A population of geese doubles every 18 months. If there are 5 geese initially, how many years will it take for there to be 111 geese?
Answers
Answer: 7 years
Step-by-step explanation:
Let t be the number of periods in which geese doubles .
The exponential growth function:\(y=Ab^t\) , where A = initial value , b= growth factor.
As per given , A = 5 , b=2
i.e. Number of geese after t periods = \(y=5(2)^t\)
Put y=111, we get
\(111=5(2)^t\\\\\Rightarrow\ \dfrac{111}{5}=2^t\\\\\Rightarrow\ 22.2=2^t\)
Taking log on both sides , we get
\(\log 22.2 = t\log 2\\\\\Rightarrow\ 1.346353=t(0.30103)\\\\\Rightarrow\ t=\dfrac{1.346353}{0.30102}\\\\\Rightarrow\ t=4.47263636\approx4.47\)
Now , total months = 4.47 x 18 =80.46≈ 80 months
since 1 year =12 months
Number of years it will take \(=\dfrac{80}{12}=\dfrac{20}{3}=6.66666666667\approx7\)
Hence, it will take 7 years (approx.)
Related Questions
100 points help plz
no links
fast
Answers
Answer:
3/4:1
Step-by-step explanation:
the ration is 3/4:1 bc you beat 1 egg for 3/4 of a cup of milk
how many 1/16 pieces are in 2/8? how many 1/8 pieces are in 10/16? how many 1/8 pieces are in 4/4?
Answers
Answer:
4/16 pieces are in 2/8, 5/8 pieces are in 10/16, 8/8 pieces are in 4/4
Step-by-step explanation:
multiply or divide both the numerator (top number) and the denominator (bottom number) by a number that will give you a common denominator
\(\frac{2*2}{8*2} =\frac{4}{16} \\\frac{10/2}{16/2} =\frac{5}{8} \\\frac{4*2}{4*2}=\frac{8}{8}\)
2) A ray is a geometric figure that consist of
A single point and a line that extends forever in one direction
b. A location that has no size or shape
c. Two points and all the collinear points between the two points
d. Two rays with a common endpoint
Answers
Answer:
A single point and a line that extends forever in one direction
Step-by-step explanation:
Could somebody please help me with this Matrix and how to decode it? i've been struggling with these. I will mark brainest for the help! Please explain as well i'd appreciate it. I provided everything for the equation in the photo!
Answers
Answer:
Step-by-step explanation:
To decode the message, we take the string of coded numbers and multiply it by the inverse of the matrix to get the original string of numbers. Finally, by associating the numbers with their corresponding letters, we obtain the original message
Can somebody help me?
Answers
Answer: (5 × 8) - (5 × 1)
Step-by-step explanation:
When you use the distributive property, you essentially distribute a number to terms it is being multiplied by in order to make the calculation process easier.
When you use the distributive property, you distribute the number outside a multiplication statement to the numbers inside. In this case, 5 is the number outside, and 8 and 1 are the numbers inside.
When you distribute the number 5 to the eight, you are left with (5 × 8). However, you must still include 1, the other number in the parentheses, to finish the equation.
With 1, you go through the same process as you did before. You distribute the number 5 to the 1 and are left with (5 × 1). However, in the original equation, you are subtracting the 8 by the 1, so you must account for the subtraction sign.
You essentially subtract the number you get from (5 × 8) by the number you get from (5 × 1). Therefore, your answer is (5 × 8) - (5 × 1).
You start at (-4,-5). You move up 3 and down 1 unit. Where do you ends
Answers
Answer: (-4,-3)
When you move up 3, your coordinates will be (-4,-2)
Then when you move down a unit, your coordinates will be (-4,-3)
Pablo solved the polynomial equations given in the table. Determine whether each polynomial is correct. Select Correct or Incorrect for each equation.
Equation
(b²+7b-9)+(4b-6b²) = -8b² + 14b-9
(4a+6)-(3a²-9a+1)=-3a²+ 13a +5
(12c-8c²)+(5c²- 10c) = -3c²+2c
Answers
The first equation is incorrect.
The second equation is correct.
The third equation is correct.
Let's go through each equation and determine whether it is correct or incorrect:
(b²+7b-9)+(4b-6b²) = -8b² + 14b-9
To determine if this equation is correct, we need to simplify both sides and check if they are equal.
On the left side:
(b²+7b-9)+(4b-6b²) = b² - 6b² + 7b + 4b - 9 = -5b² + 11b - 9
On the right side:
-8b² + 14b - 9
Comparing both sides, we can see that -5b² + 11b - 9 is not equal to -8b² + 14b - 9. Therefore, the equation is incorrect.
(4a+6)-(3a²-9a+1)=-3a²+ 13a +5
Again, we need to simplify both sides of the equation and check if they are equal.
On the left side:
(4a+6)-(3a²-9a+1) = 4a + 6 - 3a² + 9a - 1 = -3a² + 13a + 5
On the right side:
-3a² + 13a + 5
Comparing both sides, we can see that -3a² + 13a + 5 is equal to -3a² + 13a + 5. Therefore, the equation is correct.
(12c-8c²)+(5c²- 10c) = -3c²+2c
Again, let's simplify both sides and compare them.
On the left side:
(12c-8c²)+(5c²- 10c) = 12c - 8c² + 5c² - 10c = -3c² + 2c
On the right side:
-3c² + 2c
Comparing both sides, we can see that -3c² + 2c is equal to -3c² + 2c. Therefore, the equation is correct.
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By using graphical method, find optimal solution of the problem max z = 3x + y s.t 2x - y ≤ 5 -x + 3y ≤ 6 x ≥ 0, y ≥ 0
Answers
By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.
To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.
Let's start by graphing the constraints:
1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.
2. Plot the line -x + 3y = 6 using a similar process.
3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.
Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.
Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.
Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.
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Circle describe and correct each error.Graph x-5y=10X-int = (10,0)Y-int = (0,1)
Answers
The error is in the y-intercept given. The y-intercept is supposed to be (0, -2)
Explanation:Given:
\(\text{x - 5y = 10}\)To find:
The error from the x and y-intercepts given
The x-intercept is the value of x when y = 0
To get x-intercept, we will substitute 0 for y:
\(\begin{gathered} x\text{ - 5\lparen0\rparen = 10} \\ x\text{ - 0 = 10} \\ x\text{ = 10} \\ x-intercept\text{ is 10} \\ in\text{ ordered pair \lparen x, y\rparen: \lparen10, 0\rparen} \end{gathered}\)The y-intercept is the value of y when x = 0
We will substitute x with 0:
\(\begin{gathered} 0\text{ - 5y = 10} \\ -5y\text{ = 10} \\ divide\text{ both sides by -5:} \\ y\text{ = }\frac{10}{-5} \\ y\text{ = -2} \\ y-intercept\text{ is -2} \\ In\text{ ordered pair \lparen x, y\rparen: \lparen0, -2\rparen} \end{gathered}\)The error is in the y-intercept given. The y-intercept is supposed to be (0, -2)
Write an expression for the height, h, of a cylinder with a volume of 547 cubic inches
in terms of its radius, r.
Answers
The expression for the height (h) in terms of radius r is h = 547/(∏r²).
What is a cylinder?
One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.
Given that the volume of the cylinder is 547 cubic inches.
The volume of a cylinder is V = ∏r²h
Where r is the radius of the cylinder.
h is the height of the cylinder.
Putting V = 547, r = r and h = h in V = ∏r²h
547 = ∏r²h
∏r²h = 547
Divide both sides by ∏r²:
h = 547/∏r².
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Write an equation of the line that passes through (0, -1) and is perpendicular to the line y = 1/9x + 2
An equation of the perpendicular line is y =
Answers
The equation of the perpendicular line passing through (0, -1) is y = -9x - 1.
To find the equation of a line that is perpendicular to the given line y = (1/9)x + 2 and passes through the point (0, -1), we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other.
The given line has a slope of 1/9. To find the slope of the perpendicular line, we take the negative reciprocal of 1/9, which is -9.
Using the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept, we can substitute the slope and the coordinates of the given point (0, -1) into the equation.
y = -9x + b
Since the line passes through the point (0, -1), we can substitute the x-coordinate as 0 and the y-coordinate as -1 into the equation:
-1 = -9(0) + b
-1 = b
Therefore, the y-intercept (b) of the perpendicular line is -1.
Putting it all together, the equation of the line that passes through (0, -1) and is perpendicular to y = (1/9)x + 2 is:
y = -9x - 1
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x= 1/2, y=4, z=1/420z+y3+40x(x-z)
Answers
we want to find;
\(\begin{gathered} 20z+y^3+40x(x-z)\text{ -----(1)} \\ \text{ sustituting }x=\frac{1}{2};\text{ }y=4;\text{ }z=\frac{1}{4}\text{ in eqation (1)} \\ \Rightarrow20z+y^3+40x(x-z)=20(\frac{1}{4})+(4)^3+40(\frac{1}{2})(\frac{1}{2}-\frac{1}{4})=5+64+5 \\ \end{gathered}\)Therefore, 20z+ y^3 + 40x(x-z) = 74.
Which value c makes the expression x2 + 2x + c a perfect square trinomial?
Answers
The value of the c is 1 which makes the perfect square trinomial.
According to the statement
We have to find that the value of the c.
So, For this purpose, we know that the
An expression obtained from the square of the binomial equation is a perfect square trinomial.
From the given information:
The Given statement is:
x² - 2x + c
is a perfect square of the form
(x - a)² = x² - 2ax + a²
Now,compare with x² - 2x + c, then
- 2a = - 2 ⇒ a = 1,
thus
a² = 1² = 1 = c
(x - 1)² = x² - 2x + 1 ← perfect square trinomial
It means the value of c is 1.
So, The value of the c is 1 which makes the perfect square trinomial.
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A cylinder has a height of 9 inches and a diameter of 12 inches. What is its volume?
Answers
Answer:
The volume of the cylinder is 4071.5
May I have brainliest please? :)
what is 5 3/5 divided by 2 2/3
Answers
Answer:
Exact Form:
21/10
Decimal Form:
2.1
Mixed Number Form:
2 1/10
Step-by-step explanation:
Function A and Function B are linear functions.
Function A
Function B
y = 2x - 4
X
-5
-4
2
y
-11
-8
10
Which statements are true? Select all that apply.
The slope of Function A is greater than the slope of Function B.
The slope of Function A is less than the slope of Function B.
The y-intercept of Function A is greater than the y-intercept of Function B.
The y-intercept of Function A is less than the y-intercept of Function B.
Answers
Answer:
The true statements to be selected are the following:
"The slope of Function A is greater than the slope of Function B."
"The y-intercept of Function A is greater than the y-intercept of Function B."
Step-by-step explanation:
Based on the points that were provided for Function A: (-5, -11), (-4, -8), and (2, 10), we can create a linear function to represent the function. The slope of the function is 3, and the y-intercept would be 4, so the linear function of Function A would be y = 3x + 4. And the function of Function B is, as given, y = 2x - 4.
Now, we can compare the two functions and determine which statements are correct. Function A has a slope of 3 and a y-intercept of (0, 4), whilst Function B has a slope of 2 and a y-intercept of (0, -4). As both the slope and y-intercept of Function A is greater than the slope and y-intercept of Function B, the correct statements to select would be "The slope of Function A is greater than the slope of Function B." and "The y-intercept of Function A is greater than the y-intercept of Function B."
Have a great day! Feel free to let me know if you have any more questions :)
What would the answer be?
Answers
The length of the arc CD is 14.13 centimeters.
How to find the length of CD?Remember that for an arc defined by an angle a in a circle of radius R, the length of the arc is given by:
L = (a/360°)*2*pi*R
Where pi = 3.14
Here the angle is a = 45°
And R = 18cm, so we can replace that in the formula above to find the length.
L = (45°/360°)*2*3.14*18cm = 14.13cm
That is the length of the arc CD.
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A fancy restaurant is running a special on a three-course dinner for $30. Sales tax is 5%. Is $40 sufficient to cover the bill with tax and a 20% tip on the amount before tax?
Is $40 sufficient? (Yes/No)
Tax Amount: $
Tip Amount: $
Total cost of meal with tax and tip: $
Answers
Answer:
1. yes
2. $31.5
3. $6
4. 45.36
I had problems with this one too hope this helps
please help quick!!!
Answers
Answer:
1 tick mark represents 0.25 unit
Step-by-step explanation:
it goes -2.5 (tick) -2 (tick) -1.5 (tick) -1 (tick) -0.5 (tick) 0
take 2 adjacent points
1 tick mark = -2.0 -(-2.5) = +0.5 or
+0.5 - 0 = +0.5
Find the 19th term in the geometric sequence, the first term being a=4 and the common ratio being r=2
Answers
The 19th term of a geometric sequence is 1048576.
What is a geometric sequence?A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.
We have,
a = 4 and r = 2
The nth term of a geometric sequence.
= a\(r^{n-1}\)
Now,
The 19th term of a geometric sequence.
= a\(r^{n-1}\)
Substituting a and r values.
= 4 x \(2^{19 - 1}\)
= 4 x \(2^{18}\)
= 4 x 262144
= 1048576
Thus,
The 19th term of a geometric sequence is 1048576.
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Which statement best describes the values of x and y in the table
Answers
Answer:
Answer A
Step-by-step explanation:
As the value of x increases by 2 the value of y increases by 4
Jazmine is picking an outfit to wear to a party. She has 5 pairs of pants, 7 shirts, and 4 pairs of shoes to choose from. The number of possibilities Jazmine has to wear to the party is ———- than 120.
Answers
mmore
Step-by-step explanation:
Multiply them all together
What is the solution to the following system of linear equations?
HELPPPP
y=-1x+5
y=-1x+2
Answers
Answer:
No solution
Step-by-step explanation:
y= -1x+5
y= -1x+2
Let's solve
-1x + 5 = -1x + 2
5 = 2
This is not true!
So, there are No Solution.
Find the area of a rectangle whose vertices are (2,1), (2,11), (9,1), and (9,11).
Answers
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Answers
This is due to the fact that angles 2, 3, and 5 are interior angles of the triangle, and the total of the inner angles of a triangle is always 180 degrees. Therefore, m∠2 + m∠3 + m∠5 = 180°.
What precisely is a triangle?A triangle is a closed, two-dimensional geometric object composed of three line segments, known as sides, that intersect at three locations, known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all sides equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles less than 90 degrees), right (one angle equal to 90 degrees), or obtuse (all angles greater than 90 degrees). The area of a triangle can be computed using the formula A = (1/2)bh, where A is the area, b is the triangle's base, and h is the triangle's height.
Regarding the given diagram, the following claims are always true:
m∠3 + m∠4 + m∠5 = 180°
m∠5 + m∠6 = 180°\s= m∠2 (the measure of the external angle at angle 2). (the measure of the exterior angle at angle 2). And because angles 2 and 3 are likewise interior triangle angles, we get m2 + m3 = m6, which can be rearranged to yield m5 + m6 = m3 + m4 + m5 = 180°.
m∠2 + m∠3 + m∠5 = 180°
This is due to the fact that angles 2, 3, and 5 are interior angles of the triangle, and the total of the inner angles of a triangle is always 180 degrees. Therefore, m∠2 + m∠3 + m∠5 = 180°.
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What is the form of the difference of squares identity?
Answers
write the ratio as a fraction in simplest form
Answers
Dean homes deposit $15.50 dollars in his bank account each month. If his bank account had a balance of $120 at the beginning of the year, what was the amount in his bank account at the end of one year?
Answers
Given data:
The initial amount in the account is i=$15.50.
The amount deposit per month is a=$120/month.
The final amount at the end of the year is,
\(\begin{gathered} F=15.50+12(120) \\ =1,455.5 \end{gathered}\)Thus, the final amount at the end of the year is $1,455.5.
Find the volume of the composed figure. 3 in. 2 in. 4 in. 3 in. 2 in. 9 in. Enter the correct number in the box. cu in. + 9 7 8
Answers
The volume of the composed figure can be determined as,
\(\begin{gathered} V=(3\text{ in}\times2\text{ in}\times3\text{ in)+(2 in}\times4\text{ in}\times3\text{ in)+(4 in}\times2\text{ in}\times3\text{ in)} \\ V=18in^3+24in^3+24in^3 \\ V=66in^3 \end{gathered}\)Thus, the required volume is 66 cubic inch.
Classify PKM and NKO check all names that apply
Answers
Answer: VERTICAL & COMPLEMENTARY
The answers is Vertical and complementary.
What is Vertical and complementary angles?Vertical angles can be supplementary or complementary. When the angles are across from each other where the two lines intersect, they are vertical angles. If the two angles have a sum of 180 degrees, then they are supplementary angles.
If the two angles have a sum of 90 degrees, then they are complementary angles.
Given:
In first figure < PKM and <NKO are in relation of Vertical angles.
and, in II figure <NKO and <OKL are in relation of complementary angle as
angles have a sum of 90 degrees.
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