The solution of second order linear equation DE (1- tcot t) y - ty y 0 for 0 < t < T is y2(t) = sin(t). There cannot be exist a constant k such that {x^2, e^x} is a set of solutions to the given differential equation.
To check if y1(t) = t is a solution to the given differential equation, we substitute it into the DE and simplify:
(1 - t cot(t))y - t(dy/dt) = (1 - t cot(t))t - t(1) = t - t^2 cot(t) - t = t(1 - t cot(t))
So y1(t) = t is a solution to the DE.
To check if y2(t) = sin(t) is a solution, we substitute it into the DE and simplify:
(1 - t cot(t))y - t(dy/dt) = (1 - t cot(t))sin(t) - t(cos(t)) = sin(t) - t sin(t) (csc(t)) - t(cos(t)) = sin(t) - t tan(t) sin(t) - t(cos(t))
So y2(t) = sin(t) is also a solution to the DE.
To check if y1(t) and y2(t) are linearly independent, we can check if their Wronskian is nonzero. The Wronskian of two solutions y1(t) and y2(t) of a second-order linear differential equation is given by:
W(y1, y2) = y1(t) (dy2/dt) - y2(t) (dy1/dt)
Substituting y1(t) = t and y2(t) = sin(t), we get:
W(y1, y2) = t cos(t) - sin(t)
Since W(y1, y2) is not identically zero (it is zero only at certain values of t), we can conclude that y1(t) and y2(t) are linearly independent.
The general solution to the given differential equation is given by:
y(t) = c1 t + c2 sin(t)
where c1 and c2 are constants determined by the initial or boundary conditions.
Let W(x) be the Wronskian of the solutions y1(x) and y2(x) of the differential equation given by:
(1 - x^2) y'' - 2x y' + k y = 0
Then, we have:
W(x) = y1(x) y2'(x) - y1'(x) y2(x)
Substituting y1(x) = x^2 and y2(x) = e^x, we get:
W(x) = x^2 e^x - 2x e^x - x^2 e^x = -2x e^x
Since we are given that W(0) = 1, we have:
W(0) = -2(0) e^0 = 1
This gives us a contradiction, so there cannot exist a constant k such that {x^2, e^x} is a set of solutions to the given differential equation.
To know more about linear equation:
https://brainly.com/question/14627736
#SPJ4
Find the area of the figure. (Sides meet at right angles.)
4 m
3 m
2 m
4 m
3 m
2 m
4 m
The area of the figure can be found to be 53 cm ²
How to find the area of the figure ?The figure given is a composite shape so to find the area of the figure, you need to divide the shape into two other shapes.
The area of the first shape is :
= Length x Width
= 5 x 4
= 20 m ²
The area of the second shape would be :
= Length x Width
= ( 3 + 5 + 3 ) x 3
= 11 x 3
= 33 cm ²
The area of the shape is :
= 20 + 33
= 53 cm ²
Find out more on area at https://brainly.com/question/11423300
#SPJ1
Differentiate Y = 1/x
Jim ordered a sports drink and three slices of pizza for $8.50. His friend ordered two sports drinks and two slices of pizza for $8.00
can you find out how much the pizza and sports drinks cost separately? please and thanks!
The Price for one slice pizza is $1.25 and for one drink is $2.25.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Jim ordered a sports drink and three slices of pizza for $8.50.
His friend ordered two sports drinks and two slices of pizza for $8.00.
let the price for pizza be $ and for one drink is $y.
So, the system of equation is
x + 3y = 8.5....(1)
2x+ 2y= 8......(2)
Solving above two equations we get
2(8.5- 3y) + 2y= 8
17 - 6y + 2y= 8
-4y = -9
y= 9/4
y= 2.25
and, x= 8.5- 3(2.25)= 8.5- 6.75 = $1.25
Learn more about Equation here:
https://brainly.com/question/29657992
#SPJ1
what is k in this equation 2/3k = 8/15?
Answer:5/4
Step-by-step explanation:
2/3k=8/15
then,
2*15=8*3k
30=24k
k=30/24=15/12=5/4
A data set comparing a woman's shoe size to her height is represented by the table.
Shoe Size Height (inches)
7.5 63
8 70.5
12 68
7 71
9 69.5
10 70
12 75
12.5 63
14 72
Using technology, calculate the line of best fit. Identify and interpret the slope in this scenario.
The slope of the line of best fit is 0.25. Each time the shoe size increases by one, the height increases by 0.25 inches.
The slope of the line of best fit is 0.25. Each time the shoe size increases by 0.25, the height increases by one inch.
The slope of the line of best fit is 66.6. Each time the shoe size increases by one, the height increases by 66.6 inches.
The slope of the line of best fit is 66.6. Each time the shoe size increases by 66.6, the height increases by one inch.
The line of best fit is given as follows:
y = 0.25x + 72.25.
The correct option regarding the slope is given as follows:
The slope of the line of best fit is 0.25. Each time the shoe size increases by one, the height increases by 0.25 inches.
How to find the equation of linear regression?To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.
The points for this problem are given as follows:
(7.5, 63), (8, 80.5), (12, 68), (7, 71), (9, 69.5), (10, 70), (12, 75), (12.5, 63), (14,72)
Inserting these points into a calculator, the equation is given as follows:
y = 0.25x + 72.25.
The slope of 0.25 represents the rate of change of the output variable(height) relative to the input variable(shoe size).
More can be learned about linear regression at https://brainly.com/question/29613968
#SPJ1
For each ornament that a worker makes, he is paid $1.15. He makes 4 ornaments every 15 minutes. Find the amount earned by the worker if he works for 3 hours.
please reply asap!
20 points :)
Answer: Here you go.
Step-by-step explanation:
The worker makes 4 ornaments every 15 minutes, which is equivalent to 16 ornaments per hour (since 60 minutes / 15 minutes = 4, and 4 x 4 = 16).
Therefore, the worker can make 48 ornaments in 3 hours (since 3 hours x 16 ornaments per hour = 48 ornaments).
If he is paid $1.15 for each ornament he makes, then he earns $55.20 for making 48 ornaments (since 48 ornaments x $1.15 per ornament = $55.20).
Therefore, if the worker works for 3 hours making ornaments, he would earn $55.20.
Do certain car colors attract the attention of the police more than others, so that they are more likely to get speeding tickets? A few years ago a curious newspaper columnist tabulated the car color on a random sample of 120 speeding citations at the local courthouse. Here are his results:
Color Red White/Silver Gray/Black Other
Number of Speeding Tickets 16 33 39 32
He then went to the state motor vehicle registry and obtained data on the distribution of car colors for all cars registered in his state: Red 14%, White/Silver 35%, Gray/Black 23%, Other 28%.
To answer the question poised above about car color and speeding tickets, the appropriate null hypothesis is:
Group of Answer Choices:
-The observed number of speeding tickets is the same for all four color groups
-The observed counts are equal to the expected counts.
-At least one of the four car color percentages is different from the other three.
-The distribution of car colors for the speeding citations is the same as the distribution of colors for cars on the highway.
-The observed counts are all equal to 30
The appropriate null hypothesis for a random sample of car's color and speeding tickets is equals to the observed counts are equal to the expected counts.
The curious newspaper columnist tabulate the car color on a random sample. The above table showed car color and their corresponding speeding tickets. Sample size, n = 120
Registed red colour cars in his state
= 14%
Registed white/silver colour cars in his state= 35%
Registed gray/black colour cars in his state = 23%
Registed others colour cars in his state
= 28%
We habe to determine the right choice for null hypothesis from the options. For this, here we have to use chi square test of goodness of fit to test this hypothesis. We know that in chi square test, they arevalready given the observed frequencies. Then we have to find out the expected frequencies using the given percentages. So here we have to findout whether the expected frequency and observed frequency are equal or not. So the null hypothesis is The observed counts are equal to the expected counts.
To learn more about Null hypothesis, refer:
https://brainly.com/question/13135308
#SPJ4
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!
The measure of angle x is given as follows:
a. x = 30º.
How to obtain the angle measure?Angle y is complementary with the angle of 60º, meaning that the sum of their measures is of 90º, hence it's measure is given as follows:
y + 60 = 90
y = 30º.
Angle y and angle x form vertical angles, meaning that they are congruent, that is, they have the same measure, hence the measure of angle x is given as follows:
x = y = 30º.
Hence the correct option is given by option a.
More can be learned about angle measures at https://brainly.com/question/24607467
#SPJ1
A banner is made of a square and a semicircle. The square has side lengths of 24 inches. One side of the square is also the diameter of the semicircle. What is the total area of the banner? Use 3.14 for π.
The total area of the banner is approximately 800.54 square inches.
What is Quadrilateral?A quadrilateral is a four-sided polygon, having four edges and four corners
The area of the square is side length squared, or 24² = 576 square inches.
The diameter of the semicircle is also the side length of the square, so it is 24 inches.
Radius = 24/2=12 inches
The area of a semicircle is half of the area of a circle with the same radius. The area of a circle is π times the radius squared, so the area of the semicircle is:
1/2×π×12²=72π
Add Area of the square and the area of the semicircle:
576 + 72π = 800.54
Therefore, the total area of the banner is approximately 800.54 square inches.
To learn more on Quadrilateral click:
https://brainly.com/question/29934440
#SPJ1
Find (f+g)(x).
f(x) = -3x+2
g(x)=x²³
The value of the composition function ( f + g ) ( x ) = x²³ - 3x + 2
What is Composition of functions?Evaluation of a function at the value of another function is known as Composition of function. A function composition is a process in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.
Given data ,
Let the first function be represented as f ( x )
Now , the value of f ( x ) = -3x + 2
Let the second function be represented as g ( x )
Now , the value of g ( x ) = x²³
On simplifying , we get
The value of ( f + g ) ( x ) = f ( x ) + g ( x )
Substituting the values of f ( x ) and g ( x ) , we get
( f + g ) ( x ) = x²³ - 3x + 2
Hence , the composition function is ( f + g ) ( x ) = x²³ - 3x + 2
To learn more about composition of functions click :
https://brainly.com/question/17673639
#SPJ9
mr. preston sponsors the creative writing club. he decided to make booklets of his students' poems and stories to hand out at the school's activity fair. he went to a local printing shop that charges $0.25 per page in the booklet and $1.00 to bind the pages together. the booklet mr. preston is making has p pages, and he plans to make 50 booklets. pick all the expressions that represent how much mr. preston will spend making the booklets. 12.50p 50.00 50(1.25p) 50(0.25p 1.00) 12.50p 50.00p submit
We can use algebraic equations to solve this kind of problems. The correct answer is 50.00( 0.25p+ 1.00). So option number 3 is correct.
The cost of printing a single page = 0.25
The cost of printing p pages = 0.25p
Cost of print 50 booklets with p pages = 50× 0.25p = 12.50p
Cost of binding 1 booklet = $1
Cost of binding 50 booklet = 50
Cost of 50 booklets = Cost of printing 50 booklets with p pages + cost for binding 50 booklets
= 12.5p + 50.00 = 50.00(0.25p+1.00)
So the correct answer is the third option , 50.00 ( 0.25p + 1.00)
For more information regarding algebraic equations, kindly refer
https://brainly.com/question/20380548
#SPJ4
The function h is defined by the following rule.
h(x)=2x-2
Complete the function table.
X
-5
-1
1
2
h (x)
0
10
Answer: See attached.
Step-by-step explanation:
We will input the given x-values and solve for y by substituting x for the values in the original function, h(x)=2x-2.
h(-5) = 2(-5)-2 = -12
h(-1) = 2(-1)-2 = -4
h(1) = 2(1)-2 = 0
h(2) = 2(2)-2 = 2
The coordinates of the vertices of triangle XYZ are X(-2, -1), Y(6, 8), and Z(8, 4). Triangle XYZ is dilated by a scale factor of 32
with the origin as the center of dilation to create triangle X’Y’Z’.
If (x, y) represents the location of any point on triangle XYZ, which ordered pair represents the location of the corresponding point on triangle X’Y’Z’?
Responses
(x+32, y+32)
(x+32, y+32)
(23x, 23y)
(23x, 23y)
(32x, 32y)
(32x, 32y)
(x+23, y+23)
Answer: A, i think
Step-by-step explanation: edge 2020
An empty fuel tank is filled using a cylindrical pipe with diameter 8 cm. Fuel flows along this pipe at a rate of 2 metres per second. It takes 24 minutes to fill the tank. Calculate the capacity of the tank. Give your answer in litres.
The capacity of the tank is 7234.56litres
What is capacity of a tank?Capacity refers to the amount of fluid a container can hold. It expressed in units like litres (l), millilitres (ml). Capacity is also known as volume of a substance.
The capacity of the cylindrical pipe is
V = πr²h
r = 8cm
if it takes the pipe 2m per second
then it's volume in one second is
V = 3.14 ×8 × 2× 100
V = 5024cm³/s
if it takes 24 minutes
24 minutes = 24 × 60 s
= 1440s
therefore volume of the tank = 1440 × 5024
= 7234560cm³
in litres = 7234560/1000
= 7234.56litres
learn more about capacity of a tank from
https://brainly.com/question/13691899
#SPJ1
Square ABDC is shown with diagonal CB. What's true about AABC and ADCB?
ΔABC and ΔDCB would be congruent triangles by the AAS postulate.
What is congruent geometry?In congruent geometry, the shapes that are so identical. can be superimposed on themselves.
Here,
In a square, all sides are equal in length and all angles are right angles (90 degrees). Additionally, the diagonal of a square bisect each other at 90 degrees.
The lengths of AB, BC, CD, and DA are equal.
The angles ABC and CDA are both right angles (90 degrees).
The angles BAC and DCB are both 45 degrees.
So ΔABC and ΔDCB became congruent triangles by the AAS postulate.
Learn more about congruent geometry here:
https://brainly.com/question/12413243
#SPJ9
Gwen is pouring 48 drinks for a party. Each drink she pours is 8.64 fluid ounces.
The equation above represents this situation where is the total amount of fluid ounces she poured. How many total fluid ounces did she pour?
Answer: If each drink is 8.64 fluid ounces and Gwen is pouring 48 drinks, then the total amount of fluid ounces she poured is 8.64 fluid ounces * 48 drinks = 413.12 fluid ounces.
Step-by-step explanation:
Determine the lateral area and the surface area of each triangular prism by determining the area of the shape’s net.
The lateral area and the surface area of the right prism are 540 square yards and 1152 square yards, respectively.
How to determine the lateral area and the surface area of a triangular prism
Herein we find the case of a right prism with a triangular base, whose lateral area (A) and surface area (A'), both in square yards, must be determined.
The lateral area is the sum of the areas of three rectangular faces and the surface area is the sum of the lateral area and the area of the two triangles. Area formulas for rectangles and triangles are shown below:
Rectangle
A = w · l
Triangle
A = 0.5 · w · l
Where:
w - Width, in yardsl - Length, in yardsNow we determine the lateral area and the surface area of the prism:
Lateral area
A = (37 yd) · (5 yd) + (20 yd) · (5 yd) + (51 yd) · (5 yd)
A = 540 yd²
Surface area
A' = 540 yd² + 2 · 0.5 · (51 yd) · (12 yd)
A' = 1152 yd²
To learn more on surface areas of prisms: https://brainly.com/question/17351910
#SPJ1
For the matrix below. Find a basis for R3 that includes vectors in the set by removing vectors from a linearly dependent set and/or adding vectors to a set that does not span R3.
A basis for R3 that includes vectors in the set is {[1 0 -2], [3 2 -4], [0 0 1]}. This is achieved by removing the linearly dependent vector [1 0 -2] and adding the vector [0 0 1] to the set to obtain a set that spans R3.
A basis for R3 that includes vectors in the set can be found by removing vectors from a linearly dependent set and/or adding vectors to a set that does not span R3.
The set given is {[1 0 -2], [3 2 -4]}.
To check if the set spans R3, we need to calculate the determinant of the matrix created by the two vectors. The determinant of the matrix is 0, which tells us that the set does not span R3. To create a basis for R3, we need to add a third vector that is not linearly dependent on the other two. We can add the vector [0 1 1] to the set, creating the following set:
{[1 0 -2], [3 2 -4], [0 1 1]}
To check if this set spans R3, we calculate the determinant of the matrix created by the three vectors. The determinant of the matrix is -6, which is not 0.
Therefore, the set {[1 0 -2], [3 2 -4], [0 1 1]} is a basis for R3.
The complete question: For the matrix below. Find a basis for R3 that includes vectors in the set by removing vectors from a linearly dependent set and/or adding vectors to a set that does not span R3.
( matrix attached below )
Learn more about set here
https://brainly.com/question/30096139
#SPJ4
Straight angle
Obtuse angle
Match each angle description on the left with its possible angle measure, m, on the right.
Acute angle
90 m 180°
Right angle
Submit
Clear
questions
ncludi
Pass
m = 90°
m = 180°
0°
Answer:
makes no sense
Step-by-step explanation:
If
IK
and
LN
are parallel lines and mNMJ = 116°, what is mIJM?
Answer: Since IK and LN are parallel lines, then mIJM and mNMJ are supplementary, meaning that they add up to 180 degrees. Therefore, mIJM = 180° - mNMJ = 180° - 116° = 64°.
Step-by-step explanation:
If you paid $1,650.00 in property taxes on a house appraised at $112,000.00, what is the property tax rate in your neighborhood?
Express your answer rounded to the nearest hundredth of a percent
To calculate the property tax rate, you need to divide the property taxes by the appraised value of the property and then multiply by 100 to express the result as a percentage.
In this case, the property tax rate can be calculated as follows:
Property tax rate = (Property taxes / Appraised value) * 100%
= ($1,650.00 / $112,000.00) * 100%
= 0.014732142857142857 * 100%
= 1.47%
So, the property tax rate in your neighborhood is 1.47%, rounded to the nearest hundredth of a percent.
Given that cot(θ)<0 and cos(θ)<0, in which quadrant does θ lie?
if cot(θ)<0 and cos(θ)<0, then we can conclude that θ lies in the second quadrant.
What is trigonometry functions ?
Trigonometry functions are a set of mathematical functions that relate the angles of a triangle to the lengths of its sides. The three main trigonometric functions are sine, cosine, and tangent, which are commonly abbreviated as sin, cos, and tan. These functions can be defined as ratios of the sides of a right triangle.
In a right triangle, the side opposite an acute angle is called the "opposite" side, the side adjacent to the angle is called the "adjacent" side, and the hypotenuse is the side opposite the right angle. With this terminology, we can define the following trigonometric functions:
Sine (sin): The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. In other words, sin(θ) = opposite/hypotenuse.
Cosine (cos): The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. In other words, cos(θ) = adjacent/hypotenuse.
Tangent (tan): The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side. In other words, tan(θ) = opposite/adjacent.
There are also three reciprocal trigonometric functions: cosecant (csc), secant (sec), and cotangent (cot). These functions are the reciprocals of sine, cosine, and tangent, respectively.
Trigonometric functions have many practical applications in fields such as engineering, physics, and astronomy, where they are used to solve problems involving angles and distances. They also have many applications in pure mathematics, such as in the study of periodic functions and Fourier analysis.
According to given information :
To understand why θ must be in the second quadrant, we need to recall the signs of the trigonometric functions in each quadrant.
In the first quadrant, all trigonometric functions are positive.
In the second quadrant, sine is positive and cosine is negative.
In the third quadrant, both sine and cosine are negative.
In the fourth quadrant, sine is negative and cosine is positive.
Since we know that cos(θ) is negative, we can conclude that θ lies in either the second or third quadrant. However, since cot(θ) = cos(θ)/sin(θ) and cot(θ) is negative, we know that cos(θ) and sin(θ) must have opposite signs. In the third quadrant, both cos(θ) and sin(θ) are negative, so their quotient cot(θ) would be positive, which is not the case.
Therefore, we can conclude that θ lies in the second quadrant.
To know more about trigonometry functions visit:
https://brainly.com/question/25618616
#SPJ1
Answer:
If cot(θ)<0 and cos(θ)<0, then we can conclude that θ lies in the second quadrant.
What are trigonometry functions ?
Trigonometry functions are a set of mathematical functions that relate the angles of a triangle to the lengths of its sides. The three main trigonometric functions are sine, cosine, and tangent, which are commonly abbreviated as sin, cos, and tan. These functions can be defined as ratios of the sides of a right triangle.
In a right triangle, the side opposite an acute angle is called the "opposite" side, the side adjacent to the angle is called the "adjacent" side, and the hypotenuse is the side opposite the right angle. With this terminology, we can define the following trigonometric functions:
Sine (sin): The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. In other words, sin(θ) = opposite/hypotenuse.
Cosine (cos): The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. In other words, cos(θ) = adjacent/hypotenuse.
Tangent (tan): The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side. In other words, tan(θ) = opposite/adjacent.
There are also three reciprocal trigonometric functions: cosecant (csc), secant (sec), and cotangent (cot). These functions are the reciprocals of sine, cosine, and tangent, respectively.
Trigonometric functions have many practical applications in fields such as engineering, physics, and astronomy, where they are used to solve problems involving angles and distances. They also have many applications in pure mathematics, such as in the study of periodic functions and Fourier analysis.
According to given information :
To understand why θ must be in the second quadrant, we need to recall the signs of the trigonometric functions in each quadrant.
In the first quadrant, all trigonometric functions are positive.
In the second quadrant, sine is positive and cosine is negative.
In the third quadrant, both sine and cosine are negative.
In the fourth quadrant, sine is negative and cosine is positive.
Since we know that cos(θ) is negative, we can conclude that θ lies in either the second or third quadrant. However, since cot(θ) = cos(θ)/sin(θ) and cot(θ) is negative, we know that cos(θ) and sin(θ) must have opposite signs. In the third quadrant, both cos(θ) and sin(θ) are negative, so their quotient cot(θ) would be positive, which is not the case.
Therefore, we can conclude that θ lies in the second quadrant.
To know more about trigonometry functions visit:
brainly.com/question/25618616
#SPJ1
HELP: Three vertices of a parallelogram are shown in the figure below.
Give the coordinates of the fourth vertex.
Answer:
We have to find co-ordinates of the fourth vertex.
Let fourth vertex be D(x,y)
Since, ABCD is a parallelogram, the diagonals bisect each other.
Si, co-ordinate of mid-point of AC= Co-ordinate of mid-point of BD.
∴ The fourth vertex is D(−b,b)
Step-by-step explanation:
the number of pumps in use at both a six-pump station and a four-pump station will be determined. give the possible values for each of the following random variables. (enter your answers in set notation.) (a) t
For each variable, the possible values are:
a) T = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
b) X = {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6}
c) U = {0, 1, 2, 3, 4, 5, 6}
d) Z = {0, 1, 2}
Item a:
In total, there are 10 pumps, hence the possible values are all integers from 0 to 10, that is:
T = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Item b:
In the first, there are 6 pumps, and in the second 4, hence, the difference ranges from -4 to 6, that is:
X = {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6}
Item c:
The maximum number in a station is 6 pumps, hence this variable ranges from 0 to 6.
U = {0, 1, 2, 3, 4, 5, 6}
Item d:
Either none of the stations has exactly two pumps in use, or one has or both, hence the variable ranges from 0 to 2.
Z = {0, 1, 2}
The question is incomplete. The complete question is:
"The number of pumps in use at both a six-pump station and a four-pump station will be determined. Give the possible values for each of the following random variables. (Enter your answers in set notation.)
a. T = the total number of pumps in use
b. X = the difference between the numbers in use at stations 1 and 2.
c. U = the maximum number of pumps in use at either station
d. Z = the number of stations having exactly two pumps in use"
To learn more about possible values here:
brainly.com/question/14172271
#SPJ4
he following data represent the flight time (in minutes) of a random sample of six flights from Las Vegas, Nevada, to Newark, New Jersey, on United Airlines. 282, 270, 260, 266, 260, 267 Compute the range and sample standard deviation of flight time. The range of flight time is minutes.
The range of flight time is 22 minutes, and the sample standard deviation is 8.24 minutes.
To compute the range, we simply subtract the smallest value from the largest value: Range = 282 - 260 = 22.
To compute the sample standard deviation, we first calculate the mean flight time by summing the values and dividing by the sample size:
Mean = (282 + 270 + 260 + 266 + 260 + 267) / 6 = 266.17
Then we subtract the mean from each flight time, square the differences, sum the squared differences, divide by the sample size minus one, and take the square root of the result:
Standard Deviation = √((1/5) * [(282-266.17)² + (270-266.17)² +
(260-266.17)² + (266-266.17)² + (260-266.17)² + (267-266.17)²]) = 8.24.
Learn more about Random Sample:
https://brainly.com/question/24466382
#SPJ4
Complete Question:
The following data represent the flight time (in minutes) of a random sample of six flights from Las Vegas, Nevada, to Newark, New Jersey, on United Airlines. 282, 270, 260, 266, 260, 267 Compute the range and sample standard deviation of flight time. The range of flight time is minutes.
Represent the quadratic polynomial 2x2 + x – 6 using algebra tiles and determine the equivalent factored form.
The number of zero pairs needed to model this polynomial is
The zeroes of the polynomials will be x = (-1 ± 7) / 4.
What is a polynomial?A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
To represent the quadratic polynomial 2x²+ x - 6 using algebra tiles, we can use the following tiles:
Two squares with side length x, representing 2x²
One rectangle with length x and width 1, representing x
Six small squares, representing -6
We can arrange these tiles to form a rectangle as shown below:
A rectangle made of algebra tiles with 2x² squares, x rectangle, and -6 small squares]
The area of this rectangle is the same as the value of the polynomial, which is 2x²+ x - 6.
To determine the equivalent factored form of this polynomial, we need to find two binomials that, when multiplied together, give us the original polynomial. We can start by using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a = 2, b = 1, and c = -6, since our polynomial is 2x^2 + x - 6.
Plugging in these values, we get:
x = (-1 ± √(1² - 4(2)(-6))) / 2(2)
x = (-1 ± √(49)) / 4
x = (-1 ± 7) / 4
So, the two roots of the quadratic polynomial are x = 3/2 and x = -2.
Therefore, we can write the factored form of the quadratic polynomial as:
2x² + x - 6 = 2(x - 3/2)(x + 2)
To determine the number of zero pairs needed to model this polynomial, we can count the number of negative tiles (small squares) left after forming the rectangle. In this case, we have six negative tiles, which means we need six zero pairs to model this polynomial.
To know more about polynomials follow
brainly.com/question/2833285
#SPJ1
Answer:
Step-by-step explanation:
Someone help me with these math problems.
Answer:
<1=26
<2=154
<3=26
<4=26
<5=154
<6=154
<7=26
(Percent) Magnus is selling his clothes online. He is seling his leather jacket for $80 with an additional 5% for shipping and handling. How much would it cost someone to oder the leather jacket from magnus?
Answer:
$84.00
Step-by-step explanation:
$80.00 x .05 = $4.00
$80.00 + $4.00 = $84.00
Answer:
the cost is $84.00
Step-by-step explanation:
you take 80.00 x 5% tax that gives you $4.00 so the total is $84.00
Write the equation for the parabola/quadratic function containing the points
(-1, 1), (1, -5), and (2, 1).
Answer:
The equation for the parabola (quadratic function) that passes through the points (-1, 1), (1, -5), and (2, 1) is y = (6/49)(x - 2/3)^2 - 1.
Step-by-step explanation:
To write the equation of a quadratic function (parabola) given three points, we can use the vertex form of the equation:
y = a(x - h)^2 + k
where (h, k) is the vertex of the parabola and a is a scaling factor that determines the shape of the parabola.
To find the vertex of the parabola, we can use the formula:
h = (x1 + x2 + x3) / 3
k = (y1 + y2 + y3) / 3
where (x1, y1), (x2, y2), and (x3, y3) are the given points.
Substituting the given points into these formulas, we get:
h = (-1 + 1 + 2) / 3 = 2/3
k = (1 - 5 + 1) / 3 = -1
So the vertex of the parabola is (2/3, -1).
Now, we can substitute this vertex and one of the given points (e.g. (-1, 1)) into the vertex form equation and solve for a:
1 = a(-1 - 2/3)^2 - 1
2 = a(7/3)^2
a = 6/49
So the equation of the parabola is:
y = (6/49)(x - 2/3)^2 - 1
Answer: y = -2x^2 + 6x - 4
Step-by-step explanation:
The equation for this parabola/quadratic function is y = -2x^2 + 6x - 4. To arrive at this equation, we use the fact that the equation for a parabola/quadratic function is y = ax^2 + bx + c, where a, b, and c are constants. We can then substitute in the coordinates of each point to solve for a, b, and c.
For the point (-1,1), we have 1 = -2(-1)^2 + 6(-1) + c, so c = 5.
For the point (1,-5), we have -5 = -2(1)^2 + 6(1) + 5, so -2 = -2.
For the point (2,1), we have 1 = -2(2)^2 + 6(2) + 5, so -4 = -4.
And therefore, the equation is y = -2x^2 + 6x - 4.
jesse uses 3 cups of flour for every 4 tablespoons of butter. How much floud would he need for 9 tablespoons of butter?
Step-by-step explanation:
27cups of flour got to multiple