The rate of return earned on the investment of $475 five years ago in the corporate stock is 312.63%.
What is the rate of return?The rate of return is the net gain or loss of an investment expressed as a percentage of the investment's initial cost.
It is given by the formula, R= {Vf - Vi}/{Vi} x 100.
Where:
R = Rate of return
Vf = final value, including dividends and interest
Vi = initial value
Data and Calculations:Investment cost = $475
Dividends received:
1st two years = $80 ($10 x 8)
Three years = $180 ($15 x 12)
Total dividends received = $260 ($80 + $180)
Total revenue from sale = $1,700
Total proceeds = $1,960 ($1,700 + $260)
Total return = $1,485 ($1,960 - $475)
Rate of return = 312.63% ($1,485/$475 x 100)
Thus, the rate of return is 312.63%.
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Be sure that you show all of your work to reach your answer. Each step must be on a separate line. Your method to reach your answer must be clear and include explanations.
Be sure to only round at the last step for your final answer.
You plan to purchase a house for $525,000 and you will make a 20% down payment. You are evaluating two mortgages a 30-year fixed mortgage at 2.72% and a 15-year fixed mortgage at 2.25%. Your goal is to have a monthly payment that fits within your budget.
a. Which mortgage will give you the lowest monthly payment? What will that payment be? How much less will this be than the other monthly mortgage payment?
b. Assuming you take the full term of the mortgage, which mortgage will result in you paying the most interest? What will that interest be? How much more will this be than the interest on the other mortgage?
R= regular monthly payment
p= amount financed, or principal
r= rate written as a decimal
n= number of payments per year
t= number of years
Needs to be easy to read.
The mortgage that will give the lowest monthly payment is EMI1 which translates to $ 1,708.16; and method one will require payment of the highest interest.
What is mortgage?A mortgage is an arrangement between you and a lender that provides the lender the right to repossess your property if you fail to repay the loan plus interest.
Mortgage loans are used to purchase a property or to borrow money against the value of an existing home.
What is the calculation for the above?Given that:
Total amount = $525,000
Down payment = 20% = 0.2
Method 1: Time is 30 years and rate is 2.72%
Method 2: Time is 15 years and the rate is 2.25%
Loan amount = total amount less down-payment
= 525,000 - (0.2 * 525,000)
= $420, 000
Using Method 1Given that t = 30 year or 360 months
r = 2.72% or 0.0272
EMI1 = [ 420, 000 * (0.0272/12) * ( 1 + (0.0272/12)³⁶⁰]/ [( 1 + (0.0272/12)³⁶⁰ -1]
= [952 * 2.259]/1.259
EMI1 = $ 1,708.16
Using Method 2
t = 15 years or 180 months
Rate = 2.25% or 0.0225
EMI2 = [420,000 * (0.0225/12) * ( 1 + (0.0225/12)¹⁸⁰]/ [( 1 + (0.0225/12)¹⁸⁰ --1]
= [787.5 * 1.401]/0.401
EMI2 = $2,751.34
Assuming you take the full term of the mortgage, which mortgage will result in you paying the most interest?
Method 1
Interest = EMI1 x total months - loan amount
= 1,708.16 x 360 - 420,000
= $194, 937.6
Method 2
Interest = EMI2 x total months - loan amount
2,751.34 x 180 - 420,000
= $75,241.2
From the above method 1 requires the highest interest.
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What is the volume of a right circular cylinder with a radius of 6 m and a height of 9 m?
• 547 m²
. 108 m²
3247 m³
4867 m²
Help
The volume of the right circular cylinder with a radius of 6 m and a height of 9 m is 1018 m².
The volume of a substance is the total space occupied by a three-dimensional object.
The volume of a right circular cylinder with a radius of r units and a height of h units is given by the formula V = πr²h square units.
We are asked to find the volume of the right circular cylinder with a radius of 6 m and a height of 9 m.
Substituting these values in the formula, we get Volume,
V = π(6)²(9) m² = 324π m² = 1017.876 m² ≈ 1018 m².
Therefore, the volume of the right circular cylinder with a radius of 6 m and a height of 9 m is 1018 m².
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XTI
1
7 ft. =
.
.
in.
3
.
13. Calculate using the table below: 2
" . 1
5
.
Calculations
Use chapters 8 and 9 of your textbook to solve the next set of problems. Show your wor
. 1
.
Equivalences of Units in Length in the U.S. Customary System
12 inches (in.) = 1 foot (ft)
3 ft = 1 yard (yd)
5280 ft = 1 mile (mi
I
f td d,ts#=#=sr#=rs$/,% gu gu hijkojibgu yf ,tdts$_, %_g g hu
Type an integer or decimal rounded to the nearest tenth f(80)=1000(0.5)80/30
The value of the function is 157.5
How to evaluate the function?The function is given as:
f(80)=1000(0.5)^(80/30)
Evaluate the quotient
f(80)=1000(0.5)^(8/3)
Evaluate the exponent
f(80)=1000 * 0.15749013123
Evaluate the product
f(80) = 157.49013123
Approximate
f(80) = 157.5
Hence, the value of the function is 157.5
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HELP ME PLEASE PLEASE PLEASE
If the angles of a convex octagon are [tex]2x+6,x+13,2x-1,2x+12,2x-17,3x-4,3x-10,4x.[/tex] then the smallest angle is 21°.
Given The exterior angles of convex octagon are [tex]2x+6,x+13,2x-1,2x+12,2x-17,3x-4,3x-10,4x.[/tex]
and we have to find the value of smallest angle.
The sum of the angles of a convex octagon is 360°
so to calculate the smallest angle we need to find out the value of x first and which is calculated by summing up all the exterior angles and put them equal to 360.
(2x+6)+(x+13)+(2x-1)+(2x+12)+(2x-17)+(3x-4)+(3x-10)+4x=360
2x+6+x+13+2x-1+2x+12+2x-17+3x-4+3x-10+4x=360
2x+x+2x+2x+2x+3x+3x+4x+6+13-1+12-17-4-10=360
19x-1=360
19x=360+1
19x=361
x=361/19
x=19
Putting the value of x in all the angles and we will find the following:
2x+6=2*19+6=44
x+13=19+13=32
2x-1=2*19-1=37
2x+12=2*19+12=50
2x-17=2*19-17=21
3x-4=3*19-4=51
3x-10=3*19-10=47
4x=4*19=76
Hence among all the exterior angles the smallest angle is 21°.
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The values in the table represent an exponential function. What is the common ratio of the associated geometric sequence?
x y
1 9
2 36
3 144
4 576
5 2304
The common ratio of the associated geometric sequence is 4
How to determine the common ratio?The table of values is given as:
x y
1 9
2 36
3 144
4 576
5 2304
The common ratio is calculated as:
Ratio = y(2)/y(1)
This gives
Ratio = 36/9
Divide
Ratio - 4
Hence, the common ratio is 4
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PLESE HELP ME ASAP!!!
Answer:
Square Root of 7 = 7^1/2 = 2.646
Cubed Root of 7 = 7^1/3 = 1.913
Square Root of 7^3 = 7^3/2 = 3.659
Each answer choice below represents a relation by a set of ordered pairs. In which of the answer choices is the relation a
function?
Select all correct answers.
Select all that apply.
□ {(-1,6), (4,4), (7, 13), (4,8)}
{(3,6), (3, 5), (9, 12), (0, -3)}
{(-5,0), (6, 8), (3,-5), (-5,-3)}
{(7,9), (8,4), (-2,4),(-3, 14)}
{(8,3), (3, 7), (6,4), (5,4)}
C
Answer:
D, E
Step-by-step explanation:
A set of ordered pairs represents a function if no x-value is repeated in the set.
Examine choices{(-1,6), (4,4), (7, 13), (4,8)} . . . . . not a function
{(3,6), (3, 5), (9, 12), (0, -3)} . . . not a function
{(-5,0), (6, 8), (3,-5), (-5,-3)} . . . . not a function
{(7,9), (8,4), (-2,4),(-3, 14)} . . . . no repeated x-values; is a function
{(8,3), (3, 7), (6,4), (5,4)} . . . . . .no repeated x-values; is a function
A number line going from negative 3 to positive 5. A closed circle is at negative 1.5. Everything to the left of the circle is shaded. Which inequalities have the solution set graphed on the number line? Check all that apply. x Greater-than-or-equal-to -1.5 x Less-than-or-equal-to -1.5 -1.5 Less-than-or-equal-to x -1.5 Greater-than-or-equal-to x x Less-than-or-equal-to -2.5 x Greater-than-or-equal-to -2.5 -2.5 Greater-than-or-equal-to x
the inequality in the number-line is:
x ≤ -1.5
Which inequality is represented?We know that we have a closed circle at -1.5, this means that the value is a solution of the inequality.
Then we have a line that goes to the left of that circle, so the inequality will have solutions that are less than or equal to -1.5
Then the inequality is:
x ≤ -1.5
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Answer:c
Step-by-step explanation:
trust me
i cannot log in edge
only me?
hello please help with my question, I will give brainlyest!
No, John is incorrect.
Correct work shown:
[tex]\sf x^2 - 6x - 7 = 0[/tex]
[tex]\sf x^2 - 6x = 7[/tex]
[tex]\sf x^2 - 6x + 9= 7 + 9[/tex]
[tex]\sf (x-3)^2= 16[/tex]
[tex]\sf x-3=\pm \sqrt{16}[/tex]
[tex]\sf x-3= \pm 4[/tex]
[tex]\sf x= + 4 + 3 \quad or \quad x = -4 + 3[/tex]
[tex]\sf x= 7 \quad or \quad x = -1[/tex]
The correct answer should be x = 7 or x = -1
An item is regularly priced at $60. Jane bought it at a discount of 30% off the regular price. How much did Jane pay?
$
X
5
Answer:
$72
Step-by-step explanation:
100%-$60
1%-$0.60
100%-30%=70%
70%-$0.60x70=$42
Set up an algebraic equation and then solve.
An integer is 17 more than 4 times another. If the product of the two integers is - 18,
then find the two integers.
Answer:
Step-by-step explanation:
let the numbers be x& y
y=4x+17
xy=-18
x(4x+17)=-18
4x²+17x+18=0
4x²+8x+9x+18=0
4x(x+2)+9(x+2)=0
(x+2)(4x+9)=0
x=-2
x=-9/4 (rejected as it is not an integer.)
y=4×(-2)+17=-8+17=9
so numbers are -2,9
Question 3 (Essay Worth 10 points) (05.07 MC) The scatter plot shows the number of strawberries that have been picked on the farm during the month of February: A scatter plot with points showing an upward trend with points that are moderately spread out from a line of best fit. The y axis is labeled Number of Strawberries and the x axis is labeled Days in February Part A: Using computer software, a correlation coefficient of r = 0.01 was calculated. Based on the scatter plot, is that an accurate value for this data? Why or why not? (5 points) Part B: Instead of comparing the number of strawberries picked and the day in February, write a scenario that would be a causal relationship for strawberries picked on the farm. (5 points)
It's not an accurate value for the data based on the scatter plot, r = 0.01 is not an accurate value for this data, because 0.01 means practically no correlation, while the points on the graph are moderately correlated
How to illustrate the information?1. Part A:
Since the points in the scatter plot show a moderated upward trend, you must expect a correlation coefficient close to ± 0.5. A correlation coefficient of 0.01 is too close to 0, which would mean that the points are almost not correlated at all.
The correlation coefficients, r, measure the strength of the correlation of two variables and they can have values from - 1 to 1.
Here, r = - 1 is a perfect negative correlation as the points will adjust perfectly to a line with negative slope.
r = + 1 is a perfect positive correlation: the points will ajdust perfectly to a line with positive slope.
r = 0 means that the variables are not correlated at all.
Hence, the closer to zero, the worse the correlation is, and that is what r = 0.01 means, but the graph shows other thing.
Therefore, the calculated value of r = 0.01 is not accurate for this scatter plot.
2. Part B.
A causal relationship means that the explanatory variable (the independent variable) is the cause of the dependent variable.
Hence, you must find a reasonable variable that can be the cause of the number of strawberries picked.
Thus, the scenario could be:
Amout of rainfall in mm (x) Number of strawberries picked (y)
100 20
50 40
25 80
12.5 160
6.25 320
The amount of rainfall is the cause of the number of strawberries picked, and you could find a model that relates both variables.
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Please help!! If........
Answer:
26
Step-by-step explanation:
[tex]f(x)=3x^{2} -5x+4\\f(-2)=3(-2)^{2} -5(-2)+4\\=3(4)+10+4\\=12+10+4\\=26[/tex]
Answer:
26
Step-by-step explanation:
3(-2)^2 = 12
5(-2) = -10
So 12 - (-10) + 4 = 26
Find the quotient: 40 ÷ 7
Answer:
5.71428571429
Step-by-step explanation:
Which of the numbers below are some potential roots of p(x) = x3 6x2 − 7x − 60 according to the rational root theorem?
The potential roots of the function p(x)=[tex]x^{3}+6x^{2} -7x-60[/tex] are -10,-5,3,15.
Given function p(x)=[tex]x^{3}+6x^{2} -7x-60[/tex]
We have to find the potential roots of the function according to rational root theorem.
Root is the solution of an equation usually expressed as a number or an algebraic formula.
The rational root theorem is used to find the potential roots of function.
For a polynomial function:
p(x)=p[tex]x^{n}[/tex]+..............................+q
The potential roots are:
Roots =±factors of q/factors of p
Th factors of 60 are =±1,±2,±3,±4,±5,±6,±10,±12.
The factors of 1 is ±1.
So we have factors are:±1,±2,±3,±4,±5,±6,±10,±12,±15,±20/±1
The roots are =±1,±2,±3,±4,±5,±6,±0.
Factors:-10,-5,3,15.
Hence the potential roots are -10,-5,3,15.
Question is incomplete as it should includes options :-10,-7,-5,3,15,24
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Different types of angels
Step-by-step explanation:
assuming you are looking for angles and not angels:
Zero Angle (0° in Measure)
Acute Angle (0 to 90° in Measure)
Right Angle (90° in Measure)
Obtuse Angle (90 to 180° in Measure)
Straight Angle (180° in Measure)
Reflex Angle (180 to 360° in Measure)
Complete Angle (360° in Measure)
How much would we pay per barrel of crude oil if the price goes up to US$ 75 and the US$ exchange rate stays the same?
If the price of a barrel of crude oil went up to $75, the amount that would be paid per barrel is $75.
What currency is oil denominated in?The U.S. dollar is the main currency for trade around the world which includes the trade of crude oil.
This means barrels of crude oil are denominated in dollars. An increase of crude oil to $75 per barrel means that Americans would be $75 because they already use the currency that the oil is denominated in.
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Choose the most convenient method to graph the line x=−3.
Select the correct answer below:
Recognize the equation as that of a vertical line passing through the x-axis at −3
Recognize the equation as that of a horizontal line passing through the y-axis at −3
Identify the slope and y-intercept and then graph
Find the x- and y-intercepts and then graph
Answer: Recognize the equation as that of a vertical line passing through the x-axis at −3
The age of undergraduate students at the U of A has a mean (µ) of 20.66 and a population standard deviation (s) of 2.4. What percentage of students are 21 or older and thus old enough to legally order alcohol at Griff's?
Using the normal distribution, it is found that 44.43% of students are 21 or older and thus old enough to legally order alcohol at Griff's.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 20.66, \sigma = 2.4[/tex]
The proportion of students that are 21 or older is one subtracted by the p-value of Z when X = 21, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{21 - 20.66}{2.4}[/tex]
Z = 0.14
Z = 0.14 has a p-value of 0.5557.
1 - 0.5557 = 0.4443 = 44.43% of students are 21 or older and thus old enough to legally order alcohol at Griff's.
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Suppose that you and a friend are playing cards and you decide to make a friendly wager. the bet is that you will dr6aw two cards without replacement from a standard deck. if both cards are hearts, your friend will pay you $16. otherwise, you have to pay your friend $3. suppose that you and a friend are playing cards and you decide to make a friendly wager. the bet is that you will draw two cards without replacement from a standard deck. if both cards are hearts, your friend will pay you $16. otherwise, you have to pay your friend $3. step 2 of 2 : if this same bet is made 762 times, how much would you expect to win or lose? round your answer to two decimal places. losses must be expressed as negative values. round your answer to two decimal places. losses must be expressed as negative values.
If the bet is done 762 times then expected value is that we may have a loss of $1562.1if the bet is that is heart comes we will get $16 and lose $3 if not comes.
Given We will get $16 if hearts come and lose $3 when not comes and bet is made 762 times. We have to calculate the expected win after 762 times.
We know that there are 13 hearts in the standard deck of cards.
Probability is the chance of happening an event among all the events possible. The formula of calculating probability is as under:
Probability= number of items/ total number of items.
When two cards are chosen at random without replacement then the probability of getting two hearts is 13/52*12/51
=156/2652
=0.05
When two cards are chosen at random without replacement then the probability of not getting two hearts is 1-0.05
=0.95
When bet is made only 1 time expected value will be 0.05*16-0.95*3
=0.8-2.85
=-2.05 means we are expecting to lose $2.05.
When bet is made 762 times then the expected value will be -2.05*762=-1562.1.
Hence the expected value when bet is made 762 times is that we will lose $1562.1 .
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gary cycled a total of 8 kilometers by making 4 trips to work. How many trips will gary have to make to cycle a total of 10 kilometers?
Answer:
5
Step-by-step explanation:
Each trip adds up to 8/4 = 2 km
According to this, to travel 10 km is required:
10/2 = 5 trips
Hope this helps
find two consecutive even integers such that 8 times the first equals 7 times the second
Answer:
Step-by-step explanation:
let the consecutive even integers be 2x,2x+2
8×2x=7(2x+2)
16x=14x+14
16x-14x=14
2x=14
x=14/2=7
so numbers are 2×7,2×7+2
or
14,16
Z
1
t
= [?]√
X
= Z
16
Answer: [tex]8\sqrt{5}[/tex]
Step-by-step explanation:
By the geometric mean theorem,
[tex]\frac{y}{16}=\frac{4}{y}\\\\y^{2}=64\\\\y=8[/tex]
So, by the Pythagorean theorem,
[tex]8^2 + 16^2 = x^2\\\\320=x^2\\\\x=\boxed{8\sqrt{5}}[/tex]
Which choice is equivalent to the quotient shown here for acceptable values of X?
√7x² ÷ √3x
A x(√7x/3)
B √21x³
C (√7x/3)
D (√7x³/3)
The choice that is equivalent to the quotient values of X in √7x² ÷ √3x is Option C : (√7x/3).
What is the quotient about?Since the expression is √7x² ÷ √3x
So, one need to rationalize the denominator and thus:
√7x² ÷ √3x x √3x ÷ √3x
or write as √7x² x√3x ÷ √3x
or write as√(21x³)/3x
or write as √3*7*x³/3x
or write as √3*7*x/3
= √7x/√3
Therefore, The choice that is equivalent to the quotient values of X in √7x² ÷ √3x is Option C : (√7x/3).
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how to find compound rate from given values, 10 years after, and initial
The formula that calculates the compound rate from the given values is [tex]r = n(-1 + \sqrt[10n]{\frac{P + I}{P}})[/tex]
How to determine the compound interest rate?The compound interest formula is:
[tex]I = P(1 + \frac rn)^{nt} - P[/tex]
Where:
P represents the principal amountr represents the compound interest raten represents the number of times the interest is compoundedt represents the time in yearsI represents the interestWe start by adding P to both sides
[tex]P + I = P(1 + \frac rn)^{nt}[/tex]
Divide through by P
[tex]\frac{P + I}{P} = (1 + \frac rn)^{nt}[/tex]
Take the nt-th root of both sides
[tex]\sqrt[nt]{\frac{P + I}{P}} = 1 + \frac rn[/tex]
Subtract 1 from both sides
[tex]-1 + \sqrt[nt]{\frac{P + I}{P}} = \frac rn[/tex]
Multiply through by n
[tex]r = n(-1 + \sqrt[nt]{\frac{P + I}{P}})[/tex]
In this case, t = 10
So, we have:
[tex]r = n(-1 + \sqrt[10n]{\frac{P + I}{P}})[/tex]
Hence, the formula that calculates the compound rate is [tex]r = n(-1 + \sqrt[10n]{\frac{P + I}{P}})[/tex]
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According to the National Postsecondary Student Aid Study conducted by the U.S. Department of Education in 2008, 62% of graduates from public universities had student loans.
We randomly select 50 students at a time.
What is the mean of the distribution of sampling proportions? Do not round, and enter your answer as a proportion (decimal number) not a percentage.
The mean of the distribution sample is 0.62 and the standard error of the distribution sample is 0.069
What is Mean ?Mean is the study of central tendency of a data set. The average value of the data points is the mean.
It is given that
The probability that the students have the student loan is = 62% = 0.62
The probability that the students do not have student loan is
1 - p
= 1 - 0.62
= 0.38
Total number of students is
n = 50
1) [tex]\rm \mu \;\hat p[/tex] = p = 0.62
2) [tex]\rm \sigma\hat p[/tex] = [tex]\rm \sqrt {p ( 1 - p ) / n}[/tex]
= [tex]\rm \sqrt {(0.62 * 0.38) / 50}[/tex]
= 0.069
Therefore the mean of the distribution sample is 0.62 and the standard error of the distribution sample is 0.069.
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In Washington county , 850 homes were sold in 2017 . How many homes was sold in the southwest region.
The number of homes sold in the Southwest region in 2017was B. 102.
What are Regional Sales?Regional sales refer to the sales recorded by marketing and sales regions through which an organization distributes its products and services.
Recording sales by region helps management to determine regional managers' performances and contributions to the sales efforts.
Data and CalculationsSales in Washington county:
Southeast = 48%
Southwest = 12%
Northwest = 25%
Northeast = 15%
Sales of homes in the Southwest region = 102 (850 x 12%)
Question Completion with Answer Options:A. 1,020
B. 102
C. 588
D. 1,231
Thus, the homes sold in the Southwest region in 2017 were B. 102.
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What is the order of rotational symmetry for the figure?
•A. 2
B. 1
C. 4 or more
D. 3
C is the right answer.
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Na bakla na yswa!