A. The firm's shortrun total cost curve can be calculated as TC = 2K + 4L. The shortrun average cost curve function will be SAC = TC/Q, where Q is the output.
B. The firm's shortrun marginal cost function is MC = 4/Q. The shortrun total cost (STC) at 25 and 200 levels of output will be 800 and 2400 respectively. The shortrun average cost (SAC) at 25 and 200 levels of output will be 32 and 12 respectively. The shortrun marginal cost (SMC) at 25 and 200 levels of output will be 16 and 8 respectively.
C. The graph of the SAC and SMC curves is shown below.
SAC and SMC Graph
D. The SMC curve intersects the SAC curve at its lowest or minimum point because at this point, the SAC curve is at its most costefficient level, meaning that the firm's costs are minimized. This is because at this point, the marginal cost is lower than the average cost, meaning that the firm can produce additional units of output with a decreasing cost.
Help, Solve it by using Elmination, Linear Equation
Answer:
The mistake they made was that they subtracted [tex]2y[/tex] from [tex]2y[/tex] and got [tex]0y[/tex]. Instead of subtracting, they should have added it.
Stepbystep explanation:
Given:
[tex]8x+2y=44\\5x+2y=35[/tex]
We can combine the system of equations into a single equation:
[tex]13x+4y=79[/tex]
From this step, we can conclude that the answer for part b is incorrect. The mistake they made was that they subtracted [tex]2y[/tex] from [tex]2y[/tex] and got 0y. Instead of subtracting, they should have added it.
We can continue solving the system of equations by writing y in terms of x.
[tex]8x+2y=44\\2y=448x\\y=224x[/tex]
now substitute this into the single equation:
[tex]13x+4y=79\\13x+4(224x)=79\\13x+8816x=79\\3x+88=79\\3x=9\\x=3[/tex]
Since we now know that [tex]x=3\\[/tex], we can substitute this into the equation we made for y.
[tex]y=224x\\y=224(3)\\y=2212\\y=10[/tex]
The solution for the system of equations is [tex]x=3[/tex] and [tex]y=10\\[/tex].
Identify the y intercept of the graph below
b= 4
b=6
b=4
b= 10
Financial planning case 22
Victor Hernandez Considers a Career Change
Victor is somewhat satisfied with his sales career and has always wondered about a career as a teacher in a public school. He would have to take a year off work to go back to college to obtain his teaching certificate, and that would mean giving up his $40,000 salary for a year. Victor expects that he could earn about the same income as a teacher. Round your answers to the nearest dollar.
What would his annual income be after 12 years as a teacher if he received an average 4 percent raise every year? Round Future Value of a Single Amount in intermediate calculations to four decimal places. (Hint: Use Appendix A1.)
$
Victor also could earn $3,000 each year teaching during the summers. What is the accumulated future value of earning those annual amounts over 12 years assuming a 5 percent raise every year? Round Future Value of a Series of Equal Amounts in intermediate calculations to four decimal places. (Hint: Use Appendix A3.)
$
Answer: Victor's annual income after 12 years as a teacher would be $47,564 if he received an average 4 percent raise every year.
The accumulated future value of earning $3,000 each year teaching during the summers over 12 years with a 5 percent raise every year would be $41,592.
Stepbystep explanation:
To calculate Victor's annual income after 12 years as a teacher, we need to find the future value of his starting salary of $40,000 after 12 years with an average 4 percent raise every year.
Using the formula for the future value of a single amount (FV = PV * (1 + r)^n), where PV is the present value, r is the interest rate, and n is the number of years, we can calculate the future value as follows:
FV = $40,000 * (1 + 0.04)^12 = $47,564
So, Victor's annual income after 12 years as a teacher would be $47,564 if he received an average 4 percent raise every year.
To calculate the accumulated future value of earning $3,000 each year teaching during the summers over 12 years with a 5 percent raise every year, we need to use the formula for the future value of a series of equal amounts (FV = A * (1 + r)^n  1 / r), where A is the annual payment and r is the interest rate.
Plugging in the values, we get:
FV = $3,000 * (1 + 0.05)^12  1 / 0.05 = $41,592
So, the accumulated future value of earning $3,000 each year teaching during the summers over 12 years with a 5 percent raise every year would be $41,592.
There are marbles of four different colors in a bag. The
ratio of red to white to blue marbles is 3:4:5. There are half
as many green marbles as there are blue marbles. What is
the least possible number of marbles in the bag?
(A) 12
(B) 24
(C) 29
(D) 58
Answer:
(C) 29
Stepbystep explanation:
9) in Brayden's movie collection, 8 out of every 25 movies are comedy. What percentage of his movies are
not comedy?
Answer: 0.32 or 32%
Stepbystep explanation: 8/25
Please helpppp
if y+3/y3 = 6
What is the value of y?
f(x) =3(x2) (x+4)
f(x) = (3x+12) (x2)
f(x) =3(x+4) (x+2)
f(x) = 3 (x4) (x+2)
Answer:
Stepbystep explanation:
The answer is d. f(x) = 3 (x4) (x+2).
09:42 Man 13 Feb
A school carried out a report on their Year 11 students to see the impact of doing homework
regularly on final grades achieved in maths. The results are presented in the frequency tree.
Get grade B or higher
Do homework
Complete the tree.
75
6
Don't do
homework
regularly
60
b
D
Get lower than grade B
Get grade B or higher
Get lower than grade B
The percentage of students who are doing their homework regularly is 75%.
What is a Universal Set?A universal set in set theory is a set that includes itself as well as all other items. A universal set's nonexistence in set theory as it is typically expressed can be demonstrated in a number of different ways. However, a universal set is a part of several unconventional set theory variations.
To find the percentage of students who are doing their homework regularly,
We find the total students and this is 75 + 5 = 80 students
The percentage is 60/80 * 100
= 75%
Read more about universal sets here:
https://brainly.com/question/17885920
#SPJ1
help with this :) 25 point
Answer:
76°
Just know that angles on the parallel sides always add up to 180°
11. Mike plans to make contributions to his retirement account for 15 years. After the last contribution, he will start withdrawing $10,000 a quarter for 10 years. Assuming Mike's account earns 8% compounded quarterly, how large must his quarterly contributions be during the first 15 years, in order to accomplish his goal?
Answer:
To solve this problem, we need to use the formula for compound interest:
A = P * (1 + r/n)^(nt)
where:
A = future value of the account
P = present value (the contributions)
r = interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
First, we need to find the future value of the account (A) after 10 years of withdrawals at $10,000 per quarter. This means there will be 40 quarters in total ($10,000 * 40 = $400,000).
Next, we need to find the present value of the account (P) after 15 years of contributions.
Let's call the quarterly contributions "x".
We can set up the equation as follows:
$400,000 = x * (1 + 0.08/4)^(4 * 15)  $10,000 * (1 + 0.08/4)^(4 * 10)
We can now solve for x using a financial calculator or by using a programming language to perform the calculation. The result of this calculation is that Mike's quarterly contributions should be $2,597.29 in order to accomplish his goal.
Help with QUESTION 9 AND 11:
Answer:
Stepbystep explanation:
9.
f(x)=x²10x+3
=x²10x+2525+3
=(x5)²22
vertex is (5,22)
it has horizontal tangent at (5,22)
or
f(x)=x²10x+3
f'(x)=2x10
it has horizontal tangent where 2x10=0 or x=5
f(5)=5²10(5)+3
=2550+3
=22
it has horizontal tangent at (5,22)
How do I solve this problem using the Rational Zeroes Theorem?
1) Find the real number solutions of the following polynomial equation:
f(x) = 4x^5  40x^3 + 36x
Answer:
Stepbystep explanation:
The Rational Zeroes Theorem states that if a polynomial equation has a rational solution (a solution that can be expressed as a fraction of two integers), then that rational solution must be of the form p/q, where p is a factor of the constant term (in this case 36) and q is a factor of the leading coefficient (in this case 4).
Step 1: Find the factors of 36. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Step 2: For each factor of 36, divide it by each factor of 4 to get a list of possible rational solutions.
Step 3: Test each of the possible rational solutions by plugging them into the polynomial equation and seeing if they make the equation equal to zero. If a solution makes the equation equal to zero, it is a root of the polynomial.
Step 4: Once you have found all of the roots of the polynomial, you can use them to write the polynomial in factored form.
Note: This method only works for polynomials with real coefficients and will only give you the real solutions of the equation. If the polynomial has complex solutions, you will need to use a different method to find them.
Divide the numbers. Round to hundredths when necessary. 1,863.4 ÷ 12.31
Answer:
151.37
Stepbystep explanation:
Answer:
151.372868 but rounded is 151.37
Stepbystep explanation:
1863.4/12.31=151.372868 rounded is 151.37
A square a triangle and a parallelogram are used to form the figure shown. What is the area of the figure in square feet?
A) 213.04
B) 210.64
C) 231.04
D) 207
The area of the attached figure is 32 square mm
What is the area of the figure?The similar question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
A square a triangle and a parallelogram
The shapes can be combined to
a triangle and a parallelogram
So, we have
Area = Sum of individual areas
Using the dimensions of the shapes as a guide, we have the following:
Area = 0.5 * 2 * 8 + 4 * 6
This gives
Area = 32
Hence, the area is 32 square mm
Read more about area at
https://brainly.com/question/22972014
#SPJ1
PLS HELP
Matt released his new game app, Serpent of the Sphinx, and it received 548 downloads the first week. He expects the number of weekly downloads to increase by about 4% each week. You can use a function to approximate the number of weekly downloads x weeks after the release date.
Write an equation for the function. If it is linear, write it in the form h(x)=mx+b. If it is exponential, write it in the form h(x)=a(b)x.
The number of weekly downloads can be modeled using an exponential function h(x) = 548 × 1.04ˣ.
What is exponential function?
An exponential function is a mathematical function in which the value of the output is proportional to the value of a fixed number (known as the base) raised to the power of the input value. The general form of an exponential function is:
y = abˣ
where a and b are constants, x is the input value, and y is the output value. The constant a controls the vertical scaling of the function, while the constant b controls the rate of growth or decay. If b is greater than 1, the function grows rapidly as x increases. If 0 < b < 1, the function decays as x increases. If b is equal to 1, the function is a linear function.
Exponential functions are widely used in many fields, including finance, biology, physics, and engineering, to model growth and decay processes.
The number of weekly downloads can be modeled using an exponential function.
h(x) = 548 * 1.04ˣ
where x is the number of weeks after the release date, h(x) is the estimated number of weekly downloads, and 1.04 is the growth factor (1 + the expected weekly increase of 4%).
Learn more about exponential function click here:
https://brainly.com/question/2456547
#SPJ1
This table shows the results of a survey on how students get to school.
A circle graph is to be used to display the data.
Calculate the sector angle, to the nearest degree, for each method of transportation.
Transportation Number of Students
Bus 39
Bike 12
Walk 25
Car 24
The sector angle are 140.4° for bus, 43.2° for bike, 90° for walk and 86.4° for car.
What is a Pie Chart?A pie chart is a type of graph where a circle is divided into certain sectors where each sector shows a proportion of the whole.
We have to show the given data in a pie chart where each sector represents a proportion of a type of transportation.
39 students uses bus for transportation.
12 students uses bike for transportation.
25 students walk for transportation.
24 students uses car for transportation.
Total number of students = 39 + 12 + 25 + 24 = 100
Total sector angle of a circle = 360°
Sector angle for bus = (39 / 100) × 360 = 140.4°
Sector angle for bike = (12 / 100) × 360 = 43.2°
Sector angle for walk = (25 / 100) × 360 = 90°
Sector angle for car = (24 / 100) × 360 = 86.4°
Hence the sector angle for each mode of transportation is 140.4° for bus, 43.2° for bike, 90° for walk and 86.4° for car.
Learn more about Pie Chart here :
https://brainly.com/question/29148468
#SPJ1
Find the number of positive integers that satisfy both the following conditions:
* Each digit is a 1 or a 2 or a 3
* The sum of the digits is 4.
The number of positive integers that satisfy the conditions is 4
What is positive integer?The positive integers are the natural numbers or also called counting numbers. These integers are also sometimes denoted by Z+. The positive integers lie on the right side of 0 on a number line. Z+ → 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25,
To satisfy positive integers that will have sum of four with a 1, a 2 or a 3
The integers are
13
31
112
211
therefore there are only 4 positive integers that have sum of 4 with a 1 , a 2 and a3
learn more about positive integers from
https://brainly.com/question/1367050
#SPJ1
See my picture please i need it
The two provided payments of $17,000 and $3,300 due in 1 year and 2 years, respectively, would be replaced by two equal payments of $2,287.87 made in 6 months and 5 years.
How to find the two payments that would replace these paymentsTo solve this problem, we need to find two equal payments that would replace the two given payments, given the time and interest rate. We can use the present value formula to calculate these payments:
PV = C / (1 + r)^n
Where
PV is the present value,
C is the future value of the payment,
r is the interest rate per compounding period, and
n is the number of compounding periods.
For the first payment of $17,000 due in 1 year, its present value in 6 months can be calculated as:
PV1 = 17,000 / (1 + 0.08/4)^(2*2) = $14,785.28
For the second payment of $3,300 due in 2 years, its present value in 5 years can be calculated as:
PV2 = 3,300 / (1 + 0.08/4)^(4*2) = $2,424.67
To find the equal payments that would replace these two payments, we can use the annuity formula:
PMT = PV / [(1  (1 + r)^(n)) / r]
Where
PMT is the equal payment,
PV is the present value,
r is the interest rate per compounding period, and
n is the number of compounding periods.
For the two payments to be made in 6 months and 5 years, respectively, the total number of compounding periods is
4*2.5 = 10.
The equal payment can be calculated as follows:
PMT = (PV1 + PV2) / [(1  (1 + 0.08/4)^(10)) / (0.08/4)] = $2,287.87
Therefore, two equal payments of $2,287.87 made in 6 months and 5 years would replace the two given payments of $17,000 and $3,300 due in 1 year and 2 years, respectively.
Learn more about present value at:
https://brainly.com/question/30390056
#SPJ1
Leah ate 9 hot dogs every 21 hours. At that rate how many would she eat in 35 hours
Answer:
15
Stepbystep explanation:
9/21 aproximatly = 0.42 then x35 = 15
The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 5.8% per hour. How many hours does it take for the size of the sample to double?
It will take 5.189 hours to get doubled the size of Sample.
What is Exponential Function?A relation of the form y = [tex]a^x[/tex], with the independent variable x ranging over the entire real number line as the exponent of a positive number a.
Given:
Growth rate = 5.8%
The continuous exponential growth model for populations is given by:
P(t)= [tex]P_0 e^{rt[/tex]
So, r= 5.8%
r = 0.058
Now, the time taken to double the sample then P(t) = 2P(0).
So, P(t)= [tex]P_0 e^{0.058t[/tex]
2P(0) = [tex]P_0 e^{0.058t[/tex]
[tex]e^{0.058t[/tex] = 2
Taking log on both side
log [tex]e^{0.058t[/tex] = log 2
0.058 t = 0.301
t= 0.301/ 0.058
t = 5.189
Learn more about exponential Function here:
https://brainly.com/question/23064497
#SPJ1
Isosceles trapezoid KRWT is shown
Given KRWT is an isosceles trapezoid with KR and TW
Prove: WK = TR
An incomplete twocolumn proof is shown
Answer Choices:




What is the missing statement in step 3
More info is in the picture
Thank you for any help!
The supportive statement is m∠WKT ≅ m∠TRW.
What is a trapezoid?An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.
A trapezium's nonparallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.
The altitude is the measurement of the angle perpendicular to the parallel sides.
We know a trapezoid is isosceles if the two nonparallel sides are equal.
Therefore, In KWRT, [tex]\overline{WK}[/tex] ≅ [tex]\overline{TR}[/tex] and [tex]\overline{KR}  \overline{TW}[/tex].
The missing statement to support all other statements would be,
m∠WKT ≅ m∠TRW as the angle formed by the pair of the corresponding sides is equal.
learn more about trapezoids here :
https://brainly.com/question/8643562
#SPJ1
A rectangular garden 12 feet by 16 feet has a stone path along the perimeter with the same width, w. The area of the garden and path is 420 square feet.
The correct equation to find the width, w, of the stone path would be: Option B. (2w+12) (2w+16) = 420
This is because the area of the garden and path is equal to the area of the rectangle with dimensions (12+2w) and (16+2w). Therefore, we can set up the equation:
(12+2w)(16+2w) = 420
Expanding and simplifying, we get:
4w² + 56w  204 = 0
Dividing by 4, we get:
w² + 14w  51 = 0
Factoring, we get:
(w+17)(w3) = 0
Since the width of the path cannot be negative, the only valid solution is w = 3.
Learn more about mathematics here: brainly.com/question/24600056
#SPJ4
Complete question is in the image attached
Describe the relationship between precalculus and calculus. List three precalculus concepts and their corresponding calculus counterparts.
The relationship between precalculus and calculus has been explained and both precalculus and calculus deals with the tangent of the line, slope of the line, y intercept, velocity etc.
Precalculus is the study of mathematics or the course that includes algebra, trigonometry etc. to make a student for study the calculus . The precalculus covers the topics likes complex numbers, composite numbers, trigonometric functions, vectors, matrices, probability etc.
Calculus is the study of mathematics that deals with the rate of changes. Applications of the calculus are finding the slope of the curve, finding the area of region, calculation of x intercept and y intercept etc.
Both precalculus and calculus deals with the tangent of the line, slope of the line, y intercept, velocity, acceleration, area, volume etc.
Therefore, the relationship between precalculus and calculus has been explained
Learn more about Calculus here
brainly.com/question/6581270
#SPJ4
Each night different meteorologists give us the probability that it wil rain the next day.
To judge how well these people predict, we will score each of them as follows:
If a meteorologist says that it will rain with probability p, then he or she will receive a score of:
{1(1p)^2 if it does rain
(1  p^2 if it does not rain
We will then keep track of scores over a certain time span and conclude that the meteorologist with the highest average score is the best predictor of weather.
Suppose now that a given meteorologist is aware of this and so wants to maximize his or her expected score.
If this person truly believes that it will rain tomorrow with probability q, what value of p should he or she assert so as to maximize the expected score?
a)Choice of p= (I know this is p=q). What are the other answers?
b)With this choice, what is the expected payoff in terms of q?
c)
On the other hand, if the payoffs are
{1(1p)^2
{11.1p^2
Choice of p=
(a) When q = 0 or q = 1, we get p = 0.5, but for other values of q, the optimal value of p is different.
(b) When q = 1, the expected score is 1, which is the maximum possible score.
(c) The optimal value of p also depends on the value of q in this case.
a) The expected score of the meteorologist can be expressed as the weighted average of the two possible scores, where the weights are the probabilities of it raining or not raining:
Expected score = p(1  (1  q)^2) + (1  p)(1  q^2)
To maximize the expected score, we need to differentiate it with respect to p, set the derivative equal to zero, and solve for p. This gives:
2q(1  q) = 1  2p
Solving for p, we get:
p = (1  2q + 2q^2) / 2
So the optimal value of p depends on the value of q. When q = 0 or q = 1, we get p = 0.5, but for other values of q, the optimal value of p is different.
b) If the meteorologist chooses p = q, then the expected score simplifies to:
Expected score = q(1  (1  q)^2) + (1  q)(1  q^2)
= q^3 + (1  2q)q^2 + (1  q)
To find the maximum expected score, we can take the derivative of this expression with respect to q, set it equal to zero, and solve for q. This gives:
3q^2  4q + 1 = 0
This quadratic equation has two roots: q = 1/3 and q = 1. When q = 1, the expected score is 1, which is the maximum possible score. When q = 1/3, the expected score is (8/27), which is the maximum score for any value of q between 0 and 1.
c) If the payoffs are {1  (1  p)^2, 1  1.1p^2}, then the expected score of the meteorologist is:
Expected score = p(1  (1  q)^2) + (1  p)(1  1.1q^2)
To maximize this expected score, we can differentiate it with respect to p, set the derivative equal to zero, and solve for p. This gives:
2.2q^2  2q + 1 = 2p
Solving for p, we get:
p = (2.2q^2  2q + 1) / 2
So, in this scenario, the value of q also affects the ideal value of p.
To learn more about expected score here:
https://brainly.com/question/28000192
#SPJ4
The number of milligrams of Vitamin C from 100 different gummy vitamins sold in the world was collected.
Which graphical representation would be most appropriate for the data, and why?
Box plot, because the median can easily be determined from the large set of data
Stemandleaf plot, because you can see the shape of the data
Histogram, because it shows each individual data point
Bar chart, because the data is categorical
Box plot, because the median can easily be determined from the large set of data.
What exactly is a median?
The median is defined as the value in the centre of a given set of numbers or statistics. There are three main measures in mathematics that are used to calculate the average value for a given group of integers. They are the mean, the median, and the mode. These three indicators are known as central tendency measures. Mean computes the average value of the provided data. A median defines the midway value of the provided data. Mode defines the repeating value of the input data.
Now,
As, A box plot is a very visual means of displaying a concise overview of one or more sets of data. It is especially handy for quickly summarising and comparing several sets of findings from various trials. A box plot, at a glance, gives a graphical representation of the distribution of findings as well as indicators of symmetry within the data.
and it can handle a large set of data.
Hence,
Box plot, because the median can easily be determined from the large set of data.
To know more about median visit the link
https://brainly.com/question/21396105?referrer=searchResults
#SPJ1
Answer:box plots
Stepbystep explanation:
i did it
Horizontal and vertical lines are special lines. A horizontal line goes from left to right and is parallel to the xaxis. The equation is y=b. What is its slope?
A vertical line goes up and down and is parallel to the yaxis. The equation is x=a. What is its slope?
Please give at least two examples of equations for vertical and horizontal line.
Horizontal lines have a slope of zero, since the "rise" is; zero.
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
m = ( y₂  y₁ ) / ( x₂  x₁ )
Since we know that Vertical lines have an undefined slope, since the "offset" is zero, and division by zero is not allowed.
If the slope has a value of zero, the line is horizontal, neither increases nor decreases.
Therefore,
Horizontal lines always have an equation of the form; y = a
Vertical lines always have an equation of the form; x = b
Learn more about slope here:
https://brainly.com/question/2503591
#SPJ9
Select the correct answer.
What is this expression in simplest form?
X + 2/ 4x^2 + 5x +1 • 4x + 1/ x^2  4
1/(x+1)(x2) is the simplified form of the expression
Simplifying expressions into its simplest formGiven the expression below
x+2/4x²+5x+1 · 4x+1/x²4
Factorise the quadratic expressions
4x²+5x+1 = 4x²+4x + x+1
4x²+5x+1 = 4x(x+1)+1(x+1)
4x²+5x+1 = (4x+1)(x+1)
For the expression x²4
x²4 = (x+2)(x2)
Substitute
x+2/4x²+5x+1 · 4x+1/x²4 = x+2/(4x+1)(x+1) · 4x+1/(x+2)(x2)
x+2/4x²+5x+1 · 4x+1/x²4 = 1/x+1 · 1/x2
x+2/4x²+5x+1 · 4x+1/x²4 = 1/(x+1)(x2)
Hence the simplified form of the expression is 1/(x+1)(x2)
Learn more on simplifying the expression here: https://brainly.com/question/28036586
#SPJ1
A set of eight builtin bookshelves is to be constructed in a room. The floortoceiling clearance is 7 ft 5 in. Each shelf is 1 in. thick. An equal space is to be left between the shelves, the top shelf and the ceiling, and the bottom shelf and the floor. How many inches should there be between each shelf and the next? (There is no shelf against the ceiling and no shelf on the floor.)
Answer:
Stepbystep explanation:
The floortoceiling clearance is 7 ft 5 in, which is equal to 7 * 12 + 5 = 89 inches.
We need to construct 8 shelves, each of which is 1 inch thick, so the total thickness of the shelves is 8 * 1 = 8 inches.
We also need to leave an equal space between each shelf and the next, the top shelf and the ceiling, and the bottom shelf and the floor. So, there will be 7 equal spaces in total (6 between shelves and 1 between the bottom shelf and the floor).
Therefore, the space between each shelf and the next will be (89  8) / 7 = 11 inches.
Here's a step by step solution:
Calculate the total height of the room in inches: 7 ft 5 in = 7 * 12 + 5 = 89 inches.
Calculate the total thickness of all the shelves: 8 shelves * 1 inch/shelf = 8 inches.
Deduct the thickness of the shelves from the height of the room to find the total space available: 89 inches  8 inches = 81 inches.
Divide the total space available by the number of spaces (7) to find the space between each shelf and the next: 81 inches / 7 = 11 inches.
The polynomial of degree 5,
P(x) has leading coefficient 1, has roots of multiplicity 2 at x = 1 and x = 0, and a root of multiplicity 1 at
x = 5 Find a possible formula for P(x).
Answer:
Stepbystep explanation:
Given the information that the polynomial function P(x) has leading coefficient 1, has roots of multiplicity 2 at x = 1 and x = 0, and a root of multiplicity 1 at x = 5, we can use this information to find a possible formula for P(x).
A polynomial function's roots are the values of x that make the function equal to zero. If a root has multiplicity n, it means that (x  root) is a factor of the polynomial function n times.
So, based on the given information, we know that P(x) must be divisible by the factors (x  1)^2, (x  0)^2, and (x + 5), and that the leading coefficient must be 1.
Putting it all together, a possible formula for P(x) is:
P(x) = (x  1)^2 (x  0)^2 (x + 5) = (x^2  2x + 1)(x^2)(x + 5) = x^6  7x^5 + 17x^4  22x^3 + 17x^2  7x + 5
So, the possible formula for P(x) is P(x) = x^6  7x^5 + 17x^4  22x^3 + 17x^2  7x + 5.
Answer: [tex]P(\text{x}) = \text{x}^2(\text{x}1)^2(\text{x}+5)[/tex]
Explanation:
If k is a root of P(x), then xk is a factor. The multiplicity is the exponent for that factor.
For instance, the root x = 1 with multiplicity 2 leads to the factor [tex](\text{x}1)^2[/tex]
The leading coefficient is the number out front. For example, if the leading coefficient was 8, then we'd have [tex]P(\text{x}) =8\text{x}^2(\text{x}1)^2(\text{x}+5)[/tex]
However, we change that "8" to a "1" since the leading coefficient is 1 here.
That's how we get to
[tex]P(\text{x}) = 1\text{x}^2(\text{x}1)^2(\text{x}+5)[/tex] aka [tex]P(\text{x}) = \text{x}^2(\text{x}1)^2(\text{x}+5)[/tex]
Optionally if you were to expand everything out, combine like terms, and simplify then you'd get
[tex]P(\text{x}) = \text{x}^2(\text{x}1)^2(\text{x}+5) = \text{x}^5 + 3\text{x}^4 9\text{x}^3+5\text{x}^2[/tex]
I don't recommend doing this because you lose the information about the roots along with their corresponding multiplicities. It's better to keep things factored.
You can use a graphing tool like Desmos or GeoGebra to verify the answer.
Use the given minimum and maximum data entries, and the number of classes, to find the class width, the lower
class limits, and the upper class limits.
minimum = 10, maximum = 68, 7 classes
The class width is ?
The lower class limits are ?
The upper class limits are ?
Answer:
Stepbystep explanation:
213232131123123123123123
1. To find the class width, we first need to find the range of the data, which is the difference between the maximum and minimum values: 68  10 = 58. Then, we divide the range by the number of classes to get the class width: 58 / 7 = 8.29. However, we will round up to the nearest whole number, so the class width is 9.
2. The lower class limits are 10, 19, 28, 37, 46, 55, and 64, since we add the class width to the lower limit of each previous class to find the lower limit of the next class.
3. The upper class limits are 18, 27, 36, 45, 54, 63, and 68, since we add the class width to the lower limit of each class to find the upper limit of that class.
Does anyone know the reasoning for B
Answer:because angles in a triangle add up to 180 degrees.
Stepbystep explanation:
A=40
C=30
So 1804030=110