The function which represents the frog population after x years will be F(x) = [tex]1200 * (0.97)^{x}[/tex]
The population is decreasing at an average rate of 3% per year.
For decrease in population, if the rate is decreasing per year is r%, the initial population is P, after time x the equation to use would be:
net decrease = [tex]P * (\frac{100 - r}{100})^{x}[/tex]
r = Reduction
x = time duration
P = 1200
Reduction rate = 100 - 3 = 97%
Reduction rate will be 97% i.e. 0.97
Reduction after one year = 1200 * 0.97
Reduction after two years = 1200 * 0.97 *0.97
= 1200 * (0.97)²
Reduction rate after three years = 1200 * 0.97 * 0.97 * 0.97
= 1200 * (0.97)³
therefore,
Reduction rate after x years = [tex]1200 * (0.97)^{x}[/tex]
The function representing the frog population after x years is F(x) = [tex]1200 * (0.97)^{x}[/tex]
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Explain the similarities and differences between the material derivative and the reynolds transport theorem.
In Fluid Mechanics, we describe the motion of fluids using two different frames of reference- the Eulerian( fixed frame of reference wrt fluid particles; describes the rate of change of fluid flow property at a fixed position in space) and the Lagrangian (follows individual fluid particles and describes the rate of change of fluid flow properties of the particle as it passes through space).
A Material derivative is basically a Lagrangian way of expressing the rate of change of fluid flow property. It expresses the rate of change of fluid property wrt time and also the rate of change wrt space because of its movement at some velocity. It is best explained by John D Anderson jr. in his book "Computational Fluid Dynamics". He explains that the material derivative can be best understood by considering an example of imagining oneself entering a cold cave. The material derivative is the change in temperature you would feel as if you would just enter into the cave from the outside and precisely at the same time if someone throws snowballs at you. The rate of change of temperature because of your movement into the cave is the rate of change wrt space and that due to the snowball effect would be the rate of change w.r.t time.
Coming to the Reynolds Transport theorem is a powerful tool in fluid mechanics that relates the change in properties of a system to change in properties in a control volume. Since laws of thermodynamics are applicable to a system, the Reynolds transport theorem allows it to be applied to a control volume (fixed or moving, or deformable).
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Plllleaseee helppppp
The line of best fit for the given points is:
y = 0.3913x + 39.26
The graph at the end of the answer shows both the scatter plot and the line.
Applying it's concept, taking points (60, 64) and (70,67), the slope of the line is of 0.3.
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the entire set of points (x,y) given by the scatter plot in the calculator.
From the table, the points are given as follows:
(60, 65), (53, 59), (44, 57), (61, 61), (70,67).
Inserting these points into the calculator, the line of best fit is given by:
y = 0.3913x + 39.26
The graph at the end of the answer gives both the line and the scatter plot(points without the line).
How to estimate the slope?
Given two points, the slope is given by change in y divided by change in x.
Taking points (60, 64) and (70,67), the slope is given by:
m = (67 - 64)/(70 - 60) = 3/10 = 0.3.
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Find the slope of the line that passes through the points (8, -2) and (-13, 7). Enter answer as a fraction
Answer:
[tex] \frac{ - 9}{21} [/tex]
then simplify
Step-by-step explanation:
Slope =
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
Rise
(-2)-(7)=-9
Run
[tex]8 - ( - 13) = 21[/tex]
Answer: 3/-7
Step-by-step explanation:
y2-y1 over x2-x1 is slope. your parenthesis go in the order of (x,y)
8=x1 -2=y1 -13=x2 7=y2
7 - -2 = 9
-13 - 8 = -21
9/-21
simplify to get 3/-7
is 81.848 irrational number
Answer:
Yes it's is irrational
Step-by-step explanation:
Answer: rational
Step-by-step explanation:
A weaver needs 7.8 meters of yarn for one project and 2.6 meters of yarn for a second project. What is the total amount of yarn, in meters, the weaver will need for both projects, written as a decimal?
Answer:10.4 written as a decimal is 0.104
Step-by-step explanation:
right or wrong tell me in comment
For each system, choose the method of solving that seems easier to use. Explain why you made each choice. Solve each system.
2x - 3y = 4 . 2x - 5y = -6
By elimination, the solution of the system of equations, 2x - 3y = 4 and 2x - 5y = -6, is (19/2 , 5).
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
Use the elimination method since subtracting the two equations will eliminate the variable x.
2x - 3y = 4 (equation 1)
2x - 5y = -6 (equation 2)
0x + 2y = 10
y = 5
Substitute the value of y to any of the two equation and solve for x.
2x - 3y = 4 (equation 1)
2x - 3(5) = 4
2x = 4 + 15
2x = 19
x = 19/2
Hence, the solution of the system of equations is (19/2 , 5).
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Evaluate a +6 for a = 10.
06
60
16
Answer:
16
Step-by-step explanation:
a+6 where a=10
You'd substitute the number 10 where the variable 'a' is.
(10)+6
Then, you'd solve the expression.
10+6=16.
Thus, the answer is 16.
Hope this helps.
c. Estimation Estimate when first-class postage was 37 cents.
Estimation Possible year, 2005, when first-class postage was 37 cents, between 2001 and 2006.
What does that mean First class postage?First-Class mail is sent when a stamp is applied to an envelope and deposited in a mailbox. First-Class Mail is thus equivalent to "ordinary" mail. The ever-popular First-Class Mail is just one; the postal rate of the several services or "classes" that the Estimation Possible year, 2005, when first-class postage was 37 cents, between 2001 and 2006.
What is the postal rate?A fee will be assessed by a government postal service for the shipping and delivery of letters.
Assuming the value is supplied,
a) POSTAGE RATES L1=x
L2=y
y= -0.004x2+0.859x+27.53
y=28.381
b) Integers from -10 to 17 are the domain. Range: whole number between 18 and 42
c) From 2001 to 2006, first class postage cost 37 cents.
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a rectangular prism has a volume of 125 cubid inches. its width is four times its lenght. its height is one-fourth the lenght. what are the dimensions of the prism? (Please help me)
A rectangular prism has a volume of 125 cubid inches. its width is four times its lenght.
Given:
the volume of rectangular prism = 125 cubic inches
Let the length of the rectangular prism be 'x'.
width = 4x
height = x/4
volume =( x)(4x)(x/4)=125
x^3=125
x=5
Length=5
Hieght=5/4
Width=20
Rectangular prism:
In terms of geometry, a rectangular prism is a solid 3-dimensional object having six faces and a rectangular base. Rectangular prisms can be of two types, namely right rectangular prisms and non-right (oblique) rectangular prisms.
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Complete the pattern:
2 +
20 +
200 +
2,000 +
= 6
= 60
= 600
= 6,000
Answer:
2+4=6
20+40=60
200+400=600
2,000+4,000=6,000
Step-by-step explanation:
Suppose a is a 57 matrix. How many pivot columns must a have if its columns span ? why?.
The answer is Option B.
In the given choices there is some mistake so, the correct choice can be defined in the attached file. please find it.
In the given question, If the column of a matrix and the A span is equal, and then the value of A has a pivot in each row, that's why in each pivot its position in the different columns of A has the five pivot columns, that's why the choice B is correct.
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Although part of the question is missing the question is Suppose A is a 5x7 matrix. How many pivot columns must A have if its columns span R^5? Why?
a. The matrix must have nothing pivot columns. If A had fewer pivot columns, then equation A would have only the trivial solution.
b. The matrix must have nothing pivot columns. The statements "A has a pivot position in every row" and "the columns of A span " are logically equivalent.
c. The matrix must have nothing pivot columns. Otherwise, equation A would have a free variable, in which case the columns of A would not span.
d. The columns of a 57 matrix cannot span because having more columns than rows makes the columns of the matrix dependent
Each of these sequence or series formulas involves four quantities that are represented by a variable. For each fomula, describe the four quantities.
a. a n=a₁ +(n-1)d
The formula for estimating the nth term of an arithmetic sequence exists:
a n = a₁ + (n-1)d
What is meant by arithmetic sequence?A series of numbers named an arithmetic progression or arithmetic sequence (AP) contains a constant difference between the terms.
The formula for estimating the nth term of an arithmetic sequence exists:
a n = a₁ + (n-1)d
The four quantities in the formula exist a n, a₁, n, d
The description exists as follows:
an be the nth term of the sequence
a₁ be the first term of the sequence
n be the number of terms
d be the common difference
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Simplify by combining like terms. 5 f-(5 d-f)
The simplification by combining like terms of 5f - (5d - f) is 6f -5d.
According to the given question.
We have an expression 5f - (5d - f).
As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same. When we combine like terms, such as 2x and 3x, we add or subtract their coefficients.
Since, we have to combine the like terms of the given expression
5f -(5d -f).
Here 5f and -f are the like term.
So, we subtract coeffcients of f to simplify the given expression.
Therefore, the simplification of 5f - (5d -f) is given by
5f - (5d - f)
= 5f - 5d + f
= 6f - 5d
Hence, the simplification by combining like terms of 5f - (5d - f) is 6f -5d.
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what effect does eliminating the lowest value -6 from the data set have on the mean and median
By eliminating values from the given the given set , it will reduce the mean and median value. Mean = 23.5 and Median = 5
According to the question, the given set of values for the calculation of mean and median is as follows:
Values: = (-6, 3, 3, 3, 3, 5, 6, 6, 8, 10)
After eliminating -6 from the given set of values:
Values: = (3, 3, 3, 3, 5, 6, 6, 8, 10)
Now the median is the middle tern from the given set of the values:
Median = 5
And mean is : 3 + 3 + 3 + 3 + 5 + 6 + 6 + 8 + 10 / 2 = 47/2 = 23.5
Hence, the correct answer is median = 5 and mean = 23.5
What is mean and median?
The mean is the average value of the given set of the data. It is the addition of all the values and later divide it by two. Similarly, median is the middle value from the set of values provided it should be arranges in the order ascending to descending.
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direct proportion please help
Answer:
qjjsHope this helps you.
Is division of integers commutative? Give an example supporting your answer.
Answer:
No. When we change the places of the number, the results also changes
Step-by-step explanation:
4 / 2 = 2
2 / 4 = 0.5
What is an equation of the line that passes through the points (−2,5) and (−2,−8)?
Answer:
Y=5
Step-by-step explanation:
1) find gradient
2) find equation of line using the formula y-y1=m(x-x1) where m is the gradient.
70. The histogram below shows the heights of 300 ran-
domly selected high school students. Which of the
following is the best description of the shape of the
distribution of heights?
I
(a) Roughly symmetric and unimodal
(b) Roughly symmetric and bimodal
(c) Roughly symmetric and multimodal
(d) Skewed to the left
(e) Skewed to the right
The histogram is unimodal as it has only one peak point and roughly symmetric because both sides of the histogram when flipped across the axis of symmetry does not overlap completely.
What is Histogram?Histogram is a diagram consisting of rectangles whose area is proportional to the frequency of a variable and whose width is equal to the class interval.
Given is histogram that shows heights of 300 randomly selected high school students.
The shape that best describes the distribution of heights is - Roughly symmetric and unimodal. Unimodal histograms have only one peak in the distribution. It can be seen from the image that the graph has only one peak point. However, if we check the symmetry of this histogram by drawing the axis of symmetry, then both sides will not overlap completely. So it is Roughly symmetric.
Therefore, the histogram is unimodal as it has only one peak point and roughly symmetric because both sides of the histogram when flipped across the axis of symmetry does not overlap completely.
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Find the nth term of this quadratic sequence
4, 9, 16, 25, 36,
Answer:
(n+1)^2.
Step-by-step explanation:
Term: 1 2 3 4 5
Value 4 9 16 25 36
= 2^2 3^2 4^2 5^2 6^2
So, the nth term is (n + 1)^2.
After 8 years, what is the total amount of a compound interest investment of $25,000 at 3% interest, compounded quarterly?
The correct answer is: D) $31,752.78
Explanation:
The formula for compound interest is:
where A is the total amount, p is the principal invested, r is the interest rate as a decimal number, n is the number of times per year the interest is compounded, and t is the number of years.
The principal in this problem is 25,000; the interest rate is 3% = 3/100 = 0.03; the number of times the interest is compounded is 4; and the number of years is 8:
What are the vertex and range of y = |x + 3| + 2?
(−3, 2); 2 ≤ y < ∞
(−3, 2); −∞ < y < ∞
(0, 5); 2 ≤ y < ∞
(0, 5); −∞ < y < ∞
Answer:
(−3, 2); −∞ < y < ∞
Step-by-step explanation:
Which expression is equivalent to 3(4.26y − 5.07)?
Answer:
12.78y -15.21
14. MP Be Precise A standard shower drain
can drain water at the rate of 480 gallons
2
in ²3/3
hour. Create three different rates, using
the same or different units, that are all
equivalent to this rate. Be precise in the
units you choose. Then find the unit rate, in
gallons per minute.
Graw-Hill Education
A typical shower drain can remove 480 gallons of water in 3 hours.
For the first-rate;
1,440 gallons in 3 hours
We calculate the unit rate.
By Dividing the total volume by the total time,
1440 / 3 = 480 gallons/ hours
For the second rate:
960 gallons in 120 minutes
Converting minutes to hours:
120 minutes = 2 hours
We calculate the unit rate.
By dividing the total volume by the total time,
960 / 2 = 480 gallons / hour
For the third rate:
720 gallons in 1.5 hours
We calculate the unit rate.
By dividing the total volume by the total time,
720 / 1.5 = 480 gallons / hour
Now,
480 gallons/ hour = 480 / 60 gallons/ minute = 80 gallons per minute
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find the volume of this object.
PLEASE HURRY
Answer:
24 maybe?
Step-by-step explanation:
I think 24 because if you multiply all of them it gives you this answer.
Answer: Total volume= 71.21 in^3
Step-by-step explanation:
The volume of the sphere= (4/3)*π*(2^3) = 33.51 in^3
The volume of the cylinder= π*(2^2)*3 = 37.7 in^3
Total volume= 71.21 in^3
You have 7 quarters, 6
dimes, 4 nickels and 25
pennies. How much money
do you have?
Answer:2.80
Step-by-step explanation:
Answer:
$2.80
Step-by-step explanation:
One quarter is worth 25 cents. 4 quarters is a dollar.
0.25 x 7 = $1.75
----------------
One dime is worth 10 cents
0.10 x 6 = 0.60 cents
----------------
One nickel is worth 5 cents
0.5 x 4 = 20 cents
One penny is worth 1 cent
It's rather simple here. 25 pennies is 25 cents
----------------
Now, you have to add all the numbers together.
1.75 + 0.60 + 0.20 + 0.25 = 2.80
Add the correct label and your final answer is $2.80
--------------------------------------------------------------------------
Hope this helps!
Have a great day and God bless! :)
Make a conjecture about each possible value for the following scenario:
The relationship between the area of a rectangle and a
triangle with the same base and equal heights.
The conjecture that can be made with regards to the given scenario is, given that the variable in the equation for the areas of the triangle and rectangle are the same;
The area of the triangle is half the area of the rectangle What is a conjecture?A conjecture is a conclusion or opinion which is based on partial or incomplete details or information ;
An appropriate conjecture that can be made with regards to the areas of the rectangle and triangle is obtained as follows;
Let the b represent the common base length, and let h represent the common height, we have;
Area of a triangle, At = 0.5•b•h
Area of a rectangle, Ar = b•h
Which gives;
At/Ar = (0.5•b•h/b•h) = 0.5The conjecture that can be made is that the area of the triangle is half the area of the rectangle.
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Write a function g whose graph represents a translation 5 units up of the graph of f (x) =3x
The required graph of the function whose translation 5 units up of the graph of f (x) =3x is g(x) = 3x + 5.
To determine a function g whose graph represents a translation 5 units up of the graph of f (x) =3x.
Here,
Given function f(x) = 3x
Now, for the upward translation by 5 units,
The function can be changed as the output of F(x) by +5 units so,
g(x) = 3x + 5
Thus, the required graph of the function whose translation 5 units up of the graph of f (x) =3x is g(x) = 3x + 5.
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State whether sentence is true or false. If false, replace the underlined word or phrase to make a true sentence.
The ₋Law of Sines can be used to find an angle measure when given three side lengths.
Given statement 'The ₋Law of Sines can be used to find an angle measure when given three side lengths.' is False.
The correct statement is 'The ₋Law of cosines can be used to find an angle measure when given three side lengths.'
We know that an oblique triangle is a triangle which is either acute triangle or obtuse triangle but not a right triangle.
We know that the Law of Sines defines the relationship between the sides and angles of an oblique triangle.
And to use the Law of Sines we must know either two angles and one side of the triangle or two sides and one of the opposite angle to them (SSA).
But, the Law of Cosines is used to find the remaining parts of an oblique triangle.
This means, in case of the Law of Cosines when either the two sides and the angle included is given or the lengths of the three sides are given then we find the remaining angle measure.
Therefore, given statement 'The ₋Law of Sines can be used to find an angle measure when given three side lengths.' is False.
The correct statement is 'The ₋Law of cosines can be used to find an angle measure when given three side lengths.'
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the difference between the areas of the figures is less than 2
Answer:
Step-by-step explanation:
Determine whether \triangle X Y Z is an acute, right, or obtuse triangle for the given vertices. Explain.
X(1,2), Y(4,6), Z(6,6)
The triangle having vertices X(1,2), Y(4,6), Z(6,6) is obtuse.
According to the Pythagorean Inequality Theorem, a triangle whose sides measure a, b, and c where c is the largest, the triangle can be characterized as:
acute if [tex]c^{2} < a^{2} + b^{2}[/tex]obtuse if [tex]c^{2} > a^{2} + b^{2}[/tex]right if [tex]c^{2} = a^{2} + b^{2}[/tex]XY = [tex]\sqrt{(4-1)^{2} + (6 - 2)^{2} }[/tex]
∴ XY = 5
YZ = [tex]\sqrt{(6 - 4)^{2} + (6 - 6)^{2} }[/tex]
∴YZ = 2
ZX = [tex]\sqrt{(6 - 1)^{2} + (6 - 2)^{2} }[/tex]
∴ ZX = 6.4
∴The longest side is ZX = 6.4
Hence, a = XY, b = YZ and c = ZX;
Consider [tex]a^{2} + b^{2}[/tex]:
= [tex]XY^{2}[/tex] + [tex]YZ^{2}[/tex]
= [tex]5^{2} + 2^{2}[/tex]
= 29.
Now consider [tex]c^{2}[/tex]:
= [tex]6.4^{2}[/tex]
= 40.96.
Thus, [tex]c^{2} > a^{2} + b^{2}[/tex]
Hence, the triangle is obtuse.
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