A real estate company balances the books for its business on the first day of each month. It hopes to sell houses every other day of the month. The average number of houses, S, the company sells each day, t, is represented by the inverse of the function Inverse of S is equal to the quantity t squared plus 3 times t minus 4 end quantity over the quantity t squared minus 6 times t plus 6 end quantity
Which equation represents the average sales each day for the real estate company?
Answers
An inverse function which represents the average sales each day for the real estate company is: D. S⁻¹ = (t + 4)/(t - 5).
How to determine equation?In order to determine equation which represents the average sales each day for the real estate company, we would factorize the numerator and denominator of the given inverse function as follows:
Numerator = t² + 3t - 4
Next, we would solve the quadratic equation by using the factorization method:
t² + 3t - 4 = t² + 4t - t - 4
t² + 4t - t - 4 = t(t + 4) - 1(t + 4)
t² + 4t - t - 4 = (t - 1)(t + 4)
Numerator = (t - 1)(t + 4)
For the denominator, we have:
t² - 6t + 5 = t² - 5t - t + 5
t² - 5t - t + 5 = t(t - 5) - 1(t - 5)
t² - 5t - t + 5 = (t - 1)(t - 5)
Denominator = (t - 1)(t - 5)
Now, we would rewrite the inverse function as follows:
S⁻¹ = Numerator/Denominator
S⁻¹ = (t - 1)(t + 4)/(t - 1)(t - 5)
S⁻¹ = (t + 4)/(t - 5)
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Related Questions
Can someone help please
Answers
The maximum displacement of this cosine wave function is equal to 8 inches.
The frequency of this cosine wave function is equal to 1/8 Hertz.
The time (t) required for one cycle is equal to 8 seconds.
What is a cosine wave?Mathematically, a cosine wave simply refers to an equation of simple harmonic motion (SHM) and it is modelled by this mathematical expression:
y = asinωt = asin2πft ......equation 1.
Where:
a represents the amplitude or maximum displacement of a cosine wave. f represents the frequency measured in Hertz.ω represents the angular velocity.t represents the time measured in seconds.How to calculate the maximum displacement?From the information provided, the equation for this simple harmonic motion (SHM) is given by:
d = -8cos(π/4)t ......equation 2.
By comparing equation 1 and equation 2, we have the following parameters:
Maximum displacement or amplitude, a = |-8|
Taking the absolute value of a, we have:
Maximum displacement or amplitude, a = 8
For the frequency, we have:
Angular velocity, ω = 2πf
Making frequency (f) the subject of formula, we have:
Frequency (f) = ω/2π
Frequency (f) = (π/4)/2π
Frequency (f) = π/8π
Frequency (f) = 1/8 Hertz.
Finally, we would calculate the amount of time (t) required for one cycle as follows:
Time (t) = 1/f
Time (t) = 1/(1/8)
Time (t) = 8 seconds.
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Complete Question:
An object moves in simple harmonic motion described by the equation d = -8cos(π/4)t, where t is measured in seconds and d in inches. Find the following:
maximum displacement
the frequency
the time required for one cycle.
I really don't know where to start on this problem and I would like it if some could help me please.
Answers
We can draw the following picture:
Since we have a right triangle with hypotenuse equal to 28ft, we can use the trigonometric function. That is, we can write the following relationships:
[tex]\begin{gathered} \sin 30=\frac{RG}{28} \\ \text{and } \\ \cos 60=\frac{RG}{28} \end{gathered}[/tex]both give the same result.
If we use the first one, we have
[tex]\begin{gathered} RG=28\cdot\sin 30 \\ \end{gathered}[/tex]since sin30=0.5, we have
[tex]\begin{gathered} RG=28\cdot(0.5) \\ RG=14 \end{gathered}[/tex]that is, RG = 14 ft, which corresponds to the first option
Please help !! (10 pts for easy question)
Answers
Answer:
Step-by-step explanation:
If he eats 2 carrot he left with 4 carrot.
If he eats 3 carrot he left with 3 carrot.
If he eats 4 carrot he left with 2 carrot.
Step-by-step explanation:
Consider the provided information,
Max has 6 carrots. He eats more than 1 carrot. He has more than 1 carrot left.
He eats more than 1 carrot that means he can eat 2, 3, or 4 carrots.
Note. He can't eat 5 carrots because 6-5 = 1 which is not more than 1.
If he eats 2 carrot:
6-2=4
If he eats 2 carrot he left with 4 carrot.
If he eats 3 carrot:
6-3=3
If he eats 3 carrot he left with 3 carrot.
If he eats 4 carrot:
6-4=2
If he eats 4 carrot he left with 2 carrot
À La Mode Ice Cream Parlor uses the function f(x) to calculate its profits. When the parlor sells x cones, it makes f(x) dollars in profit.
What does f(50)=85 tell you?
Help please
Answers
Answer: When the Ice Cream Parlor sells 50 ice cream cones, they make $85 dollars in profit.
Step-by-step explanation:
x = cones
the function f tells us the profit for whatever x
A tank truck holds 35.3 kiloliters of oil. How many gallons does it hold?
The truck holds approximately _____ gallons of oil.
round to the nearest hundredth as needed
Answers
PLS HELP!!!
When solving the quadratic-2x² - 9x - 5 = 0, the number of real roots is:
A) 2 real roots.
B) 1 real root.
C) No real roots.
D) None of these choices are correct.
Answers
Full in the spaces to complete the equality:
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If you take out a common factor of 5t from 5t^2 + 5t, you get
5t (t + 1).
To check this, distribute the 5t to the terms in the parentheses.
5t • t = 5t^2
5t • 1 = 5t
So, 5t^2 + 5t = 5t^2 + 5t
(which means it is equal!)
A = {1, 2, 3, 4}
B = {3, 4, 5}
vertical line A intersection B vertical line =
Answers
The intersection of vertical lines A and B is 3 and 4.
How to find the intersection of the vertical linesWe are going to apply the sets theory here. In sets theory, the intersection of two elements means the values those elements have in common.
So given: A = {1, 2, 3, 4} and B = {3, 4, 5}
The intersection of A = {1, 2, 3, 4} and B = {3, 4, 5} is {3,4} since they both have 3 and 4 common.
Therefore, vertical lines A and B have intersection of 3 and 4.
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BC = 20; CD = 15. What is the value of BD − AC.
Answers
Answer:
BD - AC = 0
Step-by-step explanation:
BC = 36 , CD = 15 and BD = x
As these are forming right angled triangle,
Using Pythagorean theorem,
Taking square root on both sides
As the given shape is rectangular, the sides parallel to each other will have same values.
AB = 15 , AD = 36 and AC = x
Now,
BD - AC = 39 - 39 = 0
Hence,
BD - AC = 0
KellyConnect
Program X has an annual cost of $35,000 and, in return, is expected to save the
Company C $40,000 during the first year. Assuming the cost and savings are equally
distributed across each month, after how many months will the company recover its
investment in Program X?
Answers
The business will need 10.5 months to make back the money it invested in Program X.
How do you determine monthly costs?Actual or anticipated costs for each monthly expense are needed to calculate the average monthly expenses.
How do you figure out the return on investment?By dividing an investment's net profit (or loss) by its initial cost or outlay, we can determine the return on investment.
Program X costs $35,000 per year, but is anticipated to save $40,000 for Company C in the first year.
Considering that the savings and the cost are equal over the course of each month
So, 40000/35000 = 0.875
No. of months to recover = 0.875 × 12
= 10.5 months
Therefore, the duration it will take the business to recover its
Investment in Program X is 10.5 months.
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Find the slope and y-intercept for the line. Then write the equation of the line in slope-intercept form.
Slope =
y-intercept = (0,
Equation y
Answers
The equation of the line in slope intercept form is y=0(x)+0 or y=0.
What is slope intercept form?
The slope intercept form in the math is one of the forms used to calculate of the equation of a straight line, given the slope of the line and intercept it forms with the y-axis. The slope is the intercept form is given as, y = mx + b, where 'm' is the slope of the straight line and 'b' is the y-intercept.
The equation of any of the straight line can be written as the y=mx+c, where m is its a slope and c is its y-intercept .
Hence, the equation of the line with slope is =0 and y - intercept =0 is y=0(x)+0 or y=0.
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A. 90 degrees clockwiseB. 180 clockwiseC. 90 degrees counter clockwise
Answers
1) What we have in the polygon P is at first a
90º Rotation Clockwise because it is in the direction of the clock.
90º Rotation Clockwise
Tracing a line inside the polygon P, we can count approximately 10 units to the right in the translation.
T
I'll give brainliest!
Answers
Answer: you got 1.9 1.57 2.45 and 2.125
Step-by-step explanation:
PLEASE HELP, NO LINKS!
1. What are the key features that can be identified from a linear graph?
2. What is a relation? What makes it different from a function?
3. How can you determine the domain and range from a function?
4. What is Slope and how is it determined from a graph?
5. How do you determine the intercepts from an equation and graph.
6. Provide an example of the different forms linear equations and functions can be written.
Answers
Answer:
1 These 5 main features are the title, scale, points, labels, and line.
2. Relations are a group of ordered pairs from one set of objects to another set of objects while functions are relations that connect one set of inputs to another set of outputs. So all functions are relations while all relations are not functions.
3. To find the domain and range, we simply solve the equation y = f(x) to determine the values of the independent variable x and obtain the domain. To calculate the range of the function, we simply express x as x=g(y) and then find the domain of g(y).
4. The slope equation says that the slope of a line is found by determining the amount of rise of the line between any two points divided by the amount of run of the line between the same two points. In other words, Pick two points on the line and determine their coordinates.
5. To find the x-intercept of a given linear equation, plug in 0 for 'y' and solve for 'x'. To find the y-intercept, plug 0 in for 'x' and solve for 'y'.
6. An example of a linear equation is: 2x + y - 3 = 0. It can be written in the standard form, the slope-intercept form, and the point-slope form. Here we mainly used the slope-intercept form y=mx+c y = m x + c . To write linear equations find the slope and y-intercept and then substitute these values into the equation.
Identify the coefficient and the exponent for each term of 8x² - 2x.
The coefficients are 4 and 1. The exponents are 8 and -2.
The coefficients are 8 and -2. The exponents are 4 and 0.
The coefficients are 8 and 2. The exponents are 4 and 0.
The coefficients are 8 and -2. The exponents are 4 and 1.
Answers
The coefficient of the term 8x² is 8 and the exponent is 2 and the coefficient of the term -2x is -2 and the exponent is 1.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = abˣ in mathematics, where x is the independent variable
From the expression, a is the coefficient, x is the exponent, and b is the variable
For the term, y = abˣ, compared with the general equations;
abˣ = 8x²
a = 8 and x = 2
This indicates that the term's coefficient is 8 and its exponent is 2.
Similarly for the second term -2x
So the coefficient of the term -2x is -2 and the exponent is 1
Hence, the coefficient of the term 8x² is 8 and the exponent is 2 and the coefficient of the term -2x is -2 and the exponent is 1.
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How do I solve this?
Answers
Answer: F
Step-by-step explanation:
[tex]\sin(x+y)=\sin x \cos y+\cos x \sin y[/tex]
[tex]\tan x=2 \implies \sin x=\frac{2}{\sqrt{5}}, \cos x=\frac{1}{\sqrt{5}}\\\\\sin y=\frac{8}{17} \implies \cos y=-\frac{15}{17}\\\\\sin (x+y)=\left(\frac{2}{\sqrt{5}} \right) \left(-\frac{15}{17} \right)+\left(\frac{1}{\sqrt{5}} \right) \left(\frac{8}{17} \right)\\\\=-\frac{30}{17\sqrt{5}}+\frac{8}{17\sqrt{5}}\\\\=-\frac{22}{17\sqrt{5}}\\\\=-\frac{22\sqrt{5}}{85}[/tex]
I inserted a image of the question I’m very confused and need help with homework so I do good on test
Answers
To find the magnitude of a vector we use the following equation
[tex]\lvert\vec{v}\rvert=\sqrt[]{(v_x)^2+(v_y)^2}[/tex]This comes from taking the value of the hypotenuse by Pythagoras, graphically it can be seen in the following image:
In the case of your exercise, the values would be
[tex]\begin{gathered} v_x=x \\ v_y=y \\ \lvert\vec{v}\rvert=\sqrt[]{(x_{})^2+(y)^2} \end{gathered}[/tex]I need help with this problem it's a two-part thing
Answers
To find PQ, notice that M divides PQ into two parts with the same measure.
So, we have:
[tex]10x+3=14x-13[/tex]Now, we can solve the above equation for x, and then find PQ.
To solve the equation, we can apply the same operations on both sides of the equation, until we isolate the variable x and find its value:
[tex]\begin{gathered} 10x+3-14x=14x-13-14x \\ \\ -4x+3=-13 \\ \\ -4x+3-3=-13-3 \\ \\ -4x=-16 \\ \\ \frac{-4x}{-4}=\frac{-16}{-4} \\ \\ x=4 \end{gathered}[/tex]So, using x = 4, we obtain:
[tex]\begin{gathered} PQ=2\cdot(10x+3) \\ \\ PQ=2\cdot(10\cdot4+3) \\ \\ PQ=2\cdot(40+3) \\ \\ PQ=2\cdot43 \\ \\ PQ=86 \end{gathered}[/tex]Therefore, PQ = 86.
SLOPE-INTERCEPT FORM: PA
Xander has biked 2 miles so far this week and plans to bike an
average of 6 miles each day over the next several days. Xander
wrote the equation and created the graph to represent x, the number
of days and y, the total number of miles traveled on his bike.
a. Find the slope of the graph. Where do you see this value in
Xander's equation?
b. What value does the graph touch on the y-axis? Where do you
see this value in Xander's equation?
Answers
a) The slope of the equation is 6
b) The graph touch the y- axis at (0, 2) , (1, 8) and so on.
what is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Xander has biked 2 miles.
and, average of 6 miles each day.
So, if the number of days be x and total number of miles traveled be y.
Then , the equation to represent the situation
y= 6x+ 2
a) the slope of the equation comparing to y= mx +b
So, slope= 6
b) The graph touch the y- axis at (0, 2) , (1, 8) and so on.
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Eighth grade > T.14 Volume of spheres QX7 What is the volume of this sphere? Use a ~ 3.14 and round your answer to the nearest hundredth. 18 cm cubic centimeters Submit Docs
Answers
hello
to solve this question, we need to use the formula for volume of a sphere
[tex]\begin{gathered} v=\frac{4}{3}\pi r^3 \\ v=\text{volume} \\ r=\text{radius} \end{gathered}[/tex]from the image above, we can now find the radius of the sphere
[tex]\begin{gathered} radius=\frac{\text{diameter}}{2} \\ d=18\operatorname{cm} \\ r=9\operatorname{cm} \end{gathered}[/tex][tex]\begin{gathered} v=\frac{4}{3}\pi r^3 \\ v=\frac{4}{3}\times3.14\times9^3 \\ v=3052.08\operatorname{cm}^3 \end{gathered}[/tex]from the calculations above, the volume of the sphere is equal to 3052.08cm^3
Hello, would you be able to help me with this?
Answers
Given: An expression
[tex]\sqrt{10}[/tex]Required: To write the exponent form of the given expression.
Explanation: The square root of a number is the same as having an exponent of 1/2.
For example
[tex]\sqrt{36}=6[/tex]And in exponent form,
[tex]\begin{gathered} \sqrt{36}=(36)^{\frac{1}{2}} \\ =(6^2)^{\frac{1}{2}} \\ =6 \end{gathered}[/tex]Hence for the given expression, we can write it as
[tex]\sqrt{10}=(10)^{\frac{1}{2}}[/tex]Final Answer: Option D is correct.
The measure of USV is ________ degrees.The solution is _________________
Answers
Since ∠VST measures 90°, the measure of ∠RSV must also be 90° because the two angles are linear pair.
Since m∠RSU=51°, then the measure of ∠USV is as follows:
[tex]\begin{gathered} m\angle USV=m\angle RSV-m\angle RSU \\ m\angle USV=90\degree-51\degree \\ m\angle USV=39\degree \end{gathered}[/tex]Ben says this system of equations has one solution. Is he correct? Explain. Choose the correct answer below.Y= 1/4x-4Y= 1/4x-14 A. Ben is incorrect. Since the equations have the same slope, the system has infinitely many solutions. B. Ben is incorrect. Since the equations have the same slope and different y-intercepts, the system has no solution. C. Ben is correct. Since the equations have the same slope, the system has exactly one solution.D. Ben is correct. Since the equations have the same slope and different y-intercepts, the system has exactly one solution.
Answers
Let's begin by listing out the given information:
[tex]\begin{gathered} y=\frac{1}{4}x-4--------1 \\ y=\frac{1}{4}x-14-------2 \\ \end{gathered}[/tex]We will observe that both equations have the same slope but different y-intercept. This implies that both equations are parallel to one another. This means that both equations never intersect at any point & as such, have no solution.
Hence, the correct answer is B. Ben is incorrect. Since the equations have the same slope and different y-intercepts, the system has no solution.
Salaries of Business Graduates. Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $45,000 and $60,000. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired. What is the planning value for the population standard deviation? How large a sample should be taken if the desired margin of error is a. $500? b. $200? c. $100? d. Would you recommend trying to obtain the $100 margin of error? Explain.
Answers
3750 is the planning value for the population standard deviation.
In the sampling, one should not recommend trying to obtain the $100 margin of error since the sample size is large.
Firstly, the planning value will be:
= (60000 - 45000) ÷ 4
= 3750
Then the number will be:
= 1.96 × (3750 ÷ 500)²
= 217
Also, for error 200, the desired margin will be:
= 1.96 × (3750 ÷ 100)²
= 5403.
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According to medical data, the ages at which patients have their first hip replacement
surgery follows a normal distribution. The average age for a first hip replacement is 55
years of age, with a standard deviation of 8 years. Therefore, doctors can expect 95% of
their hip replacement surgery patients to be between what ages?
O 39-71
O 45-65
O 47-63
O 31-79
Question 4
2
Answers
95% of the people the doctor expects to have hip replacement surgery will be between the ages of 47 and 63.
What exactly are the mean and standard deviation?
The definition of average is that it is the mean value, which is the ratio of the sum of the values in a particular set to all the values in the set.
The amount of variance from the mean is shown by the standard deviation.
Given that the standard deviation is 8 years and the average age is 55.
x=x0, where x0 and are the mean age and standard deviation, respectively, defines the relationship.
The standard deviation is 8 years, while the mean age is 55 years.
The answer is that 55+8=63 and 55-8=47.
Consequently, the age range is 47 years to 63 years.
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What is the area of the parallelogram shown
Answers
You calculate for the triangle and the other part separately,
Calculate the missing information. Round dollars to the nearest cent and percents to the nearest tenth of a percent.
Item
Bar of soap
Cost
$1.17
Amount of
Markup
$0.79
Selling Price (in $)
$1.96
Percent
Markup
Based on
Cost
X%
Percent
Markup
Based on
Selling Price
%
MY N
Answers
The markup indicates the difference between the selling price and the item's cost to the business.In general, a corporation generates more money the higher the markup.The retail price of a product less its cost is known as markup, although the margin percentage is determined in a different way.
Calculate percentage on markup based on cost ?
The gross profit of a unit, which is its sales price less its cost to produce or acquire for resale, is divided by the unit's cost to determine the markup %.The markup percentage, which is computed as (12 - 8) / 8, is 50% for an item that costs the business $8 to produce but is priced at $12.Selling price = cost + markup
= 1.17+0.78
=1.96
percentage markup based on cost = markup/cost*100
0.78/1.17*100
= 66.66
percentage on selling = percentage on markup cost/100+percentage on cost
= 66.66/100%+66.66
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The composition DWhat are the coordinates of point S"?Pozx. 70D, 1(x, y) is appliedto ARST to create the image of AR"S"T", which is notshown.(를)121082+ol 들이-14-12-10-3-6422 4 6 8 10 12x8-10-12-14
Answers
SOLUTION
Step 1 :
In this question, we are meant to find the co-ordinates of S,
Where the compostion
ANSWER ASAP!! Raise the monomial to a power: -2m^3n^2t to the power of 4
Answers
Answer:
2^5m^15n^10
Step-by-step explanation:
Answer:
16m^12n^8t^4
Step-by-step explanation:
when raising exponents to another exponent you multiply the exponents
in triangle ABC the angle bisectors drawn from vertices a and b intersect at the point d find the angle abd if angle a =a, angle b=b
Answers
Answer:
According to the below diagram, the angle bisectors of ∠A and ∠B are intersecting at point D.
Step-by-step explanation: