The yield to maturity (YTM) of the bonds is 10.77%.
How to calculate the yield to maturity (YTM) of a bond?To calculate the yield to maturity (YTM), we need to use the following formula:
YTM = [(Annual Interest Payment + (Par Value - Market Price) / Years to Maturity) / (Par Value + Market Price) / 2] x 100%
Where:
Annual Interest Payment = Coupon rate x Par value
Par value = RM1,000
Market Price = RM980
Years to Maturity = 3
Coupon rate = 10%
First, let's calculate the annual interest payment:
Annual Interest Payment = Coupon rate x Par value = 10% x RM1,000 = RM100
Next, we can substitute the given values in the formula:
YTM = [(100 + (1,000 - 980) / 3) / (1,000 + 980) / 2] x 100%
YTM = 10.77%
Therefore, the yield to maturity (YTM) of the bonds is 10.77%.
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A recipe uses 4 cups of milk to make 20 servings. If the same amount of milk is used for each serving, how many servings can be made from three quarts?
Answer:
4=20
3=?
so 20×3 divide by 4 = 15
Step-by-step explanation:
Answer:25
Step-by-step explanation: 25 25 25
Element X decays radioactively with a half life of 8 minutes. If there are 470 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 10 grams? y
The decay of Element X can be modeled by the equation:
N = N0 * (1/2)^(t/t1/2)
where N is the amount of Element X remaining after time t, N0 is the initial amount of Element X, t1/2 is the half-life of Element X, and ^(t/t1/2) denotes exponentiation with base 1/2.
We know that the initial amount of Element X is 470 grams, the half-life is 8 minutes, and we want to find the time it takes for Element X to decay to 10 grams. Let t be the time in minutes.
Then, we can set up the following equation:
10 = 470 * (1/2)^(t/8)
Dividing both sides by 470, we get:
(1/47) = (1/2)^(t/8)
Taking the natural logarithm of both sides, we get:
ln(1/47) = (t/8) * ln(1/2)
Solving for t, we get:
t = -8 * ln(47)/ln(2)
t ≈ 59.3
Therefore, it would take about 59.3 minutes, to the nearest tenth of a minute, for Element X to decay to 10 grams.
Dion bought 3 pounds of oranges and 2 pounds of grapefruit. Write an expression to represent the amount of money Dion spent on the fruit. Then evaluate the expression. How much did Dion spend?
Answer:
eeeeejjbbvvv g gyuuu u grrtyyu
1. What is (f⋅g)(x)?
f(x)=x^2+2x−6
g(x)=x^4+3
Enter your answer in standard form in the box.
2. Question
WHAT IS : (f−g)(x)? its not the same question as 1
f(x)=x^4−x^2+9
g(x)=x^3+3x^2+12
Enter your answer in standard form in the box.
Answer:
[tex]\textsf{1.} \quad \left(f \cdot g \right)(x)=x^6+2x^5 -6x^4+3x^2+6x -18[/tex]
[tex]\textsf{2.} \quad\left(f -g \right)(x)=- x^4+x^2+2x-9[/tex]
Step-by-step explanation:
To calculate (f ⋅ g)(x), multiply function f(x) by function g(x) by distributing the parentheses:
[tex]\begin{aligned}\left(f \cdot g \right)(x)&=(x^2+2x-6)(x^4+3)\\&=x^2 \cdot x^4 +x^2 \cdot 3+2x \cdot x^4+2x \cdot 3 -6 \cdot x^4 -6 \cdot 3\\&=x^6+3x^2+2x^5+6x -6x^4 -18\\&=x^6+2x^5 -6x^4+3x^2+6x -18\\\end{aligned}[/tex]
To calculate (f - g)(x), subtract function g(x) from function f(x) by applying the distributive law -(a + b) = -a - b:
[tex]\begin{aligned}\left(f -g \right)(x)&=(x^2+2x-6) - (x^4+3)\\&=x^2+2x-6 - x^4-3\\&=- x^4+x^2+2x-6 -3\\&=- x^4+x^2+2x-9\end{aligned}[/tex]
Note: The standard form of a polynomial is expressed by writing the term with the highest degree first, followed by the other terms in order of decreasing powers.
Between ecery pair of distinct points, there is a positive unique number called the , which can be determined as the of the corresponding real numbers of the two points
The missing term of question is "distance".
Define distinct points?Distinct points refer to points that are not the same. In other words, if two or more points have different locations or coordinates, they are considered distinct points.
Distance is a measure of the length or space between two points, lines, or other objects. It is typically expressed as a non-negative number and can be determined using various formulas depending on the context and the nature of the objects being measured.
The missing term in the question is "distance". The sentence can be completed as:
"Between every pair of distinct points, there is a positive unique number called the "distance", which can be determined as the "absolute value of the difference" of the corresponding real numbers of the two points."
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Find the measurment of line segement
DE and EF?
Answer:
Step-by-step explanation:
[tex]n\sqrt{2}=10[/tex]
Solve for n.
[tex]n\sqrt{2} =10\\\\\frac{n\sqrt{2} }{\sqrt{2} }=\frac{10}{\sqrt{2} }[/tex]
Rationalize the denominator.
[tex]n=\frac{10}{\sqrt{2} }\cdot \frac{\sqrt{2} }{\sqrt{2} }\\\\n=\frac{10\sqrt{2} }{2}[/tex]
Reduce to lowest terms.
[tex]n=\frac{10\sqrt{2} }{2} \div\frac{2}{2}\\\\n=5\sqrt{2}[/tex]
The question in is the image
Solve the right triangle. Round decimal answers to the nearest tenth.
Step-by-step explanation:
1) length of YZ:
[tex]YZ=\sqrt{XZ^2-XY^2} ;= > \ YZ=8.485=8.5;[/tex]
2) angle X:
[tex]m \angle X=arccos(\frac{XY}{XZ});= > \ m \angle X=arccos\frac{1}{3}=70.6 к;[/tex]
3) angle Z:
[tex]m \angle Z=arcsin(\frac{XY}{XZ});= > \ m \angle Z=arcsin\frac{1}{3}=19.4 к;[/tex]
Explain how you would find the area of the figure below
Find the value of x
Answer:
26
Step-by-step explanation:
(6x + 4) + (4x + 6) = 90
180 - (4x + 6) = (6x + 4) + 90
Rearrange the equation.
180 - (-90) = (6x + 4) + (4x + 6)
270 = 6x + 4 + 4x + 6
270 = 10x + 10
260 = 10x
26 = x
I don't know if this is correct, so I apologize if its wrong.
Answer:
x = 8
Step-by-step explanation:
According to the picture,
These given two angles are complementary. That is, those two angles are added up to 90°.
Therefore,
( 6x + 4 ) + ( 4x + 6 ) = 90
Combine like terms.
6x + 4 + 4x + 6 = 90
10x + 10 = 90
Subtract 10 from both sides.
10x = 90 - 10
10x = 80
Divide both sides by 10.
x = 8
Area = 63 square feet
7 ft
l ft
What is the unknown measurement of the rectangle
Answer:
9 ft
Step-by-step explanation:
63 divided by 7 is 9.
Hope this helped!
Use the bar graph to find the experimental probability of rolling a 5.
Answer:19?
Step-by-step explanation:
A radioactive substance has a half-life of 8 years. How much of the original 3.2 grams of the substance would be left after 36 years? Which equation best models this situation?
The exponential function [tex]A = 3.2 \times \frac{1}{2}^{\frac{36}{8}}[/tex] determines the amοunt of substance after 36 years to be 0.2 grams.
What is an exponential function?The fοrmula for an exponential functiοn is [tex]f(x) = a^x[/tex], where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The amοunt of a radioactive substance left after a certain number of half-lives can be calculated using the expοnential equation formula -
[tex]A = A_0 \times \frac{1}{2}^{\frac{t}{T}}[/tex]
where -
A0 is the initial amοunt of the substance
A is the amοunt of the substance remaining after t years
T is the half-life οf the substance
In this case, the half-life is 8 years, sο T = 8.
We want tο know how much of the original 3.2 grams of the substance wοuld be left after 36 years, so t = 36.
We can plug these values intο the formula to get -
[tex]A = 3.2 \times \frac{1}{2}^{\frac{36}{8}}[/tex]
A ≈ 0.2 grams
Therefοre, after 36 years, only about 0.2 grams of the original 3.2 grams of the substance wοuld be left.
The equation that best mοdels this situation is -
[tex]A = 3.3 \times \frac{1}{2}^{\frac{t}{8}}[/tex]
where A represents the amοunt of the substance remaining after t years, in grams.
Therefοre, the equation is [tex]A = 3.2 \times \frac{1}{2}^{\frac{36}{8}}[/tex].
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Any help will be awesome
On a coordinate plane, the x-axis is labeled Number of Days and the y-axis is labeled Number of Computers. A line goes through points (3, 36), (4, 48), (5, 60). The graph shows a proportional relationship between the number of computers produced at a factory per day. In three days, 36 computers are produced; 48 computers are produced in 4 days; and 60 computers are produced in 5 days. Find the unit rate of computers per day using the graph. Unit rate: computers per da
The unit rate is 12 computers per day (36/3 = 12; 48/4 = 12; 60/5 = 12). This means that the factory produces 12 computers per day.
What are computers?Computers are electronic devices that are used to store, process, and output data. They are used to perform a variety of tasks, from simple calculations to complex research projects. Computers consist of hardware, such as processors, memory, and storage devices, and software, which provides instructions for the hardware to follow.
The unit rate is the number of units produced per unit of time. To calculate the unit rate of computers per day using the graph, divide the number of computers produced by the number of days. Using the graph, 36 computers are produced in 3 days, 48 computers are produced in 4 days, and 60 computers are produced in 5 days.
Therefore, the unit rate is 12 computers per day (36/3 = 12; 48/4 = 12; 60/5 = 12). This means that the factory produces 12 computers per day. The graph produced shows a proportional relationship between the number of computers produced at a factory per day.
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Rahul bought a pencil for Rs. 73.50, a pen for Rs. 68.75 and a paint box for Rs. 112.35. He gave Rs. 500 to the shopkeeper and got back Rs. 345.40. He, however, returned Rs. 100 back to the shopkeeper. Was Rahul correct in returning Rs. 100 to the shopkeeper?
Answer:
Yes he was correct in returning the 100
Step-by-step explanation:
Pen 68.75
Pencil 73.50
Paint box 112.35
Add all together, you get 254.60
If he paid 500 to the shopkeeper, he will collect (500.00-254.60) =245.40
If the shopkeeper gave him 345.40, then he had an excess and should give back the 100
70 points! Complete each proof using the most appropriate method.
All statements and reasons are shown below.
What is triangle?A triangle is a closed two-dimensional geometric shape that has three sides, three angles, and three vertices. Triangles are one of the basic shapes in geometry and can be classified according to the length of their sides (scalene, isosceles, or equilateral) or the size of their angles (acute, right, or obtuse). The sum of the angles of a triangle is always 180 degrees, and the Pythagorean theorem can be used to find the length of one side if the other two sides are known in a right triangle.
According to the given figure:
4. In ΔFGH and ΔFJH,
Statement Reason
GH = JH (Given)∠FGH = ∠FJH (each 90°)FH = FH (Common)ΔFGH ≅ ΔFJH (by R.H.S rule)5. In ΔTVY and ΔXWY,
Statement Reason
TY = XY (Given)∠TVY = ∠XWY (Given)∠VYT = ∠WYX (Vertically opposite angle)ΔTVY ≅ ΔXWY (by A.A.A rule) angle-angle-angle ruleTV = XW (by C.P.C.T)6. In ΔKML and ΔPMN,
Statement Reason
KL = PN (Given)∠KLM = ∠PNM (KL║NP and LN is transversal line, so this is alternate interior angle)∠LKM = ∠NPM (Alternate interior angle)ΔKML ≅ ΔPMN (by A.S.A rule) angle-side-angle ruleLM = NM (by C.P.C.T)To know more about types of triangle, visit:
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Question: What price should the restaurant sell the large square pizza (12 inch side) for, so that both pizzas cost the same amount per square inch?
According to the question the height of Ruben’s school is 360 inches.
What is school?School is a place where students can learn and grow in their knowledge. It is a place where students can gain an education and become well-rounded individuals. School is a place where people can make friends, learn from each other, and explore new ideas and topics. School is a place where teachers and staff provide guidance to help students succeed in their academics and extracurricular activities.
To find the height of Ruben’s school using similar triangles and a mirror, we can use the following formula:
height of school / height of Ruben = distance from mirror to school / distance from mirror to Ruben
Plugging in the given values, we get:
height of school / 72 = 425 / 85
Cross-multiplying and solving for height of school, we get:
height of school = 72 x 425 / 85
height of school = 360 inches
Therefore, the height of Ruben’s school is 360 inches.
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Which correctly renames
7
8
and
5
6
using a common denominator?
A.
42
48
and
40
48
B.
42
48
and
30
48
C.
14
16
and
15
18
D.
28
24
and
20
24
Because the denominators of both fraction have been changed to 7/8=21/24 and 5/6=20/24, respectively,
What does it mean to be a denominator?In mathematics, a denominator is the lowest number in such a fraction that indicates how many equal parts are split into a whole. It is a fraction's divisor.
What term do you use instead of denominator?Divisor is another synonym for denominator. In a common fraction, the integer under the line is described by both of these terms. Similar to this, when discussing statistical values, the term "denominator" refers to the entire population or number out of which samples are selected.
Common denominator is going to be [tex]24[/tex]
[tex]8=2*2*2\\6=2*3\\24=2*2*2*3[/tex]
[tex]8[/tex] should be multiplied by [tex]3[/tex]
[tex]6[/tex] should be multiplied by [tex]4[/tex]
[tex]7/8=(7*3)/(8*3)=21/3\\5/6=(5*4)/(6*4)=20/24\\7/8=21/24\\5/6=20/24[/tex]
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inverse trig ratio can someone pls answer the rest of these i don’t understand them answers are already there but i need to see how they are done
We're given the angle measure to be 46 for No. 8. The length of 1 leg is x and the hypotenuse is 28.
We can use cosine to solve this. Since cosine is adjacent over hypotenuse, we can do cos(46) = x/28. Cross multiply to get cos(46)*28 = x. That solves to be 19.5
Using this principle allows us to solve the other ones. I'll let you figure them out.
TLDR: We can use the definition of trig functions to plug in what we know and place variables where we don't have enough information to find the length of a side.
describe what we mean by cost, revenue and profit
Answer:
In business and economics, cost, revenue, and profit are key concepts that relate to the financial aspects of a business.
Cost refers to the expenses incurred by a business in order to produce, sell or distribute its products or services. This includes direct costs, such as the cost of raw materials, labor and overhead expenses, as well as indirect costs, such as marketing and administrative expenses.
Revenue, on the other hand, refers to the income generated by a business through the sale of its products or services. Revenue can be calculated by multiplying the price of a product or service by the number of units sold.
Profit is the difference between revenue and cost, and is a measure of how much money a business earns after all of its expenses are paid. A business earns a profit when its revenue exceeds its total costs, including both fixed and variable costs.
Profit can be further broken down into gross profit and net profit. Gross profit is the difference between revenue and the direct cost of producing or delivering a product or service. Net profit, on the other hand, is the profit that remains after all expenses, including indirect costs, taxes and interest payments, have been deducted from revenue.
In summary, cost refers to the expenses incurred by a business, revenue refers to the income generated by the sale of products or services, and profit is the difference between revenue and cost, indicating how much money a business earns after all expenses are paid.
Step-by-step explanation:
Is 5 9/10 bigger than 5 5/6?
Answer:
5 9/10
Step-by-step explanation:
find the same denominator
in this case 30
9x3=27 and 5x5=25
since 27 is bigger, the fraction is also bigger
Answer:
5\6 is smaller than 9\10
Step-by-step explanation:
Find the least common denominator or LCM of the two denominators:
LCM of 6 and 10 are 30
Next, find the equivalent fraction of both fractional numbers with denominator 30
For the 1st fraction, since 6 × 5 = 30,
[tex]\frac{5}{6} = \frac{5.5}{6.5} =\frac{25}{30}[/tex]
Likewise, for the 2nd fraction, since 10 × 3 = 30,
[tex]\frac{9}{10} =\frac{9.3}{10.3} =\frac{27}{30}[/tex]
Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction
[tex]\frac{25}{30} < \frac{27}{30} 0r \frac{5}{6} < \frac{9}{10}[/tex]
Mr. Hamstra’s car holds 14 2/5 gallons of gas and averages 20 miles per gallon. About how far can Mr. Hamstra travel when his tank is 1/4 full?
Mr. Hamstra can travel about 70 miles when his tank is 1/4 full.
How is gas mileage calculated? What is it?The distance a car can go on a given quantity of gasoline is measured as gas mileage, also known as fuel efficiency. By dividing the distance driven by the amount of gasoline used, one may determine gas mileage. For instance, a car's gas mileage is 25 mpg (300/12 = 25) if it can go 300 miles on 12 gallons of petrol. Many variables, including traffic, speed, weather, road gradient, and vehicle maintenance, can have an impact on gas mileage.
Given that, Mr. Hamstra’s car holds 14 2/5 gallons of gas and averages 20 miles per gallon.
Thus, when his tank is 1/4 full, it contains:
1/4 * 14 2/5 = 14 2/5 / 4 = 3 1/2 gallons.
Hence, Mr. Hamstra can travel about 70 miles when his tank is 1/4 full.
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Which transformations map the strip pattern onto itself?
b b
b
b b
P
a reflection across a vertical line
a horizontal translation only
a horizontal translation and a gidé refecion
a horizontal translation and a 180° rotation
Answer:
The strip pattern has a vertical axis of symmetry, so a reflection across a vertical line will map the strip pattern onto itself. Therefore, the correct answer is "a reflection across a vertical line."
Step-by-step explanation:
$650 is invested in an account at 3
simple interest per year. Write an
explicit formula representing the
account balance in any given year,
and use this formula to find the
balance in the 25th year.
5. The value of the account at yearly intervals is given below.
6. The balance in the 25th year in the account will be $1,137.5.
What is simple interest?Let P be the principal, R be the rate of interest, and T be the time. Then the interest rate is given as,
The formula for interest is written as,
I = (PRT)/100
5. The simple interest is given as,
I = 650 x (3/100)
I = $19.5
End of first year = 650 + 19.5 - $669.50
End of second year = 669.5 + 19.5 = $689
End of third year = 689 + 19.5 = $708.50
End of fourth year = 708.50 + 19.5 = $728
End of fifth year =728 + 19.5 = $747.50
6. The balance after 25 years is given as,
A = $650 + ($650 x 3 x 25) / 100
A = $650 + $487.5
A = $1,137.5
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Find the value of the given expression, and most importantly show the steps please.
Answer:
Step-by-step explanation:
[tex]16^\frac{1}{n}=2[/tex] (since by definition [tex]\sqrt[n]{16} =16^\frac{1}{n}[/tex])
[tex](2^4)^\frac{1}{n}=2[/tex]
[tex]2^\frac{4}{n}=2[/tex]
[tex]2^\frac{4}{n}=2^1[/tex]
∴[tex]\frac{4}{n} =1[/tex] (indices must be equal when bases are equal)
∴[tex]n=4[/tex]
What is the value of 8.3?
The answer is 6.03 did this help?
Yesterday, Dustin biked 4 1/2 miles, jogged 2 3/4 miles, and swam 3 1/8 miles. How many miles did he travel while exercising?
10 3/8. I had this exact question for homework and answered this and got it correct, so I'm pretty sure this is correct :)
Find m < G in the image below (help asap please!!!)
Answer: m∠G = 41°
Step-by-step explanation:
Opposite angles of parallelograms are congruent. This means that m∠G = m∠E, so we can write an equation using the given information.
Given:
m∠G = m∠E
Substitue:
5x - 9 = 3x + 11
Add 9 to both sides of the equation:
5x = 3x + 20
Subtract 3x from both sides of the equation:
2x = 20
Divide both sides of the equation by 2:
x = 10
Then, we will substitute this value of x back into the expression for m∠G.
5x - 9 = 5(10) - 9 = 50 - 9 = 41°
Calculate the trade discount (in $). Round your answer to the nearest cent.
The trade discount is $15.75.
What is trade discount?A trade discount is a regular reduction from a product's regular, established price. The use of trade discounts allows a company to adjust the final price based on the volume or status of each customer.
It is important to note that trade discounts are not the same as early-payment discounts. (Early-payment discounts of 1% or 2% are typically recorded by the seller in an account such as Sales Discounts and by the buyer in an account such as Purchase Discounts using the periodic inventory method.) Neither the seller nor the buyer keeps a separate account for trade discounts.
We must first determine the product's list price in order to determine the trade discount.
List price: $75 plus $3.75 equals $78.75
As the trade discount rate is 20%, the following discount is offered:
Discount = 0.2 times List price = 0.2 times $78.75 = $15.75
The trade discount is therefore $15.75.
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