The mean excess return of the value-weighted index portfolio is 19.458%, and the mean return of the index portfolio, adjusted for the risk-free rate, is 21.458%.
To calculate the mean excess return of the value-weighted index portfolio, we need to first calculate the total market capitalization of the three stocks:
Total Market Cap = $3,000 + $2,000 + $1,500 = $6,500
Next, we can calculate the weight of each stock in the index portfolio as follows:
Weight of Stock A = $3,000 / $6,500 = 0.4615
Weight of Stock B = $2,000 / $6,500 = 0.3077
Weight of Stock C = $1,500 / $6,500 = 0.2308
The capitalization-weighted beta of the portfolio can then be calculated as the sum of the product of each stock's weight and its beta:
Beta of Index Portfolio = (0.4615 x 0.15) + (0.3077 x 0.95) + (0.2308 x 1.7) = 1.081
The mean excess return of the index portfolio can be calculated using the single-index model as:
Mean Excess Return = Beta of Index Portfolio x Standard Deviation of Market-Index Portfolio
= 1.081 x 18%
= 19.458%
Finally, we need to adjust for the risk-free rate to obtain the actual mean return of the index portfolio. If the risk-free rate is 2%, then the mean return of the index portfolio would be:
Mean Return = Mean Excess Return + Risk-Free Rate
= 19.458% + 2%
= 21.458%
Therefore, the mean excess return of the value-weighted index portfolio is 19.458%, and the mean return of the index portfolio, adjusted for the risk-free rate, is 21.458%.
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The schoolyard at Kenny’s school is a square that is 50 yards long on each side. What is the area of thr schoolyard? A.)2,500yd square B.)2,000yd square
C.) 250 yd square
D.) 200 yd square
Answer:
A) 2,500 square yards
Step-by-step explanation:
Hope this helps! Pls give brainliest!
The number of home runs a baseball player earned each season in his career are listed. 10, 14, 20, 25, 29, 30, 30, 31, 32, 35, 39, 40 Which of the following box plots best represents the data given? A box plot uses a number line from 6 to 45 with tick marks every one unit. The box extends from 20.5 to 38 on the number line. A line in the box is at 32. The lines outside the box end at 11 and 43. The graph is titled Career Home Runs and the line is labeled Number of Home Runs. A box plot uses a number line from 10 to 49 with tick marks every one unit. The box extends from 20.5 to 32 on the number line. A line in the box is at 30. The lines outside the box end at 12 and 46. The graph is titled Career Home Runs and the line is labeled Number of Home Runs. A box plot uses a number line from 7 to 46 with tick marks every one unit. The box extends from 22.5 to 33.5 on the number line. A line in the box is at 30. The lines outside the box end at 10 and 40. The graph is titled Career Home Runs and the line is labeled Number of Home Runs. A box plot uses a number line from 6 to 45 with tick marks every one unit. The box extends from 23.5 to 36 on the number line. A line in the box is at 30. The lines outside the box end at 9 and 39. The graph is titled Career Home Runs and the line is labeled Number of Home Runs.
The correct box plot is
A box plot uses a number line from 7 to 46 with tick marks every one unit. The box extends from 22.5 to 33.5 on the number line. A line in the box is at 30. The lines outside the box end at 10 and 40.
We have the data:
10, 14, 20, 25, 29, 30, 30, 31, 32, 35, 39, 40 .
So, First Quartile(Q1) = ((n + 1)/4)th Term.
= (12+1)/4
= 13/4
= 3.25 th term
= (20+25)/2
= 22.5
and, Second Quartile or median (Q2) = ((n + 1)/2)th Term.
Q₂ = ((12 + 1)/2)th term
= 6.5th term
= 30
and, Third Quartile(Q3) = (3(n + 1)/4)th Term.
Q₃ =3 (3.25)
= 9.75
= 33.5
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The County Times charges a bulk rate of $24.55 per column inch. SE Company has contracted for the bulk rate for the year. SE Company plans to run a half page ad (65.5 column inches) in every Wednesday’s newspaper for nine weeks. What is the total cost of this campaign? Round to the nearest cent.
The total cost of SE Company's advertising campaign will be $14,436.23.
The first step is to calculate the cost of the half-page ad for one week:
65.5 column inches × $24.55 per column inch = $1604.025
Since the ad will run for nine weeks, the total cost of the campaign is:
$1604.025 × 9 = $14,436.225
Therefore, the total cost of SE Company's advertising campaign will be $14,436.23.
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Find the value of c that makes.....
The solution to the equation as it is given in (8) above is -21.
What is subtraction and multiplication properties of equality?According to the subtraction property of equality, If you subtract the same number from both sides of an equation, the equation remains true.
Also by the multiplication property of equality, If you multiply both sides of an equation by the same number (except zero), the equation remains true. These can be used to solve the question in (7) above
Given;
280 = -8(-14 + x)
280 = 112 - 8x
280 - 112 = -8x
x = -21
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The wingspan (in feet) of the actual airplane is equal to 87.5 feet.
A property of equality which you would use to solve the equation -15 = x/3 + 18 is: D. Subtraction property of equality and multiplication of equality.
The solution of the equation 280 = -8(-14 + x) is: B. x = -21.
How to determine the wingspan (in feet) of the actual airplane?Based on the scale model, we can logically deduce that the airplane has a length of 12.2 inches and a wingspan of 12.5 inches. This ultimately implies that, we would convert from inches to feet as follows;
1 inch = 1/12 feet
12.2 inches = 12.2 × 1/12 = 12.2/12 feet.
Therefore, the scaled factor is given by;
Scale factor = (85.4 × 12/12.2)
For the actual length of the wingspan with a scaled length of 12.5 inches, we have:
12.5 inches = 12.5/12 feet
Actual length of wingspan = 12.5/12 × (85.4 × 12/12.2)
Actual length of wingspan = 87.5 feet.
Question 7-15 = x/3 + 18
x/3 = -15 - 18 ⇒ (Subtraction property of equality)
x/3 = -33
x = 3(-33) ⇒ (Multiplication property of equality)
x = -99
Question 8280 = -8(-14 + x)
280 = 112 - 8x
8x = 112 - 280
x = -168/8
x = -21
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A formula for the area, A, of the circular pool is given by the equation A=\pi\left(r-3\right)^2.
Which is a formula for r?
The formula for the variable r is r = √A/π
What is subject of formula?The subject of formula can be defined as the variable that is allowed to alone in an equation.
The variables is made to be written on one end of the equality sign.
It is also described as the variable that is worked out in an equation.
From the information given, we have that;
the formula for the area of the circular pool is;
A = πr²
Such that;
A is the area of the circler is the radiusWe then have;
r = √A/π
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What is an equation of a line, in point-slope form, that passes through (1, −7) and has a slope of −2/3? A: y+7=2/3(x+1) B: y+7=−2/3(x−1) C: y−7=2/3(x−1) D: y−7=−2/3(x+1)
PLEASEEE help ima trying to get my work out the way
The equation of the line in point-slope form that passes through (1, -7) and has a slope of -2/3 is y + 7 = -2/3(x-1). Correct option is B.
The point-slope form of a linear equation is given by:
y - y₁ = m(x - x₁)
where m is the slope of the line and (x₁, y₁) is a point on the line.
We are given a point (1, -7) that the line passes through and a slope of -2/3. Therefore, we can substitute these values into the point-slope form equation to obtain:
y - (-7) = (-2/3)(x - 1)
Simplifying this equation, we get:
y + 7 = (-2/3)x + (2/3)
Taking 2/3 common from right sides, we get:
y + 7 = -2/3(x-1)
Therefore, Correct option is B.
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Solve for v. v + 1.26 = 9.86
Answer:
v = 8.6
Step-by-step explanation:
The first step to solve for x in the equation v + 1.26 = 9.86 is to isolate the variable (v) on one side of the equation.
Looking at the equation, this can be done by subtracting 1.26 from both sides of the equation.
Shown below:
v + 1.26 - 1.26 = 9.86 - 1.26
v = 8.6
As a result, v = 8.6
xKavinsky
Answer:
[tex]\mathrm{v=8.6}[/tex]Step-by-step explanation:
[tex]\mathrm{v + 1.26 = 9.86}[/tex]
Subtract -1.26 to both sides:-
[tex]\mathrm{v + 1.26-1.26 = 9.86-1.26}[/tex]
Simplify :-
[tex]\mathrm{v=8.6}[/tex]
_____________________
Hope this helps!
18. The following table shows the number of motor registration and the sales of "Gorkhali Motor Tyres" by a whole-sale dealer in Kathmandu for the term of 10 years. Years: 2 3 4 5 6 7 62 65 70 48 53 73 Motor registration in (000 nos.) No. of tyres sold in (000 nos.) 1 60 68 60 8 9 10 65 82 72 62 80 40 52 62 60 81 85 (a) Find the coefficient of correlation between the motor registration and number of tyres to sold. (b) Interpret your result. (c) Test the significance of the result. (d) Compute the two regression coefficients. (e) Estimate the number of tyres to be sold when the expected motor registration is 92,000?
The regression equation is:
y = 20.85 + 0.735 * x
How to solveYear Motor registration (000 nos.) No. of tyres sold (000 nos.)
2 62 65
3 65 70
4 48 53
5 53 73
6 60 68
7 68 60
8 60 8
9 9 10
10 65 82
11 72 62
12 62 80
13 40 52
(a) In order to ascertain the coefficient of correlation between the registration of the motor and the number of tires sold, we can apply the following formula:
r = Σ[(xi - x_mean)(yi - y_mean)] / √[Σ(xi - x_mean)^2 * Σ(yi - y_mean)^2].
To do this, we need to determine the mean values for the motor registration (x) and the number of tyres purchased (y).
[tex]x_m_e_a_n = (62 + 65 + 48 + 53 + 60 + 68 + 60 + 9 + 65 + 72 + 62 + 40) / 12 = 664 / 12 = 55.33\\y_m_e_a_n = (65 + 70 + 53 + 73 + 68 + 60 + 8 + 10 + 82 + 62 + 80 + 52) / 12 = 733 / 12 = 61.08[/tex]
Now, we can calculate the required sums for the correlation formula:
Σ(xi - x_mean) = -39
Σ(yi - y_mean) = -39
Σ(xi - x_mean)^2 =3543
Σ(yi - y_mean)^2 = 6649
Σ[(xi - x_mean)(yi - y_mean)] = 2604
Now, we can calculate the correlation coefficient:
r = 2604 / √(3543 * 6649) ≈ 0.556
(b) Interpret your result:
With a correlation coefficient, r, between -1 and 1 going up to 0.556, it shows up as a significant positive relationship.
So when the number of car registrations augments, the sales of tires will also go up.
(c) Test the significance of the result:
As the t-statistic is listed as 1.934, we can analyze it using the critical t-value from a t-distribution table which is around 2.228.
Consequently, since the t-statistic (1.934) is lower than the critical t-value (2.228), the correlation between them is not statistically significant at the 0.05 level.
(d) Compute the two regression coefficients:
The two regression coefficients can be calculated using the following formulas:
b1 = Σ[(xi - x_mean)(yi - y_mean)] / Σ(xi - x_mean)^2
b0 = y_mean - b1 * x_mean
Using the previously calculated values:
b1 = 2604 / 3543 ≈ 0.735
b0 = 61.08 - 0.735 * 55.33 ≈ 20.85
The regression equation is:
y = 20.85 + 0.735 * x
(e) Estimate the number of tyres to be sold when the expected motor registration is 92,000:
Using the regression equation, we can predict the number of tyres to be sold when the expected motor registration is 92,000 (92 in thousands):
y = 20.85 + 0.735 * 92 ≈ 87.81
We estimate that when the expected motor registration is 92,000, approximately 87,810 tyres will be sold.
It should be stated that the relationship was not considered to be statistically relevant so care is advised.
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Use a graphing calculator or other technology to answer the
question.
Which quadratic regression equation best fits the data set?
ŷ-1229.14x² - 379.14x + 32.86
ŷ 32.86x² - 379.14x + 1229.14
y= 32.86x² - 379.14x
y = 32.86x² + 379.14x1229.14
The quadratic regression equation that best fits the data-set is given as follows:
y = 32.86x² - 379.14x + 1229.14.
How to obtain the quadratic regression equation?To find the quadratic regression equation, we need to insert the points (x,y) into a quadratic regression calculator.
Considering the table in this problem, the points on the data-set are given as follows:
(3, 330), (4, 276), (5, 263), (6, 86), (7, 174), (8, 198), (9, 553).
Inserting these points into a calculator, the quadratic regression equation is given as follows:
y = 32.86x² - 379.14x + 1229.14.
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a. Use the appropriate formula to find the value of the annuity.
b. Find the interest.
Periodic Deposit
$7000 at the end of each year
Rate
6.5% compounded annually
Click the icon to view some finance formulas.
COD
Time
20 years
a. The value of the annuity $
(Do not round until the final answer. Then round to the nearest dollar as needed.)
According to the information, the interest earned on the annuity over the 20-year period is $78,066.89.
How to find the value of the annuity?To find the value of the annuity, we can use the formula:
V = PMT x [(1 + r)^n - 1] / rwhere:
PMT = periodic paymentr = interest rate per periodn = number of periodsIn this case, PMT = $7,000, r = 6.5% per year compounded annually, and n = 20 years.
First, we need to convert the annual interest rate to a periodic interest rate. Since the interest is compounded annually, the periodic interest rate is the annual rate divided by the number of periods in a year:
i = r / m
where,
m = number of compounding periods per year.
In this case, since the interest is compounded annually, m = 1, so:
i = 6.5% / 1 = 0.065
Now we can plug in the values and solve for V:
V = $7,000 x [(1 + 0.065)^20 - 1] / 0.065
V = $218,066.89
Therefore, the value of the annuity is: $218,066.89.
How to find the interest earned on the annuity over the 20-years period?To find the interest earned on the annuity over the 20-year period, we can subtract the total amount deposited from the total value of the annuity:
Interest = V - (PMT x n)Interest = $218,066.89 - ($7,000 x 20)Interest = $78,066.89Learn more about interest in: https://brainly.com/question/30393144
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What is the 3D shape that would form if the following
Answer:
These are all the 3D shapes ;cone, cylinders, cuboid,cubes, sphere, rectangular prism, pyramid
find the area of two rectangles that make a patio
Answer:
Step-by-step explanation:
picture?
Select the correct answer. Solve the equation by using the quadratic formula. x^2+2x=6
The Value of x in the equation x^2+2x=6 is 1.645 or -3.654.
Rearranging the Given equation and Putting all values on other side of Zero.
x^2+2x=6
x^2+2x-6=0 ____________(1)
It can be seen that we can not have the multiples that counts of 6 so that they have a subtraction value 2. therefore, Using the Quadratic Formula for the above equation,
x=(-b±√(b²-4ac))/(2a) ___________(2)
where
a=1
b=2
c=-6
putting the values of a,b,c in the equation (2)
x=(-2±√(4²-4*1*(-6)))/(2*1)
x=(-2±2√7)/2
x=(-1±√7)/2
Solving the Values of x in simplified form, we get x=1.645 and -3.654.
Therefore, The Value of x in the equation x^2+2x=6 is 1.645 or -3.654.
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Find a. the mean b. the deviation from the mean for each data item: and c. the sum of the deviations in part b. 146, 153, 155, 160, 161
Answer:
a. The mean of the data set is:
(146 + 153 + 155 + 160 + 161) / 5 = 155
b. The deviation from the mean for each data item is:
146 - 155 = -9
153 - 155 = -2
155 - 155 = 0
160 - 155 = 5
161 - 155 = 6
c. The sum of the deviations from the mean is:
-9 + (-2) + 0 + 5 + 6 = 0
Note that the sum of the deviations from the mean is always zero, since the positive deviations cancel out the negative deviations.
what concepts of algebra 2 would you use in real life explain your scenario and how the concepts apply and provide a worked example for each concept
There are numerous concepts in algebra 2 that can be applied in real life scenarios. Some of which are linear equations and quadratic functions. The linear equation, for instance, helps to estimate that the cost i.e. of gas for a trip.
What algebra 2 concepts have practical applications in real life?Linear equations can be used in real-life for calculating distances, rates and costs. For instance, during plan for a road trip, it can be used to estimate distance, time it takes to travel, estimated cost of gas etc.
An illustration is when one is planning a road trip from New York to Los Angeles. We can estimate that the distance between the two cities is 2,800 miles and car has average fuel efficiency of 25 miles per gallon.
If gas costs $3.50 per gallon, We can use the linear equation to get the cost of trip which is:
= Distance / Miles per gallon * Price per gallon
= 2,800 / 25 * 3.50
= $392.
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
The correct statements regarding the scatter plot are given as follows:
The line of best fit gives the best approximation between the SAT score and the GPA.The line of best fit can be used to predict the GPA based on the SAT score.A reasonable prediction of GPA for a SAT score of 2100 is a GPA of 3.5.What is the scatter plot?The scatter plot, as shown by the image given in the problem is a series of points of the data-set in the following format:
(SAT score, GPA).
There is a positive association between the data, as the line of best fit, which gives the best approximation between the SAT score and the GPA, and can be used to predict the GPA based on the SAT score, is increasing.
For a SAT score of 1700, an expected GPA is of about 3.1, considering the intersection of y = 3.1 with the line of fit when x = 1700.
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Help me Ive been on this question for a minute.
DM me on IG 1.rockkyy!!
The recursive formula is 5/6
What is recursive formula?You should know that a recursive formula is an equation used to describe a sequence in which terms are defined using one or more previous terms along with an initial condition.
The given parameters are
aₓ = a(n-1) + 2
Where aₓ = 2aₓ₋1
= 2*5(₃₋₁) = 5(3-1) + 2
= 10₂ = 10 + 2
Taking the log of both sides
Log₂10 - Log12 = 0
Dividing by 10 we have
10/12 = 5/6
therefore the recursive formula is 5/6
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HELPPP ASAPPP !!!
2. Point A on the graph below represents Nate's house, and Point B represents Nate's favorite restaurant. B A If each unit on the graph represents 3/4 of a mile, how many miles does Nate live from his favorite restaurant?
Answer:
10miles I think
Step-by-step explanation:
The required distance between, Nate's house and the restaurant is 7.5 miles.
From the graph,
Consider point C on the graph, which is 6 and 8 units apart from A and B respectively.
The distance between, Nate's house and the restaurant is given as,
AB = √[AC² + BC²]
AB = √[6² + 8²]
AB = 10 units
Now 1 unit = 3/4 miles
AB = 10 * 3/4
AB = 7.5 miles
Thus, the required distance between, Nate's house and the restaurant is 7.5 miles.
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The city council voted on a new tax. The council has 60 members and 70% of the council members voted in favor of the new tax. How many members voted in favor of the tax?
A clothing company has determined that if the price of a T-shirt is K40, then 150 will be demanded by T-shirt wearers. When the price is K45, then 100 T-shirts are demanded by T- shirts wearers. (a) Find the price-demand equation, assuming that it is linear. (b) Find the revenue function. (c) Find the number of items sold that will give the maximum revenue. What is the maximum revenue? (d) What is the price of each item when maximum revenue is achieved?
The solution is : The price per unit is $48, when 30 units are demanded.
Here, we have,
Since we have given that
At price of $12 per unit, the number of units demanded = 40 units
At price of $18 per unit, the number of units demanded = 25 units.
So, the coordinates would be
(40,12) and (25,18)
As we know that x- axis denoted the quantity demanded.
y-axis denoted the price per unit.
So, the slope would be
m = -2/5
So, the equation would be
5y + 2x = 140
So, if 30 units are demanded, the price per unit would be
y = $48
Hence, the price per unit is $48, when 30 units are demanded.
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complete question:
Suppose consumers will demand 40 units of a product when the price is $12 per unit and 25 units when the price is $18 each. Find the demand equation assuming that it is linear. Find the price per unit when 30 units are demanded.
Which experimental design will NOT result in a randomized sample?
A.
Selecting every 5th person from the class lists for each section of an algebra course
B.
Assigning a unique number to every medical study applicant and then using a random number generator to assign applicants to three different treatement goups
C.
Using all students from sections 1 and 2 of a statistics course to constitute two samples
D.
Dividing a list of voters into Democrats and Republicans and then selecting every 10th name from each of the two resulting lists
The experimental design that will not result in a randomized sample is C.Using all students from sections 1 and 2 of a statistics course to constitute two samples
What is Random sampling ?Random sampling can be regarded as the part of the sampling technique whereby each of the sample that is been involved in the population will have an equal probability of being chosen.
It should be noted that in this , the sample is chosen randomly which is unbiased representation , and in the third option, we can see that all the population was using.
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algebra 2: pls answer asap write the equation that best represents the graph
Step-by-step explanation:
Notice how we have 3 relative extrema , this means our equation has a degree of 4.
Notice how at root 1, our graph bounces off the curve.
This means we have a multiplicity of 2 there so one of our roots are
[tex](x - 1) {}^{2} [/tex]
For roots -3, and 4, our graph just passes through the x axis so those are roots with a multiplicity of 1.
[tex](x + 3)[/tex]
[tex](x - 4)[/tex]
So our equation is
[tex]y = (x - 1) {}^{2} (x + 3 )(x - 4)[/tex]
The graph passes through(-1,-2) so let see if we need any constant
[tex] - 2 = a( - 2) {}^{2} (2)( - 5)[/tex]
[tex] - 2 = - 40a[/tex]
[tex] \frac{1}{20} = a[/tex]
So our equation now is
[tex] \frac{1}{20} (x - 1) {}^{2} (x + 3)(x - 4)[/tex]
The equation that best represents the graph is p(x) = (x + 3)(x - 4)(x - 1)²
The equation that best represents the graphFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following properties
Zeros with multiplicities of 1 at x = -3 and x = 4Zeros with multiplicities of 2 at x = 1So, the base equation of the function is
p(x) = a(x + 3)(x - 4)(x - 1)²
Set a = 1
So, we have
p(x) = (x + 3)(x - 4)(x - 1)²
Hence the function is p(x) = (x + 3)(x - 4)(x - 1)²
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Bill purchases new furniture for her first apartment. The furniture costs $1,426.25 (including the tax and delivery). If the furniture place is offering an annual rate of 15.45% to finance the purchase with a SI (simple interest) add-on loan with a term of 4 years, what are the monthly payments?
$48.07 would be the monthly payments on the loan.
We must first determine the total amount of interest charged over the course of the 4-year term in order to determine the monthly payments on a basic interest add-on loan.
The formula for simple interest is:
I = P * r * t
where I is the interest charged, P is the principal (the amount borrowed), r is the annual interest rate as a decimal, and t is the time period in years.
In this case, P = $1,426.25, r = 0.1545 (15.45% expressed as a decimal), and t = 4 years. So, the total amount of interest charged is:
I = $1,426.25 * 0.1545 * 4
I = $881.25
Adding the interest to the principal, we get the total amount paid over the 4-year term:
Total amount = $1,426.25 + $881.25
Total amount = $2,307.50
We must divide the sum by the number of months left in the loan term in order to get the monthly installments. As the loan period is 4 years long, there are 48 months:
Monthly payment = Total amount / Number of months
Monthly payment = $2,307.50 / 48
Monthly payment = $48.07
Therefore, the monthly payments on the loan would be $48.07.
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Evaluate 5z - 3z for z = 3.
The value of the expression 5z - 3z, when z is equal to 3, is 6.
What is the value of the expression for z = 3?Given the expression in the question:
5z - 3zAlso, z = 3Evaluating an expression simply means substituting the given value of a variable into the expression and simplifying the result.
Given the expression 5z - 3z, we are given the value of z as 3.
Hence, we substitute z with 3 in the expression:
5z - 3z
Plug in z = 3
5(3) - 3(3)
Simplifying further using the order of operations (multiplication before subtraction), we get:
15 - 9
= 6
Therefore, the value of the expression is 6.
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the sequence is 1,3.5,6,8.5.find the sum of the first terms
Your class hopes to collect at least 325 cans of food for the annual food drive. there were 135 cans donated the first week and 89 more the second week.
A. Write an inequality that describes this situation. Let c represent the number of cans of food that must be collected by the end of the third week for your class to meet or surpass its goal.
B. How many cans are needed to meet or surpass the goal
a.) [tex]135 + 89 + \text{C} \geq 325[/tex]
[tex]224 + \text{C} \geq 325[/tex]
b.) [tex]224 + \text{C} \geq 325[/tex]
[tex]\text{C} \geq 325 - 224[/tex]
[tex]\text{C} \geq 101[/tex]
whats the calculate the expression of l/2 l=50?
The value of the expression l/2 when l=50 is 25.
Given information:
The expression l/2 means "half of l".
The expression is l/2 where l is variable.
In this case, the value of l is given as 50. So to calculate the expression, you just need to substitute 50 for l in the expression and simplify:
If l = 50, then
l/2 = 50/2 = 25
Therefore, the value of the expression l/2 when l=50 is 25.
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Use transformations of the graph of y=1/x to graph the rational function, and state the domain and range
r(x) = 2x-9/x-4
Answer:
We can use the transformations of the graph of y=1/x to graph the rational function r(x) = 2x-9/x-4.
First, we will shift the graph of y=1/x to the right by 4 units to get the graph of y=1/(x-4). Next, we will stretch the graph vertically by a factor of 2 to get the graph of y=2/(x-4). Finally, we will shift the graph down by 9 units to get the graph of r(x) = 2x-9/x-4.
The domain of r(x) is all real numbers except x=4, since that would make the denominator zero. The range of r(x) is also all real numbers except y=2, since that would make the numerator zero.
Here is a rough sketch of the graph of r(x), using the transformations:
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-- -- -- -- -- -- -- -- -- -- -
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x=4 y=2
Note: This graph is not to scale and is intended to show the general shape of the graph.
Hillary’s teacher asked her to write a description of the transformations to the parent cosine function that would result in this function. Which statements in her description are true about function h? To create the graph of function h, the graph of the parent function is horizontally compressed by a factor of . Then it undergoes a phase shift left units. Next it is vertically compressed by a factor of and vertically shifted up 4 units. The period of function h is half the period of the parent function, and it has an amplitude 3 units greater than that of the parent function. h(x)=-3cos(2x-pi)+4
The statements of description are true about function h as:
The horizontally compressed by a factor of 1/2.
The vertically shifted up 4 units.
The period of function h is half the period of the parent function.
The given function h(x) = -3cos(2x-π)+4 and compare it with the parent cosine function f(x) = cos(x).
First, let's look at the expression: -3cos(2x-π).
The factor of -3 represents a vertical compression by a factor of 3 from the parent function, which means the amplitude is three times smaller.
The argument 2x-π represents a horizontal compression by a factor of 2 and a phase shift to the right by π/2 units.
The period of the cosine function is 2π, but the period of -3cos(2x-pi) is π. Therefore, the period of h(x) = -3cos(2x-π)+4 is half that of the parent function.
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Translate the figure 2 units right and 2 units down.
Plot all of the points of the translated figure.
You may click a plotted point to delete it.
-10-9-8-7
s
3
10
9
8
-10
4
678 9 10
In order to translate a figure 2 units right and 2 units down, these steps should be followed:
How to explain the shapeInitially, draw the original figure.
Subsequently, sketch a vector from the origin (0,0) leading towards the point (2,2). By doing so, you parallelly instigate defining an amount of how you desire to transform said figure.
Create a novel focal point by augmenting the vector to each central point within the pre-existing image. Hence, if the prime pictorial contains, for instance, points (x,y), then this fresh peak will exist as (x+2,y+2).
Interconnect aforementioned new points in accordance with the formation that is desirable for the translated rendering of the initial diagram.
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