A field currently holds 20 tulips. The number of tulips will grow by 70% each year. The field can only sustain 300 plants. Use th logistic growth model to predict the population in the next 3 years,
Answers
Answer: \(98.26\)
Step-by-step explanation:
Given
Current population of tulips is 20
Each year it grows 70%
Field can sustain 300 tulips
After 1 year population becomes
\(\Rightarrow 20(1+70\%)\\\Rightarrow 20(1.7)\\\Rightarrow 34\)
after 2 years it is
\(\Rightarrow 34(1+0.7)\\\Rightarrow 34\times 1.7\\\Rightarrow 57.8\)
After 3 years
\(\Rightarrow 57.8(1+0.7)\\\Rightarrow 98.26\)
after n years, the tulips becomes
\(\Rightarrow 20(1.7)^n\)
Related Questions
What is 25 x 65 / 73?
Answers
25x65=1625
1625/73=22.26
I NEED HELP PLS HURRY
1. Write each expression with a single exponent:
a. (10^7)²
b. (10^9)³
c. (10^6)³
d. (10^2)³
e. (10³)²
f. (10^5)^7
Answers
b. 10^27
c. 10^18
d. 10^6
e. 10^6
f. 10^35
multiply the exponents.
Answer:
We use the rule,
\((a^b)^c = a^{bc}\)
a. (10^7)²
\((10^7)^2 = 10^{(7)(2)} = 10^{14}\)
10^14
b. (10^9)³
\((10^9)^3 = 10^{(9)(3)} = 10^{27}\)
10^27
c. (10^6)³
\(10^{(6)(3)}= 10^{18}\)
10^18
d. (10^2)³
\(10^{(2)(3)} = 10^{6}\)
10^6
e. (10³)²
\(10^{(3)(2)}=10^{6}\)
10^6
f. (10^5)^7
\(10^{(5)(7)} = 10^{35}\)
10^35
Step-by-step explanation:
Fatima purchased a new mattress when it was on sale. The sale price was 20% less than the regular price. If the sale price was $358, what was the original price? (Round your answer to the nearest dollar).
Answers
well, the regular price is really "x", which oddly enough is 100%, but we also know that $358 is really the discounted price by 20%, namely 100% - 20% = 80%, so we know that 358 is really just 80% of "x", so
\(\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 358& 80 \end{array} \implies \cfrac{x}{358}~~=~~\cfrac{100}{80} \\\\\\ \cfrac{x}{358}=\cfrac{5}{4}\implies 4x=1790\implies x=\cfrac{1790}{4}\implies x\approx 448\)
100% - 20% = 80% or 0.08
358 / 0.8 = $447.50
Check
447.50 * 0.8 = 358
A number is between 40 and 45 . It has prime factors of 2 and 11. What is the number?
Answers
Answer: 42
Step by step:
42 is divisible by both 7 and 2
Answer:
44
Step-by-step explanation:
4 x 11 = 44
2 x 22 = 44
concert tickets cost $30,$40 or $50 if you buy a ticket online you pay an extra $3 as a booking fee. what percentage of each tickets price is the booking fee?
Answers
Answer:
$30 = 10%
$40 = 13.34%
$50 = 16.67%
Step-by-step explanation:
To find the answer you divide the cost of the ticket by the booking fee to get your answer.
The booking fee of $30 is 10%,$40 is 7.5% and $50 is 6%.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The percentage is also called the indicating hundredths.
The percentage of x of the y is given as,
x/y × 100
Thus, a percentage of $3 of $30 will be,
3/30 x 100 = 10%
The percentage of $3 of $40 will be,
3/40 x 100 = 7.5%
The percentage of $3 of $50 will be,
3/50 x 00 = 6%.
Hence "The booking fee of $30 is 10%,$40 is 7.5% and $50 is 6%".
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An aquarium has 5 gallons of water in it and is being filled up at a rate of g gallons every m minute. The amount of water w in the tank can be represented by the equation
w = 5 + g - m. Write an equation that can be used to find the number of minutes m the tank has been filled if we know w and g.
Write an equation that can be used to find the number of minutes g the tank has been filled if we know w and a.
Answers
Answer:
m=5+g-w
Step-by-step explanation:
This should be the answer based on the equation given.
Answer:
See belowStep-by-step explanation:
The equation for the amount of water is:
w = 5 + gmSolve for m:
gm = w - 5m = (w - 5)/gNow solve for g:
gm = w - 5g = (w - 5)/mHELP ME LOOK AT THE PHOTO
Answers
Answer:
The answer to the question provided is 7.
Step-by-step explanation:
\(7x + 9 = 8x + 2 \\ \frac{ - 8x \: \: \: \: = - 8x}{ - 1x + 9 = 2 } \\ \frac{ \: \: \: \: \: \: \: \: - 9 = - 9}{ \frac{ - 1x}{ - 1} = \frac{ - 7}{ - 1} } \\ x = 7\)
[I apologize if this isn't the answer]
Question 1: need help asap
Answers
2 of the same sides on both triangles are given
so 49/28 = 1.75
if the bottom of triangle 1 is 91 then you must divide 91/1.75 to give the length of the second triangle
= 52in.
4 examples of one step equation
Answers
Answer:
Step-by-step explanation:
x + 14 = 20
4 = x²
x/4 = 50
x - 7 = 1
This is a safe space please answer how you are feeling today and why!!
Answers
Answer:
feeling good
Step-by-step explanation:
I am just happy
cos xº [Hint: Change degree into radian] find the derivative from definition
Answers
The derivative of the function cos(xº) in radians is y' = -sin(xπ/180)
Finding the derivative of the functionFrom the question, we have the following function definition that can be used in our computation:
cos(xº)
Changing the degree into radian, we have
cos(xπ/180)
Express as a function
So, we have
y = cos(xπ/180)
When the cosine function is differentiated, we have
y' = -sin(xπ/180)
Hence, the differentiated function is y' = -sin(xπ/180)
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Given 3 + 7 + 11 + 15 + … find S20
Answers
Answer:
Hi
Please mark brainliest ❣️
Which expression is equivalent to StartRoot 8 x Superscript 7 Baseline y Superscript 8 Baseline EndRoot? Assume x greater-than-or-equal-to 0.
x y squared StartRoot 8 x cubed EndRoot
2 x cubed y cubed StartRoot x y squared EndRoot
2 x cubed y Superscript 4 Baseline StartRoot 2 x EndRoot
4 x cubed y Superscript 4 Baseline StartRoot x EndRoot
Answers
The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.
To understand why this is the case, let's break down each expression and simplify them step by step:
StartRoot \(8 x^7 y^8\) EndRoot:
We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.
Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.
(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:
Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.
Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.
Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.
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(If A + B + C = 180, prove that): sin(B + 2C) + sin(C + 2A) + sin(A + 2B) = 4sin(A-B)/2.cos(B-C)/2.,cos(C-A)/2
Answers
Using trigonometric ratio it is proved that sin(B + 2C) + sin(C + 2A) + sin(A + 2B) = 4sin(A-B)/2.cos(B-C)/2.cos(C-A)/2 when A + B + C = 180.
What is trigonometric ratio?
Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios.
We can start by using the sine addition formula to expand each of the sine terms in the left-hand side of the equation -
sin(B + 2C) = sin(B)cos(2C) + cos(B)sin(2C) = 2sin(B)cos(C)²
sin(C + 2A) = sin(C)cos(2A) + cos(C)sin(2A) = 2sin(C)cos(A)²
sin(A + 2B) = sin(A)cos(2B) + cos(A)sin(2B) = 2sin(A)cos(B)²
Substituting these expressions into the left-hand side of the equation, we get -
2sin(B)cos(C)² + 2sin(C)cos(A)² + 2sin(A)cos(B)²
Factoring out the 2, we can rewrite this as -
2(sin(B)cos(C)² + sin(C)cos(A)² + sin(A)cos(B)²)
Using the trigonometric ratio identity sin(2x) = 2sin(x)cos(x), we can rewrite each of the cosine squared terms as a product of sines and cosines -
cos(C)² = (1/2)(1 + cos(2C)) = (1/2)(1 + 2cos(C)sin(C))
cos(A)² = (1/2)(1 + cos(2A)) = (1/2)(1 + 2cos(A)sin(A))
cos(B)² = (1/2)(1 + cos(2B)) = (1/2)(1 + 2cos(B)sin(B))
Substituting these expressions into the previous equation, we get -
2(sin(B)(1/2)(1 + 2cos(C)sin(C)) + sin(C)(1/2)(1 + 2cos(A)sin(A)) + sin(A)(1/2)(1 + 2cos(B)sin(B)))
Simplifying and grouping the terms, we get -
sin(B)sin(C)cos(C) + sin(C)sin(A)cos(A) + sin(A)sin(B)cos(B)
Using the sine addition formula again, we can rewrite each of the cosine terms as a product of sines -
cos(C) = sin(A + B)
cos(A) = sin(B + C)
cos(B) = sin(C + A)
Substituting these expressions into the previous equation, we get -
sin(B)sin(C)sin(A + B) + sin(C)sin(A)sin(B + C) + sin(A)sin(B)sin(C + A)
We can rearrange this expression by factoring out a sin(A-B)/2 sin(B-C)/2 sin(C-A)/2 term -
sin(A-B)/2 sin(B-C)/2 sin(C-A)/2 (cos(A) - cos(B) + cos(B) - cos(C) + cos(C) - cos(A))
Simplifying the terms in parentheses, we get -
sin(A-B)/2 sin(B-C)/2 sin(C-A)/2 (0)
Therefore, the left-hand side of the equation simplifies to 0, which is equal to the right-hand side of the equation -
4sin(A-B)/2.cos(B-C)/2.cos(C-A)/2
Therefore, we have proven that sin(B + 2C) + sin(C + 2A) + sin(A + 2B) = 4sin(A-B)/2.cos(B-C)/2.cos(C-A)/2.
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Use the method of successive differences to determine the next number in the given sequence 3, 7, 17, 33, 55, 83, 117
Answers
The next number in the sequence is 151.
What is the successive differences?
The method of successive differences involves finding the differences between consecutive terms in a sequence and using that information to predict the next term in the sequence.
To use this method for the sequence 3, 7, 17, 33, 55, 83, 117:
Find the differences between consecutive terms:
7 - 3 = 4
17 - 7 = 10
33 - 17 = 16
55 - 33 = 22
83 - 55 = 28
117 - 83 = 34
Check if the differences are constant. In this case, they are increasing by 6 each time.
Use this information to predict the next term in the sequence:
117 + 34 = 151
So, the next number in the sequence is 151.
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What is the measurement of angle BAD? (angle BDC = 34, angle BDA = 37)
Answers
Since ∠BDA is an inscribed angle measuring 25°, the arc it intercepts, AB, must measure 50°. For the same reason, the arc intercepted by ∠BDA must measure 64°. That's a total of 114° out of the semicircle ABCD, which leaves 66° out of the 180° half-circle. That's the measure of arc BC.
Define measurement?Associating numbers with physical quantities and events is the process of measuring. The sciences, engineering, building, and other technological professions, as well as practically all daily activities, all depend on measurement.An object or event's attributes are quantified through measurement so that they can be compared to those of other things or occurrences. Measurement, then, is the process of establishing how big or little a physical quantity is in relation to a fundamental reference quantity of the same kind.Comparing a physical quantity with a recognized standard quantity of some kind is the process of measurement.Comparison of an unknown fixed quantity with a known fixed quantity of the same kind is measurement.To learn more about measurement refer to:
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Since ∠BDA is an inscribed angle measuring 25°, the arc it intercepts, AB, must measure 50°. For the same reason, the arc intercepted by ∠BDA must measure 64°. That's a total of 114° out of the semicircle ABCD, which leaves 66° out of the 180° half-circle. That's the measure of arc BC.
Define measurement?
Associating numbers with physical quantities and events is the process of measuring.The sciences, engineering, building, and other technological professions, as well as practically all daily activities, all depend on measurement.An object or event's attributes are quantified through measurement so that they can be compared to those of other things or occurrences.Measurement, then, is the process of establishing how big or little a physical quantity is in relation to a fundamental reference quantity of the same kind.Comparing a physical quantity with a recognized standard quantity of some kind is the process of measurement.Comparison of an unknown fixed quantity with a known fixed quantity of the same kind is measurement.To learn more about measurement refers to:
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Use the diagram below to answer the questions about the Law of Cosines.
Answers
Based on the Law of Cosines; it was proven that:
cos Θ = x/acos (180 - C) = x/aa² + b² + 2bx = c²Please note that the given equation on number 3 is wrong. The correct equation should be: a² + b² + 2bx = c². The explanation why the given equation is incorrect will be explained later.
Based on the unshaded triangle, we can find that:
cos Θ = x/a
Next, we will prove that: cos (180 - C) = x/a
Remember that:
cos (A + B) = cos A cos B - sin A sin B
Law of Cosines: c² = a² + b² - 2ab. cos C
cos C = - [c² - (a² + b²)] /2ab ... (i)
Then:
cos Θ = cos (180 - C)
cos (180 - C) = cos 180 . cos C - sin 180 . sin C
We subtitute equation (i):
cos (180 - C) = (-1) (- [c² - ((a² + b²)] / 2ab) - 0 sin C
cos (180 - C) = [c² - (a² + b²)]/ 2ab ... (ii)
If we focus on the unshaded triangle, we can find an equation of a, where:
a² = h² + x² ... (iii)
And if we combine both triangle into a giant triangle, we can make another equation of c. where:
c² = (x + b)² + h² ... (iv)
We will subtitute equation (iv) into equation (ii):
cos (180 - C) = [c² - (a² + b²)]/ 2ab
cos (180 - C) = [(x + b)² + h² - (a² + b²)] / 2ab
cos (180 - C) = [x² + b² + 2bx + h² - a² - b²] / 2ab
cos (180 - C) = [x² + 2bx + h² - a²] / 2ab ... (v)
We subtitute equation (iii) into equation (v):
cos (180 - C) = [x² + 2bx + h² - a²] / 2ab
cos (180 - C) = [a² + 2bx - a²] / 2ab
cos (180 - C) = 2bx / 2ab
cos (180 - C) = x/a --> PROVEN!
Next, we will try to show why the given equation of a² + b² - 2bx = c² is incorrect.
We know that:
a² + b² - 2ab cos C = c²
c² = (x + b)² + h²
We will try to find the value of cos C:
a² + b² - 2ab cos C = (x + b)² + h²
a² + b² - 2ab cos C = x² + b² + 2bx + h²
a² - 2ab cos C = a² + 2bx
- 2 ab cos C = 2bx
cos C = - x/a
We will subtitute the value of cos C under the Law of Cosines:
c² = a² + b² - 2ab cos C
c² = a² + b² - 2ab (- x/a)
c² = a² + b² + 2bx --> PROVEN!
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Y x 6 for y=2/3 please help asap
Answers
2/3 x 6 = (2x6) / 3 = 4
Through (14,-4) and
perpendicular to y=x+5
Answers
Answer:
y = -x + 10
Step-by-step explanation:
Find the geometric mean of 4 and 8
Answers
Answer:
\(4\sqrt2\)
Step-by-step explanation:
1) a=4 and b=8
2) Let geometric mean is g. \(g=\sqrt ab\) or you can do \(g=\sqrt 4 times8\)
3) g=\(4\sqrt2\)
what's the answer? (Zearn)
Answers
Answer:
Step-by-step explanation:
Write an equation of the line. helppp
Answers
Answer:
y=-x-4
Step-by-step explanation:
Just ask.
Hope this helped! :)
Answer:
y = -1x - 4
Step-by-step explanation:
Slope (m) = -1
Point on line: (-1,-3)
b from graph: -4
point intercept form: y=mx+b
Use values given and plug into this equation:
(-3)=(-1)(-1)+b
(-3)=(1)+b
b=-4
Using slope-intercept form we find the resulting equation:
y = -1x - 4
We can check if this is right because b is the y intercept. On the graph we see that the y intercept of the line is at -4, so this equation is correct.
I can fix any mistakes if needed. Consider marking brainliest thanks :)
Find an ordered pair (x, y) that is a solution to the equation.
3x-y=6
Answers
For example, if we let x = 2, then:
3x - y = 6
3(2) - y = 6
6 - y = 6
-y = 0
y = 0
So, when x = 2, y = 0, and the ordered pair (2, 0) is a solution to the equation 3x - y = 6.
Simplify each expression. Use a slash () to show a fraction. Do not use any spaces.
-(3)^2
Answers
Answer:
The answer would be -9
Step-by-step explanation:
-(3)^2
-(9)
-9
Following order of operations (PEMDAS)
A printer needs to make a poster that will have a total of 500 cm2 that will have 3 cm margins on the sides and 2 cm margins on the top and bottom. What dimensions of the poster will give the largest printed area?
Answers
Answer:
width of 27.386 cm and height of 18.257
Step-by-step explanation:
Let x = width of entire poster.
Area of entire poster is 500 cm².
Height of entire poster is area/width = 500/x
area of printed are = (x - 6)(500/x - 4)
A = 500 - 4x - 3000/x + 24
A = -4x - 3000/x + 524
Now we take the derivative of the area with respect to the width, x.
A' = -4 + 3000/x²
A' = 3000/x² - 4
Set the derivative equal to zero and solve for x to find a maximum value.
3000/x² - 4 = 0
3000/x² = 4
4x² = 3000
x² = 750
x = 27.386
500/27.386 = 18.257
Answer: width of 27.386 cm and height of 18.257
PLZZZZZZZZZZZZZ HELP Simplify the expression.
–5^4
Answers
Answer:
625
Step-by-step explanation:
All it is saying to do is to do -5x-5x-5x-5
Answer:
625
Step-by-step explanation:
–5^4 is simply -5 times -5 4 times
the negatives cancel each other
out
Rebecca carries a balance on her credit card each month. Today is the first day of the new, 28-day billing cycle. The current balance is x and the APR is 24%. Rebecca is buying a friend an expensive gift that costs $1,400 that she plans to put on her credit card. This will be her only purchase this month, and she will be making this purchase on the last day of the month. If her finance charge will be $51, write and solve an equation to determine her current balance on her credit card.
Answers
Answer:
Average date*Interest=Finance charge
Previous debt*2%´+1400*2%=51
Previous debt=1150
Step-by-step explanation:
X=Previus Debt
Debt= Previus debt + 1400
Finance Charge 51.
Debt=1400+1150= 2550
Average debt= Previus debt + 1400
Average date*Interest=Finance charge
Previous debt*2%´+1400*2%=51
Previous debt=1150
Interest capital Debt Payment
1 51 213 2,338 264
2 47 213 2,125 259
3 43 213 1,913 255
4 38 213 1,700 251
5 34 213 1,488 247
6 30 213 1,275 242
7 26 213 1,063 238
8 21 213 850 234
9 17 213 638 230
10 13 213 425 225
11 9 213 213 221
12 4 213 0 21
please help me with this please i need the amswers for today,
Answers
The coordinates of each points are:
A = (-0.5, -5)
B = (0.8, -1.8)
C = (-2.6, -2.2)
D = (-1.5, -8.9)
E = (2.5, -6.5)
F = (-1.5, 3.1)
G = (-2.4, 4.1)
H = (1.5, 3)
I = (2.7, 1.5)
J = (-1.5, 0)
K = (-6.5, 0)
We have,
The coordinates of each point are in an ordered form.
i.e
(x, y)
x is the x-axis value.
y is the y-axis value.
Thus,
A = (-0.5, -5)
B = (0.8, -1.8)
C = (-2.6, -2.2)
D = (-1.5, -8.9)
E = (2.5, -6.5)
F = (-1.5, 3.1)
G = (-2.4, 4.1)
H = (1.5, 3)
I = (2.7, 1.5)
J = (-1.5, 0)
K = (-6.5, 0)
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answers
The true statements are, The radius of the circle is 3 units, The center of the circle lies on the x-axis and The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
What is Circle?Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.
Standard form of a circle is given by the equation,
(x - h)² + (y - k)² = r²
where, (h, k) is the center of the circle and r is the radius of the circle.
The given equation of a circle is x² + y² - 2x - 8 = 0.
(x² - 2x + 1) + y² (- 8 - 1) = 0
(x - 1)² + y² = 9,
(x - 1)² + (y - 0)² = 3², which is in the standard form.
(1, 0) is the center of the circle.
(1, 0) is a point on the X axis. So the center of the circle lies on the X axis.
Radius of the circle is 3.
Hence the statements The radius of the circle is 3 units, The center of the circle lies on the x-axis and The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9 are all true.
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Suppose Lorenzo and Neha are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Lorenzo chooses Right and Neha chooses Right, Lorenzo will receive a payoff of 6 and Neha will receive a payoff of Neha Left RightLorenzo Left 8, 4 4, 5 Right 5, 4 6, 5The only dominant strategy in this game is for _________ (Neha/Lorenzo) to choose ______________(Right/Left)t .The outcome reflecting the unique Nash equilibrium in this game is as follows: Lorenzo chooses ___________ (Right/Left) and Neha chooses _________ (Right/Left) .
Answers
Answer:
In the field of economics, more specifically game theory, describes the interaction involving candidates where one cannot have an advantage over the other if the latter makes no change in their strategy - is referred to as the Nash Equilibrium.
The correct option has been inserted in the blank and underlined, please see below:
The only dominant strategy in this game is for Neha to choose Right.The outcome reflecting the unique Nash equilibrium in this game is as follows: Lorenzo chooses Right and Neha chooses Right.
Hope that answers the question, have a great day!