The $7,834.54 borrowed at 18.6% annual interest rate with the landscape architect's monthly payment of $500, gives the number of months it will take to repay the debt as approximately 19 months
What is a monthly payment?Monthly payment on a loan, is the amount the person who takes the loan, pays each month in order to settle the loan in a given time period.
The monthly payment formula is presented as follows;
[tex] \displaystyle{M = \frac{P \cdot \left( \frac{r}{12} \right) \cdot \left( 1 + \frac{r}{12} \right)^{n} }{\left( 1 + \frac{r}{12} \right)^{n} - 1} }[/tex]
Where;
M = The amount the landscape architect paid monthly = $500
P = The amount loaned or borrowed = $7,834.54
r = The interest per annum = 18.6%
n = The number of monthly payment made
Therefore;
[tex] \displaystyle{500 = \frac{7834.54 \cdot \left( \frac{0.186}{12} \right) \cdot \left( 1 + \frac{0.186}{12} \right)^{n} }{\left( 1 + \frac{0.186}{12} \right)^{n} - 1} }[/tex]
Evaluating the above equation gives;
[tex] \displaystyle{500 = \frac{121.43537.1 \cdot 1.0155^{n} }{1.0155^{n} - 1} }[/tex]
[tex] \displaystyle{500 \times (1.0155^{n} - 1) = 121.43537.1 \cdot 1.0155^{n} }[/tex]
[tex] \displaystyle{500 \times 1.0155^{n} - 121.43537.1 \cdot 1.0155^{n} ) = 500 }[/tex]
Which by taking natural logarithms of both sides gives;
n•ln(1.0155) = ln(1.32077843609)
n = ln(1.32077843609) ÷ ln(1.0155) ≈ 18.09
Rounding up to the nearest month gives;
The number of months it will take the architect to pay the debt is approximately 19 months
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find the measure of angle 1 and angle 2
Answer:
Angle 1 is 132 and angle 2 is 48
Step-by-step explanation:
Since 132 plus 18 make the 180 line.
determine whether or not the given procedure results in a binomial distribution. if not, identify which condition is not met. surveying 35 people to determine if a particular brand of candy bar is their favorite.
No, the given procedure doesn't result in a binomial distribution.
We can identify if a given procedure results in binomial distribution by observing whether these four conditions are met or not.
1: Each observation should be independent, it must not depend on the result of previous observation.
2: The probability of success should stay same from trial to trial.
3: n is fixed (the number of observations)
4: There are only two outcomes success or failure.
Surveying 2828 people to determine which statistics courses they have taken.
3 is satisfied since n is fixed
1 is satisfied since each observation is independent
4 is not satisfied since there can be more than 2 answers from the people (statistics courses can be many).
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Find the distance between each pair of points
Answer: 14: [tex]\sqrt{5}[/tex]
16:[tex]\sqrt{26}[/tex]
Step-by-step explanation:
Points for 14: (2,0) and (0,-1)
-1 - 0 = -1
0 - 2 = -2
Use the equation of a triangle [tex]c^{2} =a^{2} +b^{2}[/tex]
[tex]\sqrt{-1^{2} +-2^{2} } =\sqrt{5}[/tex]
Points for 16: (2,2) and (-3,3)
I need help! for Finding the distance between points G and W. please!!!
Hello!
To find the distance:
⇒ we must simply minus the coordinate of W from the coordinate of G
[tex]G - W=\dfrac{-1}{3} -(-1\dfrac{2}{3} )=-\dfrac{1}{3} +\dfrac{5}{3} =\dfrac{4}{3}[/tex]
Thus the distance between W and G is 4/3
Hope that helps!
Elwyn is packing food for a family picnic.He has prepared 15 sandwiches and 30 corn dogs.He wants everyone to have an identical number of sandwiches and corn dogs and with nothing leftover.How many members at the maximum can be served
In order for everyone to have an identical number of sandwiches and corn dogs, with nothing left over, a maximum of 15 people, each person gets 2 corn dogs and 1 sandwich. Note that this is an HCF problem.
What is the calculation justifying the above?The HCF (Highest Common Factor) of two numbers is the highest number among all of the provided numbers' common factors. The HCF of 10 and 30, for example, is 10 since 10 is the highest common factor of 10 and 30.
In this case, the HCF is 15.
Proof:
We can divide 30/15 and still get an integer
= 2
hence we can distribute the sandwiches in 15 ways making 15 people. Hence, each person will get 2 Corn Dogs leaving no remainder.
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Determine los ángulos de un triángulo con lados de longitud 7,6 & 9 pies respectivamente y encuentre su área.
Por la ley de coseno se encuentra que las medidas de los ángulos internos del triángulo son aproximadamente 50.977°, 41.752° y 87.271°, respectivamente. El área del triángulo según la fórmula de Herón es aproximadamente 20.976 pies cuadrados.
¿Cómo determinar los ángulos y el área del triángulo?
En esta pregunta tenemos conocimiento de las medidas de los tres lados del triángulo, a partir de los cuales debemos hallar las medidas de sus ángulos internos y el área de la figura geométrica. Primero, se determina la medida de los ángulos mediante la ley del coseno:
cos α = (7² - 6² - 9²) / (- 2 · 6 · 9)
α ≈ 50.977°
cos β = (6² - 7² - 9²) / (- 2 · 7 · 9)
β ≈ 41.752°
cos γ = (9² - 7² - 6²) / (- 2 · 7 · 6)
γ ≈ 87.271°
Finalmente, se determina el área mediante la fórmula de Herón:
Semiperímetro
s = 0.5 · (7 + 6 + 9)
s = 11
Fórmula de Herón
A = √[11 · (11 - 7) · (11 - 6) · (11 - 9)]
A ≈ 20.976
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What is the slope that passes through 1,7 and 9,5
Answer:
-1/4 is the slope.
Step-by-step explanation:
To find the slope of the given points, we can use the formula:
y2-y1/x2-x1
So, in this case, subtract 5 and 7, and subtract 9 and 1.
5-7=-2
9-1=8
-2/8
Now, simplify.
-1/4 is the slope.
Help please need urgent help
In the picture we can see there is a line with an intersection line.
∠3=(13x+7)° and ∠6 =(9x+59)°. The angles ∠5=4°, Option A is correct.
Given that,
In the picture we can see there is a line with an intersection line.
A transversal is a line that creates angles when it crosses two parallel lines (or lines on a plane) at various points.
∠3 =(13x+7)° and
∠6 =(9x+59)°
In the parallel lines alternatives angles are always equal.
So,
∠3=∠6
13x+7=9x+59
13x-9x=59-7
4x=52
x=52/4
x=13
Now,
∠3 =(13x+7)°=(13×13+7)°=(169+7)°=176°
∠6 =(9x+59)°=(9×13+59)°=(117+59)°=176°
Now,
From the supplementary angles.
∠5+∠6=180°
∠5=180°-∠6
∠5=180°-176°
∠5=4°
Therefore, We got the angles ∠5=4°, Option A is correct.
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How do you find the Least Common Multiple (LCM) of a number?
Answer:
by dividing with a small number like 2
Step-by-step explanation:
the LCM of 4 is4
Need this done asap need to be turned in the next 20min please help
A polynomial function of degree zero or one that contains a straight line as its graph exists directed to as a linear function in calculus and related fields then the function exists described as: y = 9000 + 1500 h.
What is meant by linear function?The terms "linear function" in mathematics apply to two different but related ideas: A polynomial function of degree zero or one that contains a straight line as its graph exists directed to as a linear function in calculus and related fields.
The given parameters exists:
Initial = 9000
Rate = 1500
The function exists estimated as: y = Initial + Rate × h
Where h represents the number of hours.
Let the equation be y = Initial + Rate × h
Substituting the values in the above equation, we get
y = 9000 + 1500 × h
y = 9000 + 1500 h
Therefore, the function is represented as: y = 9000 + 1500 h
The complete question is:
A 21,000-gallon swimming pool contains 9000 gallons of water when a hose is placed in the pool and begins adding water at a rate of 1500 gallons per hour. Use the Segment tool to plot a graph representing the volume of water in the pool over time from when the hose is placed in the pool until the pool is full.
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Pregunta, si hay 3% de probabilidades de encontrara algo especial en una caja cuantas cajas debería abrir para encontrarlo?
The number of boxes that should be opened to find it is 98 boxes.
What is probability?Probability simply means the likelihood of the occurence of an event.
When there is a 3 percent chance or finding something special in a box,the number of boxes that will be opened will be illustrated thus:
Let the number of boxes be 100.
Therefore, the number of boxes will be:
= Total boxes - Percentage given
= 100 - 3
= 97
In this case, the 98th box will give the person the chance of getting it.
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Are the following Exponential?
1) y = x^2
2) y = 2^
3) f(x) = 10 • (1/4)x
4) f(x) = 3(x)^3
5) f(t) = -2 • (0.25)^t
6) y = 0.5(5)^x
Answer-up=898-8-79
Step-by-step explanation:
two boats leave an island at the same time. boat a travels due north for 21 miles and boat b travels due west for 18 miles. what is the compass bearing of boat a from boat b? what is the relative bearing of boat b from boat a
Boat B's relative bearing to Boat A is 27.65
Relative bearing: What is it?The angle between the travel direction and another direction is known as the relative bearing. From the current direction, this angle is measured in a clockwise motion. As an illustration, a ship is now moving at a bearing of 050°. From the ship's present direction, a relative bearing of 010° is calculated. Bearings can be used to show both the direction and the angle of a certain location. In math, bearings are three-digit angles measured clockwise from a protractor's zero-degree point. On your GCSE math test, the north direction (or starting point) is typically given in the question text.
Given the data, we can infer that
According to the Pythagoras Theorem,
In a right triangle,
c²=a²+b²
where
c is the hypotenuse
a and b are the legs
In this problem
Let
c ----> the distance between the boats
a -----> the horizontal distance between the boats
b -----> the vertical distance between the boats
substitute the values,
c²=21²+18²
c=√(21²+18²)
c=27.65
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Find the X and Y values.
The answer should be written as a coordinate point (x,y)
(reward 50 points)
Answer:
The solution is (10, 11)
Step-by-step explanation:
We have the following equations to work with
[tex]\dfrac{1}{2}x + 6 = 2x + 31\\2.5x + 6 = 31\\[/tex]
Subtract 6 from both sides
[tex]\\\\\Rightarrow 2.5x = 31 - 6 = 25[/tex]
Divide by [tex]2.5x[/tex] on both sides:
[tex]\Rightarrow x = \dfrac{25}{2.5} = 10[/tex]
Substitute for x in the first equation
[tex]y = \dfrac{1}{2}x + 6\\\\\rightarrow y= \dfrac{1}{2}\times 10 + 6\\\\\rightarrow y=5 + 6 = 11\\\\[/tex]
So the So the solution is
about 9% of the population has a particular genetic mutation. 800 people are randomly selected. find the mean for the number of people with the genetic mutation in such groups of 800.
Using the binomial distribution, it is found that the mean for the number of people with the genetic mutation in such groups of 800 is of 72
What is the binomial probability distribution?
It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
E(X) = np
In this problem, we have that:
About 9% of the population has a particular genetic mutation, hence p = 0.09
800 people are randomly selected, hence n = 800.
Then, the mean is given by:
E(X) = np = 800 x 0.09= 72
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solve the following system of equations algebraically
x+y-z=6
2x-3y+2z=-19
-x+4y-x=17
Answer: {x,y,z}={-11/14,27/7,-41/14}
Step-by-step explanation:
System of Linear Equations entered :
[1] x+y-z=6
[2] 2x-3y+2z=-19
[3] -x+4y-x=17
Equations Simplified or Rearranged :
[1] x + y - z = 6
[2] 2x - 3y + 2z = -19
[3] -2x + 4y = 17
Solve by Substitution :
// Solve equation [1] for the variable y
[1] y = -x + z + 6
// Plug this in for variable y in equation [2]
[2] 2x - 3•(-x +z +6) + 2z = -19
[2] 5x - z = -1
// Plug this in for variable y in equation [3]
[3] -2x + 4•(-x +? +6) = 17
[3] -6x = -7
// Solve equation [2] for the variable z
[2] z = 5x + 1
// Plug this in for variable z in equation [3]
[3] -6x = -7
[3] 14x = -11
// Solve equation [3] for the variable x
[3] 14x = - 11
[3] x = - 11/14
// By now we know this much :
x = -11/14
y = -x+z+6
z = 5x+1
// Use the x value to solve for z
z = 5(-11/14)+1 = -41/14
// Use the x and z values to solve for y
y = -(-11/14)+(-41/14)+6 = 27/7
Solution :
{x,y,z} = {-11/14,27/7,-41/14}
What is the slope of this graph? Responses −4 negative 4 −14 negative 1 fourth 4 4 14 1 fourth Number graph ranging from negative 10 to 10 on both the x and y axis. A line passes through the point begin ordered pair 1 comma negative 2 end ordered pair and the point begin ordered pair 0 comma 2 end ordered pair
The slope of the graph that passes through points (1, -2) and (0, 2) is: -4.
How to Find the Slope of a Graph?Using two points on a given graph, (x1, y1) and (x2, y2), the slope (m) of the graph can be calculated by plugging the coordinates of the two points into the slope formula:
Slope (m) = change in y/change in x = (y2 - y1)/(x2 - x1).
Given two points on a line as shown in the graph attached below, (1, -2) and (0, 2), the slope of the graph is calculated as:
Let,
(1, -2) = (x1, y1)
(0, 2) = (x2, y2)
Plug in the values:
Slope of the graph (m) = (2 - (-2))/(0 - 1)
Slope of the graph (m) = (2 + 2)/(0 - 1)
Slope of the graph (m) = 4/-1
Slope of the graph (m) = -4.
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Answer:
the other guy is right I got 100% on my quiz
Step-by-step explanation:
A group of friends wants to go to the amusement park. They have no more than $325 to spend on parking and admission. Parking is $16.50, and tickets cost $38.50 per person, including tax. What is the maximum number of people who can go to the amusement park?
Maximum 8 people can go to the amusement park.
What is arithmetic?Mathematical arithmetic is the study of the properties of the standard operations on numbers, such as addition, subtraction, multiplication, division, exponentiation, and root extraction. One of the branches of mathematics,
1, deals with the application of addition, subtraction, multiplication, and division to nonnegative real numbers, occasionally incorporating transfinite cardinals.
Given Data
$325 to spend on parking and admission. Parking is $16.50, and tickets cost $38.50 per person, including tax.
Parking = $16.50
Total money = $325
Money left after spending money on parking:
$325 - $16.50
$308.5
Now, dividing money left by fees of admission;
Cost of ticket = $38.5
Money left = $308.5
Number of people who can go inside=
= [tex]\frac{308.5}{38.5}[/tex]
= 8.01
Maximum 8 people can go to the amusement park.
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Let point P be the weighted average of points A(7,3) and B(-3,-10), where point A weights three times as much as point B. What are the coordinates of point P?
A (-2,-27/4)
B (2,-7/2)
C (9/2, -1/4)
D (6,-1/3)
According to the question,
If B weighs x, then A would be 3x. So, P would be 2x, i.e., P divides A & B in 1:3 internally.
Coordinates of A (7, 3)
Coordinates of B (-3, -10)
Let coordinates of P be (x, y)
P(x) = 7 × (1) + (-3 × 3) / 3+1 = -2/4 = -2
P(y) = (3 × 1) + (-10 × 3) / 3+1 = -27/4
P(x, y) = (-2, -27/4)
Therefore, the correct answer is option A.
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How do I do this
It's due tomorrow
Slopes are mentioned below.
Define slope.Slope, usually referred to as rise over run, is the "steepness" of the line. By dividing the difference in y values between two points by the difference in x values, we may determine slope. A line's slope often indicates the steepness and direction of the line. By calculating the difference between the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.
Given Data
Formula
y = mx +c
1) y = [tex]\frac{-3}{2}[/tex]x -1
Slope = [tex]\frac{-3}{2}[/tex]
2) y = [tex]\frac{7}{4}[/tex]x - 4
Slope = [tex]\frac{7}{4}[/tex]
3) -x - 2
Slope = -1
4) 4x - 5
Slope = 4
5) y = 5x + 1
Slope = 5
6) y = [tex]\frac{3}{4}[/tex]x - 1
Slope = [tex]\frac{3}{4}[/tex]
7) y = [tex]\frac{-1}{5}[/tex]x +2
Slope = [tex]\frac{-1}{5}[/tex]
8) y = -4x -5
Slope = -4
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I need help on this question
To find the scale factor we just need to divide the final measurement by the initial measurement, then we have:
[tex]\begin{gathered} k=\frac{1120}{28} \\ k=40 \end{gathered}[/tex]Therefore, the scale factor is 40
i don’t know how to solve this problem
Answer:
x = 5, y = 25
Step-by-step explanation:
I use the substitution method to solve. (I hope I got the equations correct)
6x + y = 55 ---1
10x + 3y = 125 ---2
From 1: y = 55 - 6x ---3
Substitute 3 into 2:
10x + 3(55 - 6x) = 125
10x + 165 - 18x = 125
- 8x = - 40
x = 5
Substitute x into 3
y = 55 - 6(5) = 25
Heatheris participating in arace that is broken up into 1/5 mile sections. each section has to be run by a different person and each team member can only run once ifthe race is s5 1/5 miles long, how many please will heather need on her team?
Based on the distance of the race and the length of the sections, the number of people that Heather will need to be on her team are 26 people
How to find the number of people needed?The entire race has a length of 5 1/5 miles and this length will be divided into sections that are 1/5 miles long.
Only one member of the team can run in each of these sections so enough people are needed on Heather's team to run the 1/5 mile sections.
The number of people to be in a team can be found by the formula:
= Length of race / Length of sections
= 5 1/5 miles / (1/5)
= 26/5 ÷ 1/5
= 26/5 x 5/1
= 26 people
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HELP ASAP PLEASE I'LL GIVE BRANLIEST
Answer:
B
Step-by-step explanation:
reduction is [tex]\frac{4}{5}[/tex] per plant , that is
[tex]\frac{4}{5}[/tex] × $6 = 0.8 × $6 = $4.80 per plant
total cost = 5 × $4.80 = $24.00
I dont understand the steps to getting to the answer.
Answer:
(a) Fermat's little theorem states that for any prime p , we have
a^p-1 = 1 (mod p).
for any integer ,a. Then
999999 = 1000000 - 1 = 10^6 - 1 = 1 - 1 = 0 (mod 7)
so 7 does indeed divide 999,999.
(b) Generalizing, we have
10^12n - 1 = 999...999 (12n nines) = (10^n)^12 - 1 = 0 (mod 13)
for positive integer, n. Now, since 1 = 1001 - 1000 and -1 = (mod 1001) , it follows that 10^3 is its own inverse modulo 1001, i.e.
10^3 x = 1 (mod 1001) -----> x = 10^3
This means
10^12n = (10^3 x 10^3)^2n = 1^2n = 1 (mod 1001) ----> 10^12n - 1 = 0 (mod 1001)
Construct a polynomial function with the following properties: fifth degree, 3 is a zero of multiplicity 4,-4 is the only other zero, leading coefficient is 3.
The required polynomial function is y=3(x+3)⁴(x-4 ) for the conditions as mentioned fifth degree, 3 is a zero of multiplicity 4,-4 is the only other zero, leading coefficient is 3.
What is Polynomial function?In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only involves non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.
What is multiplicity?The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.
Here the given conditions are:
Fifth degree, 3 is a zero of multiplicity 4,-4 is the only other zero, leading coefficient is 3.
Let y be the f(x) and x be the variable.
Now, x+3 is the first term and x-4 be the second term with their multiplicity 4 and 1.
y=3(x+3)⁴(x-4)
For the above-mentioned fifth-degree conditions, the necessary polynomial function is y=3(x+3)⁴(x-4); 3 is a zero of multiplicity 4,-4 is the only other zero, leading coefficient is 3.
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Carson works in a department store selling clothing. He makes a guaranteed salary of $450 per week, but is paid a commision on top of his base salary equal to 15% of his total sales for the week. How much would Carson make in a week in which he made $1575 in sales? How much would Carson make in a week if he made x dollars in sales?
The amount of money that Carson make in a week in which he made $1575 in sales is $686.25.
How to calculate the amount?From the information, Carson makes a guaranteed salary of $450 per week, but is paid a commision on top of his base salary equal to 15% of his total sales for the week.
Therefore, the amount that he will be paid when he sees $1575 will be:
Base salary + Commission
= $450 + (15% × $1575)
= $450 + $236.25
= $686.25
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PLEASE SOLVE ASAP!!!!
Answer:
(0, 6)
(-1 , 5)
Step-by-step explanation:
What is the value of y
The answer is 7^6. But just put a 6 in the box.
The reason is because 7 x 7 x 7 x 7 x 7 x 7 = 117,649.
Also, 7^6 is equivalent to 117,649.
So, the answer is 7^6 or just 6.
Mark me Brainliest. :)
HELP THIS IS TIME Multiply.
(-2/3)(5/4)
Enter your answer as a fraction, in simplest form, in the box.
Answer:
-5/6 Is the correct answer.,
Answer:
-5/6.
Step-by-step explanation:
-2/3 * 5/4
= (-2*5/(3*4)
= -10/12
= -5/6.