The limiting matrix is [tex]\bar{P}[/tex]=[tex]\left[\begin{array}{ccc}0.75&0.25\\0.75&0.25\\\end{array}\right][/tex].
What is meant by transition matrix?Mathematicians frequently refer to "transition matrices" in a variety of situations. The term "change of coordinates matrix" is occasionally used in the context of linear algebra. As an alternative term for a stochastic matrix, or a matrix that describes transitions, it is employed in the theory of Markov chains. Use row operations to try to create the identity matrix to the left while augmenting the matrix of the second basis with the matrix of the first basis. Afterward, the transition matrix will be on the right. Row 1 should be multiplied by 1 as follows: R1=R1 R 1=-R 1 R1=R1.
The given transition matrix is:
P=[tex]\left[\begin{array}{ccc}0.9&0.1\\0.3&0.7\\\end{array}\right][/tex]
Let S=[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}0.9&0.1\\0.3&0.7\\\end{array}\right][/tex][tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex] =[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}0.9a+0.1b\\0.3a+0.7b\\\end{array}\right][/tex]=[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]
Here, 0.9a+0.1b=0, 0.3a-0.3b=0
So, a=b
a+b=1
a=b=1/2
S=[tex]\left[\begin{array}{ccc}0.5\\0.5\\\end{array}\right][/tex]
This S is called the stationary matrix
P=[tex]\left[\begin{array}{ccc}0.9&0.1\\0.3&0.7\\\end{array}\right][/tex]
P=det[tex]\left[\begin{array}{ccc}0.9-\lambda&0.1\\0.3&0.7-\lambda\\\end{array}\right][/tex]=0
λ²-1.6λ+0.6=(λ-1)(λ-0.6)=0
λ₁=1, λ₂=0.6
x=[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]
Px=λx
[tex]\left[\begin{array}{ccc}0.9&0.1\\0.3&0.7\\\end{array}\right][/tex][tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex] =1[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]
0.9a+0.1b=a
a=b
v₁=[tex]\left[\begin{array}{ccc}1\\1\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}0.9&0.1\\0.3&0.7\\\end{array}\right][/tex][tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex] =0.6[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]
0.9a+0.1b=0.6a
b=-3a
v₂=[tex]\left[\begin{array}{ccc}1\\-3\\\end{array}\right][/tex]
V=[tex]\left[\begin{array}{ccc}1&1\\1&-3\\\end{array}\right][/tex]
V⁻¹=(1/4)[tex]\left[\begin{array}{ccc}3&1\\1&-1\\\end{array}\right][/tex]
D=[tex]\left[\begin{array}{ccc}\lambda_{1} &0\\0&\lambda_{2}\\\end{array}\right][/tex]
D=[tex]\left[\begin{array}{ccc}1&0\\0&0.6\\\end{array}\right][/tex]
P=VDV⁻¹
Pⁿ=VDⁿV⁻¹
[tex]\bar{P}[/tex]=[tex]\left[\begin{array}{ccc}0.75&0.25\\0.75&0.25\\\end{array}\right][/tex]
This is the required limit matrix.
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Mrs.Galicia dropped a ball from the top of a tower. At the same time, her son, Antonio, launches a rocket from a different level of the tower.
The height of the tennis ball in feet after t seconds can be represented by the quadratic function: b(t)=-t^2-4t+22.
The height of Antonio's rocket after t seconds can be represented by the linear function: p(t)=-2t+12.
What are the two solutions to this system? Show your work algebraically.
Explain which solution is not reasonable in this situation.
After how many seconds do the rocket and the ball reach the same height.
The system's two potential fixes are
t = 3.099 tennis ball
launch of a rocket, t = 6
Antonio's rocket's height is the unreasonable solution, because the path was followed should not be a linear function.
At 2.32 seconds, the rocket and tennis ball both reach the same height.
How can the two systems be solved?The two equations of motion are
b(t) = -t² - 4t + 22.
p(t) = -2t + 12
The answer to the quadratic equation is
b(t) = -t^2 - 4t + 22.
t = 3.099 OR t = -7.099
use positive hence t = 3 seconds
The linear equation's answer is
t = 6
The linear equation is the answer that is unreasonable in this case. because projectile motion does not follow a linear path
duration to reach the same height
-2t + 12 = -t^2 - 4t + 22.
-t^2 - 2t + 10
When the equation is solved,
t = 2.3166 OR -4.3166
select the positive number.
t = 2.32 s
2.32 s is needed to reach the same height.
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Find ℎ(−5) when ℎ(x) = −3|x − 1| + 4
Answer:
ℎ(−5) is −14.
Step-by-step explanation:
To find the value of ℎ(−5), we plug −5 in for x in the expression for ℎ(x):
ℎ(−5) = −3|−5 − 1| + 4
To evaluate the absolute value, we need to find the distance between −5 and 1 on the number line. Since the absolute value function is always non-negative, the distance between −5 and 1 will be positive.
To find the distance between −5 and 1, we subtract the smaller number from the larger number:
|−5 − 1| = |−6| = 6
Now we can plug this value into the expression for ℎ(−5) to find its value:
ℎ(−5) = −3 * 6 + 4
ℎ(−5) = −18 + 4
ℎ(−5) = −14
Therefore, the value of ℎ(−5) is −14.
Please help asap this is my last class I need to finish and I’m super behind!!
The table below represents a linear function.
What is the rate of change?
(Picture below)
The rate of change of the linear function represented by the table is a = 4.
What is the rate of change of the linear function?
A general linear function is written as:
f(x) = a*x + b
Where a is called the slope and is also the rate of change of the function, and b is the y-intercept.
If we know two points on the line, (x₁, y₁) and (x₂, y₂), then the rate of change can be computed with the following formula:
a = (y₂ - y₁)/(x₂ - x₁)
In this case we have a table with some points on that line, we can use any two we want.
For example, I will use the first two, these are:
(-4, -21) and (-3, -17)
Then the rate of change of the linear function is given by:
a = (-17 + 21)/(-3 + 4) = 4/1 = 4
The rate of change is a = 4.
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Sarah has $12000 to invest and decides to invest it in a
mutual fund that has averaged a compound rate of return of
15.2% for each of the last 6 years. How many years will
it take for her money to grow to $600 000 if this fund
continues to average 15.2% during the time invest? Round
off your answer to the nearest year.
O 15
0 28
0 45
0 43
Answer:
Step-by-step explanation:
as he walked along the beach, johnny counted seashells and starfish that washed up in the sand. johnny counted 9 seashells. that is 3 more than the number of starfish he counted. which equation can you use to find how many starfish johnny counted?
Answer:
There’s 3 starfish and 9 seashells.
Step-by-step explanation:
3 x _ = 9
9 / 3 = 3
3 starfish
what shape is the cross section of a triangular pyramid sliced by a plane that is perpendicular to its base?
The shape of the cross section of a triangular pyramid sliced by a plane that is perpendicular to its base is triangle.
What is meant by cross section?The non-empty intersection of a solid body in three dimensions with a plane, or its equivalent in higher dimensions, is referred to as a cross section in geometry and science. Many parallel cross-sections are produced when an object is sliced. The boundary of a cross-section in three dimensions that is parallel to two of the axes, that is, parallel to the plane determined by these axes, is sometimes referred to as a contour line.
A triangle-shaped pyramid essentially has a triangle-shaped base. The cross section formed when an imaginary line is produced to cut through perpendicular to the base will still have a triangular orientation, but it will be smaller than it was when the pyramid's original triangular orientation or sides were there.
Therefore, the shape of the cross section of a triangular pyramid sliced by a plane that is perpendicular to its base is triangle.
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What’s the equation for this graph
Answer:
rise/run
Step-by-step explanation:
Which of the following options have the same value as 40\%40%40, percent of 848484?
Choose 2 answers:
Choose 2 answers:
(Choice A)
A
40\cdot 8440⋅8440, dot, 84
(Choice B)
B
0.4\div 840.4÷840, point, 4, divided by, 84
(Choice C)
C
\dfrac{40}{100}\cdot 84
100
40
⋅84start fraction, 40, divided by, 100, end fraction, dot, 84
(Choice D)
D
84 \div 4084÷4084, divided by, 40
(Choice E)
E
0.4\cdot 840.4⋅840, point, 4, dot, 84
On calculating, the 40% of 84 is found to be 33.6.
What is an expression? What is a expression? What is a mathematical equation? A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.Given is that to find the 40% of 84.
Assume that the 40% of 84 is equivalent to [x]. Then, we can write -
x = (40/100) x 84
x = 4/10 x 84
x = 8.4 x 4
x = 33.6
Therefore, on calculation, the 40% of 84 is equivalent to 33.6.
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Can someone help with a step by step answer to This?
And a an answer to what the end behaviors are, Thank you to whoever helps.
The end behaviours of the functions are f(x) = x⁴ - x³ - 16x³ + 4x + 48
As x ⇒ +∝, f(x) ⇒ +∝ and as x ⇒ -∝, f(x) ⇒ -∝
How to determine the end behaviours of the functions?The equation of the function is given as
f(x) = x⁴ - x³ - 16x³ + 4x + 48
Calculate f(∝) and f(-∝).
So, we have
f(∝ ) = ∝ ⁴ - ∝ ³ - 16∝ ³ + 4∝ + 48
So, we have;
f(∝) = ∝
Also, we have
f(-∝ ) = -∝ ⁴ - (-∝) ³ - 16(-∝) ³ - 4∝ + 48
Evaluate;
f(∝) = -∝
This means that the end behaviours of the functions are;
As x ⇒ +∝, f(x) ⇒ +∝
as x ⇒ -∝, f(x) ⇒ -∝
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Sofia is dividing 8 by 22. If she continues the process, what will keep repeating in the quotient?.
The integer numbers that will be repeating in the quotient is 36, the decimal representation of the fraction is 0.3636...
When 8 is divided by 22 we get the fraction 8/22 , when simplified this fraction gives 4/11 .
Now we will divide the numerator by the denominator we get:
4 ÷ 11 = 0.363636...
Thus, it is a repeating decimal .
Hence the numbers 36 will constantly repeat itself.
A quotient is the result of dividing two numbers. The quotient is a mathematical phrase that can also be used to refer to the integer component of a division, fraction, or ratio.
The term "quotient" has been used in many mathematical disciplines to depict structures generated by disassembling larger structures. Given a set with an equivalence relation specified on it, a "quotient set" having particular equivalence classes as items can be formed.
A quotient group is generated by dividing a group into numerous comparable co-sets, and a quotient space is formed by dividing a vector space into numerous comparable linear subspaces.
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Given f (x) = -2x+1 and g(x) =3x determine the value of f (4) + g(-1)
Answer:
-11
Step-by-step explanation:
f(4)=-2(4)+1
f(4)= -8+1
f(4)= -7
g(x)= 3(-1)
g(x) = -4
f(4)+g(-1)= -7+(-4)
-7-4
-11
hopes this helps
Answer:
-11 just took the test and that was mine
Step-by-step explanation:
On a sunny fall day, Paul and his family go to an orchard to pick apples for their famous apple
pies. First, they pick enough Golden Delicious apples to fill a bag. Then, they pick enough
Honeycrisp apples to fill another bag. The bag of Honeycrisp apples weighs 18 pounds. In all,
Paul's family picks 22 pounds of apples.
Which equation can you use to find the weight w of the Golden Delicious apples?
w + 18 = 22
Type here to search
W
18
Submit
= 22
Solve this equation for w to find the weight of the Golden Delicious apples.
pounds
w 18 = 22
Bi
18w = 22
Work it out
Vide
The equation that can use to find the weight w of the Golden Delicious apples w + 18 = 22.
The weight of the Golden Delicious apples is 4 pounds.
What is a linear equation?
The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x + 3 = 8 only has one variable.
Given that, Paul's family picks 22 pounds of apples.
They pick a bag of Honeycrisp apples weighs 18 pounds.
Assume that they take Golden Delicious apples with weight w.
Then the total weight of the bag is 18 + w.
The equation is
18 + w = 22
Subtract 18 from both sides:
18 + w - 18 = 22 - 18
w = 4
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What are the 4 types of slope lines?
The four types of slope lines are positive, negative, zero and undefined.
Slope is the term that measure the extent of steepness of any figure or any curve. If we want to find the equation of the line, then the slope is the most useful term. The general formula for determining the slope between two points (x₁, y₁) and (x₂, y₂) is expressed as
m = (y₂ - y₁)/(x₂ - x₁) where m is the slope .
There are generally four types of slope.
If the value of both the numerator and denominator are positive or negative, then the slope is said to be positive means line goes upward.If the value of either the numerator or denominator is negative, then the slope is said to be negative means line goes downward.If the value of the numerator is zero, then slope is said to be zero means line is parallel to x-axis.If the value of the denominator is zero, then the slope is said to be undefined means line is parallel to y-axis.Learn more about Slope at:
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Is this a false or true statement? Extrapolation is the use of the regression line to estimate a mean of y-values for an x-value that is far outside the x-range of data
This is False in light of the stated statement. Due to the employment of a regression line to calculate the mean of y for x that are outside the x-range of the data.
How is regression calculated?
Y = mX + b, where X is the predictive (independent) factor, m is really the approximately slope, and b is the expected intercept, is the methodology for simple linear regression.
The relationship between scattered data points in any set is shown by a regression line. When there is a linear pattern, it displays the relationship between the dependent y variable and independent x variables.
The correlation between the independent variables (IVs) and the dependent variable is described by a linear regression equation (DV). The DV for the IV values you indicate can also be predicted for new values.
Hence we get the required answer.
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What is the vertex of â XYZ â XYZ?
The measure of the vertex X in the given triangle XYZ is 90° .
In the question ,
it is given that ,
that there is a triangle XYZ ,
and the measure of vertex Y is 45° and vertex Z is 45° ,
By Applying the Angle Sum Property of triangle ,
measure of angle X + angle Y + angle Z = 180°
So , X + 45° + 45° = 180
Adding the terms ,
X + 90° = 180°
Subtracting 90° from both sides of the equation ,
we get,
X = 180° - 90°
X = 90°
Therefore , the measure of the vertex X is 90° , so the triangle XYZ is a right triangle .
The given question is incomplete , the complete question is
What is the measure of the vertex X of the triangle XYZ which have ∠Y = 45° and ∠Z = 45° ?
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The tangent of O in this triangle is Which equation must be true?
The correct answer is option D, which states tan∝ = 1/2
What is Trigonometry
The field of mathematics concerned with the relationships between triangle sides and angles, as well as the pertinent functions of any angles is Trigonometry.
Solution:
we are given that tanθ = 1/2
this implies θ = 45°
We know that the sum of all interior angle of triangle is 180°
so, it can be calculated that the value of
angle ∝ = 45°
Therefore, tan∝ = 1/2
The correct answer is option D, which states tan∝ = 1/2
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Please help me I don’t know the answer. :(
Maria spent $12.50 at the post office. She bought three times as many $0.41 stamps as $0.02 stamps. How many of each did she buy?
The numbers of $0.02 stamps and numbers of $0.41 stamps, if Maria spent $12.50 at the post office. Three times as many $0.41 stamps were purchased by her as $0.02 stamps are 10 and 30 respectively.
What is the equation?The equals sign is used in equations to indicate the equality of two expressions in a formula.
Given:
Maria spent $12.50 at the post office. She bought three times as many $0.41 stamps as $0.02 stamps.
Write the equations as shown below,
3x = y and 0.02 x + 0.41 y = 12.5
Here, x = number of 0.02 stamps and y = number of 0.41 stamps.
Solve the equation by substituting the value of x,
x = 10 and y = 3 × 10 = 30
As a result, there are 10 and 30 $0.02 stamps and $0.41 stamps, respectively.
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20 pionts if you help me!!!! and brainlest !!!!
in the GIF TYSM ⇅
a. The solution to the system of equations is: (4, 12).
b. The graph is shown below.
c. (4, 12) is the point of intersection. It confirms the solution from part a.
What is the Solution of a System of Equations?The solution of a system of equations can be described as the value of x and y of a point, that makes both equations true. It is the point where the two lines of the equations of the system intersect.
If we are given two tables, the ordered pair that appears in both table is considered the solution of the system.
a. The ordered pair, (4, 12) appears in both tables. Therefore, the solution is: (4, 12).
b. The graph of the ordered pairs from each table are sketched in the image shown below, where the green line is for the first table, and the blue line is for the second table.
c. The point of intersection of the graph is (4, 12), this confirms the solution from part a.
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What is AAS ASA SSS SAS?
The rules AAS, ASA, SSS and SAS are congruence rule of triangle and the each rules has been explained
The rules AAS, ASA, SSS and SAS are congruence rule of triangle
SSS rule is side-side-side rule, it states that if three sides of the one triangle and three sides of the other triangles are equal, then both triangles are congruent
SAS rule is side-angle-side rule, it states that if two sides and one included angles between the sides of the one triangle is equal to the two sides and one included angles between the sides of the other triangle, then both triangles are congruent
ASA rule is angle-side-angle rule, it states that if two angles and one included side between the angle of the one triangle is equal to the two angles and one included sides between the angles of the other triangle, then both triangles are congruent
AAS rules is angle-angle-side rule, it states that if two angles and one non included sides of the one triangle is equal to the two angles and one non included sides of the another triangle, then both triangles are congruent
Therefore, the AAS, ASA, SSS and SAS are the rules of congruence of the triangle
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A shipping container will be used to transport several 50-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 27500 kilograms. Other shipments weighing 9500 kilograms have already been loaded into the container. Write and solve an inequality which can be used to determine xx, the number of 50-kilogram crates that can be loaded into the shipping container.
Answer:
To write and solve an inequality that can be used to determine the number of 50-kilogram crates that can be loaded into the shipping container, we need to first find the total weight of the crates that can be loaded into the container. The maximum weight that can be loaded into the container is 27500 kilograms, and other shipments weighing 9500 kilograms have already been loaded, so the total weight of the crates that can be loaded is 27500 kilograms - 9500 kilograms = 18000 kilograms.
Next, we need to divide the total weight of the crates that can be loaded by the weight of each crate to find the number of crates that can be loaded. Since each crate weighs 50 kilograms, the number of crates that can be loaded is 18000 kilograms / 50 kilograms = 360 crates.
To express this as an inequality, we can use the following equation:
x <= 360
This inequality states that the number of crates that can be loaded into the shipping container (x) must be less than or equal to 360. Therefore, the number of 50-kilogram crates that can be loaded into the shipping container is x <= 360.
Step-by-step explanation:
Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x2 + y2 = 2.
The area of the surface = [tex]\pi \sqrt{14}[/tex] sq. units
As given in the question the part of,
plane ⇒ x + 2y = 3z = 1
cylinder = [tex]x^{2} + y^{2} = 3[/tex]
Let take P = projection on plane x + 2y + 3z = 1
The surface area of the equation is given by,
∫∫ₚ √{1+(∂z/∂x)² + (∂z/∂y)²} dA
Using the coordinate of the cylinder,
x = n cos [tex]\alpha[/tex] , y = n sin [tex]\alpha[/tex]
= [tex]x^{2} + y^{2} = (n cos \alpha )^{2} + n sin \alpha ^{2}[/tex]
= [tex]n^{2} (cos^{2}\alpha + sin^{2}\alpha )[/tex]
= [tex]n^{2}[/tex] x 1 = [tex]n^{2}[/tex]
= [tex]n^{2}[/tex] = 2 ⇒ n = [tex]\sqrt{2}[/tex]
Therefore, P = {(r,θ)/ 0 ≤ r ≤ [tex]\sqrt{2}[/tex], 0 ≤ θ ≤ 2π}
x +2y + 3z =1
⇒ z = 1/3(1 - x - 2y)
∂z/∂x = -1/3 ; ∂z/∂y = -2/3
According to the formula of surface area,
= ∫∫ₚ √{1+ (-⅓) ² + (-⅔) ²} dA
= 14 /3 [tex]\int\limits_0^{2\pi } \int\limits_0^{\sqrt{3} }[/tex] dA is an area of region P
= [tex]\sqrt{14}[/tex] / 3 [tex]\int\limits_0^{2\pi } \int\limits_0^{\sqrt{3} }[/tex]r. dr. d[tex]\alpha[/tex]
= [tex]\sqrt{14}[/tex] / 3 [tex]\int\limits_0^{2\pi }[/tex] [tex][r^{2} / 2 ]^{\sqrt{3} }_0[/tex] .d[tex]\alpha[/tex]
= [tex]\sqrt{14}[/tex] /3 [tex]\int\limits_0^{2\pi }[/tex]3/2. d[tex]\alpha[/tex]
= [tex]\sqrt{14}[/tex] /2 [tex][\alpha ]^{2\pi }_ 0[/tex]
= [tex]\sqrt{14}[/tex] /2[[tex]2\pi[/tex] - 0]
= [tex]\pi \sqrt{14}[/tex]
Therefore, the area of the surface = [tex]\pi \sqrt{14}[/tex] sq. units
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Deepa needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 4. 25 hours and charged her $167 for parts. The total was $655. 75. Write and solve an equation which can be used to determine xx, the cost of the labor per hour.
The cost of the labor per hour is 115 hours.
The equation is going to be:
4.25x + 167 = 655.75
your x is going to be:115
The duration was 4.25 hours.
The parts cost 167.
Cost in full: 655.75
so the price per hour is x.
As a result, when you write your equation, the total number of hours (multiplied by the cost per hour) will be added to the cost of the parts, and the sum of these two amounts will be your total cost.
In order to solve the problem, you must deduct the cost of each component from the total cost. This should give you the following result: 4.25x = 488.75
After that, divide 4.25 by each side as you normally would.
The cost of labor per hour follows. 115
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How do I simplify the expression
The value of the equation A = n³ ( 2n )⁻² is given by A = ( n / 4 )
What are the laws of exponents?
When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the equation be represented as A
Now , the value of A is
A = n³ ( 2n )⁻²
On simplifying the equation using the laws of exponents , we get
The value of A = n³ / ( 2n )²
Taking the powers to the value of 2n , we get
The value of A = n³ / 4n²
On dividing the numerator and denominator by n² , we get
The value of A = n / 4
Therefore , the value of A = n / 4
Hence , The value of the equation A = n³ ( 2n )⁻² is given by A = ( n / 4 )
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productivity is defined by the formula of outputs divided by ______ for a specified period of time.
Productivity is referred as the formula for the outputs divided by inputs in a given specified period of time.
All created products and services are considered as outputs. Along with labor, inputs also include capital, supplies, and energy. A common definition of productivity is the ratio of input volume to output volume. In other words, it assesses how effectively an economy uses labor and capital as production inputs to create a particular amount of output.
The simplest productivity calculation yields a straightforward ratio: Total output divided by total input is productivity. By dividing total output by total input, the labor productivity equation can be used to calculate employee productivity. Let's say your business spent 1,500 labor hours to produce $80,000 worth of goods or services (input). To determine the labor productivity of your business, divide 80,000 by 1,500, which results in the number 53.
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the dolphins at the washington aquarium are fed 1/2 of a bucket of fish each day. the sea otters are fed 2 1/3 times as much fish as the dolphins. how many buckets of fish are the sea otters fed each day?
The number of buckets of fish that the sea otters fed each day is 7/6 buckets .
In the question ,
it is given that ,
the number of buckets of fish that the dolphin are fed at the Washington aquarium = 1/2 bucket
the sea otters are fed [tex]2\frac{1}{3}[/tex] times as many as fish .
So , the number of buckets that are fed to otters is = (7/3) × (number of buckets eaten by fish)
Substituting the values of number of buckets eaten by fish ,
we get
= (7/3) × (1/2)
Simplifying further ,
we get ,
= 7/6 buckets .
Therefore , the sea otters are fed 7/6 buckets of fish each day .
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The area of a rectangle is 105 sq in and the length of one side is 7 in. what is the length of the perimeter?
Answer:
Step-by-step explanation:
yall weird ok
-4(-x-8)...................
Answer:
Step-by-step explanation:
-4(-x-8)
= (-4)(-x+-8)
= (-4)(-x)+(-4)(-8)
= 4x+32
Josh's father is paying for a $20 meal. He has a 15%-off coupon for the meal. After
the discount, a 7% sales tax is applied. What does Josh's father pay for the meal?
The amount paid for meal is obtained as $18.19.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
A percentage can be converted into a fraction or a decimal by dividing it by 100.
Given that,
The price of the meal is $20.
The percent discount is 15%.
And, the percent tax is 7%.
Now, the final amount paid can be calculated as follows,
(20 - 15% of 20) + 7% of (20 - 15% of 20)
= (20 - 15/100 × 20) + 7/100 × (20 - 15/100 × 20)
= 17 + 7/100 × 17
= 17 + 1.19
= 18.19
Hence, the amount paid by the father for meal is $18.19.
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Formula: A = P (1 + ht
Solve the problem by answering the following questions:
An initial investment of $5575 is appreciated for 12 years in an account that earns 3.25%
interest, compounded semiannually. Find the amount of money in the account at the end
of the period.
i. What does each of these variables represent:
A:
P:
r:
n:
t: 12
ii. List all the known and the unknown for the problem.
iii. Use the given formula and show your work in finding the unknown.
iv. Briefly, explain what your finding means.
The amount of investment after compound interest will be $8183.24.
What is compound interest?Compound interest is the addition of interest to the principal sum of a loan or deposit or interest on interest plus interest.
In finance and economics, interest is the payment of an amount above the repayment of the principal sum by a borrower or deposit-taking financial institution to a lender or depositor at a specific rate by a borrower or depositor. It differs from a fee that the borrower may pay to the lender or a third party.
The formula calculates compound interest is calculated by the formula,
[tex]A=P(1+\dfrac{r}{100})^{nt}[/tex]
Here,
A = Amount
P = Principle amount
r = rate of interest
n= Number of times amount compounded
t = time
The compounded amount will be calculated as,
A = 5575 ( 1 + 0.0325 )¹²
A = 5575 x 1.4678
A = $8183.24
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How much do you need to deposit into your account that pays 8% interest compounded quarterly to have a balance of $4500 after 10 years?
Answer: 810
Step-by-step explanation: