9514 1404 393
Answer:
a) f: all real numbers except 1 and 2; g: all real numbers except 2
b) f(x) = 5/(x -2) . . . . x = 2 is a vertical asymptote
c) f(x) = -5/4, -5/3, -5/2, undefined, undefined, 5, 5/2
g(x) = -5/4, -5/3, -5/2, -5, undefined, 5, 5/2
d) f(x) is also undefined at x=1
Step-by-step explanation:
a) Any question about the domain of a function concerns the values of the variable for which the function is defined, or not. A rational function, such as these, will be undefined when its denominator is zero. So the question of domain becomes a question of the values of x that make the denominator zero.
The zeros of the denominator of f(x) can be found by factoring it.
x^2 -3x +2 = (x -1)(x -2)
These factors are zero when x=1 and when x=2. Hence, these values are excluded from the domain of f(x).
domain of f(x): all real numbers except x=1 and x=2
Then, by inspection, the domain of g is similar, but a little different:
domain of g(x): all real numbers except x=2
__
b) Based on our work for part (a), we find that f(x) can be factored and simplified like this.
\(f(x)=\dfrac{5x-5}{x^2-3x+2}=\dfrac{5(x-1)}{(x-1)(x-2)}\\\\\boxed{f(x)=\dfrac{5}{x-2}\quad x\ne1}\)
There will be a vertical asymptote at x=2. The attachment shows a graph of f(x) with its vertical asymptote.*
__
c) The difference between the two functions is that f(x) is undefined at x=1.
x = -2, -1, 0, 1, 2, 3, 4
f(x) = -5/4, -5/3, -5/2, undef, undef, 5, 5/2
g(x) = -5/4, -5/3, -5/2, -5, undef, 5, 5/2
__
d) The functions differ in that f(x) is undefined at x=1, whereas g(x) is not.
_____
* The fact that f(x) is undefined at x=1, but there is no vertical asymptote at that point, means the function has a "hole" in its graph there. This is illustrated on the graph by an open circle, meaning the function is not defined at that point.
A study comparing one group of participants who are randomly assigned to receive a drug with another group of participants who are randomly assigned to receive a placebo is called a _____ research design.
A study comparing one group of participants who are randomly assigned to receive a drug with another group of participants who are randomly assigned to receive a placebo is called a randomized controlled trial (RCT).
The purpose of an RCT is to evaluate the effectiveness of a treatment or intervention by comparing it to a control group that receives a placebo or alternative treatment. This design is commonly used in clinical research to establish causal relationships between treatments and outcomes.
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find the area of this shape
please
Total area = 12 + 18 = 30cm²
Answer:
Area of the right angled triangle:-
= height × base ÷ 2
= 4 cm × 6 cm ÷ 2
= 4 cm × 3 cm
= 12 cm²
Area of the rectangle:-
= length × breadth
= 6 cm × 3 cm
= 18 cm²
Area of the figure:-
= 12 cm² + 18 cm²
= 30 cm²
Last year, a car dealership sold 144 new cars and 108 used cars. Since then, the number of new cars sold is increasing by 8 cars each year, while the number of used cars sold has been decreasing by 5 cars each year.
In how many years will the number of new cars sold be twice the number of used cars sold?
A. 2 years
B. 4 years
C. 6 years
D. 0 years
The diameter of a circle increased from 25cm to 25.8cm. Find the percentage increase in its circumference.
Answer:
3.1% increase
Step-by-step explanation:
Diameter1=25cm
Radius1=12.5cm
Circumference1=2x22/7x12.5
Diameter2=25.8cm
Radius2=12.9cm
Circumference2=2x22/7x12.9
% increase =Circumference2-Circumference1/Circumference2 x 100%= 2x22/7x12.9-2x22/7x12.5 / 2x22/7x12.9 x100%
12.9-12.5/12.9 x 100%
0.4/12.9 x 100%
4/129 x 100%
3.1%
Factor: 117n + 90
Show your work don’t solve for n
To factor an expression, we can identify common factors between each terms, and take them out.
Solving the Question117n + 90
Both terms have the common factor of 9. Factor this out:
= 9(13n + 10)
13 and 10 do not have a common factor. Therefore, this is the final factored expression.
Answer9(13n + 10)
A demographer predicts that the population, P, of a town t years from now can be modeled by the function P(t) = 6t^4 - 5t^3 + 200t + 12000. What will the population of the town be two (2) years from now?
A demographer predicts that the population, P, of a town t years from now can be modeled by the function P(t) = 6t^4 - 5t^3 + 200t + 12000. What will the population of the town be two (2) years from now?
SOLUTION:To calculate the population of the town be two (2) years from now, replace t into 2:
\( \dashrightarrow \sf{P(t) = 6t^4 - 5t^3 + 200t + 12 \: 000}\)
\(\sf\dashrightarrow \sf{P(2) = 6(2)^4 - 5(2)^3 + 200(2) + 12\:000}\)
\(\dashrightarrow \sf{P(2) = 6(16) - 5(8) + 200(2) + 12\:000}\)
\(\dashrightarrow \sf{P(2) = 96 - 40 + 400 + 12\:000}\)
\( \dashrightarrow\sf{P(2) = 56 + 400 + 12\:000}\)
\( \dashrightarrow\sf{P(2) = 456 + 12\:000}\)
\( \dashrightarrow\sf{P(2) = 12\:456}\)
ANSWER:The population of the town be two (2) years from now is 12, 456.If you would like to learn more about functions, kindly please take your time to visit this following links:
https://brainly.com/question/13654156https://brainly.com/question/26382648https://brainly.com/question/4883547https://brainly.com/question/25653505https://brainly.com/question/12195089Which values are in the solution set of the inequality -23x+13≥-1?
Answer:
x = 0
Step-by-step explanation:
-23 × 0 = 0
0 + 13 = 13
13 > -1
Can u please help?.........................
The coordinates of the point P on the directed line segment that partitions the segment into a ratio of 2 to 3 is the ordered pair (3, 0).
How to determine the coordinates of point P?In this scenario, we would use line ratio to determine the coordinates of the point P on the directed line segment that partitions the segment into a ratio of 3 to 2.
In Mathematics, line ratio can be used to determine the coordinates of the point P and this is modeled by this mathematical expression:
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
Substituting the given parameters into the line ratio formula, we have;
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
P(x, y) = [(2(9) + 3(-1))/(2 + 3)], [(2(6) + 3(-4))/(2 + 3)]
P(x, y) = [(18 - 3)/(5)], [(12 - 12)/5]
P(x, y) = [15/5], [0/5]
P(x, y) = [3, 0]
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Complete Question:
Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(-1, -4), B(9, 6); to 3. The coordinates of P are?
Write the equation of the line tangent to \( f(x)=x^{5} \) when \( x=-2 \) \[ y=-80 x-192 \] \[ y=80 x-192 \] \[ y=80 x+128 \] \[ y=-80 x+128 \]
According to the question the equation of the line tangent to \(\( f(x) = x^5 \) when \( x = -2 \) is \( y = 80x + 128 \).\)
To find the equation of the line tangent to \(\( f(x) = x^5 \) when \( x = -2 \)\), we need to determine the slope of the tangent line at that point and use the point-slope form of a linear equation.
The derivative of \(\( f(x) \) is \( f'(x) = 5x^4 \).\)
Substituting \(\( x = -2 \)\) into the derivative, we get \(\( f'(-2) = 5(-2)^4 = 80 \).\)
The slope of the tangent line is 80, and we have the point \(\((-2, f(-2)) = (-2, (-2)^5) = (-2, -32)\).\)
Using the point-slope form, the equation of the tangent line is:
\(\[ y - (-32) = 80(x - (-2)) \]\)
Simplifying:
\(\[ y + 32 = 80(x + 2) \]\)
\(\[ y + 32 = 80x + 160 \]\)
\(\[ y = 80x + 128 \]\)
Therefore, the equation of the line tangent to \(\( f(x) = x^5 \) when \( x = -2 \) is \( y = 80x + 128 \).\)
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According to the question the equation of the tangent line to y = 80x + 120.
To find the equation of the line tangent to, we need to determine the slope of the tangent line at that point and use the point-slope form of a linear equation.
\(\( f(x)=x^{5} \)\)
The derivative of
f'(x) = 5x⁴
Substituting into the derivative, we get
f(-2) = x⁵ = (-2)⁵ = -32
f'(-2) = 5(-2)⁴ = 80
The slope of the tangent line is 80, and we have the point
Using the point-slope form, the equation of the tangent line is:
y - f(x) = f'(x) (x + 2)
y = 80x + 120.
Therefore, the equation of the line tangent to y = 80x + 120.
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What is the weight of a 24 square foot 2 inch thick aluminum plate with a unit weight of 15 lbs?
Weight of a 24 square foot, 2 inch thick aluminum plate will be: 720 lbs.
What is unitary method?A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.
Given:
Weight of 1 square foot, 1 inch thick plate = 15 lbs.To find: weight of a 24 square foot, 2 inch thick aluminum plate
Finding:
By unitary method, we get:
Weight of 1 square foot aluminum plate = 15 lbs.
Weight of 24 square foot aluminum plate = 15(24) lbs = 360 lbs.
Again, by unitary method, we get:
Weight of 1 square foot, 1 inch thick aluminum plate = 15 lbs.
Weight of 24 square foot, 1 inch thick aluminum plate = 15(24) lbs = 360 lbs.
Weight of 24 square foot, 2 inch thick aluminum plate = 360(2) lbs = 720 lbs.
Hence, Weight of 24 square foot, 2 inch thick aluminum plate = 720 lbs.
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1.55y-(5y-17)/100=0.02
Answer:
Multiply to remove the fraction, then set equal to 0 and solve.
Exact Form: y = − 1/10
Decimal Form: y = − 0.1
Step-by-step explanation:
Answer:
y = -1/10 or -0.1
Step-by-step explanation:
Multiply both sides of the equation by 100.
To find the opposite of 5y−17, find the opposite of each term.
The opposite of −17 is 17.
Combine 155y and −5y to get 150y.
Subtract 17 from both sides.
Subtract 17 from 2 to get −15.
Divide both sides by 150.
Reduce the fraction
to lowest terms by extracting and canceling out 15.
Suad Alwan, the purchasing agent for Dubai Airlines, has determined that the second plane took 20,000 hours to produce. Using an 80% learning curve and a $35-per-hour labor change, he wants to determine the cost of the four additional planes. Time required for the fourth unit = hours (round your response to the nearest whole number).
Based on an 80% learning curve and the given information that the second plane took 20,000 hours to produce, the time required for the fourth unit is approximately 10,714 hours.
The learning curve concept suggests that as cumulative production doubles, the time required to produce each unit decreases by a certain percentage. In this case, the learning curve is 80%, meaning that the time required to produce each subsequent unit decreases by 20%.
To determine the time required for the fourth unit, we can use the learning curve formula:
Time for nth unit = Time for the first unit * (n^log(learning curve))
Given that the second plane took 20,000 hours to produce, we can use this information to calculate the time for the fourth unit:
Time for fourth unit = 20,000 * (4^log(0.8))
Evaluating the expression, we find that the time required for the fourth unit is approximately 10,714 hours.
Therefore, according to the 80% learning curve, the fourth unit would require approximately 10,714 hours to produce.
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find a linear and an exponential equation that matches f(2)=12 and f(4)=48
The exponential equation that matches the coordinate is 3(2)^x while the linear equation is y = 6x
Exponential equationThe standard exponential equation is expressed as y= ab^x
where
a is the base
x is the exponent
Given the coordinates (2, 12) and (4, 48)
12 = ab^2
48 = ab^4
Find the ratio
4 = b^2
b = 2
Sice ab^2 = 12
4a = 12
a = 3
The exponential equation that matches the coordinate is 3(2)^x
For the linear equation
The standard form is y = mx + b
m is the slope = 48-12/4-2
Slope = 12/2
Slope = 6
For the y-intercept
12 = 6(2) + b
b = 0
Hence the required linear equation is. y = 6x
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Someone help me out with this
If your good at math PLEASE HELP ME!
Katherine bought some cans of sardines and corned beef. She gave the store owner Php 200 as payment. However, the owner told her that the amount is not enough. What could be the reasons? What mathematical statement would represent the given situation?
Answer:
need more info
Step-by-step explanation:
i need more information to answer this
If a cube has a side length of 5 inches, what would be the volume of that
cube?
2 points
*
Answer:
125 inches^3
Step-by-step explanation:
To solve for cubes it is L^3 or Length Cubed. Whcih is simply L×L×L where L is Length.
Which expression does not factor? m3 1 m3 – 1 m2 1 m2 – 1
The expression that does not factor on the mentioned is m² + 1.
Why it cannot be factor?Because other expression can be factored, while m² + 1 has no factor form. For make it clear we can calculate to find the form expression and find the calculate power or result.
m³ + 1 =
The formula to calculate it is, a³ + b³ = m³ + 1³ And then it could be, (m + 1) (m² - m + 1).m³ - 1 =
The formula to calculate it is, a³ + b³ = m³ - 1³ a³ + b³ = (a + b) (a² - ab + b²)And then the power could be, (m - 1)(m² + m + 1²) = (m-1)(m² + m + 1).m² - 1 =
The formula to calculate it is, a² - b² = (a + b)(a - b).and then it could be, m² - 1 = (m + 1)(m - 1).
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What does the Harby-Weinberg equation?
The equation is represented as follows:
p^2 + 2pq + q^2 = 1
The Hardy-Weinberg equation is a mathematical formula used in genetics to predict the frequency of genetic traits in a population. The equation is named after the scientists G. H. Hardy and W. Weinberg, who independently developed it in 1908 and 1909, respectively.
The equation states that the frequency of a genetic trait in a population will remain constant over time as long as certain conditions are met. These conditions are:
No mutations occur in the gene responsible for the trait
There is no natural selection for or against the trait
There is random mating within the population
The population size is large
The Hardy-Weinberg equation can be used to calculate the frequency of the dominant and recessive alleles (versions of a gene) in a population, and the probability of different genotypes (the combination of alleles an individual has) and phenotypes (the physical expression of the trait) within that population.
Where p is the frequency of the dominant allele, q is the frequency of the recessive allele, and p^2 represents the proportion of homozygous dominant individuals, 2pq represents the proportion of heterozygous individuals and q^2 represents the proportion of homozygous recessive individuals.
The Hardy-Weinberg equation is a useful tool for understanding how genetic traits are inherited and how they change over time. It is widely used in population genetics, evolutionary biology and medical genetics.
It is also important to notice that the Hardy-Weinberg equilibrium is a theoretical concept that is rarely met in real populations due to the existence of genetic drift, migration, mutation, nonrandom mating and natural selection.
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evaluate the expression:2(x^2-1)+4y when x=4 and y=3
Step-by-step explanation:
To evaluate the expression 2(x^2-1)+4y when x=4 and y=3, we substitute x=4 and y=3 into the expression and simplify:
2(x^2-1)+4y
= 2(4^2-1)+4(3) (substitute x=4 and y=3)
= 2(16-1)+12
= 2(15)+12
= 30+12
= 42
Therefore, when x=4 and y=3, the value of the expression 2(x^2-1)+4y is 42.
What is the value of cos Z?? HeLP
Answer:
Below
Step-by-step explanation:
Remember for RIGHT triangle , Cos Z = adjacent leg / hypotenuse
cos z = 48/50 = 24/25
A student investigating study habits asks a simple random sample of 16 student at her school how many minutes they spent on their English homework the previous night. Suppose the actual parameter values for this variable are mu = 45 minutes and sigma = 15 minutes. Which of the following best describes what we know about the sampling distribution of means for the student's sample? O mu x = 45; sigma x unknown; shape of distribution unknown O mu x = 45; sigma x = 15; distribution approximately Normal O mu x = 45; sigma x = 15; shape of distribution unknown O mu x = 45; sigma x = 3.75; distribution approximately Normal O mu x = 45; sigma x = 3.75; shape of distribution unknown
The best description about the sampling distribution of means for the student's sample is mu x = 45, sigma x = 3.75, shape of distribution unknown.
What is Sampling Distribution?Sampling distribution is defined as the probability distribution of a statistical measure which is got by the repeated sampling of a specific population.
Given that,
μ = 45 minutes and σ = 15 minutes
Sampling distribution of means for the student's sample is :
μₓ = μ = 45
σₓ = σ / √n, where n is the sample size.
σₓ = 15 / √(16) = 15 / 4 = 3.75
Now since the sample size 16 which is less than 30, shape of the distribution is unknown.
Hence the sampling distribution is, μₓ = 45, σₓ = 3.75, and the shape of distribution is unknown.
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The student performed a different single transformation on PQR to create JKL. The coordinates of vertex K are (4,1). What could be the single transformation the student performed?
The single transformation which this student performed include the following: a reflection over the y-axis.
What is a reflection over the y-axis?In Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).
By applying a reflection over the y-axis to the coordinate of the given triangle PQR, we have the following coordinates:
(x, y) → (-x, y).
Coordinate P = (-1, 1) → Coordinate J' = (-(-1), 1) = (1, 1).
Coordinate Q = (-4, 1) → Coordinate K' = (-(-4), 1) = (4, 1).
Coordinate R = (-4, 4) → Coordinate L' = (-(-4), 4) = (4, 4).
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2. The table shows distance, y, that Mario runs in x minutes.
Mario’s Running Speed
Time,
(min) Distance,
(mi)
7 | 1
21 | 3
35 | 5
(a) Based on the information in the table, write an equation that can be used to model the relationship between the time (x) and distance (y). Show your work.
(b) What is the rate of change for this linear relationship? Show your work.
(c) What is Mario’s distance given that he ran for 70 minutes? Show your work.
Answer:
Two players, A and B alternatively toss a fair coin (A tosses the coin first, then B tosses the coin, then A, then B and so on). The sequence of heads and tails is recorded. If there is a head followed by a tail (HT sub-sequence), the game ends and the person who tosses the tail wins. What is the expected length of this game? Let T number of coin tosses until the game ends. Find E(T). Round answer to 3 decimals
The E(T) is 4 when A and B, two players, alternately toss a fair coin (A tosses the coin first, then B tosses the coin, then A, then B and so on).
Given that,
A and B, two players, alternately toss a fair coin (A tosses the coin first, then B tosses the coin, then A, then B and so on). The heads and tails are recorded in order. The game is over and the winner is the person who throws the tail if there is a head followed by a tail (HT sub-sequence).
We have to find what is the anticipated game length. Let the game continue for T number of coin tosses. Find E (T).
We know that,
Here,
E(T )=first time sequence HT occurs
E(T) = P(first H)× P(expected number till 1st T |first H)+ P(first T)× P(expected number till 1st HT |first T)
E(T) =0.5×(1+2)+0.5×(1+E(T))
0.5×E(T)=0.5×4
E(T) =4
Therefore, The E(T) is 4 when A and B, two players, alternately toss a fair coin (A tosses the coin first, then B tosses the coin, then A, then B and so on).
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Solve for t:
t + 7 = 21
A: t= 28
B: t= 14
C: t= -28
D: t= -14
t + 7 = 21
---Subtract 7 from both sides
t + 7 - 7 = 21 - 7
t = 14
Hope this helps!! :)
Answer:
B) t = 14
Step-by-step explanation:
3. Jess starts a savings account using
a $50,000 life insurance inheritance
when she is 22 years old. Jess wants
to retire when the account has one
million dollars. If the account's
interest rate is 9% compounded
annually, calculate how long it will
take to reach one million dollars. At
what age will Jess retire?
Jess will retire at about 41.98 years historic or round her forty second birthday.
To calculate how lengthy it will take for Jess's financial savings account to attain one million dollars, we can use the system for compound interest:
A = P(1 + r/n)(nt)
Where:
A = Total quantity (one million bucks in this case)
P = Principal quantity (initial credit score of $50,000)
r = Annual hobby price (9% as a decimal, so 0.09)
n = Number of instances the hobby is compounded per yr (in this case, compounded annually)
t = Number of years
Substituting the given values into the formula, we have:
1,000,000 = 50,000(1 + 0.09/1)(1t)
Simplifying:
20 = (1.09)t
To clear up for t, we want to take the logarithm of each aspects of the equation. Let's use the herbal logarithm (ln) for this calculation:
ln(20) = ln(1.09)t
Using the logarithmic property, we can go the exponent t in front:
ln(20) = t * ln(1.09)
Now we can remedy for t with the aid of dividing each aspects by using ln(1.09):
t = ln(20) / ln(1.09)
Using a calculator, we discover that t ≈ 19.98 (rounded to two decimal places).
Therefore,
It will take about 19.98 years to attain one million bucks in Jess's financial savings account.
To decide at what age Jess will retire, we add the time it takes to attain one million bucks to her preliminary age of 22:
Age at retirement = 22 + 19.98 ≈ 41.98
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*50 POINTS*
Select each function that has an inverse that is also a function for all values of x.
A. F(x) = 2x^2 + 4x - 3
B. F(x) = 2x + 3
C. F(x) = 3/2(x) + 2
D. F(x) = 2x^3 + 2
E. F(x) = 2x^4 + 3x^2 - x + 1
Considering the condition for an inverse function, it is found that the functions that also have an inverse for all values of x are given by:
B. F(x) = 2x + 3
C. F(x) = 3/2(x) + 2
D. F(x) = 2x^3 + 2
What is the condition for an inverse function?A function f(x) has an inverse if it does not have any horizontally aligned points, that is, if f(a) = f(b), then a = b.
Polynomial functions of even degrees have horizontally aligned points, hence functions A and E do not have inverses.
The other polynomial functions, with odd degrees, have inverses.
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PLEASE HELP I WILL MARK YOU BRAINLIEST PLEASE.
Answer:
The length of the piggy bank is 6 cubic inches long, and the height of the piggy bank is 8 cubic inches high. So next, you multiply 6 and 8 together, which is 48. Therefore, the volume of the piggy bank is 48 cubic inches^3.
Step-by-step explanation:
30pts!!!
What is the value of y?
Enter your answer in the box.
Answer:
x = 5
y = 15
Step-by-step explanation:
This is an isosceles triangle so angles ∠B and ∠C are congruent.
We can write the following equation to first find the value of x then the value of y:
5x = 25
Divide both sides by 5.x = 5
The sum of interior angles in a triangle is equal to 180°.
25 + 25 + 7y + 25 = 180
Add like terms.75 + 7y = 180
Subtract 75 from both sides to isolate the variable.7y = 105
Divide both sides by 7.y = 15
What does this mean?
Suggested to look at picture
Linear functions: Y = mx + b
m = slope (rate of change) ***when it is linear, the slope is constant.
b = y-intercept (starting point)
x = input
y = output
y = 8 - 1.25x
Answer:
Step-by-step explanation:
You need to find out if the equation is linear or not. A linear equation will have a constant change. So as x increases by 1, y decreases by 1.25. You would check every line given and see if it continues the same. If so then it is a linear equation. Your slope is the rate of change, meaning how much does x and y increase or decrease. Your b is where the equation starts. You would find b at the top of the table. The first # on this is 0. 8 is your b. x is the input that is multiplied to the slope to receive the output:y.