The bat colony will cover an area of 80,000 square miles in 1.612 hours.
What is defined as the circle?A circle is the collection of all the points together in plane that are equally distant from the a given point known as the circle's center. A circle is represented by the symbol. A radius of a circle is a line segment that connects the center of a circle toward any point on the circle.
Now, as per the given question;
The area covered (A) by the colony, evaluated in square miles, is depicted by the mentioned geometrical formula as the bat colony emerges from a cave & spreads out in a circular pattern:
A = π R²
R = the bat's distance from the cave, calculated in miles.
Furthermore, each bat moves at a constant speed, and distance is depicted by the following kinematic formula:
R = r₀ + rΔt
r₀ = The bat's initial distance from the cave, estimated in miles.
r = Bat speed, estimated in miles per hour.
Δt = Time, expressed in hours.
Substitute the value of R in the formula of area.
A = π (r₀ + rΔt)²
(r₀ + rΔt)² = A/ π
(r₀ + rΔt) = √(A/ π)
rΔt = √(A/ π) - r₀
Δt = (√(A/ π) - r₀)/r
r = 99 miles per hour
The distance between the bat and the cave has now been substituted, and time has been cleared:
A = area of 80,000 square miles
π = 3.14
r₀ = 0 miles per hour
Substituting all the values in the A we calculate the time.
Δt = (√( 80,000/3.14) - 0)/99
On solving;
Δt = 1.612 (approx)
Thus, It will take 1.612 hours for the bat colony to cover an area of 80,000 square miles.
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The complete question is-
The Brazilian free-tailed bat can travel 99 miles per hour. after sunset, a colony of bats emerges from a cave and spreads out in a circular pattern. how long before these bats cover an area of 80,000 square miles? use pi = 3.14.
7. One hundred three and one half gallons drained in the last 9 minutes from a pool. The water drains at a constant rate. How many gallons drain per minute from the pool?
The Number of Gallons drained per minute from the pool is; 931.5 gallons drained per minute
What is the constant rate?Constant rate is simply a rate that remains unchanged regardless of change in parameters.
Now, we are told that One hundred three and one half gallons drained in the last 9 minutes from a pool. Thus;
Amount of gallons that drained from pool = 103¹/₂ gallons = 207/2 gallons
Time it took to drain = 9 minutes
Thus;
Number of Gallons drained per minute from the pool = (207/2)/9
Number of Gallons drained per minute from the pool = (207 * 9)/2
Number of Gallons drained per minute from the pool = 931.5 gallons drained per minute
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2. Does being able to use a sequence of rigid transformations to specify how one shape
got to another shape prove that two shapes are congruent? Why or why not?
If two shapes can be mapped onto one another using rigid transformations, then yes, they can be said to be congruent.The preimage of right angle triangle and a right angle triangle are the example of congruent shapes.
Two shapes are considered to be congruent if they can be mapped onto one another using rigid transformations (a sequence of one or more rotations, translations, and reflections). A congruent triangle is produced by any series of rigid transformations applied to a triangle.
Now, let's learn about Rigid transformation
A rigid transformation of the plane, also known as an isometry, keeps length intact. "Rigid transformations" include reflections, translations, rotations, and combinations of these three transformations.
Example: The preimage of right angle triangle and a right angle triangle are the example of congruent shapes.
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is a proper subset different from a regular subset? is an empty set a proper subset? provide an example of a set for your classmates to solve for both a proper subset and an empty set. check and respond to the replies to your examples.
yes proper subset is different from a regular subset. The empty set is a proper subset of every set except for the empty set
A proper subset of a set A is a subset of A that cannot be equal to A. In other words, if B is a proper subset of A, then all elements of B are in A but A contains at least one element that is not in B.
Subset: If A and B are sets and every element of A is also an element of B, then:
A is a subset of B, denoted by A ⊆ B.
or equivalently, B is a superset of A, denoted by B ⊇ A.
Any set is considered to be a subset of itself. No set is a proper subset of itself. The empty set is a subset of every set. The empty set is a proper subset of every set except for the empty set.
For example, A = {1, 2, 3, 4, 5} and B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
A = {1, 2, 3} and B = {1, 2, 3}
Here, A is a subset of B, or we can say that B is the superset of A.
Proper Subset: If A is a subset of B, but A is not equal to B (that is, there exists at least one element of B which is not an element of A), then
A is also a proper (or strict) subset of B; this is written as A ⊊ B.
For example A = {1, 2, 3} and B = {1, 2, 3, 4}.
Clearly, A is not equal to B and element {4} belongs to set B but is absent in set A, so we have one element in set B which is not an element of set A. Thus, A can be called a proper subset of B.
Hence, a proper subset of a set A is a subset of A that is not equal to A. In other words, if B is a proper subset of A, then all elements of B are in A but A contains at least one element that is not in B, thus the proper subset may or may not be the same.
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What expressions are equivalent to the given expression
The value of the given expression is equivalent to [tex]y^{-5} x^{-2}[/tex], that is, option 5.
An exponent is a number or variable that is placed above and to the right of the expression to which it applies. It tells us the number of times the expression is used as a factor.
Here, we are given an expression as follows-
To simplify this expression we can use the following property of exponentials-
[tex]a^{l} a^{k} = a^{k+l}[/tex]
This holds true for all real values of a, k and l.
Thus, we can write the given expression as-
[tex]y^{-8} y^{3} x^{0} x^{-2} = y^{-8+3} x^{0-2}[/tex]
= [tex]y^{-5} x^{-2}[/tex]
Thus, the value of the given expression is equivalent to [tex]y^{-5} x^{-2}[/tex].
From the given options, thus, option number 5, is the correct answer.
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what the product of 6 and x
Answer:
6x
Step-by-step explanation:
Because, 6 multiplied by x, we know that if there is just an x, we add a 1, so it would be 1x. 1x multiplied by 6 is 6x.
Hope this helps you!
Answer:
6x
Step-by-step explanation:
The product means multiply
6*x
6x
Graph the image of the
quadrilateral below using a scale
factor of & = 3/2.
The coordinates of the vertices of the image are Q'(x, y) = (- 1.5, 6), T'(x, y) = (0, - 3), R'(x, y) = (1.5, 3) and S'(x, y) = (3, - 3), respectively.
What is the image of a quadrilateral after applying a dilation factor?
A dilation is a kind of rigid transformation, that is, a transformation applied on geometric loci such that its Euclidean distance is conserved. According to the statement, we must the following dilation to generate the image:
P'(x, y) = (3 / 2) · P(x, y)
If we know that Q(x, y) = (- 1, 4), T(x, y) = (0, - 2), S(x, y) = (2, - 2) and R(x, y) = (1, 2), then the vertices of the images are:
Q'(x, y) = (3 / 2) · (- 1, 4)
Q'(x, y) = (- 1.5, 6)
T'(x, y) = (3 / 2) · (0, - 2)
T'(x, y) = (0, - 3)
R'(x, y) = (3 / 2) · (1, 2)
R'(x, y) = (1.5, 3)
S'(x, y) = (3 / 2) · (2, - 2)
S'(x, y) = (3, - 3)
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25 POINTS PLEASE HELP
rewrite the equation to 2y - 4x = 10 in function notation where f (x) = y
Answer:
I think it's, Y = 2x + 5
Step-by-step explanation:
* You move the -4x to the right side.
* Divide 2 from both sides
And you will end up with this answer.
F(x) means the equation
and we are solving for Y here.
Find value of x.
3x + 6 - 6 = 248
Answer:
x=82.7
Step-by-step explanation:
3x+6-6=248
3x=248
x=82.7
Answer:
[tex]82.6[/tex]Step-by-step explanation:
Simplify both sides of the equation:3x + 6 − 6 = 248
3x + 6 + − 6 = 248
( 3x ) + ( 6 + − 6 ) = 248 (ℂ )
3x = 248
Divide both sides by 3:3x / 3 = 248 / 3
x = 248 / 3
x = 82.6
Which has the greater area, the space between the circle and the inside square or the space between the circle and the outside square. The length between one corner to the opposite corner of the inside square is equal to 10
Answer:The space between the circle and the outside circle
Step-by-step explanation:
The space between the circle and the outside circle
If 1 is added to a number and the sum is tripled, the result is 11 more than the number. Find the number
[tex] \large{ \star \boxed{ \tt \: Answer : \boxed{ \tt{4}}}}[/tex]
Please see the attached picture for full solution !
-------- Happy LearninG <3 --------
F (n) = 3n-1
(n) = n² - 2n-3.
д.с
Find F(g(9))
The function F(g(9))= 179
Given ,Function F (n) = 3n-1
g(n) = n² - 2n-3
g(9)= 9²-2(9)-3
= 81-18-3
g(9) = 60
F(g(9))=F(60)
= 3(60)-1
= 179
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x.
In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain.
The whole set of values that the function's output can produce is referred to as the range. The set of values that might be a function's outputs is known as the co-domain.
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2(3x-2)-4x+1= 9 solve for x
Answer:x=6
Step-by-step explanation:
6x-4-4x+1=9
subtract 1 from both sides
6x-4-4x=8
add 4 to both sides
6x-4x=12
subtract 6x by 4x
2x=12
divide by 2 on both sides
x=6
solve for x
3/9 = x/12
Simplify your answer as much as possible.
Answer:
Step-by-step explanation: We can begin by rewriting the equation. That would look like so:
3/9 = x/12
We need to solve for x. Our first step is to identify a common denominator. Let's list the multiples of each denominator.
9: 9, 18, 27, 36
12: 12, 24, 36
Our common denominator is 36.
Now, let's cross multiply:
3 x 12 = 36
9 x ? = 36
36 ÷ 9 = 4
x = 4
Final answer: 3/9 = 4/12, where x = 4.
Nesecito ayuda es con procedimiento
Evaluando la expresión:
b^2*(c + d) - a^2*(m + n) + 2x
En los corresopondientes valores obtendremos:
b^2*(c + d) - a^2*(m + n) + 2x = 161/6
¿Como evaluar expresiones matematicas?
Veamos la segunda expresión en la imagen, está es:
b^2*(c + d) - a^2*(m + n) + 2x
Uso está por que es la unica que puedo leer bien en la imagen.
Queremos evaluar está expresion, se nos dan los valores:
a = 1 d = 4
b = 2 m = 1/2
c = 3 n = 2/3
p = 1/4 x = 0
Solo hay que reemplazar las variables por los números correspondientes. Si reemplazamos x por 0 obtendremos:
b^2*(c + d) - a^2*(m + n) + 2*0 = b^2*(c + d) - a^2*(m + n)
Ahora reemplacemos c = 3 y d = 4:
b^2*(3+ 4) - a^2*(m + n) = b^2*7 - a^2*(m + n)
Ahora remplazamos m y n, asi obtendremos:
b^2*7 - a^2*(1/2 + 2/3) = 7*b^2 - (3/6 + 4/6)*a^2 = 7b^2 - (7/6)*a^2
Finalmente reemplazamos b y a, asi obtendremos:
7*(2)^2 - (7/6)*1^2 = 7*4 - 7/6 = 28 - 7/6 = 161/6
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Two hundred people hiked around the largest lake. About how many miles did they travel? Use the standard algorithm to solve. The largest lake is 15.33
Using proportions, it is found that they traveled a total of 3066 miles around the lake.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, that can be either direct(cross multiplication) or inverse(line multiplication), deriving from proportional relationships.
One example of application of proportions is for unit rate problems, in which we find the unit rate for a single person, and then the total amount for a number n of people is given by n multiplied by the unit rate.
For this problem, we have that:
The largest lake has a distance of 15.33 miles.200 people hiked around the lake.Hence the total distance traveled by all these people is given as follows:
200 x 15.33 = 3066 miles.
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if the first and third of three consecutive odd integers are added, the result is 63 less than five times the second integer. find the third integer.
The value of third consecutive odd is 23
• In Mathematics, algebra is a branch which only deals with symbols and the rule for the manipulation of these symbols. Algebra is divided into different sub branches such as advanced algebra, linear algebra, elementary algebra, abstract algebra etc.
• The basics of algebra contains numbers, variables, constants, expressions and equations. The basic four operations of algebra are addition, subtraction, multiplication, division.
Let the first consecutive odd integer be x
Second consecutive integer = x+2
Third consecutive integer = x+4
We are given that
First + third = 5(Second) – 63
x + x + 4 = 5 (x+2) -63
2x + 4 = 5x +10 -63
-3x = -57
3x = 57
x = 19
First Consecutive odd = 19
Second Consecutive odd = 21
Third Consecutive odd = 23
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Graph y = -1/-3 x + 4
The festival that the total attendance for 2014 will be twice the attendance in 2012. What is the projected attendance for 2014?
The projected attendance for 2014 in the form of linear equation is written as y = 2x.
What is linear equation in two variables?A linear equation in two variables is one that is written in the form ax + by + c = 0, where a, b, and c are real numbers as well as the coefficients of x and y, i.e. a and b, are not equal to zero.
For instance, 10x+4y = 3 and -x+5y = 2 are two-variable linear equations.The solution to such an equation is just a pair of values, one is for x and one for y, which also equalizes the 2 sides of an equation.Now, for the given question;
Let us consider that the total attendance in 2012 be 'x'.
And the total attendance in 2014 be 'y'.
Then, the total attendance for 2014 will be twice the attendance in 2012.
Thus,
y = 2x.
Therefore, the linear equation which shows the condition that the total attendance for 2014 will be twice the attendance in 2012 is y = 2x.
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5. What is the missing side length, x, in this
right triangle?
16 yd
20 yd
A.
4 yards
B.
8 yards
C. 12 yards
D. 16 yards
X
5
Answer: 12
Step-by-step explanation: we know that a^2 + b^2 = c^2, pythagorean theorem. We're given a and c in this case, which are 16 and 20 respectively. so that means 16^2 + x^2 = 20^2. After evaluating the equation, we get 256+ x^2 =400. now subtract 256 from both sides and then we get x^2 = 144. take the square root of both sides and we end up with x = 12.
A school had 300 students in 2013 and 450 students in 2015. What was the average rate of growth in student per year?
[tex]450 - 300 = 150 \\ 150 \div 2 = 75t \\ the \: average \: rate \: of \: growth \: per \: year \: is \: 75 \: student \: per \: year[/tex]
I will AWard Brainlist!! Please Help its A Math Problem !! Find the length of P.
p=3.5
use the sine law
sin 90/7 = sin 30/p
then cross multiply to solve
enter the expression −2c⃗ 6d⃗ in the answer box using the notation just described. express your answer in terms of c⃗ and d⃗ . use the vector button under the templates menu in the answer box to create vectors.
The expression [tex]-2\vec C+6\vec D[/tex] in the ordered pair notation is (16,-16).
The vector components of a vector are represented as the ordered pair of its x and y components.
For example, if a vector has x - component 'a' and y- component 'b' , then the ordered pair notation for the vector is (a, b), where the vector is [tex]a \vec i+b \vec j[/tex].
Now the vector C has its x- component = -2
y- component of C = -1
Therefore, ordered pair notation of C = (-2, -1)
x- component of D = 2
y-component of D = -3
Therefore, ordered pair notation of D = (2,-3)
So the expression [tex]-2\vec C+6\vec D[/tex] = -2 (-2,-1) +6 (2,-3) = (4,2) + (12, -18)
= (16, -16) in the ordered pair notation.
That is, the vector [tex]\bold {-2\vec C+6\vec D}[/tex] is a vector with x-component 16 and y-component -16.
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can you simply sq 3 + 5? yes or no and why?
What is the measure of angle ABE?
Please help!
Answer:
50 degrees
Step-by-step explanation:
The angle of ABE is opposite to angle CBD, which means that ABE = CBD
It is a math rule, all opposite angles are equal.
Part B
A new machine with better technology produces 210 gel pens every fifteen minutes. What is the constant of proportionality in the relationship between the number of gel pens and the number of minutes
The constant of proportionality i
Proportionality constant of p is = 14 t
WHAT IS PROPORTIONALITY CONSTANT ?The constant proportional relationship between two variables. The proportionality constant, k, is defined as k = y/x. This is equivalent to the equation for the slope of a line through the origin, m = y/x. The value of m, which will be the same as the value of k, or the constant or proportionality, can be discovered using the equation for the slope of the line.
CALCULATIONy = kx
The rate k = 210 ÷ 15 = 14 gel pens per minute
"p" is number of pens, "t" is number of minutes
p = 14t
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What is the image point of (9, -2) after a translation right 1 unit and down 1 unit
Answer:
( 10 , -3 )
Step-by-step explanation:
→ See which coordinate is affected by a translation right
x
→ Apply
( 10 , y )
→ See which coordinate is affected by a translation down
y
→ Apply
( 10 , -3 )
carol decides to send out a survey to see what her coworkers think of the new dress code policy. if she chooses a sample of the population that gives each person an equal chance of participating, this would be a(n) sample.
This is the random sampling is used in the statement.
According to the statement
We have to find that the about the sampling.
So, For this purpose, we know that the
A sample is an outcome of a random experiment. once we sample a chance variable, we obtain one specific value out of the set of its possible values. that exact value is termed a sample.
From the given information:
if she chooses a sample of the population that offers everyone an equal chance of participating, this might be a(n) sample.
Then
According to this, there is random sampling is used.
Random sampling is a part of the sampling technique in which each sample has an equal probability of being chosen.
So, This is the random sampling is used in the statement.
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convert 15 feet per second into yards per hour using unit cancellation
Answer:
626 times 6261 plus 276262
Step-by-step explanation:
i buy 626 cookies and 1000 million water how much did i eat and drink?
consists of the following steps: conceptualize a process or problem to be studied, collect research data, analyze the data, and draw conclusions.
The scientific method consists of the following steps: conceptualize a process or problem to be studied, collect research data, analyze the data, and draw conclusions.
Which of the following study design categories focuses on observing and documenting behavior?
Several various kinds of non-experimental studies in which behavior is routinely observed and documented are collectively referred to as observational research. A variable or combination of variables must be described in order to be the focus of observational research.What are some examples of biological processes that have an impact on development?
An individual's physical makeup can alter as a result of biological processes. and several biological processes that have an impact on development include weight gain, changes in motor skills, puberty's hormonal changes, and cardiovascular deterioration.Learn more about documenting behavior
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