Answers
Hello there. To solve this question, we need to pay attention to the data given by the question and set up an equation for the amount of rabbits in that colony.
In the year 2000 there were 1200 rabits in a colony, and it was observed that their population was increasing at a rate of 21% each year
For this type of question, we call f(x) the function that shows the population in a certain time x.
This function varies directly to the initial population and grows exponentially according to the rate .
Thus, we have that f(x) = P0 * (1+r)^x
In this case, P0 = 1200 and r = 0.21 (21% converted into decimals)
f(x) = 1200 * (1 + 0.21)^x
f(x) = 1200 * 1.21^x
This is the function that models the population of this colony for a year x.
To find how many rabbits you'll have in the year 2007, plug in x = 7
f(7) = 1200 * 1.21^7
Calculate the value
f(7) = 1200 * 3.797 = 4556
In which year will the population be equal to 5000
Making f(x) = 5000, we solve for x
5000 = 1200 * 1.21^x
Divide both sides of the equation by 1200
25/6 = 1.21^x
Take the natural log on both sides of the equation
ln(25/6) = ln(1.21^x)
Apply the logarithm power rule: log(a^b) = b * log(a)
ln(25/6) = x * ln(1.21)
Rewriting 1.21 as 121/100 = (11/10)², we get:
ln(25/6) = 2x * ln(11/10)
Divide both sides of the equation by a factor of 2ln(11/10)
x = ln(25/6)/(2ln(11/10)) approx. 7.4867 years
Rounding up to the next year, x = 8 years.
Related Questions
I need help on prime factorization just describe how to do it for me
Answers
Prime factorization is a way of expressing a number as a product of its prime factors. A prime number is a number that has exactly two factors, 1 and the number itself.
For example, if we take the number 30. We know that 30 = 5 × 6, but 6 is not a prime number. The number 6 can further be factorized as 2 × 3, where 2 and 3 are prime numbers. Therefore, the prime factorization of 30 = 2 × 3 × 5, where all the factors are prime numbers.
Let us take another example and solve for its prime factorization
Prime factorization of 72
Hence, the prime factorization of 72 = 2³×3².
Finally,
Given the function f(x), whose graph is shown, place the black dot at the point the corresponds to f^-1(-1)
Answers
Given: Graph of a function f(x) is provided.
Required: To find the inverse of the function
[tex]f^{-1}(-1)[/tex]Explanation: The inverse of a function is determined by interchanging the domain and the range. The domain is the input values, and the range is the output values where the function is defined.
Hence, to find the inverse of the function at x=-1, we need to look at the graph and find out at which value of x, the value of f(x), is -1. Since if
[tex]\begin{gathered} f(a)=-1 \\ then,f^{-1}(-1)=a \end{gathered}[/tex]Hence we need to look at which point on the x-axis of the given function we have f(x)=-1. This is the point (-3,-1) as
[tex]\begin{gathered} f(-3)=-1 \\ \Rightarrow f^{-1}(-1)=-3 \end{gathered}[/tex]Hence the point corresponding to the inverse is (-1,-3). The point is shown below in the graph-
Final Answer: The point corresponding to the inverse of f at x=-1 is (-1,-3).
Simplify the expression showed question … which is the correct answer
Answers
Okay, here we have this:
We need to simplify the following expression:
[tex]\begin{gathered} (5^{-4}(25)^4)^2 \\ =(5^{-4}(5^2)^4)^2 \\ =(5^{-4}\cdot5^8)^2 \\ =(5^{-4+8})^2 \\ =(5^4)^2 \\ =5^8 \end{gathered}[/tex]Finally we obtain that the correct answer is the option B.
Please help will mark Brainly
Answers
Using the properties of a linear function we get the value of y as 2 when x is 0.
A linear function is of the form: y = mx + c , where m is the slope
Now the function satisfies (-4,3) and (4,5)
So we substitute these values in the function.
At (-4,3) we get 3 = -4m + c
At (4,5) we get 5 = 4m + c
Adding the two equation we get:
2c = 8
or, c = 4
Now at c = 4 , and at (4,5) we get
5 = 4m + 2
or, m = 3/4
So the linear function is of the form :
y = 3/4 x + 2
or, 4y = 3x + 8
Now at x = 0 ,
4y = 8
or, y = 2
A function which graph (in Cartesian coordinates) is a non-vertical straight in the plane is known as a linear function as from real numbers to the real numbers in calculus and related mathematical fields. When the input variable is modified, the output often changes in a manner that is proportionate to the input variable's change.
To learn more about linear function visit:
https://brainly.com/question/21107621
#SPJ9
A person places $531 in an investment account earning an annual rate of 6.1%,compounded continuously. Using the formula V = Pe", where V is the value of theaccount in t years, P is the principal initially invested, e is the base of a naturallogarithm, and ris the rate of interest, determine the amount of money, to thenearest cent, in the account after 16years.
Answers
This is the solution, Qxk:
Step 1: Let's review the information provided to us to answer the problem correctly:
Principal = $ 531
Interest rate = 6.1% (0.061) compounded continously
Term = 16 years
Step 2: Let's find the future value of this investment, as follows:
V = Pe^t*r
V
Find the sum of all multiples of 7 between 1 to 200, inclusive.
Answers
Answer:
2842
Explanation:
The first multiple of 7 =7
The last multiple of 7 before 200 = 196
This problem forms an arithmetic sequence where:
• The first term, a= 7
,• The last term, l = 196
To determine the sum, we find first the number of multiples of 7 between 7 and 196.
[tex]\begin{gathered} \text{Number of multiples=}\frac{196}{7} \\ =28 \end{gathered}[/tex]For a sequence with first and last terms, its sum is:
[tex]\begin{gathered} S_n=\frac{n}{2}(a+l) \\ =\frac{28}{2}(7+196) \\ =14\times203 \\ =2842 \end{gathered}[/tex]The sum of all multiples of 7 between 1 to 200 is 2842.
•
Every ten minutes, Frankie follows a pattern in creating a new group of drawings. Below, you can see how many total drawings Frankie has created by the end of each ten-minute interval.
If he continues to follow this pattern, at the end of seventy minutes, how many total drawings will Frankie have created?
will give 199 points
Answers
Answer: 54 patterns
Step-by-step explanation:
12+17=19+14=33+21=54
please help ASAP!!!!!
Answers
The first question
[tex]\frac{5x^2-28x-12}{x-6}[/tex]can be rewritten by polynomial division since the quadratic polynomial is not easy to factorize by inspection
The 2nd question
[tex]\frac{x^2+11x+28}{x+4}=\frac{(x+7)(x+4)}{x+4}=x+7[/tex]so, it can be solved by inspection.
The 3rd question
[tex]\frac{6x^2+2x+7}{3x-2}[/tex]can be rewritten by polynomial division since the quadratic polynomial is not easy to factorize by inspection
Finally, 4th question
[tex]\frac{x^2-x-35}{x-6}[/tex]can be rewritten by polynomial division.
can you show me like on a same graph like mine
Answers
Given the general quadratic equation:
[tex]ax^2+bx+c=0[/tex]The general solution of the quadratic equation is given by the expression:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]From the problem, we have the quadratic equation:
[tex]3x{}^2+2x-225=0[/tex]Identifying the coefficients:
[tex]\begin{gathered} a=3 \\ b=2 \\ c=-225 \end{gathered}[/tex]Then, using the general solution formula:
[tex]\begin{gathered} x=\frac{-2\pm\sqrt{4+2700}}{6}=\frac{-2\pm52}{6} \\ \\ \Rightarrow x_1=\frac{25}{3} \\ \\ \Rightarrow x_2=-9 \end{gathered}[/tex]And the solutions on the number line are:
Complete the grouped relative frequency distribution for the data. (Note that we are using a class width of 4.)Write each relative frequency as a decimal rounded to the nearest hundredth, not as a percentage.Relativefrequency Temperature 109 112 110 94 102 106 104 94 108 105 103 107 105 101 93103 99Relative Frequency 93 to 9697 to100101 to 104105 to 108109 to 112
Answers
Above you have the given 17 data ordered from least to greatest.
To find the relative frequency:
1. Frequency: Identify the number of data that goes in each temperature range:
93 to 96: 3 data (93,94,94)
97 to 100: 1 data (99)
101 to 104: 5 data (101, 102, 103, 103, 104)
105 to 108: 5 data (105, 105, 106, 107, 108)
109 to 112: 3 data (109, 110, 112)
2. Relative frequency: Find the ratio of the number of data you get in step 1 (Frecuency) to the total number of data (17):
93 to 96:
[tex]\frac{3}{17}\approx0.18[/tex]97 to 100:
[tex]\frac{1}{17}\approx0.06[/tex]101 to 104:
[tex]\frac{5}{17}\approx0.29[/tex]105 to 108
[tex]\frac{5}{17}\approx0.29[/tex]109 to 112
[tex]\frac{3}{17}\approx0.18[/tex]Then, the relative frequencies are:
93 to 96: 0.18
97 to 100: 0.06
101 to 104: 0.29
105 to 108: 0.29
109 to 112: 0.18
Answer: the other person is correct
Step-by-step explanation:
You want to walk from home to a grocery store that is 1/2 miles away. You stop for a rest after 1/4 miles. How much farther do you have to walk? Write your answer as a fraction in simplest form.
Answers
Answer: 1/4
Step-by-step explanation:
1/2-1/4=1/4 because 1/4x2=2/4 and 2/4=1/2
Answer: 1/4 mile
Step-by-step explanation: so 1/2 = 2/4. You stop after 1/4, so subtract. You get 1/4, meaning you have to walk 1/4 mile. Also, r u sure you're in college, cuz this problem is pretty easy.
I believed I solved correctly but want a double check pls
Answers
We have the original price P and it will increase a rate r%, we can express is as
[tex]P+P\cdot r[/tex]As we can see, P is the original price and P*r is what's going to be added to the original price, we can even simplify it to
[tex]P(1+r)[/tex]That's a generic expression to find it, so here we have P = 153 and r = 19% = 0.19, then
[tex]\begin{gathered} P(1+r)=153(1+0.19) \\ \\ 153(1+0.19)=153\cdot1.19 \\ \\ 153\cdot1.19=182.07 \end{gathered}[/tex]The price will be $182.07
Lottery: I buy one of 5000 raffle tickets for $1. The sponsors then randomly select one grand prize worth $500, two second prizes worth $200 each, and three third prizes at $100 each. Create the probability distribution for this raffle and calculate my expected value. Enter each row of your table as a separate line, but don't worry too much about formatting. Tables should look similar to those given in questions 1 and 3. Don't forget to give your expected value.
Answers
To give the probability distribution, we need to calculate the probability of each possible outcome and the value of this outcome.
We have 5000 raffle, 1 will win the first prize, 2 will win the second prize, 3 will win the third prize and the rest 4994 will win no prize.
The first prize is $500, but the raffle cost $1, so the outcome is actually $499.
The second prizes are $200 each, minus the cost we have an outcome of $199.
The third prizes are $100 each, minus the cost we have an outcome of $99.
The others will not receive prizes, but they will still have the cost of $1, so the outcome is -$1.
The first prize is 1 in 5000, so the probability is 1/5000
The second prizes are 2 in 500, so the probability is 2/5000
The third prizes are 3 in 5000, so the probability is 3/5000
The lost is the rest of the 4994 in 500, so the probability is 4994/5000
So, the table for the probability distributions is:
Value gained | P(x)
$499 | 1/5000
$199 | 2/5000
$99 | 3/5000
-$1 | 4994/5000
To calculate the expected value, we multiply the value by its probability and add them:
[tex]\begin{gathered} E(x)=499\cdot\frac{1}{5000}+199\cdot\frac{2}{5000}+99\cdot\frac{3}{5000}-1\cdot\frac{4994}{5000}_{} \\ E(x)=\frac{499}{5000}+\frac{398}{5000}+\frac{297}{5000}-\frac{4994}{5000} \\ E(x)=\frac{499+398+297-4994}{5000} \\ E(x)=-\frac{3800}{5000} \\ E(x)=-0.76 \end{gathered}[/tex]So, the expected value if -$0.76.
I need a very fast answer to this question please I’m in a hurry
Answers
To find f(3 + h) we need to substitute x = 3 + h, into the function, as follows:
[tex]\begin{gathered} f(x)=\frac{1}{(3+h)+2} \\ \text{ Combining similar terms:} \\ f(x)=\frac{1}{h+(3+2)} \\ f(x)=\frac{1}{h+5} \end{gathered}[/tex]
Find two values of angle A between 2pi where sin A = [tex] \frac{ - \sqrt{2 } }{2} [/tex]
Answers
Answer:
Explanation:
First of all, we know that
[tex]\sin \frac{\pi}{4}=\frac{\sqrt[]{2}}{2}[/tex]And knowing the unit circle, we know that the sine takes negative values in 3rd and 4th quadrants. Therefore, from the above value of the angle, If we go π radians counterclockwise, we encounter negative values of sine; hence,
[tex]\sin \lbrack\frac{\pi}{4}+\pi\rbrack=-\frac{\sqrt[]{2}}{2}[/tex][tex]\rightarrow\sin \frac{5\pi}{4}=\frac{-\sqrt[]{2}}{2}[/tex]The second value of the angle that yields the above value for sine is found by adding π/2 radians to the angle above (we are now in the 4th quadrant)
[tex]\sin \frac{5\pi}{4}+\frac{\pi}{2}=-\frac{\sqrt[]{2}}{2}[/tex][tex]\rightarrow\sin \frac{7\pi}{4}=-\frac{\sqrt[]{2}}{2}[/tex]Hence, the two values of angles between 0 and 2π are 5π/4 and 7π/4.
How much sales tax will Justin pay on a computer priced at $1,723.42 if the sales tax rateis 9.25 percent?
Answers
Given : the price of the computer = $1,723.42
The sales tax = 9.25% = 9.25/100 = 0.0925
The sales tax = 9.25% of $1,723.42 = 0.0925 * $1,723.42 = $159.42 (to the nearest cent)
So,
The sales tax = $159.42
Use the change of base formula to evaluate the expression then convert it to a logarithm in base eight round to the nearest thousandth
Answers
Recall that the change of base formula for logarithms is:
[tex]\log_a(b)=\frac{\log_x(b)}{\log_x(a)}.[/tex]Using the change of base formula for logarithms to the given logarithm we get:
[tex]\log_354=\frac{\log_8(54)}{\log_8(3)}.[/tex]Therefore:
[tex]\log_3(54)=3.631.[/tex]And:
[tex]undefined[/tex]Paul is planning to sell bottled water at the local carnival. Paul's profit (in dollars) from selling b bottles of water is given by the formula P=1.05b-151.
Answers
Explanation :
• The standard linear function takes the form of y = mx +c
• Since the Pauls profit is given by the formula ,P = 1.05b -151,, The curve of this profit is in line with the slope ,m = 1.05, as comparing with the standard linear fuction.
,• Therefore, Paul profit is increasing at a rate of 1.05 dollar per bottle.,
Could you please help me out with figuring out how to do this 216 into a scientific notation
Answers
In order to express a small number (less than zero) in scientific notation we just have to move the decimal point until we reach the last digit, the exponent we use must be a negative number and it represents the number of times we moved the dot.
In this case, we initially had the number 0.216, as you can see, we have three digits on the right of the point, then we must move the dot 3 times, then the representation in the scientific notation of this number is:
0.216 = 216×10⁻³
i really need help can you help me?
Answers
1. Madison's work is correct. Her there is no mistake
2. Kaleb's work is not correct. His mistake was when he divided by 4
10. In July, Ariel recorded the height of a pine tree and how quickly it was expected to grow in thenext several monthsQ. Write an equation for the table.Height ofTree (inches)b. What does theторе represent608c. What does the y-intercept represent?
Answers
Using the table to find the equation:
Let x is the number of months, and y is the height of the tree
The general form of the line y = mx + c
where m is the slope and c is the y-intercept
So, at the beginning at x = 0 , y = 600
So,
600 = m * 0 + c
c = 600
When x = 3 , y = 602
so,
602 = 3m + 600
solve to find m
602 - 600 = 3m
3m = 2
m = 2/3
So,
[tex]y=\frac{2}{3}x+600[/tex]b. What does the slope represent?
The slope represents the rate of growth each month
which mean the tree grow (2/3) inches per month
c. What does the y-intercept represent?
y-intercept represents the first height of the tree
What is the equation of the boundary of this inequality?
Answers
We have the following:
[tex]y<-3x-5[/tex]The slope of the line -3 and the y-intercept is -5
So the equation of the boundary line is:
[tex]\begin{gathered} y=-3x-5 \\ \end{gathered}[/tex]3. Mindi forgot to pay her water bill of $79.45, and it is now 28days late. Below is the water department's late fee charges.1-10 Days Late$1.50 per day11-20 Days Late10-Day Late Fee+$2.00 per additional day21-30 Days Late10-Day Late Fee+20-Day Late Fee+$2.50 per additional dayHow much will Mindi owe if she pays her water bill today?
Answers
The amount she was supopose to pay = $79.45
It's now 28 days late . The charges will be $2.50 per additional day. Therefore,
[tex]total\text{ additional fe}e=2.50\times28=\text{ \$70}[/tex]The amount she will pay if she pays today will be
[tex]70+79.45=\text{ \$}149.45[/tex]YOU BE THE TEACHER Your friend solves the equation 9x2 = 36. Is your friend correct? 9x2 = 36 x = 4 x= 14 x= +2 O yes O no Explain your reasoning.
Answers
ANSWER
Yes
EXPLANATION
Your friend is correct.
First he divided both sides by 9: 36 divided by 9 is 4
Then he did the square root, which has two results: one positive and one negative. This gives +2 and -2.
Another way to check the result is to replace it into the equation. If the equation is true, then the result is correct:
[tex]\begin{gathered} 9(2)^2=36 \\ 9\cdot4=36 \\ 36=36\text{ }\rightarrow\text{ true} \\ \\ 9(-2)^2=36 \\ 9\cdot4=36 \\ 36=36\text{ }\rightarrow\text{ true} \end{gathered}[/tex]Find the midpoint of the segment with the following endpoints.(4,5) and (9, 2)
Answers
Answer: (6.5, 3.5)
Explanation:
The midpoint between two points can be found by taking the mean of the x coordinates, and the mean of the y coordinates.
The points we have are:
(4, 5) where we will call
[tex]x_1=4,y_1=5[/tex]and also the point
(9, 2) where we will call
[tex]x_2=9,y_2=2[/tex]Now, the midpoint will be at
[tex](x_m,y_m)[/tex]Where xm is the mean of the x coordinates, and ym is the mean of the y coordinates:
[tex]x_m=\frac{x_1+x_2}{2}[/tex]subtituting the values:
[tex]x_m=\frac{4+9}{2}=\frac{13}{2}=6.5[/tex]we have xm, now we need ym:
[tex]y_m=\frac{y_1+y_2}{2}[/tex]Substituting the values
[tex]y_m=\frac{5+2}{2}=\frac{7}{2}=3.5[/tex]Thus, the midpoint is at:
[tex](x_m,y_m)=(6.5,3.5)[/tex]A parabola can be drawn given a focus of (-5, 9) and a directrix of y = 5. Write the equation of the parabola in any form. 12 10 8 6 4 cu 2 -12 -10 -8 -6 -4 -2 2 4 6 8 10 12 -2 directrix 1 -6 -8 F(-5,9) -10 -12
Answers
The distance from the directrix to the focus is 4, so p=2. So the vertex of the parabola is (-5,7). Having this we get that
[tex]\begin{gathered} 4p(y-k)=(x-h)^2 \\ 8(y-7)=(x+5)^2 \end{gathered}[/tex]
7) A spherical balloon is inflated so that its radius increases at a rate of 2 cm/sec. How fastis the volume of the balloon increasing when the radius is 3 cm?4(Use V =for the volume of a sphere)3A) 7270 cm/sec B) 791 cm/sec C) 70 cm/sec D) 8210 cm/sec
Answers
The formula for the volume of a sphere is given by:
[tex]V=\frac{4}{3}\pi r^3[/tex]Since we are asked the rate of change of the volume with repect to time, we take the derivative on both sides, taking into account the chain rule:
[tex]\frac{dV}{dt}=\frac{d(\frac{4}{3}\pi r^3)}{dt}[/tex]taking out the constants:
[tex]\frac{dV}{dt}=\frac{4}{3}\pi\frac{d(r^3)}{dx}[/tex]Now we derivate, using the chain rule, that is:
[tex]\frac{df(g(x))}{dx}=f^{\prime}(x)g^{\prime}(x)[/tex]Applying the rule:
[tex]\frac{dV}{dt}=\frac{4}{3}\pi(3r^2)\frac{dr}{dt}[/tex]Simplifying:
[tex]\frac{dV}{dt}=4\pi(r^2)\frac{dr}{dt}[/tex]We have the following known values:
[tex]\begin{gathered} \frac{dr}{dt}=\frac{2\operatorname{cm}}{s} \\ r=3\operatorname{cm} \end{gathered}[/tex]Replacing we get:
[tex]\frac{dV}{dt}=4\pi(3)^2(2)[/tex]Solving we get:
[tex]undefined[/tex]Try to evaluate 1001/2 without using a calculator. Enter DNE if the number is not real.
Answers
Rational exponent rule
[tex]a^{\frac{m}{n}}=\sqrt[n]{a^m}[/tex]Applying this rule to the case given:
[tex]100^{\frac{1}{2}}=\sqrt[]{100^1}=\sqrt[]{100^{}}=10[/tex]I need to know what a cordanate plain is
Answers
A coordinated plane is
Using the identity sin? 0 + cos²0 1, find the value of sin 0, to the nearesthundredth, if cos 0 = 0.52 and 3
Answers
we have that
sin^2(x)+cos^2(x)=1
we have
cos(x)=0.52
the angle lie in the IV quadrant
substitute
sin^2(x)+0.52^2=1
sin^2(x)=0.7296
sin(x)=(+/-)0.85
but
the angle lie in IV quadrant
so
is negative
sin(x)=-0.85Part 2
cos(x)=-0.54
III quadrant
the sine is negative too
substitute
sin^2(x)+(-0.54)^2=1
sin^2(x)=0.7084
sin(x)=-0.84