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Suppose 20 rabbits are taken to an island. the rabbit population then triples every year. the function f(x)
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hope this helps!
p.s. can i have brainliest?
This question is about exponential growth and the rabbit population on an island.
Explanation:The subject of this question is Mathematics. Specifically, it involves exponential growth and a function that represents the rabbit population on the island over time. Let's define the function f(x) to represent the population of rabbits at year x.
Based on the information given, the initial population is 20 rabbits. The population triples every year, which means that for each year x, the population is f(x) = 20 * 3^x.
For example, after 1 year, the population would be f(1) = 20 * 3^1 = 60 rabbits. After 2 years, the population would be f(2) = 20 * 3^2 = 180 rabbits, and so on.
Learn more about Exponential growthhttps://brainly.com/question/34350466
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George purchased a new car with the special 2.9% financing. If the car's price was $19,999 and he financed it for five years, find his monthly payment.
A. $357.46
B. $358.47
C. $199.99
D. $343.25
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P = C*{(i/12)/[1-(1+i/12)^-12t}
C = Cost of the car = $19,999; i = financing rate = 2.9% = 0.029; t = time of payment in years = 5 years
Therefore,
P = 19999*{(0.029/12)/[1-(1+0.029/12)^-12*5} = $358.47
B. is the correct answer.
Correct Answer is B which is $ 358.47 for monthly payment
Find 2004-04-02-04-00_files/i0340000.jpg. Round the answer to the nearest tenth.
A.
46.1°
B.
47.2°
C.
54.9°
D.
79.0°
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The problem is to calculate the angles of the triangle. However, it is not clear which angle you have to calculate, so we are going to calculate all of them
we know that
Applying the law of cosines
c²=a²+b²-2*a*b*cos C------> cos C=[a²+b²-c²]/[2*a*b]
a=12.5
b=15
c=11
so
cos C=[a²+b²-c²]/[2*a*b]---> cos C=[12.5²+15²-11²]/[2*12.5*15]
cos C=0.694------------> C=arc cos (0.694)-----> C=46.05°-----> C=46.1°
applying the law of sines calculate angle B
15 sin B=11/sin 46.1-----> 15*sin 46.1=11*sin B----> sin B=15*sin 46.1/11
sin B=15*sin 46.1/11-----> sin B=0.9826----> B=arc sin (0.9826)
B=79.3°
calculate angle A
A+B+C=180------> A=180-B-C-----> A=180-79.3-46.1----> A=54.6°
the angles of the triangle are
A=54.6°
B=79.3°
C=46.1°
What is the length of a garden hose that is stretched diagonally corner-to-corner across a yard that measures 72 meters long and 60 meters wide? Round to the nearest meter.
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length = sqrt (72^2 + 60^2)
= 94 meters to nearest meter
Here, we need to find the length of the hose which is diagonally placed in the rectangular garden.
The length is given as = 72 meters
The width is given as = 60 meters
We will use Pythagoras theorem here.
Hypotenuse² = Perpendicular² + Base²
Hypotenuse² = 72² + 60²
Hypotenuse² = √8,784 meters²
Hypotenuse = 93.72 meters
Thus, the length of diagonal hose will be = 93.72 meters
a man made lake is stocked with 10,000 fish. This population is expected to decline by an annual rate of 15%. Predict the fish population 5 years after the lake is stocked
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10,000*15% = 1,500 or you could do 10,000*.15 = 1,500
That is a loss of 1,500 fish per year.
If you want to think of this as a proportion then you would do
Year/fish lost
1/1,500 = 5/x
X=5*1,500
X=7,500
The population of the fish after 5 years equals
10,000-7,500 = 2,500
So your answer is 2,500 fish are left
The population will be approximately 4,437 fish after 5 years.
To predict the fish population 5 years after the lake is stocked,
We can use the formula for exponential decay:
[tex]\[ P = P_0 \times (1 - r)^t \][/tex]
Where:
P is the final population[tex]\( P_0 \)[/tex] is the initial populationr is the annual rate of decline (expressed as a decimal)t is the number of yearsGiven:
[tex]\( P_0[/tex] = 10,000 (initial population)r = 0.15 (annual rate of decline, expressed as 15% or 0.15)t = 5 (number of years)Substituting the values into the formula:
[tex]\[ P = 10,000 \times (1 - 0.15)^5 \][/tex]
[tex]\[ P = 10,000 \times (0.85)^5 \][/tex]
Calculating:
P ≈ 10,000 × 0.443705
P ≈ 4437.05
So, the fish population 5 years after the lake is stocked is approximately 4437 fish.
Need help on this as soon as possible
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h=sqrt(16+36)
h=sqrt(52)
h=sqrt(4*13)
h=sqrt(4) sqrt(13)
h=2 sqrt(13)
Total Area: T.A.=2*(4*6/2)+[4+6+2 sqrt(13)] (8)
T.A.=2*(12)+[10+2 sqrt(13)](8)
T.A.=24+(10)(8)+[2 sqrt(13)](8)
T.A.=24+80+16 sqrt(13)
T.A.=104+16 sqrt(13)
Answer:
( 104+16 sqrt(13) )
HEEEELLLPP!!!!!!!!!!!!!!!WILL GIVE THE BRAIN!!!!!POINTS!!!!!!!
plz
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The given function f(x) = - 3x + 2 is a linear function, so its parent function must have to be a linear function.
The parent linear function is f(x) = x
Note that you can derive the above function from x by first multiplying it with -3 and then adding 2.
So the correct option is option C
find its area. w(-2,0). x(-3,3). y(2,0),z(1,3)
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A tree's root is 9 feet below ground and spans a radius of 6 feet. If the total length of the tree from root tip to top is 23 feet, what is the tree's elevation above ground?
a. 14 feet
b. 17 feet
c. 26 feet
d. 32 feet
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You know the tree goes 9 feet underground and the tree is 23 feet tall from root to top
You can subtract how far the tree goes underground by the length of the tree to get the answer
23 - 9 = 14
The answer is A) 14 feet
Hope this helps!
A ball is thrown downward from the top of a 190-foot building with an initial velocity of 21 feet per second. the height of the ball h after t seconds is given by the equation h equals negative 16 t squared minus 21 t plus 190. how long after the ball is thrown will it strike the ground?
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1- You have the following information give in the problem above:
- The ball is thrown downward from the top of a 190-foot building with an initial velocity of 21 feet per second.
- The height of the ball h after t seconds is given by this equation: h=-16t²-21t+190.
2- h=0 when the ball strikes the ground, then you have:
-16t²-21t+190=0
3. When you solve the quadratic equation shown above, you obtain:
t=2.85 seconds
The answer is: 2.85 seconds.
The ball hits the ground after approximately 4.16 seconds.
To find the time at which the ball strikes the ground, we need to determine when h(t) = 0. Given the equation for height:
[tex]\[ h(t) = -16t^2 - 21t + 190 \][/tex]
we can set h(t) to 0 and solve for t:
[tex]\[ -16t^2 - 21t + 190 = 0 \][/tex]
Using the quadratic formula, we can find the roots of this equation:
[tex]\[ t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
where a = -16 , b = -21, and c = 190. Plugging in the values, we get:
1. Find the discriminating value [tex]\( \Delta = b^2 - 4 \times a \times c \)[/tex]:
[tex]\[ \Delta = (-21)^2 - 4 \times (-16) \times 190 = 441 + 12160 = 12601 \][/tex]
2. Calculate the roots:
[tex]\[ t = \frac{-(-21) \pm \sqrt{12601}}{2 \times -16} \\ \[ t = \frac{21 \pm \sqrt{12601}}{-32} \][/tex]
Since we're interested in the positive value (representing the time when the ball hits the ground), we'll only consider the root with the "minus" sign:
[tex]\[ t = \frac{21 - \sqrt{12601}}{-32} \approx \frac{-21 + \sqrt{12601}}{32} \approx \frac{21 - \sqrt{12601}}{32} \][/tex]
Using a calculator, let's approximate the result:
[tex]1. Compute \( \sqrt{12601} \approx 112.24 \),\\2. Then calculate \( 21 + 112.24 \approx 133.24 \),\\3. Divide by 32 to get \( t \approx \frac{133.24}{32} \approx 4.16375 \).[/tex]
Rounding to a more readable result, we can say that the ball hits the ground after approximately 4.16 seconds.
The two lines, P and Q, are graphed below: Line P is drawn by joining ordered pairs negative 8,15 and 6, negative 12. Line Q is drawn by joining ordered pairs 4,16 and negative 9,10 Determine the solution and the reasoning that justifies the solution to the systems of equations
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Answer:
[tex]\text{Solution: }\left(-\dfrac{2654}{435},\dfrac{1644}{145}\right)[/tex]
Step-by-step explanation:
Line P is drawn by joining ordered pairs (-8,15) and (6,-12)
Using two point formula of line. Find equation of line P
[tex]\dfrac{y-15}{x-(-8)}=\dfrac{-12-15}{6-(-8)}[/tex]
[tex]\dfrac{y-15}{x+8}=\dfrac{-27}{6+8)}[/tex]
[tex]\dfrac{y-15}{x+8}=\dfrac{-27}{14}[/tex]
[tex]y=\dfrac{-27}{14}(x+8)+15[/tex]
[tex]y=\dfrac{-27}{14}x+\dfrac{-27}{14}\times 8 + 15[/tex]
[tex]y=\dfrac{-27}{14}x-\dfrac{3}{7}[/tex]
[tex]\text{Equation of line P:}y=\dfrac{-27}{14}x-\dfrac{3}{7}[/tex]
Line Q is drawn by joining ordered pairs (4,16) and (-9,10)
Using two point formula of line. Find equation of line Q
[tex]\dfrac{y-16}{x-4}=\dfrac{10-16}{-9-4}[/tex]
[tex]\dfrac{y-16}{x-4}=\dfrac{-6}{-13}[/tex]
[tex]\dfrac{y-16}{x-4}=\dfrac{6}{13}[/tex]
[tex]y=\dfrac{6}{13}(x-4)+16[/tex]
[tex]y=\dfrac{6}{13}x-\dfrac{6}{13}\times 4 + 16[/tex]
[tex]y=\dfrac{6}{13}x+\dfrac{184}{13}[/tex]
[tex]\text{Equation of line Q:}y=\dfrac{6}{13}x+\dfrac{184}{13}[/tex]
Using graphing find solution of system of equation.
We draw the line on graph and see the intersection point.
Please see the attachment of the line.
Answer:
(−2, 4), because it is the point of intersection of the two graphs
Step-by-step explanation:
BECAUSE
Assume that the starting point of a path in such a grid is labeled the origin ≡ (0,0). the destination is the point (m,n). in other words, there are (n+1) streets in the x direction and and (m+1) streets in the y direction; and any portion of of any of these streets can be used to reach the destination. find the total number of distinct paths; assuming that all streets are available.
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if there is a direct street from (0,0) to (m,n) : (m+1)*(n+1)+1
Which one of the following statements is true?
A. If f is continuous on (a, b), then f attains an absolute maximum value and f attains an absolute minimum inside the interval (a, b).
B. If f '(x) > 0 on the interval (a, b), then f is decreasing on the interval
(a, b).
C. If f and g are increasing on the interval (a, b), then f + g is increasing on (a, b).
D. None of the above.
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A tangent-tangent angle intercepts two arcs that measure 124 and 236. what is the measure of the tangent-tangent angle?
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The measure of the external angle is the semi difference of the arcs that it covers.
let
x-----> the measure of the tangent-tangent angle
∠ x=(1/2)*[236-124]----> 56°
the answer is
the measure of the tangent-tangent angle is 56 degrees
Answer:
the measure of the tangent-tangent angle is 56 degrees.
Step-by-step explanation:
apex
Bryant collects a set of 20 data representing the lengths of worms he found in the garden. The variance of the set of measurements is 36. What is the standard deviation from the mean? _____ millimeters
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Given:
set of 20 data
variance of 36
Find the standard deviation from the mean.
The formula for the standard deviation is the square root of the variance.
Standard deviation = √36
Standard deviation = 6
Kevin and randy muise have a jar containing 68 coins, all of which are either quarters or nickels. the total value of the coins in the jar is $13.40. how many of each type of coin do they have?
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x: number of quarters
y: number of nickels
We now write the system of equations:
x + y = 68
0.25x + 0.05y = 13.40
Solving the system we have:
x = 50
y = 18
Answer:
they have:
quarters = 50
nickels = 18
Kevin and Randy have 50 quarters and 18 nickels.
Explanation:To solve this problem, we can set up a system of equations. Let's use the variables x for the number of quarters and y for the number of nickels. We can then write two equations based on the given information:
Equation 1: x + y = 68 (the total number of coins is 68)
Equation 2: 0.25x + 0.05y = 13.40 (the total value of the coins is $13.40).
We can start by solving Equation 1 for x in terms of y:
x = 68 - y. Now we can substitute this expression for x into Equation 2:
0.25(68 - y) + 0.05y = 13.40
Simplifying, we get 17 - 0.25y + 0.05y = 13.40.
Combining like terms, we have 0.20y = 3.60.
Dividing both sides by 0.20, we find y = 18. Plugging this value back into Equation 1, we can solve for x:
x + 18 = 68
x = 68 - 18 = 50.
Therefore, Kevin and Randy have 50 quarters and 18 nickels.
Trip bought an ice cream cone that is 4 inches tall with a radius of 2 inches the cone has a mass of about 3 ounces when empty after it is filled with ice cream and topped with a Hemisphere of ice cream with a radius of 2 inches it has a mass of 35 ounces what is the density of the ice cream use 3.14 for pie round your answer to the nearest thousand your answer will be in ounces per cubic inches
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[volume of the cone]=(1/3)*pi*r²*h
for r=2 in
h=4 in
[volume of the cone]=(1/3)*pi*2²*4-----> 16.747 in³
volume of the hemisphere=(4/6)*pi*r³
for r=2 in
volume of the hemisphere=(4/6)*pi*2³----> 16.747 in³
[the density of the ice cream]=mass ice cream/volume ice cream
mass ice cream=35 oz-3 oz-----> 32 oz
volume ice cream=volume of a cone +volume of hemisphere
volume ice cream=16.747+16.747----> 33.494 in³
density ice cream=32/33.494-----> 0.955 ounces/in³
the answer is
0.955 ounces/in³
Luis makes $23.10 per hour at his job for the first 40 hours he works each week. if he works more than 40 hours, then luis makes $34.65 per hour. if luis works 46 hours in one week, how much does he earn?
a. $1,062.60
b. $1,097.25
c. $1,131.90
d. $1,593.90 please select the best answer from the choices provided a b c d
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The correct option is (C)
Frank owns 300 acres of land. If he divides the land into 1/2 acre plots, how many plots will he have?
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hope that helps
Anyone know this geometry question?
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Corresponding parts of congruent triangles are the same
A ________ sample is a sample in which each member of the population has a known, nonzero, chance of being selected for the sample.
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is selective
A random sample is a subset of a population where every individual has an equal and known chance of being selected, providing a representative segment for study.
A random sample is a sample in which each member of the population has a known, nonzero, chance of being selected for the sample. This means that in a random sample, every individual in the larger population has an equal opportunity to be included. There are various methods to achieve a random sample, such as simple random sampling, stratified sampling, or using random digit dialing. Random samples are crucial because they tend to be representative of the population, thereby allowing the results of studies to be generalizable.
What is the approximate area of the shaded sector in the circle below
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so plug in the numbers A= (3.14)(4.5)(4.5)= 63.62 is the total area
150*63.62=9543 9543/360=26.5
So the answer is 26.5 cm ^2
Which of following equations is equivalent to the slope formula?
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You and a friend go to the movies and split the cost of the movie tickets and snacks. you pay the bill. you tell your friend he owes only $9 because you owe him $4 from the last time you went to the movies. how much was the total bill
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Total bill = $13 x 2 = $26
Answer: $26
Two rafts are traveling In opposite directions on a straight river. The raft going with the current is traveling at a speed of 12 mph. The raft going against the current is traveling at a speed of 70 miles per hour. Both rafts travel the river for two hours. Which equation represents the situation? Assume the raft traveling with the current travels X miles in the raft traveling against the current travels y miles.
A. 12/x - 7/y = 1/2
B. 12x + 7y = 2
C. x/12 - y/7 = 2
D. x/12 + y/7 = 4
E. 12x + 7y = 4
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Time taken by the raft going with the current to travel x miles is:
12/x hours
Time taken by the raft going against the wind is:
7/y
Total time taken for both raft is 4 hours thus:
12/x+7/y=4
hence the answer is:
D. x/12 + y/7 = 4
What is the value of x
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45 + (2x - 5) = 180
45 + 2x - 5 = 180
2x + 40 = 180
2x = 140
x = 70
Answer: x = 70
Graph the function f(x) = x3 – 3x – 2. Based on the graph, which value for x is a double root of this function? a.–2 b.–1 c.1 d.2
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1. You have the following function given in the problem:
f(x)=x3–3x–2
2. When you give values to the x and plot each point obtained, you obtain the graph shown in the figure attached.
3. Based on the graph and analizing the alternate form:
f(x)=(x-2)(x+1)²
As you can see, there is two roots x=-1, then, you can conclude that the correct answer is the option b, which is:
b) -1
Answer:
B) -1
Step-by-step explanation:
Kali earns $8 per hour. She worked x hours on both Monday and Tuesday. She also worked 5 hours on Thursday. The expression which represents Kali’s earnings for the week is shown.
Image in screenshot!
Which number should go into the box to complete the expression?
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It is given that:
Kali earns $ 8 per hour.
This means that if she works for n hours then this earning for n hours will be given by: $ 8n
She works x hours on both Monday and Tuesday.
This means that the earning of x hours is: $ 8x
and hence the earning for both Monday and Tuesday is:$ 2(8x)
She also worked for 5 hours on Thursday.
Hence, the earning for Thursday is: 5×8=40
The total earning of the week is given by:
2(8x)+5(8)
what is the measure of AB
Answers
make sure your calculator is in Degree mode.
Claire says the area of a square with a side length of 100 centimeters is greater than the area of a square with a side length of 1 meter. Is she correct? Explain
Answers
100 cm=1 m
this implies that both squares are the same hence their areas will be the same. Thus we conclude that Claire was wrong, neither of the area of the squares is greater than the other one.