the rate of change in the temperature per hour is the quotient of the change of temperature divided by the change in hours. Since we have
1:00 AM =1 hr - 87 degrees
7:00 PM=19 hrs - 45 degrees,
then the rate is
[tex]\frac{45-87\text{ }}{19-1}=\frac{-42}{18}=-\frac{7}{3}=-2.33[/tex]Then, the temperature changed -2.33 degrees per hour.
units givenQuestion 2 (3 points)toUsing the Rectangular Prism in the picture, find the Lateral Area, the Area of a Single Base,and the TOTAL Surface Area:.12 cm825 cm10 cmUse the face with dimensions 10cm x 5cm as the base.Lateral Area =cm²Single Base Area =64188 in48cm²
Solution:
Given the rectangular prism;
Where;
[tex]\begin{gathered} length,l=10cm \\ \\ width,w=5cm \\ \\ height,h=2cm \end{gathered}[/tex]Thus, the lateral area, L is;
[tex]\begin{gathered} L=2(l+w)h \\ \\ L=2(10+5)2 \\ \\ L=4(15) \\ \\ L=60cm^2 \end{gathered}[/tex]ANSWER:
[tex]Lateral\text{ }Area=60cm^2[/tex]Also, the single base area, B, is;
[tex]\begin{gathered} B=l\times w \\ \\ B=10\times5 \\ \\ B=50cm^2 \end{gathered}[/tex]ANSWER:
[tex]Single\text{ }Base\text{ }Area=50cm^2[/tex]Then, the surface area, S, is;
[tex]\begin{gathered} S=L+2B \\ \\ S=60+2(50) \\ \\ S=60+100 \\ \\ S=160cm^2 \\ \\ \end{gathered}[/tex]ANSWER:
[tex]Surface\text{ }Area=160cm^2[/tex]find the measure of the angles in the following triangles.x=______missing angle measures:_______ ______
First, we have to use the interior angles theorem
[tex]x-2+72+x=180[/tex]Then, we solve for x
[tex]\begin{gathered} 2x+70=180 \\ 2x=180-70 \\ 2x=110 \\ x=\frac{110}{2} \\ x=55 \end{gathered}[/tex]Then, we use this value to find each angle
[tex]\begin{gathered} (x-2)=55-2=53 \\ x=53 \end{gathered}[/tex]Hence, the interior angles are 72°, 55°, and 53°A pyramid has a square base with sides of length s. The height of the pyramid is equal to of the length of a side on the base. Which formularepresents the volume of the pyramid?OA. V = ¹8³OB. V=¹8³OC. V=8³OD. V=35³OE V=65³
Given,
The measure of the length of the side of square is s.
The height of the pyramid is 1/2 of the length of the side.
Required
The volume of the square pyramid.
The formula for the volume of the square pyramid is,
[tex]Volume\text{ =}\frac{side\times side\times height}{3}[/tex]Substituting the values then,
[tex]\begin{gathered} Volume\text{ =}\frac{s\times s\times s}{3\times2} \\ =\frac{s^3}{6} \end{gathered}[/tex]Hence, the volume of the pyramid is s^3/6.
Which of the following is equivalent to a rhombus? *O A rectangle with congruent diagonalsA parallelogram where opposite angles are congruentA parallelogram with two consecutive congruent sidesA quadrilateral where consecutive angles are supplementary
A parallelogram with two consecutive congruent sides.
1) Since a rhombus is a quadrilateral with 4 congruent sides. Then we can examine the options and state that
2) Given that a rhombus has congruent opposite angles, with four congruent sides.
3) The answer is
A parallelogram with two consecutive congruent sides.
With two consecutive sides, the whole polygon will have congruent sides.
A sample has a mean of M = 90 and a standard devia-tion of s 20.=a. Find the z-score for each of the following X values.X = 95X = 80X = 98X = 88X = 105X = 76
Answer:
[tex]\begin{gathered} X=95,z=0.25 \\ X=80,z=-0.5 \\ X=98,z=0.4 \\ X=88,z=-0.1 \\ X=105,z=0.75 \\ X=76,z=-0.7 \end{gathered}[/tex]Explanation:
Given a sample with the following:
• Mean,M = 90
,• Standard deviation, s = 20
To find the z-score for each of the given X values, we use the formula below:
[tex]\begin{equation*} z-score=\frac{X-\mu}{\sigma}\text{ where }\begin{cases}{X=Raw\;Score} \\ {\mu=mean} \\ {\sigma=Standard\;Deviation}\end{cases} \end{equation*}[/tex]The z-scores are calculated below:
[tex]\begin{gathered} \text{When X=95, }z=\frac{95-90}{20}=\frac{5}{20}=0.25 \\ \text{When X=80, }z=\frac{80-90}{20}=\frac{-10}{20}=-0.5 \\ \text{When X=98, }z=\frac{98-90}{20}=\frac{8}{20}=0.4 \end{gathered}[/tex][tex]\begin{gathered} \text{When X=88,}z=\frac{88-90}{20}=\frac{-2}{20}=-0.1 \\ \text{When X=105, }z=\frac{105-90}{20}=\frac{15}{20}=0.75 \\ \text{When X=76, }z=\frac{76-90}{20}=\frac{-14}{20}=-0.7 \end{gathered}[/tex]The textbook isn't helping with the screenshot problem below.
From the frequency distribution, the measures are given as follows:
a) Total number of observations: 27.
b) The width of each class is of 5.
c) The midpoint of the second class if of 20.5.
d) The modal class is Class 12 - 17.
e) If another class was added, the limits would be 48 - 53.
What is represented by the frequency distribution?The frequency distribution gives the number of observations that is located in each class.
Hence the total number of observations is given by the sum of the frequencies, as follows:
Total = 9 + 1 + 3 + 8 + 6 = 27.
The modal class is class with the highest number of observations, hence it is of:
Class 12-17.
The width of a class is given by the subtraction of the limits, hence:
Width = 47 - 42 = ... = 23 - 18 = 17 - 12 = 5.
For an added class, the lower bound would be one more than the last class, while the upper bound would be five added to the lower bound, hence the limits are:
48 - 53.
The midpoint of each class is given by the mean of the coordinates, hence, for the second class, it is of:
Midpoint = (18 + 23)/2 = 41/2 = 20.5.
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2 multiplied by the square root of 8
Note that the square root of 8 is written as:
[tex]\sqrt[]{8}[/tex]2 multiplied by the square root of 8 will then be expressed as:
[tex]\begin{gathered} 2\sqrt[]{8} \\ 2\text{ }\times\sqrt[]{8} \\ 2\text{ }\times\text{ }\sqrt[]{4}\text{ }\times\text{ }\sqrt[]{2} \\ 2\text{ }\times\text{ 2 }\times\text{ }\sqrt[]{2} \\ 4\text{ }\times\text{ }\sqrt[]{2} \\ 4\sqrt[]{2} \end{gathered}[/tex]Find the largest angle of △TUV. Assume that s is a positive number.
Remember that
In any triangle: The shortest side is always opposite the smallest interior angle. The longest side is always opposite the largest interior angle
so
In this problem
the largest interior angle is opposite to the longest side (TU)
that means
the largest interior angle is14. Which points are on the graph by = 3x - 12? Select all that apply. (A) (B) (C) (D) (-2,0) (0,-2) (6,-3) (8,2) M 23 hp
6y=3x-127
Replace the values of x , y in the equation by the coordinates values given on each option, and check if the equality remains.
A. (x,y) = (-2,0)
6y=3x-127
6(0) =3(-2)-127
0 = -6-127
0= -133
zero is not equal to -133.
A. is not
B. (0,-2)
6(-2) = 3(0)-127
-12 = -127
B is not
C, (6,-3)
6(-3) = 3(6)-127
-18 = 18-127
-18 = -109
C is not
D (8,2)
6(2) = 3(8)-127
12 = 24-127
12=-103
D is not
None of the points are in the graph
Garrick gets paid $4.70 an hour with time-and-a-half for overtime(over 40 hours). How much did he earn one week when he worked 46hours?a. $195.05b. $220.90c. $230.30d. $188
Solution
For this case we can calculate the total with the following formula:
Fixed amount= 40*4$.70= $188
And now for the remain hours we can do this:
Extra = 6* 1.5*$4.70= $42.3
Then the total amount is:
Fixed amount+ Extra = 188$ + 42.3$ = $230.3
Then the answer is:
c. $230.30
Hi how are you today can you please help me with this question
$ 119.607
Explanation
we can easily solve this by using a rule of three
Step 1
Let
actual price(2020)=price of 2019 + 2%
so
actual price(2020)= 102 % and
price ( 2019)=100 %
let x represents the cost for 2019, so
[tex]\begin{gathered} \text{if} \\ 122\Rightarrow\text{ 102\%} \\ x\text{ }\Rightarrow\text{ 100 \%} \end{gathered}[/tex]the proportion would be
[tex]\begin{gathered} \frac{122}{102\text{ \%}}=\frac{x}{100\text{ \% }} \\ \text{ Multiply both sides by 100 \%} \\ \frac{122}{102\text{ \%}}\cdot100=\frac{x}{100\text{ \% }}\cdot100 \\ 119.607=x \end{gathered}[/tex]therefore, the cost in January of 2019 is
$ 119.607
I hope this helps you
You roll two 4-sided number cubes. Let X be the sum of the numbers on the two cubes P(X=3)
Notice that, since we are rolling two dices, we are dealing with 2 independent events
Let's suppose that the numbers on each dice are 1,2,3,4.
Then, if we roll two dices, there are 16 possible pairs (in principle)
(1,1)
(1,2)
...
(1,4)
(2,1)
...
(4,4)
Each of those pairs is equally probably than the others
Know, we need to identify the pairs that add up 3:
(1,2) and (2,1) are the only possibilities
Finally, we obtain the probability:
[tex]P(x=3)=\frac{2}{16}=\frac{1}{8}=0.125[/tex]Which is none of the options.
Another possibility is that the dices are cubes:
So, the possible combinations that can be obtained by throwing 2 cubes are:
(1,1)...(1,6),(2,1),...(6,6) Which are 36 possible combinations
And there are only 2 combinations that add up to 3: (2,1),(1,2)
So, the probability of adding up 3 is:
[tex]P(x=3)=\frac{2}{36}=\frac{1}{16}=0.0625[/tex]55°Angle FGH is a right angle.The measure of angle FGJ is 559.The measure of angle JGH is xº.What is the value of x?toХS
Given angle FGH is a right angle. This means angle FGH is 90 degrees
But
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials andthe probability of obtaining a success. Round your answer to four decimal places.P(X ≤ 4), n = 8, p = 0.4
Given:
n = 8, p = 0.4
To find:
P(X ≤ 4)
To determine the given probability, we will apply the binomial probability formula:
[tex]\begin{gathered} $$P(x=X)=^nC_x\times p^x\times q^{n-x}$$ \\ n\text{ = number of trials} \\ p\text{ = number of success} \\ q\text{ = number of failure} \end{gathered}[/tex][tex]P\left(X≤4\right)\text{ = P\lparen x = 0\rparen + P\lparen x = 1\rparen + P\lparen x =2 \rparen + P\lparen x = 3\rparen + P\lparen x = 4\rparen}[/tex][tex]\begin{gathered} p\text{ + q = 1} \\ q\text{ = 1- p} \\ q\text{ = 1 - 0.4} \\ q\text{ = 0.6} \\ \\ P(x=0)=\text{ }^8C_0\times(0.4)^0\times(0.6)^{8-0} \\ P(x\text{ = 0\rparen = 0.01679616} \\ \\ P(x=1)=\text{ }^8C_1\times(0.4)^1\times(0.6)^{8-1} \\ P(x\text{ = 1\rparen = 0.08957952} \end{gathered}[/tex][tex]\begin{gathered} P(x=2)=\text{ }^8C_2\times(0.4)^2\times(0.6)^{8-2} \\ P(x\text{ = 2\rparen = 0.20901888} \\ \\ P(x=3)=\text{ }^8C_3\times(0.4)^3\times(0.6)^{8-3} \\ P(x\text{ = 3\rparen = 0.27869184} \\ \\ P(x=4)=\text{ }^8C_4\times(0.4)^4\times(0.6)^{8-4} \\ P(x\text{ = 4\rparen = 0.2322432} \end{gathered}[/tex][tex]\begin{gathered} P(X≤4)\text{ = 0.01679616 + 0.08957952 + 0.20901888 + 0.27869184 + 0.2322432} \\ \\ P\left(X≤4\right)\text{ = 0.8263296} \\ \\ To\text{ 4 decimal place, P\lparen X \le4\rparen is 0.8263} \end{gathered}[/tex]The lowest airport in the world is Atyrau Airport in Kazakhstan at 72 feet below sea level. How would we represent this elevation using negative numbers? 6.NS.5
ANSWER
-72 ft
EXPLANATION
We can draw a number line:
If the 0 of the number line is sea level, we would normally say that all positive numbers are those that are above sea level and negative numbers those that are below sea level.
Therefore, to represent an elevation that is below sea level, we'd write it as a negative number: -72 ft
21. The table below shows the frequency of chirps for the striped ground cricket compared to the ambient temperature, in degrees Fahrenheit.Chirps per SecondTemperature208916722093188417811675157017821569Draw a scatterplot for this data, using x to represent the chirping frequency and y to represent temperature.131415161718192021226768697071727374757677787980818283848586878889909192939495
Using a graphing calculator :
The scatter plot will look thus:
Is 128 degrees plus 62 degrees supplementary or complimentary?
Let's begin by identifying key information given to us:
One angle = 128 degrees, Second angle = 62 degrees
Complementary angle are angles that sum up to 90 degrees
Supplementary angles are angles that sum up to 180 degrees
We will proceed to sum these two angles together. We have:
[tex]\begin{gathered} 128^{\circ}+62^{\circ}=180^{\circ} \\ \therefore These\text{ angles are supplementary angles since they sum up to 180 degr}ees \end{gathered}[/tex]Therefore, these angles are supplementary angles since they sum up to 180 degrees
What are the coordinates of vertex C'after rotating the figure 180° about theorigin?у6BID42A АEXo024 6A. (-6,4)B. (4.-6)C. (4,6)D. (-4,-6)
Vertex C (4, 6 ) Rotation 180º about the origin CCW c' (-4, -6)
C (x, y ) C ' (-x, -y )
________________
Answer
Option D
Complete the general solution to [tex]y = arcsin - \frac{ \sqrt{3} }{2} [/tex]y=___+-2πkSelect all that apply.π/3(2π)/3(4π)/3(5π)/3
To find the general solution to y we need take the sine function in both sides of the equation given:
[tex]\begin{gathered} \sin y=\sin (\sin ^{-1}-\frac{\sqrt[]{3}}{2}) \\ \sin y=-\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]Now, we have to find the value of y for which the sine function is equal to the right side. From the properties of the sine function and its definition we conclude that y has to be:
[tex]y=\frac{5\pi}{3}[/tex]Therefore the general solution is:
[tex]y=\frac{5\pi}{3}\pm2\pi k[/tex]Solve for w.182- w = 252
Given the equation :
[tex]182-w=252[/tex]solve for w, so:
subtract 182 from both sides:
[tex]\begin{gathered} 182-w-182=252-182 \\ \\ -w=70 \\ \end{gathered}[/tex]multiply both sides by -1
[tex]w=-70[/tex]So, the value of w = -70
I need help with this question please1) Picture2) In(2x) + ln(7) = 4
1) We must solve for x the following equation:
[tex]e^{5x}=25.[/tex]To solve this equation, we take the natural logarithm to both sides of the equation:
[tex]\begin{gathered} \ln (e^{5x})=\ln (25), \\ 5x\cdot\ln e=\ln 25. \end{gathered}[/tex]Now, we use the following results:
[tex]\begin{gathered} \ln e=1, \\ \ln (25)=\ln (5^2)=2\cdot\ln 5. \end{gathered}[/tex]Replacing these results in the equation above, we have:
[tex]5x=2\cdot\ln 5.[/tex]Solving for x, we get:
[tex]x=\frac{2}{5}\cdot\ln 5\cong0.64.[/tex]2) We must solve for x the following equation:
[tex]\ln (2x)+\ln (7)=4.[/tex]To solve this problem, we isolate the part that involves the x:
[tex]\ln (2x)=4-\ln (7)\text{.}[/tex]Now, using the following property:
[tex]\ln y=z\rightarrow y=e^z\text{.}[/tex]with:
[tex]\begin{gathered} y=2x, \\ z=4-\ln 7. \end{gathered}[/tex]we have:
[tex]\ln (2x)=4-\ln 7\rightarrow2x=e^{4-\ln 7}.[/tex]Solving the last equation for x, we get:
[tex]x=\frac{1}{2}\cdot e^{4-\ln 7}\cong3.90.[/tex]Answers
1) The value of x that solves the first equation is 0.64 to two decimal places.
2) The value of x that solves the second equation is 3.90 to two decimal places.
Review of the base of a logarithm
We can define the logarithm in base a through the following equations:
[tex]\begin{gathered} \log _aa=1, \\ \log _aa^x=x\cdot\log _aa=x\cdot1=x\text{.} \end{gathered}[/tex]When we use as a base the Euler number e ≅ 2.718, the logarithm is called "natural" and we use the following notation for it:
[tex]_{}\log _e=\ln .[/tex]With this notation, we have the following properties:
[tex]\begin{gathered} \ln e=1, \\ \ln e^x=x\cdot\ln e=x\cdot1=x\text{.} \end{gathered}[/tex]What should be true about the line of best fit? Check all that apply.
A. The line of best fit must have an equal number of points above and below the line.
B. The line must show the relationship between the two variables.
C. The line of best fit should minimize the distance between itself and the data points.
D. The line of best fit has to cross through at least 2 points in the scatter plot.
E. The line of best fit could be used as a prediction tool showing a trend in the data.
F. The line of best fit should be an exact representation of the data points.
The line of best fit could be used as a prediction tool showing a trend in the data and the line of best fit should minimize the distance between itself and the data points thus options (C) and (E) will be correct.
What is a graph?The graph is a geometrical representation of a function and can be plotted by taking x's and y's corresponding values within the interval.
For example plot of y = x³ ,y = sinx.
A scatter point represents the relation or function.
If a line is used to predict the function then the distance between the points to the line must be minimized.
The line is useful for the representation of the data point.
Hence "The line of best fit could be used as a prediction tool showing a trend in the data and the line of best fit should minimize the distance between itself and the data points".
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A county is planning to expand its train service. To better understand the current service, the county planner looked at which train stations are along or not along various train lines
Solution
(a)
5 stations are along the orange line
(b)
8 stations
The number of fish in a fish tank doubles each week. The function y=equals 3 (2)^x represents the population, where X is the number of one week periodsa. Describe the domains and range of the function. Then graph the functionb. Find and interpret the y intercept c. How many fish are in the tank at the end of first week?d. How many fish are in the tank after 4 weeks?
a. The domain of the function is the set of values of the independent variable (x) on which the function acts, in this case, the independent variable is time, since the time can only take positive values, the domain would be [0,∞) or x≥0.
The range is all the possible values that the dependent variable can take, in this case, the dependent variable is the population of fish, then it can't be a negative number, since you can't have for example -1 fish, then, again, the interval would be [0,∞) or y≥0
A graph of the function looks like this:
b. We can find the y-intercept by making x equals 0 in the formula of the function, like this:
y= 3*(2)^x
y= 3*(2)^0
y= 3*1, since any number raised to zero equals 1
y=3
Since x equals zero represents the initial time, the y-intercept represents the initial population of fish, then at the beginning, there were 3 fish.
c. We just have to replace 1 for x, and then calculate y, like this:
y= 3*(2)^x
y= 3*(2)^1
y= 3*(2)
y=6
At the end of the first week, there will be 6 fish.
d. Now, we just have to replace 4 for x, like this:
y= 3*(2)^4
y= 3*16
y=48
Then, after 4 weeks, there will be 48 fish
solve2cos²x+3sin x=0
One of the most important trigonometric identities is the one below
[tex]\cos ^2x+\sin ^2x=1[/tex]Then,
[tex]\Rightarrow\cos ^2x=1-\sin ^2x[/tex]Use this result in the equation given by the problem
[tex]\begin{gathered} 2\cos ^2x+3\sin x=0 \\ \Rightarrow2(1-\sin ^2x)+3\sin x=0 \\ \Rightarrow2-2\sin ^2x+3\sin x=0 \end{gathered}[/tex]Furthermore,
[tex]\begin{gathered} \Rightarrow2\sin ^2x-3\sin x-2=0 \\ \Rightarrow2\sin ^2x-3\sin x=2 \\ \Rightarrow\sin x(2\sin x-3)=2 \end{gathered}[/tex]Set y=sinx
[tex]\begin{gathered} \Rightarrow y(2y-3)=2 \\ \Rightarrow y=-\frac{1}{2},y=2 \end{gathered}[/tex]Thus,
[tex]\begin{gathered} \sin x=-\frac{1}{2},\sin x=2 \\ \Rightarrow\sin x=-\frac{1}{2} \\ \text{if sinx=2, then x is not a real number} \end{gathered}[/tex]Finally,
[tex]\begin{gathered} \sin x=-\frac{1}{2} \\ \Rightarrow x=\sin ^{-1}(-\frac{1}{2})=-\frac{\pi}{6} \end{gathered}[/tex]Then, the answer is
[tex]x=-\frac{\pi}{6}+2n\pi,\text{ n is an integer}[/tex]The answer is x=-pi/6+2n*pi
What is the surface area of the following solid? *13 ft 12ft 5ft 5ft
In order to calculate the total surface area we just need to sum the area of the different faces.
From the picture we see that we have the following faces.
- 2 x A (two triangles)
- S (a rectangle)
- T (a rectangle)
- B (the base rectangle)
Now me calculate the area of each one:
[tex]A\text{ = }\frac{1}{2}\cdot12\cdot5\text{ = }30[/tex][tex]S\text{ = 5}\cdot5=\text{ 25}[/tex][tex]B=12\cdot5=60[/tex][tex]T=13\cdot5=65[/tex]Now that we have the area of each face, we sum all the areas, taking in account the ones that appears twice:
[tex]\text{Total area = 2}\cdot A+S+T+B=2\cdot30+25+60+65=210[/tex]And, because the lenghts are measured in ft, the final answer is:
[tex]\text{Total area = 210 ft}^2[/tex]Note:
[tex]\text{Area of a triangle = }\frac{1}{2}\cdot\text{base}\cdot\text{height}[/tex][tex]\text{Area of a rectangle = base }\cdot\text{ height}[/tex]factorize 5m^3-10m^2+8m+2
The expression 5m³ - 10m² + 8m + 2 cannot be factorized
How to factorize the polynomial?From the question, the polynomial is given as
5m^3-10m^2+8m+2
Rewrite the polynomial properly
So, we have
5m³ - 10m² + 8m + 2
Next, we represent the above expression on a graph
From the attached graph, we can see that the polynomial expression only cross the x-axis at x = -0.197
This implies that the expression cannot be factored
So, we cannot further rewrite the given expression
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pls today I have it for tomorrow
Answer:
6/5 x 5/3 is 2
if that's what you need help with
step-by-step explanation
Hi thank you so for all your time and help in advance
Question:
Solution:
Remember the following definition :
[tex]\cos (x)=\frac{adjacent\text{ side to the angle x }}{hypotenuse}[/tex]thus, if:
[tex]\cos (x)=\frac{adjacent\text{ side to the angle x }}{hypotenuse}=\frac{\sqrt[]{3}}{2}[/tex]then, according to the given triangles in the problem, the only angle that fulfills this, is:
[tex]x=30[/tex]so that, the correct answer is:
[tex]x=30[/tex]
Suppose a city's population grows by 5% each year. How long will it take for the population of the city to triple? Answer to the nearest hundredth of a year.
Since it is given that the population grows by 5% each year, it follows that the Exponential Growth Function is the appropriate function that can be used to model the problem.
The Exponential Growth Function is given by:
[tex]y=a(1+r)^t[/tex]Where
• a is the initial amount.
,• r is the percent of increase in decimal.
,• t is the time.
,• y is the amount after time t.
Since we want when the initial population will triple, substitute y=3a into the equation:
[tex]3a=a(1+r)^t[/tex]Substitute r=5%=0.05 into the equation:
[tex]3a=a(1+0.05)^t[/tex]Solve the resulting equation for t:
[tex]\begin{gathered} 3a=a(1+0.05)^t \\ \Rightarrow a(1+0.05)^t=3a \\ \Rightarrow a(1.05)^t=3a \\ Divide\text{ both sides by a:} \\ \Rightarrow(1.05)^t=3 \\ \text{Take logarithm of both sides:} \\ \Rightarrow\ln (1.05)^t=\ln 3 \\ \Rightarrow t\ln (1.05)=\ln 3 \\ \Rightarrow t=\frac{\ln 3}{\ln (1.05)}\approx22.52\text{ years} \end{gathered}[/tex]The population will triple after about 22.52 years.