Answer: Slope: 4 Y-intercept: 0
Step-by-step explanation:
I NEED HELP special right triangle 45-45-90
Answer:
x=6
y=9
Step-by-step explanation:
Someone please help i don’t understand
Answer: you just add all the sides
Step-by-step explanation:
Of the relations graphed below, three are functions and one is not.
Which of the relations is NOT a function?
a. Graph A
b. Graph B
c. Graph C
d. Graph D
Answer:
Graph B
Step-by-step explanation:
the line is at some point perpendicular to the y-axis, there is no unique y value for this x value, which contradicts the definition of a function.
Use the given conditions to write an equation for the line in the indicated form.
Passing through (2, 2) and perpendicular to the line whose equation is y = 4x + 7;
point-slope form
A)y=-4x-10
B)y-2=-1/4(x-2)
C)y-2=1/4(x+2)
D)y-2=1/4(x-2)
Answer:
B) y - 2 = (-1/4)(x - 2)
Step-by-step explanation:
Start with the equation of the given line: y = 4x + 7.
Determine the slope of the given line, which is 4.
Since the perpendicular line has a negative reciprocal slope, the perpendicular line's slope is -1/4.
Use the point-slope form of a linear equation: y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope.
Substitute the values x₁ = 2 and y₁ = 2 into the point-slope equation: y - 2 = (-1/4)(x - 2).
Simplify by distributing -1/4 to (x - 2): y - 2 = (-1/4)x + 1/2.
Add 2 to both sides to isolate y: y = (-1/4)x + 1/2 + 2.
Simplify further: y = (-1/4)x + 5/2.
The equation in point-slope form for the line passing through (2, 2) and perpendicular to y = 4x + 7 is y - 2 = (-1/4)(x - 2), which matches option B.
Find the first three nonzero terms in the Taylor polynomial approximation to the DE V" +9y + 5y3 = cos(10t), y(0) = 0, y' (0) = 1.
The first three non zero terms in the Taylor polynomial approximation to the given DE is y(t) = t + t²/2 -(3/2)t³ .
In the question ,
it is given that ,
the differential equation is
y'' + 9y + 5y³ = Cos(10t) ...equation(1)
y(0) = 0, y'(0) = 1
for y = 0 , the differential equation is
y''(0) + 9y(0) + 5{y(0)}³ = Cos90)
y''(0) + 9 + 5 = 1 ;
y''(0) = 1.
differentiating equation(1) with respect to "t" , we have
y''' + 9y' + 15y²y' = -10Sin(10t)
y'''(0) + 9y'(0) + 15{y(0)}².y'(0) = -10Sin(0)
y'''(0) + 9 + 0 = 0
y'''(0) = -9
The Taylor series is given by
y(t) = y(0) + y'(0)t + 1/2.y''(0)t² + 1/3!.y'''(0)t³ + ....
Now substituting the values of y(0) , y'(0) , y''(0) , y'''(0) , we have
y(t) = 0 + 1.t + 1/2.t² + 1/6.(-9)t³ + ....
= t + t²/2 - 3/2.t³ + ...
Therefore , the first three terms are t , t²/2 , -3/2.t³ .
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Use f(x) = 1
2
x and f -1(x) = 2x to solve the problems.
f(2) =
1
f−1(1) =
⇒ 2
f−1(f(2)) =
⇒ 2
f−1(−2) =
1
⇒ -4
f(−4) =
2
⇒ -2
f(f−1(−2)) =
2
⇒ -2
In general, f−1(f(x)) = f(f−1(x)) =
Using the function f(x) = 1/2 x and the inverse of the function f⁻¹(x) = 2x, the solutions of the given are :
f(2) = 1, f⁻¹(1) = 2, f⁻¹(f(2)) = 2
f⁻¹(-2) = -4, f(-4) = -2, f(f⁻¹(-2)) = -2
Given a function,
f(x) = 1/2 x
And an inverse function,
f⁻¹(x) = 2x
We have to find the values of the following.
f(2) = 1/2 × 2 = 1
f⁻¹(1) = 2 × 1 = 2
f⁻¹(f(2)) = f⁻¹(1) = 2 × 1 = 2
f⁻¹(-2) = 2 × -2 = -4
f(-4) = 1/2 × 4 = -2
f(f⁻¹(-2)) = f (-4) = 1/2 × 4 = -2
So, in general, f⁻¹(f(x)) = f(f⁻¹(x))
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For the equation f(x) = 1.1 * (0.44) ^ x state the initial value C, the growth or decay factor a, and percent change R for each unit increase in x
c = (Type an integer or a decimal)
a = (Type an integer or a decimal)
R = % (Simplify your answer. Type an integer or a decimal)
The parameters of the exponential function in this problem are given as follows:
c = 1.1.a = 0.56.R = -56%.What is an exponential function?The standard format of an exponential function is given as follows:
y = c(1 - a)^t.
This is the case for a decaying exponential function, and the meaning of each parameter is given as follows:
c is the initial value, value assumed by y when t = 0.a is the decay rate.In this problem, the function is given as follows:
f(x) = 1.1(0.44)^x.
Hence the values for the parameters are given as follows:
c = 1.1, which is the initial value.a = 0.56, as 1 - a = 0.44 -> a = 0.56.Then the percent of change is of -56%, as it is a decaying exponential function with a = 0.56.
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let y1,y2 be independent random variables both having the uniform(0,1) distribution. re- call that the density function and distribution function of a uniform random variable y
A uniform random variable's density function is f(y) = 1 for y 1 and 0 otherwise. F(y) = 0 for y 0, F(y) = y for 0 y 1, and F(y) = 1 for y > 1 define the distribution function.
A uniform random variable's density function is f(y) = 1 for y 1 and 0 otherwise. Accordingly, the likelihood of any specific outcome of y is the same, and the likelihood of any range of outcomes is equal to the length of the range. F(y) = 0 for y 0, F(y) = y for 0 y 1, and F(y) = 1 for y > 1 define the distribution function. Accordingly, the length of the range multiplied by the likelihood of any specific occurrence yields the cumulative probability of any range of outcomes. Since the likelihood of any specific result in that range is 1 and the range's length is 0.5, for instance, the cumulative probability of 0 y 0.5 is 0.5. Since the likelihood of any given result within that range is still 1, but the range's length is 0.5, the cumulative probability of 0.5 y 1 is 0.75. The chance of any range of outcomes for y1 and y2 if they are independent random variables both having the uniform(0,1) distribution is just the sum of their respective cumulative probabilities.
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What is the probability that both events will occur? Two dice are tossed. Event A: the first die is a 5 or 6. Event B: The second die is not a 1
Answer: The probability that both events A and B will occur is 5/18 or 0.28.
Step-by-step explanation:
To determine the probability that both events A and B will occur, we need to calculate the probabilities of each event separately and then multiply them together.
Event A: The probability of rolling a 5 or 6 on the first die is 2 out of 6 (since there are two favorable outcomes out of six possible outcomes on a fair six-sided die). Therefore, the probability of event A is 2/6 or 1/3.
Event B: The probability of not rolling a 1 on the second die is 5 out of 6 (since there are five favorable outcomes out of six possible outcomes). Therefore, the probability of event B is 5/6.
To find the probability that both events A and B occur, we multiply the probabilities:
Probability(A and B) = Probability(A) * Probability(B) = (1/3) * (5/6) = 5/18.
Toothpaste Ken is traveling for his business. He has a new 0.85-ounce tube of toothpaste that’s supposed to last him the whole trip. The amount of toothpaste Ken squeezes out of the tube each time he brushes varies according to a Normal distribution with mean 0.13 ounces and standard deviation 0.02 ounces. If Ken brushes his teeth six times on a randomly selected trip, what’s the probability that he’ll use all the toothpaste in the tube?
Using the normal distribution, it is found that there is a 0.2798 = 27.98% probability that he’ll use all the toothpaste in the tube.
In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.When a variable is multiplied by a constant, both the mean and the standard deviation are multiplied by the constant.In this problem:
Brushes 6 times.Each time, mean of 0.13 ounces, hence, for the 6 times, \(\mu = 0.13(6) = 0.78\)Each time, standard deviation of 0.02 ounces, hence, for the 6 times, \(\sigma = 0.02(6) = 0.12\).The probability that he’ll use all the toothpaste in the tube is 1 subtracted by the p-value of Z when X = 0.85, hence:
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{0.85 - 0.78}{0.12}\)
\(Z = 0.583\)
\(Z = 0.583\) has a p-value of 0.7202.
1 - 0.7202 = 0.2798
0.2798 = 27.98% probability that he’ll use all the toothpaste in the tube.
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Select the correct answer.
A drugstore sells vitamins in bottles with different pill counts. The price of each bottle is shown in the table below.
Price
Number of
Pills
50
100
150
$1.85
$3.70
$5.55
$7.40
$9.25
200
250
About how much does one vitamin cost?
$1.85
$0.37
$0.92
$0.04
$0.02
Answer:
Step-by-step explanation:
The approximate cost of one vitamin is $0.04 thus option (A) is correct.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
As per the given number of pills and cost.
The cost per pill from the first raw = $2.05/50 = $0.041
The cost per pill from the second raw = $4.10/100 = $0.041
The cost per pill remains constant in all so this is a direct proportion.
Hence "The approximate cost of one vitamin is $0.04".
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The complete structured question is below,
please help will give brainliest
Answer:
3v/B = h
Step-by-step explanation:
b/c v=BH/3
3v=bh
h=3v/b
hope it helps
Find the coordinates of the orthocenter of a triangle with vertices at each set of points on a coordinate plane.
a. (0,0), (7,3), (3,51)
b. (5,3), (8,6), (4,10)
.
a. The orthocenter is .
(Type an ordered pair. Simplify your answer.)
b. The orthocenter is.
(Type an ordered pair. Simplify your answer.)
9514 1404 393
Answer:
a. (24, 2)
b. (8, 6)
Step-by-step explanation:
The orthocenter is the point where the altitudes of the triangle coincide. For an obtuse triangle, it will be outside the triangle. For a right triangle, it will be the right angle vertex. Of course, each altitude is a line through a vertex and perpendicular to the opposite side.
To make finding the orthocenter as easy as possible, we want to find a simple way to write an equation for a line through a point and perpendicular to the segment between two other points. For segment end points (x1, y1) and (x2, y2), the line between them will have slope (y2 -y1)/(x2 -x1). The perpendicular line has a slope that is the opposite reciprocal of this: -(x2 -x1)/(y2 -y1). Then the point-slope equation of the perpendicular through point (x3, y3) is ...
y -y3 = -(x2 -x1)/(y2 -y1)(x -x3)
This can be rearranged to something resembling standard form:
(x2 -1x)(x -x3) +(y2 -y1)(y -y3) = 0
(x2 -x1)x +(y2 -y1)y = (x2 -x1)x3 +(y2 -y1)y3 . . . . line through P3, ⊥ to P1P2
__
a.For the first altitude, we choose P1 = (0, 0), P2 = (7, 3), and P3 = (3, 51). This gives ...
(x2 -x1) = 7 -0 = 7(y2 -y1) = 3 -0 = 3altitude equation = 7x +3y = 7·3 +3·51 = 174For the second altitude, we choose P1 = (0, 0), P2 = (3, 51), and P3 = (7, 3). This gives ...
(x2 -x1) = 3 -0 = 3(y2 -y1) = 51 -0 = 51altitude equation = 3x +51y = 3·7 +51·3 = 174Finding the point of intersection of these two equations can be done an of a number of ways. Cramer's Rule provides a quick solution:
x = ((3)(-174) -(51)(-174))/(7·51 -3·3) = 8352/348 = 24
y = ((-174)(3) -(-174)(7))/348 = 696/348 = 2
The orthocenter for the triangle is (24, 2).
__
b.We can use the method just described, or we can verify the triangle is a right triangle, as it appears to be when the points are plotted.
The slope of P1P2 is (6 -3)/(8 -5) = 3/3/ = 1.
The slope of P2P3 is (10 -6)/(4 -8) = 4/-4 = -1
These slopes have a product of -1, so the segments are perpendicular. The vertex P2 has the right angle, hence is the orthocenter.
The orthocenter for the triangle is (8, 6).
It takes 5 hr for 2 bricklayers to build a park wall. How long would it take 8 bricklayers to complete the job?
The function Y=4.75+2.20(X-1) can be used to determine the cost in dollars for a taxi ride in Houston, TX. What is the rate of change of the cost in dollars with respect to the number of miles?
Answer:
2.20 dollars/mile
Step-by-step explanation:
Given the function:
y = 4.75 + 2.20(x-1)
Before we get the rate of change of the cost, we need to write the expression in the form y = mx+c where;
m is the rate of change of the cost
From the function given:
y = 4.75 + 2.20(x-1)
Open the parenthesis
y = 4.75 + 2.20x -2.20
y = 2.20x + 2.55
On comparing with the standard
m = 2.20
Hence the rate of change of the cost in dollars with respect to the number of miles is 2.20 dollars/mile
Bennett Griffin and Chula Garza organized Cole Valley Book Store as a corporation; each contributed $71,500 cash to start the business and received 5,600 shares of common stock. The store completed its first year of operations on December 31, current year. On that date, the following financial items for the year were determined: December 31, current year, cash on hand and in the bank, $69,250; December 31, current year, amounts due from customers from sales of books, $43,500; unused portion of store and office equipment, $72,500; December 31, current year, amounts owed to publishers for books purchased, $12,400; one-year note payable to a local bank for $3,200. No dividends were declared or paid to the stockholders during the year.
Required:
Complete the following balance sheet as of the end of the current year. Some information has been given below.
What was the amount of net income for the year? (Hint: Use the retained earnings equation [Beginning Retained Earnings + Net Income − Dividends = Ending Retained Earnings] to solve for net income.)
he net income for the year is $16,550.
Calculation of the net income for the year:Retained earnings equation is:Beginning Retained Earnings + Net Income − Dividends = Ending Retained EarningsWhere, Beginning Retained Earnings = $0 (not given)Ending Retained Earnings = $16,550 (calculated from balance sheet)Dividends = $0 (not given)
Therefore,Net Income = Ending Retained Earnings - Beginning Retained Earnings + Dividends= $16,550 - $0 + $0= $16,550 Balance Sheet of Cole Valley Book Store as of December 31, current year:Current assets Cash on hand and in bank = $69,250 Amounts due from customers from sales of books = $43,500 Total current assets = $112,750 Property, plant, and equipment Unused portion of store and office equipment = $72,500
Total assets = $185,250Liabilities Amounts owed to publishers for books purchased = $12,400 One-year note payable to a local bank = $3,200 Total liabilities = $15,600 Stock holders' Equity Common stock, 5,600 shares at $71,500 = $400,400 Retained earnings, beginning = $0Net income = $16,550 Retained earnings, ending = $16,550 Total stockholders' equity = $416,950Total liabilities and stockholders' equity = $185,250 + $15,600 + $416,950= $617,800
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Please help.
Complete the equation for the function that is represented by the graph.
f(x)=?
Does this represent exponential growth or exponential decay?
The function represents an exponential decay, as it is a decreasing function.
How to classify a function as exponential growth or exponential decay?A function is classified as exponential growth if it is an increasing function, that is, the function is increasing over it's entire domain.
A function is classified as exponential decay if it is an decreasing function, that is, the function is decreasing over it's entire domain.
As the function in this problem is decreasing, it is an exponential decay function.
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2. Write down the numbers 1 to 16 in your workbook. From that list write down the numbers that are: a) neither composite nor prime
The number which is neither prime οr cοmpοsite is 1.
What is wοrd prοblem?Wοrd prοblems are οften described verbally as instances where a prοblem exists and οne οr mοre questiοns are pοsed, the sοlutiοns tο which can be fοund by applying mathematical οperatiοns tο the numerical infοrmatiοn prοvided in the prοblem statement. Determining whether twο prοvided statements are equal with respect tο a cοllectiοn οf rewritings is knοwn as a wοrd prοblem in cοmputatiοnal mathematics.
Here the number between 1 tο 16 is,
=> 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16.
Prime numbers are the number which is divided by 1 and itself. Then,
Prime numbers = 2,3,5,7,11,13
Cοmpοsite numbers are numbers which are have mοre than οne factοrs. Then,
Cοmpοsite numbers = 4,6,8,9,10,12,14,15,16.
Then number which is neither prime nοr cοmpοsite is 1.
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The mass of an electron is approximately 9.11 × 10 -28 grams. Find the mass of 401,000,000 electrons. 3.65311 × 10-19 grams 3.65311 × 10-18 grams 3.65311 × 10-17 grams 3.65311 × 10-20 grams
Answer:
\(Total\ Mass = 3.65311 * 10^{-19}\) grams
Step-by-step explanation:
Given
\(Mass = 9.11 * 10^{-28}g\)
Required
Determine the mass of 401,000,000 electrons
To do this, we simply multiply the mass of 1 electron by the number of electrons.
This gives:
\(Total\ Mass = 401,000,000 * 9.11 * 10^{-28}\)
\(Total\ Mass = 3653110000 * 10^{-28}\)
Express 3653110000 as a standard form
\(Total\ Mass = 3.65311 * 10^9 * 10^{-28}\)
Apply law of indices:
\(Total\ Mass = 3.65311 * 10^{9-28}\)
\(Total\ Mass = 3.65311 * 10^{-19}\)
Hence, the mass of 401000000 electrons is \(3.65311 * 10^{-19}\ grams\)
Which of the following represents the series? –13 + (–7) + (–1) + 5 + 11
Answer:
Adding +6 in turn
Step-by-step explanation:
-13+6=(-7)
(-7)+6=(-1)
(-1)+6=5
5+6=11
11+6=17
17+6=23
23+6=29
29+6=35
........... And so on
if it helped uh please mark me a brainliest :))brainliest to correct quickly
Answer:
8 4/20
0.2
-8 1/10
Step-by-step explanation:
write a real-life word problem that involves one-variable equation. Discuss how you would go about solving this problem.
help pls
Answer:
A waiter at a restaurant earns 10 dollars per hour. How much money is earned in 4 hours?
Equation: m = 10h
m = money earned
h = hours worked
Plug in 4 for (h)
m = 10(4)
m = 40 dollars
The waiter earns 40 dollars in 4 hours.
Step-by-step explanation:
Enter the degree of the polynomial below:
9x2 + 3x8 + 6x + 586 -7x5
\( \large \mathfrak{Answer : }\)
The degree of a polynomial is the highest power among its terms .
i.e 8 for the above expression :
9x² + 3x⁸ + 6x + 586 - 7x⁵
my bowl of easter candy has colorful foil-wrapped chocolate eggs. there are 5 gold, 7 blue, and 10 pink. when callie brooke raids the candy bowl, what is the probability that she reaches in without looking and gets a chocolate candy wrapped in pink foil? give your answer as a percent (including the percent sign) rounded to the nearest 0.01%.
If my bowl of easter candy has colorful foil-wrapped chocolate eggs. there are 5 gold, 7 blue, and 10 pink. The probability that she reaches in without looking and gets a chocolate candy wrapped in pink foil is 0.45.
How to find the probability?Total color = 5 gold + 7 blue + 10 pink
Total color = 22
Now let find the probability that she reaches in without looking and gets a chocolate candy wrapped in pink foil
Probability (pink) = 10/22
Probability (pink) = 0.45
Therefore the probability of Callie Brooke getting a pink foil-wrapped chocolate egg is 10/22, or approximately 0.45.
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Select the correct answer from each drop-down menu. For the figure shown, point D is a midpoint of , and point J is a midpoint of . A figure shows a double-sided arrow. The points on the left and right arrows are A, B, L, and F, G, H. The points on the upper and lower lines are C, D, E, and K, J, I. Since reflecting the points C, B, A, L, and K across line maps these points onto E, F, G, H, and I, respectively, the opposite angles are congruent. Since reflecting the points L, K, J, I, and H across line maps these points onto B, C, D, E, and F, respectively, the opposite sides and , , and and are congruent.
The first blank is BAL and FGH
The second blank is AL
The third blank is CE and KI
The fourth and final blank is GH
According to the statement
we have given a diagram in which there are some angles and from these angles we have to find that the
Which opposite angles are congruent
The opposite side of AB
With GF angle which angle are congruent
Two angles are which are opposite to each other.
So, from a diagram it is clear that The angles which are congruent with each other is BAL and FGH. Because there positions are perfectly opposite and same to each other.
And The opposite side of AB is AL because it is present at opposite position to each other.
And with GF angle GH are congruent angles.
So, The first blank is BAL and FGH
The second blank is AL
The third blank is CE and KI
The fourth and final blank is GH
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DISCLAIMER: This question is incomplete.Please see the complete question below.
QUESTION:
Select the correct answer from each drop-down menu.
For the figure shown, point D is a midpoint of , and point J is a midpoint in figure.
Since reflecting the points C, B, A, L, and K across line maps these points onto E, F, G, H, and I, respectively, the opposite angles
are congruent. Since reflecting the points L, K, J, I, and H across line maps these points onto B, C, D, E, and F, respectively, the opposite sides are congruent.
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Please help!
Olivia's mom decided to wallpaper the living room. At the store, the wallpaper was selling for $11.68 for a roll with 100 linear feet. What is the price per linear foot of the wallpaper?
A direct mail appeal for contributions from a university’s alumni and supporters is considered to be too costly if less than 28%
28
%
of the alumni and supporters provide monetary contributions. To determine if a direct mail appeal is cost effective, the fundraising director sends the direct mail brochures to a simple random sample of 165
165
people on the alumni and supporters mailing lists. They receive monetary contributions from 36
36
people. Does this evidence demonstrate that the direct mail campaign is not cost effective? Use a 0.05
0.05
level of significance.
Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places.
The test statistic is given as follows:
z = -1.77.
As the test statistic is less than the critical value for the left-tailed test, this evidence demonstrates that the direct mail campaign is not cost effective.
How to obtain the test statistic?
The equation for the test statistic is given as follows:
\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)
In which:
\(\overline{p}\) is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.The parameters for this problem are given as follows:
\(p = 0.28, n = 165, \overline{p} = 0.2182\)
The critical value for a left tailed test with a significance value of 0.05 is given as follows:
z = -1.645.
The test statistic is then given as follows:
\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)
\(z = \frac{0.2182 - 0.28}{\sqrt{\frac{0.28(0.72))}{165}}}\)
z = -1.77.
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Quantitative Problem: You own a security that provides an annual dividend of $150 forever. The security’s annual return is 7%. What is the present value of this security? Round your answer to the nearest cent. $ 2142.86
The present value of the security is $2142.86, rounded to the nearest cent.
What is value?Value is a subjective concept that is based on personal beliefs, experiences, and backgrounds. It is the appreciation of something, whether tangible or intangible, that is based on a person's perception of its worth. Value is often used to describe the worth or importance of something or someone, and can be expressed in monetary terms or in terms of the usefulness of something. Ultimately, value is the measure of how much something is worth to an individual.
The present value of this security is $2142.86. This is determined by using the formula:
Present Value = Dividend / (1 + R)t
Where Dividend is the annual dividend of $150, R is the rate of return which is 7%, and T is the time in years which is 1.
Therefore, the present value of the security is:
150 / (1 + 0.07)¹ = $2142.86
Thus, the present value of the security is $2142.86, rounded to the nearest cent.
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2 1/2 + (345-206) - 3 1/3
Answer:
139 should be the answer
Step-by-step explanation:
3459-684 HELP ME WWWWWWWW