In linear equation , 8.65% is the YTM .
What is a formula for linear equations?
A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b). Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.Assuming face value to be $1000
Coupon = (0.09 * 1000) / 2 = 45
Number of periods = 8 * 2 = 16
Price = 102% of 1000 = 1020
YTM = 8.65%
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Write 670,000,000 in scientific notation.
6.7 × 109
0.67 × 109
67 × 108
6.7 × 108
6.7×10 8 is your correct answer
Answer:
the scientific notation is: [tex]6.7 ~x~10^{8}[/tex]
Step-by-step explanation:
The proper format for scientific notation is;
[tex]a~x~10^{b}[/tex]where a is a number or decimal number such that the absolute value of a is greater than or equal to one.
Given:
[tex]670,000,000[/tex]Thus, the scientific notation is:
[tex]6.7 ~x~10^{8}[/tex]Hope this helps!Answered by:AshTheNekoIan drove home from college traveling an average speed of 61.5 mph and drove back to the college the following week at an average speed of 65.2 mph. If the total round trip took 11 hours, how much time did it take Ian to drive from home back to college? Express the time in hours and minutes. Round to the nearest minute.
(Blank) hours (Blank) minutes
Show your work!
Explain your answer!
Do not spam answers!
Thanks!
Time taken in hours from home to college is; 5 hours 20 minutes
How to calculate time from speed?We are given;
Going home DATA:
Speed rate = 61.5 mph
Distance = x miles
Time taken = distance/speed = x/61.5 hrs
Going to college DATA:
Speed rate = 65.2 mph
Distance = x miles
Time taken = x/65.2 hrs
Thus, the equation set up is:
x/61.5 + x/65.2 = 11
Multiply through by (61.5 * 65.2) to get;
65.2x + 61.5x = 11 * (61.5 * 65.2)
126.7x = 44107.8
x = 44107.8/126.7
x = 348.1279 miles
Thus;
Time in hours from home to college = 348.1279/65.2
Time in hours from home to college = 5.34 hours = 5 hours 20 minutes
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Divide 38 in two parts such that one part is 18 more than the other
Answer:
10 and 28
Step-by-step explanation:
let x be one number then the other is x + 18 ( 18 more than the other ), then
x + x + 18 = 38
2x + 18 = 38 ( subtract 18 from both sides )
2x = 20 ( divide both sides by 2 )
x = 10
and x + 18 = 10 + 18 = 28
the 2 numbers which divide 38 into the 2 parts are 10 and 18
is it tru
e or false that parallel lines are always perpendicular lines
You sell a smartphone that was originally priced at $600 but is now on sale for 20% off. You give a loyal customer an additional 10% discount. What is the total percent of discount the customer receives on the purchase? A.
Answer: 30%
Step-by-step explanation: just add the 20% and 10% and you get 30%
Use differences to find a pattern in the sequence.
3,8,15,28,51,88,143
Assuming that the pattern continues, the eighth term should be
Answer:
220
Step-by-step explanation:
You want to use differences to find the pattern and the next term in the sequence 3, 8, 15, 28, 51, 88, 143.
First differencesSubtracting each term from the next, we find the sequence of first differences to be ...
5, 7, 13, 23, 37, 55
Second differencesThe first differences are not constant, so we know the sequence is not linear. They are not in an arithmetic progression, so we know the sequence is not quadratic. They do not have a common ratio, so we know the sequence is not exponential.
The second differences are the differences of the sequence of first differences. They are ...
2, 6, 10, 14, 18
Third differencesThe differences of the terms of the 2nd-difference sequence are constant: 4.
4, 4, 4, 4, 4
Constant 3rd differences mean the original sequence can be described by a 3rd degree polynomial. The coefficients found by a calculator are shown in the attachment.
Next termSince we know the third differences are constant, we can work our way back up the chain of differences to find the next term of the original sequence.
next 2nd difference = 18 +4 = 22
next 1st difference = 55 +22 = 77
next sequence term = 143 +77 = 220
The eighth term should be 220.
__
Additional comment
The n-th term is ...
f(n) = 2/3n^3 -3n^2 +28/3n -4
In the addition problems below A, B, and C are digits. If C is placed in the tens
column instead of the ones column as shown at the right, the sum is 97. What are
the values of A, B, and C?
AB + C = 52
AB+ (C x 10) = 97
The values of A, B, and C are mathematically given as
A=48/BB=48/AC=5This is further explained below.
What are the values of A, B, and C?Generally, the equation for the statement is mathematically given as
AB + C = 52
AB+ (C x 10) = 97....1
Using the substitution technique we have
AB = 52- C ....2
Subbing 2 in 1
AB+ (C x 10) = 97
Therefore
52- C + 10C = 97
9C=97-52
9C=45
C=5
In conclusion,
AB = 52- C
AB = 52- 5
AB=48
A=48/B
Hence
B=48/A
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Translate this sentence into an equation.
54 is the sum of 12 and Rhonda's height.
Use the variable r to represent Rhonda's height.
Answer:
54=12+r
Step-by-step explanation:
'Sum' means to add.
54 = 12 + rhonda's height
54 = 12 + r
3. An object is dropped from a 450-meter tower. The height of the falling object is given
by y(t) = 450-4.9t2, with height y in meters and time t in seconds.
(a) Use the basic derivative rules to compute y' (2).
Using basic derivative rules the value of y' (2) is 19.6 .
Derivative rules in calculus square measure accustomed realize the derivatives of various operations and differing types of functions like power functions, exponent functions, exponential functions, etc. Some vital spin off rules are:Power Rule ,Sum/Difference Rule ,Product Rule ,Quotient Rule,Chain Rule The power rule of derivatives says d/dx (xⁿ) = nxⁿ⁻¹We have given a function of t y(t) = 450-4.9t².
On differentiating with respect t , we get
y'(t) = 2 × 4.9t
y'(t) = 9.8 t ......(1)
Putting t = 2 in equation (1) , we get
y'(2) = 9.8 × 2
= 19.6
Hence , value of y'(2) is 19.6
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reflection across y = -x please I need help I will mark you brainless
This question: Submit Fritz plans to fence off a square feed lot and then cross-fence to divide it into four smaller feed lots. If he uses 924 feet of fencing, then how much area will be fenced in?
Answer:
23,716 ft
Step-by-step explanation:
Let the side length of each of the four smaller lots be s.
Then, Fritz will use 12s feet, which is equal to 924.
This means s=77.
This means the area of each smaller square is 77²=5929, and thus the total area is 23,716 ft.
Why was his velocity 0? Explain.
ALGEBRA 1 HW!! PLEASE HELP I WILL GIVE BRAINLYEST also pls explain what the heck an explicit formula is..
Answer:
explicit formula is a mix of different upgraded formulas
Step-by-step explanation:
teach me simple equation solving an equation using tansposing method class 7 pleaseee pls
Any given equation can be solved with the help of transpose method by following the steps mentioned below, but first understand what is linear equation.
What is a linear equation?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. It is of the form -
y = ax + b
Given a simple equation and we have to solve the equation using transpose method.
We will learn about transpose method of equation solving with the help of an example. Assume that you have to solve the following expression -
4(x + 9) = 3(x + 7)
STEP - 1 - Identify the unknown variable.
In the expression given, the unknown variable is x.
STEP - 2 - Solve the Left hand side and Right hand side to make both sides simpler.
In the expression given, we will simplify both sides -
4(x + 9) = 3(x + 7)
4x + 4 × 9 = 3x + 3 × 7
4x + 36 = 3x + 21
STEP - 3 - Transfer the terms that containing variable one Left hand side of equation and the constant terms on the right hand side.
Apply Step 3 -
4x - 3x + 36 = 21
4x - 3x = 21 - 36
STEP - 4 - Solve for unknown variable.
We have -
4x - 3x = 21 - 36
x = - 15
Therefore, any given equation can be solved with the help of transpose method by following the steps mentioned above.
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if n represents a number, then write an expression for the product of the number with a number that is seven more than it.
Answer: N * (n+7) = n^2 + 7n
Step-by-step explanation:
This equation would be the number, n, times n+7 because n+7 is 7 more than n. To do this, you have an equation like this:
N * (N+7). You would then do distributive property, and n*n would be n squared, and n*7 would be 7n. This would give you a combined answer of n squared + 7n, or n^2 +7n.
The governor of state A earns $54,900 more than the governor of state B. If the total of their salaries is $310,850, find the salaries of each
The salaries of each will be 127975 and 182875.
How to compute the value?Lat the salaries of B = b
Let the salary of A = b + 54900
Therefore, we will add them together to get the value:
b + b + 54900 = 310850
2b + 54900 = 310850
2b = 310850 - 54900
2b = 255950
b = 255950/2
b = 127975
a = b + 54900 = 127975 + 54900 = 182875
Therefore, the salaries of each will be 127975 and 182875.
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What is the slope of the line
Answer:
its 1/3
Step-by-step explanation:
see picture for referance
Could someone please help me solve this, I have a few hours left and I’m really struggling so bad
Answer:
8
Step-by-step explanation:
shirts = 10, price per shirt = $9
shirts = 25, price per shirt = $8.40
Linear equation be:
y = mx + b
x = 10 , 25
y = 9 , 8.40
9 = 10m + b
8.4 = 25m + b
9 = 10 m + b b = 9 - 10m
8.4 = 25m + b 8.4 = 25m + 9 - 10m
8.4 - 9 = 15m m = -0.6/15 = -0.04
m = - 0.04
b = 9 - 10m = 9 - 10(-0.04) = 9+0.4 = 9.4
b = 9.4
The linear equation =
y = mx + b
y = -0.04x + 9.4
Hope this helped xx ?<3
Please answer quick!!! TYSM!
Answer:
10
Step-by-step explanation:
[tex]x=0 \implies x\in \{-15, -12, 0, 10\} \\ \\ \therefore f(0)=11-|0-1|=10[/tex]
help pleaseeeeeeeeeeeeeeeeeeee
6.2E15
Here ; E stands for "times 10 to the power of or simply it replaces 10^ "
#17 Write an inequality for
the situation below:
Bring at least $9 for dinner
tomorrow.
The inequality will be:
x ≥ $9
Which says that x can be equal to or larger than $9.
How to write an inequality?An inequality is a mathematical statement that relates two or more mathematical elements (variables, expressions, etc.) in such a way that there is not a equality like in an equation (an equality can be a solution, but not necessarily)
For example, if x represnts what you bring for dinner, we know that x needs to be at least $9.
So x = $9 is a solution.
But if x is a larger value than $9, it also is a solution.
This situation is represented by the inequality:
x ≥ $9
Which says that x can be equal to or larger than $9.
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I have attached the problem in a picture below!
Answer:
A. The solution set is x = 5 or -7
Step-by-step explanation:
[tex] \sqrt[4]{ {x}^{2} + 2x } = \sqrt[4]{35} \\ {({x}^{2} + 2x) }^{ \frac{1}{4} } = {(35)}^{ \frac{1}{4} } \\ {x}^{ \frac{1}{2} } + {2x}^{ \frac{1}{4} } = {35}^{ \frac{1}{4} } \\ {x}^{2} + 2x = 35 \\ {x}^{2} + 2x - 35 = 0 \\ (x - 5)(x + 7) = 0 \\ x = 5 \: or \: - 7[/tex]
Therefore, the answer is A. as the solution is x = 5 or -7
Translate the sentence into an equation.
Five times the sum of a number and 3 equals 7.
Use the variable x for the unknown number.
Answer:
5(x+3) = 7
Step-by-step explanation:
5(x+3) = 7
Help please will mark brainliest
Answer:
B
Step-by-step explanation:
because it most reasonable
also you times the number as much as the exponents
Answer:
A. (5^8)/(5^9)
Step-by-step explanation:
Using the properties of exponents, in this case case the Power of Quotient Rule, can be changed into the one in A.
If y = x³ +3,
find the value of y when x = -1
Answer:
Step-by-step explanation:
y = x^3 + 3
y = (-1)^3 + 3
y = -1 + 3
y = 2
In Town A, homeowners pay a $25 monthly usage fee and $3 per hundred cubic feet for water. In Town B,
homeowners pay $2.00 per hundred cubic feet and a $50 monthly usage fee for water.
2.
1. Can these situations be represented by linear functions? Why? Why not?
Predict: If you graph both of these water costs on the same axes, will the graphs form the same line,
intersect at one point, or form two separate lines that never intersect? Explain your reasoning.
3. Write equations, in slope-intercept form, for a homeowner's monthly water cost in Town A and Town B,
where y is the total cost for x hundred cubic feet of water.
The homeowners pay a $25 monthly usage fee and $3 per hundred cubic feet for water number line is- 75,100
Given:
In Town A
$25 monthly usage fee
$3 per hundred cubic feet for water.
In Town B,
homeowners pay $2.00 per hundred cubic feet and a $50 monthly
For town A=25×3=75
For town B=50×2=100
When we write numbers on a number line, we can easily compare them and execute simple arithmetic operations on them. A number line's origin is defined as zero (0). The numbers to the left of 0 are all negative, whereas the numbers to the right of 0 are all positive. So, as we walk towards the right on a number line, the value of numbers increases.
A number line includes both positive and negative numbers. A negative number line is formed by the segment of the number line to the left of zero.
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Measures of Variation, Standard Deviation, Population Variance, Population. Can someone help?
To solve this problem one must be aware of the concepts of standard deviation and variance of raw data.
There is a direct formulae to calculate the variance of the data,
Variance = [tex]σ^{2} =\frac{Sigma(xi-m)^{2}}{n}[/tex]
Now here we need to verify ∑x and ∑[tex]x^{2}[/tex].
∑x = 21+19+15+32+27
= 114
and ∑[tex]x^{2}[/tex] = [tex]21^{2} +19^{2} +15^{2} +32^{2} +27^{2}[/tex]
= 441+361+225+1024+729
= 2780
So, the given relation is true.
Now the variance of the given data by putting the values in the formulae is equal to 45.2.
And Standard deviation=[tex]\sqrt{Variance}[/tex]
= [tex]\sqrt{45.2}[/tex]
= 6.72
And for population α²=36.16 and deviation=6.01.
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You, Newton, and Descartes have
17 stampers in all. Newton and Descartes each
have 6. How many stampers do you have?
I will have 5 stampers
How to calculate the number of stampers left ?I, Newton and Descartes have 17 Stampers in total
Newton and Descartes have 6 stampers each
6 + 6
= 12
The number of stampers left for me can be calculated as follows
= 17 - 12
= 5
Hence I have 5 stampers
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ans : 27.......................
[tex] \frac{(243 {)}^{2n/5} . {3}^{2n + 1} }{ {9}^{n + 1}. {3}^{2(n - 2)} } \\ [/tex]
please give step by step explanation...
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: \dfrac{((243 {)}^{2n/5} ) \sdot( {3}^{2n + 1}) }{ ({9}^{n + 1}) \sdot( {3}^{2(n - 2)} )}[/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{(3{)}^{5(2n/5)} ) \sdot( {3}^{2n + 1}) }{ ({3 }^{2(n + 1)}) \sdot( {3}^{2(n - 2)} )}[/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{(3{)}^{2n} \sdot( {3}^{2n + 1}) }{ ({3 }^{(2n + 2)}) \sdot( {3}^{(2n - 4)} )}[/tex]
let's break it up :
[tex] \sf 3 {}^{2n} = (3 {}^{2n -4} ) \sdot(3 {}^{4} )[/tex][tex] \sf 3 {}^{(2n + 1)} = (3 {}^{2n -4} ) \sdot(3 {}^{5} )[/tex][tex] \sf 3 {}^{(2n + 2)} = (3 {}^{2n -4} ) \sdot(3 {}^{6} )[/tex]now let's take [tex]{ \sf {3}^{(2n-4)}} [/tex] common here ~
[tex]\qquad \sf \dashrightarrow \: \dfrac{(3{)}^{(2n - 4)} (3 {}^{4} \sdot{3}^{5}) }{ {(3 )}^{(2n - 4)}(3 {}^{6} \sdot1)}[/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{{} (3 {}^{4} \sdot{3}^{5}) }{ (3 {}^{6} \sdot1)}[/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{{} 3 {}^{9} }{ 3 {}^{6} }[/tex]
[tex]\qquad \sf \dashrightarrow \: 3 {}^{3} [/tex]
[tex]\qquad \sf \dashrightarrow \: 27[/tex]
Answer:
27Step-by-step explanation:
[tex]\sf \cfrac{243^{\frac{2n}{5}}\cdot \:3^{2n+1}}{9^{n+1}\cdot \:3^{2\left(n-2\right)}}[/tex]
[tex]\sf 9^{n+1}\cdot \:3^{2\left(n-2\right)}[/tex]
Simplify:-
[tex]\sf 3^{4n-2}[/tex][tex]\sf \cfrac{3^{2n}\cdot \:3^{2n+1}}{\boxed{\bf 3^{4n-2}}}[/tex]
Now, Factor:-
[tex]\sf 243^{\frac{2n}{5}}[/tex][tex]= \boxed{\bf 3^{2n}}[/tex][tex]\sf \cfrac{3^{2n}\cdot \:3^{2n+1}}{3^{4n-2}}[/tex]
Now, let's simplify:-
[tex]\sf \cfrac{3^{2n}}{3^{4n-2}}[/tex][tex]=\boxed{\bf 3^{-2n+2}}[/tex][tex]\sf 3^{-2n+2}\cdot \:3^{2n+1}[/tex]Simplify:-
[tex]\sf 3^{-2n+2}\cdot \:3^{2n+1}[/tex]Apply the exponent rule:-
[tex]\sf 3^{-2n+2+2n+1}[/tex][tex]\sf 3^3[/tex][tex]\sf 27[/tex]Therefore, your answer is 27.
______________________
Hope this helps!
Have a great day!
expanded:
Kaleb compared the perimeters of two
posters hanging on his bedroom wall.
60 cm
What is the perimeter
of the football poster?
86 cm
What is the perimeter
of the basketball poster?
Which poster has a
greater perimeter?
catam
55 cm
Answer:
1. The perimeter of the basketball poster is 240.
The perimeter of the football poster is 282.
3. Football poster has the greater perimeter.
Step-by-step explanation:
To find the perimeter of the basketball poster you multiply the given side by 4 since there is 4 sides. So 60 * 4 = 240.
To find the perimeter of the football poster you use the formula 2(l+w). So our l (length) is 86, while our w(width) is 86. So plug it in the formula.
2(55+86)=282.
282 > 240, which means that the football poster has a greater perimeter.
Hope that helps, have a good day!! :D
