The total amount Debra ended up paying for the equipment was $28,541.60 and the amount of interest Debra paid on the loan was $14,041.60
(a) To find the total amount Debra ended up paying for the equipment (including the down payment and monthly payments), we need to add the down payment to the total amount of the loan, and then add the total amount of the monthly payments made over the two years.
Total amount of the loan = $14,500 - $1,300 (down payment) = $13,200
Total amount paid = Down payment + Total amount of the loan + Total amount of monthly payments
Total amount paid = $1,300 + $13,200 + ($585.04 x 24) [since there are 24 monthly payments in 2 years]
Total amount paid = $1,300 + $13,200 + $14,041.60
Total amount paid = $28,541.60
Therefore, the total amount Debra ended up paying for the equipment (including the down payment and monthly payments) was $28,541.60.
(b) To find the amount of interest paid on the loan, we need to subtract the total amount borrowed from the total amount paid, and then subtract the down payment. This will give us the total amount of interest paid over the two years.
Total interest paid = Total amount paid - Total amount borrowed - Down payment
Total interest paid = $28,541.60 - $13,200 - $1,300
Total interest paid = $14,041.60
Therefore, the amount of interest Debra paid on the loan was $14,041.60.
To know more about the financial mathematics visit:
brainly.com/question/28221298
#SPJ1
Which table shows a proportional relationship between x and y?
Responses
x 1 2 3 4
y 4 10 12 16x 1 2 3 4 y 4 10 12 16 ,
x 2.5 3 5 6
y 5 6 10 15x 2.5 3 5 6 y 5 6 10 15 ,
x 7 14 28 35
y 1 2 4 5x 7 14 28 35 y 1 2 4 5 ,
x 1 3 4 7
y 2 5 8 14
(PLS HURRY I NEED TO GET THIS DONE)
(65 POINTS FOR THE RIGHT ANSWER)
The proportional relationship between x and y is shown by the table:
x 7 14 28 35
y 1 2 4 5
Explain about the proportional relationship:A connection among two factors that changes proportionally is referred to as a proportional relationship. If y=kx, where k is just the proportionality constant, can be used to represent two quantities, x and y, then they are said to be proportional.
This implies that the ratio between both always remains the same and that as x increases, y increases, and as x drops, y decreases.The proportional connection equation's graph is a line that passes directly through the origin.From the given options, consider the table:
x 7 14 28 35
y 1 2 4 5
As per proportional relationship.:
y=kx
k = y/x (must be same in all cases)
k = 1/7
k = 14/2 = 1/7
k = 4/28 = 1/7
k = 5/35 = 1/7
As all the k value for the given values of x and y are found equal.
Thus, the proportional relationship between x and y is shown by the table:
x 7 14 28 35
y 1 2 4 5
know more about the proportional relationship:
https://brainly.com/question/12242745
#SPJ1
Find a quadratic equation which has solutions x=square root of 10and x=-square root of 10. Write the quadratic form in the simplest standard form x^2+bx+c
The quadratic equation in standard form can be written as:
y = x² - 10
How to find the quadratic equation?Remember that for a quadratic equation whose solutions are x₁ and x₂, the quadratic can be written as:
y = (x - x₁)*(x - x₂)
Here the solutions are:
x = √10
x = -√10
Then we can write:
y = (x+ √10)*(x - √10)
Expanding that we will get:
y = x² + √10x - √10x + √10*-√10
y = x² - 10
That is the quadratic.
Learn more about quadratic equations at:
https://brainly.com/question/1214333
#SPJ1
The table below shows the number of deaths in the U.S. in a year due to a variety of causes. For these questions, assume these values are not changing from year to year, and that the population of the United States is 312 million people.
Cause Deaths
Passenger car occupant 13,100
Motorcycle driver 4,500
Tornado 553
Skydiving 56
a) What is the probability that an American chosen at random died as a passenger car occupant last year?
Give your answer as a fraction or decimal. If decimal, make sure your answer is accurate to at least 2 significant figures (values after leading zeros)
LicenseQuestion 1. Points possible: 2
Unlimited attempts.
The table below shows the number of deaths in the U.S. in a year due to a variety of causes. For these questions, assume these values are not changing from year to year, and that the population of the United States is 312 million people.
Cause Deaths
Passenger car occupant 13,100
Motorcycle driver 4,500
Tornado 553
Skydiving 56
b) What is the probability that you died as a passenger car occupant last year?
Make sure your answer is accurate to at least 2 significant figures (values after leading zeros)
LicenseQuestion 2. Points possible: 2
Unlimited attempts.
The table below shows the number of deaths in the U.S. in a year due to a variety of causes. For these questions, assume these values are not changing from year to year, and that the population of the United States is 312 million people.
Cause Deaths
Passenger car occupant 13,100
Motorcycle driver 4,500
Tornado 553
Skydiving 56
c) What is the probability that you will die as a passenger car occupant next year?
Make sure your answer is accurate to at least 2 significant figures (values after leading zeros)
LicenseQuestion 3. Points possible: 2
Unlimited attempts.
The table below shows the number of deaths in the U.S. in a year due to a variety of causes. For these questions, assume these values are not changing from year to year, and that the population of the United States is 312 million people.
Cause Deaths
Passenger car occupant 13,100
Motorcycle driver 4,500
Tornado 553
Skydiving 56
d) What is the probability that an American chosen at random will die as the result of a tornado next year?
Make sure your answer is accurate to at least 2 significant figures (values after leading zeros)
LicenseQuestion 4. Points possible: 2
Unlimited attempts.
The table below shows the number of deaths in the U.S. in a year due to a variety of causes. For these questions, assume these values are not changing from year to year, and that the population of the United States is 312 million people.
Cause Deaths
Passenger car occupant 13,100
Motorcycle driver 4,500
Tornado 553
Skydiving 56
e) What is the probability that you will die as the result of a tornado next year?
Make sure your answer is accurate to at least 2 significant figures (values after leading zeros)
a) The probability that an American chosen at random died as a passenger car occupant last year is 0.0042.
b) The probability that you died as a passenger car occupant last year is 0.0042
c) The probability that you will die as a passenger car occupant next year P(C) is 0.0042.
d) The probability that an American chosen at random will die as the result of a tornado next year is 0.0000018
e) The probability that you will die as the result of a tornado next year is 0.0000018
What are the probabilities?The given probabilities are determined as follows:
The probability that an American chosen at random died as a passenger car occupant last year is:
P(A) = 13,100 / 312,000,000
P(A) = 0.0042
b) The probability that you died as a passenger car occupant last year is:
P(B) = 13,100 / 312,000,000
P(B) = 0.0042
c) The probability that you will die as a passenger car occupant next year P(C) would be 0.0042 since the values do not change.
d) The probability that an American chosen at random will die as the result of a tornado next year is:
P(D) = 553 / 312,000,000
P(D) = 0.0000018
e) The probability that you will die as the result of a tornado next year, P(E) = 0.0000018
Learn more about probability at: https://brainly.com/question/24756209
#SPJ1
Zoe makes a total of $72.85 selling cookies and cupcakes at a bake sale. If she sells 17 cupckaes for $3.25 each, how many cookies does she sell at $1,60 each?
PLEASE SHOW WORK
and I have to pass it pls
Answer: 11 Cookies
Step-by-step explanation:
let C be cookies
17($3.25) + 1.60C = $72.85
$55.25 + 1.60C = $72.85
1.60C = $17.60
C=11
She sells 11 cookies
Answer:
11
Step-by-step explanation:
To be able solve, you need to do 17 x 3.25, which would give you 55.25. Then you need to subtract 72.85 by 55.25, which is 17.60. Now divide 17.60 by 1.60. This should give you 11. Therefore, she sold 11 cookies.
I AM SO SORRY IF THIS DIDN'T MAKE SENSE!
Is the following parallelogram actually a rectangle?
15 m
37 m
V 114
The given parallelogram is not a rectangle.
How to find a rectangle ?One of the tests for a rectangle is if a right angled triangle can be created by diagonally dividing the rectangle .
The test for a right - angled triangle is the Pythagorean Theorem which is :
Side ² + Side ² = Hypotenuse ²
Using, the dimensions, check to see if there is a right triangle :
7. 2 ² + 9. 1 ² = 12 ²
134. 65 ≠ 144
There is no right angled triangle so this is a parallelogram that is not a rectangle .
Find out more on rectangles at https://brainly.com/question/28497588
#SPJ1
evaluate the expression 8 - 12 - (-6)
Answer:
2
Step-by-step explanation:
A rectangular patio has a length of (1 + 2x) yards and a width of (2 - 3x) yards. Which correctly describes the area and perimeter of the patio?
Area of the patio is -6x² + x + 2 square yards and perimeter of the patio is 6 - 2x yards.
What is a yard?A yard is a unit of measurement used to measure length or distance in both the US customary system and the British imperial system. One yard is equal to 3 feet or 36 inches. In the US customary system, a yard is equal to 0.9144 meters, while in the British imperial system, it is equal to 0.9144 meters or 3 feet. Yards are commonly used for measuring larger distances, such as in construction or landscaping, as well as in some sports like American football and cricket.
The area of the rectangular patio is given by multiplying its length by its width, so the area is:
A = (1 + 2x)(2 - 3x)
Now using distributive property we get,
A = 2 - 3x + 4x - 6x²
Simplifying further, we get:
A = -6x² + x + 2
Therefore, the area of the patio is described by the quadratic equation -6x² + x + 2.
To find the perimeter of the patio, we add up the lengths of all four sides. The length and width are given as (1 + 2x) and (2 - 3x), respectively, so the perimeter is:
P = 2(1 + 2x) + 2(2 - 3x)
Simplifying this expression, we get:
P = 2 + 4x + 4 - 6x
P = 6 - 2x
Therefore, the perimeter of the patio is described by the linear equation 6 - 2x.
To know more about yard visit:
brainly.com/question/14516546
#SPJ1
you want to hire a band for a school dance. The live band charges $75 to play for three hours and each student will pay a $2.00 admission prices, p. a, how much money will you make if 100 students attend the dance
b, how much money will you make if 100 students attend the dance
c, how many students would need to attend the dance for you to “break even” after you aging the band?
Answer:
38 stduentstudents
Step-by-step explanation:
2(100)=$200, if 100 students attend.
38(2)=$76
Breaking even means getting back the same amount you spent. The exact answer would be 37.5, but you can't have half a student.
Halla el valor de (2+3) ² =
Identifica la base, el exponente y
resuelve: (-8) ² =
La siguiente fracción 3/5 expresado en porciento es:
5/a = 7/5 halla el valor de a:
El número mixto 20 0 a fracción impropia es igual a:
3
(2+3)²=25, base=2+3, exponente=2, (-8)²=64, 3/5 expressed as a percent is 60%, a=7, 20 0/3 = 60/3 = 20/1.
What is percentage?
Percentage is a way of expressing a fraction or decimal as a portion of 100. It is often used to describe proportions or rates in various fields, such as finance, economics, and statistics.
What is exponent?
An exponent is a mathematical operation that involves raising a number to a power. The exponent represents the number of times the base is multiplied by itself. For example, in 2^3, 2 is the base and 3 is the exponent, and it means 2 multiplied by itself three times, resulting in 8.
According to the given information:
(2+3)² = (5)² = 25. The base is (2+3), the exponent is 2, and the result is 25.(-8)² = 64. The base is -8, the exponent is 2, and the result is 64.To express 3/5 as a percentage, we multiply by 100: 3/5 x 100 = 60%. Therefore, 3/5 is equal to 60%.To solve 5/a = 7/5 for a, we cross-multiply to get 5 x 5 = 7a. Simplifying, we get 25 = 7a, so a = 25/7.To convert the mixed number 20 3/3 to an improper fraction, we first multiply the whole number (20) by the denominator of the fraction (3), which gives us 60. Then we add the numerator of the fraction (3) to get 63. So 20 3/3 as an improper fraction is 63/3, which simplifies to 21.To know more about percentage, exponent visit:
https://brainly.com/question/12158443
#SPJ1
Find the area of the regular polygon.
Answer:
This is a right angle
Step-by-step explanation:
There is a square inside of the triangle.
francine can type 3,420 words in 1 hour and 30 minutes at this rate how any words can she type per minute
Francine can type 38 words per minute at this rate.
To find out how many words Francine can type per minute, we need to convert the time she took to type the words into minutes. Since there are 60 minutes in 1 hour, 1 hour and 30 minutes is equivalent to 1 × 60 + 30 = 90 minutes.
Next, we can use the formula:
words per minute = total words / total minutes
where "total words" is the number of words Francine typed (3,420) and "total minutes" is the time she took in minutes (90).
Substituting these values into the formula, we get:
words per minute = 3,420 / 90 = 38
To learn more about rate here:
https://brainly.com/question/23634231
#SPJ1
Downtown Mathville is laid out as a 6 x 6 square grid of streets (see diagram below). Your apartment is located at the southwest corner of downtown Mathville (see point H). Your math classroom is located at the northwest corner of downtown Mathville (see point M). You know that it is a 12-block walk to math class and that there is no shorter path. Your curious roommate (we’ll call her Curious Georgia) asks how many different paths (of length 12 blocks – you don’t want to back track or go out of your way) could you take to get from your apartment to the math class. It should also be clear that no shorter path exists. Can you solve Curious Georgia’s math problem?
Answer: 924 paths
Step-by-step explanation:
Since there is no shorter path, we know that the path must consist of 6 blocks to the north and 6 blocks to the east. Thus, the problem is equivalent to finding the number of ways to arrange 6 N's (for north) and 6 E's (for east) in a sequence such that no two N's are adjacent and no two E's are adjacent.
Let's denote N by 1 and E by 0. Then the problem is equivalent to finding the number of 12-digit binary sequences (i.e., sequences consisting of 0's and 1's) such that there are no consecutive 1's or consecutive 0's.
We can solve this problem using dynamic programming. Let F(n,0) be the number of n-digit binary sequences that end in 0 and have no consecutive 0's, and let F(n,1) be the number of n-digit binary sequences that end in 1 and have no consecutive 1's. Then we have the following recurrence relations:
F(n,0) = F(n-1,0) + F(n-1,1)
F(n,1) = F(n-1,0)
with initial values F(1,0) = 1 and F(1,1) = 1.
Using these recurrence relations, we can compute F(6,0) and F(6,1), and the total number of valid sequences is F(6,0) + F(6,1) = 132. Therefore, there are 132 different paths of length 12 blocks from your apartment to the math class.
Given: △XYZ
and AY←→
is an auxiliary line that is parallel to XZ←→
Prove: The sum of the interior angles in △XYZ
is 180°
The answers are:
[tex]m \angle1+ m\angle2 + m\angle3=180^o[/tex] is the sum of interior angles in a triangle.
[tex]m \angle1+ m\angle5 = m\angle AYX[/tex] is Definition of parallel lines.
[tex]m \angle AYX+m\angle 4=180^o[/tex] Definition of a straight angle
[tex]m\angle5=m\angle2[/tex] is Substitution
[tex]m \angle1+ m\angle5 + m\angle4=m \angle AYX+m\angle 4[/tex] Substitution
Describe Angles?An angle in geometry is the measurement of the amount of rotation that occurs between two lines, rays, or line segments that have a shared endpoint, or vertex. Angles are expressed in terms of degrees, radians, or other angular measuring units.
A protractor, a tool with a semicircular or circular scale and degree markings, can be used to measure angles. Angles may also be labelled using symbols, such as ∠ABC or ∠PQR, in which the letter in the middle of the symbol designates the vertex of the angle.
An auxiliary line that is parallel to XZ given is the triangle formed by XYZ and AY.
[tex]m\angle 1+m\angle 2+m\angle3=180^o[/tex] Definition of the sum of interior angles in a triangle
[tex]m\angle1=m\angle AYX[/tex] Corresponding angles are congruent (alternate interior angles)
[tex]m \angle 2 = m \angle 4[/tex] Corresponding angles are congruent (alternate interior angles)
[tex]m \angle AYX + m \angle 4 = 180^o[/tex] Definition of a straight angle
[tex]m \angle 1 + m \angle 5 = m \angle AYX[/tex] Definition of parallel lines
[tex]m \angle 5 = m \angle 2[/tex] Substitution
[tex]m \angle 1 + m \angle 2 + m \angle 3 = m \angle 1 + m \angle 5 + m \angle 4[/tex] Substitution
[tex]m \angle 1 + m \angle 5 + m \angle 4 = m \angle AYX + m \angle 4[/tex] Substitution
[tex]m \angle 1 + m \angle 2 + m \angle 3 = m \angle AYX + m \angle 4[/tex] Transitive property of equality
[tex]m \angle 1 + m \angle 2 + m \angle 3 = 180^o[/tex] Substitution
To know more about congruent visit:
brainly.com/question/2493273
#SPJ1
Assume that adults have IQ scores that are normally distributed with a
mean of μ = 100 and a standard deviation o= 15. Find the probability
that a randomly selected adult has an IQ between 85 and 115.
Click to view page 1 of the table. Click to view page 2 of the table.
...
The probability that a randomly selected adult has an IQ between 85
and 115 is.
(Type an integer or decimal rounded to four decimal places as needed.)
Assume that adults have IQ scores that are normally distributed with a
mean of μ = 100 and a standard deviation o= 15. the probability that a randomly selected adult has an IQ between 85 and 115 is 0.6826.
How to find the probability?Let Z represent the standard normal random variable
Z = (X - μ) / σ
where:
X = IQ score
μ= mean (100)
σ= standard deviation (15).
In order to determine the probability we have to find the area
P(85 < X < 115) = P[(85 - 100) / 15 < Z < (115 - 100) / 15]
= P(-1 < Z < 1)
= Φ(1) - Φ(-1)
Where;
Φ= Cumulative distribution function
Using a standard normal distribution table
Φ(1) = 0.8413
Φ(-1) = 0.1587
So,
P(85 < X < 115) =0.8413 - 0.1587
= 0.6826
Therefore the probability is 0.6826.
Learn more about probability here:https://brainly.com/question/13052151
#SPJ1
Please help if your good at (FUNCTION TABLE) and (nonlinear or liner or nor or both)
Please help ASAP look at the picture !
Answer:
Linear
Step-by-step explanation:
The table represents a consistent function and is therefore linear.
The perimeter of a rectangle is 42.4 inches. The length of the rectangle is three times its
width. What is the length of the rectangle?
The length of the rectangle is 15.9 inches. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
The four fundamental operations, often known as "arithmetic operations," can be used to explain any real number. Operations like quotient, product, sum, and difference come after operations like division, multiplication, addition, and subtraction in mathematics.
We are given that the perimeter of a rectangle is 42.4 inches and the length is three times its width.
Let the width be 'x'.
So, length will be 3x.
From this, we get
⇒ Perimeter = 2 (length + width)
⇒ 42.4 = 2 (3x + x)
⇒ 42.4 = 2 (4x) (Using addition operation)
⇒ 42.4 = 8x (Using multiplication operation)
⇒ x = 5.3 (Using division operation)
So,
⇒ Length = 3 * 5.3
⇒ Length = 15.9 inches
Hence, the length of the rectangle is 15.9 inches.
Learn more about arithmetic operations from the given link
brainly.com/question/30283549
#SPJ1
Need answers ASAP!!!
Also, I will give Brainliest to whoever includes an explanation on what 9 ⁻³ means.
The given exponents 9⁻³/9¹² in the form 9ⁿ is 9⁻¹⁵ respectively.
What is Exponentiation?A number's power or exponent, in other words, tells how many times it must be multiplied by itself.
Any integer, fraction, or decimal can serve as the basis in this situation.
Additionally, the exponent might have either a positive or negative value.
Subtract the exponents to divide exponents (or powers) with the same base.
Given that division is the inverse operation of multiplication, it stands to reason that, just as exponents are added when multiplying numbers with the same base, exponents are subtracted when dividing numbers with the same base.
So, we have the exponents as;
9⁻³/9¹²
Then, solve as follows:
9⁻³/9¹²
9⁻³⁻¹²
9⁻¹⁵
Therefore, the given exponents 9⁻³/9¹² in the form 9ⁿ is 9⁻¹⁵ respectively.
Know more about Exponentiation here:
https://brainly.com/question/11975096
#SPJ1
Luka and Dana are making cookies for the Westland pantry. They only have up to 6 hours to bake! They can bake 32 chocolate chip cookies in an hour(x), and 20 snickerdoodle cookies in an hour(y). They need it make at least 150 cookies. Which inequality represents the situation?
Option 3. x+y≤6 , 32x + 20y ≥ 150. The inequality 32x + 20y ≥ 150 ensures that they bake enough cookies to meet the requirement of making at least 150 cookies.
The right disparity that addresses what is happening is:
32x + 20y ≥ 150
To see the reason why, we want to consider the quantity of treats Luka and Dana can heat in every hour and the all out number of hours they need to prepare. We should expect they have H hours to prepare, where H = 6 for this situation.
Luka and Dana can prepare 32 chocolate chip treats in 60 minutes, so they can heat a sum of 32x treats in x hours. Likewise, they can prepare a sum of 20y snickerdoodle treats in y hours. To make no less than 150 treats, they need to prepare a mix of chocolate chip and snickerdoodle treats in every hour, with the end goal that the complete number of treats they make in H hours is something like 150.
Thus, the imbalance 32x + 20y ≥ 150 guarantees that they heat an adequate number of treats to meet the necessity of making somewhere around 150 treats.
To learn more about inequality, refer:
https://brainly.com/question/21746543
#SPJ1
if a1 = 6 and an =5an-1 then find the value of a6
To find the value of a6, we need to first determine the value of a2, a3, a4, and a5 using the given recurrence relation:
a1 = 6
a2 = 5a1 = 5(6) = 30
a3 = 5a2 = 5(30) = 150
a4 = 5a3 = 5(150) = 750
a5 = 5a4 = 5(750) = 3750
Now, we can find a6 using the recurrence relation:
a6 = 5a5 = 5(3750) = 18750
Therefore, the value of a6 is 18750.
Lauren works at a reception hall and is setting tables for a retirement party. She takes a basket of 98 soup spoons, and she places 8 soup spoons on every table she sets.
Write an equation that shows how the number of soup spoons remaining, y, depends on the number of tables Lauren sets, x.
y=
The equation that shows how the number of soup spoons remaining, y, depends on the number of tables Lauren sets, x, is:
y = 98 - 8x
The initial number of soup spoons, 98, is reduced by 8 for each table Lauren sets. Therefore, the number of soup spoons remaining after x tables have been set is 98 - 8x.
F(x)=x-1/x+1 show that f(2x)=3f(x)+1/f(x)+3?
The proof that f(2x)=3f(x)+1/f(x)+3 is shown below.
Mathematical functionTo show that f(2x) = 3f(x) + 1/f(x) + 3, we substitute 2x for x in the expression for f(x):
f(x) = x - 1 / x + 1
f(2x) = 2x - 1 / 2x + 1
Next, we substitute x into the expression for f(x) and add the result to itself twice:
f(x) = x - 1 / x + 1
f(x) + f(x) + f(x) = (x - 1 / x + 1) + (x - 1 / x + 1) + (x - 1 / x + 1)
= 3x - 3 / 3x + 3
We can simplify the expression by dividing both the numerator and denominator by 3:
f(x) + f(x) + f(x) = x - 1 / x + 1
= (1/3) (3x - 3) / (1/3) (3x + 3)
= (x - 1) / (x + 1)
= f(x)
Now, we substitute f(x) and f(2x) back into the original equation:
f(2x) = 2x - 1 / 2x + 1
3f(x) + 1/f(x) + 3 = 3(x - 1 / x + 1) + 1/(x - 1 / x + 1) + 3
= (3x - 3 / x + 1) + (1 / (x - 1 / x + 1)) + 3
= (3x - 3 + (x + 1) / (x - 1)) / (x + 1)
= (2x + 2) / (x + 1)
= 2(x + 1) / (x + 1)
= 2
Thus, we have shown that f(2x) = 3f(x) + 1/f(x) + 3.
More on mathematical functions can be found here: https://brainly.com/question/30223712
#SPJ1
HELLLLLLP!!! I WILL GIVE BRAINLIEST!!!
The expression that is equivalent to 6x2y + 2xy^5 include:
2(3x²y + xy^5).
2xy(3x + y⁴)
xy(6x + 2y⁴)
What is an expression?An expression can refer to a variety of things depending on the context in which it is used.
In mathematics and computer programming, an expression typically refers to a combination of numbers, variables, operators, and/or functions that are evaluated to produce a value. For example, "2 + 3" is an expression that evaluates to "5"
Learn more about expressions on;
https://brainly.com/question/723406
#SPJ1
A person invested $840 in an account growing at a rate allowing the money to double every 10 years. How long, to the nearest tenth of a year would it take for the value of the account to reach $1,540?
It would take approximately 7.5 years (or 7 years and 6 months) for the value of the account to reach $1,540, assuming the money grows at a rate allowing it to double every 10 years.
HOW CAN WE CALCULATE THE AMOUNT?To solve this problem, we can use the formula for exponential growth:
[tex]A = P * (1 + r)^t[/tex]
where:
A = final amount (in this case, $1,540)
P = principal amount (initial investment, in this case, $840)
r = rate of growth (as a decimal, in this case, the rate at which the money doubles every 10 years, or 1/10 = 0.1)
t = time (in years, which we need to find)
Plugging in the values:
[tex]1,540 = 840 * (1 + 0.1)^t[/tex]
Dividing both sides of the equation by 840:
[tex]1.83333... = (1.1)^tTaking the natural logarithm of both sides:ln(1.83333...) = ln((1.1)^t)Using the property of logarithms that ln(a^b) = b * ln(a), we get:ln(1.83333...) = t * ln(1.1)Finally, dividing both sides by ln(1.1) to solve for t:t = ln(1.83333...) / ln(1.1)[/tex]
Using a calculator, we can find that t ≈ 7.5 (rounded to the nearest tenth of a year).
So, it would take approximately 7.5 years (or 7 years and 6 months) for the value of the account to reach $1,540, assuming the money grows at a rate allowing it to double every 10 years.
To know more about amount visit,
https://brainly.com/question/25658867
#SPJ1
A real estate company offered two plans to new employee: plan A is a salary of 2500 per month plus a 6% commission on sales. Plan B is a salary of 3000 per month plus a 4% commission on sales for what amount of monthly sales is plan A better then Plan B
In Linear equation, The of sales/month (x) has to exceed 25,000 units for Plan A to be superior to Plan B.
What is linear equation?
An algebraic equation with simply a constant and a first- order( direct) element, similar as y = mx b, where m is the pitch and b is the y- intercept, is known as a linear equation.
The below is sometimes appertained to as a" direct equation of two variables," where y and x are the variables. Equations whose variables have a power of one are called direct equations. One illustration with only one variable is where layoff b = 0, where a and b are real values and x is the variable.
Let x be # sales/month:
Plan A: $2500 + 6%•x
Plab B: $3000 + 4%•x
For Plan A to be better than Plan B: Plan A > Plan B
So inequality would be: $2500 + 6%•x > $3000 + 4%•x, then solve for x:
2%•x > $500 or x > $500/0.02
x > 25,000
Therefore, the of sales/month (x) has to exceed 25,000 units for Plan A to be superior to Plan B.
Learn more about Linear equation
brainly.com/question/11897796
#SPJ1
In Linear equation, The of sales of the month (x) has to exceed 25,000 units for Plan A to be superior to Plan B.
What is linear equation?
A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. It is an equation of the form:
y = mx + b.
To solve this system of linear equations, we can use the method of elimination or substitution.
Let x be sales of the month:
Plan A: $2500 + 6% × x
Plan B: $3000 + 4% × x
For Plan A to be better than Plan B: Plan A > Plan B
So inequality would be: $2500 + 6%×x > $3000 + 4%×x
then solve for x:
=> 2500+0.06x > 3000+0.04x
=> 0.06x-0.04x > 3000-2500
=> 0.02x > 500
=> x > 500/0.02
=> x > 25000
Therefore, the of sales of the month (x) has to exceed 25,000 units for Plan A to be superior to Plan B.
To learn more about Linear equation refer the below link
https://brainly.com/question/11897796
#SPJ1
a senior math contest began at 6:00 am on a Sunday and ended 1000 min later then did the contest get over
The senior math contest ended at 10:40 pm on Sunday
What time did the contest get overIf the senior math contest began at 6:00 am on a Sunday and ended 1000 minutes later, we can add 1000 minutes to the starting time to find the ending time.
To do this, we can first convert the starting time of 6:00 am into minutes. There are 60 minutes in one hour, so 6:00 am is equivalent to:
6 hours × 60 minutes/hour = 360 minutes
Now, we can add 1000 minutes to this starting time:
360 minutes + 1000 minutes = 1360 minutes
Finally, we can convert this total number of minutes back into hours and minutes.
Since there are 60 minutes in one hour, we can divide 1360 minutes by 60 to get:
1360 minutes ÷ 60 = 22 hours and 40 minutes
Therefore, the senior math contest ended at 10:40 pm on the day (Sunday).
Read more about expression at
https://brainly.com/question/15775046
#SPJ1
A cube is shown. Describe the shape resulting from a horizontal cross section, a vertical cross section, and an angled cross section.
horizontal cross section: _____
vertical cross section: _____
angled cross section: _____
The shape resulting from a horizontal cross section, a vertical cross section, and an angled cross section of the cube are:
horizontal cross section: square.
vertical cross section: square.
angled cross section: rectangle.
How to determine the cross section?In this exercise, you are required to use a graphing tool to investigate and determine the cross-sections of the given three-dimensional geometric object (cube), by passing different planes through them.
By critically observing the cross-sections of the three-dimensional geometric object (cube) I used, we can reasonably infer and logically deduce the following types of quadrilateral based on the cross-sections;
A horizontal cross section would produce a square.
A vertical cross section would produce a square.
An angled cross section would produce a rectangle.
Read more on cross-sections here: https://brainly.com/question/1924342
#SPJ1
PLEASE HELP
(a) How many total trees are included in the histogram?
(b) What is the least common height range of the trees?
Answer:
a. 31 total trees
b. Least common range is 85-90
Step-by-step explanation:
A. On the side of the chart it is labeled frequency. That is where you will find the number of tree per height range. The tops of the bars indicate the number is directly across.
B. Looking at the lowest bar or the smallest amount of trees indicate the lowest range or the least common range.
[tex]\left\{\frac{1}{2^n}\:+\:\frac{\left(-1\right)^n}{n+1}\::\:n\:\:N\right\}[/tex]
Find max, min, sup and inf
The maximum value of the sequence is [tex]1/6[/tex], the minimum value is 0, the supremum is [tex]1/2[/tex], and the infimum is 1/6.
The given sequence is: [tex]{1/(2 ^ n) + ((- 1) ^ n)/(n + 1) / n * N}[/tex]
To find the maximum and minimum values of the sequence, we can start by taking the first few terms and looking for patterns:When [tex]n = 1,[/tex] the sequence evaluates to: [tex]1/2 + (-1)^1 / 2 * 2 = 0[/tex]
When [tex]n = 2,[/tex] the sequence evaluates to: [tex]1/4 + (-1)^2 / 3 * 2 = 1/6[/tex]
When [tex]n = 3,[/tex] the sequence evaluates to: [tex]1/8 + (-1)^3 / 4 * 2 = 7/96[/tex]
When [tex]n = 4,[/tex] the sequence evaluates to: [tex]1/16 + (-1)^4 / 5 * 2 = 17/240[/tex]
It appears that the sequence oscillates between positive and negative values, with the negative values getting smaller as n increases.
Therefore, the minimum value of the sequence is at n = 1, where it evaluates to 0.
The maximum value occurs at n = 2, where it evaluates to 1/6.
To find the supremum and infimum of the sequence, we can start by considering the upper and lower bounds of each term separately.The term [tex]1/(2 ^ n)[/tex] has a lower bound of 0 and an upper bound of 1.
The term [tex]((- 1) ^ n)/(n + 1) / n * N[/tex] has a lower bound of [tex]-1/4[/tex] and an upper bound of [tex]1/4[/tex].
Therefore, the supremum of the sequence occurs when [tex]n = 1[/tex], where the sequence evaluates to [tex]1/2[/tex].
The infimum of the sequence occurs when [tex]n = 2[/tex], where the sequence evaluates to [tex]1/6.[/tex]
In summary, the maximum value of the sequence is [tex]1/6[/tex], the minimum value is 0, the supremum is [tex]1/2[/tex], and the infimum is [tex]1/6.[/tex]
Learn more about maximum and minimum values here:
https://brainly.com/question/14316282
#SPJ1
According to a study done by De Anza students, the height for Asian adult males is normally distributed with an average
of 66 inches and a standard deviation of 2.5 inches. Suppose one Asian adult male is randomly chosen. Let X = height of
the individual
The middle 40% of heights fall between what two values? Sketch the graph, and write the probability statement
The probability statement is written below:
P(62.8 ≤ X ≤ 69.2) = 0.4What is the probability statement?The middle 40% of heights fall between the 10th and 90th percentiles of the standard normal distribution.
The z-scores of the 10th and 90th percentiles are -1.28 and 1.28 respectively.
The heights in the given normal distribution are found using the formula:
X = μ + zσwhere
X is the height,μ is the mean height = 66 inchesσ is the standard deviation = 2.5 inchesz is the z-score.The height of the 10th percentile is:
X = 66 + (-1.28)(2.5)
X = 62.8 inches
The height of the 90th percentile is:
X = 66 + (1.28)(2.5)
X = 69.2 inches
Therefore, the middle 40% of heights fall between 62.8 inches and 69.2 inches and the probability statement will be P(62.8 ≤ X ≤ 69.2) = 0.4
Learn more about normal distribution at: https://brainly.com/question/4079902
#SPJ1
Finding the Mean and Median 42,5,25,2,35
The mean of the given set of numbers is 21.8. and median is 25.
Define meanIn mathematics and statistics, the mean is a measure of central tendency that represents the average value of a set of numbers. It is calculated by adding up all the numbers in the set and then dividing by the total number of values. The mean is also known as the arithmetic mean or average.
To find the mean and median of the given set of numbers, we can follow these steps:
Arrange the numbers in order from smallest to largest: 2, 5, 25, 35, 42.
To find the mean, add up all the numbers and divide by the total number of numbers:
Mean = (2 + 5 + 25 + 35 + 42) / 5
= 109 / 5
= 21.8
Therefore, the mean of the given set of numbers is 21.8.
To find the median, we need to find the middle number in the ordered list. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.
In this case, there are 5 numbers, so the median is the middle number, which is 25.
Therefore, the median of the given set of numbers is 25.
To know more about average, visit:
https://brainly.com/question/27193544
#SPJ1