Therefore , the solution of the given problem of function comes out to be the zeros of the function y = x² + x - 2 are x = -2 and x = 1, and the polynomial in factored form is y = (x + 2)(x - 1).
What is function?All of the subjects, including actual and fictitious locales and arithmetic variable design, will be covered in the midterm exam questions. a schematic illustrating the connections between various components that work together to produce the same outcome. A service is made up of many unique parts that work together to produce unique outcomes for each input. Every postbox has a specific location that could serve as a refuge.
Here,
We can draw points for different values of x and y to graph the function => y = x² + x- 2:
|x| |y=x²+x-2|
|---|-----------|
|-3 | 4 |
|-2 | 0 |
|-1 | -2 |
|0 | -2 |
|1 | 0 |
|2 | 6 |
|3 | 12 |
We can use the elements in the table above to plot them on a graph and link them to create a parabolic shape.
We can search for the values of x where the function y = 0 to determine the function's zeros.
Using the zeros we discovered, we can recast the function as the polynomial in factored form is:
=> y = (x + 2)(x - 1)
Therefore, the zeros of the function y = x² + x - 2 are x = -2 and x = 1, and the polynomial in factored form is y = (x + 2)(x - 1).
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PLEASE HELP EASY A fair number cube is rolled twice. Determine whether each event is more or less likely than rolling the same number both times.
Select the correct button in the table to show the likelihood of each event.
Step-by-step explanation:
a probability is always the ratio
desired cases / totally possible cases
the probably for the second roll to roll the same number as in the first roll again, is actually pretty high.
it means that we "accept" any result in the first roll. that makes this a 6/6 = 1 probability.
and then for the second roll we have the usual 1/6 probability (to roll the same number again).
so, we have
6/6 × 1/6 = 1/6 = 0.166666666...
P(even, odd) is the probability to roll first an even number (3 out of 6 = 3/6 = 1/2) and then an odd number (again 3 out of 6 = 1/2) :
1/2 × 1/2 = 1/4 = 0.25
so, this is more likely.
P(2, 5) is the probability to roll first a 2 (1 out of 6 is 1/6) and then a 5 (again 1 out of 6 is 1/6) :
1/6 × 1/6 = 1/36 = 0.027777777...
so, this is less likely.
P(odd, 1) is the probability to roll first an odd number (3 out of 6 = 1/2) and then a 1 (1 out of 6 = 1/6) :
1/2 × 1/6 = 1/12 = 0.083333333...
so, it is less likely.
6TH GRADE MATH, What is the y intercept in the equation y= 4x - 8??
PLEASE HELP EASY A fair number cube is rolled twice. Determine whether each event is more or less likely than rolling the same number both times.
Select the correct button in the table to show the likelihood of each event..
Answer:
p (even,odd)- more likely
p(2,5) - less likely
p(odd,1)- less likely
Find the equation of a parabola with a focus at (-4, 7) and a directrix of
y = 1,
Oy-7=(x+4)²
Oy-3=(x+4)²
Oy+4= (-4)²
Oy-4=(+4)²
According to the question,the equation of the parabola is y = (x + 4)² - 6.
What is equation?An equation is a statement that equates two expressions using mathematical symbols. It is a mathematical statement that two expressions are equal in value. Equations can involve numbers, variables, and constants. Equations are used to solve real-world problems such as determining the speed of a car from the distance traveled and time elapsed.
The equation of a parabola with a focus at (-4, 7) and a directrix of y = 1 is given by:
y = (x + 4)² + 4.
This equation is derived from the standard equation of a parabola:
y = (x - h)² + k,
where (h, k) is the coordinates of the focus.
In this case, the coordinates of the focus are (-4, 7), so the equation becomes:
y = (x + 4)² + 7.
The directrix of the parabola is a line, so its equation is given by:
y = 1.
Substituting this equation into the equation of the parabola, we get:
(x + 4)² + 7 = 1
(x + 4)² = -6
y = (x + 4)² - 6.
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The life spans of Mr. Short and Mr. Long were
in a ratio of 3:7. Mr. Long lived 44 years longer
than Mr. Short. How long did Mr. Long live?
Find the 66th derivative of the function f(x) = 4sin(x)
The 66th derivative of f(x) is the same as the second derivative of f(x). Thus, we can calculate the 66th derivative as follows f''(x) = -4sin(x).
What is derivative?The derivative of a function is the rate at which the function changes with respect to its input variable. It is a fundamental concept in calculus and is used in many areas of mathematics, science, and engineering.
According to question:The derivative of the function f(x) = 4sin(x) with respect to x is:
f'(x) = 4cos(x)
Taking the derivative again, we get:
f''(x) = -4sin(x)
Taking the derivative 3 times, we get:
f'''(x) = -4cos(x)
Taking the derivative 4 times, we get:
f''''(x) = 4sin(x)
We notice that the derivative of f(x) repeats every 4 times, alternating between sin(x) and cos(x) with a sign change. Therefore, to find the 66th derivative of f(x), we can simplify the calculation by considering the remainder when 66 is divided by 4:
66 mod 4 = 2
This means that the 66th derivative of f(x) is the same as the second derivative of f(x). Thus, we can calculate the 66th derivative as follows:
f''(x) = -4sin(x)
Therefore, the 66th derivative of f(x) is:
f^(66)(x) = f''(x) = -4sin(x)
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The image show a quadrilateral
We have proved that quadrilateral ABCD is a square below.
The perimeter of ABCD = 4 × AB
The area of ABCD= (AB)² .
What is a square?A square is a two-dimensional, four-sided shape with all sides of equal length and all angles of 90 degrees. I
Proof that Quadrilateral ABCD is a Square:
We can prove that quadrilateral ABCD is a square by using the properties of a square.
A square is also a quadrilateral with four equal sides and four right angles.
In the image, we can see that side AB = side CD, and side AD = side BC.
Furthermore, we can see that the angles A, B, C, and D are all right angles=90 degree
This means that the quadrilateral ABCD is a square.
Finding the Perimeter of ABCD:
The perimeter of a square is equal to the sum of its four sides.
In the image, we can see that the sides AB, CD, AD, and BC are all equal. Therefore, the perimeter of ABCD=
4 × AB
= 4 × CD
= 4 × AD
= 4 × BC.
Finding the Area of ABCD:
The area of a square is equal to the length of one of its sides squared. In the image, we can see that the sides AB, CD, AD, and BC are all equal. Therefore, the area of ABCD= (AB)²
= (CD)²
= (AD)²
= (BC)².
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We have proved that quadrilateral ABCD is a square below.
Perimeter of ABCD is 4 × AB
The area of ABCD= (AB)².
What is a square?A square is a two-dimensional, four-sided shape with equal-length edges and 90-degree angles on each side.
The quadrilateral ABCD is a square, therefore:
Using the characteristics of a square, we can demonstrate that the parallelogram ABCD is a square.
A quadrilateral with four equal edges and four right angles is a square.
As seen in the picture, side AB corresponds to side CD and side AD corresponds to side BC.
In addition, we can see that the orientations A, B, C, and D are all 90-degree right angles.
The parallelogram ABCD is a square as a result.
Finding ABCD's Perimeter:
The sum of a square's four edges determines its perimeter.
The sides AB, CD, AD, and BC are equal on the picture, as can be seen. Consequently, the ABCD boundary
4 × AB
= 4 × CD
= 4 × AD
= 4 × BC
Finding the Area of ABCD:
A square's area is equivalent to the square of one of its sides. The sides AB, CD, AD, and BC are equal on the picture, as can be seen.
Consequently, ABCD's area equals (AB)².
= (CD)²
= (AD)²
= (BC)².
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The clear image of quadrilateral attached below,
Find Sn for the arithmetic series where a1 = 3, an = 42, n = 14
To find Sn for an arithmetic series, you can use the following formula: Sn = (n/2) * (a1 + an).
In this case, Sn = (14/2)*(3 + 42) = 189.
To explain step-by-step:
1. Find the number of terms in the series, n = 14
2. Find the first term in the series, a1 = 3
3. Find the last term in the series, an = 42
4. Plug the values into the formula, Sn = (n/2)*(a1 + an)
5. Simplify the equation and solve, Sn = (14/2)*(3 + 42) = 189
A company has a fixed cost of $1277 each day to run their factory and a variable cost of $1.93 for each widget they produce. How many widgets can they produce for $2127?
The company can produce approximately 425 widgets for $2127.
What is cost function ?
The key concept used here is the concept of cost functions, which is an important concept in economics and business. A cost function is a mathematical function that expresses the total cost of production as a function of the level of output produced. In this case, the cost function is a linear function of the form C = a + bx, where C is the total cost, a is the fixed cost, b is the variable cost per unit, and x is the level of output.
Finding the number of widgets the company can produce given a fixed cost and a variable cost per widget :
To solve this problem, we can set up an equation that relates the total cost to the number of widgets produced.
Let x be the number of widgets produced.
The total cost C is given by:
C = fixed cost + variable cost
C = 1277 + 1.93x
We want to find the number of widgets produced for a total cost of $2127. So we can set up an equation:
2127 = 1277 + 1.93x
Subtracting 1277 from both sides gives:
850 = 1.93x
Dividing both sides by 1.93 gives:
x ≈ 439.9
Since we can't produce a fractional number of widgets, we need to round down to the nearest integer. Therefore, the company can produce approximately 425 widgets for $2127.
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Given that x + 1/2 = 5, what is 2*x^2 - 3x + 6 - 3/x +2/x^2
pls help me soon
Step 1: x + 0.5 = 5
Step 2: x = 4.5
Step 3: 2*x^2 - 3x + 6 - 3/x +2/x^2 = 2(4.5)^2 - 3(4.5) + 6 - (3/4.5) + (2/(4.5)^2)
Step 4: 2*4.5^2 - 3*4.5 + 6 - 3/4.5 + 2/(4.5)^2 = 44.25 - 13.5 + 6 - 0.666666667 + 0.044444444 = 36.04444444
he theorem to prove is: X
is a positive continuous random variable with the memoryless property, then X∼Expo(λ)
for some λ
. The proof is explained in this video, but I will type it out here as well. I would like to get some clarification on certain parts of this proof.
Proof
Let F
be the CDF of X
, and let G(x)=P(X>x)=1−F(x)
. The memoryless property says G(s+t)=G(s)G(t)
, we want to show that only the exponential will satisfy this.
Try s=t
, this gives us G(2t)=G(t)2,G(3t)=G(t)3,...,G(kt)=G(t)k
.
Similarly, from the above we see that G(t2)=G(t)t2,...,G(tk)=G(t)1k
.
Combining the two, we get G(mnt)=G(t)mn
where mn
is a rational number.
Now, if we take the limit of rational numbers, we get real numbers. Thus, G(xt)=G(t)x
for all real x>0
.
If we let t=1
, we see that G(x)=G(1)x
and this looks like the exponential. Thus, G(1)x=exlnG(1)
, and since 0
, we can let lnG(1)=−λ
.
Therefore exlnG(1)=e−λx
and only exponential can be memoryless.
So there are several parts that I am confused about:
Why do we use G(x)=1−F(x)
instead of just F(x)
?
What does the professor mean when he says that you can get real numbers by taking the limit of rational numbers. That is, how did he get from the rational numbers mn
to the real numbers x
?
In the video, he just says that G(x)=G(1)x
looks like an exponential and thus, G(x)=G(1)x=exlnG(1)
. How did he know that this is an exponential?
G(x) is defined instead of F(x) because the property of memoryless is expressed in terms of G(x). Next, professor refers that there is rational numbers in the set of real numbers, so rational number is dense. G(x) is an exponential distribution with some rate parameter λ because G(x) has the memoryless property.
The reason why the function G(x) is defined as G(x) = P(X > x) = 1 - F(x) instead of just F(x) is because the memoryless property is expressed in terms of G(x).
Specifically, the memoryless property says G(s+t) = G(s)G(t), which means that the probability of X being greater than s+t is equal to the probability of X being greater than s multiplied by the probability of X being greater than t. This property is easier to work with when expressed in terms of G(x) rather than F(x).
When the professor says that taking the limit of rational numbers gives you real numbers, he is referring to the fact that the set of rational numbers is dense in the set of real numbers. This means that between any two real numbers, there exists a rational number.
In the context of the proof, this means that if G(mn) = G(t)^mn holds for all rational numbers mn, then it also holds for all real numbers x = mn, where mn is the limit of a sequence of rational numbers.
To see why G(x) = G(1)x looks like an exponential function, we can rewrite it as G(x) = e^(ln(G(1))x). Now, suppose we define λ = -ln(G(1)). Then we have G(x) = e^(-λx), which is the probability density function of an exponential distribution with rate parameter λ.
Thus, the assumption that G(x) has the memoryless property implies that G(x) is an exponential distribution with some rate parameter λ.
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Let V be a 3 dimensional vector space with A and B its subspace of dimension 2 and 1 respectively if A
∩
B
=
0
then A
V=A-B
B
V=A+B
C
V=AB
D
none of the above
The 3-dimensional vector space represented in the form subspace dimensions A and B is given by option B. V = A + B.
V be 3-dimensional vector space.
Subspace of dimensions of A and B are 2 and 1 respectively.
And A ∩ B = 0.
It follows that every vector in A is linearly independent of every vector in B.
This implies,
Any vector v in V can be expressed uniquely as a sum of a vector in A and a vector in B.
Let v be an arbitrary vector in V.
A has dimension 2, it has a basis of two linearly independent vectors.
Let {a1, a2} be such a basis.
B has dimension 1, it has a basis consisting of a single nonzero vector b.
Then, any vector v in V can be expressed uniquely as
v = c1a1 + c2a2 + cb,
where c1, c2, and c are scalars.
Thus,
V = A + B.
Therefore, the correct answer to represents 3 dimensional vector space V as option(B). V = A + B.
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Is this a quadrilateral, parallelogram, rectangle,rhombus,square or trapezoid 
As all the sides of the closed figure are equal to each other, the quadrilateral here is a square.
What is a square?A square is a closed, two-dimensional (2D), object with four corners. With four sides and four vertices, a quadrilateral is referred to as a square. All four sides of a square are equal and parallel.
In other words, a square is a polygon or quadrilateral with four sides. An equiangular quadrilateral is a shape in which all of the angles are of equal size.
Here in the given figure, we can see a quadrilateral is given.
We can see that all the sides of the quadrilateral are given to be equal to each other.
We can conclude from the observation that the quadrilateral is a square as the sides are all equal to each other.
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can you solve this question? k=?
The value of the constant k that makes the function continuous everywhere is [tex]k = \frac{7}{48}$[/tex]
How to find the value of K?For the function to be continuous everywhere, we need to ensure that the limit of f(x) as x approaches 7 from the left is equal to the limit of f(x) as x approaches 7 from the right.
From the left, we have:
[tex]$$\lim_{x\to7^-}f(x) = \lim_{x\to7^-}kx^2 = k(7)^2 = 49k$$[/tex]
From the right, we have:
[tex]$$\lim_{x\to7^+}f(x) = \lim_{x\to7^+}(x+k) = 7+k$$[/tex]
For the function to be continuous at x=7, we need:
[tex]$$\lim_{x\to7^-}f(x) = \lim_{x\to7^+}f(x)$$[/tex]
Therefore, we need:
[tex]$$49k = 7 + k$$[/tex]
Solving for k:
[tex]$$49k - k = 7$$[/tex]
[tex]$$48k = 7$$[/tex]
[tex]$k = \frac{7}{48}$$[/tex]
Therefore, the value of the constant k that makes the function continuous everywhere is [tex]k = \frac{7}{48}$[/tex]
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each of the cars on the left has th esame solution as on of the card ont the right find the cards with macthing solutions to coplete the sentece below.[tex]6x - 72 = -18[/tex]
Answer:
x=9
Step-by-step explanation:
this is solved by using cover and cancel so we can isolate the x variable
1) first add 72 to both sides.
6x=54
2) second divide both sides by 6
3) x=9
Need help aglebra, please quick, here is screenshot.
The perimeter of the figure is 24 feet.
What exactly is perimeter in mathematics?The perimeter of a shape is the distance between its edges. Learn how to calculate the perimeter of various shapes by adding the side lengths.
To calculate the perimeter of the figure, add the lengths of all the sides. To calculate the perimeter of the figure, add the lengths of all the sides. Label the diagram's points as follows:
Beginning at the top left and working our way clockwise, we have:
A at (0, 4)
B at (6, 4)
C at (6, 0)
D at (4, 0)
E at (4, 2)
F at (2, 2)
G at (2, 0)
H at (0, 0)
Using the distance formula, we can now calculate the length of each side:
[tex]AB = \sqrt{((6-0)^2 + (4-4)^2)}= 6 feet[/tex]
[tex]BC = \sqrt{((6-6)^2 + (0-4)^2)} = 4 feet[/tex]
[tex]CD = \sqrt{((4-6)^2 + (0-0)^2)} = 2 feet[/tex]
[tex]DE = \sqrt{((4-4)^2 + (2-0)^2)} = 2 feet[/tex]
[tex]EF = \sqrt{((2-4)^2 + (2-2)^2)} = 2 feet[/tex]
[tex]FG = \sqrt{((2-2)^2 + (0-2)^2)} = 2 feet[/tex]
[tex]GH = \sqrt{((0-2)^2 + (0-0)^2) }= 2 feet[/tex]
[tex]HA = \sqrt{((0-0)^2 + (4-0)^2)}= 4 feet[/tex]
The perimeter is equal to the sum of these lengths:
Perimeter = 6 + 4 + 2 + 2 + 2 + 2 + 2 + 4
= 24 feet
As a result, the figure's perimeter is 24 feet.
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$690 is invested in an account earning 2.2% interest (APR), compounded quarterly.
Write a function showing the value of the account after t years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.
a) A function showing the value of the account after t years, where the annual growth rate can be found from a constant, is f(x) = 690 (1+0.0055)^4t.
b) The percentage of growth per year (APY) is 2.2%.
What is a function?A function is a mathematical expression that shows the relationship between variables.
An example of a mathematical function is an equation that shows the relationship between y and x variables.
Principal = $690
APR = 2.2%
APR per quarter = 0.0055 (2.2%/4)
Compounding = Quarterly
Investment period = t years
Let f(x) = the value of the account after t years.
Future value function, (FV) = PV × (1 + r) ^ n
Where PV = present value or investment
r = compounding rate per period
n = the investment period
Therefore, f(x) or FV = 690 (1+0.0055)^4t.
APY = 100 [(1 + Interest/Principal)(365/Days in term) - 1]
2.2% = 100 [(1 + $15.18/$690)(365/365) - 1]
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A bag has 4 blue marbles, 3 green marbles, and 5 red
marbles. You select 2 marbles one at a time without
replacement.
Determine the probability the first marble is blue and
the second marble is green Round your answer to
the hundredths place.
The probability of selecting a blue marble on the first draw and a green marble on the second draw is 0.09.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
There are 12 marbles in total in the bag, so the probability of selecting a blue marble on the first draw is 4/12.
After the first marble is drawn, there are 11 marbles left in the bag, so the probability of selecting a green marble on the second draw, given that the first marble was blue and has already been removed, is 3/11.
To determine the probability of both events occurring together, we multiply the probabilities. Therefore, the probability of selecting a blue marble on the first draw and a green marble on the second draw is:
(4/12) * (3/11) = 0.0909
Rounding to the hundredth place, the probability is approximately 0.09.
Therefore, the probability of selecting a blue marble on the first draw and a green marble on the second draw is 0.09.
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Which function is represented by this graph?
A. ƒ(x) = −x² + x − 6
B. f(x) = x² – 5x +6
C. f(x) = -x² + 5x - 6
D. f(x)= x²-x+6
Answer:
Equation of B represents this graph
The events A and B are mutually exclusive. If P(A) = 0.2 and P(B) = 0.4, what is P(A or B)?
Round your answer to two decimal places.
Consider the following energy diagram and determine which of the following statements is true A) At equilibrium, we expect [Reactants} < [Products) EN E R B) At equilibrium, we expect [Reactants) > [Products) P C) At equilibrium, we expect k < 1. D) At equilibrium, we expect K = 1 Rxn-
At equilibrium we expect [Reactants} < [Products) from the the profile that has been shown.
What is the energy profile diagram?An energy profile diagram, also known as an energy diagram or reaction coordinate diagram, is a graphical representation of the energy changes that occur during a chemical reaction or a physical process. It shows the energy levels of the reactants, products, and any intermediate species that may form during the reaction.
The horizontal axis of an energy profile diagram represents the reaction coordinate, which is a measure of the progress of the reaction from the reactants to the products. The vertical axis represents the energy of the system.
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Hello, is there any one to solve it please
Graph the function for the given domain, write the range. g(x) = 1/(x2+6)
Domain: {-6, -4, -2, 0, 2, 4, 6}
1/42,1/22,1/10,1/6 are domain of function .
What are a function's domain and range?
The set of all possible inputs and outputs is known as a function's domain, and the same is true for its range. Important features of a function are the domain and range.
The range contains all of the function's output values, while the domain contains all of the real numbers that can be used as input values.
g(x) = 1/(x²+6)
Domain: {-6, -4, -2, 0, 2, 4, 6}
G(-6) = 1/(-6² + 6) = 1/42
G(-4) = 1/(-4² + 6) = 1/22
G(-2) = 1/(-2² + 6) = 1/10
G(0) = 1/(0+6) = 1/6
G(2) = 1/(2² + 6) = 1/10
G(4) = 1/(4² + 6) = 1/22
G(6) = 1/(6² + 6) = 1/42
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Find the values of x and y. ADEF = AQRS
(5y-7) ft
D
E
123⁰
F
S
S
(2x + 2)° R
= 0, y =
Q
38 ft
P
As the two triangles are congruent to each other, using that we can get the value of x = 13 and y = 9.
What are congruent triangles?Whether two or more triangles are congruent depends on the size of the sides and angles. As a result, a triangle's three sides and three angles determine its size and shape.
Two triangles are said to be congruent if their respective side and angle pairings are both equal.
Now in the given question,
The triangles are congruent so,
ED = QR
5y -7 = 38
⇒ 5y = 38+7
⇒ y = 45/5
⇒ y = 9
Now as the sum of angles in a triangle are 180°,
∠E +∠D +∠F = 180°
⇒ ∠F = 180 - 123 - 29
⇒ ∠F = 28°
As per congruency,
(2x+2) ° = 28°
⇒ 2x = 28-2
⇒ x = 26/2
⇒ x = 13
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The complete question is:
Find the values of x and y. ADEF = AQRS
(5y-7) ft
D
E
123⁰
F
S
S
(2x + 2)° R
= 0, y =
Q
38 ft
P
this question, you are given a boxplot and a set of data. Calculate the required values and fill them in on the boxplot.
A Psychologist randomly select 10 TV cartoon shows and counted the number of incidents of verbal and physical violence in each. The counts were as follows:
11; 13; 14; 15; 15; 16; 21; 26; 30; 31
a)Find the maximum, minimum and median values and plot them on the boxplot.
b)Determine Q1, Q2 and Q3 and plot them on the boxplot.
c)Determine the Inter Quartile Range.
d)Beyond which values will you find outliers?
e)Does this data set have outliers? Explain your answer.
f)Discuss the skewness (if there is) of the data set.
a) The maximum value for this data set is 31, the minimum value is 11 and the median value is 15.5.
b) Q1 13.5
Q2 15.5
Q3 24
c) 10.5
d) lower than 11 or higher than 31
e) Yes.
f) This data set is slightly positively skewed.
What is median?The median is the middle value of a set of data when the values are arranged in numerical order. It is used to find the middle value of a set of numbers or observations.
A. The values can be plotted on the boxplot as follows:
Maximum: 31
Minimum: 11
Median: 15.5
B. To find Q1, Q2 and Q3, the data must first be sorted from lowest to highest: 11; 13; 14; 15; 15; 16; 21; 26; 30; 31. Q1 is the median of the lower half of the data set (11, 13, 14, 15 and 15), which is 13.5. Q2 is the median of the entire data set (15.5). Q3 is the median of the upper half of the data set (16, 21, 26, 30 and 31), which is 24. The values can be plotted on the boxplot as follows:
Q1: 13.5
Q2: 15.5
Q3: 24
C. The Interquartile Range (IQR) is calculated by subtracting Q1 from Q3: IQR = Q3 - Q1 = 24 - 13.5 = 10.5.
D. Outliers are values that are significantly greater or lower than the majority of the data set. In this data set, values that are lower than 11 or higher than 31 would be considered outliers.
E. Yes, this data set has outliers. The value 11 is significantly lower than the majority of the data set, and the value 31 is significantly higher than the majority of the data set.
F. This data set is slightly positively skewed, as the majority of the data points are clustered around the lower end of the range, and there is a longer tail of higher values. This is indicated by the fact that the median (15.5) is lower than the mean (19.4).
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a) The maximum value of the given dataset is 31, while the minimum value is 11 and the median is 15.5.
b) Q1 = 14,
Q2 = 15.5,
Q3 = 21
c) (IQR) = 7
d) Any values below 11 or above 31
e) Yes
f) slightly positively skewed.
What is Median?Median is a measure of central tendency that is calculated by taking the middle value of a set of numbers when the values are arranged in ascending or descending order.
a) Maximum value: 31,
Minimum value: 11,
Median value: 15.5
b) Q1 = 14,
Q2 = 15.5,
Q3 = 21
c) The Interquartile Range (IQR) is calculated by subtracting Q1 from Q3:
Inter Quartile Range (IQR) = Q3-Q1
=21-14
= 7
d) Any values below 11 or above 31 can be considered as outliers.
As 11 is the lowest value given and 31 is the highest value.
e) Yes, this data set has outliers. The values 31 and 11 are both outliers since they are beyond the range of the Inter Quartile Range (IQR).
The value 11 is significantly lower than the majority of the data set, and the value 31 is significantly higher than the majority of the data set.
f) This data set is slightly positively skewed.
As the majority of the data points are clustered around the lower end of the range, and there is a longer tail of higher values.
This is indicated by the fact that the median (15.5) is lower than the mean.
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The bar graph in the following graphic represents fictional net exports in billions of dollars for five countries.
Net exports are obtained by subtracting total imports from total exports; a negative net export means the
country imported more goods than it exported.
Net Exports (Billions of dollars)
United States
Denmark
China
Germany
Spain
-150 -100
-50
Net Exports (Billions of dollars)
What is the sum of net exports for Germany and China ?
a.
-80 billion dollars
b. 180 billion dollars
0 50 100 150
C. 90 billion dollars
d. 150 billion dollars
[tex]80[/tex] billion dollars' worth of net exports were made by China and Germany. The first claim is accurate.
What do the terms "export" and "import" mean?Export is the process of supplying goods and services to some other nation. Contrarily, importing is the act of acquiring goods from outside and transferring them into one's own nation.
What does GDP export mean?The domestic product (GDP) is a measure of all the products and services generated in the United States; thus, changes in exports change significantly in the demand for goods and services made in the United States abroad.
The total of China's and Germany's net exports would be:
[tex]50[/tex] billion + [tex]30[/tex] billion [tex]= 80[/tex] billion
As a result, Germany & China's consolidated net exports amounted to [tex]80[/tex] billion u.s. dollars, reflecting answer option (a).
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(If A + B + C = 180, prove that): sin(B + 2C) + sin(C + 2A) + sin(A + 2B) = 4sin(A-B)/2.cos(B-C)/2.,cos(C-A)/2
Using trigonometric ratio it is proved that sin(B + 2C) + sin(C + 2A) + sin(A + 2B) = 4sin(A-B)/2.cos(B-C)/2.cos(C-A)/2 when A + B + C = 180.
What is trigonometric ratio?
Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios.
We can start by using the sine addition formula to expand each of the sine terms in the left-hand side of the equation -
sin(B + 2C) = sin(B)cos(2C) + cos(B)sin(2C) = 2sin(B)cos(C)²
sin(C + 2A) = sin(C)cos(2A) + cos(C)sin(2A) = 2sin(C)cos(A)²
sin(A + 2B) = sin(A)cos(2B) + cos(A)sin(2B) = 2sin(A)cos(B)²
Substituting these expressions into the left-hand side of the equation, we get -
2sin(B)cos(C)² + 2sin(C)cos(A)² + 2sin(A)cos(B)²
Factoring out the 2, we can rewrite this as -
2(sin(B)cos(C)² + sin(C)cos(A)² + sin(A)cos(B)²)
Using the trigonometric ratio identity sin(2x) = 2sin(x)cos(x), we can rewrite each of the cosine squared terms as a product of sines and cosines -
cos(C)² = (1/2)(1 + cos(2C)) = (1/2)(1 + 2cos(C)sin(C))
cos(A)² = (1/2)(1 + cos(2A)) = (1/2)(1 + 2cos(A)sin(A))
cos(B)² = (1/2)(1 + cos(2B)) = (1/2)(1 + 2cos(B)sin(B))
Substituting these expressions into the previous equation, we get -
2(sin(B)(1/2)(1 + 2cos(C)sin(C)) + sin(C)(1/2)(1 + 2cos(A)sin(A)) + sin(A)(1/2)(1 + 2cos(B)sin(B)))
Simplifying and grouping the terms, we get -
sin(B)sin(C)cos(C) + sin(C)sin(A)cos(A) + sin(A)sin(B)cos(B)
Using the sine addition formula again, we can rewrite each of the cosine terms as a product of sines -
cos(C) = sin(A + B)
cos(A) = sin(B + C)
cos(B) = sin(C + A)
Substituting these expressions into the previous equation, we get -
sin(B)sin(C)sin(A + B) + sin(C)sin(A)sin(B + C) + sin(A)sin(B)sin(C + A)
We can rearrange this expression by factoring out a sin(A-B)/2 sin(B-C)/2 sin(C-A)/2 term -
sin(A-B)/2 sin(B-C)/2 sin(C-A)/2 (cos(A) - cos(B) + cos(B) - cos(C) + cos(C) - cos(A))
Simplifying the terms in parentheses, we get -
sin(A-B)/2 sin(B-C)/2 sin(C-A)/2 (0)
Therefore, the left-hand side of the equation simplifies to 0, which is equal to the right-hand side of the equation -
4sin(A-B)/2.cos(B-C)/2.cos(C-A)/2
Therefore, we have proven that sin(B + 2C) + sin(C + 2A) + sin(A + 2B) = 4sin(A-B)/2.cos(B-C)/2.cos(C-A)/2.
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for a given positive integer n, output all the perfect numbers between 1 and n, one number in each line.
Perfect numbers between 1 and n (where n is a positive integer) are 6, 28, 496, 8128.
A positive integer that is the sum of its appropriate divisors is referred to as a perfect number. The sum of the lowest perfect number, 6, is made up of the digits 1, 2, and 3. The digits 28, 496, and 8,128 are also ideal.
Perfect numbers are whole numbers that are equal to the sum of their positive divisors, excluding the number itself. Examples of perfect numbers include 6 (1 + 2 + 3 = 6), 28 (1 + 2 + 4 + 7 + 14 = 28) and 496 (1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 496).
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The complete question is:
What are all the perfect numbers between 1 and n (where n is a positive integer)?
Alberto believes that because all squares can be called
rectangles, then all rectangles must be called squares.
Explain why his reasoning is flawed. Use mathematical
terminology to help support your reasoning.
Alberto's statement is flawed because all squares can be called rectangles, but not vice versa
Reason why Alberto's statement is flawedAlberto's reasoning is flawed because all squares can be called rectangles, but not all rectangles are squares.
While it is true that squares meet the definition of rectangles, not all rectangles meet the definition of squares.
A square is a special type of rectangle with all sides equal in length.
Therefore, Alberto's argument violates the logical concept of implication, where the truth of one proposition (squares can be called rectangles) does not necessarily imply the truth of the converse (all rectangles must be called squares).
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One month Maya rented 5 movies and 3 video games for a total of $34. The next month she rented 2 movies and 12 video games for a total of $73. Find the rental cost for each movie and each video game. Rental cost for each movie: s Rental cost for each video game: s 3 Es
The rental cost for each movie and each video game is $3.5 and $5.5 respectively.
What is the the rental cost for each movie and each video game?Let
cost of each movie = x
Cost of each video game = y
5x + 3y = 34
2x + 12y = 73
Multiply (1) by 4
20x + 12y = 136
2x + 12y = 73
subtract the equations to eliminate y
18x = 63
divide both sides by 18
x = 63/18
x = 3.5
Substitute x = 3.5 into (1)
5x + 3y = 34
5(3.5) + 3y = 34
17.5 + 3y = 34
3y = 34 - 17.5
3y = 16.5
y = 16.5/3
y = 5.5
Therefore, $3.5 and $5.5 is the rental cost of each movie and video game respectively.
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What is the coefficient of the fourth term in the expansion of (x - y)^4?
Answer: the distribution to the x and the 3 makes the solution 4
Step-by-step explanation: i got you broski