Answer:
Step-by-step explanation:
[tex]\text{here is the missing text:} \\ \\ \text{ Suppose a company issues an annual coupon bond with a maturity of 2 years,} \\ \\ \text{ price of $950 \ par \ value \ of $1,000, and coupon rate of 5\% They also issue an}[/tex]
[tex]\text{ annual zero-coupon bond with a maturity of 1 year, price of $900, \ and \ par \ value \ of \ $1,000.}[/tex]
[tex]\text{To determine the 1-year spot rate using the 1-year zero bond.} \\ \\ FV = PV \times (1 + S_1) \\ \\ 1+ S_1 = \dfrac{FV}{PV} \\ \\ 1 + S_1 = \dfrac{1000}{900} \\ \\ S_1 = 11.11\%[/tex]
[tex]\text{PV of the 2-year bond = 950} \\ \\ Annual coupon = 1000 \times 5\% = \$50 \\ \\ \\ 950 = \dfrac{50}{(1+S_1) }+ \dfrac{(50+1000)}{(1+S_2)^2} \\ \\ 950 = \dfrac{50}{1.1111}+ \dfrac{1050}{(1+S_2)^2} \\ \\ \dfrac{1050}{(1+S_2)^2}=950 -45\\ \\ \dfrac{1050}{(1+S_2)^2}=905 \\ \\ (1+S_2)^2 = \dfrac{1050}{905} \\ \\ 1 + S_2= \sqrt{(1.16022)} \\ \\ S_2 = 7.714\%[/tex]
[tex]\text{the arbitrage-free price of the 2-year bond}= \dfrac{1000}{(1+0.07714)^2} \\ \\ = \mathbf{\$861.90}[/tex]
GIVING BRAINLIEST!!!
Which statement best describes the expression (5 x 3 − 12) x 8?
A) Subtract the product of 5 and 3 from the product of 12 and 8.
B) Multiply the difference of 12 and 8 by the product of 5 and 3.
C) Multiply the difference of 5 and 3 by 8, then subtract 12.
D) Subtract 12 from the product of 5 and 3, then multiply by 8.
Answer:
D.
Explanation:
PEMDAS method. First do the parentheses. Multiply first, then subtract 12 from that number. Once finished with the parentheses, multiply by 8.
The price of a new car was 12,500 it is reduced to 11,625 work out the percentage reduction
Answer:
93%.
Step-by-step explanation:
% Decrease = Decrease ÷ Original Number × 100
Divde 11,625 by 12,500 and multiply the answer by 100.
11,625 ÷ 12,500 × 100 = 93
The percentage reduction is 93%.
Help !!
Determine the value of y, if x is 7.
y = x2 – 5
find the solution of given expression
[tex] \sqrt{2545 \times 2545} [/tex]
Answer:
√{2545×2545}=√2545²=±2545
In ABC, what is the measure of C?
108°
20°
18°
36°
Answer:
36
Step-by-step explanation:
b is 3x bigger then a and c but all add to 180
so 108 is b you have 72 left 72/2 for and c is 36
what percent can you turn 3/2 into
Answer:
150℅
Step-by-step explanation:
3/2×100/1
2 in 100=50
so50×3=150℅
1.02 sinusoidal graph
WHAT IS THE AMPLITUDE OF THE SINUSOIDAL FUNCTION?
Enter your answer in the box.
___
Answer:
[tex]\displaystyle 5[/tex]
Step-by-step explanation:
[tex]\displaystyle \boxed{y = -5cos\:(\frac{39}{64}\pi{x} + \frac{\pi}{2}) + 1} \\ \\ y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{32}{39}} \hookrightarrow \frac{-\frac{\pi}{2}}{\frac{39}{64}\pi} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{3\frac{11}{39}} \hookrightarrow \frac{2}{\frac{39}{64}\pi}\pi \\ Amplitude \hookrightarrow 5[/tex]
OR
[tex]\displaystyle \boxed{y = -5sin\:(\frac{39}{64}\pi{x} + \pi) + 1} \\ \\ y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-1\frac{25}{39}} \hookrightarrow \frac{-\pi}{\frac{39}{64}\pi} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{3\frac{11}{39}} \hookrightarrow \frac{2}{\frac{39}{64}\pi}\pi \\ Amplitude \hookrightarrow 5[/tex]
As you can see, the right-centred photograph displays the trigonometric graph of [tex]\displaystyle y = -5cos\:\frac{39}{64}\pi{x} + 1,[/tex]in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph farthest to the left], accourding to the horisontal shift formula above. Also keep in mind that −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so be very careful with your calculations. So, between both photographs, we can tell that the cosine graph [centre right photograph] is shifted [tex]\displaystyle \frac{32}{39}\:unit[/tex]to the right, which means that in order to match the sine graph [photograph farthest to the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{32}{39}\:unit,[/tex]which means the C-term will be negative, and by perfourming your calculations, you get [tex]\displaystyle \boxed{-\frac{32}{39}} = \frac{-\frac{\pi}{2}}{\frac{39}{64}\pi}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = -5cos\:(\frac{39}{64}\pi{x} + \frac{\pi}{2}) + 1.[/tex]Intermediate, we have two sine graphs [centre left photograph and the photograph farthest to the left]. The left-centred photograph displays the trigonometric graph of [tex]\displaystyle y = -5sin\:\frac{39}{64}\pi{x} + 1.[/tex]So, just like before, we need to figure out the appropriate C-term that will horisontally shift the graph back into position ["position", meaning shifting this sine graph back in plase (matching the sine graph in the photograph on the left)]. So, between the two photographs, we can tell that the left-centred sine graph is shifted [tex]\displaystyle 1\frac{25}{39}\:unit[/tex]to the right, which means that in order to match the leftward sine graph, we need to shift the graph BACKWARD [tex]\displaystyle 1\frac{25}{39}\:unit,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-1\frac{25}{39}} = \frac{-\pi}{\frac{39}{64}\pi}.[/tex]So, when shifted back into original position, the sine graph is [tex]\displaystyle y = -5sin\:(\frac{39}{64}\pi{x} + \pi) + 1.[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [-6\frac{22}{39}, 1],[/tex]from there to [tex]\displaystyle [-3\frac{11}{39}, 1],[/tex]they are obviously [tex]\displaystyle 3\frac{11}{39}\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle 3\frac{11}{39}.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, and in case you want to be certain, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 1,[/tex]in which each crest is extended five units beyond the midline, hence, your amplitude. Now... the sine graph in the photograph farthest to the right is the OPPOCITE of the sine graph in the photograph farthest to the left, and the reason for this is because of the negative inserted in front of the amplitude value. Whenever you insert a negative in front of the amplitude value of any trigonometric equation, the whole graph reflects over the midline. Keep this in mind moving forward. So, overall, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
I need showing work for this question for finding the volume of it
Choose the correct simplification of (8x + 3y)(2x - 4y). (5 points)
16x2 + 26xy + 12y2
16x2 + 26xy - 12y2
16x2 - 26xy + 12y2
16x2 - 26xy - 12y2
Answer: [tex]16x^{2} - 26xy - 12y^{2}[/tex]
Which point is located on the line represented by y = -3x + 4? A) (4,8) B) (4-8) C) (-4, 8) D) (-4,-8)
Answer:
B
Step-by-step explanation:
To determine which point lies on the line, substitute the x- coordinate of the point into the equation and if the value equals the y- coordinate of the point then it lies on the line.
A (4, 8)
y = - 3(4) + 4 = - 12 + 4 = - 8 ≠ 8 ← not on line
B (4, - 8 )
y = - 3(4) + 4 = - 12 + 4 = - 8 ← lies on line
C (- 4, 8 )
y = - 3(- 4) + 4 = 12 + 4 = 16 ≠ 8 ← not on line
D (- 4, - 8 )
y = - 3(- 4) + 4 = 12 + 4 = 16 ≠ - 8 ← not on line
The point lying on the line is (4, - 8 ) → B
Solve for x:
x/7 - 6 = 3
A. 27
B. -63
C. -27
D. 63
Answer:
D. 63
Step-by-step explanation:
First, add 6 to both sides:
[tex]\frac{x}{7}[/tex] - 6 = 3
[tex]\frac{x}{7}[/tex] = 9
Multiply each side by 7
x = 63
So, the correct answer is D. 63
Simplify 6⋅ (x+3)
Apply the distributive property.
6x+6⋅3=x⋅76x+6⋅3=x⋅7
Multiply 66 by 33.
6x+18=x⋅76x+18=x⋅7
Move 77 to the left of xx.
6x+18=7x
Move all terms containing x to the left side of the equation.
subtract 7x7x from both sides of the equation.
6x+18−7x=06x+18-7x=0
Subtract 7x7x from 6x6x.
−x+18=0-x+18=0
Subtract 1818 from both sides of the equation.
−x=−18-x=-18
Multiply each term in −x=−18-x=-18 by −1
Multiply −1-1 by −1-1.
1x=(−18)⋅−11x=(-18)⋅-1
Multiply xx by 11.
x=(−18)⋅−1x=(-18)⋅-1
Multiply−18-18 by −1-1.
x=18
The sum of two numbers is 25. The difference between twice the first number and the second number is -10. Find the numbers
Answer:
The five most important sample values are sample minimum, sample maximum, median, lower quartile, and upper quartile.
Min=−10
Max=25
M=7.5
Q1=−10
Q3=25
Step-by-step explanation:
The five-number summary is a descriptive statistic that provides information about a set of observations. It consists of the following statistics:
1. Minimum (Min) - the smallest observation
2. Maximum (Max) - the largest observation
3. Median M - the middle term
4. First Quartile Q1 - the middle term of values below the median
5. Third Quartile Q3 - the middle term of values above the median
Arrange the terms in ascending order.
−10,25
The minimum value is the smallest value in the arranged data set.
−10
The maximum value is the largest value in the arranged data set.
25
Find the median.
7.5
The lower half of data is the set below the median.
−10
The upper half of data is the set above the median.
25
what is the value of 2 ones, 8 tenths and 14 hundredths
Answer:
2.814
Step-by-step explanation:
Answer:
14802
Step-by-step explanation:
2.142 Dag into gram and milligram
Answer:
21.42g 21420mg
Step-by-step explanation:
2.142x10=21.42g
2.142x10000=21420mg
Which matrix equation represents the system of linear equations?
3x-9y-Z=-4
-2x + y - 8z = 1
5x + 2y + 2z = 9
-175 x 3
1 1 - 8
y = -2
9 2 2
-4 -9
N
LO
3 -9
-111x
-4
-2
1 - 8
y =
1
B
5
2
2
N
9
x
3 -9
-4
х
-1
-2
1
1 ll y =
8
ir N
2
9
Z
2
9514 1404 393
Answer:
B
Step-by-step explanation:
When solving multiple choice problems, a reasonable strategy is to look for ways to identify one answer as good, or other answers as bad.
Here, all of the constant vectors in the equations are different, so we can decide the answer based on that.
The only equation with the correct constant vector is choice B.
_____
The constants in the equations are -4, 1, 9 — the values to the right of the equal sign.
Q1: How do you divide a segment into given ratios?
Answer: To find the point P that divides a segment AB into a particular ratio, determine the ratio k by writing the numerator over the sum of the numerator and the denominator of the given ratio. Next, find the rise and the run (slope) of the line. Finally, add (k. the run) to the x-coordinate of A and add (k.
Step-by-step explanation: Hope this helps :)
An online gaming company offers two different plans for unlimited access. Plan A has a one-time $27
membership fee and is $6.50 a month. Plan B has a $14.50 membership fee and $9.00 a month. For which months is Plan A cheaper? For which months is Plan B cheaper?
please help i really need this....
Answer:
愚蠢的他媽的
Step-by-step explanation:
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A group of 3 friends went to a movie. They paid $15 for a bucket of popcorn. All the
movie tickets were the same price. They paid $51.75 total. Which equation represents
the cost of the tickets?
Answer:
51.75- 15= 36.75
36.75/3= 12.25 per ticket
Answer:
51.75 - 15 / 3
Step-by-step explanation:
$15 for a bucket of popcorn is separate from the tickets, so you subtract that from the sum.
Then you should have 36.75.
36.75 / 3 = 12.25
I hope this helped!
Stay safe! <3
please help!!
Which equation does the graph of the systems of equations solve?
Answer:
you have to solve the first step and up and down
Step-by-step explanation:
with times hait
1. A coin is tossed and a single die is rolled. What is the theoretical
probability that the coin shows tails and the die shows an even number?
1/4
1/2
3/6
1/3
Answer:
A
Step-by-step explanation:
The chance the coin will show 'tails' is 1/2, since there are only 2 sides to a coin. The chance that the die will show an even number is also 1/2, since half of the numbers on a die are even, and half are odd. But, since both of these events depend on each other, or in other words, are dependent, we have to multiply both numbers. 1/2 x 1/2 = 1/4, therefore your answer is A.
Twenty years ago a small town in Texas had a population of 10,000. The population has increased 8% each year since then. What is the current population of this town? a. The population of this town is approximately 46,609 b. The population of this town is approximately 115,292 c. The population of this town is approximately 256,140 d. The population of this town is approximately 109,856
Answer:
Not totally sure if this will help,
The answer is a: "The population of this town is approximately 46,609"
I just took the test and This was the correct answer. Hope this helps!
Answer:.
The population of this town is approximately 46,609
Step-by-step explanation:
a
Independent Practice
Complete the statement.0.25 m= cm
A.
25
B.
0.0025
C.
2.5
D.
250
Answer:
0.25 meters is the same as A. 25 centimeters
Explanation:
multiply the length value (0.25) by 100 to get to cm from m
hope this helps chu <3
ill mark brainlist plss help
Answer:
18.5
Step-by-step explanation:
Im struggling a bit can someone help me :)
Answer:
1
Step-by-step explanation:
Which one is the height?
Answer:
The 3mm
Step-by-step explanation:
Answer:
3m is the height or altitude.
Whats the y-int?
Whats the domain and range?
Answer:
Y intercept is (0,50) or b=50
Describe the transformation of the graph of f into the graph of g as either a vertical stretch or compression. (Be sure to include the stretching/compression factor as well f(x) = √x and g(x) =5√x
5 in
3 in
8 in
4 in
Find the lateral surface area of the triangular prism.
A)
84 in?
B)
90 in?
o
96 in 2
D)
104 in
Answer:
I would say that C is the correct answer
On a bicycle ride, Betty rode 7 miles in 2 hours.
At the same rate of speed, how far could she ride in 8 hours?
Answer:
28
Step-by-step explanation:
I'm not sure if this is right
She rode 7 miles in 2 hours, so because she is going at the same speed you times/multiply 7 x 4 in order to determine the miles. I timed it by 4 because 2 hours times 4 = 8 hours.
Hope that helped because I believe it is right :)
Is anyone able to help me with this question rq pls
Answer:
B. 196πx² + 392πx + 196π
Step-by-step explanation:
Total surface area of a sphere = 4πr²
Radius, r = 7x + 7
Total surface area of a sphere = 4πr²
= 4 * π * (7x + 7)²
= 4π * (7x + 7) * (7x + 7)
= 4π * 49x² + 49x + 49x + 49
= 4π * (49x² + 98x + 49)
= 196πx² + 392πx + 196π
B. 196πx² + 392πx + 196π