The required product are as follows,
A: -4p²q²-3pq = 4c²[1 - 3c²] B: 4c²-12c⁴ = 4c²[1 - 3c²]
C: 3m²+9m³ = 3m²{1 + 3m} D: c³+c⁷ = c³[1 + c⁴]
E: 24x⁴ - 16x⁸ = 8x⁴[3 - 2x²]
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
(a)
Given expression,
-4p²q²-3pq = -pq (4pq + 3)
Similarly,
B: 4c²-12c⁴ = 4c²[1 - 3c²]
C: 3m²+9m³ = 3m²{1 + 3m}
D: c³+c⁷ = c³[1 + c⁴]
E: 24x⁴ - 16x⁸ = 8x⁴[3 - 2x²]
Thus, the required products has be illustrated above.
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what’s the answer plwase and thank you i’m so stuck i just want a good grade.
as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.
[tex]\stackrel{f(x)}{y}~~ = ~~10(\sqrt[7]{x}+9)\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~10(\sqrt[7]{y}+9)} \\\\\\ \cfrac{x}{10}=\sqrt[7]{y}+9\implies \cfrac{x}{10}-9=\sqrt[7]{y} \\\\\\ \left( \cfrac{x}{10}-9 \right)^7=(\sqrt[7]{y})^7 \implies \left( \cfrac{x}{10}-9 \right)^7=\stackrel{f^{-1}(x)}{y}[/tex]
Given the function f(x)=3x^5 and g(x)=7*4^x, Which statement is true
A. f(5)>g(5)
B.f(5)
C.f(5)=g(5)
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output.
What is a function?The process of evaluating a function is typically straightforward when we have the function in the form of a formula. For instance, it is possible to evaluate the function f(x)=53x2 by first squaring the input number, multiplying by 3, and then subtracting the result from 5.
The algebraic expression should often take one of the following forms: addition, subtraction, multiplication, or division. Bring the variable to the left and the remaining values to the right to determine the value of x.
To determine the outcome, simplify the values. The abscissa is the x value of the point (x, y). It shows how far a point is from the origin or from the x-axis' horizontal axis.
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for the first three seconds of the day, the arrival rate at the book store is 29 customers per second. the book store is capable of serving 27 customers per second. the last customer's arrives exactly three seconds after the start of the day. assume that the system is empty at the start and that no customer who arrives leaves without being served. 01-05-56 (round your answer to 2 decimal places.) how long will that customers be in the book store (in seconds)?
The last customer will be in the book store for 3.22 seconds.
The solution can be calculated using Little's Law, which states that the average number of people in a system equals the average arrival rate multiplied by the average time spent in the system.
Using this formula, we can calculate the time that the last customer will spend in the book store.
Little's Law: Average number in system = Average arrival rate x Average time in system
Average number in system = 29 customers/second x 3 seconds = 87 customers
Average time in system = 87 customers/27 customers/second = 3.22 seconds
Therefore, the last customer will be in the book store for 3.22 seconds.
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The measure of angle FGH is 60°.
The measure of angle
JGH is 35%.
FGJ is x°.
The measure of angle
Find the value of x.
x = 0
X
S
G
F
to
35°
60°
H
x = 60° - 35°
x = 25°
The measure of angle FGJ is 25°
Solve the problem. Express your answer to the correct number of significant figures. 6.221 x 7.11 - 13.7
The answer in the correct number of significant figures is 30.5.
What is the significant figure?
Significant figures are the number of digits in a value, often a measurement, that contributes to the degree of accuracy of the value. We start counting significant figures at the first non-zero digit.
We have given,
6.221 × 7.11 − 13.7
first, we determine the product of 6.221 and 7.11 and round the value to a minimum number of significant figures which is "3" since 7.11 has "3" significant figures and 6.221 has "4" significant figures
so Product = 6.221 × 7.11 = 44.2
now we do the subtraction and round the answer to a minimum decimal number
44.2 - 13.7
30.5
Hence, the answer in the correct number of significant figures is 30.5.
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A) Using the perfect square chart, ESTIMATE the squares of the following values:
a) 1.5
b) 4.7
c) 8.1
d) 13.3
e) 19.9
Now, using your calculator, CALCULATE the squares of each of the above values.
RECORD your calculations beside the corresponding estimates.
All the values after squares are,
a) 2.3
b) 22.1
c) 65.6
d) 176.9
e) 396
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
The numbers are,
a) 1.5
b) 4.7
c) 8.1
d) 13.3
e) 19.9
Now, Find all the squares as;
a) 1.5
⇒ 1.5² = 1.5 × 1.5
= 2.25
= 2.3
b) 4.7
⇒ 4.7² = 4.7 × 4.7
= 22.09
= 22.1
c) 8.1
⇒ 8.1²= 8.1 × 8.1
= 65.61
= 65.6
d) 13.3
⇒ 13.3² = 13.3 × 13.3
= 176.89
= 176.9
e) 19.9
⇒ 19.9² = 19.9 × 19.9
= 396.01
= 396
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Find the slope passing the line (3,4) and (8, -3)
Answer: -1 2/5 i think im not sure (check explaination)
Step-by-step explanation:
slope formula= y2-y1/x2-x1
-3-4/8-3=-7/5,-1 2/5
at a local college, an admissions officer surveys the incoming class of 1,000 first-year students concerning their preference of major. the officer randomly selects 100 of them and asks if they intend to major in liberal arts. of the 100 first-year students, 62 state they intend on majoring in liberal arts. assuming the conditions for inference have been met, what is the 95% confidence interval for the true proportion of first-year students who intend on majoring in liberal arts?
The 95% confidence interval for the true proportion of first-year students who intend on majoring in liberal arts is estimated to be between 0.58 and 0.66.
To calculate the 95% confidence interval for the true proportion of first-year students who intend on majoring in liberal arts, we need to calculate the point estimate and margin of error. The point estimate is the proportion of first-year students who stated they intend on majoring in liberal arts
(62/100 = 0.62).
The margin of error is 1.96 times the standard error
(SE = √(p(1-p)/n) = √(0.62(1-0.62)/100) = 0.04).
The lower bound of the 95% confidence interval is the point estimate minus the margin of error
(0.62 - 0.04 = 0.58).
The upper bound of the 95% confidence interval is the point estimate plus the margin of error
(0.62 + 0.04 = 0.66).
Therefore, the 95% confidence interval for the true proportion of first-year students who intend on majoring in liberal arts is estimated to be between 0.58 and 0.66.
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3. A mature blue whale may have a length of 28.0 m. How far from a con-
cave mirror with a focal length of 30.0 m must a 7.00-m-long baby blue
whale be placed to get a real image the size of a mature blue whale?
Answer:
2.00 m in front of the concave mirror with a focal length of 30.0 m
Step-by-step explanation:
To find the distance from a concave mirror with a focal length of 30.0 m at which a 7.00-m-long baby blue whale must be placed to get a real image the size of a mature blue whale, we can use the mirror equation:
1/u + 1/v = 1/f
Where u is the distance between the object and the mirror, v is the distance between the image and the mirror, and f is the focal length of the mirror.
We know that v is negative because the image is real, and the same size of the mature blue whale that is 28m.
So, we can substitute the values we know into the equation:
1/u - 1/28 = 1/30
We can solve for u by multiplying both sides by 30u and getting:
30 - 28u = u
So u = 2m
Therefore, the 7.00-m-long baby blue whale must be placed 2.00 m in front of the concave mirror with a focal length of 30.0 m to get a real image the size of a mature blue whale.
Find the open interval(s) on which the curve given by the vector-valued function is smooth. (Enter your answer using interval notation.)r(t)=8t^2i+7t^3j
The curve is smooth for [tex]t\neq 0[/tex] on the intervals (-∞, 0), (0, ∞)
We have to consider the curve
[tex]r(t) = 8t^{2}i + 7t^{3}j[/tex]
Now, the objective is to find the open intervals when on which the curve given by the vector valued function is smooth, using the result.
The parametrization of the curve represented by the vector valued function
[tex]r(t) = f(t)i + g(t)j + h(t)k[/tex]
This equation is smooth on an open interval when f'(t), g'(t), and h'(t) are continuous on [tex]l[/tex] and r'(t) [tex]\neq[/tex] 0 for any value of t in the interval.
Now, we know the vector equation:
[tex]r(t) = 8t^{2}i + 7t^{3}j[/tex]
Differentiating r(t) with respect to r,
[tex]r'(t) = 16t i + 21t^{2} j[/tex]
At t = 0, equate r'(t) = 0.
[tex]r'(0) = 16(0) + 21(0)^{2}[/tex]
Therefore, the curve is smooth for all values except 0, as we can see above.
Hence, the curve is smooth for [tex]t\neq 0[/tex] on the intervals (-∞, 0), (0, ∞).
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give an example of a time in which you had to rely on data to convince a group or team of a recommendation you were making. how did you decide which data points to use?
The data points to use is based on two companies knowledge to accomplice.
Here in this question we have been given an example of our time in a school team in which you have to realize on data to convince a group about the recommendation.
Here we also know that when we were making any recommendation to convince a group we have to keep its positive wherever we response to a question about the time you had to convince someone to do something your way.
Here we have also know that you may be tempted so may be tempted to put a negative spin on situation.
So, in order to accomplish the we have to accomplice and will have knowledge two companies knowledge to accomplice
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A system of linear equations with more equations than unknowns is sometimes called an overdetermined system. Can such a system be consistent? Illustrate your answer with a specific system of three equations in two unknowns. chosse from the below option.a)Yes, overdetermined systems can be consistent. For example, the system of equations below is consistent because it has the solutionAnswer: (Type an ordered pair here _____)x1=2, x2=4, x1+x2=6b) Yes, overdetermined systems can be consistent. For example, the system of equations below is consistent because it has the solutionAnswer: (Type an ordered pair here _____)x1=2, x2=4, x1+x2=8c)No, overdetermined systems cannot be consistent because there are fewer free variables than equations. For example, the system of equations below has no solution.x1=2, x2=4, x1+x2=12d)No, overdetermined systems cannot be consistent because there are no free variables. For example, the system of equations below has no solution.x1=2, x2=4, x1+x2=24
a) Yes, overdetermined systems can be consistent. For example, the system of equations below is consistent because it has the solution (2,4)
x1=2, x2=4, x1+x2=6
An overdetermined system of linear equations can have infinitely many solutions if the equations are dependent, meaning they are linearly dependent and can be derived from one another by a linear combination. If a system of equations is dependent, it means that the equations are not providing new information.
b) No, overdetermined systems cannot be consistent because there are no free variables. For example, the system of equations below has no solution.
x1=2, x2=4, x1+x2=8
An overdetermined system of linear equations that is not dependent means that the equations are providing new information, but the system has no solutions because there are no free variables, which means there is no way to satisfy all the equations.
d) No, overdetermined systems cannot be consistent because there are no free variables. For example, the system of equations below has no solution.
x1=2, x2=4, x1+x2=24
An overdetermined system of linear equations that is not dependent means that the equations are providing new information, but the system has no solutions because there are no free variables, which means there is no way to satisfy all the equations.
c) is not a valid option as it contains a mix of concepts of dependent and independent systems and also the system of equations is inconsistent.
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I need help with this I have 5 minutes to get it done
Step-by-step explanation:
1.
equilateral triangle. all sides and also all angles are equal.
the sum of all angles in a triangle is always 180°.
so,
6x = 180/3 = 60°
x = 10
2.
all 3 angles are equal, so, also all 3 sides are equal.
6x - 5 = 5x
x - 5 = 0
x = 5
3.
again, all 3 angles are equal.
3x = 180/3 = 60
x = 20
4.
the 2 sides are marked as equally long.
4x = 40
x = 10
5.
isoceles triangle with 60° angle in top, that means it is again an equilateral triangle.
3x + 8 = 4x - 4
8 = x - 4
12 = x
6.
again all angles are equal.
4x = 60
x = 15
A farmer has 100 m of fencing to enclose a rectangular pen. Which quadratic equation gives the area (A) of the pen, given its width (w)?A(w) = w2 – 50wA(w) = w2 – 100wA(w) = 50w – w2A(w) = 100w – w2
The area of the rectangular pen is represented by the quadratic equation [tex]A(w) = 50w - w^{2}[/tex].
Let w be the width of rectangular pen.
We have been given that a farmer has 100 m of fencing to enclose a rectangular pen. This means that perimeter of pen is 100 meter.
Since the perimeter is 2 times the length and width of rectangle.
Perimeter of a rectangle = 2 (Width + Length)
Upon substituting our given values in above formula we will get,
[tex]100 = 2(w + length)\\50 = w + length\\50-w = Length[/tex]
Area of a rectangle = Width x Length
[tex]Area of a rectangle = w (50-w)\\= 50w - w^{2}[/tex]
Let us represent area in terms of width of rectangle as:
[tex]A(w) = 50w - w^{2}[/tex]
Therefore, the area of the rectangular pen is represented by the quadratic equation [tex]A(w) = 50w - w^{2}[/tex].
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(Graphing Linear Equations MC)
A middle school club is planning a homecoming dance to raise money for the school. Decorations for the dance cost $120, and the club is charging $10 per student that attends.
Which graph describes the relationship between the amount of money raised and the number of students who attend the dance?
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 120 through the point 2 comma 100
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 120 through the point 2 comma 140
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 120 through the point 2 comma negative 140
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 120 through the point 2 comma negative 100
Answer:
"going from the point 0 comma negative 120 through the point 2 comma negative 100"
Step-by-step explanation:
Let y be the total income from the homecoming dance, and x the number of students who purchase tickets (at $10 each). We are told that it costs $120 for the decorations.
The income from ticket sales would be:
1) the number of tickets sold times $10/ticket, or $10
2) Less the expenses of decorating (-$120)
We can write the total income as:
y = $10x - $120
The graph of this function would be a straight line that has a y-intercept of -$120. Before any ticket is sold, the cost of decorations must be considered. If no tickets are sold (x=0), the total income is -$120.
Using the equation, we can calculate the income when 2 tickets are sold (x=2):
y = $10x - $120
y = $10*(2) - $120 [two tickets sold]
y = -$100
Summary
y = $10x - $120
(0,-$120)
(2,-$100)
This matches the statement "going from the point 0 comma negative 120 through the point 2 comma negative 100" provided in the answer options.
See the attached graph.
2. is line parallel to line ? choose the best justiication. a. line is parallel to line because triangle is a dilation of triangle by a scale factor of 3 from point . b. line is parallel to line because triangle is a dilation of triangle by a scale factor of 2 from point . c. line is parallel to line because triangle is a dilation of triangle by a scale factor of from point . d. line is not parallel to line because there is no dilation that sends triangle to triangle .
Line is not parallel to line because no scaling from point can transform triangle into triangle.
Line is not parallel to line because there is no transformation that can send triangle to triangle. A transformation is a function that changes the location, size, or orientation of an object. A dilation of a shape is a transformation that changes its size, either making it larger or smaller, but does not change its orientation. To determine if two lines are parallel, one must consider if a dilation from a point can send one line to the other. In this case, there is no dilation from point that can send triangle to triangle, so line is not parallel to line.
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answer the screenshot
a) The solution that is in the interval -2≤rs - 1 is x=0.5, which is the approximation of the solution correct to two decimal places.
b) The remaining zeros of f(x) are -8i.
What are zeros?a) Generally, One way to approximate the solution of this equation is to use the method of bisection. The bisection method starts by finding the midpoint of the interval in which the solution is known to exist, and then determining which half of the interval the solution must lie in. This process is repeated until a sufficiently accurate approximation of the solution is found.
Another way to approximate the solution is to use a numerical method like the Newton-Raphson method. The Newton-Raphson method starts with an initial approximation of the solution and then uses the derivative of the function to find a better approximation.
However, for the given polynomial equation, the solution can be directly found by factoring it, which will give the roots of the polynomial equation.
By factoring 8x³+3x²-7x+6=0, we can get (2x-3)(4x+1)(x-2) = 0
so the roots are x = -0.25, 0.5, and 2
b)
The remaining zeros of f(x) are -8i.
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Please help me quick
Answer:
A) I think that the answer is: 1x+3y=4x+1y
But I am not 100% sure so.
B) I don't know sorry
How many edges does this polyhedron have?
The polyhedron with 10 vertices and 7 faces has 15 edges.
What is polyhedron?
A polyhedron is a three-dimensional object or solid that has flat faces, straight edges, and sharp corners or vertices. It is a geometric shape that is bounded by a finite number of polygons, which are shapes with straight sides.
Based on the Euler's formula for polyhedra, which states that the number of vertices plus the number of faces minus the number of edges is always equal to 2, we can solve for the number of edges:
10 (vertices) + 7 (faces) - E (edges) = 2
Simplifying the equation:
10 + 7 - E = 2
17 - E = 2
E = 17 - 2
E = 15
Therefore, the polyhedron with 10 vertices and 7 faces has 13 edges.
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a spider is on the rim of an empty conical cup when it spies a fly one third of the way around the rim. the cone is 36 cm in diameter and 24 cm deep. in a hurry for lunch, the spider chooses the shortest path to the fly. how long is this path?
The length of the shortest path is 44.69cm.
To find the length of the shortest path, we need to calculate the distance between the two points on the rim of the conical cup where the spider and the fly are located. Since the cone is symmetric, we can find the distance by considering a cross-section of the cone through the center of the cup.
In this cross-section, the spider and the fly are located on a circumference of radius 18 cm (half of the diameter of the cone). The distance between the spider and the fly is one-third of this circumference, or (2pi18 cm)/3 = 12*pi cm.
However, since the cone is 24 cm deep, the shortest path between the spider and the fly is not a straight line, but a curved path along the surface of the cone. To find the length of this path, we need to use the Pythagorean theorem to find the distance between the two points on the surface of the cone.
The height of the cone is 24cm, and the distance between the two points on the circumference is 12pi cm. Using the Pythagorean theorem, we can calculate the length of the shortest path as the square root of (12pi)^2 + 24^2 = 12pi cm + 576 = √(144π^2+ 576)cm=44.69 cm.
So, the length of the shortest path is √(144*π^2+ 576)cm = 44.69cm
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How would I solve this?
The price of one slice of pizza is $3.5, and the price of one drink is $3.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let x be the price of one slice of pizza and y be the price of one drink.
The system of equations can be written as:
3x + 2y = 16.50
4x + 4y = 26
To find the price of one slice of pizza and the price of one drink, we can use the substitution or elimination method.
After solving the equation for x and y we get the values as:
x = 3.5 and y = 3
So, the price of one slice of pizza is $3.5, and the price of one drink is $3.
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a card is drawn at random from a standard $52$-card deck. what is the probability that it is an odd number ($3,$ $5,$ $7,$ $9$) or a $\spadesuit$ (or both)?
The probability that the randomly drawn card is an odd number (3, 5, 7, 9) or of spade suit is 25/52.
Now, According to the question:
We are informed that a card is drawn at random from a standard 52-card deck.
We are asked the probability that the randomly drawn card is an odd number (3, 5, 7, 9) or of spade suit.
We assume the event of drawing an odd card from the random pick to be A, and the event of drawing a card of spade suit to be B.
The number of outcomes favorable to event A = 16 {4 odd cards of each of the 4 suits, that is, 4×4 = 16}.
The total number of possible outcomes = 52 {The number of cards in the deck}.
Therefore, the probability of event A, P(A) = 16/52.
The number of outcomes favorable to event B = 13 {The 13 cards of spade suit}.
The total number of possible outcomes = 52 {The number of cards in the deck}.
Therefore, the probability of event B, P(B) = 13/52.
The number of outcomes favorable to events A and B both = 4 {4 odd cards of the spade suit}.
The total number of possible outcomes = 52 {The number of cards in the deck}.
Therefore, the probability of events A and B both, P(A ∩ B) = 4/52.
The probability that the randomly drawn card is an odd number or of spade suit is represented by P(A ∪ B), which is calculated by the formula:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 16/52 + 13/52 - 4/52 = 25/52.
Hence, the probability that the randomly drawn card is an odd number (3, 5, 7, 9) or of spade suit is 25/52.
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the distance between Orlando and jacksonville
The distance between Orlando and Jacksonville is approximately 230 miles.
What is the distance?
Distance refers to the measurement of the separation between two points in space. It can be thought of as the length of the path between two points, and it can be measured in various units such as meters, feet, miles, kilometers, etc.
The distance between Orlando and Jacksonville is approximately 230 miles (370 km) if you take the most direct route by car. The driving distance between Orlando and Jacksonville is around 4 hours and 30 minutes. It could vary depending on the route taken and traffic conditions.
Hence, the distance between Orlando and Jacksonville is approximately 230 miles.
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Solve for x. Round to the nearest tenth, if necessary.
By using a trigonometric relation, we will see that the value of x on the right triangle is x = 53.4
How to find the value of x on the right triangle?
We want to find the value of x on the given right triangle, which is one of the cathetus of the triangle (the adjacent cathetus of the shown angle).
We know one angle of 51°, and the opposite cathetus of that angle, which has a measure of 66 units.
Here we can use the trigonometric relation:
tan(a) = (opposite cathetus)/(adjacent cathetus)
Replacing the known values, we will get:
tan(51°) = 66/x
Solving that for x, we will get:
x = 66/tan(51°) = 53.4
The measure of the adjacent cathetus is 53.4 units.
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What is the condition for a triangle whose two sides are 6cm 8cm then the third side is?
Answer:
10cm
Step-by-step explanation:
Pythagoras
(6×6) + (8×8) = □×□
36 + 64 = 100
square root of 100 = 10
Answer:
Step-by-step explanation:
The condition for a triangle whose two sides are 6cm and 8cm is the triangle should be right angled triangle.
so by this condition,
=> (hypotenuse)^2 = (base)^2 + (perpendicular)^2
=> (hypotenuse)^2 = (6)^2 + (8)^2
=> hypotenuse = 10 cm
so the thisrd side of triangle is 10cm.
lin rides 6 miles on her bike in 48 minutes at a constant speed how many minutes per mile does she ride
The number of minutes per mile that Lin does ride will be 8 minutes per mile.
Lin rides at a speed of 6 miles / 48 minutes = 0.125 miles per minute. For us to convert this to minutes per mile, we have to take the reciprocal of this value, which is 1 / 0.125 = 8 minutes per mile.
To convert speed from miles per minute to minutes per mile, you can take the reciprocal of the value which means is the upside value and top. In this case, 0.125 miles per minute to minutes per mile is 8 minutes per mile.
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I need help for this asappp
Answer:
9.919742348374221
Step-by-step explanation:
(x+5)(x)=x^2+5x. (x^2+5x)/2; x=
9.919742348374221
si A/4 = B/9 y A + B = 169; halle el valor de "A"
El número A = 52 es una solución del sistema de ecuaciones lineales.
¿Cómo resolver un sistema de ecuaciones lineales mediante métodos algebraicos?
En esta pregunta tenemos un sistema de dos ecuaciones lineales con dos incógnitas, de modo que existe la posibilidad de una solución única. Primero, escriba el sistema de ecuaciones descrito en el enunciado de la pregunta:
A / 4 = B / 9
A + B = 169
Segundo, despeje la variable A de la segunda ecuación del sistema de ecuaciones:
B = 169 - A
Tercero, elimine la variable B en la primera ecuación del sistema de ecuaciones y despeje la variable A:
A / 4 = (169 - A) / 9
9 · A = 4 · (169 - A)
9 · A = 676 - 4 · A
13 · A = 676
A = 52
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Identify the true statements about the correlation coefficient, ????. if two variables are negatively correlated, when one variable increases, the other variable also increases. the correlation coefficient is not affected by outliers. a correlation coefficient of zero means that no relationship exists between the two variables. the sign of ???? describes the direction of the association between two variables. when the data points in a scatter plot are randomly scattered, the correlation between the two variables is weak. the value of ???? ranges from negative one to positive one.
a. Since both a strong-positive and weak-positive correlation are formally considered to be "growing," this is ambiguous (positive slope). In the same way, negative correlation. Speaking strictly in terms of truth or untrue, I would classify this as false
b. This is once more a little tricky. When "r" is zero, there isn't any evidence of a linear link. It doesn't necessarily follow that the variables don't correlate with one another. The answer is probably True if this is a course on statistics for beginners. If not, False.
c. This is simple to understand. Inverse relationships are indicated by negative coefficients. One grows while the other shrinks (or vice versa). False.
d. The range of the coefficient r is [0, 1] (inclusive), not (0,1). In this case, True if the text suggests [0,1].
e. Simple and accurate
f. Plain and simple, FALSE. Quite a high correlation coefficient
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two components of a minicomputer have the following joint pdf for their useful lifetimes x and y. what is the probability that the lifetime x of the first component exceeds 3?
Therefore , the solution of the given problem of probability comes out to be 1/ ( 1+ y)x².
What precisely is involved in the probability process?Evaluating the chance that a claim is true or that a particular event will happen is the focus of the mathematical field known as probability theory. A chance can be represented by any number between 0 and 1, with 1 denoting certainty and 0 typically expressing the possibility of occurrence. The possibility or possibility that a happening will occur is represented diagrammatically as probability. Figures 0 and 1, percentage ranging 0% - 100%, and some other characters can be used to represent probabilities. the percentage of times, out of all possible possibilities, that an incidence occurred within a good set with equally likely options.
Here,
Probability for X (for x≥0)
=> [tex]\int\limits^{ \infty}_{ 0}[/tex]x e⁻ˣ⁽¹⁺ⁿ⁾ dy
=> -e⁻ˣ [tex]\int\limits^{ \infty}_{ 0}[/tex]de⁻ˣⁿ
=>e⁻ˣ
Probability for X exceed 3
=> [tex]\int\limits^{ \infty}_{ 3}[/tex]f(x)dx
=> [tex]\int\limits^{ \infty}_{ 3}[/tex]e⁻³dx
=> e⁻³
Probability for y ≥ 0
=> [tex]\int\limits^{ \infty}_{ 3}[/tex]xe⁻ˣ⁽¹⁺ⁿ⁾ dy
=> [tex]\int\limits^{ \infty}_{ 3}[/tex]x/1 + y d e⁻ˣ⁽¹⁺ⁿ⁾ = 1/ ( 1+ y)x²
Therefore , the solution of the given problem of probability comes out to be 1/ ( 1+ y)x².
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