Part A: Alligators: [tex]\(A(t) = 20 \times (1 + 0.25)^t\), Crocodiles: \(C(t) = 25 + 10t\).[/tex]
Part B: After 4 years: Alligators: ~38, Crocodiles: 65.
Part C: Alligators and crocodiles equal: Solve [tex]\(20 \times (1 + 0.25)^t = 25 + 10t\).[/tex]
Part A:
Let's define the functions to represent the number of alligators and crocodiles in the swamp over the years.
For alligators:
[tex]\[A(t) = A_0 \times (1 + r)^t\][/tex]
Where:
[tex]- \(A(t)\) is the number of alligators in the swamp after \(t\) years.\\- \(A_0\) is the initial number of alligators (20 in this case).\\- \(r\) is the growth rate per year (25% or 0.25).\\- \(t\) is the number of years.[/tex]
For crocodiles:
[tex]\[C(t) = C_0 + n \times t\][/tex]
Where:
[tex]- \(C(t)\) is the number of crocodiles in the swamp after \(t\) years.\\- \(C_0\) is the initial number of crocodiles (25 in this case).\\- \(n\) is the number of new crocodiles joining each year (10 in this case).\\- \(t\) is the number of years.[/tex]
Part B:
To find the number of alligators after 4 years, we use the formula:
[tex]\[A(4) = 20 \times (1 + 0.25)^4\][/tex]
To find the number of crocodiles after 4 years, we use the formula:
[tex]\[C(4) = 25 + 10 \times 4\][/tex]
Part C:
To find when the number of alligators and crocodiles are the same, we set [tex]\(A(t) = C(t)\) and solve for \(t\).[/tex]
[tex]\[20 \times (1 + 0.25)^t = 25 + 10 \times t\][/tex]
This equation can be solved numerically to find the value of \(t\) when the number of alligators and crocodiles are the same.
Stephen wants to use the Triangle Proportionality Theorem to determine the relationships on his map. He knows the angle between the park, the bus stop, and his home. Which other angle does he need to know?
Select one:
a. Bus stop, park, and his friend's house
b. Bus stop, park, and his home
c. His friend's house, grocery store, and his home
d. Park, his home, and grocery store
Answer:
C. His friend's house, grocery store, and his home.
Step-by-step explanation:
Triangle Proportionality Theorem-
If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.
So if the line joining the park, bus stop and friend's house, grocery store will be parallel, Stephen can use triangle proportionality theorem.
When two lines are crossed by another line i.e the transversal, the angles in matching corners are called corresponding angles. And when the corresponding angles are equal then the two lines are parallel.
The corresponding angle of the angle between the park, the bus stop, and his home is the angle between his friend's house, grocery store, and his home.
Therefore, he needs to measure that angle.
Which graph represents the solution of 3x + 2y ≥ 4 and x + 3y ≤ 2?
The graph that represents the solution of linear inequalities 3x + 2y >= 4 and x + 3y <= 2 is attached below. The shaded region represents the solution of the inequalities.
What is meant by graphing a linear inequality?
To graph the solution set of an inequality with two variables, first graph the boundary with a dashed or solid line depending on the inequality. If given a strict inequality, use a dashed line for the boundary. If given an inclusive inequality, use a solid line. Next, choose a test point not on the boundary. If the test point solves the inequality, then shade the region that contains it; otherwise, shade the opposite side.
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What is the quotient (2x3 − 3x2 − 14x + 15) ÷ (x − 3)?
a. 2x2 + 3x − 5
b. 2x2 − 3x + 5
c. 2x2 − 3x − 5
d. 2x2 + 3x + 5
Answer: The correct option is (a) [tex]2x^2+3x-5.[/tex]
Step-by-step explanation: We are given to find the quotient in the following division :
[tex]Q=\dfrac{2x^3-3x^2-14x+15}{x-3}.[/tex]
To find the quotient, first we will try to factorize the numerator and then we will try to divide by the denominator.
We have
[tex]Q\\\\\\=\dfrac{2x^3-3x^2-14x+15}{x-3}\\\\\\=\dfrac{2x(x-3)+3x(x-3)-5(x-3)}{x-3}\\\\\\=\dfrac{(x-3)(2x^2+3x-5)}{(x-3)}\\\\=2x^2+3x-5.[/tex]
Thus, the required coefficient is [tex]2x^2+3x-5.[/tex]
Option (a) is CORRECT.
Your total bill at a restaurant is $24.89 you were very pleased with your service so you decide to leave a 20% tip what is the amount of the tip you will leave your waiter
The amount of tip I would leave for the waiter is $24.89
A tip is a form of payment that is given to someone who renders a service. The amount of tip that was given is a percentage of the total bill at the restaurant.
The value of the tip can be determined by multiplying the percentage of tip by the total bill at the restaurant
Value of the tip = percentage tip x total bill at the restaurant
20% x $24.89
0.2 x $24.89 = $4.98
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What is the value of x?
a. 71°
b. 142°
c. 152°
d. 76°
This circle centered at the origin and the Length of its radius is 8. What is the equation of the circle?
Answer: B
Step-by-step explanation: The equation would be x^2+y^2=64 or 8^2
My last question someone help
Divide.
8.64÷(−0.27)
Enter your answer in the box.
32 is your answer hope it helped :) welcome
Which statements are true about the ordered pair (7, 19) and the system of equations?
{2x-y=-5
{x+3y=22
select each correct answer.
A.The ordered pair (7, 19) is a solution to the first equation because it makes the first equation true.
B.The ordered pair (7, 19) is a solution to the second equation because it makes the second equation true.
C.The ordered pair (7, 19) is not a solution to the system because it makes at least one of the equations false.
D.The ordered pair (7, 19) is a solution to the system because it makes both equations true.
Andrea and sula ran a race on a track that was 100 meters long.When andrea crossed the finish line sula was exactly 5 meters behind her.The next day they ran another race and andrea agreed to start 5 meters behind the starting line.If the girls run the same speed as the day before who will win the race ? When the winner crosses he finish line where will the other girl be?
On the second day, Andrea will still win by 0.026 seconds and the other girl will be at 99.75 meters on the track.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Andrea and Sula ran a race on a track that was 100 meters long.
Let us assume that Andrea completed the 100m race in 10 secs.
∴ Andrea's speed is (100/10) = 10m/sec.
Also given that Sula was exactly 5 meters behind her.
∴ In 10 secs she completed 95 meters, and her speed is
= (95/10) = 9.5m/sec.
The next day they ran another race and Andrea agreed to start 5 meters behind the starting line and both the girls run at the same speed,
∴ Andrea has to run 105 meters, so she'll complete the race in
(105/10) secs.
= 10.5 secs.
Sula has to run only 100 meters, so the time needed for her to complete is,
= (100/9.5) secs.
= 10.526 seconds.
So, on the next day, Andrea will win again by (10.526 - 10.5) secs
= 0.26 secs.
∴ When the winner crosses the finish line the other girl will be,
(10.5×9.5) meters = 99.75 meters on the track.
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How would you graph the solution set of x + 4 > -9?
open circle on -13 and shaded to the right
closed circle on -13 and shaded to the right
open circle on -5 and shaded to the right
closed circle on -5 and shaded to the right
Answer:
give the other person brainly
its A
Step-by-step explanation:
Is it possible for 0 and a positive number to have a common multiple?
Determine the n-intercept of the graph of the graph of the car value equation v= -1385n + 18,790
Answer:
13.57
Step-by-step explanation:
We have been given an equation [tex]v=-1385n+18,790[/tex], which represents the value of a car. We are asked to find the n-intercept of our given equation.
We know that the n-intercept will be at [tex]v=0[/tex].
[tex]0=-1385n+18,790[/tex]
Subtracting 18,790 from both sides of our equation we will get,
[tex]0-18,790=-1385n+18,790-18,790[/tex]
[tex]-18,790=-1385n[/tex]
Now, we will divide both sides of our equation by [tex]-1385[/tex].
[tex]\frac{-18,790}{-1385}=\frac{-1385n}{-1385}[/tex]
[tex]13.566787=n[/tex]
[tex]n\approx 13.57[/tex]
Therefore, the n-intercept of our given graph is approximately 13.57.
How many complex roots does the polynomial equation have?
3x5−2x+1=0
Answer : The given polynomial equation can have 0,2 or 4 complex roots.
Explanation:-
Given polynomial equation is [tex]3x^5-2x+1=0[/tex] which is a polynomial of degree 5.
We know that the complex roots always occur in pair ,therefore the number of complex roots in any polynomial must be an even number but less than equal to the degree of polynomial.
Thus, the given polynomial equation has 4 complex roots.
Answer:
The polynomial equation have 4 complex roots.
Step-by-step explanation:
We are given a polynomial equation as:
[tex]3x^5-2x+1=0[/tex]
clearly the polynomial equation is a equation of degree 5 hence, the polynomial equation has atmost 5 roots.
Now we find the roots of the equation by it's graph.
we could clearly see that the graph ofthe function passes through the point (-1,0). hence -1 is the root of the polynomial equation, other than this point the graph does not touches or pass through the x-axis.
Hence, the other four roots of the polynomial equation are complex.
Hence, the polynomial equation has 4 complex roots.
Identify the vertical asymptotes of f(x) = quantity x plus 6 over quantity x squared minus 9x plus 18.
Annabelle traded $2250 for euros, immediately changed her mind, and then promptly traded her euros back into dollars. Which of these amounts is she most likely to have?
It costs a flat fee of $3.15 to make an international call plus $0.05 for every minute that you talk. if you were charged $5.10 for making an international call, for how many minutes did you talk?
what is 5p+2q-3p-3q
members of the wide waters club pay 105 dollars per summer season, plus 9.50 each time they rent a boat. Nonmembers must pay 14.75 each time they rent a boat. How many times would a member and a non-member have to rent a boat in order to pay the same amount?
When multiplying integers, if there is an odd number of negative factors, then the product is?
Answer:
The product of an odd number of negative factors is negative.
Step-by-step explanation:
The factor -1 can be factored from any negative number. Then the product of some number of negative numbers is the product of that number of positive numbers and -1 raised to that power.
An even power of -1 is 1.
An odd power of -1 is -1. So, the product of an odd number of negative factors is negative.
_____
Examples
(-2)(-3)(-4)(5) = (2)(3)(4)(5)(-1)³ = -120 . . . . the product of an odd number of negative factors is negative(-2)(-3)(4)(5) = (2)(3)(4)(5)(-1)² = 120 . . . . . the product of an even number of negative factors is positive_____
Comment on this result
This is helpful to remember when considering the solutions to polynomial inequalities. Once the factored form of the polynomial is found, the solution will depend on the signs of the factors. For example, consider ...
(x +4)(x -2)(x -3) < 0
The zeros of these factors are -4, 2, 3. At each of these values of x, the sign of one of the factors will change. For x<-4, all three factors are negative, so the inequality is true. For -4<x<2, only two of the factors are negative, so the inequality is false. For 2<x<3, one of the factors is negative, so the inequality is again true. For 3<x, all factors are positive, so the inequality is false. Then the solution is (x < -4) ∪ (2 < x < 3).
See the graph for a plot of this polynomial and the solution to the inequality.
In a class of 80 students, 42 received a grade of
a. what fraction of the class did not receive an a? reduce to the lowest terms.
42 received an A
so 40-42 = 38 did not
the fraction would be 38/80, divide both numbers by 2
38/80 reduces to 19/40 did not receive an A
Out of 80 students, 38 did not receive an A, resulting in the fraction who did not receive an A being 19/40 after simplifying.
Explanation:In a class of 80 students, if 42 received a grade of A, then the number of students who did not receive an A is the total number of students minus the number who did receive an A. So, 80 students − 42 students = 38 students. The fraction of the class that did not receive an A is 38 out of 80, which can be simplified by dividing both the numerator and the denominator by their greatest common factor, which is 2.
Therefore, the reduced fraction is 19/40.
The fraction of the class that did not receive an A is 19/40 which, if we converted into a percentage, would be 47.5%.
darius spends 35% of his time doing math homework. alex spends 2/5 of his time doing math homework. who spends more homework time on math? explain
(Once again I am doing this question because no one answered it last time. thanks)
After taxes, Alexandra's take home pay is 9/10 of her salary before taxes. Enter and solve an equation to find Alexandra's salary before taxes for the pay period that resulted in $486 of take-home pay. let s represent your variable.
Alexandra's salary before taxes for the pay period was $
I need the equation and the answer for the question above this sentence.
Listen I really need help i'm struggling in math okay.
Identify which type of correlation the given scatterplot possesses, if a correlation exists.
A.
no correlation
B.
positive correlation
C.
negative correlation
D.
correlation is impossible to determine
Answer:
B. Positive correlation
Step-by-step explanation:
Positive correlation is nothing but when the values of x increase, the corresponding y values are also increase.
When we look at the scatter plot, when x increase, the y also increase.
Therefore, it is a positive correlation.
Hope this will helpful.
Thank you.
considering the one-time deposit and monthly rent, the equation y=1200+400x can be used to represent y, the total cost of renting an apartment for x months. what is the amount of the deposit?
A staircase handrail is made from congruent parallelograms. in parallelogrampqrs, pq = 17.5, st = 18, and m∠ qrs = 110° . find m∠ pqr.
To find angle PQR in a parallelogram, we can use the Exterior Angle Theorem. By subtracting the measures of the other two angles in triangle QRS from 180 degrees, we find that angle PQR is 70 degrees.
Explanation:To find the measure of angle PQR, we can use the fact that opposite angles in a parallelogram are congruent. This means that angle PQR is equal to angle STQ. Since STQ is an exterior angle of triangle QRS, we can use the Exterior Angle Theorem to find its measure by subtracting the measures of the other two angles in the triangle from 180 degrees.
Given that angle QRS is 110 degrees, we can find angle STQ by subtracting the measures of angles QRS and QSR from 180 degrees:
angle STQ = 180 - (110 + 180) = -110 degrees
However, angles cannot have negative measures, so we need to find the equivalent positive measure. Adding 180 degrees to -110 degrees gives us angle STQ = 70 degrees. Therefore, angle PQR is also equal to 70 degrees.
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Which equation is a trigonometric identity?
what is the ratio 15:75 in lowest terms? as a ratio
Answer:
1 : 5
Step-by-step explanation:
Landon is standing in a hole that is 5.1 ft deep. He throws a rock, and it goes up into the air, out of the hole, and then lands on the ground above. The path of the rock can be modeled by the equation y = -0.005x 2 + 0.41x - 5.1, where x is the horizontal distance of the rock, in feet, from Landon and y is the height, in feet, of the rock above the ground. How far horizontally from Landon will the rock land?
Train a has a speed of 15 miles per hour greater than that of train
b. if train a travels 150 miles in the same time train b travels 120 miles, what are the speeds of the two trains