The issue price (present value) of the bonds issued by Frontier World is $42,223,423.81.
What is the present value?The present value refers to the discounted future cash flows of the bonds (including interests and the repayment of the bonds).
The present value represents the current price of the bonds, at which they are issued.
The present value can be computed using the online finance calculator.
N (# of periods) = 20 (10 x 2)
I/Y (Interest per year) = 6% (Market Rate)
PMT (Periodic Payment) = $1,375,500
FV (Future Value) = $39,300,000
Bond Interest Rate = 7%
Semi-Annual Interest Payments:June 30 = $1,375,500 ($39,300,000 x 3.5%)
Dec. 31 = $1,375,500 ($39,300,000 x 3.5%)
Results:
Present Value (PV) = $42,223,423.81
Sum of all periodic payments = $27,510,000 ($1,375,500 x 20)
Total Interest = $24,586,576.19
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Question Completion:Required: 1-a. If the market rate is 6%, calculate the issue price. (FV of $1, PV of $1, FVA of $1, and PVA of $1)
Hector left his house at (-7,11) on a map of coleville and walked to the zoo at (-7,3) from there he walked east to his friends house. He walked a total distance of 25... if each unit on the map represents one block, what are the coordinates of Hectors friends house?
The coordinates of Hector's friend's house are (18,3).
What is the Coordinate System?A Cartesian coordinate system or coordinate system can be used to locate any point, and that point can then be shown as an ordered pair (x, y) known as coordinates. The origin, symbolized by the letter "O," is the point where the two number lines cross. The X-axis and Y-axis of a number line are the horizontal and vertical axes, respectively.Given:
Coordinates of Hector's house = (-7,11)
Coordinates of zoo = (-7,3)
He walked a total distance of 25 blocks from the zoo towards the east.
This means that he walked horizontally on the y-axis to reach his friend's house. So, the y-coordinate remains 3 and only the x-coordinate varies.
To find the coordinates of Hector's friend's house,
As given each unit on the map represents one block.
25 units = 25 blocks
Adding 25 units to the x- coordinate of the zoo keeping the y-coordinate same to obtain the required coordinates.
- 7 + 25 = 18
Therefore, the coordinates of Hector's friend's house are (18,3).
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need help asap
do please asap
help
The diagram attached below shows the rectangles with the following:
a. Perimeter = 30 cm; b. Perimeter = 30 cm
c. Length = 8 cm; Width = 4 cm
Length = 10 cm; Width = 2 cm
Length = 7 cm; Width = 5 cm
What is the Perimeter of a Rectangle?A rectangle is a four sided shape that has two opposite sides that are parallel and equal to each other.
The perimeter of a rectangle is the sum total of all the four sides of the rectangle and can be calculated using the formula:
Perimeter of a rectangle =2(length + width).
3. a. The diagram of the rectangle that has the following parameters is shown as rectangle 1 in the image attached below, where:
Length of rectangle = 10 cm
Width of rectangle = 5 cm
Perimeter of rectangle 1 = 2(10 + 5) = 30 cm
b. Rectangle 2 in the diagram shows the parameters given:
Length of rectangle = 20 cm
Width of rectangle = 10 cm
Perimeter of rectangle 2 = 2(20 + 10) = 60 cm
c. Rectangles 3, 4 and 5 shows the different measures a rectangle with a perimeter of 24 cm can be:
Rectangle 3: Length = 8 cm; Width = 4 cm
Rectangle 4: Length = 10 cm; Width = 2 cm
Rectangle 4: Length = 7 cm; Width = 5 cm
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Which angle relationships are correct? check all that apply. ∠1 and ∠8 are alternate exterior angles. ∠4 and ∠6 are same side interior angles. ∠5 and ∠7 are vertical angles. ∠2 and ∠8 are corresponding angles. ∠3 and ∠6 are alternate interior angles.
A) ∠1 and ∠8 are alternate exterior angles
B) ∠4 and ∠6 are same side interior angles
E) ∠3 and ∠6 are alternate interior angles
Let's check the each options.
A) ∠1 and ∠8 are alternate exterior angles
The exterior angles are ∠1, ∠2, ∠7 and ∠8.
This is correct.
B) ∠4 and ∠6 are same side interior angles.
∠4 and ∠6 are inside the line m and n, they are in the same side, you can see it on the figure.
This is correct
C) ∠5 and ∠7 are vertical angles
∠5 and ∠7 are supplementary angles.
This is not correct.
D) ∠2 and ∠8 are corresponding angles
These are same side of exterior angles.
This is not correct.
E) ∠3 and ∠6 are alternate interior angles
These are interior angles and alternative to each other.
This is correct.
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The value of 18C7 is the same as the value of 18Cn, where n = ?
Answer:
i think n = 7 idrk
Step-by-step explanation:
gl
pls help i need you
this is a maths question and i really hope the first person to see this question solves it
The percentage profit on the cost of the skirt is 11.1%
Here, the cost of gloves is £4
And the profit on gloves is 100% which will be equal to 4
The selling price of gloves will be = 8
As given in the question,
The total selling price of both items is £48
So, the selling price of a skirt will be = 48-8
= 40
Now, let the Total Cost of both items be x
Then, x*120÷5= 48
On solving the equation we get the x= 40
So, the cost price of the skirt will be = 40 - 4 = 36
Profit percentage of the skirt =( Selling price - cost price÷ cost price)*100
= (40-36÷ 36)*100
=(4÷ 36)*100
= 11.1℅
Hence, the profit percentage on the skirt will be 11.1℅
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The graph of the function f(x) = x - 3x² - 4 is shown below. Choose the best description of
the roots.
&
5
0
OTwo real roots and one non-real roots.
O Four real roots and no non-real roots.
O Two real roots and no non-real roots.
O Two real roots and two non-real roots.
5
The description which represents the roots is Four real roots and no non-real roots.
What is a function?A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.
The graph is given below;
The function can be written as;
f(x) = [tex]x^4[/tex] - 3x² - 4
Then the values of x for which the value of the function is zero will be;
f(x) = 0
f(x) = [tex]x^4[/tex] - 3x² - 4 = 0
Then the function will be f(x) = [tex]x^4[/tex] - 3x² - 4. Then Four real roots and no non-real roots.
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pls help ASAP
A jeweler wants to make a silver alloy to be used to make necklaces. How many ounces of a silver alloy that costs $5.50 per ounce should be mixed with one that costs $8.00 per ounce to make a new 20-ounce alloy that costs $7.00 per ounce?
$5.50 grade oz
$8.00 grade oz
Thank you :)
Answer and Explanation:
Let x be the total weight of the silver alloy costing $3.50 per ounce and y be the the total weight of the other that costs $7.00 per ounce.
The total weight of the resulting alloy is 30 ounces.
x+y=30x+y=30
Each ounce of the mixture must cost $6.30. The total cost of the resulting silver alloy is:
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8 ounces of silver alloy that costs $5.50 per ounce should be mixed with 12 ounces of silver alloy that costs $8.00 per ounce to make a new 20-ounce alloy that costs $7.00 per ounce.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Let x be the number of ounces of silver alloy which costs $5.50 per ounce and y be the number of ounces of silver alloy that costs $8.00 per ounce.
We have,
x + y = 20
5.50x + 8.00y = 7 × 20
From the first equation, x = 20 - y
Substituting this in the second equation,
5.5 (20 - y) + 8y = 140
(5.5 × 20) - 5.5y + 8y = 140
110 + 2.5y = 140
2.5y = 30
y = 12
x = 20 - y = 20 - 12 = 8
Hence the number of $5.50 cost per ounce silver alloy used is 8 ounces and the other alloy used is 12 ounces.
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The points (0,k) and (1,4) fall on a line with a slope of 9. What is the value of k?
Answer:
k = - 5
Step-by-step explanation:
calculate the slope between the 2 points using the slope formula and equate to 9
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, k ) and (x₂, y₂ ) = (1, 4 )
m = [tex]\frac{4-k}{1-0}[/tex] = [tex]\frac{4-k}{1}[/tex] = 4 - k
then equating to 9
4 - k = 9 ( subtract 4 from both sides )
- k = 5 ( multiply both sides by - 1 )
k = - 5
what is 859x85 i need help is way to hard lmk if u know
Answer: 73015
Step-by-step explanation:
multiply both of them together
In September, a website had 12,719 visitors. In October, the website had 24,150 more visitors
than it did in September. The website had the same number of visitors in November as it did in
October. How many visitors did the website have in September, October, and November
combined?
Answer:
86457
Step-by-step explanation:
Could someone please help me name the proofs?
PLEASE HELP ASAP!
I think the first blank is "Given", the third is "Angle addition postulate", And the 6th is "90 degrees". Check this?
∠FED and ∠DEW are complementary because it is a sum of 90 degrees.
By the law of addition of complementary angles,m∠FED + m∠DEW = 90°
m∠FED + m∠DEW = m∠FEW by the Angle addition postulate.
By the substitution property of equality, m∠FEW = 90°.
The ∠FEW is a right angle by the definition of right angles.
How to Interpret Complementary Angles?Complementary Angles defined as angles that sum up to 90 degrees.
Now, we are given that;
∠FED and ∠DEW are complementary.
We want to prove that ∠FEW is a right angle. Thus;
∠FED and ∠DEW are complementary because it is a sum of 90 degrees.
By the law of addition of complementary angles, we can say that;
m∠FED + m∠DEW = 90°
Also,
m∠FED + m∠DEW = m∠FEW by the Angle addition postulate.
By the substitution property of equality, m∠FEW = 90°.
The ∠FEW is a right angle by the definition of right angles.
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If someone could help me with these two problems please.
( will mark brainliest if correct )
Answer:
1st- x=140°
2nd-x=90°
Step-by-step explanation:
The interior angle of a 9 -sided polygon is 140x9=1260
divide by 9
The interior angles of a triangle always add up to 180
90°each
how do you turn 1 2/3 into a digit
Answer: 5/3
Step-by-step explanation:
[tex]\displaystyle\\1\frac{2}{3}=\\\\\frac{1*3+2}{3}=\\\\\frac{3+2}{3} =\\\\\frac{5}{3}[/tex]
Out of 260 students, 140students like Dashain, 150students
like Tihar and 120 students do not like these festivals.
Represent the above information in a venn-diagram.
find the number of students who like both festivals.
How many students like only one festivals.
Step-by-step explanation:
students who like both festivals
140+150=290
290-260=30
=30
students who like one festival
260-150=110
=110
Jupiter is 6.3 x 108 (630 million kilometers) from Earth. Calculate how long it would take to reach Jupiter if you traveled at
If you just want to conduct a flyby and aren't planning to stay, it will take you approximately 600 days, and if you want to enter orbit, it will take you about 2,000 days.
WHAT IS LIGHT YEAR ?Astronomical distances are expressed in terms of a light-year, which is also spelt light year. Its length is approximately 9.46 trillion kilometers, or 5.88 trillion miles.
HOW LONG IT WOULD TAKE TO REACH JUPITER FROM EARTH ?NASA's Pioneer 10 was the first spacecraft to ever travel across the distance between the Earth and Jupiter. On March 3, 1972, it was launched, and on December 3, 1973, it arrived. There were 640 days of flight time altogether.
However, Pioneer 10 was passing by while en route to study the outer solar system. Before NASA lost communication with it, the spacecraft traveled another 11 years into deep space after approaching the planet at a distance of 130,000 kilometers, where it snapped the first-ever close-up images of Jupiter.
Pioneer 11 launched and touched down one year later. It traveled there in 606 days, flying by Jupiter at a considerably closer distance (21,000 kilometers), and also stopped by Saturn.
The Voyager spacecraft arrived next. Voyager 1 arrived on March 5, 1979, in only 546 days, and Voyager 2 took 688 days.
Consequently, it will take between 550 and 650 days to complete a flyby.
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If there are 12 dogs and 42 cats at a pet daycare, fill out all of the possible ratios of
dogs to cats that could be made.
There are 12 dogs for every 42 cats (12:42 ratio)
There are
dogs for every cats try
Type in an equivalent ratio of dogs and cats.
Tickets to a Broadway show cost $40 for adults and $10 for children. The total receipts for 1420 tickets at one performance were $41,800. How many adult and how many child tickets were sold?
The number of adult tickets sold is 920 , and the number of child tickets sold is 500 .
In the question ,
it is given that
ticket cost for adult = $40
ticket cost for children = $10
and the number of total tickets sold is 1420
let the number of adult tickets sold = x
and the number of children ticket sold = y
According to the question
total tickets sold = number of adult tickets sold+ number of children ticket sold
Substituting the values, we get
x+y = 1420
y = 1420 - x ...(i)
the total receipts for adult tickets= $40x
the total receipts for children tickets= $10y
given that total amount of tickets sold = $41800
According to the question
40x + 10y = 41800
Substituting the value of y from equation(i) , we get
40x + 10(1420-x) = 41800
40x + 14200 - 10x = 41800
30x + 14200 = 41800
30x = 27600
x = 920
and y = 1420 - 920
y = 500
Therefore , the number of adult tickets sold is 920, and the number of child tickets sold is 500 .
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The points (h,0) and ( – 9, – 6) fall on a line with a slope of 6. What is the value of h?
Answer:
-8
Step-by-step explanation:
[tex]\frac{-6-0}{-9-h} = 6\\6(-9-h)=-6\\-9-h=-1\\-h=8\\h=-8[/tex]
Graph each equation by using the x and y intercepts
Question 2: 5x-2y=7
The x and y intercepts are (7/5, 0) and (0, -7/2) respectively.
What are x and y intercepts?A line crosses the x-axis at the x-intercept, and the y-intercept is where the line crosses the y-axis.We can graph linear equations by considering intercepts.Since the x-intercept lies on the horizontal axis, it is also known as the horizontal intercept.Since the y-intercept lies on the vertical axis, it is also referred to as the vertical intercept.Given equation is 5x-2y = 7.
To find the x-intercept substitute y = 0 in the equation and then solve,
5x - 0 = 7
x = 7/5
So the x-intercept is (7/5, 0).
Similarly, to find the y-intercept substitute x = 0 in the equation and then solve,
0 - 2y = 7
y = -7/2
So the y-intercept is (0, -7/2).
Now, graph the intersections of (7/5, 0) and (0, -7/2).
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17.) Find the unit rate. You earn $77.65 for working 8 hours.
A) $9.71 per hour
B) $19.41 per 2 hours
C) $10.05 per hour
D) $12.94 per hour
The graph of the equation 2x-3y=7 is a line. Find the x- and y-intercepts and graph the line using these two points.
x-intercept, 7/2
y-intercept, -7/3
What is intercept?The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively. the location on the y axis where a graph crosses it. • x = 0 at the same location. An intercept in mathematics is a location on the y-axis through which the line's slope passes. It is a place on the y-axis where a straight line or a curve crosses. This is reflected in the equation for a line, which is written as y = mx+c, where m denotes slope and c denotes the y-intercept.
Given that,
The graph of the equation 2x-3y=7 is a line.
2x-3y=7
Divide 7 on both sides
2x/7- 3y/7=1
[tex]\frac{x}{7/2}- \frac{y}{7/3} =1[/tex]
x-intercept, 7/2
y-intercept, -7/3
Therefore, x-intercept, 7/2, y-intercept, -7/3.
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Can someone help me?? I really need the help and I would appreciate it! Thank you so much in advance! :)
y= -1/2 x - 5 write in slope intercept form.
Answer:
Hii! This is already written in slope intercept form.
For a refresher, slope intercept form is [tex]y=mx+b[/tex]
[tex]y[/tex] = y-coordinate
[tex]m[/tex] = slope
[tex]x[/tex] = x-coordinate
[tex]b[/tex] = y-intercept
In this equation,
[tex]m[/tex] is [tex]-1/2[/tex]
[tex]b[/tex] is [tex]-5[/tex]
Hope this answers your questions.
A retail company is studying the number of employees, based on job classification, such as employee, manager, and senior manager. Which of the following displays could be used to represent the data, and why?
O Bar chart; because job classification is categorical
O Box plot; because job classification is categorical
O Circle graph; because job classification is numerical
O Histogram, because job classification is numerical
The display to represent the data of the number of employees based on job classification is A. Bar chart; because job classification is categorical.
What is categorical data?Categorical data refers to the data types that can be grouped instead of calculated numerically.
Some examples of categorical data include sex, age group, educational level, job classification, and racial categories.
Bar charts and histograms are handy for representing categorical data because they use rectangular bars with heights or lengths to represent proportional values.
Thus, the correct display for the categorical data of job classification is Option A.
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Answer:
A
Step-by-step explanation:
Bar Chart
Suppose 38% of students chose to study German their senior year, and that meant that there were 190 such students. How many students chose not to take German their senior year?
Answer: 310
Step-by-step explanation:
(190/38) x 100 = 500 total students
500-190 = 310 students
4.) Johnny played a video four times in a row. Each time he played he lost 15 points. How
many points did he lose in all after playing the games?
1-19
2-60
3-(-60)
4- (-19)
Complete the process of solving the equation.
Fill in the missing term on each line. Simplify any fractions.
5(y + 1) = 5
y + 1 =
Divide both sides by 5
Subtract 1 from both sides
Answer:
Step-by-step explanation:
5(y + 1) = 5
Divide both sides by 5
=> 5(y + 1)/5 = 5/5
=> y + 1 = 1 [ 5 in numerator and 5 in denominator cancel]
Subtract 1 from both sides
y + 1 -1 = 1 - 1
y + 0 = 0
=> y = 0
Sanjay bought 4 packages of bottled water. A package contains 25 bottles of water that cost $1.20 each. Sanjay can use the
calculation below to find the total cost of the water.
4 x (25 x 1.2)
How can Sanjay simplify the calculation using only the associative property of multiplication?
Drag and drop the appropriate number or expression into each
According to the associative property of multiplication, the expression to find the cost will be (1.2 × 25) × 4 based on the property and the value is $120.
How to illustrate the information?It should be noted that the associative property of multiplication simply means that when multiplying three numbers, the answer will be the same regardless of how the numbers are grouped.
In this case, Sanjay bought 4 packages of bottled water and a package contains 25 bottles of water that cost $1.20 each.
From the information, the expression is illustrated as 4 x (25 x 1.2). It should be noted that this can also be written as (1.2 × 25) × 4 based on the property and the answer will be $120.
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A table shows temperature changes over a period of a week.
a. Why would a circle graph inaccurately display the data?
b. Which type of graph would best display the data?
a) A circle graph inaccurately displays the data because the data is not about parts of a whole.
b) Line graph would best display the data.
What are circle graphs?A circle is divided into sectors that each represent a component of a whole to create a circle graph, which is a visual representation of data.
What are line graphs?An individual data point is connected by a line in a line graph, sometimes referred to as a line plot or a line chart. A line graph shows numerical values over a predetermined period of time.
a) Since circle graphs are designed to depict data consisting of parts of a whole, a data set consisting of temperature variations over the course of a week would be wrongly displayed by one.
b) Since line graphs are the most appropriate for a data set that is tied to time, a line graph would be the most effective way to display the given data.
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what are the coordinates of point A? Enter an exact value or doubt to the nearest hundredth.
The coordinate of Point A is ([tex]\frac{1}{2} ,\frac{\sqrt{3} }{2}[/tex])
Given in the question;
From the figure,
To see the graph:
To find the coordinates of point A.
Now, According to the question and picture :
Point A is on the unit circle and
The angle between point A and the origin and
The X - axis is [tex]\frac{\pi }{3}[/tex] = 60°.
The radius of the unit circle is 1.
So, the x - coordinate of point A is :
X cos 60° = 1/2
The Y coordinate of point A is :
X sin 60° = [tex]\frac{\sqrt{3} }{2}[/tex]
Hence, The coordinate of Point A is ([tex]\frac{1}{2} ,\frac{\sqrt{3} }{2}[/tex]).
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Find the distance between points (6, 16) and (-1, 14)
[tex] = \sqrt{( {x2 - x1})^{2} + ( {y2 - y1})^{2} } \\ = \sqrt{ (- 1 - 6 )^{2} + ( {14 - 16)}^{2} } \\ = \sqrt{( { - 7)}^{2} + ( { - 2)}^{2} } \\ = \sqrt{49 + 4} \\ = \sqrt{53} [/tex]
ATTACHED IS THE SOLUTION