Question Help: How much should be invested today at 6.25% compounded quarterly to have $18,000 in 13 years?
When 6.25% is compounded quarterly to get $18,000 in 13 years, the total amount is $22,478.16 in compound interest.
what is interest ?Divide the total by the yield curve, the length of time, and other factors to arrive the simple interest. Simple return = money + return + hours is the marketing formula. This method allows it easiest to calculating interest. The most typical technique to figure approximately interest is as a portion of the principal sum. He will only pay his share of the 100% extra, for example, if he borrows $100 from a neighbor and agrees to pay it back with 5% interest. $100 (0.05) = $5. When you borrow, you must pay interest, and when you give it out, you must charge interest. Interest is often determined like an indicator of the overall of both the loan total.
given
Amount = Principal (1 + rate of interest) number of years
= $1,200 (1 + 0.032) 8
= $1,200 1.286582318
= $22,478.16 is the amount in compound interest.
The remaining amount is $40,478.16.
When 6.25% is compounded quarterly to get $18,000 in 13 years, the total amount is $22,478.16 in compound interest.
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[10 Points] In the standard numbering (shortlex ordering) of strings over the alphabet {a,b,c} what number corresponds to string cbbca cba cbc ?
The number corresponds to the given string is 237880
What is common ratio?
In a geometric sequence, ratio of each term to its immediately preceding term is always constant and is known as common ratio.
The shortlex ordering places the shortest sequences at the front of the list of sequences by cardinality (length), while sequences of the same length are arranged lexicographically.
Given: cbbca cba cbc
length =11
We need to find the number of strings that precede the given string over {a,b,c}
Number of strings of length 0 = 1
Number of strings of length 1 = 3
Number of strings of length 2 = 3²
'
'
'
'
'
Number of strings of length 10 = 3¹⁰
In general, number of strings formed withy length n = 3ⁿ
Add all the strings of length 0 to 10
1+3+3²+......................+3⁻¹⁰
By simple geometric sum formula ,
we have
= (3¹¹⁻¹)/(3-1) = 88573
Number of strings of length 11 starting with either 'a' or 'b' = 2*3¹⁰
Number of strings of length 11 starting with 'ca' = 3⁹
Number of strings of length 11 starting with 'cba' = 3⁸
Number of strings of length 11 starting with 'cbba' or 'cbbb' = 2*3⁷
Number of strings of length 11 starting with 'cbbcaa' or 'cbbcab' = 2*3⁵
Number of strings of length 11 starting with 'cbbcaca' = 3⁴
Number of strings of length 11 starting with 'cbbcacbab' or 'cbbcacbaa' = 2*3²
Number of strings of length 11 starting with 'cbbcacbaca' = 3
Number of strings of length 11 starting with 'cbbcacbacba' or 'cbbcacbacbb' = 2
Total number of strings of length 11 preceding the given string is :
2+3+2*3² +3⁴+ 2*3⁵+ 2*3⁷+3⁸+3⁹ + 2*3¹⁰
= 149306
The number corresponds to the given string
= 88573 + 149306 +1
= 237880
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Numbers in thousands) of forest fires over the year and the number in hundred thousands) of acres burned for 7 recent years are shown.Number of fires x | 69 58 47 84 62 57 72Number of acres burned y | 64 53 42 79 57 52 67The correlation coefficient for the data is r = 1 and a = 0.05. Should regression analysis be done?The regression analysis (should/should not) be done.
The correlation coefficient of 1 indicates a strong positive linear relationship between the number of forest fires and the number of acres burned.
However, the correlation coefficient alone does not determine if regression analysis should be done or not. Other factors such as the purpose of the analysis, the distribution of the data, and the presence of outliers should also be considered.
In general, if the relationship between the two variables is of interest and there is sufficient evidence of a linear relationship, then regression analysis may be appropriate. However, a final decision requires a deeper understanding of the problem and the data.
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Point P is equidistant from both [AB] and [AC]. Use congruence to show that P lies on the bisector of BAC.
Hint: To find the distance from P to either line we draw a perpendicular from the point to the line. So, the figure becomes:
Based on the RHS rule of congruency of triangles, APC and APB are congruent, therefore, P lies on the bisector of BAC.
How can it be proved that P lies on the bisector of BAC?To prove that P lies on the bisector of BAC:
Sketch the angle and its bisector.Draw perpendiculars from any point along the bisector onto the two angles' two arms. The two arms, the bisector, and the two perpendiculars you sketched have now joined to form two triangles.Based on two equal angles (the bisected angle), right angles, and a similar side, the two triangles are said to be congruent (RHS congruence rule). As a result, the perpendiculars are of equal length, and the angle's bisector is equally spaced from its sides.
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A baking club wants to form an executive committee. There are 4 people in the baking club, including Mark. In how many ways can the baking club form an executive committee with 2 people?
The number of ways that baking club form an executive committee with 2 people will be 6.
What are permutation and combination?A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.
A baking club wants to form an executive committee. There are 4 people in the baking club, including Mark.
The number of ways that baking club form an executive committee with 2 people will be given as,
⁴C₂ = 4! / [(4 - 2)! x 2!]
⁴C₂ = 4 x 3 x 2! / (2! x 2 x 1)
⁴C₂ = 2 x 3
⁴C₂ = 6
The number of ways that baking club form an executive committee with 2 people will be 6.
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On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 108 and a standard deviation of 17. Suppose one individual is randomly chosen. Let X = IQ of an individual.
Answer:
Step-by-step explanation:
Find the probability that X is less than 92:
We can use the cumulative distribution function (CDF) of a normal distribution to find the probability that X is less than 92. The CDF of a normal distribution with mean μ and standard deviation σ is given by:
F(x) = (1/2) * [1 + erf((x-μ)/(σ * sqrt(2)))]
Where erf is the error function.
So, the probability that X is less than 92 can be calculated as:
P(X < 92) = F(92) = (1/2) * [1 + erf((92-108)/(17 * sqrt(2)))]
This value can be calculated using a calculator or statistical software.
Find the probability that X is between 92 and 126:
We can use the CDF to find the probability that X is between 92 and 126. The probability that X is between 92 and 126 is equal to the difference between the CDF values at 126 and 92:
P(92 < X < 126) = F(126) - F(92)
This value can also be calculated using a calculator or statistical software.
Find the IQ of an individual that is in the top 10% of the population:
To find the IQ of an individual that is in the top 10% of the population, we need to find the value of X that corresponds to a cumulative probability of 0.9. This can be done by solving for X in the CDF equation:
F(X) = 0.9
X = μ + σ * inverse_CDF(0.9)
Where inverse_CDF is the inverse cumulative distribution function and can be calculated using a calculator or statistical software. The value of X that corresponds to a cumulative probability of 0.9 is the IQ of an individual that is in the top 10% of the population.
Help ASAP! Due tonight! Will mark brainliest-
This may sound wrong or confusing but I have a cousin in college and he said that it should be 3-6!
ved Match each equation of a tangent line to the correct tangent on the graph of the function f(x) = 0.1x³ + 2. y = 0.3x + 1.8 y = 4.8x - 10.8 y = 2.7x + 7.4 - y = 2.7x+3.6 y = 1.2x + 7.4 y = 4.8x + 1.8 -2 -1 10 3 1 y = 0.3x - 10.8 f(x) = 0.1x³ + 2/ 2/ 3 y = 1.2x+3.6
y = 0.3x + 1.8 matches f(x) = 0.1x³ + 2
y = 1.2x + 7.4 matches f(x) = 0.1x³ + 2
y = 2.7x + 3.6 matches f(x) = 0.1x³ + 2
y = 4.8x + 1.8 does not match f(x) = 0.1x³ + 2
y = 4.8x - 10.8 does not match f(x) = 0.1x³ + 2
y = 0.3x - 10.8 does not match f(x) = 0.1x³ + 2
What is a tangent line?A tangent line is a straight line that touches a given curve at a single point and has the same slope as the curve at that point. In other words, it is a line that locally approximates the curve at that point. The tangent line is often used to study the behavior of a function near a particular point and can provide valuable information about the properties of the curve
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The interval [0,3] is partitioned into n equal subintervals, and a number xi is arbitrarily chosen in the ith subinterval for each i. Then lim n -> infinity n E i=1 (6xi-3)/n
The limit of the sum (6xi-3)/n as n approaches infinity is 9, which means that as the number of subintervals in the interval [0,3] becomes larger and larger, the sum of the values (6xi-3)/n approaches 9.
The limit is a concept in mathematics that helps us understand what happens as a function or a sequence approaches a certain value.
In this particular problem, we are looking at the limit of a sum of values as the number of subintervals in the interval [0,3] approaches infinity.
The interval [0,3] is divided into n equal subintervals and a number xi is chosen arbitrarily in the ith subinterval. We then look at the sum of the values (6xi-3)/n for all n subintervals.
Mathematically, we can write this sum as:
S = (6xi-3)/n for i = 1, 2, ..., n
And the limit of S as n approaches infinity can be written as:
lim n -> infinity S = lim n -> infinity (6xi-3)/n
Now, we use the concept of a Riemann Sum to evaluate the limit of this sum. A Riemann Sum is a way of approximating the area under a curve by breaking it down into rectangles and summing their areas.
In our case, we can think of the sum S as a Riemann Sum for the function f(x) = 6x-3 over the interval [0,3]. As n approaches infinity, the width of the subintervals approaches 0, and the sum S approaches the definite integral of f(x) over [0,3].
Using the fundamental theorem of calculus, we can find the definite integral of f(x) over [0,3] as:
∫f(x)dx = 6x^2/2 - 3x evaluated from 0 to 3
And this value is 9, so the limit of S as n approaches infinity is 9.
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Use an equation to find the value of k so that the line that passes through (k,4) and (3,-2) has a slope of m=-1
K=
Complete the square in the expression. Then factor the perfect square trinomial.
x2−32x
The perfect square polynomial is x² - 32x + 256 and the factored form is (x - 16)(x - 16)
How to factor perfect square polynomials?A perfect square trinomial is defined as an algebraic expression that is obtained by squaring a binomial expression.
A perfect square polynomial can be represented as follows;
ax² + bx - c = 0
Hence, the perfect square trinomial is x² - 32x + 256.
Now, let's factorise it.
x² - 32x + 256.
x² - 16x - 16x + 256
x(x - 16) -16(x - 16)
Therefore,
(x - 16)(x - 16)
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Answer: x²-32x+16²
Step-by-step explanation:
(x-a)²=x²-32x+a² where .2ax=-32x so, 2a=32 then a=16
then (x-16)²=x²-32x+16²
Write the answer in the form (x,y)
solve. |3x+2| = |2x-5|
Answer:
[tex]3x + 2 = 2x - 5 \\ 3x - 2x = - 5 - 2 \\ x = - 7[/tex]
Step-by-step explanation:
please make me as brainlest
Step-by-step explanation:
I hope it will help you...
help pls. Ramon is filling cups with juice. Each cup is shaped like a cylinder and has a diameter of 4.6 inches and a height of 7 inches. How much juice can Ramon pour into 6 cups? Round to the nearest hundredth and approximate using π = 3.14.
116.27 cubic inches
303.32 cubic inches
697.65 cubic inches
2,790.58 cubic inches
Accidental question that had been put out
Answer:
Step-by-step explanation:
ss
decide which of the two given functions is linear and find its equation.x=0,1,2,3,4f(x)=6,10,14,18,22g(x)=8,10,12,16,22
The function f(x) is linear and equation is y = 4x + 6 where x=0,1,2,3,4
What exactly is a function?A function is defined as a relationship between a group of inputs that each have one output. A function is a connection between inputs in which each input is associated to exactly one output. Every function has a domain and a co-domain, as well as a range. In general, a function is denoted as f(x), where x represents the input. A function's generic representation is y = f(x).
In mathematics, there are several types of functions. Some examples include:
When there is a mapping for a range for each domain between two sets, this is referred to be an injective function or a one to one function.
Surjective functions, also known as Onto functions, are used when more than one element is transferred from domain to range.
Polynomial function: A function made up of polynomials.
Inverse Functions: A function that may be used to inverse another function.
Now,
For function f(x)=6,10,14,18,22, g(x)=8,10,12,16,22 for x=0,1,2,3,4
f is a function because y increases 4 for each increase of 1 in x
slope = 4
intercept = f(0) =6
Hence Equation is y = 4x + 6 where x=0,1,2,3,4
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is 5.9 bigger than 5.99?
Answer:
no
Step-by-step explanation:
5.9 is close to 5.10
5.99 is close to 6
5.9 + 0.1 = 5.10
5.99+0.1 = 6
Answer:
Hi there! 5.9 is NOT bigger than 5.99
Step-by-step explanation:
5.9 is 0.09 less than 5.99.
Hope this helps!
Brainiest? Can you click on the crown on this answer? Thanks!
What are the factor's of 54.
Answer:
1, 2, 3, 6, 9, 18, 27 and 54
Step-by-step explanation:
A factor is a number that divides another number without leaving a remainder
Factors of 54:
1 × 54 = 54
2 × 27 = 54
3 × 18 = 54
6 × 9 = 54
9 × 6 = 54
18 × 3 = 54
27 × 2 = 54
54 × 1 = 54
The factors are: 1, 2, 3, 6, 9, 18, 27 and 54
Sally saved $182 in March. Her father gave her $20 for every
$50 she saved. How much did Sally's father give her?
Answer:
72.8 or 72 4/5
Step-by-step explanation:
MTH115 – Principles of Mathematics
Assignment 4.2 – Technology 4
Recreate this table in a spreadsheet. Use built-in commands to find the column, row, and overall totals. After that, answer the given questions by using cell references in the spreadsheet. Round your answer to the whole percentage. Upload your sheet as an excel file.
Expenses
Rent Labor Supplies Total
Business 1 750 1300 2500
Business 2 1500 975 3600
Business 3 1200 850 1850
Business 4 450 1600 2900
Business 5 3200 5200 1000
Business 6 980 360 5600
Total
a. Labor makes up what percent of the total?
b. What percent of the total was Business 4's expenses?
c. Business 5's labor cost is what percent of the total labor expenses?
d. Supplies makes up what percent of Business 5's expenses?
Answer: I'm sorry, I am not able to create or upload spreadsheets in this platform due to recent restrictions. However, you can easily create this table in a spreadsheet program like Microsoft Excel and use built-in functions to find the desired information.
To answer the questions:
a. To find the percentage of the total that Labor makes up, you would divide the total Labor expenses by the overall Total expenses, then multiply by 100 to express the answer as a percentage.
b. To find the percentage of the total that Business 4's expenses make up, you would divide Business 4's Total expenses by the overall Total expenses, then multiply by 100 to express the answer as a percentage.
c. To find Business 5's labor cost as a percentage of the total labor expenses, you would divide Business 5's Labor expenses by the overall Labor expenses, then multiply by 100 to express the answer as a percentage.
d. To find the percentage of Business 5's expenses that Supplies make up, you would divide Business 5's Supplies expenses by Business 5's Total expenses, then multiply by 100 to express the answer as a percentage.
Step-by-step explanation:
expand the expression -2/5(10+5/6m-20n)
-4-1/3m+8n is the simplified form of the expression -2/5(10+5/6m-20n)
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is -2/5(10+5/6m-20n)
Minus two by five times of ten plus five by six m minus twenty n.
In the expression m and n are the variables and minus and plus are the operators.
Apply distributive property to solve the expression.
-2/5(10)-2/5(5/6)m+2/5(20n)
-4-1/3m+8n
Hence, -4-1/3m+8n is the simplified form of the expression -2/5(10+5/6m-20n)
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an outdoor theater currently has 1,375 ft next year 125 news seats will be added there will be 25 ft in each row after the new seeing has been added how many rows would a theater have after the new seats have been added?
The total number of rows in the Theater after 125 seats are added is 60 rows.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
The Outdoor theater currently has 1,375 seats.
If we add 125 new seats then the number of seats are
= 1375 + 125
= 1500
Each row have 25 seats in one row.
Then, the total number of rows in Theater
= 1500/25
= 60 rows.
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A land surveyor measured these lengths to find the distance, d, across a pond.
What is d, to the nearest tenth of a meter?
A
B
C
16.0 meters
19.2 meters
20.0 meters
Q
24 m
10 m
Р
12 m
The value of AB to the nearest tenth of a meter is 21 meter.
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
Two triangles are similar, if the ratio of their corresponding sides are in the same proportion
Triangle ABC and CDE are proportional, hence:
AB / DE = AC / CE
substituting:
AB / 7 = (12 + 6)/6
AB = 21 meter
The value of AB is 21 meter.
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will give brainliest. A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
81 9 72 36 27
Which statement is the best prediction about the slices of pie the college will need?
A. The college will have about 480 students who prefer pie.
B. The college will have about 640 students who prefer pie.
C. The college will have about 1,280 students who prefer pie.
D. The college will have about 1,440 students who prefer pie.
Someone please help me
The required solution is given as,
1. 2/5 of the sum of 8 and 4
2. 2/5 [8 + 4]
3. 4 4/5
The expression model is defined as the model of the given situation in the form of an expression using variables and constants.
Here,
From the figure,
It can be concluded that it is 2/5 times the sum of 8 and 4,
Also
= 2/5[8 + 4]
Simplify
= 2/5[12]
= 24/5
= 4 4/5
Thus, the required solution is given as,
1. 2/5 of the sum of 8 and 4
2. 2/5 [8 + 4]
3. 4 4/5
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Trish drive 18 1/8 miles yesterday she drove 13 2/3 miles today write and addition sentence to show how many miles Trish drove in all
There are 31 19/24 miles Trish drive in all.
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Given that;
Trish drive 18 1/8 miles yesterday she drove 13 2/3 miles today.
Hence, Total miles Trish drive in all is,
⇒ 18 1/8 + 13 2/3
⇒ 145/8 + 41/3
⇒ (145 × 3 + 41 × 8 ) /24
⇒ (435 + 328) / 24
⇒ 763/24
⇒ 31 19/24 miles
Thus, Total miles Trish drive in all is, 31 19/24 miles.
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which of the following correctly ranks the magnitudes of the electric field at the four labeled points from largest to smallest?
The electric field at points A and C is the same, since they are both the same distance away from the center of the charge. Therefore, the electric field at A and C is the largest, while the electric field at B and D is the smallest. Thus, the correct answer is A. A, C, B, D.
The electric field is determined by the magnitude of the charge, the distance between the charge and the point where the electric field is measured, and the direction of the electric field. In this case, point A and C are the same distance away from the center of the charge, while points B and D are further away. Therefore, the electric field at points A and C is the strongest.
the complete question is :
which of the following correctly ranks the magnitudes of the electric field at the four labeled points from largest to smallest?
Options :
A. a, b, c, d
B. b, c, d, a
C. b, d, c, a
D. d, c, b, a
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I don’t understand these questions
Order of fractions from smallest to largest:
4/15, 3/10, 11/15, 17/20, 9/101/4, 1/3, 2/5, 2/3, 3/4 4/3, 7/5, 5/3, 7/4, 9/4 13/10, 13/6, 11/5, 25/6, 21/5How to order fractions3/10, 4/15, 9/10, 11/15, 17/20If sorted we first equate the denominator to 60.
18/60, 16/60, 54/60, 44/60, 51/60
So if sorted from smallest to largest, the order becomes:
4/15, 3/10, 11/15, 17/20, 9/10
1/4, 1/3, 2/3, 3/4, 2/5If sorted we first equate the denominator to 60. it becomes:
15/60, 20/60, 40/60, 45/60, 24/60
So if sorted from smallest to largest, the order becomes:
1/4, 1/3, 2/5, 2/3, 3/4
9/4, 4/3, 5/3, 7/4, 7/5If sorted we first equate the denominator to 60. it becomes:
135/60, 80/60, 100/60, 105/60, 84/60
So if sorted from smallest to largest, the order becomes:
4/3, 7/5, 5/3, 7/4, 9/4
21/5, 13/6, 25/6, 11/5, 13/10If sorted we first equate the denominator to 30. it becomes:
126/30, 65/30, 125/30, 66/30, 39/30
So if sorted from smallest to largest, the order becomes:
13/10, 13/6, 11/5, 25/6, 21/5
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An airplane crosses the Atlantic Ocean (3000) miles with an airspeed of 5000 miler per hour
The time required to cross the airplane Atlantic Ocean is (3/5) hours.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
We know, Distance = Speed×Time.
Given, Distance is 3000 miles and the speed is 5000 miles per hour.
Therefore, 3000 = 5000×t.
t = 3000/5000.
t = 3/5 hours.
Q. An airplane crosses the Atlantic Ocean (3000) miles with an airspeed of 5000 miles per hour, What is the time required to cover the distance?
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The perimeter of a rectangle is 108 cm. If the length is 30 cm, how wide is the rectangle?
A) First write an equation you can use to answer this question. Use w as your variable in the equation.
The equation is
B) Solve your equation in part [A] to find the width of the rectangle.
Answer: The rectangle is
cm wide.
Answer:
Step-by-step explanation:
A) The equation for the perimeter of a rectangle is given by 2 * (length + width), so we can write the equation for this rectangle as:
2 * (30 + w) = 108
B) To find the width of the rectangle, we can solve for w:
60 + 2w = 108
2w = 48
w = 24
So, the width of the rectangle is 24 cm.