4. Devin determined the deer population in a rural area is periodic. In 2007, the deer population was at its minimum of 50 deer. By 2010, it had reached its maximum of 250. Estimate the deer population in 2015. Show and EXPLAIN all steps to get full marks. 5. Pegah is floating in an inner tube in a wave pool. She is 0.75m from the bottom of the pool when she is at the lowest point of the wave. Emily starts timing at this point. In 1.25s, she is on the crest of the wave, 2.25m from the bottom of the pool. a) Draw a graph to represent two cycles of this scenario. Show how you got the answers below and label them on the graph. h b) Write an equation to model your graph.
Answers
4. Using a sinusoidal function, we can model the periodic deer population in a rural area. The equation can be expressed as: P(t) = A sin (B(t - C)) + D, where A is the amplitude, B is the period, C is the horizontal shift, and D is the vertical shift. We can use the given data to find the values of these parameters and then use the equation to estimate the deer population in 2015.
To find A, we can subtract the minimum from the maximum population and divide the result by 2. Therefore, A = (250 - 50) / 2 = 100.
To find B, we can use the fact that the period is the time it takes for the function to repeat itself. Since the maximum population occurred in 2010, which is three years after the minimum population in 2007, the period is 3. Therefore, B = 2π / 3.
To find C, we can use the fact that the minimum population occurred in 2007. Therefore, C = 2007.
To find D, we can use the fact that the minimum population is 50. Therefore, D = 50.
Now we can substitute these values into the equation and estimate the deer population in 2015 by setting t = 8 (since 2007 + 8 years = 2015). P(8) = 100 sin(2π/3(8-2007)) + 50 ≈ 150. Therefore, the estimated deer population in 2015 is 150.
5. a)
The graph represents two cycles of Pegah's position in the wave pool as a function of time. The horizontal axis represents time in seconds, and the vertical axis represents height in meters. The red dots represent the positions at which Emily timed Pegah.
The graph consists of two parts: a decreasing sinusoidal curve and an increasing sinusoidal curve. The minimum points occur when Pegah is at the lowest point of the wave, and the maximum points occur when Pegah is at the crest of the wave.
The distance from the bottom of the pool to the crest of the wave is the amplitude, which is 2.25 - 0.75 = 1.5 m. The period is the time it takes for the function to repeat itself, which is 2.5 s (the time it takes for Pegah to go from the lowest point to the crest and back to the lowest point). Therefore, the equation can be expressed as h(t) = -1.5 cos(2π/2.5 t) + 2.
b) The equation for the graph is h(t) = -1.5 cos(2π/2.5 t) + 2. The amplitude is -1.5 and the period is 2.5.
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Related Questions
Jake has $4,000 invested at 8% annual interest. He has $2,800 more to invest. At what rate
must he invest the $2,800 to have a total annual interest of $628?
Answers
Step-by-step explanation:
with $4,000 invested, Jake has
8% × $4,000 = $320 annually.
in order to have annual interest $628, he has to get more interest $(628-320) = $308.
the rate should be:
308/2800 × 100%
= 308 /2800 × 100%
= 11%
Answer:
11%
Step-by-step explanation:
Simple Interest Formula
I = Prt
where:
I = interest earnedP = principalr = interest rate (in decimal form)t = time (in years)Given:
P = $4,000r = 8% = 0.08t = 1 yearTo calculate the interest Jake will earn on his initial investment of $4,000 substitute the given values into the formula and solve for I:
\(\implies \sf I=4000(0.08)(1)=320\)
As he wants to have a total annual interest of $628, he must earn the following interest on his second investment:
\(\implies \sf 628-320=308\)
Given:
I = $308P = $2,800t = 1 yearTo calculate the interest rate for the $2,800 investment, substitute the given values into the formula and solve for r:
\(\implies \sf 308=2800(r)(1)\)
\(\implies \sf r=\dfrac{308}{2800}\)
\(\implies \sf r=0.11\)
\(\implies \sf r=11\%\)
Therefore, Jake must invest $2,800 at the rate of 11%.
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pls help asap if you can!!!
Answers
The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent
How to determine the statementTo determine the correct statement, we need to know the properties of a parallelogram.
These properties includes;
Opposite sides are parallel. Opposite sides are congruent. Opposite angles are congruent. Same-Side interior angles (consecutive angles) are supplementary. Each diagonal of a parallelogram separates it into two congruent triangles.The diagonals of a parallelogram bisect each other.Learn more about parallelogram at: https://brainly.com/question/10744696
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find the area of the region bounded by the curve y= 18 x2−6x−72, the x-axis, and the lines x=−3 and x=3.
The area of the region is (Type an exact answer.)
Answers
The area of the region y = 18x² - 6x - 72, bounded by the curve x-axis and lines x = -3 and x = 3 is equal to -54 square units.
To find the area of the region bounded by the curve y = 18x² - 6x - 72, the x-axis, and the lines x = -3 and x = 3,
Use definite integration.
The area can be calculated by integrating the absolute value of the function y = 18x² - 6x - 72 over the interval [-3, 3].
To find the area, use the following integral,
A = ∫₋₃³ |18x² - 6x - 72| dx
Let's break down the integral into two parts, as the function inside the absolute value changes sign at the roots,
A = ∫₋₃³(18x² - 6x - 72) dx + ∫₋₃³ (-18x² + 6x + 72) dx
Now, integrate each part separately,
For the first part, integrating (18x² - 6x - 72) dx from -3 to 3,
∫₋₃³ (18x² - 6x - 72) dx
= [6x³ - 3x² - 72x] [-3 to 3]
= [(6(3)³ - 3(3)² - 72(3)) - (6(-3)³ - 3(-3)² - 72(-3))]
= [162 - 54 - 216] - [(-162) - 54 + 216]
= -54 - 162 - 54 + 216
= -54
For the second part, integrating (-18x² + 6x + 72) dx from -3 to 3,
∫₋₃³ (-18x² + 6x + 72) dx = [-6x³ + 3x² + 72x] [-3 to 3]
= [(-6(3)³ + 3(3)² + 72(3)) - (-6(-3)³ + 3(-3)² + 72(-3))]
= [(-162 + 27 + 216) - (-162 + 27 - 216)]
= 54 + 162 - 54 - 162
= 0
Adding the two parts together,
A = -54 + 0
= -54
Therefore, the area of the region bounded by the curve y = 18x² - 6x - 72, the x-axis, and the lines x = -3 and x = 3 is -54 square units.
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La suma de las probabilidades de todos los posibles resultados de un experimento aleatorio debe ser igual a
Answers
Respuesta: Uno
La suma de la probabilidad de todos los resultados posibles de un experimento aleatorio debe ser igual a uno.
Porque algunos resultados más ocurren en cada sendero y la suma de todas las probabilidades es 100% o uno.
Espero haber ayudado, buena suerte! :)
Consider function f(x) = 1/x on interval 2, 7.
Find the average slope:
Answers
The average slope of the function f(x) = 1/x on the interval [2, 7] is -1/14.
To find the average slope of the function f(x) = 1/x on the interval [2, 7], you can use the following steps:
average slope = (f(7) - f(2)) / (7 - 2)
1. Calculate the values of the function at the endpoints of the interval: f(2) = 1/2 and f(7) = 1/7.
f(7) = 1/7
f(2) = 1/2
Substituting these values in the formula, we get:
average slope = (1/7 - 1/2) / (7 - 2)
2. Determine the change in the y-values: Δy = f(7) - f(2) = (1/7) - (1/2) = -5/14.
Simplifying the expression, we get:
average slope = (-5/14) / 5
3. Determine the change in the x-values: Δx = 7 - 2 = 5.
Dividing the numerator and denominator by 5, we get:
average slope = -1/14
4. Calculate the average slope by dividing the change in the y-values by the change in the x-values:
average slope = Δy/Δx
= (-5/14) / 5
= -5/70
= -1/14.
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If you have 2 1/2 yards of fabric and want to make 3 pillows how much fabric will you need to use for each pillow
Answers
We know that
• You have 2 1/2 yards of fabric.
,• You want to make 3 pillows.
To find the number of yards of fabric you can use for each pillow, we just have to divide. We know that 2 1/2 is equivalent to 5/2 yards.
\(\frac{\frac{5}{2}}{3}=\frac{5}{2\cdot3}=\frac{5}{6}\)Therefore, you can use 5/6 yards of fabric for each pillow.uh i need help now pls ty
Answers
Answer:
2 and 3/4
Step-by-step explanation:
The pattern is to add 2/4 each time. to find the 6th term, add 2/4 three more times.
1 and 1/4 + 2/4 = 1 and 3/4
1 and 3/4 + 2/4 = 2 and 1/4
2 and 1/4 + 2/4 = 2 and 3/4
WILL GIVE BRAINLIST NO LINKS Ursula has 3 line segments that are the same size. What kind of triangle can she make?
A. equilateral triangle
B. isosceles triangle
C. scalene triangle
D. right triangle
Answers
Answer:
Equilateral triangle
Step-by-step explanation:
Equalateral triangles has 3 60 degre angles, and 3 congruent sides
A chemical compound requires 8 ounces of chemical A and 12 ounces of chemical B. A mixture contains 24 ounces of chemical A and 30 ounces of chemical B. How can you fix the mixture to make the chemical compound?
Answers
I might always be wrong.
Explanation:
Since 8x3=24 and since 12x3=36 you need to add 6oz of chemical B to have 24oz of chemical A and 36oz of chemical B.
Take 1/3 of the total mixture to have 8oz of chemical A and 12oz of chemical B.
Let X and Y be two independent random variable, uniformly distributed over the interval (-1,1). 1. Find P(00). Answer: 2. Find P(X>0 min(X,Y) > 0). Answer: 3. Find P(min(X,Y) >0|X>0). Answer: 4. Find P(min(X,Y) + max(X,Y) > 1). Answer: 5. What is the pdf of Z :=min(X, Y)? Ofz(x):= (1 - x)/2 if z € (-1,1) and fz(z) = 0 otherwise. Ofz(x) = (- 1)/2 if z € (-1,1) and fz(2) = 0 otherwise. Ofz(2) := (2-1)/2 for all z. Ofz(2) := (1 - 2)/2 for all z. 6. What is the expected distance between X and Y? E [X-Y] = [Here, min (I, y) stands for the minimum of 2 and y. If necessary, round your answers to three decimal places.]
Answers
The values are:
P(0)= 1/4P(X>0 min(X,Y) > 0) = 1/2P(min(X,Y) >0|X>0) = 1/4P(min(X,Y) + max(X,Y) > 1) = 3/4 Z :=min(X, Y) fZ(z) = (1 - |z|)/2 if z ∈ (-1,1) and fZ(z) = 0 otherwise. E [X-Y] =01. P(0<min(X,Y)<0) = P(min(X,Y)=0)
= P(X=0 and Y=0)
Since X and Y are independent
= P(X=0) P(Y=0)
Since X and Y are uniformly distributed over (-1,1)
P(X=0) = P(Y=0)
= 1/2
and, P(min(X,Y)=0) = (1/2) (1/2)
= 1/4
2. P(X>0 and min(X,Y)>0) = P(X>0) P(min(X,Y)>0)
So, P(X>0) = P(Y>0)
= 1/2
and, P(min(X,Y)>0) = P(X>0 and Y>0)
= P(X>0) * P(Y>0) (
= (1/2) (1/2)
= 1/4
3. P(min(X,Y)>0|X>0) = P(X>0 and min(X,Y)>0) / P(X>0)
= (1/4) / (1/2)
= 1/2
4. P(min(X,Y) + max(X,Y)>1) = P(X>1/2 or Y>1/2)
So, P(X>1/2) = P(Y>1/2) = 1/2
and, P(X>1/2 or Y>1/2) = P(X>1/2) + P(Y>1/2) - P(X>1/2 and Y>1/2)
= P(X>1/2) P(Y>1/2)
= (1/2) * (1/2)
= 1/4
So, P(X>1/2 or Y>1/2) = (1/2) + (1/2) - (1/4)
= 3/4
5. The probability density function (pdf) of Z = min(X,Y) is given by:
fZ(z) = (1 - |z|)/2 if z ∈ (-1,1) and fZ(z) = 0 otherwise.
6. The expected distance between X and Y can be calculated as:
E[X - Y] = E[X] - E[Y]
E[X] = E[Y] = 0
E[X - Y] = 0 - 0 = 0
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in a fruit basket there were 24 oranges and the rest were lemos if 20% of fruits were lemons how many fruits were there altogether
FAST
Answers
Answer:30
Step-by-step explanation:
The difference between the record high and low temperaturs in Charlotte, North Carolina, is 109°F. The record low temperature was -5°F. Write and solve an equation to find the record high temperature.
Answers
Answer: 104 degrees farenheit
Step-by-step explanation: H = record high temperature. -5 + 109 = H. -5+109 = 109 + (-5) = 109-5 = 104. H = 104.
Answer:
104
Step-by-step explanation:
Let x = record high and y = record low temperature in Charlotte. The difference between the records high and low, x and y, is 109 degrees Fahrenheit, so x - y = 109. Record low is -5, so x - (-5) = 109.
x + 5 = 109
x = 104
given f(x)=3x^6, findf^-1(x)
Answers
Answer:
Step-by-step explanation:
Dhddhhfjvjvmx,sfkiritifkflf,gjgi*jfckblhog
what is 28.5 inches in height?
Answers
Joy Wigens, who works at Putnam Investments, received a check for $2,670. She deposited 1/3 of the check in her Citibank account. How much money does Joy have left after the deposit?
Answers
Answer: $1,780
Step-by-step explanation:
Joy Wigens deposited 1/3 of the check of $2,670 that she received in her Citibank account.
The amount she deposited in her Citibank account was:
= 1/3 * 2,670
= $890
The amount she is left with after this deposit will therefore be:
= Check amount - deposit at Citibank
= 2,670 - 890
= $1,780
Todd made a table to show different plans he can use to save $500. Complete the table. Which plan can Todd use to save $500 in less than 16 weeks and have $20 extra? Explain how you found your answer
Answers
Todd use to save $500 in less than 16 weeks and have $20 extra in Plan C.
In plan A,
Plans for saving = $500
Amount of saving each week = $20
∴ Number of weeks needed to make goal = (500 ÷ 20) (by using division)
= 25
In plan B,
Plans for saving = $500
Amount of saving each week = $30
∴ Number of weeks needed to make goal = (500 ÷ 30) (by using division)
= 17
In plan C,
Plans for saving = $500
Amount of saving each week = $40
∴ Number of weeks needed to make goal = (500 ÷ 40) (by using division)
= 13
In plan D,
Plans for saving = $500
Amount of saving each week = $50
∴ Number of weeks needed to make goal = (500 ÷ 50) (by using division)
= 10
So, Todd use to save $500 in less than 16 weeks and have $20 extra in Plan C.
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help mee pleaseeee!!!!!!!!!!!!!!!!!!!!!!!!
thank youuu
Answers
The time that it will take the pebble to hit the ground after it is thrown is; 8.29 seconds
How to solve projectile motion problems?Projectile motion is defined as the motion of a body which experiences both vertical and horizontal motions from point of flight up to the point of landing.
The height of the pebble after t seconds is given by the equation;
h= -16t² + 24t + 900.
When the pebble hit the ground, the height of the pebble will be zero.
Thus, putting h = 0 in the given equation;
0 = -16t²+24 t+900
-4(4t² - 6t - 225) = 0
4t² - 6t - 225 = 0
Applying quadratic formula gives us;
t = [-b ± √(b² - 4ac)]/2a
Plugging in the relevant values would give us;
t = 8.29 seconds
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A train travels a total of 42 km at a constant speed of 85 km/h.
How long is its journey? Give your answer in minutes and seconds, to the nearest seconds
Answers
Answer:
formula is speed equals distance/ time.
now, speed above is 85km/h and distance is 42km.
time therefore is 42/85 which is 0.494h
now, 0.494h× 60 minutes is 29.64minutes(which is your answer in minutes)
now,29.64minutes × 60secs is 1778.82 seconds to the nearest seconds is 1779 seconds( which is your answer in seconds)
Solve the system of equations for a and b:
Answers
The solution to the system of equations in this problem is given as follows:
a = 327.9.b = 0.71.How to solve the system of equations?The system of equations for this problem is defined as follows:
42 = ab^6.15 = ab^9.From the first equation, we have that:
ab^6 = 42
a = 42/(b^6)
a = 42b^(-6).
Replacing on the second equation, we have that the value of b is obtained as follows:
15 = 42b^(-6) x b^9
15 = 42b³
b = (15/42)^(1/3)
b = 0.71.
Then the value of a is obtained as follows:
a = 42 x (0.71)^(-6)
a = 327.9.
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Graph the equation y = -1/4x + 2
Answers
Answer:
y - intercept: 2 slope: down 1(-1), right 4(40
Step-by-step explanation:
help me..
find the value of x if √x-5=0( x-5 both r under the root)
Answers
Answer:
X = 5 plz brainly me
Step-by-step explanation:
Step-by-step explanation:
\( \sqrt{x - 5} = 0 \\ \\ x - 5 = 0 \\ x = 5\)
(1 point) .
What is the equation, in standard form, of a parabola that models the values in the table?
х -2 0 4
f(x) 0 -6 78
a.) y= 6x² + 5x - 4
b.) y=-4x2–5x + 6
c.) y=5x2 + 4x = 6
d.) y=4x² + 5x- 6
please helpppp
Answers
Answer:
Correct answer D. y = 4x2 + 5x – 6
Step-by-step explanation:
just took the test
When a system of linear equations is graphed, how is the graph of each equation related to the solutions of that equation?
Answers
Answer:
The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.
Step-by-step explanation:
Multiply the starting price by the right term that uses the compound average to show that the arithmetic mean does not recover the final price while the geometric and continuous means do. Convert the percent averages to fractions.
$53. 07 x (1 + arith mean) 3 = 53.07 x (1 + #21 %) 3 = #22
$53. 07 x (1 + geom mean) 3 = 53.07 x (1 + #23 %) 3 = $ #24
$53. 07 x e cont mean x 3 = 53.07 x e #25 % x 3 = $ #26
I need help filling out numbers #21 through #26
Answers
The values for numbers #21 through #26 are as follows:
#21: 2.33% or 0.0233. #22: $56.4842. #23: 1.85% or 0.0185. #24: $56.4148. #25: 3.64% or 0.0364. #26: $57.4397
#21: 2.33% (arithmetic mean as a fraction: 0.0233)
#22: $56.4842 (result of the calculation)
#23: 1.85% (geometric mean as a fraction: 0.0185)
#24: $56.4148 (result of the calculation)
#25: 3.64% (continuous mean as a fraction: 0.0364)
#26: $57.4397 (result of the calculation)
To fill out numbers #21 through #26, we need to calculate the values for each term using the given information and convert the percentages to fractions.
#21: The arithmetic mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #21 = 2.33% = 0.0233.
#22: Multiply the starting price ($53.07) by the compound factor (1 + arithmetic mean)^3. Substitute the value of #21 into the calculation. Therefore, #22 = $53.07 x (1 + 0.0233)^3 = $56.4842.
#23: The geometric mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #23 = 1.85% = 0.0185.
#24: Multiply the starting price ($53.07) by the compound factor (1 + geometric mean)^3. Substitute the value of #23 into the calculation. Therefore, #24 = $53.07 x (1 + 0.0185)^3 = $56.4148.
#25: The continuous mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #25 = 3.64% = 0.0364.
#26: Multiply the starting price ($53.07) by the continuous factor e^(continuous mean x 3). Substitute the value of #25 into the calculation. Therefore, #26 = $53.07 x e^(0.0364 x 3) = $57.4397.
Hence, the values for numbers #21 through #26 are as calculated above.
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a factory makes 400 refrigerators every day. the factory makes 125 more stoves per day than refrigerators. which equation can be used to find x, the total number of refrigerators and stoves the factory makes in one day? responses4
Answers
By using the unitary method in linear equation, the answer is 925.
We have a factory that makes 400 refrigerators every day and makes 125 more stoves per day than refrigerators is as follows:
Let's use the unitary method in linear equation to solve this problem. We can use the following equation to find x, the total number of refrigerators and stoves the factory makes in one day:
X = 400 (number of refrigerators) + (400 + 125) (number of stoves)
X = 400 + 525
X = 925
Therefore, the factory makes 925 refrigerators and stoves every day.
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If you are standing 75 ft away from a tree and looking up at the top at a 40° angle, what is the height of the tree?
Answers
Answer:
Step-by-step explanation:
A student who studies the number of birds in groups of birds records data for this group of ducks.
Answers
Answer:
discrete and quantitative I think
Triangle PQR is transformed to triangle P′Q′R′. Triangle PQR has vertices P(8, 0), Q(6, 2), and R(−2, −4). Triangle P′Q′R′ has vertices P′(4, 0), Q′(3, 1), and R′(−1, −2).
Plot triangles PQR and P′Q′R′ on your own coordinate grid.
Part B: Write the coordinates of triangle P′′Q′′R′′ obtained after P′Q′R′ is reflected about the y-axis. (4 points)
Answers
(A) The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' is 1/2
(B) Coordinates of Δ P"Q"R"
P" (-4,0)
Q"(-3,1)
R"(1,-2)
(C) Triangles PQR and P"Q"R" are not congruent.
Given
ΔPQR is transformed into ΔP'Q'R'
Coordinates of P, Q, R are
P (8,0),
Q(6,2)
R(-2,-4)
Coordinates of P'Q'R' are
P′(4, 0)
Q′(3, 1)
R′(−1, −2)
(A) By Distance formula we can find the distance between P Q and P'Q'
Distance formula = \(D = \sqrt{(x2-x1)^{2} +(y2-y1)^{2} }\)
Where D = Distance between two points
from distance formula we can write that
PQ = \(\sqrt{(6-8)^{2} +(2-0)^{2} } = \sqrt{4+4} =2 \sqrt{2}\)
Similarly
P'Q'= √2
PQ /P'Q' = 2
hence the scale factor of dilation is 1/2 (Compression)
(B )The Coordinates of Reflection about y axis can be written for a point
(x,y) as (-x,y)
So the Coordinated of Δ P"Q"R" can be written as
P" (-4,0)
Q"(-3,1)
R"(1,-2)
(C) ΔPQR and ΔP"Q"R" are similar triangles but they are not congruent because their sides are not equal in size.
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what is ___x5=20 3x _____=6 2+ ____=16 3x____=24 9x____=34 12+____=2
Answers
Answer:
4×5=20
3×2=6
2+14=16
3×8=24
9×4=36, 36 -2 = 34
12+(-10) =2
What is a first step to solve the equation 0.3n - 15 = 0.2n - 5?
Answers
Answer:
100
Step-by-step explanation:
0.3n - 15 = 0.2n - 5
0.3n - 0.2n = - 5 + 15
0.1n = 10
10/0.1 = n
n = 100