math question. thanks if you hlep
Alexa borrows 10,000 from her aunt and they agree Alexa will pay her back including 5% simple interest.how much more will Alexa owe her aunt after 2 years assuming that no payments are made during that time??
Which term best describes the graph of y = -2
increasing
decreasing
constant
positive
Answer:
constant
Step-by-step explanation:
The term that best describes the graph of y = -2 is "constant". This is because the equation y = -2 represents a horizontal line that does not change in value as x changes
− 0.32 + 0.18 = 0.25 − 1.95
Answer:
Step-by-step explanation:
0.18-0.32 = .25-1.95
-0.14 = 1.70
obviously that equation above is not true, I suspect that there were some "x" variables on some of those numbers?
Serenity has a toy car collection. She keeps some in a display case and the rest on the
wall.
104
of her toy cars are on the wall, and 74% of her toy cars are in the display
case. What is the total number of toy cars in Serenity's collection?
If 74% are in the display, then 100% - 74% = 26% are hung on the wall.
This means 104 cars is 26% of her collection.
To find the total collection divide the number on the wall by the percentage of the collection:
104/0.26 = 400
The total number of her collection is 400 cars.
-in a random physical Sciences experiment A and B are two different events it was found that
,P(A)=2/5,P(B)=3/8 and P(A or B)=5/7
-calculate the P(B).
Answer:
3/8
Step-by-step explanation:
P(B) is given to you in the question.
Use variation of parameters to solve the equation y ′′
+3y ′
+2y=xe 3x
Provide the general solution in the form y=c 1
y 1
+c 2
y 2
+y p
where y 1
,y 2
is a fundamental set of solutions of y ′′
+3y ′
+2y=0 and y p
is a particular solution found by variation of parameters. Formulas: y p
=u 1
y 1
+u 2
y 2
, where u 1
=∫ W ′
W 1
,u 2
=∫ W ′
W 2
W 1
=det ⎣
⎡
0
f(x)
y 2
y 2
′
⎦
⎤
=−f(x)y 2
W 2
=det[ y 1
y 1
′
0
f(x)
]=y 1
f(x)
[ y 1
y 1
′
y 2
y 2
′
]=y 1
y 2
′
−y 2
y 1
′
,
Remember that det [ a
c
b
d
]=ad−cb.
The general solution to the given equation is:
y = c₁ * e⁻²ˣ + c₂ * e⁻ˣ - eˣ - 2xe⁻ˣ
where c₁ and c₂ are arbitrary constants.
To solve the equation y'' + 3y' + 2y = xe³ˣ, we first need to find a fundamental set of solutions for the homogeneous equation y'' + 3y' + 2y = 0.
The characteristic equation for the homogeneous equation is:
r² + 3r + 2 = 0
Factoring the equation, we get:
(r + 2)(r + 1) = 0
This gives us two distinct roots: r = -2 and r = -1.
Therefore, the fundamental set of solutions for the homogeneous equation is:
y₁(x) = e⁻²ˣ
y₂(x) = e⁻ˣ
Next, we need to find the Wronskian determinant, W, and its derivatives, W₁ and W₂.
W = det([y₁(x), y₂(x); y₁'(x), y₂'(x)])
= det([e⁻²ˣ, e⁻ˣ; -2e⁻²ˣ, -e⁻ˣ])
= -e⁻³ˣ
W₁ = det([0, e⁻ˣ; -2e⁻²ˣ, -e⁻ˣ])
= 2e⁻ˣ
W₂ = det([e⁻²ˣ, 0; -2e⁻²ˣ, -2e⁻ˣ])
= -2e⁻³ˣ
Now, we can find the particular solution, y_p, using the formulas:
u₁ = ∫(W₁' / W₁) dx
u₂ = ∫(W₂' / W₂) dx
Let's compute these integrals:
u₁ = ∫((2e⁻ˣ) / (-e⁻³ˣ)) dx
= -2 ∫ e²ˣ dx
= -e²ˣ
u₂ = ∫((-2e⁻³ˣ) / (-e⁻³ˣ)) dx
= -2 ∫ dx
= -2x
Now, we can find the particular solution, y_p, using the formula:
y_p = u₁ * y₁ + u₂ * y₂
y_p = (-e²ˣ) * e⁻²ˣ + (-2x) * e⁻ˣ
= -eˣ - 2xe⁻ˣ
Finally, the general solution to the given equation is:
y = c₁ * y₁ + c₂ * y₂ + y_p
= c₁ * e⁻²ˣ + c₂ * e⁻ˣ - eˣ - 2xe⁻ˣ
where c₁ and c₂ are arbitrary constants.
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The sum of the digits of a certain two digit number is 8. By reversing the digits the number is increased by 18. What is the number?
Compute $2^{10}\cdot 2^8\cdot 2^6\cdot 2^4\cdot 2^2\cdot 2^{-1}\cdot 2^{-3}\cdot 2^{-5}\cdot 2^{-7}\cdot 2^{-9}$.
\(2^{10}.2^8.2^6.2^4.2^2.2^{-1}.2^{-3}.2^{-5}.2^{-7}.2^{-9}\) = 32
We need to compute \(\bold{2^{10}.2^8.2^6.2^4.2^2.2^{-1}.2^{-3}.2^{-5}.2^{-7}.2^{-9}}\) .
This is the product of exponential numbers with same bases.
We use rules of exponents:
\(a^b.a^c=a^{b+c}\)\(a^{-b}=\frac{1}{a^b}\)Using the first rule we can rewrite
\(2^{10}.2^8.2^6.2^4.2^2.2^{-1}.2^{-3}.2^{-5}.2^{-7}.2^{-9}\)
as,
\(2^{10+8+6+4+2}.2^{-1-3-5-7-9} = 2^{10+8+6+4+2}.2^{-(1+3+5+7+9)}\)
Using the second rule,
\(2^{10+8+6+4+2}.2^{-(1+3+5+7+9)} = \frac{2^{10+8+6+4+2}}{2^{1+3+5+7+9} }\)
\(=\frac{2^{30}}{2^{25}}\)
\(\bold{= 2^5 = 32}\)
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The digits of this year, 2000 A.D., add up to 2. In how many other years since 1 A.D. has this happened?
Answer:
0002 0011 1010
0020 0101
0200 1001
2000 1100
9 times
Step-by-step explanation:
9 times is the right answer
If it takes 30 minutes for Jane to type three pages, how many hours will it take her
63
pages at the same rate?
to type
Answer:
10,5 hours
Step-by-step explanation:
Jane writes 6 pages/hour
63 / 6 = 10,5 hours
Ruby has saved $4072.24 towards her retirement by the time she is 26 years old. She initially invested $2500 in an account that earned interest compounded annually. If Ruby made the investment on her sixteenth birthday at what rate has the account been earning interest?
At 5% rate the account been earning interest.
Given that Ruby has saved $4072.24, and she initially invested $2500, we can plug in these values into the formula:
4072.24 = 2500(1 + r/1\()^{(1 )(10)\)
Simplifying the equation, we get:
(1 + r)¹⁰ = 4072.24/2500
Taking the 10th root of both sides, we have:
1 + r = (4072.24/2500\()^{(1/10)\)
Subtracting 1 from both sides, we find:
r = (4072.24/2500\()^{(1/10)\)- 1
r = 1.05000008852 - 1
r = 0.05000008852
r = 5%
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Demand history for the past three years is shown below, along with the seasonal indices for each quarter.
Year Quarter Demand Seasonal Index
Year 1 Q1 319 0.762
Q2 344 0.836
Q3 523 1.309
Q4 435 1.103
Year 2 Q1 327 0.762
Q2 341 0.836
Q3 537 1.309
Q4 506 1.103
Year 3 Q1 307 0.762
Q2 349 0.836
Q3 577 1.309
Q4 438 1.103
Use exponential smoothing with alpha (α) = 0.35 and an initial forecast of 417 along with seasonality to calculate the Year 4, Q1 forecast.
The Year 4, Q1 forecast using exponential smoothing with α = 0.35 and an initial forecast of 417, along with seasonality, is 335.88.
Exponential smoothing is a forecasting technique that takes into account both the historical demand and the trend of the data. It is calculated using the formula:
Forecast = α * (Demand / Seasonal Index) + (1 - α) * Previous Forecast
Initial forecast (Previous Forecast) = 417
α (Smoothing parameter) = 0.35
Demand for Year 4, Q1 = 307
Seasonal Index for Q1 = 0.762
Using the formula, we can calculate the Year 4, Q1 forecast:
Forecast = 0.35 * (307 / 0.762) + (1 - 0.35) * 417
= 335.88
Therefore, the Year 4, Q1 forecast using exponential smoothing with α = 0.35 and an initial forecast of 417, along with seasonality, is 335.88.
The forecasted demand for Year 4, Q1 using exponential smoothing is 335.88.
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When a 10% increase in income causes a 4% increase in quantity demanded of a good?
When a 10% increase in income causes a 4% increase in quantity demanded of a good is income inelastic.
More specifically, the income elasticity of demand is calculated as the percentage change in quantity demanded divided by the percentage change in income. In this case, we have:
Income elasticity of demand = (% change in quantity demanded) / (% change in income)
= 4% / 10%
= 0.4
Since the income elasticity of demand is less than one, we say that the good is income inelastic. we can say that the income elasticity of demand for the good is positive and less than one. This means that the quantity demanded of the good does not increase proportionally as income increases. Instead, the increase in quantity demanded is less than the increase in income.
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HELP ME ASAP I NEED HELP
Answer:
distance = 7.07 units
Step-by-step explanation:
x difference = 7
y difference = -1
using the Pythagorean theorem:
7² + -1² = d²
d² = 49 + 1 = 50
d = 7.07
Answer:
7.1
Step-by-step explanation:
distance between the x is 7 and y is 1
And to find the hypotenuse, you use the quadratic formula, 7^2 + 1^2 = c^2
c=50
and take the square root, which is 7.071, rounds to 7.1
Sorry I only have the answer key, lol, but for #13, can someone explain to me where they got 4.6 from?? ty and I don't need an explanation for 14; I just couldn't crop the photo
The measure of the side RS from the figure is 4.6 units
Midpoint theorem of a trapezium
The given figures are trapezoid. Given the following parameters
PQ = 4RS
We need to determine how PR is equivalent to 4.6
Since PQ = 18.4 from the diagram, hence;
18.4 = 4RS
RS = 18.4/4
RS = 4.6 units
Hence the measure of the side RS from the figure is 4.6 units
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Please help this is a new topic for me.
Answer:
last answer
Step-by-step explanation:
P' (2, -4)
Q' (-2, -5)
R' (1, -8)
Answer:
C. P'(2, -4) Q'(-2, -5) R'(1, -8)
Step-by-step explanation:
When you reflect something across the y-axis you change (x,y) to (-x,y).
For each point, change the x to a negative x.
P(-2, -4) --> P'(2, -4)
Q(2, -5) --> Q'(-2, -5)
R(-1, -8) --> R'(1, -8)
Hope this helps. If you have any follow-up questions, feel free to ask.
Have a great day! :)
to calculate the average of the numeric values in a list, the first step is to get the total of values in the list.
True, to calculate the average of numeric values in the list, the first step is to get the total of values in the list.
Steps to calculate the Average:
Let’s assume there are 4 numbers having values of 2,8,22,48 respectively.
To find the average we first have to take the total of all values.
2+8+22+48=80.
Our next step will be to divide this total by the number we have in our question i.e., 4.
so, our average will be 80/4= 20.
So, 20 will be our average.
So yes, it is true that to calculate the average of numeric values in the list, the first step is to get the total of all values in the list.
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what is the invariant of a class quizlet always make an explicit statement of the rules that dictate how the member variables of a class are used. these rules are called the invariant of the class. all of the functions (except the constructors) can count on the invariant being valid when the function is called. each function also has the responsibility of ensuring that the invariant is valid when the function finishes.
In the object-oriented programming paradigm, a class invariant is a property that must always be true for any instance of a class. It is a condition or a set of conditions that must be maintained by all member functions for the proper functioning of a class.
A class invariant, therefore, is a formal statement of the rules that dictate how the member variables of a class are used. All member functions (with the exception of constructors) can depend on the invariant being valid when the function is called. Each function is also responsible for ensuring that the invariant is valid when the function finishes.
The invariant represents an important constraint that must be maintained in a class. As a result, a well-defined class invariant is important for the stability and reliability of the class.
The class invariant may be a single condition or a set of conditions that need to be maintained for the class to operate correctly. These conditions may be explicitly stated in the class documentation or in the form of assert statements in the class implementation. The invariant may be as simple as a range constraint or as complex as a logical relationship between multiple variables.
In any case, the invariant must be maintained by all the member functions of the class. the invariant of a class is a set of rules that govern how the member variables of a class are used. It is a condition that must always be true for any instance of a class. The invariant is important for the stability and reliability of a class, and each member function is responsible for ensuring that the invariant is valid when the function finishes.
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The circle P has a center at (0, 0) and a point on the circle at (0, 4). If it is dilated by a factor of 4, what is the distance of the radius for circle P'.
A. 16
B. 4
C. 8
D. 1
Needs to be answered quickly
Answer:
16
Step-by-step explanation:
If one set of opposite sides of a quadrilateral are parallel but not equal, then what would be the name of the quadrilateral??
Answer:
a trapezoid i think
Step-by-step explanation:
i hope this helps
Super sorry if if im wrong
Determine the values of c so that the following functions represent joint probability distributions of the random variables X and Y: (a) f (x, y) = cxy, for x = 1, 2, 3: y = 1, 2, 3: (b) f (x, y) = c |x - y|, for x = -2, 0, 2: y = -2, 3.
Answer:
Step-by-step explanation:
To determine the values of "c" for the given functions to represent joint probability distributions of random variables X and Y, we need to ensure that the probabilities sum up to 1 and that the function satisfies all the properties of a probability distribution.
(a) For the function f(x, y) = cxy, where x = 1, 2, 3 and y = 1, 2, 3:
To find the value of "c," we need to calculate the sum of all probabilities and set it equal to 1:
∑∑ f(x, y) = c∑∑ xy = c(1 + 2 + 3) (1 + 2 + 3) = c(6)(6) = 36c
For this function to represent a joint probability distribution, the sum of all probabilities must be 1. Therefore, we have:
36c = 1
c = 1/36
So, the value of "c" for this function is 1/36.
(b) For the function f(x, y) = c |x - y|, where x = -2, 0, 2 and y = -2, 3:
Using the same approach, we calculate the sum of probabilities and set it equal to 1:
∑∑ f(x, y) = c∑∑ |x - y| = c[|-2 - (-2)| + |0 - (-2)| + |2 - (-2)| + |(-2) - 3| + |0 - 3| + |2 - 3|]
= c[0 + 2 + 4 + 5 + 3 + 1]
= c(15)
For this function to represent a joint probability distribution, the sum of all probabilities must be 1. Therefore, we have:
15c = 1
c = 1/15
So, the value of "c" for this function is 1/15.
In summary, for the functions f(x, y) = cxy and f(x, y) = c |x - y| to represent joint probability distributions, the values of "c" are 1/36 and 1/15, respectively.
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Use Pemdas to evaluate: 5c - 19, c=10
Forty percent of a number is greater than one-half the number decreased by 15. Which inequality can be used to determine the number?A 40x > x /2 - 15B 40x > 2x - 15C 0.40x > x/2 - 15D 0.4x < x/2 - 15
The inequality can be used to determine the number is 0.4x > x/2 - 15
The term inequality means the unequal relationship between the two or more expressions.
Here we have given that Forty percent of a number is greater than one-half the number decreased by 15.
And we need to find the number that is used to determine the inequality.
While we looking into the given question, let us consider x be that unknown number.
Then based on the given statement, we have divide it into two parts.
First, forty percent of the number and it can be written as 40%x or 0.4x.
Next is one-half the number is 1/2 x or x/2
When we combine the whole statement,
Then we get the inequality,
=> 0.4x > x/2 - 15
Therefore option (c) is correct.
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I don’t know the formula, and just need the answers in general. I don’t know know anything about this to be honest.
Applying the definition of bisection, m<ABD = 24°; m<CBD = 24°; m<ABC = 48°.
What is the Definition of Bisection?When an angle is bisected by a line segment, it means it divides the angle into two equal parts.
What is the Angles Addition Postulate?The angles addition postulate state that the sum of the two angles formed when an angle is bisected is equal to the measure of the angle that was bisected.
Given:
BD divides ABC into two equal angles, angles ABD and CBD.
Therefore:
m<ABD + m<CBD = m<ABC [angles addition postulate]
m<ABD = m<CBD [definition of bisector]
Substitute
3x + 6 = 7x - 18
Combine like terms
3x - 7x = -6 - 18
-4x = -24
-4x/-4 = -24/-4
x = 6
m<ABD = 3x + 6 = 3(6) + 6 = 24°
m<CBD = 7x - 18 = 7(6) - 18 = 24°
m<ABC = m<ABD + m<CBD
m<ABC = 24 + 24 = 48°
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Henry is flying a kite. The kite makes an angle of 43 with the ground. If henry is standing 100 feet from a point on the ground directly below the kite, find the length of the kite string
Answer:
x = 136.73 feet
Step-by-step explanation:
Given that,
Henry is flying a kite. The kite makes an angle of 43 with the ground. If henry is standing 100 feet from a point on the ground directly below the kite.
We need to find the length of the kite string. It can be calculated by using trigonometry.
The length of the string will be hypotenuse, 100 feet is the base.
The relation between the hypotenuse, base and angle with the ground is given by :
\(\cos\theta=\dfrac{\text{base}}{\text{Hypotenuse}}\\\\\cos(43)=\dfrac{100}{x}\\\\x=\dfrac{100}{\cos(43)}\\\\x=136.73\ \text{feet}\)
So, the length of the kite string is 136.73 feet.
Help me plsssss. Exterior angles definitions
Step-by-step explanation:
an angle that is complementary to one of the interior angles of the triangle because interior angle+exterior angle add up to 180°
need a quick answer please
Answer:
Your answer is 97.
Step-by-step explanation:
I can give an explanation if needed.
Is that correct please answer
Answer:
the answer is when 0=0 the soluthion is not n=0
Step-by-step explanation:
hope its right good luck
Marla has a large white cube that has an edge of 10 feet. She also has enough green paint to cover 300 square feet. Marla uses all the paint to create a white square centered on each face, surrounded by a green border. What is the area of one of the white squares, in square feet
This result indicates that the side length of the white square is 0. The area of one of the white squares can be determined by subtracting the area of the green border from the total area of each face of the cube.
The total area of each face of the cube is given by the formula: side length * side length.
Given that the edge of the cube is 10 feet, the total area of each face is:
Area of each face = 10 feet * 10 feet = 100 square feet
Now, let's consider the green border. Since each face has a white square centered on it, the dimensions of the white square will be smaller than the face itself.
Let's assume the side length of the white square is "x" feet. This means that the side length of the green border is (10 - x) / 2 feet on each side.
The area of the green border on each face is then:
Area of green border = (10 - x) / 2 * (10 - x) / 2 = (10 - x)^2 / 4 square feet
To find the area of the white square, we subtract the area of the green border from the total area of each face:
Area of white square = Area of each face - Area of green border
= 100 square feet - (10 - x)^2 / 4 square feet
Given that Marla has enough green paint to cover 300 square feet, we can set up the equation:
Area of white square * 6 (number of faces) = 300 square feet
(100 - (10 - x)^2 / 4) * 6 = 300
Now we can solve for x:
100 - (10 - x)^2 / 4 = 50
100 - (10 - x)^2 = 200
(10 - x)^2 = 100
Taking the square root of both sides:
10 - x = 10
x = 0
This result indicates that the side length of the white square is 0, which doesn't make sense in this context. It seems there might be an error or inconsistency in the given information or calculations.
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