8 * e^(0.002t)
When the population of the country is 1051 million, it means that:
A = 1051
Substitute the known values in the above equation
So, we have:
1051 = 999.8 * e^(0.002t)
Divide both sides by 999.8
1.0512 = e^(0.002t)
Take the natural logarithm of both sides of the equation
ln(1.0512) = ln(e^(0.002t)
Rewrite the equation as:
ln(e^(0.002t) = log(1.0512)
This gives
0.002t = log(1.0512)
Evaluate the logarithmic expression
0.002t = 0.0216
Divide both sides of the equation by 0.002
t = 0.0216/0.002
Evaluate the quotient
t = 10.8
Approximate 10.8 as 11
t = 11
11 years from 2003 is 2014
Hence, the population of the country will be 1051 million in 2014
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