Zoologists are studying two newly discovered species of insects in a previously unexplored section of rain forest. They estimate the current population of insect A to be 1.3 million and the current population of insect B to be 2.1 million. As development is encroaching on the section of rain forest where these insects live, the zoologists estimate the populations of insect A to be reducing at a rate of 3.8% and insect B to be reducing at a rate of 4.6%.
If P represents the population of each species of insect in millions, and t represents the elapsed time in years, then which of the following systems of equations can be used to determine how long it will be before the populations of the two species are equal?
Answer:
the system of equation that can be used to determine how long it will be before the populations of the two species are equal is :
[tex]\begin{cases} {\mathtt{P = 1.3 e^{-0.038 \ t}} & \\ \mathtt{P = 2.1 \ e^{-0.046 \ t}} & \end{cases}[/tex]
Step-by-step explanation:
Given that :
the current population of insect A to be 1.3 million
the current population of insect B to be 2.1 million.
As development is encroaching on the section of rain forest where these insects live, the zoologists estimate the populations of insect A to be reducing at a rate of 3.8% and insect B to be reducing at a rate of 4.6%.
The equation that can be used to determine how long it will be before the populations of the two species are equal is an equation for exponential decay, which can be represented as follows:
[tex]\mathtt{y = pe^{-rt}}[/tex]
where;
P represents the population of each species of insect in millions
t represents the elapsed time in years
r is the rate of decrease
So, we can have:
[tex]\mathtt{p_1 = 1.3 }[/tex] in million and [tex]\mathtt{p_2 = 2.1}[/tex] in million
Also for rate of decrease;
[tex]\mathtt{r_1 = 0.038}[/tex] and [tex]\mathtt{r_2 = 0.046}[/tex]
Therefore;
the exponential decay for Population of insect A can now be:
[tex]\mathtt{P = 1.3 e^{-0.038 \ t}}[/tex]
the exponential decay for Population of insect B can now be:
[tex]\mathtt{P = 2.1 \ e^{-0.046 \ t}}[/tex]
Hence, the system of equation that can be used to determine how long it will be before the populations of the two species are equal is :
[tex]\begin{cases} {\mathtt{P = 1.3 e^{-0.038 \ t}} & \\ \mathtt{P = 2.1 \ e^{-0.046 \ t}} & \end{cases}[/tex]
Answer:
A!
Step-by-step explanation:
Plato
A prisoner is trapped in a cell containing 3 doors. The first door leads to a tunnelthat returns him to his cell after 2 days’ travel. The second leads to a tunnel thatreturns him to his cell after 4 day’s travel. The third door leads to freedom after 1day of travel. If it is assumed that the prisoner will always select doors 1,2,and 3with respective probabilities 0.5,0.3, and 0.2, what is the expected number of daysuntil the prisoner reaches freedom?
Answer:
2 days
Step-by-step explanation:
Expected number of days until prisoner reaches freedom=E(x)=?
E(x)=x*p(x)
Where x is the number of days and p(x) is the probability associated with them.
X 1 2 3
P(x) 0.5 0.3 0.2
E(x)=1*0.5+2*0.3+3*0.2
E(x)=0.5+0.6+0.6
E(x)=1.7.
Thus, the expected number of days until prisoner reaches freedom are 2 days.
Please help. I need it. Bad.
Answer:
Option a.
Step-by-step explanation:
In the given triangle angle A is a right angle so triangle ABC is a right angled triangle.
Opposite side of right angle is hypotenuse. So, CB is hypotenuse.
From figure it is clear that CA is shorter that segment BA.
All angles are congruent to itself. So angle C is congruent to itself.
We know that, if an altitude is drawn from the right angle vertex in a right angle triangle it divide the triangle in two right angle triangles, then given triangle is similar to both new triangles.
So, triangle ABC is similar to triangle DBA if segment AD is an altitude of triangle ABC.
Therefore, the correct option is a.
Megan buys condiments in bulk for her restaurant. The company that she orders ketchup from charges $14.78 per gallon for orders less than 8 gallons. For orders of 8 gallons or more, the cost is $11.99 per gallon of ketchup. Which function represents this situation?
side note: f(x)= blank
Answer:
Below
Step-by-step explanation:
● Orders of 8 gallons or more can be modeled as: x》 8
● For each gallons in the situation above the company charges 11.99 per gallon so: 11.99x
● For orders that are less than 8, the comapny charges 14.78 per gallon
● => 14.78x for x < 8
So the function that represent the situation is the second one
What’s the value of X
Answer:
Step-by-step explanation:
Use the Law of Sines for this. Set it up as follows:
[tex]\frac{sin(x)}{6}=\frac{sin(61)}{6.2}[/tex] Cross multiply:
6.2sin(x) = 6sin(61) and solve for the term with the unknown in it:
[tex]sin(x)=\frac{6sin(61)}{6.2}[/tex]
Work on the right side first. Plug that into your calculator to get
sin(x) = .8464061682
Now the problem comes down to "what angle has a sine of .8464061682?" This requires the use of the inverse button on your calculator. Hit 2nd, then sin, and you will see on your screen:
[tex]sin^{-1}([/tex]
After that open parenthesis enter that big long decimal and hit equals. You should get an angle measure of 57.822 degrees. Not sure what you are rounding to.
Distance between the two points ? (-3,10) and (3,-2)
Answer:
Approximately 13.4 units.
Step-by-step explanation:
To find the distance between two points, use the distance formula. The distance formula is:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
x₁ and y₁ is one coordinate while x₂ and y₂ is the other.
Let (-3,10) be x₁ and y₁ and let (3,-2) be x₂ and y₂. Plug in the numbers and simplify:
[tex]d=\sqrt{(3-(-3))^2+(-2-10)^2}\\ d=\sqrt{6^2+(-12)^2} \\d=\sqrt{36+144} \\d=\sqrt{180}\\ d=\sqrt{36\cdot5}=6\sqrt{5}\approx13.4164[/tex]
Edit: Typo
Answer:
100
Step-by-step explanation:
In a circle whose center is O, arc AB contains 100. Find the number of degrees in angle ABO. WILL MARK BRAINLIEST FOR BEST ANSWER A)50 B)40 C)65 D)60
Answer:
It is so easy u should get this right.
First draw a circle and there is an arc that is like forming a triangle inside a circle and then ab angle is 100 degree and outside is the center of the circle. And since u try to find how much is outside it most likely means that 100-60=40
so it b 40.
Step-by-step explanation:
The number of degrees in ∠ABO is 50°. Therefore, option A is the correct answer.
Given that, in a circle whose centre is O, arc AB contains 100°.
We need to find the number of degrees in ∠ABO.
How are angles and arcs related?An arc of a circle is a section of the circumference of the circle between two radii. A central angle of a circle is an angle between two radii with the vertex at the centre. The central angle of an arc is the central angle subtended by the arc. The measure of an arc is the measure of its central angle.
According to the theorem ∠ABO=1/2 × arc AB.
So, ∠ABO=1/2 × 100°=50°
The number of degrees in ∠ABO is 50°. Therefore, option A is the correct answer.
Learn more here about arc of a circle here:
https://brainly.com/question/15448382.
#SPJ2
Polygons EFGH and E'F'G'H' are shown on the following coordinate grid:
hy
What set of transformations is performed on EFGH to form E'F'G'H'?
Answer:
A translation 3 units to the right and a 90-degree clockwise rotation
Step-by-step explanation:
10 less than k is 35 help please
Answer:
k = 45
Step-by-step explanation:
We can put this into an equation form:
k - 10 = 35
We can solve for k by adding 10 to both sides:
k = 45
Answer:
k-10=35
k=45
Step-by-step explanation:
Let's write this as an equation.
"10 less than k" means subtract 10 from k.
k-10
"is 35" means equals 35.
k-10=35
If we want to solve for k, we have to get k by itself on one side of the equation.
k-10=35
10 is being subtracted from k. The inverse of subtraction is addition. Add 10 to both sides of the equation.
k-10+10=35+10
k=35+10
k=45
Covert the verbal expression into an algebraic expression.
The product of 23 and a number x
Answer:
23×x
=23x
Hope it helps
Answer:
23x
Step-by-step explanation:
"The product of" indicates that we will be multiplying the two quantities. 23 multiplied by x can be written as 23 * x which simplifies to 23x.
The base of a right triangle is increasing at a rate of 2 meters per hour and the height is decreasing at a rate of 3 meters per hour. When the base is 9 meters and the height is 22 meters, then how fast is the HYPOTENUSE changing
Answer:
dL/dt = - 2,019 m/h
Step-by-step explanation:
L² = x² + y² (1) Where x, and y are the legs of the right triangle and L the hypotenuse
If the base of the triangle, let´s call x is increasing at the rate of 2 m/h
then dx/dt = 2 m/h. And the height is decreasing at the rate of 3 m/h or dy/dt = - 3 m/h
If we take differentials on both sides of the equation (1)
2*L*dL/dt = 2*x*dx/dt + 2*y*dy/dt
L*dL/dt = x*dx/dt + y*dy/dt (2)
When the base is 9 and the height is 22 according to equation (1) the hypotenuse is:
L = √ (9)² + (22)² ⇒ L = √565 ⇒ L = 23,77
Therefore we got all the information to get dL/dt .
L*dL/dt = x*dx/dt + y*dy/dt
23,77 * dL/dt = 9*2 + 22* ( - 3)
dL/dt = ( 18 - 66 ) / 23,77
dL/dt = - 2,019 m/h
Using implicit differentiation and the Pythagorean Theorem, it is found that the hypotenuse is changing at a rate of -2.02 meters per hour.
The Pythagorean Theorem states that the square of the hypotenuse h is the sum of the squares of the base x and of the height h, hence:
[tex]h^2 = x^2 + y^2[/tex]
In this problem, [tex]x = 9, y = 22[/tex], hence, the hypotenuse is:
[tex]h^2 = 9^2 + 22^2[/tex]
[tex]h = \sqrt{9^2 + 22^2}[/tex]
[tex]h = 23.77[/tex]
Applying implicit differentiation, the rate of change is given by:
[tex]2h\frac{dh}{dt} = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]
Simplifying by 2:
[tex]h\frac{dh}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}[/tex]
The rates of change given are: [tex]\frac{dx}{dt} = 2, \frac{dy}{dt} = -3[/tex].
We want to find [tex]\frac{dh}{dt}[/tex], hence:
[tex]h\frac{dh}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}[/tex]
[tex]23.77\frac{dh}{dt} = 9(2) + 22(-3)[/tex]
[tex]\frac{dh}{dt} = \frac{18 - 66}{23.77}[/tex]
[tex]\frac{dh}{dt} = -2.02[/tex]
The hypotenuse is changing at a rate of -2.02 meters per hour.
A similar problem is given at https://brainly.com/question/19954153
A soccer team has 18 players. 5 of the players have scored at least 4 goals this season. Approximately what percent of the players have scored
at least 4 goals?
Select the best answer from the choices provided.
O A. 1596
OB.
30%
Ос.
6096
D
7596
Answer:30%
Step-by-step explanation:you divide 18 by 100 and then multiply that by 30 and it gives you 5.4 which is close to 5 players. So 30% is the answer
As part of a chemistry experiment, Barry is making a mixture of two solutions. He uses 4 cups of solution A for every 2 cups of solution B. The table below shows the numbers of cups he uses of solution A and solution B. Solution A (cups) Solution B (cups) 4 2 8 4 12 6 16 8 Using the information from the table, choose the correct statement. A. The ratio of the number of cups of solution A to the total number of cups of the mixture is 2:3. B. The ratio of the number of cups of solution A to the total number of cups of the mixture is 3:2. C. There are 3 cups of solution A for every 6 cups of mixture. D. For each cup of solution A, there are 2 cups of solution B.
Answer:
A. The ratio of the number of cups of solution A to the total number of cups of the mixture is 2:3
Step-by-step explanation:
Solution A= 4 cups
Solution B= 2 cups
Total cups of the mixture=4+2=6
A. The ratio of the number of cups of solution A to the total number of cups of the mixture is 2:3.
Solution A= 4 cups
Mixture=6 cups
Solution A : Mixture =4 : 6
=2:3
Option A is true
B. The ratio of the number of cups of solution A to the total number of cups of the mixture is 3:2.
Solution A= 4 cups
Mixture=6 cups
Solution A : Mixture =4 : 6
=2:3
Option B not true
C. There are 3 cups of solution A for every 6 cups of mixture.
Option C states that:
Solution A=3 cups
Mixture=6 cups
Solution A : Mixture=3:6=1:2
This is not true
D. For each cup of solution A, there are 2 cups of solution B.
Option D states:
Solution A= 1 cups
Solution B= 2 cups
This is not true
It is rather
Solution A= 2 cups
Solution B= 1 cups
Therefore, option A. The ratio of the number of cups of solution A to the total number of cups of the mixture is 2:3 is the correct statement
The double number line shows that to make 4 apple pies takes 14 pounds of apples.Select the double number line that correctly labels the number of pounds of apples that are needed to make 1 , 2, and 3 pies.
Answer:
10.5 pounds of apples
Step-by-step explanation:
4 devided by 14 = 3.5
3.5* 3 = 10.5
pLEASE SOLVE THE QUESTIONS (WILL MARK BRANLIEST)
Answer:
a) 4⁻³ = 1/64 = 0.015625
b)13⁻² = 1/169 = 0.0059171598
c)(-3)⁻² = 1/-3² = 0.1111111111
Step-by-step explanation:
To solve the question above, when we have an integer ( positive or negative) that is raised to a negative power, this means the reciprocal of that integer raised to the positive power
Example:
a⁻ⁿ = 1/aⁿ
a) 4⁻³ = 1/4³
= 1/(4 × 4 × 4)
= 1/64
= 0.015625
b) 13⁻² = 1/13²
= 1/(13 × 13)
= 1/169
= 0.0059171598
c)(-3)⁻² = 1/-3²
= 1/(-3 × -3)
= 1/9
= 0.1111111111
Marsha wants to buy carpet to cover her whole living room, except for the tiled floor. The tiled
floor is 4 ft by 2 ft. Find the area the carpet needs to cover. 1)
Solve on paper. Then check your work on Zearn. 1)
1
11
3
7
tiled floor
Answer:
68.06 sq. feets
Step-by-step explanation:
Area of room's floor
11.33 × 7 = 79.33
Area of tiled floor
4.83 × 2.33 = 11.278
Area of floor needed to be carpeted
79.33-11.278= 68.06
For the given figure, justify the statement ∠1 ≅ ∠2
Answer:
JUSTIFICATION↓
∠1 ≅ ∠2 (∵ Vertically-opposite angles are equal)
Step-by-step explanation:
Since ∠1 lies vertically opposite to ∠2 and vice -versa , therefore ∠1 and ∠2 are equal to each other
A bag has six balls labeled a,b,c,d.e and f . One ball will be randomly picked, and its letter will be recorded as the outcome. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event of choosing the letter a or c . If there is more than one element in the set, separate them with commas.
We simply list all of the letters mentioned as they are the possible outcomes. We can only pick one item from the sample space. The event space is the set of outcomes where we want to happen (picking either an 'a' or 'c').
Hey There!!
To this Question, This answer going to had A Explanation to this: Sample space--
A sample space is a set which contains the set of all the possible outcomes or results that could occur while performing an experiment.
i.e. the sample space while flipping a coin is: {H,T}
The sample space while tossing a six-sided die is: {1,2,3,4,5,6}
Here it is given that:
A bag has six balls labeled: A,B,C,D,E,F
One ball will be randomly picked, and its letter will be recorded as the outcome.
This means that the sample space is given by:
Sample space={ A,B,C,D,E,F}
Now, when the event is choosing a letter from D to F.
Then the sample space is:
Sample space= {D,E,F}
Hope It Helped!~ ♡
ItsNobody~ ☆
For the function f(x) = -12x + 7, find the
matching value for x when f(x) = 17. Write
your answer as a fraction.
Answer:
[tex]\large\boxed{x=-\frac{5}{6}}[/tex]
Step-by-step explanation:
f(x) is the same value as y. Therefore, y = 17. We can place this into slope intercept form (except with a defined value for y) and solve for x.
Start by subtracting 7 from both sides. Then, divide by -12 to solve for x. Finally, simplify the fraction.
17 = -12x + 7
10 = -12x
-10/12 = x
-5/6 = x
[tex]\large\boxed{x=-\frac{5}{6}}[/tex]
2x - 3y = -5
5x - 22 = -4y
Solve In Multiplication Method
Answer:
(2, 3 )
Step-by-step explanation:
Given the 2 equations
2x - 3y = - 5 → (1)
5x + 4y = 22 → (2) [ rearranged equation ]
Multiplying (1) by 4 and (2) by 3 and adding will eliminate the term in y
8x - 12y = - 20 → (3)
15x + 12y = 66 → (4)
Add (3) and (4) term by term to eliminate y, that is
23x = 46 ( divide both sides by 23 )
x = 2
Substitute x = 2 in either of the 2 equations and evaluate for y
Substituting into (2)
5)2) + 4y = 22
10 + 4y = 22 ( subtract 10 from both sides )
4y = 12 ( divide both sides by 4 )
y = 3
Solution is (2, 3 )
If f(x) = 3x + 2 and g(x) = x2 + 1, which expression is equivalent to (fog)(x)?
(3x + 2)(x2 + 1)
O 3x 2 + 1 + 2
(3x + 2)2 + 1
3(x2 + 1) + 2
Answer:
This means you would plug in g(x) into f(x).
Step-by-step explanation:
It would look like this:
[tex]3(x^{2} + 1) + 2[/tex]
the top of a square table is144 squared metres.what is the size of the table
Answer:
12 meters x 12 meters
Step-by-step explanation:
√144 = 12
width of picture 7 3/5 cm. to fit in the frame the picture cannot be more than 7 3/10 cm. how much should the picture be trimmed
Answer:
1/5
Step-by-step explanation:
width of picture 7 3/5 cm. to fit in the frame the picture cannot be more than 7 3/10 cm. how much should the picture be trimmed
Given that :
Original Width of picture = 7 3/5 cm
Width required for picture to fit into frame=7 3/10
For picture to fit into frame:
(7 3/5 - 7 3/10) must be trimmed off from the frame.
(7 3/5 - 7 3/10)
(7 - 7) = 0
(3/5 - 3/10)
Taking the L. C. M
(6 - 3) / 10
= 2 / 10
= 1/5
THEREFORE, 1 / 5 of the width should be trimmed in other to ensure the picture fits into the frame.
When a number is divided by 9 and its quotient is 12 and a remainder of 2
Answer:
Step-by-step explanation:
_____ / 9
2/12
Multiply the divisor (9) by the quotient (12) and to the result add the remainder (2).
9 × 12 + 2 =
108 + 2 = 110
110 is the number divided.
110/9
20/12
2
5/14, 7/10, 5/6, 11/15, 19/2
Answer:
5/14 = 0.36
7/10 = 0.7
5/6 = 0.83
11/15 = 0.73
19/21 = 0.9
(round to the tenth)
so the answer is;
5/14, 7/10, 11/15, 5/6, 19/21
Step-by-step explanation:
Hope it helps!
Angie has 18 oatmeal cookies.She splits them evenly among b bags.Choose the expression that shows how many cookies are in each bag. 1.B-18 2.18/b 3.18 4.B
Answer:
2, 18/b
Step-by-step explanation:
if you divide by the number of bags you will get the number of cookies in each bag.
Answer:2,18/b
Step-by-step explanation:If you multiply the cookies in a bag by b, you will get 18
The lowest point in Asia is the Dead Sea, which is 396 meters below sea level. The lowest point in the USA is Death Valley, at 86 meters below sea level. How much high is Death Valley than the Dead Sea
Answer:
310 metres
Step-by-step explanation:
The lowest point in Asia is the Dead Sea, which is =396 meters below sea level.
The lowest point in the USA is Death Valley, a= 86 meters below sea level.
Therefore,
diference in their heights = 396-86 metres =310 metres
Answer:
310 meters higher
Step-by-step explanation:
396-86=-310
The difference btween -396 and -86 is the same as |396| and |86| so you can just subtract the positive numbers.
What is the slope of the line containing the midpoint of the segment with endpoints at (2, 4) and (0, -2) and the midpoint of the segment with endpoints at (5, 1) and (1, 5)?Express your answer in simplest form. Plzzzz help!!!!
Answer:
slope = 1
Step-by-step explanation:
midpoint of (2, 4) and (0, -2)
(2 + 0)/2 = 1 and (4 + -2)/2 = 1
(1, 1)
midpoint of (5, 1) and (1, 5)
(5 + 1)/2 = 3 and (1 + 5)/2 = 3
(3, 3)
slope = (3-1)/(3-1) = 2/2 = 1
please help me answer these in variable and constant terms 7s + 8s - 6h
Answer:
see below
Step-by-step explanation:
7s + 8s - 6h
7 8 and -6 are coefficients
s and h are variables
We can combine like terms
15s -6h
15 and -6 are coefficients and
s and h are variables
Answer:
Variable Terms: (Alphabets)
s and h
Constant terms: (Numbers)
No constants
Coefficient terms: (Numbers with alphabets)
7 , 8 and -6
50 POINTSS!! While preparing a roof, patty drops a screwdriver from a height of 80 feet. The function (h)t = -16t^2 + 80 gives the height of the screwdriver in the feet as feet after t seconds during its fall. Which of these is the graph of the function
Answer:
Graph D
Step-by-step explanation:
(h)t = -16t^2 + 80
At time t = 0 the screwdriver is at 0+80 =80 ft
As time increases the height will decrease so we can eliminate graph B
We know this is a downward parabola by the - in front of the t^2 so we can eliminate graph A
We need to find where it meets the x axis
0 = -16t^2 + 80
-80 = -16t^2
5 = t^2
t = sqrt(5)
t =2.23
This is Graph D
BRAINLIEST!!! Plz help ASAP
M(5, 7) is the midpoint of side RS.The coordinates of S are (6, 9). What are the coordinates of R?Please answer with full explanation and no non sense answers will reports. Will give brainiest to those who answered correctly with full explanation. Thank you.
Answer: R = (4, 5)
Step-by-step explanation: Midpoint is simply the center of a line. So, the equation for it is ((x1+x2)/2, (y1+y2)/2). Hence for this,
x coordinate- (6+x)/2=5
x=4
y coordinates- (9+y)/2=7
y=5
And therefore R is (4, 5)
