The answer is A cause- and- effect relationship between two variables can best be determined When the two variables are identified.
Because the cause and effect relationship is chancing when the variables are identified or there exists a direct relationship between the variable. i.e. when the variables are identified or have a retrogression between the variables.The use of a controlled study is the most effective way of establishing reason between variables. In a controlled study, the sample or population is resolve in two, with both groups being similar in nearly every way.
There are three criteria that must be met to establish a cause- effect relationship. The cause must do before the effect. Whenever the cause occurs, the effect must also do. There mustn't be another factor that can explain the relationship between the cause and effect.
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1. Find the net cost for the following:
List price $1236.92, less series discount 12/15/20
A tree is 6 feet 11 inches tall. How tall is it in inches?
in
Answer: 83 inches
Step-by-step explanation:
1. 12 inches = 1 foot
2. 12x6=72 inches
3. 72+11=83 inches
a laboratory technician had a bottle that was 5/8 full if the technician used 3/4 of the bottles content, what fractional amount is left in the bottle
Scientists have found a way to distinguish chronic-fatigue syndrome (CFS) from post-treatment Lyme disease by different proteins in a patient's spinal fluid. In a study of 3991 patients, the results to the right were found.
1538 had the protein for normal patients, CFS, and post-treatment Lyme disease;
1884 had the protein for CFS and Lyme;
408 had the protein for CFS only;
2602 had the protein for CFS;
1731 had the normal protein as well as the one for Lyme;
2798 had the protein for Lyme;
2516 had the normal protein.
Part 1
(a) There were ---- patients who only had the protein for Lyme.
(Type a whole number.)
Part 2
(b) There were ---- patients who only had the normal protein.
(Type a whole number.)
Part 3
(c) There were ---- patients who had none of the proteins.
Answer:
Part 1
(a) There were 2798 patients who only had the protein for Lyme.
Part 2
(b) There were 2516 patients who only had the normal protein.
Part 3
(c) It is not specified in the given information how many patients had none of the proteins. It is only specified that 1538 had the protein for normal patients, CFS, and post-treatment Lyme disease; 1884 had the protein for CFS and Lyme; 408 had the protein for CFS only; 2602 had the protein for CFS; 1731 had the normal protein as well as the one for Lyme; 2798 had the protein for Lyme; 2516 had the normal protein. Based on this information, it is not possible to know how many patients had none of the proteins.
Answer: There are no patients who had none of the proteins.
Step-by-step explanation: Part 1
(a) There were 408 patients who only had the protein for Lyme.
This information can be inferred from the data given: 1884 had the protein for CFS and Lyme, and 2798 had the protein for Lyme. If we subtract 1884 from 2798, we get 914 which is the number of patients who only had the protein for Lyme.
Part 2
(b) There were 2516 patients who only had the normal protein.
This information can be inferred from the data given: 1538 had the protein for normal patients, CFS, and post-treatment Lyme disease, 1884 had the protein for CFS and Lyme, and 2602 had the protein for CFS. If we add 1538, 1884 and 2602, we get 6124, then if we subtract 6124 from the total number of patients (3991) we get 2516 patients who only had the normal protein.
Part 3
(c) There were 0 patients who had none of the proteins.
This information can be inferred from the data given: 1538 had the protein for normal patients, CFS, and post-treatment Lyme disease, 1884 had the protein for CFS and Lyme, 408 had the protein for CFS only, 2602 had the protein for CFS, 1731 had the normal protein as well as the one for Lyme, 2798 had the protein for Lyme, and 2516 had the normal protein. All patients have at least one protein, therefore there are no patients who had none of the proteins.
For each part, compare distributions (1) and (2) based on their medians and IQRs. You do not need to calculate these statistics; simply state how the medians and IQRs compare. Make sure to explain your reasoning.
a. (1) 3, 5, 6, 7, 9 (2) 3, 5, 6, 7, 20
b. (1) 3, 5, 6, 7, 9 (2) 3, 5, 7, 8, 9
c. (1) 1, 2, 3, 4, 5 (2) 6, 7, 8, 9, 10
d. (1) 0, 10, 50, 60, 100 (2) 0, 100, 500, 600, 1000
The medians and IQRs of two distributions can be compared to determine how the distributions differ. If the medians and IQRs are the same, the distributions are similar. If the medians and IQRs are different, the distributions are not the same.
a. The medians and IQRs of distributions (1) and (2) are the same; both have a median of 6 and an IQR of 4.
b. The medians and IQRs of distributions (1) and (2) are the same; both have a median of 6 and an IQR of 2.c. The medians and IQRs of distributions (1) and (2) are different; distribution (1) has a median of 3 and an IQR of 2, while distribution (2) has a median of 8 and an IQR of 2.
d. The medians and IQRs of distributions (1) and (2) are different; distribution (1) has a median of 50 and an IQR of 50, while distribution (2) has a median of 500 and an IQR of 400.
The median IQRs of two distributions can be compared to determine how the distributions differ. If the medians and IQRs are the same, the distributions are similar. If the medians and IQRs are different, the distributions are not the same.
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find the volume v of the described solid s. the base of a solid s is the region enclosed by the parabola y
The volume of the solid that is in the parabola is 3.48[tex]\pi[/tex] after integration will carried out.
Parabola is a U shape curve whose eccentricity is 1.
The equation of parabola is y = 2-3x² and the x axis.
The cross section is perpendicular to y axis and the square.
The parabola is passes through the x axis put y = 0 in the equation of parabola.
0 = 2-3x²
x = [tex]\sqrt{\frac{2}{3} }[/tex]
Volume of the solid = [tex]\pi r^{2}h[/tex]
here r = y and h = dx
[tex]\pi (2-3x^{2} )^{2} dx=dv\\dv = \pi (9x^{4}-12x^{2} +4)dx\\[/tex]
Now, integrate the given equation to get the volume of the solid.
∫dv = ∫π(9x⁴-12²+4)dx
Put limits [tex]\sqrt[2]{\frac{2}{3} }[/tex] to 0
After integration and putting the limit we got V = 3.48[tex]\pi[/tex].
Hence, the volume of the solid is 3.48π.
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The complete question is:
Find the volume V of the described solid S. The base of S is the region enclosed by the parabola y = 2 − 3x2 and the x−axis. Cross-sections perpendicular to the y−axis are squares.
Step 2: Identify the words in the problem that translate into mathematical actions.
Choose one or more:
A. more
B. of
C. and
D. if
The words that can be changed into mathematical or arithmetic operators are
More = +, of = *, if=Condition.
What are arithmetic operations?
Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.
These basic mathematical operations (+, -, ×, and ÷) we use in our everyday life. Whether we need to calculate the annual budget or distribute something equally to a number of people, for every such aspect of our life, we use arithmetic operations.
The four basic arithmetic operations in Maths, for all real numbers, are:
Addition (Finding the Sum; ‘+’)
Subtraction (Finding the difference; ‘-’)
Multiplication (Finding the product; ‘×’ )
Division (Finding the quotient; ‘÷’)
Now,
we can change
More = +, of = *, if=Condition as only these makes sense according to mathematics actions.
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ANYONE GOOD AT MATH PLEASE HELP!
Answer:
Is it 0? sorry if this is wrong
Step-by-step explanation:
Answer:
f(g(0)) = -2
Step-by-step explanation:
We have our two equations, f(x) and g(x).
We work our way from the inside to the outside. Our inside equation is g(0). If we match g(x) to that, that would mean x = 0. So on that g(x) graph, when the x=0, the graph intercepts the y axis at y = 1.
Now that we know that g(0) = 1, we can plug that into the original equation, making it f(1) instead of f(g(0)). Now that we have f(1), we can go to our f(x) equation.
Matching the equations, it shows the x=1. On our f(x) graph, we'll find x=1 and trace down or up (down in this case) to the point where the graph intercepts at that point. Thats where we can then trace that point to the y axis and we see that our line hits the y axis at -2, making that the answer.
For which data set are the mean, median, and mode the same value?
4, 8, 8, 8, 4
4, 8, 6, 8, 4
4, 8, 6, 6, 6
8, 6, 4, 8, 6
Answer:
Step-by-step explanation:
the answer is : 4,8,6,6,6
= 6
Identify the type of observational study A researcher plans to obtain data by interviewing spouses of victims who perished in a tsunami. He will interview them, and people unrelated to the victims, over the next 10 years to see how closeness to a traumatic event might affect recovery time. Choose the correct type of observational study below. â“”A. prospective B. retrospective O C. cross-sectional
The type of observational study in the following scenario is considered as prospective study.
A prospective study, also known as a prospective cohort study, is a type of longitudinal study in which researchers follow and watch a group of individuals across time to collect data and track the development of outcomes. A prospective study is one that follows participants over time to see if certain outcomes, like the onset of a disease, occur and then compares those instances to any known or suspected risk or protective factors (s). It is common practice to follow a group of people, or a "cohort," for an extended period of time as part of the study. In this scenario, the researcher wants to learn how closeness to a traumatic event might effect healing time by conducting interviews with victims and witnesses over the next 10 years. Hence, it fits the criteria for a prospective observational study.
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What is the value of x?
The value of x in the given polygon is 31 degrees.
What are exterior angles?An exterior angle is an angle created by the expansion of the neighboring side and one of the sides of a closed shape construction, such as a polygon. Regardless of the number of sides in the polygons, the sum of the measures of the outside angles is equal to 360 degrees.
The sum of the exterior angle of any polygon is 360 degrees.
So,
360 = 57 + 41 + 82 +x + 62 + 87
360 = x + 329
x = 31
Hence, the value of x in the given polygon is 31.
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What are the coordinates of the midpoint of the segment whose endpoints are H (-2, 4) and K (2, –3)?
The coordinates of the midpoint of the segment whose endpoints are H (-2, 4) and K (2, –3) is (0,1/2)
What are the coordinates of midpoint of the line segment AB?Suppose we've two endpoints of a line segment as:
A(p,q), and B(m,n)
Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:
x = [tex]\dfrac{p+m}{2}[/tex]
and y =[tex]\dfrac{q+n}{2}[/tex]
Given;
The endpoints= H (-2, 4), K (2, –3)
X coordinate of midpoint;
-2+2/2=0
Y coordinate of midpoint;
4-3/2=1/2
Therefore, the midpoint will be (0,1/2)
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How many numbers did Jane write?
Jane wrote all the natural numbers from m to k (where k>m).
Answer:
k-m+1
if you have 36 and 78 for example, you would do 78-36 to find how many numbers there are plus one. so, the answer is k-m+1
Jane typed all the natural numbers between m and k (where k>m), which implies she wrote all the positive integers between m and k, inclusive. Jane would have written the numbers 5, 6, 7, 8, 9, and 10 if m was 5 and k was 10.
What are natural numbers?Natural numbers are positive integers (1, 2, 3, and so on) that can be counted and ordered. They are the most fundamental sort of number in mathematics and are frequently referred to as counting numbers. Natural numbers begin with one and continue forever; however, they do not include negative numbers, fractions, or decimals.
Natural numbers are the foundation of many mathematical ideas and are used to express the quantities of things in a collection. Natural numbers, for example, are used to define the number of sides of a polygon, the dimensions of a matrix, and the length of a number line. They are also used to indicate how much time has elapsed.
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a carnival game charges each contestant \$2$2dollar sign, 2 to spin a wheel with 555 equally likely spaces: 333 spaces result in the contestant winning nothing. 111 space results in the contestant winning a prize whose value is \$1$1dollar sign, 1. 111 space results in the contestant winning a prize whose value is \$4$4dollar sign, 4. let xxx represent a player's net gain on a spin. for example, if the spin lands on the space where the contestant wins nothing, then x
If the spin lands on the space where the contestant wins nothing, then x = 0.
If the spin lands on a space where the contestant wins $1, then x = -1 + 1 = 0. If the spin lands on a space where the contestant wins $4, then x = -2 + 4 = 2.
The expected value of x can be calculated as follows:
E(x) = (333/555) × 0 + (111/555) × (-2 + 1) + (111/555) × (-2 + 4) = (111/555) * 2 = 0.4.
So, on average, the player's net gain per spin is 40 cents.
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harold, tanya, and ulysses paint a very long picket fence. harold starts with the first picket and paints every h th picket; tanya starts with the second picket and paints every t th picket; and ulysses starts with the third picket and paints every u th picket. call the positive integer 100 h 10 t u paintable when the triple ( h , t , u ) of positive integers results in every picket being painted exactly once. find the sum of all the paintable integers. (2002,
The sum of all the paintable integers is 757.
Note that it is impossible for any of h,t,u to be 1, since then each picket will have been painted one time, and then some will be painted more than once.
h cannot be 2, or that will result in painting the third picket twice. If h=3, then t may not equal anything not divisible by 3, and the same for u. Now for the fourth and fifth pickets to be painted, t and u must be 3 as well. This configuration works, so 333 is paintable.
If h is 4, then t must be even. The same for u, except that it can't be 2 mod 4. Thus u is 0 mod 4 and t is 2 mod 4. Since this is all mod 4, t must be 2, and u must be 4, in order for 5,6 to be paintable. Thus 424 is paintable.
h cannot be greater than 4, since if that were the case then the answer would be greater than 999, which would be impossible for the AIME.
Therefore, the sum of all paintable numbers is 757.
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Fill in the blank. The symbol C represents a constant. Write this result as a linear first-order differential equation that is free of the symbol C1 and has the form dy/dx f(x, y)
The solution for the given differential equation is [tex]\frac{dy}{dx} = 12C_1e^{12x} = 12y[/tex].
We have given a differential equation:
[tex]\frac{d}{dx}(C_1e^{12x})[/tex]
since C1 is a constant,
=[tex]C_1\frac{d}{dx} (e^{12x})[/tex]
we know that [tex]\frac{d}{dx} (e^{ax}) = e^{ax}\frac{d}{dx} (ax)[/tex]
= [tex]C_1e^{12x}(12) = 12C_1e^{12x}[/tex]
Therefore, [tex]\frac{d}{dx}(C_1e^{12x}) = 12C_1e^{12x}[/tex]
Now, let y = [tex]C_1e^{12x}[/tex]
Therefore, [tex]\frac{dy}{dx} = 12C_1e^{12x} = 12y[/tex]
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The complete question is:
Fill in the blank. The symbol C represents a constant. [tex]\frac{d}{dx}C_1e^{12x}[/tex]= ____ Write this result as a linear first-order differential equation that is free of the symbol C1 and has the form dy/dx = f(x, y).
Giving brainliest! Pls and ty
The experimental probability that the puppy would be named lemon or linus is 13/50. Option D
How to solve the probabilityThe experimental probability that the pupply would be named lemon or linus can be solved by
P(A) + P(B)
where P (A) is probability of lemon
P(B) is probability of linus
The total value in the frequency table is given as 10 + 13 + 3 + 14 + 10 = 50
P(A) = 3 / 50
P(B) = 10 / 50
The probability = 3/50 + 10/50
solve using the lcm method of solving fractions. There is a common denominator
3 + 10 / 50
= 13 / 50
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Cognitive psychology question.
Signal Detection
1) How are hit and miss related? How are false alarms and correct rejection related? Explain their relationships mathematically.
Simon Effect
1) How would you design a task demonstrating the auditory version of the Simon effect?
The answers include the following below:
If the signal is present the person can decide that it is present or absent and the outcomes are called hits and misses.If the signal is absent the person can still decide that the signal is either present or absent which are called false alarms or correct rejections respectively therefore false alarms = correct rejection. A task demonstrating the auditory version of the Simon effect will be putting the hands close to or far from the loudspeakers.What is Simon effect?The Simon effect refers to the finding that people are faster and more accurate when responding to stimuli that occur in the same relative location as the response.
An appropriate task demonstrating the auditory version of the Simon effect will be putting the hands close to or far from the loudspeakers and noting how fast they react to the stimuli.
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what is the volume of the cube
Answer:
D.[tex]\sqrt[32]{2}[/tex]
I think this is right becuse V=l*w*h which is 64=4*4*4
Kulijeet makes this bead string. She threads 3 white beads for every 1 black bead. When she finishes the bead string, it contains 20 beads altogether. How many of the beads are white?
The numbers for the first eight beads that are white are; 1, 5, 9, 13, 17, 21, 25, 29
How many of the beads are white?
step1
Arithmetic Sequence
We are told that she strings in this order;
3 white1 blackNow, after the first white bead, the next white bead is the 5th bead in total.
This means the difference in interval between white beads is; 5 - 1 = 4 beads
Thus, the numbers for the first eight beads that are white are
1, (1 + 4), (1 + 4 + 4), (1 + 4 + 4 + 4)…..
Thus, we have;
1, 5, 9, 13, 17, 21, 25, 29
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4 (2 points): consider the following linear transformation of a random variable: , where is the mean and is the standard deviation. find the expected value and standard deviation of .
The standard deviation of is equal to the standard deviation multiplied by, and the anticipated value of is equal to the mean.
The mean, which is the average of the random variable, is equal to the expected value of. It is determined by summing up all of the random variable's values and dividing the total number of values in the set. The result of multiplying the standard deviation by is the standard deviation of. By taking the square root of the variance, the standard deviation—a measurement of the range of data points from the mean—is created. By dividing the total of the squares of the deviations between each data point and the mean, the variance is computed.
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Solve the given proportion X/4 = 3/6 X=
Answer:
X/4=3/6
Start off by cross multiplying the tops and bottoms, so X/4=3/6 turns into 6X=12. Now divide by 6 on both sides.
6X=12 X=2
Answer:
2
Step-by-step explanation:
Cross Multiple and Divide
X. 3
----. = ----
4. 6
So what you want to do is multiply diagonally:
(6)(X) = 6X
(3)(4) = 12
Now that we have our two answers, we put an equal sign between them.
6X = 12
Now to get X alone. Since it's being multiplied by 6, you want to do the opposite and divide.
So remember to divide on both sides to get rid of the 6.
6X divided by 6 is just X.
12 divided by 6 is 2
We got our answers, put the equal sign in-between
X = 2
If an employee contributes $150 toward her retirement each month,
and her employer agrees to match 15% of that, then what is the
total monthly retirement contribution?
Two points should be noted: The 15% is first calculated using your annual gross wage rather than your take-home pay. Second, the business match is not included in your 15%.
Should I contribute more than 15% to retirement?You probably won't need to save more than 15-20 percent as you get older if you can save 15-20 percent of your salary when you're 30 for retirement. If you stay consistent throughout your professional life, starting early is a tremendous advantage.Your actual monthly contribution will increase when your salary increases if you consistently set aside 15% of your income, which will speed up the accumulation of your retirement savings.If you are under 72 years old and have income from a job or self-employment, you are eligible to make a contribution to your Individual Retirement Account (IRA) of up to $6,000. Up to $7,000 can be contributed if you are 50 years old or older.To learn more about business refer to:
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A salesperson receives a weekly base salary of $600 on a quota of $4500. On the next $2000, she receives a commission of 11 %. On any additional sales, the commission rate is 15%. Calculate her gross earnings for a week in which her sales total $
The salesperson's gross earnings for a week, based on the informations, equals to $1,195.
What does a gross earnings means?An employees' gross pay is what they earn before taxes, benefits, and other payroll deductions are deducted from their pay. It is opposite of net pay, also known as take-home pay which is the amount left over after all withholdings are deducted.
Data
Weekly base salary of $600 on a quota of $4500.
On the next $2000, she receives a commission of 11 %.
On any additional sales, the commission rate is 15%.
Gross earning is computed as:
= Base salary + (First sales *11%) + (Additional sales*15%)
= $600 + ($2,000*11%) + ($2,500 * 15%)
= $1,195
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write an equation of the line that passes through (3,1) and (0,10)
An equation of the line that passes through two points (x1,y1) and (x2,y2) can be found using the slope-intercept form:
Slope intercept form: what is it?
Simply put, the slope-intercept form is the way to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are instantly visible. This form is frequently known as the y = mx + b form.
y = mx + b
where m is the slope of the line and b is the y-intercept.
To find the slope of the line, we use the following formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the coordinates of the points given, we get:
m = (10 - 1) / (0 - 3) = -9/3
To find the y-intercept, we can use either of the given points and the slope:
b = y - mx
Plugging in the coordinates of the point (3,1) and the slope, we get:
b = 1 + (9/3) * 3 = 4
So the equation of the line that passes through (3,1) and (0,10) is:
y = -3x + 4
It's also possible to use the point slope form of a linear equation, which is y-y1=m(x-x1)
y - 1 = -3(x-3)
y = -3x + 9
Both equations are valid and represent the same line.
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Multiply:
[-7]
3 11
2
=
b₁
b₂
b₂
The value of b1 = -21, b2 =33, and b3 = 6 in the given matrix.
What is matrix?A collection of integers lined up in rows and columns so to produce a rectangular array is called a matrix. The elements, or inputs, of the matrix are the integers.
What is multiplication of matrix?A single matrix is created through matrix multiplication, sometimes referred to as matrix product and the multiplication of two matrices. This kind of binary operation is used. A scalar multiplication occurs when an integer is multiplied by a matrix. Scalar multiplication is the process of multiplying a matrix by a scalar value.
For the given matrix multiply each term of the matrix with 3 to obtain the value of b1. b2, and b3.
[tex]3\left[\begin{array}{ccc}-7\\11\\2\end{array}\right] = \left[\begin{array}{ccc}-21\\33\\6\end{array}\right][/tex]
Hence, the value of b1 = -21, b2 =33, and b3 = 6.
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Use the information given below to find tan (a-B).
3
4
4
5'
tan a =
sin ß
I
with a in quadrant III
an (a - B) =
with ß in quadrant I
Give the exact answer, not a decimal approximation.
That since exact value of sin(A-β) depends on the cos(-β) value, which we miss, we are not able to determine the value.
How to find Sinβ using trigonometric identities?To determine (A-β), we can use trigonometric identities.
Tan(A) = 3/4 and sin() = 4/5 in Quadrant III.
The identification can be used for:
tan(A) = cos/sin(A) (A)
Sin(A) in this instance equals 3/4. * cos(A) (A)
We can adopt a different guise.
(A-sin) = sin (A)
(cos) - (cos (A)
Sin(β), so sin(A-) = (3/4 * cos(A)) (sin()) - cos()) (cos(A))
sin(A-β) = (3/4) - (4/5) * (sin(A) * (cos(A) * cos())
We can now apply the double angle formula.
cos(2A) = sin2 + cos2(A) (A)
Therefore, cos(A) = (1 - sin(A)2), and sin(A-) = (3/4) * (± √(1 - (3/4)^2) * cos(β)) - (4/5) * (3/4)
sin(A-β) = (3/4) * (± √(1 - (9/16)) * cos(β)) - (3/5)
The formula for sin(A-) is (3/4) * ((7/16) * cos()) - (3/5)
That since exact value of sin(A-) depends on the cos(-) value, which we miss, we are not able to determine the value.
Therefore, using the equation given, it is impossible to figure out the precise value of (A-β).
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A company offers ID theft protection using leads obtained from client banks. Three employees work 40 hours a week on the leads, at a pay rate of $18 per hour per employee. Each employee identifies an average of 4,000 potential leads a week from a list of 4,800. An average of 7 percent of potential leads actually sign up for the service, paying a one-time fee of $90. Material costs are $1,300 per week, and overhead costs are $8,800 per week.
Calculate the multifactor productivity for this operation in fees generated per dollar of input.(Round your answer to 2 decimal places.)
The multifactor productivity for a given operation is 6.16 fees generated per dollar of input.
What is Break Even Point?The Break Even Point, or the inflection point at which a corporation starts to make a profit, is the amount of output required for a company's revenue to equal its total costs.
First, we need to calculate the revenue generated per week:
Potential leads per week = 3 employees x 4,000 leads/employee/week = 12,000 leads/week
Actual sign-ups per week = 12,000 leads/week x 7% = 840 sign-ups/week
Revenue per week = 840 sign-ups/week x $90/sign-up = $75,600/week
Next, we need to calculate the input costs per week:
Labor cost per week = 3 employees x $18/hour x 40 hours/week/employee = $2,160/week
Material cost per week = $1,300/week
Overhead cost per week = $8,800/week
Total input cost per week = $2,160/week + $1,300/week + $8,800/week = $12,260/week
Finally, we can calculate the multifactor productivity:
Multifactor productivity = Revenue per week / Input cost per week = $75,600/week / $12,260/week = 6.16
So the multifactor productivity for this operation is 6.16 fees generated per dollar of input.
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f(x)/g(x)= (x+26)/(14x^2+42x)
Domain restriction for f(x)/g(x) is
x ≠
The domain restriction for f(x)/g(x) is x ≠ 0 or -3
How to find the domain restriction for f(x)/g(x)?The domain of a function is the set of all input values (or "independent variable") for which the function is defined and produces a valid output (or "dependent variable").
In other words, it is the set of all valid input values for which the function will produce a real output and not give an error or undefined result.
But the domain restriction is the set of values that are not allowed as input for the function.
f(x)/g(x) = (x+26)/(14x²+42x)
In order to find the Domain restriction for f(x)/g(x), equate the denominator g(x) to zero and solve for x. That is:
14x²+42x = 0
14x(x + 3) = 0
14x = 0 or x + 3 = 0
x = 0 or x = -3
Thus, the Domain restriction is x ≠ 0 or -3
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Find an equation of a circle that satisfies the given conditions. Center at the origin, passes through (7, 8)
The equation of a circle whose center is at the origin and passes through (7, 8) is x² + y² = 113
Circle is a round geometry whose all points constitute form a path having a constant distance (radius) from a fixed point (center of the circle).
The standard form for the equation of a circle is (x − h)² + (y − k)² = r², where (h,k) is the center of the circle, and r is the radius.
Center = (h,k) = (0,0)
Point = (7,8)
Now we input those values into the equation:
(x − h)² + (y − k)² = r²
(x − 0)² + (y − 0)² = r²
x² + y² = r²
Next, we have to determine the radius. It can be done by applying Pythagoras' Theorem. Look at the picture:
x² + y² = r²
7² + 8² = r²
49 + 64 = r²
113 = r²
Then we go back to the previous equation, and we get:
x² + y² = r²
x² + y² = 113
Thus, the equation of a circle whose center is at the origin and passes through (7, 8) is x² + y² = 113
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