Answer:
$1197.17185
Step-by-step explanation:
ABC bond :
Par value of bond (FV) = 1000
Period (n) = 11 years
Coupon rate (r) = 8.5% annually
Discount rate (r) = 6% = 0.06
The coupon price = 8.5% of par value
Coupon price (C) = 0.085 * 1000 = 85
Current price of bond can be computed using the relation:
= C * [1 - 1 / (1 + r)^n] / r + (FV / (1 + r)^n)
85 * [1 - 1/(1+0.06)^11]/0.06 + 1000/(1 + 0.06)^11
85 * 7.8868745 + 526.78752
670.38433 + 526.78752 = $1197.17185
Find the value of x if 12x=34^2 - 26^2
Answer:
[tex]\boxed{\sf x =40}[/tex]
Step-by-step explanation:
[tex]\sf 12x=34^2 - 26^2[/tex]
Solve the square.
[tex]\sf 12x=1156-676[/tex]
[tex]\sf 12x=480[/tex]
Divide both sides by 12.
[tex]\displaystyle \sf \frac{12x}{12} =\frac{480}{12}[/tex]
[tex]\sf x =40[/tex]
You build 7 model airplanes during the summer. At the end of the summer, you have 25 model airplanes. How many model airplanes did you have before the summer? Select the correct equation and solution. Check the solution.
Answer:
18
Step-by-step explanation:
You have 25 when you are done, but you made 7, so subtract that from 27.
25-7 equals 18.
Which three-dimensional figure is formed by the rotation given?
Answer: The bottom right
Step-by-step explanation: Take a peek at the pic :)
Write an expression to represent Vivian's change in elevation from -9.6 feet at the bottom of the Ferris wheel to 12.3 feet at
the top
Answer:
ΔE =12.3 - (-9.6) which is equivalent to 21.9 feetStep-by-step explanation:
Give the distance covered by Vivian at the bottom of the elevation to be -9.6 feet and the distance covered by Vivian at the top of the elevation to be 12.3 feet, Vivian's change in elevation will be expressed as the difference in the elevation at the bottom and the elevation at the top.
Let the initial elevation Ei = -9.6 feet
Final elevation Ef = 12.3 feet
Change in elevation ΔE = Ef - Ei
Change in elevation ΔE =12.3 - (-9.6)
Change in elevation ΔE = 12.3 + 9.6
Change in elevation ΔE = 21.9 feet
Hence the expression to represent Vivian's change in elevation from -9.6 feet at the bottom of the Ferris wheel to 12.3 feet at the top is ΔE =12.3 - (-9.6) which is equivalent to 21.9 feet
Answer:
12.3 – (-9.6)
Step-by-step explanation:
Its the answer they provided
The graph of y=√X is translated 3 units to the right and slid 5 unitsdown, what would be the resulting equation?
Answer: [tex]y=\sqrt{x-3}-5[/tex]
Step-by-step explanation:
The vertex form of a square root equation is: [tex]y=a\sqrt{x-h}+k[/tex] where
a is the vertical stretchh is the horizontal shift (positive is right, negative is left)k is the vertical shift (positive is up, negative is down)Input: h = 3 (3 units right) and k = -5 (5 units down) into the vertex form:
[tex]y=\sqrt{x-(3)}+(-5)\\\\y=\sqrt{x-3}-5[/tex]
The resulting equation is: [tex]h(x) = \sqrt{x - 3} - 5[/tex]
-------------------------------
This question is solved using the translation concept.
Translating a function f(x) a units to the right is the same as finding f(x - a).Translating a function f(x) a units down is the same as finding f(x) - a.-------------------------------
Original function:
[tex]f(x) = \sqrt{x}[/tex]
-------------------------------
Translated 3 units to the right
This is f(x - 3), so:
[tex]g(x) = f(x - 3) = \sqrt{x - 3}[/tex]
-------------------------------
Translating 5 units down
This is g(x) - 5, so:
[tex]h(x) = g(x) - 5 = \sqrt{x - 3} - 5[/tex]
Which is the resulting equation.
The image at the end of this answer compared the graph of the original function, in red, with the translated, in blue.
A similar question is given at https://brainly.com/question/23630829.
Please answer ASAP. The question is down below.
Answer: 1) c 2) d
Step-by-step explanation:
Use Pythagorean Theorem to find the hypotenuse (r): x² + y² = r²
Given: x = 2, y = 6
2² + 6² = r²
4 + 36 = r²
40 = r²
[tex]\sqrt{40}=r[/tex]
[tex]\sin \theta=\dfrac{y}{r}\quad =\large\boxed{\dfrac{6}{\sqrt{40}}}\quad \rightarrow \dfrac{6}{2\sqrt{10}}\quad \rightarrow \dfrac{3}{\sqrt{10}}[/tex]
*******************************************************************************************
[tex]\sin \theta = \dfrac{opposite(y)}{hypotenuse(r)}\quad =\dfrac{12}{20}\quad \rightarrow \dfrac{3}{5}\quad \rightarrow \large\boxed{0.6}\\\\\\\cos \theta = \dfrac{adjacent(x)}{hypotenuse(r)}\quad =\dfrac{16}{20}\quad \rightarrow \dfrac{4}{5}\quad \rightarrow \large\boxed{0.8}[/tex]
Best answer will be rated brainliest
Answer:
A. 6 and 30
B. 8 and 28
Step-by-step explanation:
we know that the area of the three squares must satisfy the Pythagorean Theorem so c² = a² + b²
where
c² is the area of the largest square
a² and b² are the areas of the smaller squares
now.. 36² = a² + b2
The sum of the areas of the smaller squares must be equal to 36
therefore
6 and 30 >>>> could be the areas of the smaller squares (6 + 30 = 36)
8 and 28 >>>> could be the areas of the smaller squares (8 + 28 = 36)
hope it clears your mind.
Please mark as the brainliest
Translate into an algebraic expression and simplify if possible. C It would take Maya x minutes to rake the leaves and Carla y minutes, what portion of the leaves do they rake in one minute if they work together?
Answer:
in one minute they rake [tex]\frac{y+x}{xy}[/tex] leaves working together.
Step-by-step explanation:
If Maya rakes the leaves in x minutes, then, in one minute she rakes [tex]\frac{1}{x}[/tex] leaves.
In the case of Carla, if she rakes the leaves in y minutes, in one minute she rakes [tex]\frac{1}{y}[/tex] leaves.
Therefore, to know the portion of leaves they can rake in one minute working together, we need to sum up both of the portions each one of them rake in one minute, this gives us: [tex]\frac{1}{x}+ \frac{1}{y}[/tex]
Now, to simplify this expression:
[tex]\frac{1}{x}+ \frac{1}{y} =\frac{y+x}{xy}[/tex]
Thus, in one minute they rake [tex]\frac{y+x}{xy}[/tex] leaves.
Read the following word problem, then choose which linear equation models the problem.
One number is 10 times another number. Their difference is 54. Find the numbers.
A. x(x) - 10 = 54
B. 10x - x = 54
C. 10x + x = 54
D. 10x(x) = 54
Which of the expressions below can be factored using the difference of squares method?
A. 9x^2 - 16y2
B. 9x-16y
C. 9x^2 + 1672
D. 9x + 16y
Answer: A. [tex]9x^2 - 16y^2[/tex] .
Step-by-step explanation:
A difference of squares problem is factored as :[tex]a^2 - b^2 = (a + b)(a - b)[/tex]For this both terms in the form of squares and a minus sign between them.From all the options only option A has both terms square and they minus sign between them.
Also, [tex]9x^2 - 16y^2= (3x)^2-(4y)^2=(3x+4y)(3x-4y)[/tex]
Here a= 3x and b= 4
Hence, the correct answer is A. [tex]9x^2 - 16y^2[/tex] .
Answer:
A
Step-by-step explanation:
David is building a bike ramp. He wants the angle that the ramp makes with the ground to be 20. If the board he wants to use for his ramp is 312feet long, about how tall will the ramp need to be at the highest point?
Answer:
it's about 106.71ft
Step-by-step explanation:
make this problem a triangle. the ramp length is 312ft, and it is the hypotenuse of the triangle. 20 is the angle between the ramp and the floor. so what I did was take the sine of 20 and get: sin(20)=x/312 then you multiply both sides by 312 to isolate the variable. multiplying sin(20) by 312 gave me 106.71 + some change idk if you're supposed to round it or not haha.
From the top of a vertical cliff 75.0m high, forming one bank of a river, the angles of depression of the top and bottom of a vertical cliff which forms the opposite bank are 22° and 58° respectively. Determine the height of the second cliff and width of the river
Answer:
a. 46.9 m b. 56.1 m
Step-by-step explanation:
a. Width of the river
The angle of depression of the bottom of the second vertical cliff from the first vertical cliff = angle of elevation of the top of the first vertical cliff from the bottom of the second vertical cliff = 58°.
Since the height of the vertical cliff = 75.0 m, its distance from the other cliff which is the width of the river, d is gotten from
tan58° = 75.0 m/d
d = 75.0/tan58° = 46.87 m ≅ 46.9 m
b. Height of the second cliff
Now, the difference in height of the two cliffs is gotten from
tan22° = h/d, since the angle of depression of the top of second cliff from the first cliff is the angle of elevation of the top of the first cliff from the second cliff = 22°
h = dtan22° = 18.94 m
So, the height of the second cliff is h' = 75.0 - h = 75.0 m - 18.94 m = 56.06 m ≅ 56.1 m
The shaded figure is a rhombus.
The area of the shaded section is 60 square units. What is the value of x?
Answer:
6
Step-by-step explanation:
the value of x is 6
so the answer is 6
Answer:
answer is 8
Step-by-step explanation:
Can I get some more help
Answer:
[tex]c. \: \sqrt{9} . \sqrt{4} [/tex]
[tex] \\ [/tex]
Step-by-step explanation:
[tex] \sqrt{9.4} \\ = \sqrt{9} \times \sqrt{4} [/tex]
the amplitude of the graph is the midline is y =
Answer:
Amplitude of 2, midline is y=4
Answer:
y=4.
Step-by-step explanation:
I hope this helps!
U
480
S
d
T
b
R.
C
P
1549
Q
Answer:
a = 26°
b = 48°
c = 26°
d = 106°
Select the correct answer. Simplify the expression. What classification describes the resulting polynomial? (3x2 − 11x − 4) − (2x2 − x − 6) A. quadratic trinomial B. linear binomial C. quadratic binomial D. linear monomial
Answer:
A : quadratic trinomial
Step-by-step explanation:
Given
(3x² - 11x - 4) - (2x² - x - 6)
Distribute both parenthesis, noting the second is distributed by - 1
= 3x² - 11x - 4 - 2x² + x + 6 ← collect like terms
= x² - 10x + 2 ← this is a quadratic with 3 terms, thus quadratic trinomial → A
Hope helped.. Mark BRAINLIEST
Thanks!!
Answer:
A. quadratic trinomial
Step-by-step explanation:
[tex](3x^2-11x-4)-(2x^2-x-6)[/tex]
Remember that polynomials are closed to subtraction, therefore, linear binomial and linear monomial can't be an option.
[tex]3x^2-11x-4-2x^2+x+6[/tex]
[tex]x^2-10x+2[/tex]
We got a quadratic equation. Once it has the c term, it is a quadratic trinomial.
Find two national number
between 2 and 3
Answer:
The answer is 2.5
Step-by-step explanation:
Formula Used is is ½ x x+y
so it is ½ x 2 + 3
½ x 5 = 2.5
Answer:
2=2/1
3=3/1
multiplying both fractions by 10.
2*10/1*10
3*10/1*10
20/10 and 30/10
so nos are 21/10.......29/10
Determine the angles of rotation. Please answer!!!
Answer:
total rotation = 90 clockwise.
Step-by-step explanation:
Rotation from B to negative y-axis = 45 degrees because B(-3,-3)
Rotation from negative y-axis to B' = 45 degrees because B(-3,3)
Therefore total rotation = 45+45 = 90 clockwise.
What is the slope of the line segment? A graph is shown. The values on the x axis are 0, 1, 2, 3, 4, and 5. The values on the y axis are 0, 4, 8, 12, 16, and 20. A straight line joining the ordered pairs 0, 0 and 1, 4 and 2, 8 and 3, 12 and 4, 16.
Answer:
4
Step-by-step explanation:
The coordinates are: A(0,0), B(1,4), C(2,8), D(3,12), E(4,16)
Using coordinates B and D, slope = (12 - 4)/(3 - 1) = 8/2
∴ slope = 4
Answer:
4
Step-by-step explanation:
2
What is the solution of the equation 6x - 3 = -51?
A. -9
B. -8
c. 8.
D. 9
Answer:
x = -8
Step-by-step explanation:
6x - 3 = -51
Add 3 to each side
6x - 3+3 = -51+3
6x = -48
Divide each side by 6
6x/6 = -48/6
x = -8
HELPPP!! Calculate the side lengths a and b to two decimal places. (there is a picture included)
Answer:
Option (D)
Step-by-step explanation:
In the given triangle ABC,
Sum of all interior angles = 180°
m∠A + m∠B + m∠C = 180°
72° + 85° + m∠C = 180°
m∠C = 180 - 157
m∠C = 23°
By applying Sine rule in the triangle,
[tex]\frac{\text{SinA}}{a}=\frac{\text{SinB}}{b}=\frac{\text{SinC}}{c}[/tex]
[tex]\frac{\text{Sin72}}{a}=\frac{\text{Sin85}}{b}=\frac{\text{Sin23}}{6.2}[/tex]
[tex]\frac{\text{Sin72}}{a}=\frac{\text{Sin85}}{b}=0.06302[/tex]
[tex]\frac{\text{Sin72}}{a}=0.06302[/tex]
a = [tex]\frac{\text{Sin72}}{0.06302}[/tex] = 15.09
[tex]\frac{\text{Sin85}}{b}=0.06302[/tex]
b = [tex]\frac{\text{Sin85}}{0.06302}[/tex]
b = 15.81
Therefore, option (D) will be the answer.
How many minutes are in 15 hours?
Answer:
900
Step-by-step explanation:
15 TIMES 60 IS 900
Hi there! Hopefully this helps!
--------------------------------------------------------------------------------------------------
Answer: There are 900 minutes in 15 hours.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Since there are 60 minutes in each hour, we need to multiply the time value by 60. Like this:
15 x 60 = 900.
arithmetic sequences (nth term)
Tick the arithmetic sequences.
In order for a sequence to be arithmetic the relations between their numbers must be the sum of a common ratio, therefore to determine which ones are arithmetic sequence we need to satisfy the following expression:
[tex]a_n - a_{n-1} = a_{n-2} - a_{n-3}[/tex]
The expression just mean that the subtraction of consecutive terms should be equal for position in the sequence.
"1, 5, 9, 13...":
[tex]13 - 9 = 5 - 1\\4 = 4[/tex]
Since the expression is valid, then this is a arithmetic sequence.
"6, 10, 15, 21...:
[tex]21 - 15 = 10 - 6\\6 = 4[/tex]
Since the expression is invalid, then this isn't a arithmetic sequence.
"2, 3, 5, 8...:
[tex]8 - 5 = 3 - 2\\3 = 1[/tex]
Since the expression is invalid, then this isn't a arithmetic sequence.
"2, -4, 8, -16...:
[tex]-16- 8 = -4 - 2\\-24 = -6[/tex]
Since the expression is invalid, then this isn't a arithmetic sequence.
"-1, 2, 5, 8...:
[tex]8 - 5 = 2 -(- 1)\\3 = 3[/tex]
Since the expression is valid, then this is a arithmetic sequence.
"73, 66, 59, 52...:
[tex]52 - 59 = 66 - 73\\-7 = -7[/tex]
Since the expression is valid, then this is a arithmetic sequence.
"6, 1, -4, -9...:
[tex]-9 - (-4) = 1 - 6\\-5 = -5[/tex]
Since the expression is valid, then this is a arithmetic sequence.
"1, 2, 4, 8...:
[tex]8 - 4 = 2 - 1\\4 = 1[/tex]
Since the expression is invalid, then this isn't a arithmetic sequence.
Find the first five terms of the patterns with these nth terms.
For [tex]3n + 3[/tex]:
[tex]3*1 + 3 = 3 + 3 = 6[/tex]
[tex]6 + 3 = 9[/tex]
[tex]9 + 3 = 12[/tex]
[tex]12 + 3 = 15[/tex]
[tex]15 + 3 = 18[/tex]
(6, 9, 12, 15, 18)
For [tex]9n - 7[/tex]:
[tex]9*1 - 7 = 9 - 7 = 2[/tex]
[tex]2 + 9 = 11[/tex]
[tex]11 + 9 = 20[/tex]
[tex]20 + 9 = 29[/tex]
[tex]29 + 9 = 38[/tex]
(2,11,20,29,38)
Write down a formula for the nth term of these patterns. The first term is n = 1.
The nth term of any arithmetic sequence is: [tex]a(n) = a(1)*(n - 1)*r[/tex]
Therefore we need to identify r in each sequence.
For (9,15,21,27,33):
[tex]r = 15 - 9 = 6[/tex]
[tex]a(n) = 1*(n - 1)*6 \\a(n) = 6*n - 6[/tex]
For (-2,-8,-14,-20,-26):
[tex]r = -8 - (-2) = -6[/tex]
[tex]a(n) = 1*(n - 1)*(-6)\\a(n) = -6*n + 6[/tex]
help me out with a and b
i Will give brainliest and follow you back if you answer first.
Answer:
Step-by-step explanation:
A = {2,8,10,14}
B= {6,8,20}
C={8,18,20,24}
A ∩ B --> intersection means elements that are in both sets A & B
A ∩ B = {8}
A∩ C = {8}
B ∩ C = {8 , 20}
A∩B ∩ C = {8}
First blue box = { 2,10, 14}
Second blue box = {18, 24}
First green box = { 8}
Second green box = { 20}
b) A ∩ B = {8}
n [ A ∩ B] = 1
Probability of the number to be a member of A∩B = 1 / 25
the hypotnuse of a 45 -45 -90 triangle measures 22√2 units. what is the length of the leg of the triangle?
Answer:
22 units.
Step-by-step explanation:
In 45- 45- 90 triangles, there is a 1 to 1 to the square root of 2 formula. Each side length measures 1x, while the hypotenuse measures x times the square root of 2.
In this case, the hypotenuse measures 22 and the square root of 2 units. To find the value of x, simply divide that by the square root of 2 units, and you get x = 22 units. Multiply that by 1, and you get 22 units, which is the length of the leg of the triangle.
Hope this helps!
A company has determined that its weekly profit is a function of the number of items that it sells. Which equation could represent the weekly profit in thousands of dollars, y, when the company sells x items? y squared = 4 x squared minus 100 y = negative x squared + 50 x minus 300 x = negative y squared minus 400 x squared = negative 6 y squared + 200
Answer:
B. y= -x^2+50x-300
Step-by-step explanation:
A. y^2=4x^2-100
B. y= -x^2+50x-300
C. x=-y^2-400
D. x^2=-6y^2+200
we are to find profits (y) when the company sells x items
Option A can be used to calculate the profit (y) squared
Option B can be used to calculate profits (y)
Option C can be used to calculate items sold(x)
Option D can be used to calculate items sold squared(x^2)
We are asked to find the weekly profit (y) function which eliminate options A, C and D leaving us with option B
Therefore, the weekly profits (y) function in thousands of dollars when the company sells x items is
B. y= -x^2+50x-300
The volume of the Atlantic Ocean is about 3.1⋅10173.1 \cdot 10^{17}3.1⋅10173, point, 1, dot, 10, start superscript, 17, end superscript cubic meters. The Mississippi River has an annual flow of 6.3⋅10116.3 \cdot 10^{11}6.3⋅10116, point, 3, dot, 10, start superscript, 11, end superscript cubic meters. how many times would the annual flow of the mississippi river fit in the atlantic ocean? write your final answer in scientific notation, and round to two decimal places.
Answer: The annual flow of the Mississippi river would fit in the Atlantic ocean [tex]4.92\times10^5[/tex] times.
Step-by-step explanation:
Given: Volume of Atlantic Ocean= [tex]3.1\times10^{17}[/tex] cubic meters
Annual flow of Mississippi river = [tex]6.3\times10^{11}[/tex] cubic meters.
then, the number of times the annual flow of the Mississippi river would fit in the Atlantic ocean = [tex]\dfrac{\text{ Volume of Atlantic Ocean}}{\text{Annual flow of Mississippi river}}[/tex]
[tex]=\dfrac{3.1\times10^{17}}{6.3\times10^{11}}\ \ \=0.492063492063\times10^{17-11}\ \ [\dfrac{a^m}{a^n}=a^{m-n}]\\\\=0.492063492063\times10^6\approx4.92\times10^5[/tex]
Hence, the annual flow of the Mississippi river would fit in the Atlantic ocean [tex]4.92\times10^5[/tex] times.
Determine whether the study is an observational study or an experiment.
Research is conducted to determine if there is a relation between hearing loss and exposure to mumps. Does the description correspond to an observational study or an experiment?
Researchers are observing those with mumps to see how it affects hearing loss at all. There may be strong correlation, weak correlation, or no correlation at all.
With an experiment, researchers would break the participants into two groups: control group and treatment group. Those in the control group get the placebo (fake treatment) while the treatment group gets the treatment applied to them. If we were dealing with an experiment for this context, then the treatment group would get exposed to mumps on purpose. Of course, this is unethical and dangerous so an experiment for this type of project is not a good idea. It's better to go with an observational study.
help me plzzzzz help
Answer:
90000 km
Step-by-step explanation:
1 hour = 3600 sec
distance = speed x time
= 25 km/s x 3600 s
= 90000 km
standard form = 9 x 10⁴