Any square-free integer can be expressed as the product of a square-free integer (which has no square factors) and a perfect square (which has only square factors). This product is unique for any given square-free integer.
Any square-free integer can be expressed as the product of a square-free integer and a perfect square. This is because a square-free integer has no square factors, so the product of a square-free integer and a perfect square would have only square factors, and thus be square-free. To show that this product is unique for any given square-free integer, we can use the fact that any integer can be expressed as the product of its prime factors and that a square-free integer has no square factors. This means the prime factors of the square-free integer are all distinct, and thus the product of the square-free integer and the perfect square can be expressed as the product of the prime factors of the square-free integer and the prime factors of the perfect square. Since the prime factors of the perfect square are all the same, the product is uniquely determined by the prime factors of the square-free integer. Thus, the product of a square-free integer and a perfect square is unique for any given square-free integer.
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Find the length of the midsegment of the trapezoid with the vertices A(0,3) ,B(2 , 5) ,C(6,4) ,D(2,0)
The length of the midsegment of the trapezoid with the vertices A(0,3) ,B(2 , 5) ,C(6,4) ,D(2,0) is; 3√2
How to find the distance between two coordinates?The length of the mid-segment of a trapezoid is half the sum of the lengths of the two parallel sides, AB and CD. T
The vertices are;
A(0,3) ,B(2 , 5) ,C(6,4) ,D(2,0)
Thus;
Length of sides AB and CD
length = √(x₂ - x₁)² + (y₂ - y₁)²
AB =√(2 - 0)² + (5 - 3)²
AB = 2√2
length = √(x₂ - x₁)² + (y₂ - y₁)²
CD = √(2 - 6)² + (0 - 4)²
CD = 4√2
Formula to use for the mid segment is;
Mid segment = (AB + CD)/2
= (2√2 + 4√2) / 2
= 3√2
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section 7.5 substitution page 15 pdf answer key 7c i can solve a linear system of equations by substitution.
Yes, substitution can be used to solve a linear system of equations.
Linear System of Equations:
A system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. A linear system in three variables determines a collection of planes The intersection point is the solution. For example, is a system of three equations in the three variables x, y, z.
The substitution technique involves separating out a single variable from one equation and utilizing that expression to replace the variable in the other equation (s). This will enable you to solve for the remaining variable or variables and discover the system's answer.
Yes, a linear system of equations can be solved via substitution.
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the fed is most likely to use which tool(s) to conduct monetary policy? group of answer choices open market operations discount rate interest on reserves (ior) rate required reserve ratio
The Federal Reserve uses three main tools to conduct monetary policy: Open Market Operations, the Discount Rate, and Interest on Reserves (IOR).
Open Market Operations involve the buying and selling of government securities in the open market, which impacts the money supply and interest rates. The Discount Rate is the interest rate the Federal Reserve charges commercial banks to borrow from it. A lower Discount Rate encourages borrowing, while a higher Discount Rate discourages borrowing. Interest on Reserves (IOR) is the interest rate the Federal Reserve pays commercial banks on their excess reserves. A higher IOR rate encourages banks to keep more of their funds in the form of reserves, while a lower IOR rate encourages banks to lend out more of their funds. The Required Reserve Ratio is also used to affect the money supply, as it determines the amount of reserves banks must keep on hand. An increase in the Required Reserve Ratio reduces the money supply, while a decrease in the Required Reserve Ratio increases the money supply.
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What does the law of demand state?
Answer:
In economics, the LOD or Law of Demand states that as the price increases on a good or service, there are less people that are willing and able to purchase that good or service.
Here is an example
On the image attached there is a Price Quantity Demanded Graph. The Line on the graph represents demand. The furthur right the line of the graph goes, the larger the quantity of demand for a good is, vice versa. The Law Of Demand is demonstrated on the graph and the table, when price (Px) is at 5, then only Quantity Demanded (Dx) equals 100. When Px = 1 then Dx = 500. As price decreases, demand increases.
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QUESTION; 01. A sarveyor standing 25°SW of a tower measure the angle of elevation of the top of the tower as 46°30' from a position 23°SE from the tower the elevation of the top is 37°15'. Determine the height of the tower if the distance between the two observations is 75m.
When you know the tower's height, you may calculate your distance from it.The answer is 92.54 feet .
Determine the height of the tower ?When you know the tower's height, you may calculate your distance from it.The tangent of the angle of elevation multiplied by the horizontal distance, or doing the calculation, is all that is required to manually determine the height.
30° vertical angle from A to the tower's summit
50 + x is the horizontal separation between A and the tower's base.
Call h to get the tower's height.
tan 30 = h / (50 + x) => 50 + x = h / tan 30 => x = h / tan 30 - 50 (1)
40° vertical angle from B to the tower's summit
The tower's base is x feet away from B in a horizontal direction.
ratio: x = h / tan40; tan40 = h / tan40 (2)
Consequently, (1) and (2) are equivalent.
Tan40 = Tan30 - 50 =
30 - 40 = 50 h/tan
1,7321h - 1,1918h = 50
0.5403h = 50
h = 50/0.5403 = 92.54
Response: 92.54 feet
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arrange the following numbers in ascending order: 147, 772,324,256,9199,946,4342,493,891,4
Recall that lim f(x) = L means: For all € > 0 there is a 6 > 0 such that for all x satisfying 0 < Ix ~ cl < & we have that |f(x) - Ll < € What if the limit does not equal L? Think about what the means in €, 6 language. Consider the following phrases: 1.€ > 0 2.6 > 0 3.0 < Ix - cl < 6 4. Wf(x) - Ll > e 5. but 6. such that for all 7. there is some 8. there is some x such that Order these statements so that they form rigorous assertion that lim flx) + L and enter their reference numbers in the appropriate sequence in these boxes:
As per the given limit, the rigorous assertion of the function is a − δ < x < a + δ
In math term function is called as a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output
Here we have given that the distance between two points a and b on a number line is given by |a−b|.
And we need to find the rigorous assertion of the function.
Then the statement is written as
=> |f(x)−L|<ε
And it can be be interpreted as the distance between f(x) and L is less than ε.
Here we have another statement that is written as
=> 0<|x−a|<δ
And it ma be interpreted as the value of x≠a and the distance between x and a is less than δ.
Here we have also important to look at the following equivalences for absolute value that the statement |f(x)−L|<ε is equivalent to the statement L−ε<f(x)<L+ε.
And the statement 0<|x−a|<δ is also equivalent to the statement a−δ<x<a+δ here we know that x≠a.
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Why do you think insurance companies offer uninsured/ underinsured coverage at a cheaper rate than collision coverage?
We can actually think that insurance companies offer uninsured/ underinsured coverage at a cheaper rate than collision coverage because the risk of a claim is typically lower for uninsured/underinsured coverage.
What is insurance?An agreement to provide compensation to another party in the event of a certain loss, damage, or injury is known as insurance, and it is a way to safeguard against financial loss. It is a type of risk management that is mostly applied to protect against the risk of a potential or unforeseen loss.
Collision coverage is for damage to the policyholder's own vehicle, while uninsured/underinsured coverage is for damage caused by another driver who does not have enough insurance to cover the costs of an accident. Since fewer drivers are uninsured or underinsured, the likelihood of a claim being made under that coverage is lower, and thus the cost is less.
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which of the following is true of a scientific theory? view available hint(s)for part a which of the following is true of a scientific theory? it generates testable hypotheses, is supported by a large body of evidence, and is broad in scope. it is only accepted after the person who formulated it has died. it is formulated by many scientists over drinks at a convention. it is a method or device that applies scientific knowledge for some specific purpose. it must demonstrate the effect of one variable by testing control groups and experimental groups.
Out of the following, the statement is It generates testable hypotheses, is supported by a large body of evidence, and is broad in scope is true of a scientific theory.
A scientific theory is a well-substantiated explanation of some aspect of the natural world that is acquired through the scientific method and repeatedly tested and confirmed through observation and experimentation. A scientific theory is not just an idea or speculation. It is a systematic way of organizing and interpreting observations that are based on facts and evidence. It is also open to being tested and disproved if new evidence arises.
A scientific theory must be supported by a large body of evidence from multiple sources to be considered valid. Furthermore, a scientific theory must be broad in scope and explain a wide range of phenomena. It must also generate testable hypotheses that can be tested and verified through experimentation and observation.
A scientific theory is not accepted until it is thoroughly tested and confirmed through numerous experiments and observations. Therefore, it is not accepted after the person who formulated it has died.
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A city has a population of 310,000 people. Suppose that each year the population grows by 8%. What will the population be after 14 years?
round your answer to the nearest whole number.
I just need help with number 2 on box A. I can record the coordinates of the triangle.
The coordinates of the ends of the image are J'(x, y) = (- 7, 7), K'(x, y) = (- 5, 2) and L'(x, y) = (- 2, 3), whose transformation formula is P'(x, y) = P(x, y) + (0, - 2 · p). A representation of the figures is in the image shown below.
How to derive the reflection formula of a figure
In this problem we find a geometric locus generated by three points on Cartesian plane that is reflected over the x-axis, whose formula is shown below:
P'(x, y) = P(x, y) + (0, - 2 · p)
Where:
P(x, y) - Original pointP'(x, y) - Resulting pointp - y-Coordinate of the original point.If we know that J(x, y) = (- 7, - 7), K(x, y) = (- 5, - 2) and L(x, y) = (- 2, - 3), then the coordinates of the image are:
J'(x, y) = (- 7, - 7) + (0, 14)
J'(x, y) = (- 7, 7)
K'(x, y) = (- 5, - 2) + (0, 4)
K'(x, y) = (- 5, 2)
L'(x, y) = (- 2, - 3) + (0, 6)
L'(x, y) = (- 2, 3)
Now we proceed to graph both the geometric locus and its image.
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A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.
Number of Hours | Total Number of Students
0 | 1
1 | 8
2 | 2
3 | 5
4 | 9
5 | 7
6 | 3
Determine the probability that a student studied for exactly 1 hour. Round to the nearest hundredth.
0.03
0.23
0.30
0.77
The probability that a student studied for exactly 1 hour is 0.23
How to determine the probability that a student studied for exactly 1 hour?Probability is a measure of the likelihood of a particular event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.
From the given table, you need notice that the number of students who study for 1 hour is 8.
In order to determine the probability that a student studied for exactly 1 hour, we need to find total number of students. That is:
Total number of student = 1 + 8 + 2 + 5 + 9 + 7 + 3 = 35
probability (exactly 1 hour) = number of exactly 1 hour/Total number
probability (exactly 1 hour) = 8/35 = 0.23
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Answer:
B
Step-by-step explanation:
find the area of the shaded part given below where the diameter is 14 cm.
Answer:
area of sector = 49π/6 cm² ≈ 25.7 cm²
Step-by-step explanation:
area of sector = (n/360°)πr²
where n = central angle of sector, and r = radius of circle
Here, we have:
n = 60°
r = d/2 = 14 cm / 2 = 7 cm
area of sector = (60°/360°)π(7 cm)²
area of sector = (1/6)π(49 cm²)
area of sector = 49π/6 cm² ≈ 25.7 cm²
each of the following situations, determine whether or not the given random variabas a binomial or geometric distribution. then, find the probability
The probability of 5 heads in 10 flips.
A coin is flipped 10 times and we want to find the probability of getting exactly 5 heads.
This situation is a binomial distribution because it involves a fixed number of trials (10) and each trial has a fixed probability of success (1/2). . The probability of obtaining exactly 6 successes in 10 trials is given by the formula P(x) = nCx * px * (1-p)n-x. In this situation, the probability is P(x) = 10C6 * 0.26 * 0.84 = 0.17496. The probability of getting exactly 5 heads can be calculated using the formula P(X=5) = 10C5 * 0.5^5 * 0.5^5 = 0.246. This is the probability of 5 heads in 10 flips.
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Complete question:What is the probability of getting 5 heads when you toss a fair coin 10 times?
Asha pulls five tiles out of a bag that contains only positive and negative x and x² tiles. She simplifies the resulting polynomial and gets x². What are all the possible sets of five tiles that she could have pulled out?
The possible sets of five tiles that she could have pulled out are (2,3),(3,2)
How to find the factors of a quadratic expression?If the given quadratic expression is of the form ax^2 + bx + c, then its factored form is obtained by two numbers alpha( α ) and beta( β) such that:
[tex]b = \alpha + \beta \\ ac =\alpha \times \beta[/tex]
Then writing b in terms of alpha and beta would help us getting common factors out.
Sometimes, it is not possible to find factors easily, so using the quadratic equation formula can help out without any trial and error.
Given;
Number of tiles asha pulled out=5
Bag contains only positive and negative x and x² tiles
So, the equation will be
-x^2+x=5
x^2-x+5=0
Now,
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
x= 1 +[tex]\sqrt{1-4*-1*-5}[/tex])/2
x=2,3
x=3,2
Therefore, the quadratic equation solution will be (2,3),(3,2)
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Express the formula v=pie r^2 • H in terms of height, H. Use that formula to find the height when the volume is 45pid and the radius is 3
Option (b) is the correct option i.e. The height is 5 units.
What precisely are volume and height?The height of an object is determined by measuring the distance between its base and its top.
As opposed to length, width, and height for a rectangular shape's area, the basic formula for volume is length, breadth, and height. The calculation is unaffected by how the different dimensions are referred to; for example, "depth" can be used in place of "height."
Given, V = πr².H
V/πr² = H
So, It can be written in terms of height, H as V/πr².
Now, If r = 3 units and V= 45π then,
H = V/πr² = 45π / π(3)²
= 45π/9π
= 5 units.
Hence, height is 5 units.
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Which of the following describes the growth rate of the exponential function in the graph below?
For each x increase of 1, the y increases by a common difference of 3.
For each x increase of 1, the y increases by a common factor of 3.
For each x increase of 1, the y increases by 4 more than the previous increase.
For each x increase of 1, the y increases by doubling and then adding 1.
The correct option regarding the growth rate of the exponential function is given as follows:
For each x increase of 1, the y increases by a common factor of 3.
How to classify the functions?A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.
A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.
As the function in this problem is exponential, the increase of the output y must be a common factor, purely.
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Alexandra invested 40% of his money in mutual funds, 40% in real estate, and 20% in stocks. If the value of the money that he invested in mutual funds, real estate, and stocks grew by 2%, 7%, and 11% respectively, what was the average growth on his total investment?
Answer:
To find the average growth on Alexandra's total investment, we need to calculate the weighted average of the growth in each of the three investments. The weighted average is calculated by multiplying the growth of each investment by its proportion of the total investment and then adding them together.
First, we need to calculate the total amount of money that Alexandra invested. Since he invested 40% in mutual funds, 40% in real estate, and 20% in stocks, we can assume he invested $100.
So the amount invested in mutual funds is 40/100 * $100 = $40
The amount invested in real estate is 40/100 * $100 = $40
The amount invested in stocks is 20/100 * $100 = $20
Then we can calculate the growth of each investment using the percentages provided:
The growth of mutual funds is 2/100 * $40 = $0.80
The growth of real estate is 7/100 * $40 = $2.80
The growth of stocks is 11/100 * $20 = $2.20
Now we can add up the growth of each investment and divide it by the total investment to find the average growth:
($0.80 + $2.80 + $2.20) / $100 = $5.80 / $100 = 0.058 or 5.8%
So the average growth on Alexandra's total investment is 5.8%.
x=8+27y by substitution
The expression can be rewritten as -
y = (1/27)x - (8/27)
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the expression as -
x = 8 + 27y
We can rewrite the expression as -
x = 8 + 27y
27y = x - 8
y = (1/27)x - (8/27)
Therefore, the expression can be rewritten as -
y = (1/27)x - (8/27)
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An airplane travels 150 miles in 3/4 hour. What is the average speed of the airplane?
Answer:
200mph
Step-by-step explanation:
For a particular company the salaries of five employees are: $45,000 $52,000 $67,000 $42,000 $56,000 A new employee is hired and her salary is $280,000. What word best describes this data set with the new employee included?
solve it to find the value of X. also find the actual length of each square[tex]perimeter of square 40cm,(x+2)cm[/tex]
The equation will be 4(x + 2) = 40 and the value of the variable 'x' will be 8.
What is the perimeter of the square?The product of the four and the edge length of the square or the sum of all the sides of the square is known as the perimeter of the square. For a square with a side length of a unit, we get:
Perimeter of the square = 4a unit
The perimeter of the square is 40 cm. And the sides length of the square is (x + 2) cm. Then the perimeter of the square is given as,
4(x + 2) = 40
Simplify the equation, then we have
4(x + 2) = 40
(x + 2) = 10
x = 10 - 2
x = 8
The equation will be 4(x + 2) = 40 and the value of the variable 'x' will be 8.
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The longer leg of a right triangle is 3cm longer than the shorter leg. The hypotenuse is 6cm longer than the shorter leg. Find the side lengths of the triangle.
In a case whereby longer leg of a right triangle is 3cm longer than the shorter leg and hypotenuse is 6cm longer than the shorter leg then the side lengths of the triangle is 9 inches.
How can the lenght be calculated?The concept that will be used is pythagoras theorem.
We can make s = the length of the shorter leg.
Where the longer leg can be expressedas (s + 3),
Then the hypotenuse is( s + 6).
From pythagoras theorem, a^2 + b^2 = c^2.
then we have s^2 + (s + 3)^2 = (s + 6)^2
[s^2 + (s + 3)(s + 3)] =[ (s + 6)(s + 6) ]
s^2 + s^2 + 6s + 9 = s^2 + 12s + 36
If we collect like terms we have
s^2 - 6s - 27 = 0
Then if we factorize we have
(x - 9)(x + 3) = 0
then
we can set the whole left side to equal 0.
x - 9 = 0, then x = 9
x + 3 = 0, then x = -3.
But we can only have positive value which sis 9, hence shortest side is 9 inches.
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Need help with questions 12!
Answer:
So the width of the rectangle measures 19.5 feet and the length measures 136.5 feet.
Step-by-step explanation:
We can use algebra to solve for the width and length of the rectangle. Let's call the width of the rectangle "w" and the length "l".We know that the perimeter of the rectangle is the sum of all four sides, so we can use the formula:P = 2l + 2wwhere P is the perimeter and l and w are the length and width of the rectangle. We know that P = 312 feet.Also, we know that the length is seven times the width, so we can express the length as:l = 7wNow we can substitute this value of l into the perimeter equation:312 = 2(7w) + 2w312 = 14w + 2w312 = 16ww = 19.5 feetNow we can use this value of w to find the length:l = 7w = 7(19.5) = 136.5 feetSo the width of the rectangle measures 19.5 feet and the length measures 136.5 feet.
help this is the only question i have left help bsf help
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Review the Monthly Principal & Interest Factor chart to answer the question:
FICO Score APR 30-Year Term 20-Year Term 15-Year Term
770–789 5.5 $5.68 $6.88 $8.17
750–769 6.0 $6.00 $7.16 $8.44
730-749 6.5 $6.32 $7.46 $8.71
710–729 7.0 $6.65 $7.75 $8.99
690–709 7.5 $6.99 $8.06 $9.27
Calculate the monthly payment, for a 15-year term mortgage, after a 15% down payment on a $315,200.00 purchase price, for a household with a 711 credit score. (2 points)
$1,776.29
$1,984.39
$2,173.56
$2,408.60
Answer: c
Step-by-step explanation:
Consider f(x) = 3x. Describe how the graph of each function compares to f.
The graph of f(x) = 3x is a vertical stretch with a factor of 3 of the graph of the parent function f(x) = x.
How to describe the transformation?The parent function for this problem is defined as follows:
f(x) = x.
The transformed function is given as follows:
f(x) = 3x.
The only transformation is a multiplication by the constant 3. As the constant has an absolute value greater than 1, the graph of f(x) = 3x is a vertical stretch with a factor of 3 of the graph of the parent function f(x) = x.
Missing InformationThe problem asks for how the graph of f(x) = 3x compares to the graph of f(x) = x.
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What type of triangle and are they congruent
Answer: AAS and both triangles are congruent
Step-by-step explanation: Hello! Since you are given two angles and one side that are congruent in both triangles, you know that they are either congruent by ASA (angle side angle congruence postulate) or AAS (angle angle side) congruence postulate. The way you tell the difference between the two is by how the congruent angles and the congruent side is shown. In ASA, the congruent side would be the included side between both congruent angles. Since the congruent side is not in between both angles and both angles do not share the congruent side to the other triangle, the triangles are congruent by AAS. The triangles two given shared angle and given congruent side is in the order of angle angle side, so the triangles are related by AAS. This means that the triangles are congruent.
Fun fact:
By CPCTC, you know that corresponding parts are congruent in congruent triangles. If you know two or more triangles are congruent, then each of their angles and sides are congruent as well.
I hope this helps you!
Three vertices of a parallelogram are shown in the figure below.
Give the coordinates of the fourth vertex.
(-3,0)
(5,-2)
what’s the domain of this function please help