Answers
An equation for the function graphed above is f(x) = 3(x - 1)/[(x + 1)(x - 3)].
What is a vertical asymptote?In Mathematics, the vertical asymptote of a function simply refers to the value of x which makes its denominator equal to zero (0).
By critically observing the graph of this function, we can logically deduce that the vertical asymptotes include the following;
x = -1
x = 3
This ultimately implies that, the equation of the denominator is given by the following quadratic function:
Q(x) = (x + 1)(x - 3)
Assuming the leading coefficient of P(x) is represented by a;
P(x) = a(x - 1)
Evaluating and solving for a in this function, we have;
f(x) = P(x)/Q(x)
f(x) = a(x - 1)/[(x + 1)(x - 3)]
f(0) = a(0 - 1)/[(0 + 1)(0 - 3)]
Since the y-intercept of this graph is at (0, 1), the value of a is given by;
1 = -a/[(1)(-3)]
1 = -a/-3
a = 3 × 1
a = 3
Substituting the value of a into the function, we have the following;
f(x) = 3(x - 1)/[(x + 1)(x - 3)]
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Related Questions
In AUVW, w = 690 inches, ZW=79° and nearest 10th of an inch.
Answers
The length v of the triangle is 240.4 inches
How to determine the length v?From the question, we have the following parameters that can be used in our computation:
w = 690 inches
∠W = 79°
∠V = 20°
The length v can be calculated using the following sine rule
v/sin(V) = w/sin(W)
Substitute the known values in the above equation, so, we have the following representation
v/sin(20°) = 690/sin(79°)
Multiply both sides of the equation by sin(20°)
So, we have the following representation
v = sin(20°) * 690/sin(79°)
Evaluate the products
v = 240.41
Hence, the length of side v is 240.4 inches
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Complete question
In ΔUVW, w = 690 inches, ∠W=79° and ∠W=20°
Calculate the length v to the nearest 10th of an inch.
Which equations can be used to find the lengths of the legs of the triangle? Select three options. 0.5(x)(x + 2) = 24 x(x + 2) = 24 x2 + 2x – 24 = 0 x2 + 2x – 48 = 0 x2 + (x + 2)2 = 100
Answers
By solving a linear equation, it can be calculated that-
First fourth and fifth option are correct
What is a linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Length of two sides of a right angled triangle = x, x+2
Area = [tex]\frac{1}{2}\times x \times (x + 2)[/tex]
By the problem,
The linear equation is
[tex]\frac{1}{2}\times x \times (x + 2) = 24\\[/tex]
0.5x(x + 2) = 24
First option is correct
x(x + 2) = 48
[tex]x^2 + 2x - 48 = 0[/tex]
Fourth option is correct
For the sixth option,
[tex]x^2 + (x + 2)^2 = 100\\x^2 + x^2 + 4x + 4 - 100 = 0\\2x^2 + 4x - 96 = 0\\2(x^2 + 2x - 48) = 0\\x^2 + 2x - 48 = 0[/tex]
Which is the third option.
First fourth and fifth option are correct
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A machine at a bakery poured out flour for 16 minutes. At the end of that time, the machine was empty. The graph shows the amount of flour (in grams)
remaining in the machine versus time (in minutes).
Find the domain and the range of the function shown.
Amount
of flour 500
(grams)
300-
Time (minutes)
Write your answers as inequalities, using x or y as appropriate.
Or, you may instead click on "Empty set" or "All reals" as the answer.
España
8
Answers
Answer:
Step-by-step explanation:
domain 800 and range 16
2. Find the value of x. 3x-9
Answers
please help me with this math real quick, please!!
Answers
4 is added to the parent function so that the output is translated up 4 units.
The measures of the angles of a triangle are shown in the figure below. Solve
for X.
Answers
Answer:
x = 5
Step-by-step explanation:
[tex](5x+6)+106+43=180[/tex]
[tex]5x=180-106-43-6=25[/tex]
[tex]x=25/5=5[/tex]
Hope this helps
prisms, pyramids and spheres have 3 dimensions - length, width, and depth. three dimensional objects have vertices, edges, and faces unless they are the solids like cylinders, cones, and spheres.
Answers
A solid figure is a three-dimensional object. That is, it has length, width, and height. Because they are three-dimensional, they have depth and occupy space in our universe. Body types are identified according to characteristics specific to each body type. In particular, we can observe the number of faces, edges, vertices, and the shape of the base.
A flat face of a solid is its face or side, as it is commonly called. The base is the surface on which the figure rests. A solid edge is a line segment where two faces meet. A vertex is an angle formed where the endpoints of two or more face segments meet.
A sphere is a solid figure that has no faces, edges, or vertices. This is because it is perfectly round. No flat sides or corners.
A cone has faces but no edges or vertices. His face is circular. A circle is a plane because it is a flat planar shape. However, since it is rounded on the outside, it does not form edges or corners.
Cylinder that has two circular faces but no edges or corners:
A pyramid has a base and at least three triangular faces. There are edges where faces meet each other or meet the bottom, vertices where two faces meet the bottom, and top vertices where all the triangle faces meet. Pyramids are named for the shape of their base.
A triangular pyramid has a triangular base and his other three triangular faces, or four triangles in total.
A pyramid has a rectangular base and a pyramid has a square base. Both have four triangular faces, for a total of five faces.
Prism:
A prism is a solid with two congruent parallel faces and any number of sides. That is, it can have any number of faces, but at least two faces must be parallel. The shape of the two parallel faces can be triangles, squares, rectangles, pentagons, hexagons, or other types of polygons. Prisms are named after the shape of the base.
Sphere:
A sphere is a geometric object that is the three-dimensional analogue of the two-dimensional circle. A sphere is a set of points that are all the same distance r from a given point in 3D space. This given point is the center of the sphere and r is the radius of the sphere. Spheres are fundamental objects in many areas of mathematics. Spherical and near-spherical shapes also occur in nature and industry. Bubbles, like soap bubbles, are spherical in equilibrium. The Earth is often approximated as a sphere in geography, and the celestial sphere is an important concept in astronomy.
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Jessica runs 3 miles in 16 minutes how many minutes does she take per mile
Answers
Answer:0.1875
Step-by-step explanation: you would take the miles and divide it my the minutes which would be 3 divided by 16 which equals 0.1875
answer the question below, find the rate of change and The means that for every ___pound(s) the turkey will take 1 hour to thaw.
Answers
How many hours per pound does it take to thaw a turkey?
Allow 30 minutes of thawing time for each pound of turkey, which translates to two to six hours for a 4- to 12-pound turkey. A 12- to 15-pound bird will thaw in six to eight hours. Still having trouble determining the thaw time of the turkey?
Hope this helps :D
Question 1-5
The expression (4c-3d)(3c+d) is equivalent to:
O 12c² 13cd 3d²
O 12c²
O 12c²
O 12c²
O 12c²
13cd3d²
5cd 3d²
5cd +3d²
3d²
Answers
The expression (4c − 3d)(3c + d) is equivalent to 12c² - 5cd - 3d²
What is Expression?An expression is combination of variables, numbers and operators.
(4c − 3d)(3c + d) is the given expression.
Four times c minus three times d into three times f c plus d.
In the given expression c and d are variables.
Plus and minus are operators.
We need to find the equivalent expression of (4c − 3d)(3c + d).
(4c − 3d)(3c + d)
4c(3c+d)-3d(3c + d)
Apply the distributive property.
12c² + 4cd - 9cd - 3d²
Add the like terms
12c² - 5cd - 3d²
Hence, 12c² - 5cd - 3d² is the equivalent expression of (4c-3d)(3c+d).
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In triangle ABC, AC = 13 cm, angle A = 4y - 71°, angle B = y + 7°, and angle C = 106 - 2y°. In triangle RST,
RT = 2x + 5 cm and angle R = 113°. Angle B is congruent to Angle S
and segment AB is congruent to segment RS.
Answers
Answer:
The length of side BC in triangle ABC is 5.525 cm, and the length of side ST in triangle RST is 0.3802x + 0.9505 cm.
Step-by-step explanation:
Since angle A and angle R are both congruent to angle B, we know that angle A = angle R = y + 7°. We can use this information, along with the angles and sides of the triangles, to find the value of y and the lengths of the sides of the triangles.
From the given information, we know that the angles of triangle ABC add up to 180°, so we can use that to find the value of y:
4y - 71° + y + 7° + 106 - 2y° = 180°
6y - 64° = 180°
6y = 244°
y = 40.67°
We can use the value of y to find the measure of angle C:
C = 106 - 2y° = 106 - 2(40.67°) = 106 - 81.34° = 24.66°
Now that we know the measure of angle C, we can use the Law of Sines to find the length of side BC:
BC / sin C = AC / sin A
BC = (AC * sin C) / sin A
BC = (13 cm * sin 24.66°) / sin (4y - 71°)
BC = (13 cm * 0.4237) / sin (4(40.67°) - 71°)
BC = 5.525 cm
We can use the same method to find the length of side ST in triangle RST:
ST = (RT * sin C) / sin A
ST = ((2x + 5 cm) * sin 24.66°) / sin (4y - 71°)
ST = ((2x + 5 cm) * 0.4237) / sin (4(40.67°) - 71°)
ST = (2x + 5 cm) * 0.4237 * 0.4514
ST = (2x + 5 cm) * 0.1901
ST = 0.3802x + 0.9505 cm
Therefore, the length of side BC in triangle ABC is 5.525 cm, and the length of side ST in triangle RST is 0.3802x + 0.9505 cm.
write an algorithm, using pseudocode, to make the robot: 1. stand up 2. walk forward until it senses a wall 3. turn around 4. walk back to the chair 5. sit down in its original starting position finally, output the total number of steps taken.
Answers
We had written an algorithm, using pseudo code.
//Define the required variables.
total_number_of_steps = 0
number_of_steps = 0
//robot stands up to walk.
stand
//the robot moves forward till the wall is not reached.
while (wall is not reached)
//the robot senses the wall with the help of arms.
raise arms
sense_the_wall
if (wall is not there)
//if the wall is not found, the robot lowers the arms
lower arms
//if wall is not detected, the robot moves forward.
step_forward
//increment the number of steps forward.
number_of_steps=number_of_steps+1
//increment the total number of steps.
total_number_of_steps=total_number_of_steps+1
else
exit
end if
end while
//else if the wall is found, lower the arms
lower arms
//the robot turns 90 degrees right once.
turn_right_90
//the robot turns 90 degrees right again.
turn_right_90
//till the number of steps does not reach 0, move
for (number_of_steps! = 0)
step
//increment the total number of steps.
total_number_of_steps=total_number_of_steps+1
//the robot moves backwards on detecting the wall, so
//decrement the number of steps.
number_of_steps = number_of_steps-1
//end the for loop.
end for
//the robot turns 90 degrees left once.
turn
//the robot turns 90 degrees left again.
turn
//the robot sits down.
sit
//display the total number of steps taken by robot
display total_number_of_steps
The last line ends the pseudocode
Stop
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question does each function describe exponential growth or decay? drag and drop the equations into the boxes to correctly complete the table. put responses in the correct input to answer the question. select a response, navigate to the desired input and insert the response. responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. responses can also be moved by dragging with a mouse. growth
Answers
A set-to-set function f is a relation that assigns one element of the set A to each element of the other set B. The set A is the domain of the function (also called the set of inputs) and the set B contains the range (also called the set of outputs).
Let's denote f as exponential function with the base 'a':
f(x) = a ˣ
where, a > 0 and a ≠ 1 and x is any real number.
1. Not an exponential function:
We have the following equation:
[tex]y = 100 (1 - 12)^{t}[/tex]
We can write the equation as:
[tex]y = 100 (-11)^{t}[/tex]
Let's denote f as exponential function with the base 'a':
f(x) = a ˣ
where, a > 0 and a ≠ 1 and x is any real number.
Therefore: a must be more than 01.
In this problem, a = -11, therefore this is not an exponential function.
2. Growth.:
The function:
[tex]y= 0.1(1.25)^{t}[/tex]
The above equation is an exponential function because is a function of the form
[tex]f(t) = ka^t[/tex]
where, a > 0 and k is constant
Therefore, k = 0.1 and a = 1.25 . So, a is greater than 1.
3. Growth:
The function:
[tex]y = {(1 - 0.03)12}^2t[/tex]
The above equation can be written as:
[tex]y = 11.64^{2t}[/tex]
which is an exponential function because is a function of the form
[tex]f(t) = a^{bt}[/tex]
where, a > 0 and b is constant.
So, a = 11.64 and b = 4 . Since a is greater than 1.
4. Decay:
The function:
[tex]y = 426(0.98)^t[/tex]
This is an exponential function because is a function of the form
[tex]f(t) = ka^t[/tex]
where, a > 0 and k is constant
So, k = 426 and a = 0.98. Since, a is less than 1.
5. Growth:
The function:
[tex]y = 2050(12)^t[/tex]
This is an exponential function because is a function of the form
[tex]f(t) = ka^t[/tex]
where, a > 0 and k is constant.
So, k = 2050 and a = 12 . Since, a is greater than 01.
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1/3x= -2/5 solve for x
Answers
Answer:
Below
Step-by-step explanation:
1/3 x = - 2/5 <=====multiply both sides of the equation by 3 to get
x = -6/5 = - 1 1/5
Students performed in a play on a Friday and a Saturday. For both performances. adult tickets cost a dollars each and student tickets costs dollars each. On Friday, they sold 125 adult tickets and 65 student tickets, and collected $1.200. On Saturdas, they sold 140 adult tickets and 50 student tickets, and collect $1,230. Write a system of equations to represent this relationship.
Answers
The system of equations is
125a + 65s = 1200
140a + 50s = 1230
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
125a + 65s = 1200
140a + 50s = 1230
-3500a - 1820s = -33600
3500a + 1250s = 30750
-570s = -2850
s = $5
student
125a + 65(5) = 1200
125a + 325 = 1200
125a = 875
a = $7 adult
the other situation means that they didn't do it right at all
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NO LINKS!! Please help me with this problem. Part 6ff
Answers
Answer:
The sequence is not arithmetic. In an arithmetic sequence, the difference between consecutive terms is constant. However, in this sequence, the difference between the terms is not constant. For example, the difference between the first and second terms is 1^5 - 2^5 = -3, while the difference between the second and third terms is 2^5 - 3^5 = -6. Since the difference between consecutive terms is not constant, this sequence is not arithmetic. Therefore, the common difference is NONE.
Answer:
No, the sequence is not arithmetic.
d = NONE
Step-by-step explanation:
An Arithmetic Sequence has a common difference between each term (the difference between each term is the same).
Given sequence:
[tex]1^5, 2^5, 3^5, 4^5, 5^5, ... = 1, 32, 243, 1024, 3125, ...[/tex]
Calculate the difference between each term:
[tex]1 \underset{+31}{\longrightarrow} 32 \underset{+211}{\longrightarrow} 243 \underset{+781}{\longrightarrow} 1024 \underset{+2101}{\longrightarrow} 3125[/tex]
As the difference between each term is not constant, the sequence is not an arithmetic sequence.
Therefore, the common difference, d = NONE.
Waves that make up light have peaks and valleys just like the ocean. What are the scientific terms for peaks and valleys?
highs and lows
crests and troughs
ebbs and flows
protos and parallax
Answers
The scientific terms for peaks and valleys is B. Crests and troughs.
What are crests?The greatest amount of upward displacement within a cycle occurs at a wave's crest point. A surface wave's crest is a region where the medium's displacement is greatest. The minimum or lowest point in a cycle, a trough is the opposite of a crest.
The crest and trough of a wave, respectively, are its highest and lowest surface portions. The wave height is the vertical distance between the crest and trough. The wavelength is the horizontal separation between two adjacent crests or troughs.
The crest is the highest point on the wave. The trough is the area that is the lowest. The wave length, also known as the wavelength, is the separation between two successive crests (or troughs), while the wave height is the overall vertical change in height between the crest and the trough.
Therefore, based on the information given, the correct option is B.
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x - y = 6
x + y = 2
Solve by elimination
Answers
Step-by-step explanation:
Add the values
x - y = 6
x + y = 2
-------------
2x = 8
--------------
Substitute for x
2x = 8
x = 8/2
x = 4
insert x = 4 into equation x - y = 6
x - y = 6
4 - y = 6
-y = 6 - 4
-y = 2
-y/-1 = 2/-1
y = -2
∴ y = -2 , x = 4
Solved by elimination
Solved by elimination Through chibabykalu16
Mr. Lee gave his four children $25.40 to share equally. How much money did each child get?
Answers
Answer:
$6.35
Step-by-step explanation:
25.40/4 = 6.35
Explanation
=25.40/4=6.35
The table represents a linear relationship. x −2 0 2 4 y −1 0 1 2 Which of the following graphs shows this relationship?
Answers
The graph that shows the linear relationship of the table is attached below.
How to Find the Graph that Represent a Linear Relationship?To determine the graph of a linear relationship, do the following:
Find the slope or rate of change = change in y / change in x.Determine the y-intercept which is the value of y when x = 0, and it represents the value on the y-axis where the line intercepts.Given the table which represents a linear relationship above, use two pairs of values, (0, 0) and (2, 1) to find the slope:
Slope = change in y / change in x = (1 - 0) / (2 - 0)
Slope = 1/2.
The y-intercept (b) = 0.
Thus, this means that the graph of the linear relationship will have a slope of 1/2 and crosses the y-axis at 0.
Thus, the graph is shown below.
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Monique buys a $4700 air conditioning system using an installment plan that requires 15% down. How much is the down payment
Answers
The value of down payment will be;
⇒ $705
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
Monique buys a $4700 air conditioning system using an installment plan that requires 15% down.
Now,
Since, Monique buys a $4700 air conditioning system using an installment plan that requires 15% down.
Hence, The value of down payment = 15% of $4700
= 15/100 × 4700
= 15 × 47
= 705
Thus, The value of down payment = $705
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Which of the following examples would NOT be able to be described by a normal Curve?
1) The height of the actresses on Broadway
2) Rolling 2 dices, 50 times, and observing the sum of the two dice
3) How many ounces of sugar in a 20 oZ container
4) The shoe size of all the students in the school?
Answers
The normal distribution does not correspond to the fact that about 65% of the data occurs within two standard deviations of the mean.
What are a normal curve's four requirements?The four features of a normal distribution are visible in this instance. The mean, median, and mode of a normal distribution are all equal and it is symmetric, unimodal, and asymptotic.The normal distribution does not correspond to the fact that about 65% of the data occurs within two standard deviations of the mean.Another nice illustration of normal distribution is a fair dice roll. In an experiment, it was discovered that the chances of rolling a one are 15–18% when the dice are thrown 100 times, and they remain the same even if they are rolled 1000 times, with an average chance of 16.7% (1/6).Explanation:
100 - 35 = 65%
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The normal distribution does not correspond to the fact that about 65% of the data occurs within two standard deviations of the mean.
What are the four conditions for a normal curve?The four characteristics of a normal distribution can be seen in this situation. A normal distribution is symmetric, unimodal, and asymptotic, and its mean, median, and mode are all equal.
The fact that around 65% of the data occurs within two standard deviations of the mean contradicts the normal distribution.
A fair dice roll is a good example of normal distribution. The results of an experiment showed that the chances of rolling a one are 15–18% when the dice are thrown 100 times, and they remain the same even if they are thrown 1000 times, with an average likelihood of 16.7% (1/6).
100 - 35 = 65%
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PLEASE HELP
Under what conditions would triangle DEF be similar to triangle ABC? Drag and drop the choices to make the statement correct.
Answers
Step-by-step explanation:
similar means that they have the same angles, and that there is one and the same scale factor for all corresponding sides and other lines (like heights).
so, either the angle F = 60° (like angle C in ABC), or DE has the same scaling factor with AB as DF has with AC.
some correct answer options are not listed, so we need to adjust to the existing ones.
remember, the sum of all angles in a triangle is always 180°.
so,
angle A + angle B + angle C = 180
40 + angle B + 60 = 180
angle B = 80°
so, angle E = 80° for the triangles to be similar.
AC × c = DF
12 × c = 16
3 × c = 4
c = 4/3
so,
AB × c = DE
9 × 4/3 = DE
36/3 = DE
DE = 12
so, either angle E = 80° or DE = 12.
Solve for the variable.
8 = y - 3
Responses
A -11-11
B 55
C 1111
D 2424
E -5
Answers
Answer:
Answer is y = 11
Step-by-step explanation:
8 = y - 3
or, 8 + 3 = y - 3 + 3
or, 11 = y
or, y = 11
How can you represent and operate on numbers that are not on the real number line?
Answers
To operate on complex numbers, we can use the standard arithmetic operations of addition, subtraction, multiplication, and division. For example, to add two complex numbers, we can add their real parts and imaginary parts separately. For instance, to add the complex numbers 3 + 2i and 1 + 4i, we can add their real parts to get 3 + 1 = 4, and add their imaginary parts to get 2 + 4 = 6. Therefore, the result of adding 3 + 2i and 1 + 4i is 4 + 6i.
Other mathematical operations that can be performed on complex numbers include taking the absolute value, finding the conjugate, and finding the complex conjugate. These operations can be used to solve equations and perform other mathematical operations involving complex numbers.
Pls award brainliest!!!
We want to look at the scatterplot before conducting a correlation analysis for all of the following reasons EXCEPT to.check for nonlinearity to test for homoscedasticity to see if there are any outliers to see if the regression line is actually the line of best fit
Answers
I think it is either A or C
bella is working two summer jobs, making $10 per hour landscaping and $15 per hour clearing tables. last week bella worked a total of 15 hours and earned a total of $180. graphically solve a system of equations in order to determine the number of hours bella worked landscaping last week, x,x, and the number of hours bella worked clearing tables last week, yy.
Answers
The solution of the system of equations by the graphical methods yields x equals 9 and y is 6 i.e, 9 hours of landscaping and 6 hours of waiting tables.
Bella worked x hours working landscaping at $10 per hour.
Total amount earned = 10x
Bella worked y hours working on clearing tables at $ 15 per hour
Amount earned = 15 y
x and y are variables as given
She worked a total of 15 hours and she gets $180 for the combined efforts.
The system of equation can be represented as:
x + y = 15
10x + 15y = 180
Now we will solve the two equations graphically:
So from the attached graph we can see that the point (9,6) is the required solution.
Hence she worked landscaping for 9 hours and clearing tables for 6 hours.
Let us solve by substitution to verify the results:
x + y = 15
or, x = 15 - y
Now 10x + 15y = 180
or, 10 (15-y) + 15y = 180
or, 150 - 10y +15y = 180
or, 5y = 180 - 150
or, y = 6
At y = 6 , x = 15 - 6 = 9
Hence (9,6) is the solution.
System of equations also known as simultaneous equations can also be solved by the elimination method.
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Consider the following measurements of the heat-producing capacity of the coal produced by two mines (in millions of calories per ton): Mine 1: 8260 8130 8350 8070 8340 Mine 2: 7950 7890 7900 8140 7920 7840 Can it be concluded that the two population variances are equal?
Answers
F0.05 (4,5)=5.19>f according to the F-distribution table. Following that, P(F>1.442)>P(F>f0.05 (94.5))=0.05. This leads us to conclude that the sample has a higher than 5% chance of producing such data under the premise that σx=σy.
We cannot conclude that the variances of the two populations are not equal based on the standards of a 95% confidence interval.
Step 1 : the mines' 1 and 2 standard deviations should be calculated. [tex]n_{x}[/tex] =5&[tex]n_{y}[/tex]=6.
To determine the sample means, use the formulas
x bar = 8260 + 8130 + 8350 + 8070 + 8340/ [tex]n_{x}[/tex]
x bar = 41150/ 5
x bar = 8230 and y bar = 7950 + 7890 + 7900 + 8140 + 7920 + 7840/ [tex]n_{y}[/tex]
y bar = 47640/6
y bar = 7940.
step 2: Now, [tex]s_{x}[/tex]provides the standard deviations.
[tex]s_{x}^{2}[/tex] =1/4i=1∑^5i=1(xi−x)^2
=1/ 4 ⋅63000
=15750
for [tex]s^{2}_{y}[/tex]
[tex]s^{2}_{y}[/tex]^2=1/5∑i=1^6(yi−y)^2
=1/5⋅54600
=10920
If we assume that the variances of the two populations are equal—
that is, σx=σy and
[tex]s_{x}^{2}[/tex] and[tex]s^{2}_{y}[/tex] are the variances of independent random samples with sizes of [tex]n_{x}[/tex]=5 and[tex]n_{y}[/tex] =6 drawn from normal populations—then we can say that the random variable exists.
The formula F is
=[tex]s_{x}^{2}[/tex]/ [tex]s^{2}_{y}[/tex]has an F distribution with
v1=nx- 1
=5- 1
=4 and
v2=ny-1
=6- 1
=5
The observed samples' f-value is f=[tex]s_{x}^{2}[/tex] / [tex]s^{2}_{y}[/tex]
=15750/10920
=1.442.
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Rewrite Y = √9x-36-4
to make it easy to graph using a translation. Describe the graph.
Answers
The simplified equation is y = 3x -40.
What do you mean by translation of graph?
Translating a graph means that moving the graph of a parent operate either vertically or horizontally. To translate a graph vertically means that to shift the graph k units upward or downward looking on the sign of k. If k is positive, shift the graph upward however if k is negative, shift the graph downward. On the opposite hand, translating a graph horizontally means that shifting the graph side wards by h units to the left or to the correct. If h>0, shift the graph to the correct however if h<0, shift the graph to the left.
Main body:
According to question:
Y = √9x-36-4
√9 can be written as 3.
y = 3x -40
Hence , the simplified equation is y = 3x -40.
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what is the population standard deviation?
Answers
The population standard deviation [tex]\sigma[/tex] is 6.697.
What is the mean absolute deviation?The average distance between each data item and the mean is known as the mean absolute deviation.
The gap between each data value and the mean in absolute terms is represented by this average.
The given data set can be arranged as 4, 7, 8, 10, 12, 12, 15, 18, 23, 26.
Mean[tex](\overline{x})[/tex] = (4 + 7 + 8 + 10 + 12 + 12 + 15 + 18 + 23 + 26)/10.
Mean[tex](\overline{x})[/tex] = 135/10 = 13.5.
We know variance[tex](\sigma)[/tex] = [tex](\[ \sum_{i=1}^{n}x_i^2 \]/n) - \overline{x}^2[/tex].
= (4² + 7² + 8² + 10² + 12² + 12² + 15² + 18² + 23² + 26²)/10 - (13.5)².
= (16 + 49 + 64 + 100 + 144 + 144 + 225 + 324 + 529 + 676)/10 - 182.25.
= 44.85
And we also know the standard deviation is [tex]\sqrt{\sigma}[/tex] = [tex]\sqrt{44.85}[/tex] = 6.697
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