Answers
Answer:
Here we have:
g(x) = 3*f( 2*x - 2) - 1
We want to know the horizontal translation used here.
We need to discuss two types of transformations here.
horizontal translation.
If we have a function f(x), a horizontal translation of N units is written as:
g(x) = f(x + N)
if N is negative, the translation is to the right.
if N is positive, the translation is to the left.
Horizontal dilation.
For a function f(x) an horizontal dilation of scale factor k is written as:
g(x) = f( x/k)
You can see that in our function we have both of these transformations.
Because we compare the translation with f(x), we assume that the horizontal translation is the first thing we did, then we must have
translation:
g(x) = f(x + N)
and now a horizontal dilation of scale factor k
g(x) = f( (x + N)/k)
Then we must have that the argument of the above function is the same as the argument of the given function.
(x + N)/k = 2*x - 2
then:
k = 1/2
(x + N)/1/2 = 2*x + 2*N = 2*x - 2
2*N = -2
N = -2/2 = -1
This means that we have a translation of 1 unit to the right.
Related Questions
The Maid of the Mist is a boat tour at the bottom of Niagara Falls. The boat carries an average of 500 people per day for a fare of $20/each. The operators estimate that for each $1 increase in fare, 20 fewer people will take the trip. (HINT: Revenue = Price x Sales)
What fare will maximize the revenue of the Maid of the Mist boat tours?
Answers
The Maid of the Mist is a boat tour at the bottom of Niagara Falls. the fare that will maximize the revenue of the Maid of the Mist boat tours is $30.
What fare will maximize the revenue of the Maid of the Mist boat tours?Generally, To maximize the revenue of the Maid of the Mist boat tours, we need to find the fare that results in the highest total revenue.
The total revenue is equal to the price of the ticket multiplied by the number of tickets sold. We are given that the boat tour currently charges a fare of $20/each and that for each $1 increase in fare, 20 fewer people will take the trip.
Let's call the number of tickets sold at a given fare "x". We can express the total revenue as a function of the fare as follows:
Total revenue = Fare * x
We are also given that for each $1 increase in fare, the number of tickets sold decreases by 20. We can express this relationship as follows:
x = 500 - (Fare - 20) * 20
Substituting this expression for x into our equation for total revenue, we get:
Total revenue = Fare * (500 - (Fare - 20) * 20)
To find the fare that maximizes the total revenue, we can take the derivative of this function with respect to Fare and set it equal to zero:
d(Total revenue)/d(Fare) = 0 = 1 - (Fare - 20) * 40
Solving for Fare, we find that the fare that maximizes the total revenue is $30.
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When a tractor pulls a plow through an agricultural field, the energy needed to pull that plow is called the draft. The draft is affected by environmental conditions such as soil type, terrain, and moisture. A study was conducted to determine whether a newly developed hitch would be able to reduce draft compared to the standard hitch. (A hitch is used to connect the plow to the tractor.) Two large plots of land were used in this study. It was randomly determined which plot was to be plowed using the standard hitch. As the tractor plowed that plot, a measurement device on the tractor automatically recorded the draft at 25 randomly selected points in the plot. After the plot was plowed, the hitch was changed from the standard one to the new one, a process that takes a substantial amount of time. Then the second plot was plowed using the new hitch. Twenty-five measurements of draft were also recorded at randomly selected points in this plot. a. What was the response variable in this study? Identify the treatments. What were the experimental units? b. Given that the goal of the study is to determine whether a newly developed hitch reduces draft compared to the standard hitch, was randomization used properly in this study? Justify your answer. c. Given that the goal of the study is to determine whether a newly developed hitch reduces draft compared to the standard hitch, was replication used properly in this study? Justify your answer. d. Plot of land is a confounding variable in this experiment. Explain why.
Answers
a. The response variable in this study is the draft.
The response variable is the variable that is being measured or predicted in a study. It is also known as the dependent variable. The treatments are the standard hitch and the new hitch. The experimental units are the 25 randomly selected points in each plot.
b. Yes, randomization was used properly in this study.
By randomly assigning one plot to use the standard hitch and the other plot to use the new hitch, the researcher is ensuring that any difference in draft observed between the two plots is not due to any other factors besides the hitch.
c. No, replication was not used properly in this study. Replication involves taking multiple measurements of the same treatment to ensure that any observed differences between treatments are not due to random variation.
By only taking 25 measurements of each treatment, it is impossible to determine whether any observed differences are due to the treatment or just random variation.
d. Plot of land is a confounding variable in this experiment.
This is because the two plots may differ in soil type, terrain, and moisture, which can all affect the draft. This means that any observed difference in draft between the two plots may be due to the hitch, but it may also be due to the difference in environment between the two plots.
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Solve the following for x
(2x-5)°
Answers
Based on the definition of isosceles triangle, the value of x is: 25.
What is an Isosceles Triangle?An isosceles triangle has two base angles that are equal and are opposite two equal sides.
The image shows an isosceles triangle that is inscribed in the circle. Therefore, the two base angles will each equal (2x - 5).
To find the value of x, create the equation below:
2(2x - 5) + 90 = 180
4x - 10 + 90 = 180
4x + 80 = 180
Subtract 80 from both sides:
4x + 80 - 80 = 180 - 80
4x = 100
Divide both sides by 4:
4x/4 = 100/4
x = 25
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What is the equation for the line that passes through the points (3, 4) and (5,8)?
Answers
Answer:
y=2x-2
Step-by-step explanation:
formula for the equation of a line is y=mx+b
formula for slope is (y2 - y1)/(x2-x1)
which makes the slope 2 (m=2)
then calculate for b which is -2
finally the formula is y = 2x - 2
write the equation in slope intercept form and graph using a table.
x + y = 5
Answers
Answer: y = -x + 5
(0, 5), (1, 4), (2, 3), (3 2) ...
2. The linear equation that represents this table of values is
x
0
1
2
3
y
4
3
2
0
Answers
The required linear equation that represents the table is y = -x + 4.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
Given that,
The values of x are 0, 1, 2, 3,
And values of y are 4, 3, 2, 1.
The linear equation that represents the values, can be written as,
y = -x + 4
When the values of x are substitute in the above equation, the values of y are,
At x = 0, the value of y = 4
At x = 1, the value of y = 3
At x = 2, the value of y = 3
And at x = 3 the value of y = 1
Hence, the required linear equation is y = -x + 4.
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pls help i will mark brainliest
Determine the value of y for the inequality 4 times the quantity y plus one fifth end quantity is less than or equal to four fifths.
y ≥ 0
y ≤ 0
y is greater than or equal to negative 1 over 40
y is less than or equal to negative 1 over 40
Answers
The value of y is less than or equal to 0 (y ≤ 0).
What is inequality?
In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.
Given:
4y + 1/5 ≤ 4/5
We have to find the value of y.
Subtract 1/5 from both sides,
4y + 1/5 - 1/5 ≤ 4/5 - 1/5
4y ≤ 3/5
Multiply both sides by 1/4
4y x 1/4 ≤ 3/5 x 1/4
y ≤ 3/20
y ≤ 0.15
Hence, the value of y is less than or equal to 0 (y ≤ 0).
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Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0
Answers
Answer:
x^4 – 6x^2 – 27 = 0 6(2x + 4)^2 = (2x + 4) + 2 6x^4 = -x^2 + 5Step-by-step explanation:
You want to identify the equations that are quadratic in form.
QuadraticA polynomial equation is "quadratic in form" if the powers of the variables are integer multiples of {0, 1, 2}, or some subset of these that includes 2. That is, it will be "quadratic" if some substitution z = f(x) is possible such that the resulting equation in z is a polynomial equation of degree 2.
x^4 – 6x^2 – 27 = 0Term are degrees 0, 2, 4, so this is "quadratic in form". The substitution z=x^2 will give a quadratic in z.
3x^4 = 2xTerm degrees are 1 and 4, so this is not quadratic.
2(x + 5)^4 + 2x^2 + 5 = 0The substitution z = (x+5)^2 is suggested by the 4th-power term, but the remaining terms cannot be written as a linear function of z. This is not quadratic.
6(2x + 4)^2 = (2x + 4) + 2
This is a straight quadratic equation. One could substitute z=2x+4, but that is not necessary. This is "quadratic in form."
6x^4 = -x^2 + 5Term degrees are 0, 2, 4, so this is "quadratic in form."
8x^4 + 2x^2 – 4x = 0Term degrees are 1, 2, 4, so this is not quadratic.
I can't remember how to do this. I need help with this.
How many roots do the functions have in common?
f(x)=x^2-9
f and g share same roots?
f and g share one root in common but each have another root not shared?
f and g share no roots in common
Answers
Answer:
f and g share no roots in common
Step-by-step explanation:
The roots of [tex]f(x)=0[/tex] are [tex]x=\pm 3[/tex].
From the graph, the roots of [tex]g(x)=0[/tex] are where the graph of [tex]g(x)[/tex] intersects the [tex]x[/tex] axis, which are at [tex]x=2, 10[/tex].
What is the domain and range for this graph?
Answers
The domain is R(-∞,∞) and the range is R(-∞,∞) for this graph.
What do you mean by the domain and range of the graph?
Graphs can be used as another tool for determining the domain and range of functions. The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values. The y-axis on a graph represents the possible output values, or range.
According to the given question,
We have a given graph in the question.
Now, we can see that line on the graph is covering both sides of the x-axis and y-axis on the graph,
Domain of the graph is R(-∞,∞).
Range of the graph is R(-∞,∞).
Therefore, the domain is R(-∞,∞) and the range is R(-∞,∞) for this graph.
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According to the given information the domain of this graph is (− ∞, + ∞) and the range of this graph 2.
What is the range and domain?Graphs may be used as another tool for determining the domain as well as range of functions. The domain of something like a graph is made up of each of the input values displayed on the x-axis since the term "domain" refers towards the set of potential input values. The y-axis of a graph represents the potential output values, or range.
What are domain and range?In order to identify the numbers of something like the autonomous variable x and acquire the domain, we simply solve the formula y = f(x). Simply put, x=g(y) will determine the function's range once we identify g's domain (y).
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A child has the magnet numbers 1 through 50 on their fridge. What is the probability that the child will choose a number that is not a multiple of 9?
Answers
The probability that the child will choose a number that is not a multiple of 9 is 90%.
What is probability?Probability refers to the chance or likelihood that an expected outcome occurs when multiple developments or events could have happened.
Probability describes the ratio between expected favorable outcomes and possible outcomes.
Probability as a ratio is described as a fractional value when it is not 100% certain or uncertain.
In such cases, probability hovers between zero and 1.
The multiples of 9 from 1 through 50 are five (9, 18, 27, 36, and 45).
The other numbers from 1 to 50 are 45 (50 - 5).
The probability of choosing a multiple of 9 is 10% (5/50 x 100).
The probability of choosing a number that is not a multiple of 9 is 90% (45/50 x 100) or (1 - 0.05).
Thus, the probability that the child chooses a non-multiple of 9 between 1 and 50 is 90%.
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Solve for x and show steps . Is the solution extraneous ? Check your work to show how you determined if the solution is extraneous or not
Square 4x-3=5
Answers
The solution of the equation 4x - 3 = 5 is not extraneous .
How to solve an equation?Extraneous solutions are values that we get when solving equations that aren't really solutions to the equation.
Therefore, let's solve the equation to know whether it is extraneous solution.
Hence,
4x - 3 = 5
add 3 to both sides of the equation
4x - 3 + 3 = 5 + 3
4x = 8
divide both sides of the equation by 4
4x / 4 = 8 / 4
x = 2
Therefore, it is not extraneous solution.
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The scale model of a building is 5.4 feet tall.
A. If the
original building is 810 meters tall, what was the scale used to
make the model?
B. If the model is made out
of tiny bricks each measuring 0.4 inch in
height, how many bricks tall is the model?
Answers
Answer:
answer in image blow
Step-by-step explanation:
The length of a piece of wire is 5/6 the length of a rope. The length of a piece of string is 1/4 the length of the rope. The length of the piece of string is 4.5 centimeters. Find the ratio of the length of the piece of wire to the length of the rope to the length of the piece of string.
Show your solution.
Answers
The ratio of the length of the piece of wire to the length of the rope to the length of the piece of string is 6:5:1.5
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
Let the length of the rope = x
Length of a piece of wire = (5/6)x
Length of a piece of string = (1/4)x
Length of the piece of string = 4.5cm
This can be written as,
4.5cm = (1/4)x
45/10 x 4 = x
x = 9 x 2
x = 18 cm
Now,
Length of the rope = 18 cm
Length of a piece of wire = 5/6 x 18 = 15 cm
Now,
Length of the rope : Length of a piece of wire : Length of a piece of string
18:15:4.5
We can simplify the ratio as,
Taking out the common factor 3.
6:5:1.5
Thus,
The required ratio is 6:5:1.5
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Mr. Pinello has 80 colored pencils and 64 markers to divide into containers for his class. He wants each container to have the same number of items. What is the greatest number of containers he can make if he wants each container to have the same number of colored pencils and markers
Answers
The greatest number of containers is 2⁴ = 16 containers.
How to find the greatest number of containers he can make?Since Mr. Pinello has 80 colored pencils and 64 markers to divide into containers for his class. He wants each container to have the same number of items. To find the number of containers, we need to find the highest common factor (H.C.F) of both numbers.
So, writing both numbers in prime factorization, we have
For the 80 colored pencils,
80 = 2 × 2 × 2 × 2 × 5
= 2⁴ × 5
Also, the prime factorization for the 64 markers, we have
64 = 2 × 2 × 2 × 2 × 2 × 2
= 2⁶
So, the highest common factor is 2⁴
So, the greatest number of containers is 2⁴ = 16 containers.
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If a student is chosen at random, what is the probability that: Write your answers in percent form. Round to the nearest tenth of a percent. a) The student has competed in none of the categories? b) The student has competed in all three of these categories? c) The student has competed in Smooth or Standard, but not Rhythm? d) The student has competed in Rhythm and Standard, but not Smooth? e) The student has competed in Rhythm.
Answers
The student has completed in Rhythm will be 57.7%
What is probability ?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics. Probability determines the likelihood of an event occurring: P(A) = f / N. Odds and probability are related but odds depend on the probability. You first need probability before determining the odds of an event occurring.
To find,
a) The student has competed in none of the categories is 10.3%
b) The student has competed in all three of these categories is 14.1%
c) The student has competed in Smooth or Standard, but not Rhythm
d) The student has competed in Rhythm and Standard, but not Smooth is 17.9%
The student has completed in Rhythm will be 57.7%
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Find the surface area of the cylinder in terms of pi
Answers
Surface area of the cylinder is 211.5 [tex]cm^{2}[/tex]
What is Surface area of the cylinder?The entire area that is occupied by the flat surfaces of the cylinder's bases and its curving surface is known as the surface area of a cylinder.
A cylinder's volume is π r² h, and its surface area is 2π r h + 2π r².
Diameter is 9 cm, and height is 19 cm,
therefore r = 4.5 cm and height is 19 cm.
A = 2 r² π + 2 r π h
A = 2 * 4.5*4.5 π + 2 ·* 4.5* 19 π
A = 40.5 π + 171 π
A = 211.5 [tex]cm^{2}[/tex]
Surface area of the cylinder is 211.5 [tex]cm^{2}[/tex]
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Which of the following describes a situation in which the total distance a baseball player travels is 0 meter from his starting point? (5 points)
The player runs 3 meters forward and then runs 3 meters in the opposite direction.
The player runs 4 meters forward and then runs 3 meters in the opposite direction.
The player runs 3 meters forward and then runs 0 meter in the opposite direction.
The player runs 3 meters forward and then runs 4 meters in the opposite direction.
Answers
The total distance a baseball player travels is 0 meter from his starting point in the first case when he runs 3 meters forward and then runs 3 meters in the opposite direction.
What is distance ?
A measurement of how far away two things or points are might be quantitative or occasionally qualitative.
If an object covers the same distance in the forward and opposite direction, it will cover 0 meter from his starting point.
It happens because when it covers a distance say 5 Km in forward direction and then, when it goes in the opposite direction with equal distance, it reaches to its starting point from where it was started.
Hence, If the player runs 3 meters forward and then runs 3 meters in the opposite direction, h will be at his starting point or we can say, he will cover 0 meter from his starting point.
However, in all other cases, the distance is not equal in both forward and opposite direction.
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A waterfall has a height of 1200 feet. A pebble is thrown upward from the top of the falls with an initial velocity of 20 feet
per second. The height, h, of the pebble after t seconds is given by the equation h= -16+201+1200. How long after
the pebble is thrown will it hit the ground? Use a graphing calculator to solve the problem.
Help pleasee asap
Answers
Answer:
Below
Step-by-step explanation:
h = height = 0 when it hits the ground
sooooo...
0 = -16t^2 + 20t + 1200 <==== you equation ommited the t' s and 20t
Use Quadratic Formula a = -16 b = 20 c = 1200
to find t = 9.3 s
6.20 Let the random variable Y possess a uniform distribution on the interval (0, 1). Derive the a distribution of the random variable W = Y. b distribution of the random variable W = VY.
Answers
Distribution of the random variable W = Y. b distribution of the random variable W = VY is derived.
What is Random Variable?
A continuous random variable is a random variable where the data or value can assume infinitely many values ( meaning it’s a continuous set of data. )
For example a random variable measuring the time taken for someone to cook rice is continuous since there are an infinite number of possible times that can be done.
a) If the random variable Y has a uniform distribution on the interval (0, 1), then the probability density function (PDF) of Y is given by:
[tex]f_Y(y) = 1 for 0 < y < 1[/tex]
= 0
If we let W = Y, then the PDF of W is simply the same as the PDF of Y, since W and Y are equal. Therefore, the PDF of W is given by:
[tex]f_W(w) = 1 for 0 < w < 1[/tex]
= 0
b) If we let W = VY, where V is a constant, then the PDF of W is given by:
[tex]f_W(w) = f_Y(w/V) / |V|[/tex]
Substituting in the expression for the PDF of Y, we get:
[tex]f_W(w) = 1/|V| for 0 < w/V < 1[/tex]
= 0
If V > 0, then this reduces to:
[tex]f_W(w) = 1/V for 0 < w < V[/tex]
= 0
If V < 0, then the range of w is reversed and the PDF becomes:
[tex]f_W(w) = -1/V for V < w < 0[/tex]
= 0
The normalization factor [tex]|V|[/tex] is necessary because the transformation
W = VY stretches or compresses the original uniform distribution on the interval (0, 1) by a factor of [tex]|V|[/tex].
Hence, Distribution of the random variable W = Y. b distribution of the random variable W = VY is derived.
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find the range of the function y = 1/2x + 2 if the domain is {-4, -2, 0}
Answers
The range of the function y = 1/2 x + 2 is {0, 1, 2}, if the domain of the function is {-4, -2, 0}.
What is function?An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable.
The given function is,
y = 1/2 x + 2.
Also, the domain of the function is {-4, -2, 0}.
Since, the domain of the functions defines the values of x,
And range defines the value of y in function.
The value of y at x = -4
y = 1/2(-4) + 2 = -2 + 2 = 0
At x = -2,
y = 1/2(-2) + 2 = -1 + 2 = 1
At x= 0,
y = 1/2 (0) + 2 = 2
The values of y are 0, 1 and 2.
Hence, the range of the function is {0, 1, 2}.
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PLEASE HELP ASAP The set of all numbers greater than -10 and less than -3
Answers
Answer
-15
Step-by-step explanation: your welcome
What fraction is equal to 75% of 1/2
Answers
Answer:
equal 3/8 or 0.375 siuuuuu
The monthly salaries (in thousands of dollars) of a sample of 5 sales representatives are as follows.
8, 6, 12, 11, 13
Send data to calculator
Find the standard deviation of this sample of monthly salaries. Round your answer to two decimal places.
0
Answers
The standard deviation of the sample of monthly salaries is 2.74
What is Standard deviation?The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the deviation of each data point from the mean, the standard deviation may be determined as the square root of variance. The bigger the deviation within the data collection, the further the data points deviate from the mean; hence, the higher the standard deviation, the more dispersed the data.
>Standard deviation gauges a dataset's dispersion from its mean.
>It is determined as the variance's square root.
Detailed Calculation:Mean = [tex]\frac{(8+6+12+11+13)}{5} = 10[/tex]
Variance = [tex]\frac{((8-10)^{2}+(6-10)^{2}+(11-10)^{2}+(13-10)^{2} )}{(5-1)} = 6[/tex]
Standard deviation = [tex]\sqrt{7.5} = 2.7386[/tex]
when rounded off to two decimals 2.7386≈2.74.
The standard deviation of the sample of monthly salaries is 2.74
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Which of the following is the best description of a simple random sample of size n from a population of size N.
A) Any method of sampling in which individuals are selected in a completely haphazard fashion.
B) Any method of sampling in which every group of individuals of size n is equally likely to be selected.
C) Any method of sampling in which every individual is equally likely to be selected.
D) Any method of sampling in which each individual has a probability of n/N of being selected.
E) Any method of sampling that involves the use of a random digits table.
Answers
The best description of a simple random sample of size n from the population of size N is that any method of sampling in which every individual is equally likely to be selected. The correct answer is option C.
What is simple random sampling?Simple random sampling is a kind of probability sampling in which the researcher randomly chooses a subset of participants from a population. Every member of the population has an equal chance of being chosen. Then, the data is collected from as large a percentage as possible of this random subset.
A simple random sample is identical to a random sample. The difference is that in a simple random sample, each member in the population has an equal chance of being selected. With random sampling, each member does not automatically have an equal chance of being selected.
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What is the area of the remaining figure?
Answers
Answer:
136 in^2
Step-by-step explanation:
The rectangle withOUT the missing part is 20 X 8 = 160 in^2
now subtract the 4-12 traingle
160 - 1/2 (4 X 12) = 136 in^2
Answer:
area of triangle = 1/2bh
= 1/2(4)(20-8)
= 1/2(4)(12)
= 24 in²
area of rectangle = lw
= 20(8)
= 160 in²
answer
= area of rectangle - area of triangle
= 160 - 24
= 136 in²
Therefore, the area of the remaining figure is 136 in²Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-In a right triangle the length of a hypotenuse is c and the length of one leg is a. Find the length of the other leg b, if:
c=5, a=3
Answers
Answer:
b=4
Step-by-step explanation:
[tex]a^{2}+b^{2}=c^{2}[/tex]
[tex]3^{2}+b^{2}=5^{2}[/tex]
[tex]9+b^{2}=25[/tex]
[tex]b^{2}=16[/tex]
[tex]\sqrt{b^{2}} = \sqrt{16}[/tex]
b=4
Which of the following are irrational? Explain how you know?
a. √27
b. 5.0287
c. √49
d. _³√125
Answers
c. √49 and d. _³√125 are irrational numbers .
RATIONAL NUMBERS
A rational number is a number that can be written in the form p/q , where p and q are integers and q ≠ o.
IRRATIONAL NUMBER
An irrational number is a number that cannot be written as the ratio of two integers. Its decimal form does not stop and does not repeat.
a. √27 = 5.196152.
Do you think the decimal part stops after 5.196152? No, it is never-ending. Therefore, it is a non-terminating decimal with non-repeating numbers.
The number 5.1961524227... can't be written in p/q form. So √27 is an irrational number.
b . The number 5.1961524227... can't be written in p/q form. So it is an irrational number.
c. The number √49 can be written in p/q form as 7/1 . So √49 is an irrational number.
d. The number 3√125 can be written in p/q form as 5/1 . So it is an irrational number.
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The supply and demand curves for a business dealing with wheat are:
Supply: p = 1.55 + 0.00014x^2
Demand: p = (2.358 - 0.007x)^2
where p is the price in dollars per bushel and x is the quantity in bushels per day. Use a graphing utility to graph the supply and demand equations and find the market equilibrium. (The market equilibrium is the point of intersection of the graphs for x > 0. Round your answers to 2 decimal places.)
x= ________ bushels
p = $_________
Answers
Given curves:
p = 1.55 + 0.00014x²p = (2.358 - 0.007x)²See the attached, where both curves and their intersection is shown.
According to this we have:
x = 96.05p = $2.84Answer:
x = 96.05 bushels
p = $2.84
Step-by-step explanation:
Graph the two equations (see attachment).
The market equilibrium is the point of intersection of the graphs for x > 0.
From inspection of the graph, the point of intersection is (96.05, 2.84).
Therefore:
x = 96.05 bushelsp = $2.84Julian's carpet has an area of 160 square feet. He hires the Carpet Pro carpet cleaning service, which is able to clean 9 square feet of his carpet every minute. Therefore, in the first minute, CarpetPro is able to clean 9 square feet of Julian's carpet (leaving 151 square feet remaining to be cleaned). In the second minute, the cleaner is again able to clean 9 square feet of carpet (leaving 142 square feet to be cleaned), etc. Which of the following functions expresses the number of square feet that still remain to be cleaned after t minutes from the time that the carpet cleaner began cleaning this carpet. O A(t) = 220 - 9t O A(t) = 220 - 0.1^t O A(t) = 220(0.1)^t O A(t) = 220(0.9t) O A(t) = 220 - 0.9t
Answers
The function that expresses the area of the 160 square feet carpet remaining after t minute is; A(t) = 160 - 9·t
What is a mathematical function?A function is a rule that maps the elements of a set known as the input of the function, to the elements of another set, known as the output of the function, such that each element of the input is mapped to exactly one element of the output set.
The area Julian's carpet covers = 160 square feet
The area the Carpet Pro cleaning service is able to clean every minute = 9 square feet.
A table of values showing the area of the carpet remaining after each minute of cleaning by Carpet Pro, can be presented as follows;
Time, t (minute) [tex]{}[/tex] Area remaining to be cleaned (square feet), A(t)
0 [tex]{}[/tex] 160
1 [tex]{}[/tex] 151
2 [tex]{}[/tex] 142
3 [tex]{}[/tex] 133
4 [tex]{}[/tex] 124
5 [tex]{}[/tex] 115
The change in the area of the carpet remaining is a constant and therefore, the first difference of the values in the above table is a constant which indicates that the relationship is a linear relationship, with an equation of the form y = m·x + c
Where;
m = The slope = (151 - 160)/(1 - 0) = -9
c = The y-intercept The value of the function when the input (time) is zero, which is 160
c = 160
x = The number of minutes that elapse, t
y = The number of square feet remaining after t minutes, A(t)
Plugging in the above value, we get;
A(t) = -9·yt + 160
The function that expresses the number of square feet remaining A(t) after t minutes from the time the carpet cleaner began cleaning the carpet is; A(t) = 160 - 9·t
The possible options based on a similar question posted online and the 160 square feet area of the carpet specified in the question are;
A(t) = 160 - 9·t
A(t) = 160 - 0.1^t
A(t) = 160·(0.1)^t
A(t) = 160·(0.9·t)
A(t) = 160 - 0.9·t
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