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?
Answers
Answer: Obtion B
[tex]P = 1.3e ^ {-0.038t}\\\\P = 2.1e ^ {-0.046t}[/tex]
Step-by-step explanation:
The equation for exponential decay has the following form:
[tex]y = pe ^{-rt}[/tex]
Where
p is the initial population
r is the rate of decrease
t is time.
In this problem we have to:
The current population of insect A to be 1.3 million and the current population of insect B to be 2.1 million.
So
[tex]p_1 = 1.3[/tex] in millions
[tex]p_2 = 2.1[/tex] in millions
We also need the populations of insect to be reduced at a rate of 3.8% and insect to be reduced at a rate of 4.6%.
so:
[tex]r_1 = 0.038\\\\r_2 = 0.046[/tex]
then the exponential decay equation for insect A is:
[tex]P = 1.3e ^ {-0.038t}[/tex]
the exponential decay equation for insect B is:
[tex]P = 2.1e ^ {-0.046t}[/tex]
Finally, the system of equations is:
[tex]P = 1.3e ^ {-0.038t}\\\\P = 2.1e ^ {-0.046t}[/tex]
The answer is the Option B
Related Questions
CAN SOMEONE HELP ME ANSWER THIS
Answers
Answer:
The area of the triangle is 24 square feet.
Step-by-step explanation:
To find the area of the triangle you have to multiply the base and height, and then multiply the answer with 1/2.
First, multiply the base of the triangle, which is 8 feet, with the height of the triangle, which is 6 feet. Then your answer will be 48 and you can multiply that with 1/2, or divide it by two. The final answer will be 24 square feet.
Pls help!!
complete the equations so that the solution of the equations is (-3,5)
y=__x-10
3x-__y=-19
Answers
Answer:
y=-5x-10
3x-2y=-19
We can actually see here that the completed equations are:
1. y = -5x - 10
2. 3x - 2y = -19
How we arrived at the solution?To find the missing values in the equations such that the solution is (-3, 5), we substitute the values of x = -3 and y = 5 into the equations and solve for the missing values.
For the equation y = x - 10:
Substituting x = -3 and y = 5:
5 = -3 - 10
5 = -3__ - 10
5 + 10 = -3__
15 = -3__
__ = -5
Therefore, the missing value is -5. The completed equation is:
y = -5x - 10
For the equation 3x - y = -19:
Substituting x = -3 and y = 5:
3(-3) - 5 = -19
-9 - 5 = -19
-9 + 19 = 5
10 = 5__
__ = 2
Therefore, the missing value is 2. The completed equation is:
3x - 2y = -19
The completed equations are:
y = -5x - 103x - 2y = -19When x = -3 and y = 5, both equations will have a solution of (-3, 5).
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how many angles measure 70 degrees
Answers
The answer is 3. A, D, and C are vertical angles and match to the angle marked 70 degrees.
Plz help me with this
Answers
Answer: Equivalent
Step-by-step explanation:
When given a system of equations, the definitions of the solution are:
Consistent & Independent: exactly ONE solution (lines intersect)Consistent & Dependent: INFINITE solutions (same line)Inconsistent: NO solutions (parallel lines)In the given graph, the lines are the same, which means they have INFINITE solutions --> The system is Consistent & Dependent = Equivalent
Solve for u.
35 = u/2 + 12
THaNks :)
Answers
35-12=u/2
23=u/2
u=46
Answer
Answer:
The value of u is 46
Step-by-step explanation:
The given expression is;
[tex]35=\frac{u}{2} +12[/tex]
We multiply through by 2 to get;
[tex]2\times35=2\times \frac{u}{2} +12\times 2[/tex]
[tex]70=u +24[/tex]
Group similar terms to obtain;
[tex]70-24=u[/tex]
[tex]46=u[/tex]
The value of u is 46
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In 15 minutes Frankita created 15 drawings. In 30 minutes she created 17 drawings. In 45 minutes she created 20 drawings. In 60 minutes she created 24 drawings. If Frankita continues making drawings in the same pattern, how many total drawings will Frankita have created at the end of 90 minutes?
A. 19
B. 28
C. 33
D. 35
Answers
Answer:
D. 35
Step-by-step explanation:
the pattern followed by Frankita is:
15 min = 15 drawing
30 min = 17 drawing : increase by 2 (15+2 = 17)
45 min = 20 drawing : increase by 3 (17+3 = 20)
60 min = 24 drawing : increase by 4 (20+4 = 24)
75 min = 29 drawing : increase by 5 (24+5 = 29)
90 min = 35 drawing : increase by 6 (29+6 = 35)
PLEASE HELP!!!!!!!!!!!!!Lance is 5 feet tall. His shadow is 8 feet long. At the same time of day trees shadow is 32 feet long. What is the height of the tree in feet.
Answers
Answer:
20 ft
Step-by-step explanation:
The right triangles formed by Lance and his shadow and the tree and it's shadow are similar, hence the ratios of corresponding sides are equal.
Let the height of the tree be h, then
[tex]\frac{5}{h}[/tex] = [tex]\frac{8}{32}[/tex] = [tex]\frac{1}{4}[/tex]
cross- multiply to obtain
h = 5 × 4 = 20
The height of the tree is 20 ft
Answer:
20 feet
Step-by-step explanation:
5 feet Object = 8 feet shadow
8 feet shadow = 5 feet Object
8 feet shadow = 5 feet Object
1 foot shadow = 5 ÷ 8 = 5/8 foot object
1 foot shadow = 5/8 foot object
32 feet shadow = 5/8 x 32 = 20 feet object
kendra is doing her math homework. For each problem, she uses 1/2 sheet of paper. how many sheet of paper does she need to complete 10 problem?
Answers
Answer:
5
Step-by-step explanation:
each problem takes 1/2 so 1 page fits 2 problems and 2 can go into 10 5 times
Answer:
5 sheets of paper
Step-by-step explanation:
if it only took her half a page to do one problem, then she could fit 10 problems on 5 pages since 1/2 of 10 is 5
i hope this helps :)
41) Gabriella invests $8,193 in a retirement
account with a fixed annual interest rate of
8% compounded 6 times per year. What
will the account balance be after 18 years?
A) $31,340.53 B) $37,085.87
C) $34,252.67 D) $40,729.29
Answers
Answer:
Option C. [tex]\$34,252.67[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=18\ years\\ P=\$8,193\\ r=0.08\\n=6[/tex]
substitute in the formula above
[tex]A=\$8,193(1+\frac{0.08}{6})^{6*18}=\$34,252.67[/tex]
Use substitution to solve the linear system of equations.
y = x - 2
2x + 4 = y
1. (-6,8)
2. (6,8)
3. (-6,-8)
4 .(6,-8)
Answers
Answer:
3.(-6,-8)
Step-by-step explanation:
y=x-2
2x+4=y
x-2=2x+4
x=2x+6
-x=6
x=-6
y=-6-2
y=-8
Step 1: Wherever you see a y in the equation: 2x + 4 = y insert x - 2
2x + 4 = x - 2
Step 2: Combine like terms
x's go with x's. To do this subtract the x from the right side to both sides
(2x - x) + 4 = (x - x) - 2
x + 4 = 0x - 2
x + 4 = -2
Normal numbers go with normal numbers (4 and -2). Bring the 4 to the right side by subtracting it to both sides
x + (4 - 4) = -2 - 4
x + 0 = -6
x = -6
Step 3: To solve y put -6 where you see an x in the equation: y = 2x + 4
y = 2(-6) + 4
y = -12 + 4
y = -8
(-6,-8)
Hope this helped!
If Melissa estimates she would read 250 but she read 290 what is the percent error
Answers
Answer: 13.8%
Step-by-step explanation:
Percent error = approximate-exact/exact x 100
250-290/290 x 100 = |-13.8| = 13.8%
I thought of a number. My number doubled is 20 bigger than 200. Find my number.
Answers
Answer:
110
Step-by-step explanation:
200+20=220
220/2=110
Answer:
110?
Step-by-step explanation:
because 110 times 2 is 220. and 220 is 20 bigger than 200.
2, 6, 18, 54,....
Find the common ratio of the given sequence, and write an exponential function which represents the sequence. Use n = 1, 2, 3, ...
A) 3; f(n) = 2(3)n-1
B)
1
3
; f(x) = 2(3)n-1
C) 3; f(n) = 2(
1
3
)n-1
D)
1
3
; f(n) = 2(
1
3
)n-1
Answers
Answer:
3; [tex]f(n)=2(3)^{n-1}[/tex]
Step-by-step explanation:
The given sequence is
2, 6, 18, 54,....
The first term is [tex]f(1)=2[/tex]
The common ratio is obtained expressing a subsequent term over a previous term.
The common ratio is [tex]r=\frac{6}{2} =3[/tex]
The the nth term of the sequence is given by:
[tex]f(n)=f(1)(r^{n-1})[/tex]
[tex]f(n)=2(3)^{n-1}[/tex]
The exponential function which represents the sequence is
[tex]f(n)=2(3)^{n-1}[/tex]
Answer:
A
Step-by-step explanation:
i got it correct on usatestprep
Find the value of x in the triangle shown below
Answers
Answer:
The answer is A. sq. root of 11
Step-by-step explanation:
Use a2+b2=c2
So, 25+b2=36
b2=11
b=sq root 11
Clay can run one lap around the track in 1/4 of an hour. How many hours will it take him to run 5 1/3 laps around the track?
Answers
The time it will take him to run 5 and 1/3 loops around the track is 4/3 hours.
What is the rate?The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
Clay can run one lap around the track in 1/4 of an hour. The number of hours that takes him to run 5 and 1/3 laps around the track will be given as,
⇒ (5 + 1/3) x (1/4)
⇒ (16/3) x (1/4)
⇒ 4/3 hours
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In your own words, describe the process for solving a system of linear equations using the Substitution method.
Answers
Answer with explanation:
For any system of linear equations, we can use a method called substitution method for solving the equations.
We make one variable, from either of the equations, the subject of that equation and substitute it in the other equation.
This way, we get to find the value of the remaining variable and next we substitute this value in one of the equations to get the value of the variable left.
Final answer:
To solve linear equations using substitution, identify the unknowns, isolate a variable in one equation, substitute into the other to solve for one variable, then back-substitute to find the other variable and check the solutions for accuracy.
Explanation:
Solving Systems of Linear Equations Using Substitution
To solve a system of linear equations using the substitution method, one must follow a series of steps. Step one is to identify what needs to be determined, which in this case, is the values for the variables, known as the unknowns. In step two, find an equation in the system where one variable can be easily isolated. Next, in step three, express this isolated variable in terms of the other variable.
Once you have this expression, you move to step four, where you substitute this expression into the other equation in the system. This allows you to solve for the one remaining variable, eliminating the need for the original substituted variable. After finding this value, you proceed to step five and substitute it back into the expression from step three to find the value of the other variable.
Step six is an important verification step - checking the solutions. Substitute the values found for both variables back into the original equations to ensure that they satisfy both equations. If they do, you have found the solution to the system. If not, you need to review your steps to find any possible mistakes.
2х - Зу = 16
5x - Зу = 13
Answers
Answer:
[-1, -6]
Step-by-step explanation:
Since both coefficients next to your y's are identical use the Elimination Method by multiplying one of the equations by -1 to form additive inverses, meaning they result in 0:
-1[{2x - 3y = 16}]↷
{5x - 3y = 13}
{-2x + 3y = -16
{5x - 3y = 13
----------------
3x = -3 [Divide by 3]
x = -1
y = -6 [plug in "-1" back into both equations to confirm their authenticities]
https://youtu.be/zcC7wsn3b2g
Watch the above You-Tube link and subscribe for more information on how to solve a system of equations in two to three variables [USERNAME: MATHEMATICS WIZARD].
I am joyous to assist you anytime.
The total cost of 6 boxes of candy is $14.10. What is the average cost of one item?
Answers
The average cost of one box of candy is 2.35 per box
it’ll be $2.35 per box
How to find the answer:
14.10 divided by 6 = 2.35
Make a table and graph the function Y=3x+2
Answers
Answer:
Step-by-step explanation:
Just by looking at y = 3x + 2, we can see that the slope of the line representing this function is 3 and the y-intercept is 2 (or (0, 2) ).
Plot (0, 2). Starting from that point, move your pencil 1 unit to the right and 3 units up, plotting another dot there.
Draw a straight line thru your two dots.
A table and graph that represents the linear function y = 3x + 2 is shown in the image below.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + b
Where:
m represent the slope or rate of change.x and y are the points.b represent the y-intercept or initial value.Since the given linear equation y = 3x + 2 is in slope-intercept form, we would start by plotting its y-intercept on a graph;
y = 3(0) + 2
y = 2.
Lastly, we would use an online graphing calculator to plot the given linear equation for the values in its domain as shown in graph D attached above.
In conclusion, the slope of this linear equation y = 3x + 2 is equal to 3 and it does not represent a proportional relationship.
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Solve the following compound inequality. 2x - 2 > -6 OR -2x < -12
A. x > 6
B. x > -2
C. -2 < x < 6
D. x < -2 OR x > 6'
Answers
Answer:
B. x > -2Step-by-step explanation:
2x - 2 > -6 add 2 to both sides
2x - 2 + 2 > - 6 + 2
2x > -4 divide both sides by 2
2x/2 > -4/2
x > -2
or
-2x < -12 change the signs
2x > 12 divide both sides by 2
2x/2 > 12/2
x > 6
We have x > -2 or x > 6. Therefore x > -2.
I'll make you brainliest Easyquestion 6th grade multiply and add fractions pleaze answer it ASAP
Answers
Answer:
C
Step-by-step explanation:
Area (A) = length × width
A = 7 [tex]\frac{1}{2}[/tex] × 9 [tex]\frac{1}{8}[/tex]
Change both mixed numbers to improper fractions
7 [tex]\frac{1}{2}[/tex] = [tex]\frac{15}{2}[/tex]
9 [tex]\frac{1}{8}[/tex] = [tex]\frac{73}{8}[/tex]
Hence
[tex]\frac{15}{2}[/tex] × [tex]\frac{73}{8}[/tex]
= [tex]\frac{15(73)}{2(8)}[/tex]
= [tex]\frac{1095}{16}[/tex]
= 68 [tex]\frac{7}{16}[/tex]
Answer:
= 68 7/8
Step-by-step explanation:
I think it's correct
If X = 2 centimeters, Y = 4 centimeters, and Z = 7 centimeters, what is the area of the object?
A.
28 square centimeters
B.
56 square centimeters
C.
36 square centimeters
D.
24 square centimeters
Answers
Answer:
56 square centimeters
Step-by-step explanation:
2*4 =8
8*7 =56
The total area is 36 square cm if the X = 2 centimeters, Y = 4 centimeters, and Z = 7 centimeters option (C) is correct.
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
We have:
X = 2 centimeters, Y = 4 centimeters, and Z = 7 centimeters
Here no other details have been provided, so we are assuming we have two rectangles dimensions for the first is 2×4, and for the second 4×7
Total area = 2×4 + 4×7 = 8+28 = 36 square cm
Thus, the total area is 36 square cm if the X = 2 centimeters, Y = 4 centimeters, and Z = 7 centimeters
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Anne bought 3 hats for $19.50. which equation could be used to find the cost of each equation?
Answers
Answer:
19.50x 3 or 19.50+19.50+19.50
Step-by-step explanation:
You could either multiply it or divide!
Hope I helped!!
:)
_ _ _cos b =1/2[sin(a+b)+sin(a-b)]
A) cos b
B) sin b
C) sin a
D) cos a
Answers
Answer:
sin a
Step-by-step explanation:
let the unknown term be x.
[tex]x.cos \: b = \frac{1}{2}(sin(a + b) + sin(a - b)) \\ or \: x = \frac{ \frac{1}{2} 2sinacosb}{cosb} \\ or \: x = sin \: a[/tex]
you have to remember that:
2sinAcosB=sin(A+B)+sin(A-B)
(-2.5)+(-4.5)=7 how to justify this?
Answers
Answer:
Negative + Negative = positive.
Positive + Positive= Negative
Negative + Positive= Negative
Step-by-step explanation:
What you solving is the first choice Negative + Negative = positive.
So positive is the answer of course!!!
Plz Mark Brainlistt!!!!! plzzzz
Answer:
False
Step-by-step explanation:
No solution. Incorrect equation. -2.5 -4.5 is = -7 which is NOT ≠ to 7
Which equation can be used to represent "three minus the difference of a number and one equals one-half of the difference of three times the same number and four”?
Answers
Answer:
You never gave any options, but the right answer is 3-(x+1)=1/2(3x+4)
Step-by-step explanation:
Answer:
3 - (n - 1) = (1/2)(3n - 4)
Step-by-step explanation:
Next time, please share the possible answer choices. Thank you.
"three minus the difference of a number and one"
can be represented algebraicallyl as 3 - (n - 1), where n is the number.
"one-half of the difference of three times the same number and four” can be represented by (1/2)(3n - 4).
The desired equation is thus:
3 - (n - 1) = (1/2)(3n - 4)
Can someone please help me? Homework is due tom
Answers
Answer:
5 7/8
Step-by-step explanation:
12 3/4 = 12 6/8
1 3/8 = 1 3/8
5 1/2 = 5 4/8
1 3/8+5 4/8 = 6 7/8
12 6/8 = 11 14/8
11 14/8-6 7/8 = 5 7/8
Hey Guys! Im new here and hoping to really get to use this website! Hope you guys could answer my question!
The length of a rectangle is three centimeters less than the width. If the area of the rectangle is 54cm^2, find the dimensions of the rectangle.
Answers
Answer:
Width =9 cm
Length =6 cm
Step-by-step explanation:
Let x be width, then length is x − 3
Let area be E. Then we have: E = x ⋅ (x −3)
54= x^2-3x
x^2-3x-54=0
We then do the Discriminant of the equation:
D=9+216
D=225
X1=3+15 over 2. which is 9
X2= 3-15. over 2. which is -6 Which is declined, since we can't have negative width and length.
Therefore x is 9. So width
So width = x = 9cm and length is x-3 = 9-3cm=6 cm
Can someone plz help with Math inequalities. PLZ EXPLAIN!!! Just everything to do with them and timelines with them and stuff. Eg: 625 Thanks
Answers
Answer:
>6x=25<
Step-by-step explanation:
You will take the numbers (however many) multiply them and then use the two signs (greater than less than) to figure which it is. For additional help ask your teacher :)
Thank of it this way:
2 > 1 : this means that this little Pac-Man want to eat the bigger number so it would be the same if you have
1 < 2 : here 2 it's still greater then 1
1/2 = 0.5 : here we don't have a pacman but you know that 1/2 It's actually 0.5
So now if you have:
2n > -4 [divide by 2]
n > -2
And if you have a (image) Then this means that x is greater that -2 but it's less than 1, so x would be between -2 and 1
Hope this helps, ask any questions if you have.
When does the price of an item increase?
Answers
when it rises in popularity so they can raise the price and people will pay more for it (eg freddos /-/)
or sometimes the item price increases because it has cost the company more to make the product (eg shipping fares) so they need to charge more so they can still earn a profit (like fuel?)
When the Production of any good in a Particular year, is in decline, and if that good is very much essential for Human Being, then the Price of that Commodity increases.
Usually most of Natural good that is found on earth is very essential for Human being. So, when production of that good Decreases, then Price of that Commodity increases.