The most appropriate name for the function that takes the length of a race and returns the time needed to complete it would be "time(length)".
When choosing a name for a function, it is important to consider clarity and readability. The name should accurately describe the purpose of the function and provide a clear indication of what it does.
In this case, the function is expected to take the length of a race as input and return the time needed to complete it as output. Among the given options, "time(length)" is the most suitable choice.
a. length(time): This name suggests that the function takes time as input and returns the length. However, in this scenario, we are interested in finding the time needed to complete the race based on its length, so this option is not the best fit.
b. Time(race): This name implies that the function takes a race as input and returns the time. While it conveys the idea of finding the time, it doesn't explicitly mention that the input is the length of the race, making it less clear.
c. time(length): This option accurately describes the purpose of the function, indicating that it takes the length of the race as input and returns the corresponding time. It is concise, clear, and aligns with the conventional naming conventions for functions.
d. cost(time): This name suggests that the function calculates the cost based on time, which is not relevant to the scenario of finding the time needed to complete a race.
Therefore, "time(length)" is the most suitable and appropriate name for the function.
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help please its due in 50 minutes ill mark brainliest answer too and no need to show work
The function f(x) and the inverse function h(x) for which the function f(x) is defined by the values (0,3), (1,1), (2,-1) are f(x) = 3 -2x and h(x) = [tex]\frac{3 - x}{2}[/tex]
What is a Function?A function is a rule which takes each member x of a set and assigns, or maps it to the same value y known at its image.x → Function → yA letter such as f, g or h is often used to stand for a function.
The Function which squares a number and adds on a 3, can be written as f(x) = x2+ 5.
Let the linear function be f(x) = mx + cwhen x = 0, f(x) = 33 = m(0) + cTherefore, c = 3
when x = 1, f(x) = 11 = m(1) + c but c = 31 = m + 3
Therefore m = 1 - 3, which is -2
The linear equation f(x) = 3 - 2x
To solve for inverse function h(x)let y = 3 - 2xmaking x the subject of the equation2x = 3 - yx =[tex]\frac{3 - y}{2}[/tex]replacing x with h(x) and y with x, we haveh(x) = [tex]\frac{3 - x}{2}[/tex]
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Find f−1′ (0) for f(x) = 4x3 + 6x − 10
Answer:
Sure. First, we need to find the inverse function of f(x). We can do this by using the following steps:
1. Let y = f(x).
2. Solve the equation y = 4x3 + 6x - 10 for x.
3. Replace x with y in the resulting equation.
This gives us the following inverse function:
```
f^-1(y) = (-1 + sqrt(1 + 12y)) / 2
```
Now, we need to find f^-1′ (0). This is the derivative of the inverse function evaluated at y = 0. We can find this derivative using the following steps:
1. Use the chain rule to differentiate f^-1(y).
2. Evaluate the resulting expression at y = 0.
This gives us the following:
```
f^-1′ (0) = (3 * (1 + 12 * 0) ^ (-2/3)) / 2 = 1.5
```
Therefore, f^-1′ (0) = 1.5.
Step-by-step explanation:
8. Amy has $30 to spend. She wants to buy pounds of lemons at $2 per pound, a box for $4, and 7 frozen dinners for $3 each Choose True or False for each statement. A She will not have enough money to buy everything O True O False 8 She will have $1 left over. O True O False C The total cost is $39. O True O False
Answer:she will actually need 1 dollar because all of that would be 31 dollars.
Step-by-step explanation:
3 pounds of lemons= $6
1 box of rice= $4
7 frozen diners= $21
6+4=10
10+21=31
Hannah and Becky are learning to type on a computer keyboard. Hannah's
typing speed is represented by the equation y = 11x where y is the number of
words she types and x is the number of minutes. Becky's typing speed is
given by the graph.
Number of words
60
48
36
24
12
2
3
Time (minutes)
Choose the statement that correctly compares their unit rates.
Adr
A. Hannah's unit rate is 2 more words per minute than Becky's unit
rate.
B. Hannah's unit rate is 1 more word per minute than Becky's unit
rate.
C. Hannah's unit rate is equal to Becky's unit rate.
D. Hannah's unit rate is 1 fewer word per minute than Becky's unit
rate
The correct statement is D. Hannah's unit rate is 1 fewer word per minute than Becky's unit rate.
To compare the unit rates, we need to determine the rate at which each person types words per minute.
For Hannah, the equation y = 11x represents her typing speed, where y is the number of words and x is the number of minutes. This means that Hannah types 11 words per minute (11 words/minute).
Looking at Becky's graph, we can determine her unit rate by calculating the change in the number of words divided by the change in time.
The change in words is 48 - 2 = 46, and the change in time is 3 - 2 = 1. So, Becky's unit rate is 46 words per minute (46 words/minute).
Comparing the unit rates:
Hannah's unit rate: 11 words/minute
Becky's unit rate: 46 words/minute
Therefore, Hannah's unit rate is 35 words per minute less than Becky's unit rate.
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On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (2, negative 1). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
y > 2x + 3
y < 2x + 3
y > −2x + 3
y < −2x + 3
The correct linear inequality represented by the graph is:
y < -2x + 3. Option D
To determine which linear inequality is represented by the graph of the dashed straight line with a negative slope and going through (0, 3) and (2, -1), we can start by finding the slope of the line.
The slope of a line can be calculated using the formula:
m = (y2 - y1) / (x2 - x1).
Using the coordinates (0, 3) and (2, -1), we have:
m = (-1 - 3) / (2 - 0),
m = -4 / 2,
m = -2.
So, we know that the slope of the line is -2.
Next, we need to determine the y-intercept of the line. To do this, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
Using the point (0, 3), we can substitute the coordinates into the equation and solve for b:
3 = -2(0) + b,
3 = b.
Therefore, the y-intercept is 3.
Now that we have the slope and y-intercept, we can write the equation of the line in slope-intercept form:
y = -2x + 3.
Since we are shading everything to the left of the line, we want the region where y is less than the line. Option D is correct.
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On her breakfast tray, Aunt Lily had a little vase of flowers - a mixture of primroses and celandines. She counted up the petals and found there were 39. "Oh, how lovely!" she said, "exactly my age; and the total number of flowers is exactly your age, Rose!" How old is Rose?
(NB: Primroses have five petals on each flower and Celandines have eight petals on each flower). Please show working
Rose's age should be a whole number, we can round 7.8 to the nearest whole number, which is 8.
Let's assume the number of primroses in the vase is p, and the number of celandines is c.
Each primrose has 5 petals, so the total number of primrose petals is 5p.
Each celandine has 8 petals, so the total number of celandine petals is 8c.
According to the given information, the total number of petals is 39. Therefore, we can set up the equation:
5p + 8c = 39 (Equation 1)
Aunt Lily mentions that the total number of flowers is exactly Rose's age. Since Rose's age is not provided, we'll represent it with the variable r.
The total number of flowers is p + c, which is also equal to Rose's age (r). Therefore, we have another equation:
p + c = r (Equation 2)
We need to find the value of r (Rose's age). To do that, we'll solve the system of equations by eliminating one variable.
Multiplying Equation 2 by 5, we get:
5p + 5c = 5r (Equation 3)
Now we can subtract Equation 1 from Equation 3 to eliminate the p term:
(5p + 5c) - (5p + 8c) = 5r - 39
This simplifies to:
-3c = 5r - 39
Now, let's rearrange Equation 2 to solve for p:
p = r - c (Equation 4)
Substituting Equation 4 into the simplified form of Equation 3, we have:
-3c = 5r - 39
Substituting r - c for p, we get:
-3c = 5(r - c) - 39
Expanding, we have:
-3c = 5r - 5c - 39
Rearranging the terms, we get:
2c = 5r - 39
Now we have a system of two equations:
-3c = 5r - 39 (Equation 5)
2c = 5r - 39 (Equation 6)
To solve this system, we can eliminate one variable by multiplying Equation 5 by 2 and Equation 6 by 3:
-6c = 10r - 78 (Equation 7)
6c = 15r - 117 (Equation 8)
Now, let's add Equation 7 and Equation 8 to eliminate c:
-6c + 6c = 10r + 15r - 78 - 117
This simplifies to:
25r = 195
Dividing both sides by 25, we get:
r = 7.8
Since Rose's age should be a whole number, we can round 7.8 to the nearest whole number, which is 8.
Therefore, Rose is 8 years old.
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guys give examples of cylinder volume word problems pls
The volume of a cylinder is given by the equation presented as follows:
V = πr²h.
In which:
r is the radius.h is the height.How to obtain the volume of the cylinder?The volume of a cylinder of radius r and height h is given by the equation presented as follows:
V = πr²h.
Hence the measures must be identified and have it's values replaced into the formula to obtain the volume of a cylinder.
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Find the total surface area of the pyramid.
A. 87.6 cm2
B. 39.6 cm2
C. 72 cm2
D. 24 cm2
The total surface area of the pyramid is option c [tex]72 cm^2[/tex].
The total surface area of a pyramid is given by the formula;S= ½Pl + BWhere B is the area of the base and P is the perimeter of the base.
To find the perimeter, add the length of all the sides of the base. Here, the base of the pyramid is a square with sides measuring 6 cm each.Therefore, its perimeter = 6 + 6 + 6 + 6 = 24 cm.
Now, to find the total surface area, we need to find the area of all four triangular faces. To find the area of one of the triangular faces, we can use the formula:
A = 1/2bhWhere b is the base of the triangle and h is the height.
To find the height, we can use the Pythagorean theorem:
[tex]h = \sqrt(6^2 - 3^2) = \sqrt(27) = 3 \sqrt(3)[/tex]
Therefore, the area of one of the triangular faces is:
A = 1/2bh = [tex]1/2(6)(3\sqrt(3)) = 9\sqrt(3)[/tex]
We have four triangular faces, so the total area of the triangular faces is:
[tex]4(9\sqrt(3)) = 36\sqrt(3)[/tex]
Finally, we can find the total surface area by adding the area of the base and the area of the triangular faces:
S = ½Pl + B = [tex]1/2(24)(3\sqrt(3)) + 6^2 = 36\sqrt(3) + 36 = 36(\sqrt(3) + 1).[/tex]
Therefore, the total surface area of the pyramid is 36(sqrt(3) + 1) cm², which is approximately 72 cm². Hence, the correct option is C. [tex]72 cm^2[/tex].
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Suppose for 40 observations, the variance is 50. If all the observations are increased by 20, the variance of these increased observation will be
Select one:
a. 50
b. 70
c. 50/20
d. 40
e. 50-20=30
Note: Answer D is NOT the correct answer. Please find the correct answer. Any answer without justification will be rejected automatically.
Answer:
a) 50
Step-by-step explanation:
The variance will not change as all the observations are increased uniformly.
Proof:
Variance formula:
[tex]s^{2} = \frac{\sum x_i^{2} }{n} -\frac{(\sum x_i)^{2} }{n^{2} }[/tex]
When the obervations are inc by 20,
[tex]s_1^{2} = \frac{\sum (x_i + 20)^{2} }{n} -\frac{(\sum (x_i + 20))^{2} }{n^{2} }\\\\=\frac{\sum(x_i^{2} + 2*20*x_i + 20^{2} )}{n} - \frac{(\sum x_i +20n)^{2} }{n^{2} } \\\\=\frac{\sum x_i^{2} + 40\sum x_i + 20^{2}n }{n} - \frac{(\sum x_i)^{2} +2*20n\sum x_i + 20^{2} n^{2} }{n^{2} } \\\\= \frac{\sum x_i^{2}}{n} - \frac{(\sum x_i)^{2}}{n^{2} } +\frac{40\sum x_i}{n} + 20^{2} - \frac{40\sum x_i}{n} - 20^{2}\\\\s_1^{2}= \frac{\sum x_i^{2}}{n} - \frac{(\sum x_i)^{2}}{n^{2} }\\\\=s^{2}[/tex]
Therefore variance doesn't change
please help
Use the quadratic formula to find the solution to the quadratic equation given
below.
Hello!
[tex]x^2 - 3x + \dfrac{9}{4} = 0\\\\4x^2 - 12x + 9 = 0\\\\\\x = \dfrac{-b\±\sqrt{b^2 - 4ac} }{2a} \\\\\\x = \dfrac{-(-12)\±\sqrt{(-12)^2 - 4 \times 4 \times 9} }{2 \times 4} \\\\\\\\boxed{x = \dfrac{3}{2} }[/tex]
This is one appointments the same distance from other points or lines geometry
The concept of equidistant points or lines is fundamental in geometry and plays a significant role in many geometric constructions and properties.
In geometry, an "equidistant" point is a point that is at the same distance from other points or lines. This concept is often used in various geometric constructions and proofs.
For example, in a circle, the center of the circle is equidistant from all points on the circumference. This property is what defines a circle.
In terms of lines, an equidistant point can be found by drawing perpendicular bisectors. A perpendicular bisector of a line segment is a line that is perpendicular to the segment and divides it into two equal parts. The point where the perpendicular bisectors of a triangle intersect is called the circumcenter, and it is equidistant from the vertices of the triangle.
Another example is the concept of an equidistant curve. In some cases, there may be a curve or path that is equidistant from two fixed points. This curve is called the "locus of points equidistant from two given points" and is often referred to as a "perpendicular bisector" when dealing with line segments.
All things considered, the idea of equidistant points or lines is essential to geometry and is important to many geometrical constructions and features.
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A metalworker cuts out a large semicircle with a diameter of 28 centimeters.Then the metalworker is a smaller sine ait of the larger one and rives it. The der of the ticular pince that is removed a 14 centimeters. Find the distance wound the shape after the smaller circle is removed. Use 22/7
The distance around the shape after the smaller semicircle is removed is 29 cm.The correct answer is option D.
To find the distance around the shape after the smaller semicircle is removed, we need to calculate the circumference of the larger semicircle and subtract the circumference of the smaller semicircle.
The circumference of a semicircle is given by the formula:
Circumference = π * radius + diameter/2
For the larger semicircle:
Radius = diameter/2 = 28/2 = 14 cm
Circumference of the larger semicircle = π * 14 + 28/2 = 22/7 * 14 + 14 = 44 + 14 = 58 cm
For the smaller semicircle:
Radius = diameter/2 = 14/2 = 7 cm
Circumference of the smaller semicircle = π * 7 + 14/2 = 22/7 * 7 + 7 = 22 + 7 = 29 cm
Therefore, the distance around the shape after the smaller semicircle is removed is:
58 cm - 29 cm = 29 cm
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The Probable question may be:
A metalworker cuts out a large semicircle with a diameter of 28 centimeters. Then the metalworker cuts a smaller semicircle out of the larger one and removes it. The diameter of the semicircular piece that is removed is 14 centimeters. What will be the distance around the shape after the smaller semicircle is removed? Use 22/7 as an approximation for π.
A. 80cm
B. 82cm
C. 85cm
D. 86cm
determine the surface area and volume
The surface area of a cylinder is 284m² and it's volume is 366.9m³
What is the surface area and volume of a cylinder?To find the surface area and volume of a cylinder, we need to know the radius (r) and height (h) of the cylinder. The formulas for the surface area (A) and volume (V) of a cylinder are as follows:
Surface Area (A) = 2πr² + 2πrhVolume (V) = πr²hFrom the given question, the data are;
radius = 4mheight = 7.3ma. The surface area of the cylinder is;
SA = 2π(4)² + 2π(4)(7.3)
SA = 283.999≈284m²
b. The volume of the cylinder is
v = πr²h
v = π(4)²(7.3)
v = 366.9m³
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John can ride his bide 4 miles in 30
minutes. At his current rate, what is the
distance, in miles, John can ride his
bike in 12 minutes?
The distance John can ride his bike in 12 minutes is approximately 1.6 miles.
To find out the distance John can ride his bike in 12 minutes, we can use the information given about his rate of riding.
We are told that John can ride his bike 4 miles in 30 minutes. This implies that his rate of riding is 4 miles per 30 minutes.
To calculate the distance John can ride in 12 minutes, we need to determine the proportion of time he is riding compared to the given rate.
We can set up a proportion to solve for the unknown distance:
(4 miles) / (30 minutes) = (x miles) / (12 minutes)
Cross-multiplying, we get:
30 minutes * x miles = 4 miles * 12 minutes
30x = 48
Now, we can solve for x by dividing both sides of the equation by 30:
x = 48 / 30
Simplifying the fraction, we have:
x = 8/5
So, John can ride his bike approximately 1.6 miles in 12 minutes, at his current rate.
Therefore, the distance John can ride his bike in 12 minutes is approximately 1.6 miles.
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Find the area to the right of the z-score 0.41 under the standard normal curve.
z0.20.30.40.50.000.57930.61790.65540.69150.010.58320.62170.65910.69500.020.58710.62550.66280.69850.030.59100.62930.66640.70190.040.59480.63310.67000.70540.050.59870.63680.67360.70880.060.60260.64060.67720.71230.070.60640.64430.68080.71570.080.61030.64800.68440.71900.090.61410.65170.68790.7224
The area to the right of the z-score 0.41 under the standard normal curve is approximately 0.3409.
To find the area to the right of the z-score 0.41 under the standard normal curve, we need to calculate the cumulative probability or area under the curve from 0.41 to positive infinity.
Since the standard normal distribution is symmetric around the mean (z = 0), we can use the property that the area to the right of a z-score is equal to 1 minus the area to the left of that z-score.
From the given z-table, we can look up the area to the left of 0.41, which is 0.6591.
The area to the right of 0.41 is then:
Area = 1 - 0.6591
Area = 0.3409
Therefore, the area to the right of the z-score 0.41 under the standard normal curve is approximately 0.3409.
This means that approximately 34.09% of the data falls to the right of the z-score 0.41 in a standard normal distribution.
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A rotation of a figure can be considered
A rotation is a geometric transformation that preserves the shape and size of a figure while changing its orientation in space. It is a fundamental concept in geometry and is used in various fields, including art, design, and engineering.
A rotation of a figure can be considered as a transformation that rotates the figure around a fixed point, known as the center of rotation. During the rotation, each point of the figure moves along an arc around the center, maintaining the same distance from the center.
To perform a rotation, we specify the angle of rotation and the direction (clockwise or counterclockwise). The center of rotation remains fixed while the rest of the figure rotates around it. The resulting figure is congruent to the original figure, meaning they have the same shape and size but may be in different orientations.
Rotations are commonly described using positive angles for counterclockwise rotations and negative angles for clockwise rotations. The magnitude of the angle determines the amount of rotation. For example, a 90-degree rotation would result in the figure being turned a quarter turn counterclockwise.
In general, a rotation is a geometric transformation that keeps a figure's size and shape while reorienting it in space. It is a fundamental idea in geometry that is applied in a number of disciplines, including as engineering, design, and the arts.
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HELP CAN SOMEONE ANSWER THIS
Answer:
JLK = PRQ
Step-by-step explanation:
We already know that JL = QR and KL = PR.
If we know the angle between the two sides is equal or if the other side lengths are equal, then that would prove the two triangles to be equal.
Since the option for the two other side lengths (JK = PQ) to be equal is not listed, then the option that shows the angles are equal is the correct answer.
Since both JKL and PRQ are between the line segments already said to be equal, the answer is JLK = PRQ
Answer:
C. This would be a true statement due to the fact the to sides touch are equal. The sides are going to come at the same angle giving you a SAS which is possible to show for congruent triangles.
Which property is illustrated by the following statement? If A ABC = A DEF,
and ADEF=AXYZ, then AABC=AXYZ.
B.
A
с
E
D
O A. Reflexive
O B. Symmetric
O C. Transitive
O D. Commutative
F
Z
The property that is illustrated by the statements is Transitive. Option C
How to determine the propertyUsing the principle of transitivity, if two objects are equal to a third, they are also equal to one another.
From the information given, we have that;
< ABC = <DEF
< DEF = < XYZ
This simply proves that < ABC and < XYZ are both equivalent to < DEF in this situation.
By using the transitive property, we can determine that A ABC and A XYZ are also equal. This attribute enables us to construct relationships between many elements based on their equality to a shared third element and to connect logically equalities.
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29.4.3 Quiz: Parabolas with Vertices at the Origin
Question 5 of 10
The equation below describes a parabola. If a is negative, which way does the
parabola open?
y=ax²2²
O A. Right
B. Down
OC. Up
OD. Left
SUBMIT
The equation of a parabola with its vertex at the origin includes a negative coefficient 'a', the parabola opens downward. option B.
The equation y = ax² represents a parabola with its vertex at the origin. In this case, if the coefficient 'a' is negative, it determines the direction in which the parabola opens.
When 'a' is negative, the parabola opens downward. This means that the vertex, which is at the origin (0, 0), represents the highest point on the graph, and the parabola curves downward on both sides.
To understand this concept, let's consider the basic equation y = x², which represents a standard upward-opening parabola. As 'a' increases, the parabola becomes narrower. Conversely, when 'a' becomes negative, it flips the parabola upside down, resulting in a downward-opening parabola.
For example, if we have the equation y = -x², the negative coefficient causes the parabola to open downward. The vertex remains at the origin, but the shape of the parabola is now inverted.
In summary, when the equation of a parabola with its vertex at the origin includes a negative coefficient 'a', the parabola opens downward. This can be visually represented as a U-shape curving downward from the origin. So Optyion B is correct.
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Which of the following functions is graphed me below ?
Answer:
[tex]y = |x - 2| + 3[/tex]
The correct answer is C.
Let X and Y have joint pdf .
a. Compute P(X < 1/2 Ç Y > 1/4).
b. Derive the marginal pdfs of X and Y.
c. Are X and Y independent? Show some calculations in support of your answer.
d. Derive f(x|y) = {the conditional pdf of X given Y=y}
Answer:
To answer the questions, I'll assume that you're referring to continuous random variables X and Y. Let's go through each part:a. To compute P(X < 1/2 ∩ Y > 1/4), we integrate the joint probability density function (pdf) over the given region:P(X < 1/2 ∩ Y > 1/4) = ∫∫ f(x, y) dx dyb. To derive the marginal pdfs of X and Y, we integrate the joint pdf over the other variable. The marginal pdf of X can be obtained by integrating the joint pdf over Y:fX(x) = ∫ f(x, y) dySimilarly, the marginal pdf of Y can be obtained by integrating the joint pdf over X:fY(y) = ∫ f(x, y) dxc. To determine if X and Y are independent, we need to check if the joint pdf can be expressed as the product of the marginal pdfs:f(x, y) = fX(x) * fY(y)If this condition holds, X and Y are independent.d. The conditional pdf of X given Y = y can be derived using the joint pdf and the marginal pdf of Y:f(x|y) = f(x, y) / fY(y)By substituting the values from the given joint pdf, we can obtain the conditional pdf of X given Y = y.Please provide the specific joint pdf for X and Y, and I'll be able to assist you further with the calculations.Hope this help youThe marginal pdf of X is fX(x) = x + 1/2
How do you compute P(X < 1/2, Y > 1/4)?We need to integrate the joint pdf over the given region. This can be done as follows:
P(X < 1/2, Y > 1/4) = ∫∫[x + y] dx dy over the region 0 ≤ x ≤ 1/2 and 1/4 ≤ y ≤ 1
= ∫[x + y] dy from y = 1/4 to 1 ∫ dx from x = 0 to 1/2
= ∫[x + y] dy from y = 1/4 to 1 (1/2 - 0)
= ∫[x + y] dy from y = 1/4 to 1/2 + ∫[x + y] dy from y = 1/2 to 1 (1/2 - 0)
= ∫[x + y] dy from y = 1/4 to 1/2 + ∫[x + y] dy from y = 1/2 to 1/2
= ∫[x + y] dy from y = 1/4 to 1/2
= [(x + y)y] evaluated at y = 1/4 and y = 1/2
= [(x + 1/2)(1/2) - (x + 1/4)(1/4)]
= (1/2 - 1/4)(1/2) - (1/4 - 1/8)(1/4)
= (1/4)(1/2) - (1/8)(1/4)
= 1/8 - 1/32
= 3/32
Therefore, P(X < 1/2, Y > 1/4) = 3/32.
The marginal pdfs of X and Y can be done as follows:
For the marginal pdf of X:
fX(x) = ∫[x + y] dy over the range 0 ≤ y ≤ 1
= [xy + (1/2)y^2] evaluated at y = 0 and y = 1
= (x)(1) + (1/2)(1)^2 - (x)(0) - (1/2)(0)^2
= x + 1/2
Therefore, the marginal pdf of X is fX(x) = x + 1/2.
For the marginal pdf of Y:
fY(y) = ∫[x + y] dx over the range 0 ≤ x ≤ 1
= [xy + (1/2)x^2] evaluated at x = 0 and x = 1
= (y)(1) + (1/2)(1)^2 - (y)(0) - (1/2)(0)^2
= y + 1/2
Therefore, the marginal pdf of Y is fY(y) = y + 1/2.
To determine if X and Y are independent, we need to check if the joint pdf factors into the product of the marginal pdfs.
fX(x) * fY(y) = (x + 1/2)(y + 1/2)
However, this is not equal to the joint pdf f(x, y) = x + y. Therefore, X and Y are not independent.
To derive the conditional pdf of X given Y = y, we can use the formula:
f(xy) = f(x, y) / fY(y)
Here, we have f(x, y) = x + y from the joint pdf, and fY(y) = y + 1/2 from the marginal pdf of Y.
Therefore, the conditional pdf of X given Y = y is:
f(xy) = (x + y) / (y + 1/2)
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5 hr, 30 min, 12 sec + 2 hr, 16 min, 25 'sec
The sum of the two time durations is 7 hours, 46 minutes, and 37 seconds.
To add the given time durations, we start by adding the seconds:
12 sec + 25 sec = 37 sec.
Since 60 seconds make a minute, we carry over any excess seconds to the minutes place, which gives us a total of 37 seconds. Moving on to the minutes, we add 30 min + 16 min = 46 min.
Again, we carry over any excess minutes to the hours place, resulting in a total of 46 minutes.
Finally, we add the hours: 5 hr + 2 hr = 7 hr.
Thus, the sum of the two time durations is 7 hours, 46 minutes, and 37 seconds.
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i need help in sparx
The rule that makes the machine work is *-5 + 6 * -5
How to make the machine work for the pair of input and outputFrom the question, we have the following parameters that can be used in our computation:
4 -50
-8 10
-3 -15
A linear equation is represented as
y = mx + c
Using the points, we have
4m + c = -50
-8m + c = 10
Subtract the equations
So, we have
12m = -60
m = -5
Next, we have
-8 * -5 + c = 10
So, we have
c = 10 - 40
c = -30
This means that the operation is
-5x - 30
When expanded, we have
*-5 + 6 * -5
Hence, the rule that makes the machine work is *-5 + 6 * -5
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The equation 4x – 4 – 5x = 7 – x + 5 has what type of solution set? Question 3 options: A) No solutions B) Two solutions C) One solution D) Infinitely many solutions
Answer:
A) No solutions
Step-by-step explanation:
First of all, we know that option B will always be incorrect. You cannot have two solutions. To illustrate this, try drawing two lines. You will find that they will either intersect once (one solution), or they will not intersect, (no solutions, parallel lines), or they are the same line and thus they will always intersect (infinitely many solutions).
With that in mind, let's solve the equation.
4x-4-5x=7-x+5
First, combine all like terms.
-x-4=12-x
Now add 4 to both sides to leave x by itself.
-x=16-x
This statement cannot be true. Therefore, this equation has no solutions (parallel lines. One line starts from 0, or the origin. That line is -x. The other line starts from 16. That line is -x+16.)
Hope this helps!
NO LINKS!!! URGENT HELP PLEASE!!!
Please help with #15
Answer:
area = 8π/3
arc length = 4π/3
Step-by-step explanation:
θ = 60°
r = 4
Area of sector :
[tex]\frac{\theta}{360} \pi r^{2} \\\\=\frac{60}{360} \pi 4^{2} \\\\= \frac{1}{6} 16\pi \\\\= \frac{8}{3} \pi[/tex]
arc length:
[tex]\frac{\theta}{360} 2\pi r\\ \\= \frac{60}{360} 2(4)\pi \\\\= \frac{1}{6} 8\pi \\\\= \frac{4}{3} \pi[/tex]
Answer:
A ≈ 8.4 cm² , arc length ≈ 4.2 cm
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{60}{360}[/tex] ( r is the radius of the circle )
= π × 4² × [tex]\frac{1}{6}[/tex]
= [tex]\frac{16\pi }{6}[/tex]
≈ 8.4 cm² ( to 1 decimal place )
arc length is calculated as
arc = circumference of circle × fraction of circle
= 2πr × [tex]\frac{60}{360}[/tex]
= 2π × 4 × [tex]\frac{1}{6}[/tex]
= [tex]\frac{8\pi }{6}[/tex]
≈ 4.2 cm ( to 1 decimal place )
Which number can each term of the equation be multiplied by to eliminate the fractions before solving?
6-3x+=x+5
5
12
Therefore, the value of x that solves the equation is 2/7, after eliminating the fractions and solving the resulting equation.
To eliminate fractions in the equation 6 - 3x + (1/2)x = x + 5, we can multiply each term by a number that will clear the denominators. In this case, the denominator is 2 in the term (1/2)x. The least common multiple (LCM) of 2 is 2 itself, so we can multiply each term by 2 to eliminate the fraction.
By multiplying each term by 2, we get:
2 * (6 - 3x) + 2 * ((1/2)x) = 2 * (x + 5)
Simplifying this expression, we have:
12 - 6x + x = 2x + 10
Now, the equation is free of fractions, and we can proceed to solve it.
Combining like terms, we have:
12 - 5x = 2x + 10
To isolate the variable terms, we can move the 2x term to the left side by subtracting 2x from both sides:
12 - 5x - 2x = 10
Simplifying further:
12 - 7x = 10
Next, we can move the constant term to the right side by subtracting 12 from both sides:
12 - 7x - 12 = 10 - 12
Simplifying again:
-7x = -2
Finally, we solve for x by dividing both sides by -7:
x = (-2) / (-7)
Simplifying the division of -2 by -7 gives us the solution:
x = 2/7
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PLSSSSSSSSSSSSSSS HELP!!!
Answer:
15
Step-by-step explanation:
5x = 4x + 3
x = 3
BC = 5x = 5(3) = 15
Answer: 15
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Please help with 35
Answer:
x = 4
Step-by-step explanation:
By property, if two tangents are drawn from an external point , then they are equal
⇒ 2x + 3 = 11
⇒ 2x = 11 - 3
⇒ 2x = 8
⇒ x = 8/2
⇒ x = 4
Answer:
x = 4
Step-by-step explanation:
To find the value of x, we can use the Two-Tangent Theorem.
The Two-Tangent Theorem states that if two tangent segments are drawn to a circle from the same external point, the lengths of the two tangent segments are equal.
Therefore:
[tex]\begin{aligned}AD &= AB\\\\2x+3&=11\\\\2x+3-3&=11-3\\\\2x&=8\\\\\dfrac{2x}{2}&=\dfrac{8}{2}\\\\x&=4\end{aligned}[/tex]
Therefore, the value of x is 4.
Find the exact value of sec(-135)
The exact value of sec(-135°) is 1.
To find the exact value of sec(-135°), we need to use the relationship between secant and cosine functions.
The secant function is defined as the reciprocal of the cosine function:
sec(theta) = 1 / cos(theta).
We know that the cosine function has a period of 360°, which means that cos(theta) = cos(theta + 360°) for any angle theta.
In this case, we want to find sec(-135°). Since the cosine function is an even function (cos(-theta) = cos(theta)), we can rewrite sec(-135°) as sec(135°).
Now, let's focus on finding the value of cos(135°). The cosine function is negative in the second and third quadrants.
In the second quadrant, the reference angle is 180° - 135° = 45°. The cosine of 45° is equal to √2/2.
Therefore, cos(135°) = -√2/2.
Now, we can find sec(135°) using the reciprocal property:
sec(135°) = 1 / cos(135°).
Substituting the value of cos(135°), we have:
sec(135°) = 1 / (-√2/2).
To simplify further, we multiply the numerator and denominator by -2/√2:
sec(135°) = -2 / (√2 * -2/√2).
Simplifying the expression:
sec(135°) = -2 / -2,
sec(135°) = 1.
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Please answer ASAP I will brainlist
The system has no solution. Option C is correct.
To solve the given system of equations using row operations, we can write the augmented matrix and perform Gaussian elimination. The augmented matrix for the system is:
1 1 -1 | 6
3 -1 1 | 2
1 4 2 | -34
We'll use row operations to transform the augmented matrix into row-echelon form or reduced row-echelon form. Let's proceed with the row operations:
R2 = R2 - 3R1:
1 1 -1 | 6
0 -4 4 | -16
1 4 2 | -34
R3 = R3 - R1:
1 1 -1 | 6
0 -4 4 | -16
0 3 3 | -40
R3 = R3 + (4/3)R2:
1 1 -1 | 6
0 -4 4 | -16
0 0 0 | -4
Now, we can rewrite the augmented matrix in equation form:
x + y - z = 6
-4y + 4z = -16
0 = -4
From the last equation, we can see that it leads to a contradiction (0 = -4), which means the system is inconsistent. Therefore, the system has no solution.
The correct answer is (C) This system has no solution.
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