Final answer:
To find the total number of road kill in the three collections, we set up and solve an equation. Each species is assigned a variable, and using the information given, we can find the number of animals in each collection.
Explanation:
To find the total number of road kill in the three collections, we need to determine how many animals are in each collection. Let's assign variables to each species: bobcats = x, beavers = 16.1%x, foxes = x + 4, otters = x - 4, fishers = 16.1%. Given that each collection makes up one-third of the total, we can set up the equation: x + 16.1%x + x + x - 4 + 16.1%x = (1/3) * total. Simplifying the equation, we get 3.3x - 4 = (1/3) * total. Since beavers make up 16.1% of the total, we can substitute 16.1%x for beavers in the equation: 3.3x - 4 = (1/3) * total. Solving for x, we get x = (4 + (1/3) * total) / 3.3. Since bobcats and beavers have the same number, x = 16.1%x, which can be written as x = 0.161x. Equating the two, we get x = 0.161x. Finally, solving for x, we find that x = 0.161x, which simplifies to x = 0.161x. Therefore, each collection has the following numbers of animals: bobcats = 0.161x, beavers = 16.1%x, foxes = x + 4, otters = x - 4, and fishers = 16.1% total.
What is the answer to
3n-5=7n+11
Pablo is buying chips and salsa for a party and has a budget of no more than $36.Chips cost $3 per bag and a container of salsa costs $4
How to get my mother to celebrate her birthday, she thinks that it is not important and that she should not celebrate her birthday, how do i convince her to celebrate her birthday? Please help me...!
Which of the following sets of four numbers has the largest possible standard deviation? (1, 2, 5, 6) (4, 5, 5, 6) (1, 3, 5, 7) (6, 7, 8, 9)
m∠6 is (2x – 5)° and m∠8 is (x + 5)°. What is m∠3?
Answer:
m∠3=115°.
Step-by-step explanation:
It is given from the figure that line q is parallel to s and r is the transversal.
Since, m∠6 and m∠8 forms a linear pair as they are on the straight line r, therefore using the linear pair property, we have
m∠6+m∠8=180°
⇒[tex]2x-5+x+5=180^{\circ}[/tex]
⇒[tex]3x=180^{\circ}[/tex]
⇒[tex]x=60^{\circ}[/tex]
Thus, the measure of ∠6 is [tex]2x-5=2(60)-5=120-5=115^{\circ}[/tex]
Now, m∠3=m∠6=115° as both m∠3 and m∠6 forms the alternate interior angle pair.
Therefore, the measure of m∠3=115°.
Compute the amount of interest earned in the following simple interest problem. A deposit of $1,295 at 7% for 180 days = _____. (Note: Use 365 days in a year)
The interest earned on a deposit of $1,295 at a 7% annual rate for 180 days is approximately $44.70.
To compute the amount of interest earned we can use the simple interest formula:
Interest = Principal × Rate × Time
Since simple interest does not complicate by itself, and the time is less than a year, we'll adjust the time and rate accordingly.
First, we express the annual interest rate as a decimal by dividing the percentage by 100:
Rate = 7% / 100 = 0.07
Next, we convert the time period of 180 days into years, considering there are 365 days in a year:
Time = 180 days / 365 days/year = 0.49315 years (approximately)
Now, let's plug the values into the simple interest formula:
Interest = $1,295 × 0.07 × 0.49315
Calculating the interest:
Interest = $44.70
At sumer camp the ratio of boys to girls is 7:3 if there were 63 boys how many girls were there
If ƒ(x) = 2x2 + 3, then which of the following represent ƒ(x + 1)?
A. 2x^2 + 2
B. x^2 + 3
C. 2x^2 + 4x + 1
D. 2x^2 + 4x + 5
Answer:
option (d) is correct.
[tex]f(x+1) = 2x^2+4x+5[/tex]
Step-by-step explanation:
Given : [tex]f(x) = 2x^2 + 3[/tex]
We have to choose out of given option which represent f(x + 1)
Consider the given function [tex]f(x) = 2x^2 + 3[/tex]
Since we have to find f( x + 1 ) , replace x by x + 1 in the given function f(x) , we have,
[tex]f(x+1) = 2(x+1)^2+3[/tex]
Using algebraic identity, [tex](a+b)^2=a^2+b^2+2ab[/tex] , we have,
[tex]f(x+1) = 2(x^2+1+2x)+3[/tex]
Simplify the expression by multiplying 2 with each term in bracket, we have,
[tex]f(x+1) = 2x^2+2+4x+ 3[/tex]
Simplify , we have,
[tex]f(x+1) = 2x^2+4x+5[/tex]
Thus, option (d) is correct.
In the game of roulette, a player can place a $4 bet on the number 22 and have a 1/38 probability of winning. If the metal ball lands on 22, the player gets to keep the $4 paid to play the game and the player is awarded $140. Otherwise, the player is awarded nothing and the casino takes the players $4. What is the expected value of the game to the player? If you played the game 1000 times, how much would you expect to lose? ...?
Final answer:
The expected value of the game to the player is $3.68. If played 1000 times, the player would expect to lose $320.
Explanation:
Expected value for the game:
Probability of winning (landing on 22): 1/38Payout for winning: $140 + $4 initial bet = $144Cost of playing (losing bet): -$4Expected value = (Probability of winning * Payout for winning) + (Probability of losing * Cost of losing)Expected value = (1/38 * $144) + (37/38 * -$4)Expected value = -$0.2105 per gameExpected Loss in 1000 Games:
Expected loss per game = -$0.2105Expected loss in 1000 games = Expected loss per game * Number of gamesExpected loss in 1000 games = -$0.2105 * 1000Expected loss in 1000 games = -$210.50Therefore, you can expect to lose an average of $210.50 if you play this game 1000 times.
Which of the following points are solutions to the system of inequalities shown below? Check all that apply. x + y 5 + 2 y > 2 A. (1, 1) B. (5, 2) C. (2, 5) D. (3, 6) E. (1, -1) F. (2, -5)
The points that are solutions to the system of inequalities x + y 5 + 2 y > 2 below are (5, 2), (3, 6), (1, 1). Options B, C, A, and D. For is mathematically given as
What are inequalities?Generally, inequalities are simply defined as the relationship between two non-equal expressions using a symbol like "not equal to," "greater than," or "less than."
In conclusion, The points (5, 2), and (2, 5), (1, 1) are the ones that are the solutions to the system of inequalities x + y 5 + 2 y > 2 below (3, 6).
For (5, 2),
5 + 2* 5 + 2 *2 > 2
19>2
For (2, 5)
2 + 5* 5 + 2*5 > 2
37>2
For (3, 6).
3 + 6*5 + 2*6 > 2
45>2
For (1, 1)
1 + 1* 5 + 2*1 > 2
8>2
For (1, -1)
1 + -1* 5 + 2 *-1 > 2
-6<2
For (2, -5)
2 + -5* 5 + 2*-5 > 2
−33<2
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what is the value of h in the figure below?
the answer on APEX is 6
What is the length of chord in O below?
A. 5 units
B. 5.70 units
C. 2.5 units
D. 10 units
The length of chord CD is 5 unit.
What is Chord?The line segment connecting any two locations on a circle's circumference is referred to as the chord of the circle. It should be emphasised that the diameter is the circle's longest chord, which runs through its centre.
We have,
As, the distance to both chords are 5.70 unit.
and, both chords are 90 degrees from the line then the chords are identical.
As, the length of Chord AB = 5 unit then the length of chord CD =5.
Thus, the length of chord CD is 5 unit.
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Roberto wrote the number 60, if the rule is subtract 3, what is the fifth number in the pattern?
The temperature, t, in Burrtown starts at 21°F at midnight, when h = 0. For the next few hours, the temperature drops 4 degrees every hour. Which equation represents the temperature, t, at hour h?
A. t = 21h + 4
B. t = 4h + 21
C. t = –4h + 21
D. t = –21h + 4
Answer:
C. t = –4h + 21
Step-by-step explanation:
We know that when h = 0, t = 21°F. Replacing h = 0 in equation A and D we get:
A.
t = 21h + 4
t = 21(0) + 4
t = 4
D.
t = –21h + 4
t = –21(0) + 4
t = 4
So, none of them are correct.
The temperature drops 4 degrees every hour, this means that for h = 1 then t = 21 - 4 = 17. Replacing h = 1 in equation B and C we get:
B.
t = 4h + 21
t = 4(1) + 21
t = 25
C.
t = –4h + 21
t = –4(1) + 21
t = 17
In consequence, C is the correct option.
Ben has $3.40 consisting of quarters and dimes. How many coins of each kind does he have if he has 22 coins?
Show a system of equation to represent the word problem.
There are 8 quarters and 14 dimes.
Step-by-step explanation:Let there are x quarters.
and y dimes.
Also as we know,
1 quarter= 0.25 dollar
Hence, x quarter= $ 0.25x
and 1 dime= $ 0.10
Hence, y dimes= $ 0.10y
Ben has $3.40 consisting of quarters and dimes.This means that:
0.25x+0.10y=3.40
Also, in non-decimal form it could be written as:
25x+10y=340
He has 22 coinsThis means that:
x+y=22
Now on solving it graphically we see what is the point of intersection of the two lines or system of linear equations.
We get the point of intersection as: (8,14)
i.e. x=8 and y=14
Hence, there are 8 quarters.
and 14 dimes.
Which of these problem types can not be solved using the Law of Sines?
A. SSS
B. ASA
C. AAS
D. SAS
Answer: The correct option are A, B and D.
Explanation:
The law of sine states that,
[tex]\frac{\sin A}{a} =\frac{\sin B}{b}=\frac{\sin C}{c} [/tex]
Where A, B, C are interior angles of the triangle and a, b, c are sides opposite these angles respectively as shown in below figure.
Since we need the combination of two angles and one side or two sides and one angle.
The Law of sine is useful for AAS and SSA type problems.
Reason for correct option:
In option A three sides are known but no angle is not given, therefore the SSS problem can not be solved by Law of sine and the option A is correct.
In option B a side is known and two inclined angle on that line are known. But to use Law of sine we want the line and angle which in not inclined on that line, therefore the ASA problem can not be solved by Law of sine and the option B is correct.
In option D two sides and their inclined angle is known. But to use Law of sine we want the side and angle which in not inclined on that line, therefore the SAS problem can not be solved by Law of sine and the option D is correct.
Reason for incorrect option:
In option C, the two consecutive angles are given and a side which makes the second angle with base side, therefore the first angle is opposite to the given side, so the law of sine can be used for AAS problems.
Therefore, option C is incorrect.
is .485 lower than .5
In 2007, the FDIC’s insurance limit was $100,000 per person per bank. If Sam had a $150,000 savings account and $80,000 checking account at Bank J, a $95,000 money market account at Bank K, and a $200,000 savings account at Bank L, how much of Sam’s money was FDIC insured? a. $295,000 b. $300,000 c. $375,000 d. $525,000
What is the value of x+2x when x=4 ? Enter your answer in the box.
WHICH CONSTRUCTION DOES THE IMAGE BELOW DEMONSTRATE??
A square circumscribed about a circle
A square inscribed in a circle
The circumcenter of a square
The incenter of a square
Answer:
This is a square inscribed in a circle.
Step-by-step explanation:
Y=log x If y=10, then what is x?
A.
10
B.
1
C.
100
D.
10^2
3.
What is 10*9*8*7*6*5*4*3*2*1?A.
10! or 3628800
B.
100
C.
1000
D.
10^10
Answer:
First question, x= 10^10.
Second question is 10!. or 362880
Step-by-step explanation:
First Question:
Simple logx has a base of 10, i.e log10 x,
the question will be 10 = log10 x,
when taking the base "10" from the right side to the left, the number on the left side becomes the power of the base, in this case 10 from the right will be base and 10 from the left will power and log will vanish.
x=10^10.
Another example with different numbers
Y=logx if Y= 12, What is x?
The base is ten when not given,so:
12=logx
10^12=x
Second Question;
simple multiplication just multiply the numbers.
10! is pronounced as 10 factorial,
5! will be 5x4x3x2x1=120
What is the value of the function y = 2x + 3 when x=−1
5
2
1
−5
Answer:
I took the test its 1
Step-by-step explanation:
which ordered pair is a solution of the equation: y=4x/
1.(1,3)
2.(-1,-4)
3.(-4,-1)
4.(1,-4)
A rancher has 100 meters of fencing to enclose two adjacent rectangular corrals. The rancher wants the enclosed area to be 350 square meters. What dimensions should the rancher use to obtain this area?
Final answer:
The dimensions of each corral should be 40 meters by 10 meters.
Explanation:
To find the dimensions of the rectangular corrals, we can set up an equation using the perimeter and area of the enclosed space. Let's call the length of one corral x and the width y. The perimeter of the two corrals is 2x + 2y, which equals 100 meters. The area of the enclosed space is xy, which equals 350 square meters.
Using these equations, we can solve for x and y. Rearranging the perimeter equation, we get x = 50 - y. Substituting this into the area equation, we have (50 - y)y = 350.
Simplifying the equation, we get y^2 - 50y + 350 = 0. This is a quadratic equation that can be factored as (y - 35)(y - 10) = 0. Therefore, the possible values for y are 35 and 10.
Since we are looking for positive values for the dimensions, we choose the values y = 10 and x = 50 - y = 50 - 10 = 40. Therefore, the dimensions of each corral should be 40 meters by 10 meters.
To find the dimensions of the rectangular corrals, we can set up a system of equations. By solving the system of equations, we find that the dimensions of the rectangular corrals can be either 25 meters by 14 meters or 7 meters by 50 meters to obtain a total area of 350 square meters.
Explanation:To find the dimensions of the rectangular corrals, we can set up a system of equations. Let x represent the width of one corral and y represent the length. Since the rancher wants to enclose a total of 350 square meters, we have the equation xy = 350. The perimeter of each corral is 2x + y, so the total amount of fencing used would be 4x + 2y.
Given that the total fencing available is 100 meters, we can set up the equation 4x + 2y = 100. Now we can solve the system of equations:
xy = 3504x + 2y = 100By substituting the value of y from the first equation into the second equation, we can solve for x. After finding the value of x, we can substitute it back into the first equation to find the corresponding value of y. The solutions will give us the dimensions of the rectangular corrals.
Let's solve the system of equations:
350 = x(100 - 2x)350 = 100x - 2x^22x^2 - 100x + 350 = 0x^2 - 50x + 175 = 0(x - 25)(x - 7) = 0The solutions for x are x = 25 and x = 7. Plugging these values back into the equation xy = 350, we find that the corresponding values for y are y = 14 and y = 50, respectively. Therefore, the dimensions of the rectangular corrals can be either 25 meters by 14 meters or 7 meters by 50 meters to obtain a total area of 350 square meters.
What is the ratio 4:6 in simplest form?
Four less than the quotient of a number and 3 is - 10
To solve the equation, let’s translate the given information into an algebraic equation. The solution to the equation is x = -18.
Explanation:To solve the equation, let’s translate the given information into an algebraic equation. Let the number be represented by 'x'. The quotient of the number and 3 is x/3. The problem states that four less than the quotient of a number and 3 is -10, so we can write the equation as:
x/3 - 4 = -10
To solve for x, we can start by adding 4 to both sides:
x/3 = -6
Next, we can multiply both sides of the equation by 3 to isolate x:
x = -18
Therefore, the solution to the equation is x = -18.
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What is the quotient and remainer for 32÷6?
Find the equation of the line tangent to the graph of y = cos(2x) at x = pi/4 ...?
Which of the following quadratic functions has a graph that opens downward?
Check all that apply.
A. y=2x-x^2
B. y= 1/3x^2-8x-13
C. y=2/3x^2-13x+5
D. y= -(3+x^2)
...?
D. Y=-(3+x^2)
A. Y=2x-x^2
Answer:
The answers are a) y=2x-x^2 and d) y=-(3+x^2) and in the attached file are the graphs.
Step-by-step explanation:
Quadratic equations are those where the exponent of the unknown term is squared, that is, the unknown is elevated to exponent 2. They have the general form of a trinomial:
ax2 + bx + c = 0
where a, b and c are real numbers and are called coefficients. Thus, a is the coefficient of x2, b is the term or coefficient of x and c is the independent term.
Matt had a full jar of marbles. He gave Kayla 3/4 of the marbles. Then Kayla returned 1/3 of a jar's worth of marbles to the jar. How much of the jar is now full of marbles?