Let X and Y be independent random variables, uniformly distributed in the interval [0, 1 Find the CDF and the PDF of X-Y
Let X and Y be independent random variables, uniformly distributed in the interval [0, 1 ]. The CDF of X - Y is FZ(z) = (1/2)(1+z)^2 for -1 ≤ z ≤ 0, 1 - (1/2)(1-z)^2 for 0 ≤ z ≤ 1, 0 for z < -1 or z > 1. The PDF of X - Y is fZ(z) = z + 1 for -1 < z < 0, 1 - z for 0 < z < 1, 0 otherwise.
To find the CDF of X - Y, we first note that the range of X - Y is [0, 1]. Let Z = X - Y, then:
FZ(z) = P(Z ≤ z) = P(X - Y ≤ z)
We can write this as an integral over the joint distribution of X and Y:
FZ(z) = ∫∫[X - Y ≤ z] fXY(x, y) dx dy
Since X and Y are independent, the joint distribution is simply the product of their marginal distributions:
fXY(x, y) = fX(x) fY(y) = 1 * 1 = 1
for 0 ≤ x, y ≤ 1.
Thus, we have:
FZ(z) = ∫∫[X - Y ≤ z] dx dy
= ∫∫[Y ≤ X - z] dx dy
= ∫0^1 ∫0^(x-z) 1 dy dx + ∫0^1 ∫(x-z)^1 1 dy dx
= ∫0^(1+z) (1-z) dx
= (1/2)(1+z)^2 for -1 ≤ z ≤ 0
= 1 - (1/2)(1-z)^2 for 0 ≤ z ≤ 1
Therefore, the CDF of X - Y is:
FZ(z) =
(1/2)(1+z)^2 for -1 ≤ z ≤ 0
1 - (1/2)(1-z)^2 for 0 ≤ z ≤ 1
0 for z < -1 or z > 1
To find the PDF of X - Y, we differentiate the CDF:
fZ(z) = dFZ(z)/dz =
z + 1 for -1 < z < 0
1 - z for 0 < z < 1
0 otherwise
Therefore, the PDF of X - Y is:
fZ(z) =
z + 1 for -1 < z < 0
1 - z for 0 < z < 1
0 otherwise
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Can Anyone Help?
A poster is to have a total area of 245cm2. There is a margin round the edges of 6cm at the top and 4cm at the sides and bottom where nothing is printed.What width should the poster be in order to have the largest printed area?
The poster should have width ____ cm
Answer: The poster should have width 17.50 CM
Step-by-step explanation:
Given that boasted I have a total area 245 cm square area of a poster is 200 and 45 20 m square. And it is in the rectangle format. So we know that the poster is always in the rectangle format and the area of rectangular area is equal to L N T W. So 245 will be equal to Ln tW. From this. We need to find L. So L is equal to 245 divided by W. Now consider the diplomatic representation of the poster. So it has mentioned that there is a margin around the edges of six cm at the top. This is 6cm and four cm at the sites. All the four sides 3 sides are four cm. So from this we need to find land and the doctor posted area that is printed area. The first wine printed with www. Z. Quilter. Now let this be total birth will be W. And this will be four and this will be four. Therefore posted with will be we need to find this part alone. So W -4 -4 will give the this part with. So W -4 -4. So post printed with PW will be equal to W -8. Similarly printed lunch will be equal to The total length is already we have found 245 by W. And we need to find this part length. So we have to subtract six and four from the total length so that that will give them this part length, So -6 -4. So printed length will be equal there 245 Divided by W -10. And we know that formula for area of a rectangle. Urz D is equal to L W. Now substitute the printed with and printed length in the area formula. We have to find the printed area. So Printed area Zeke Walter W -8 into 245 Divided by W -10. To simplify this, we get 325 minus 10. W -100 and 30,960 W. to the power of -1. Now fine D A by D. T. Not D D. This is D. W. So this is equal to differentiation of constant alma zero, this is minus 10 plus 900 and 60 W. to the power of -2 and equate this to be equal to zero. We out to find the maximum width so D A by D W is equal to zero, therefore minus 10 1960 W. To the power of -2 will be equal to zero. To simplify this, we get them maximum with value the W is equal term I wrote off 196. Therefore the value of W. Z quilter plus or minus 14. We will neglect the negative values since we cannot be negative. So one we assume the positive values. So what will be equal to 14 and length will be equal to 245 divided by 14, So which will be equal to 17.50 centimeters. And they have concluded that At W is equal to 14 cm and lunch will be equal to 17.50 cm needed to print the largest area. I hope you found the answer to school. Thank you.
determine the factor of the shape, needed in a fraction or whole number please help
Therefore, the scale factor of the dilation of the shape is 2.
What is scale factor?A scale factor is a ratio that describes the proportional relationship between two similar figures. It represents how much larger or smaller one figure is compared to the other, and it is calculated by dividing a corresponding measurement (such as side length, perimeter, or area) of the larger figure by the corresponding measurement of the smaller figure. Scale factor is used in mathematics, particularly in geometry and measurement, to describe the transformation of one figure into another through dilation or resizing. It is represented by a number or a ratio, such as 2:1 or 1/2, which indicates how many times larger or smaller the new figure is compared to the original.
Here,
In the given picture, it appears that the distance from the center of dilation (the origin) to the pre-image (the original figure) is 4 units, and the distance from the center of dilation to the image (the transformed figure) is 8 units. The scale factor of the dilation is equal to the ratio of the distance from the center of dilation to the image and the distance from the center of dilation to the pre-image.
So, the scale factor of the dilation is:
8 units ÷ 4 units = 2
Therefore, the scale factor of the dilation is 2.
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1. Find an equation for the line with the given properties.
Perpendicular to the line x = 5; containing the point (5,6)
y =
2. Find an equation for the line with the given properties. Use lowercase letter x for the variable.
Parallel to the line 7x - y = -7; containing the point (0,0)
y =
3. Find an equation for the line with the given properties.
Slope undefined; containing the point (8,2)
For the first question, the equation for the line is y = -x + 11. This comes from the fact that the slope for a line perpendicular to the line x = 5 is -1. From there, we can use the point (5,6) to calculate the y-intercept, which is 11.
For the second question, the equation for the line is y = 7x. This comes from the fact that the slope for a line parallel to the line 7x - y = -7 is 7. Since the point (0,0) is already on the line, the equation is already solved.
For the third question, the equation for the line is x = 8. This comes from the fact that the slope for a line with an undefined slope is 0. Since the point (8,2) is already on the line, the equation is already solved.
What is tangent and how do you calculate it from the unit circle?
Answer:
The unit circle has many different angles that each have a corresponding point on the circle. The coordinates of each point give us a way to find the tangent of each angle. The tangent of an angle is equal to the y-coordinate divided by the x-coordinate.
11/12 x 8/25 x 15/16 x 9/44
In each of Problems 6 through 9, determine the longest interval in which the given initial value problem is certain to have a unique twice- differentiable solution. Do not attempt to find the solution. 6. ty" + 3y = 1, y(1) = 1, y'(1) = 2 7. t(t – 4)y" + 3ty' + 4y = 2, y(3) = 0, y'(3) = -1 8. y" + (cost)y' + 3( In \t]) y = 0, y(2) = 3, y'(2) = 1 9. (x - 2)y"+y' +(x - 2)(tan x) y = 0, y(3) = 1, y'(3) = 2 = ) y( = = = - =
(a) The interval (-∞, ∞).
(b) The interval (-∞, ∞).
(c) The interval (-∞, ∞).
(d) The interval (-π/2, π/2) \ {0}.
(a) The longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution is the interval where the coefficient function, 3t, is continuous and bounded. Since 3t is a continuous and bounded function for all t in the interval (-∞, ∞), the given initial value problem is certain to have a unique twice-differentiable solution for all t in (-∞, ∞).
(b) The longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution is the interval where the coefficient functions, t(t - 4), 3t, and 4, are continuous and bounded. Since t(t - 4), 3t, and 4 are continuous and bounded functions for all t in the interval (-∞, ∞), the given initial value problem is certain to have a unique twice-differentiable solution for all t in (-∞, ∞).
(c) The longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution is the interval where the coefficient functions, cost and In|t|, are continuous and bounded. Since cost and In|t| are continuous and bounded functions for all t in the interval (-∞, ∞), the given initial value problem is certain to have a unique twice-differentiable solution for all t in (-∞, ∞).
(d) The longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution is the interval where the coefficient functions, x - 2, 1, and (x - 2)tanx, are continuous and bounded. Since x - 2, 1, and (x - 2)tanx are continuous and bounded functions for all x in the interval (-π/2, π/2) \ {0} , the given initial value problem is certain to have a unique twice-differentiable solution for all x in (-π/2, π/2) \ {0}.
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The given question is incomplete, the complete question is:
determine the longest interval in which the given initial value problem is certain to have a unique twice- differentiable solution. Do not attempt to find the solution. (a) ty" + 3y = 1, y(1) = 1, y'(1) = 2 (b) t(t – 4)y" + 3ty' + 4y = 2, y(3) = 0, y'(3) = -1 (c) y" + (cost)y' + 3( In |t|) y = 0, y(2) = 3, y'(2) = 1 (d) (x - 2)y"+y' +(x - 2)(tan x) y = 0, y(3) = 1, y'(3) = 2
a plumber can do a job in 5 hours, and his apprentice can do the same job in 8 hours. What part of the job is left if they start the job and work together for 2 hours.
1. If the angle between the vectors a and b is π/4 and | a × b | = 1, then a. b is equal to
Answer:
We can use the formula |a × b| = |a| |b| sin θ to solve for the magnitude of the cross product |a × b|, where θ is the angle between vectors a and b. In this case, we have |a × b| = 1 and θ = π/4, so we can write:
1 = |a| |b| sin(π/4)
Simplifying, we have:
|a| |b| = √2
Now, we need to find the dot product a · b. We know that:
a · b = |a| |b| cos θ
where θ is the angle between vectors a and b. Since we're given the angle between a and b, we can substitute θ = π/4 and use the value we found for |a| |b|:
a · b = (√2) cos(π/4) = (√2)/2
Therefore, a · b is equal to (√2)/2.
Step-by-step explanation:
T
AD
View Instructions
Interpreting a Dot Plot
DAR
3 4 5
1 2
Number of pets at home
6
How many people have 2 pets at home?
How many people have at least 3 pets at home?
How many more people have 2 pets than 5 pets?
How many people have less than 3 pets at home?
11
10 HELP MEEE
If we total up the dots plot for 3, 4, and 5 pets, we find that 3 people have 2 pets at home, 10 individuals have at least 3 pets at home.
What is the 1 pet in the world?The fact that dogs are the most common pet in the world shouldn't be shocking. There is a reason why there are tens of millions of dogs living in the United States alone, which is why some people say that dogs are a man's greatest friend. Around the world, at least one dog is kept in one-third of all households.
What exactly is a house pet?A fully domesticated animal kept constitutes a "household pet." a pet kept by you for personal company, like a dog, cat, reptile, bird, or mouse. Any kind of horse, cow, pig, sheep, goat, chicken, turkey, other captive fur-bearing animal is not considered a household pet, nor is any animal that is typically kept for food or profit.
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The total number of people with pets at home is 11, which is the sum of the heights of the columns.
What is equation?
A math equation is a method that links two claims and represents equivalence using the equals sign (=). An equation is a mathematical statement that establishes the equivalence of two mathematical expressions in algebra.
Based on the given dot plot, we can answer the following questions:
How many people have 2 pets at home?
Answer: Two people have 2 pets at home, as indicated by the two dots in the second column.
How many people have at least 3 pets at home?
Answer: Six people have at least 3 pets at home, as indicated by the dots in the third column and beyond.
How many more people have 2 pets than 5 pets?
Answer: There are no dots in the last column, which represents 5 pets. Therefore, the difference between the number of people with 2 pets and those with 5 pets is 2 - 0 = 2.
How many people have less than 3 pets at home?
Answer: Three people have less than 3 pets at home, as indicated by the dots in the first two columns.
Therefore, the total number of people with pets at home is 11, which is the sum of the heights of the columns.
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Does 9:45 am and 9:45 pm considered total of 12 hours
Answer:
Yes. If you are asking if the duration between those two times is a total of 12 hours, the answer is yes.
Step-by-step explanation:
9:45am is 12 hours away from 9:45pm. This applies to all times and their am/pm counterparts such as 12am/12pm.
find the following answer
The cardinality of set from the given vein diagram is found as 2.
Explain about the cardinality of set?Think about set A. The set A is said to be finite and so its cardinality is same to the amount of elements n if it includes precisely n items, where n ≥ 0. |A| stands for the cardinality of such a set A.
It turns out that there are two kinds of infinite sets that we need to determine between since one form is much "bigger" than the other. Particularly, one type is referred to as countable and the other as uncountable.
From the given figure
Set A = {8 , 8, 3, 6}
Compliment of Set B (elements not present in set B):
Set [tex]B^{c}[/tex] = {8, 8, 6(pink), 3(white)}
Thus,
(A∩ [tex]B^{c}[/tex] ) = {8, 8} (present in both set)
n (A∩ [tex]B^{c}[/tex] ) = 2 (cardinal number)
Thus, the cardinality of the set from the given vein diagram is found as 2.
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HELP what is the answer to this using systems of equations
y=1/8x−1
−5x+4y=−13
Answer:
x = 2
y = -3/4
Step-by-step explanation:
1. Substitute y=1/8x -1 in −5x+4y=−13
-5x+4(1/8x -1) = -13
2. Solve for x
-5x + 4/8x - 4 = -13
-9/2x - 4 = -13
-9/2x = -9
x = 2
3. Now that you know x = 2, plug it into y=1/8x - 1 to find what y is.
y= 1/8(2) - 1
y= 2/8 - 1
y= -3/4
What is the equation of the circle in the standard (x, y) coordinate plane that has a radius of 4 units and the same center as the circle determined by x^2 + y^2 - 6y + 4=0?
A. x² + y^2 = -4
B. (x+3)^2 + y^2 = 16
C. (x-3)^2 + y^2 = 16
D. x^2 + (y+3)^2 = 16
E. x^2 + (y-3)^2 = 16
Answer:
E. x² + (y - 3)² = 16
Step-by-step explanation:
The equation of a circle in the standard (x, y) coordinate plane with center (h, k) and radius r is given by:
[tex]\boxed{(x - h)^2 + (y - k)^2 = r^2}[/tex]
To find the equation of the circle with a radius of 4 units and the same center as the circle determined by x² + y² - 6y + 4 = 0, we need to first write the equation of the second circle in the standard form.
We can complete the square for y to rewrite this equation in standard form. To do this move the constant to the right side of the equation:
[tex]\implies x^2 + y^2 - 6y + 4 = 0[/tex]
[tex]\implies x^2 + y^2 - 6y = -4[/tex]
Add the square of half the coefficient of the term in y to both sides of the equation:
[tex]\implies x^2 + y^2 - 6y +\left(\dfrac{-6}{2}\right)^2= -4+\left(\dfrac{-6}{2}\right)^2[/tex]
[tex]\implies x^2 + y^2 - 6y +9= -4+9[/tex]
[tex]\implies x^2 + y^2 - 6y +9=5[/tex]
Factor the perfect square trinomial in y:
[tex]\implies x^2+(y-3)^2=5[/tex]
[tex]\implies (x-0)^2 + (y-3)^2=5[/tex]
So the center of this circle is (0, 3) and its radius is √5 units.
Since the new circle has the same center, its center is also (0, 3).
We know its radius is 4 units, so we can write the equation of the new circle as:
[tex]\implies (x - 0)^2 + (y - 3)^2 = 4^2[/tex]
[tex]\implies x^2 + (y - 3)^2 = 16[/tex]
Therefore, the equation of the circle in the standard (x, y) coordinate plane with a radius of 4 units and the same center as the circle determined by x² + y² - 6y + 4 = 0 is x² + (y - 3)² = 16.
To find:-
The equation of circle which has a radius of 4units and same centre as determined by x² + y² - 6y + 4 = 0.Answer:-
The given equation of the circle is ,
[tex]\implies x^2+y^2-6y + 4 = 0 \\[/tex]
Firstly complete the square for y in LHS of the equation as ,
[tex]\implies x^2 + y^2 -2(3)y + 4 = 0 \\[/tex]
Add and subtract 3² ,
[tex]\implies x^2 +\{ y^2 - 2(3)(y) + 3^2 \} -3^2 + 4 = 0 \\[/tex]
The term inside the curly brackets is in the form of a²-2ab+b² , which is the whole square of "a-b" . So we may rewrite it as ,
[tex]\implies x^2 + (y-3)^2 -9 + 4 = 0 \\[/tex]
[tex]\implies x^2 + (y-3)^2 - 5 = 0 \\[/tex]
[tex]\implies x^2 + (y-3)^2 = 5\\[/tex]
can be further rewritten as,
[tex]\implies (x-0)^2 + (y-3)^2 = \sqrt5^2\\[/tex]
now recall the standard equation of circle which is ,
[tex]\implies (x-h)^2 + (y-k)^2 = r^2 \\[/tex]
where,
(h,k) is the centre.r is the radius.So on comparing to the standard form, we have;
[tex]\implies \rm{Centre} = (0,3)\\[/tex]
Now we are given that the radius of second circle is 4units . On substituting the respective values, again in the standard equation of circle, we get;
[tex]\implies (x-h)^2 + (y-k)^2 = r^2 \\[/tex]
[tex]\implies (x-0)^2 + (y-3)^2 = 4^2 \\[/tex]
[tex]\implies \underline{\underline{\red{ x^2 + (y-3)^2 = 16}}}\\[/tex]
and we are done!
QUICK ANSWER THIS PLEASE What is the constant of proportionality between the corresponding areas of the two pieces of wood?
3
6
9
12
Answer:
Step-by-step explanation:
D
The base of a triangle is 3 inches shorter than its height. Its area is 275 square inches. Set up a quadratic equation and solve to find its base and height.
Answer: hope its help
Let's start by assigning variables to the unknown quantities in the problem. Let h be the height of the triangle in inches, and let b be the base of the triangle in inches.
According to the problem, the base of the triangle is 3 inches shorter than its height. This can be expressed as:
b = h - 3
The formula for the area of a triangle is:
A = (1/2)bh
We are given that the area of the triangle is 275 square inches, so we can substitute these values into the formula to get:
275 = (1/2)(h)(h-3)
Simplifying the right-hand side, we get:
275 = (1/2)(h^2 - 3h)
Multiplying both sides by 2 to eliminate the fraction, we get:
550 = h^2 - 3h
Rearranging this equation to standard quadratic form, we get:
h^2 - 3h - 550 = 0
Now we can solve for h using the quadratic formula:
h = (-b ± sqrt(b^2 - 4ac)) / (2a)
In this case, a = 1, b = -3, and c = -550, so we can substitute these values into the formula to get:
h = (-(-3) ± sqrt((-3)^2 - 4(1)(-550))) / (2(1))
Simplifying the expression inside the square root, we get:
h = (3 ± sqrt(2209)) / 2
We can ignore the negative solution since height must be positive, so we get:
h = (3 + sqrt(2209)) / 2 ≈ 29.04
Now that we know the height of the triangle is approximately 29.04 inches, we can use the equation b = h - 3 to find the length of the base:
b = 29.04 - 3 = 26.04
Therefore, the base of the triangle is approximately 26.04 inches, and the height is approximately 29.04 inches.
Step-by-step explanation:
The function rule for this graph is Y equals___ X + ___
The answer is below in case someone needs it.
The function rule for this graph is y = -1/2(x) + 2.
How to determine an equation of this line?In Mathematics, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁) or [tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)[/tex]
Where:
m represent the slope.x and y represent the points.At data point (0, 2), a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
[tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)\\\\y - 2 = \frac{(0- 2)}{(4 -0)}(x -0)[/tex]
y - 2 = -1/2(x)
y = -1/2(x) + 2.
In this context, we can reasonably infer and logically deduce that an equation of the line that represents this graph in slope-intercept form is y = -1/2(x) + 2.
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Mr. James is enlarging a logo for printing
on the back of a T-shirt. He wants to enlarge a logo that is 3 inches by
5 inches so that the dimensions are 3 times larger than the original. How
many times as large as the original logo will the area of the printing be?
The area of the enlarged logo will be 9 times larger than the original logo.
When an object is enlarged or scaled up how does it area change ?
When an object is enlarged or scaled up by a factor of [tex]k[/tex], both its length and width are multiplied by [tex]k[/tex]. Therefore, the new length is [tex]k[/tex] times the original length, and the new width is [tex]k[/tex] times the original width.
The area of the new object is the product of the new length and width, which is ([tex]k[/tex] times the original length) multiplied by ([tex]k[/tex] times the original width), or [tex]k^2[/tex] times the original area.
Therefore, the area of an object increases by a factor of [tex]k^2[/tex] when the object is enlarged or scaled up by a factor of [tex]k[/tex].
Calculating how many times larger the area of the enlarged logo will be :
The original logo has dimensions of 3 inches by 5 inches, so its area is 3 x 5 = 15 square inches.
Mr. James wants to enlarge the logo so that the dimensions are 3 times larger than the original. This means the new dimensions will be 9 inches by 15 inches.
To determine how many times larger the area of the enlarged logo will be, we need to compare the areas of the original logo and the enlarged logo. The area of the enlarged logo is 9 x 15 = 135 square inches.
To find out how many times larger the area of the enlarged logo is compared to the original logo, we divide the area of the enlarged logo by the area of the original logo:
135 square inches ÷ 15 square inches = 9
Therefore, the area of the enlarged logo will be 9 times larger than the area of the original logo.
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two cards are drawn at random from an ordinary deck of 52 cards what is the probability that thee are no sixes
there is an 85% chance that the two cards drawn at random from an ordinary deck of 52 cards will not be sixes.
The probability of drawing a card from an ordinary deck without replacement can be determined using the concept of conditional probability. Conditional probability is the probability of an event occurring, assuming that another event has already occurred.
In order to calculate the probability that the two cards drawn are not sixes, we can use the formula:
P(A and B) = P(A) x P(B|A)
Where A and B represent two independent events, P(A) is the probability of event A occurring, and P(B|A) is the conditional probability of event B occurring given that event A has already occurred.
The probability of drawing the first card that is not a six is:
P(A) = 48/52 = 0.9231
The probability of drawing the second card that is not a six, given that the first card drawn was not a six, is:
P(B|A) = 47/51 = 0.9216
Therefore, the probability of drawing two cards at random from an ordinary deck of 52 cards and having neither of them be a six is:
P(A and B) = P(A) x P(B|A) = 0.9231 x 0.9216 = 0.8503 or approximately 85%.
This means that there is an 85% chance that the two cards drawn at random from an ordinary deck of 52 cards will not be sixes.
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Solve the following equations. Show your complete solutions.
A.
1)x+7=18
2)x-13 15
3) 8x=64
4)5x-13-12
I need a complex solution
And pls can u not simplyfy it
Answer:
1. x = 11
Step-by-step explanation:
1. x + 7 = 18
move 7 to right then change the sign
x = 18 - 7
x = 11
2. x - 13 = 15
move -13 to right then change the sign
x = 15 + 13
x = 28
3. 8x = 64
8 8
divided by 8 both side
x = 8
4. 5x-13-12=0 it this the correct given?
add same variable
5x = 13 + 12
5x = 25
5 5
divided by 5 both side
x = 5
Graph the function to find the zeros. Rewrite the function with the polynomial in factored form.
y=x²+x-2
The zeros of the function are ? .
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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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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A store purchased a stylus for $22.00 and sold it to a customer for 20% more than the purchase price. The customer was charged a 6% tax when the stylus was sold. What was the customer’s total cost for the stylus?
Answer: $27.98
Step-by-step explanation:
22.00 × .2= 4.40
22 + 4.40 = 26.40
26.40 × .06 = 1.584
26.40 + 1.584 = 27.984
Round to the nearest hundred so the total paid by the customer would be 27.98
question 1 write an inequality and a word sentence that represent the graph. let x represent the unknown number.
The inequality is X > 0 and a word sentence represent the graph is X the graph of a number line with an open circle on zero and an arrow pointing to the right.
The inequality X > 0 represents the graph of a number line with an open circle on zero to left and an arrow pointing to the right. This means that any value of X that is greater than zero is a valid solution for the inequality.
In other words, X can be any positive number, such as 1, 2, 3, and so on. However, X cannot be zero or any negative number, as those values do not satisfy the inequality. Therefore, the word sentence that represents this inequality is "X is greater than zero."
This means that X must be a positive number, and it can be any value that is greater than zero.
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What is the equation of the line that is parallel to the
given line and passes through the point (-3, 2)?
V(o, 3)
O 3x - 4y = -17
(-3,2
O 3x - 4y = -20
4x + 3y = -2
4x + 3y = -6
The equation of the line that is parallel to the given line and passes through the point (-3, 2) is 3x - 4y = -17.
What is the formula for a parallel line equation?If the line's equation is axe + by + c = 0 and the coordinates are (x1, y1).
To find the equation of a line parallel to a given line, we must first understand that parallel lines have the same slope. As a result, we must first determine the slope of the given line.
3x - 4y = -17 is the given line. To determine its slope, solve for y and write the equation in slope-intercept form:
-3x - 4y = -3x - 17 y = (3/4)x + (17/4)
This line has a 3/4 slope.
Now we want to find the equation of a parallel line that passes through the point (-3, 2). Because the new line is parallel to the given line, it has a slope of 3/4.
We can write the equation of the new line using the point-slope form of the equation of a line as:
y - y1 = m(x - x1)
where m represents the slope and (x1, y1) represents the given point (-3, 2).
When m = 3/4, x1 = -3, and y1 = 2, we get:
y - 2 = (3/4)(x - (-3))
y - 2 = (3/4)(x + 3)
Divide both sides by 4 to get rid of the fraction.
4y - 8 = 3x + 9
3x - 4y = -17
As a result, the equation of the parallel line that passes through the point (-3, 2) is 3x - 4y = -17.
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Shallow Drilling, Inc. has 76,650 shares of common stock outstanding with a beta of 1.47 and a market price of $50.00 per share. There are 14,250 shares of 6.40% preferred stock outstanding with a stated value of $100 per share and a market value of $80.00 per share. The company has 6,380 bonds outstanding that mature in 14 years. Each bond has a face value of $1,000, an 8.00% semiannual coupon rate, and is selling for 99.10% of par. The market risk premium is 9.79%, T-Bills are yielding 3.21%, and the tax rate is 26%. What discount rate should the firm apply to a new project's cash flows if the project has the same risk as the company's typical project?
Group of answer choices
The discount rate that should be applied to a new project's cash flows is the Weighted Average Cost of Capital (WACC). To calculate WACC, you need to first calculate the cost of debt. This is done by taking the face value of the bonds ($1000) multiplied by the coupon rate (8%) multiplied by (1 - the tax rate (26%)), which equals 5.92%. The cost of debt is then calculated by taking the market value of the debt (6,380 x $1,000 x 99.1%) and dividing this by the total market value of the debt plus the market value of the equity (6,380 x $1,000 x 99.1% + 76,650 x $50 + 14,250 x $80), which equals 5.22%.
Next, you need to calculate the cost of equity using the Capital Asset Pricing Model (CAPM). This is done by taking the risk-free rate (3.21%) plus the market risk premium (9.79%) multiplied by the firm's beta (1.47), which equals 17.18%.
The WACC is then calculated by taking the cost of equity multiplied by the proportion of equity (76,650 x $50 + 14,250 x $80 divided by the total market value of the debt plus the market value of the equity) plus the cost of debt multiplied by the proportion of debt (6,380 x $1,000
Find the area of the parallelogram. Round to the nearest hundredth if necessary.
Answer:
Step-by-step explanation:
5m(4m) = 20m^2
Answer this imagine please
Answer:
B) Group 2
Step-by-step explanation:
Group 1 wrote it correctly because there are 3 groups of 4x and 3 groups of 3
Group 2 wrote it incorrectly because that would mean 9 groups of 4x, which is not the case here
Group 3 wrote it correctly because 3(4x) + 3(3) = 3(4x+3) due to the Distributive Property
Group 4 wrote it correctly because it is an expansion of Group 3's expression
A screen has a zoom of 140%, which means that images on the screen are 140% as long and 140% as wide as when they are printed on a sheet of paper. An image of a house is 17 cm tall when printed on a sheet of paper. How tall would the image of the house be on the screen? Give your answer in centimetres (cm).
Answer:
23.8 cm
Step-by-step explanation:
17 * 140% = 17 * 1.4 = 23.8 cm
The image of the house would be 23.8 cm tall on the screen.
To calculate the height of the image of the house on the screen, we can use the given zoom factor of 140%.
The zoom factor of 140% means that the images on the screen are 140% as long and 140% as wide compared to when they are printed on a sheet of paper.
To calculate the height of the image on the screen, we need to multiply the printed height by the zoom factor (140% or 1.4).
Height on the screen = Printed height * Zoom factor
Height on the screen = 17 cm * 1.4
Height on the screen = 23.8 cm
Therefore, the image of the house would be 23.8 cm tall on the screen.
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A large random sample of American students in seventh grade showed that
20
%
20%20, percent of them were reading below grade level.
Based on this data, which of the following conclusions are valid?
Choose 1 answer:
Choose 1 answer:
(Choice A) About
20
%
20%20, percent of all American students in seventh grade were reading below grade level.
A
About
20
%
20%20, percent of all American students in seventh grade were reading below grade level.
(Choice B)
20
%
20%20, percent of this sample was reading below grade level, but we cannot conclude anything about the population.
B
20
%
20%20, percent of this sample was reading below grade level, but we cannot conclude anything about the population.
(Choice C) About
20
%
20%20, percent of all American students were reading below grade level.
C
About
20
%
20%20, percent of all American students were reading below grade level.
The appropriate inference from the data is (B) Since [tex]20%[/tex] of this group read below grade level, we cannot draw any generalizations about the population. Thus, option B is correct.
What is the percent of the sample?A representative sample is a subset of data, often drawn from a wider population, that can show qualities that are similar.
Because the data produced contains more manageable, smaller representations of the larger group, representative sampling aids in the analysis of bigger groups.
Although the sample may be representative of seventh-grade American students, it is not necessarily representative of all seventh-graders or all American children. Hence, without additional data or research, we cannot extrapolate the sample's results to the overall population.
Therefore, 20%20, percent of all American students in seventh grade were reading below grade level.
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