To calculate how long it would take to pay off a $1000 balance with an interest rate of 14% APR when making minimum payments of $20 each month, we need to consider the monthly interest and the decreasing balance.
First, let's calculate the monthly interest. The annual interest rate is 14%, so the monthly interest rate would be 14% divided by 12 months, which is approximately 1.167%.
Now, let's determine how much of the minimum payment goes towards interest each month. The remaining amount after deducting the interest is used to decrease the balance.
In the first month, the interest on the $1000 balance would be 1.167% of $1000, which is approximately $11.67. So, after making a $20 minimum payment, $11.67 is subtracted from the balance, resulting in a new balance of $988.33.
In the subsequent months, the same process is repeated. The interest is calculated based on the new balance, and the minimum payment is made. This continues until the balance reaches zero.
Given the small minimum payment of $20 and the interest accumulating on the balance, it would take significantly longer than 3 months, 1 year, or 3 years to pay off the $1000 balance. Therefore, the correct option is 6 years.
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After x hours of rainfall today, Yvette recorded the amount of rain in inches, y, in a rain gauge. The table shows the
linear relationship for the recorded rainfall.
Rain Gauge
Time, x (hours)
3 4 5
Amount of Rain in Gauge, y (inches) 3.75 4.5 5.25
How many inches of rain was in the gauge before the rain began today, and what was the rate at which the rain fell
in inches per hour?
A. There was 0 inches in the rain gauge before the rain began, and the rain fell at a rate of 1.25 inches per hour.
B. There was 2.5 inches in the rain gauge before the rain began, and the rain fell at a rate of 1.25 inches per hour.
C. There was 3 inches in the rain gauge before the rain began, and the rain fell at a rate of 0.75 inch per hour.
D. There was 1.5 inches in the rain gauge before the rain began, and the rain fell at a rate of 0.75 inch per hour.
The correct option is D, There was 1.5 inches in the rain gauge before the rain began, and the rain fell at a rate of 0.75 inch per hour.
How to write the linear equation?A general linear equation is written as:
y = ax + b
Where a is the slope and b is the y-intercept.
If a line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
We can use the first two points:
a = (4.5 - 3.75)/(4 - 3)
a = 0.75
Then we can write:
y = 0.75x + b
replacing the values of the first point we will get:
3.75 = 0.75*3 + b
3.75 - 0.75*3 = b = 1.5
Then the rate is 0.75 and the initial amount is 1.5
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Please if you know the answer tell me it and the steps also thank you.
Step-by-step explanation: Well to begin, you take 15$ and multiply it by 4, since he wants to buy 4 of those tickets, which is 60$. Then, take the 10$ and multiply it by 2 since he wants 2 of those tickets, which is 20$, you then apply 10% to 60 and 20 by taking 10 percent of 60, then adding it to 60 once have that, which is 66, you take the 3% and find 3% of 66, then add the answer of that to 66, which is 67.98$, you then do the same thing to the 20$.
Sorry if this didnt help, im sure it didnt because im a very bad explainer, but i tried..
This is a extra credit, I NEED HELPP, it needed by tomorrow
I HAVE TO FIND < JKL
By using the property of incenter, measures of the sides and the angles will be,
JK = 21.2 units
KL = 26.63 units
JL = 28.33 units
m ∠K = 36°
Since, By the property of incenter,
PM = PN = PO = 7 units
∠MJP = ∠OJP = 32°
∠NLP = ∠OLP = 22°
By the triangle sum theorem,
m∠JKL + m∠KLJ + m∠LJK = 180°
2(m∠NKP) + 2(m∠NLP) + 2(m∠MJP) = 180°
2(m∠NKP) + 2(22°) + 2(32°) = 180°
2(m∠NKP) = 180° - 108°
m∠NKP = 36°
From ΔJMP,
tan(32°) = MP / MJ
tan(32°) = 7/MJ
MJ = 11.20
From ΔPOL,
tan(22°) = OP / OL
tan(22°) = 7/OL
OL = 17.33
From ΔKNP,
tan(36°) = NP / KN
tan(36°) = 7 / KN
KN = 9.63
Therefore, We get;
JK = JM + MK = 21.2 units
KL = LN + KN = 26.63 units
JL = JO + OL = 28.33 units
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Mandy sells computers for a company called computer world. she earns 5% commission on her sales. Her commission last month was $700. What was Mandys total sales fot that month.
Answer: Mandy sold 14,000$ in total sales
Step-by-step explanation: Divide the 5% and the 700, to get a total of 140, then multiply by 100. Hope this helps!
An elevator and a worker both lifted a 100 kg object from floor 1 to floor 4 (10 m). If the elevator reached floor 4 before the worker, which of the following statements is true?
a.The elevator and the worker both did the same amount of work, but the elevator provided more power
b. the elevator and the worker both did the same amount of work, but the worker provided more power
c .The elevator did more work and provided more power than the worker
d. The worker did more work and provided more power than the elevator
The elevator and the worker both did the same amount of work, but the elevator provided more power. a.
The object is lifted to the same height the elevator and the worker both did the same amount of work against gravity is given by the formula W = mgh
m is the mass of the object, g is the acceleration due to gravity, and h is the height lifted.
The work done by both the elevator and the worker is W = (100 kg) x (9.8 m/s²) x (10 m)
= 9800 J.
Power is defined as the rate at which work is done, given by the formula P = W/t
t is the time taken to do the work.
Since the elevator reached floor 4 before the worker took less time for the elevator to do the work.
The elevator provided more power than the worker.
The formula states that when an object is raised to a specific height using a lift and a worker they both exerted an equal amount of effort against gravity.
W = mgh where m is the object's mass, g is its gravitational acceleration, and h is the height raised.
The lift's and the worker's combined work is given by W = (100 kg) x (9.8 m/s²) x (10 m)
= 9800 J.
According to the formula P = W/t power is the pace at which work is completed t is the amount of time required to complete the task.
Since the lift arrived at level 4 prior to the worker the lift's work was completed more quickly.
The lift was more powerful than the employee.
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Which expression is equivalent to
Help ‼️‼️‼️
The equivalent expression to 2/3 - 1/4x + 1/2x - 1/6 is given as follows:
1/2 + 1/4x.
What are like terms?Like terms are terms that share these two features:
Same letters. (algebraic variables).Same exponents.If two terms are like terms, then they can be either added or subtracted, that is, we can use them to simplify an expression.
The expression for this problem is defined as follows:
2/3 - 1/4x + 1/2x - 1/6.
The like terms are simplified as follows:
2/3 - 1/6 = 4/6 - 1/6 = 3/6 = 1/2.-1/4x + 1/2x = -1/4x + 2/4x = x/4.Hence the simplified expression is given as follows:
1/2 + 1/4x.
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What is the volume of the pyramid?
Answer: 11100 m
Step-by-step explanation: I'm Walter H. White
please help it's easy
The order of the steps which can be used to determine an unknown value using proportion method is as follows:
Option B ---> D---> E---> A----> C.
What is a ratio?A ratio can be defined as the expression that compares the quantity of a value that can be found in another value.
The correct step that can be used to find the a missing value when proportion method is used is as follows;
Step 1: Identify the two quantities being compared
Step 2: Write the ratio for the two known quantities
Step 3: Write a ratio that has the unknown and the know quantity.
Step 4: Equate the two ratios
Step 5: Cross multiply and solve for the unknown quantity. Describe the solution.
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Solve for X
15 + x = y
What's the coefficients and degree of each term?
7x^2 - 8x^4 + 6x^3 - 1 - x
First term:
degree = ______ coefficient = _______
Second term:
degree = ______ coefficient = _______
Third term:
degree = ______ coefficient = _______
Fourth term:
degree = ______ coefficient = _______
Fifth term:
degree = _______ coefficient = ______
What's the leading coefficient, degree of the leading term, and degree of the polynomial?
Thanks!
The coefficients and degree of each term are:
First term: degree = 2, coefficient = 7The coefficients and degree of each termSecond term:
degree = 4, coefficient = -8
Third term:
degree = 3, coefficient = 6
Fourth term:
degree = 0, coefficient = -1 (constant term)
Fifth term:
degree = 1, coefficient = -1
To find the leading coefficient, degree of the leading term, and degree of the polynomial, we need to identify the term with the highest degree:
The leading term has the highest degree: -8x^4
Leading coefficient = -8
Degree of the leading term = 4
Degree of the polynomial = 4
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HELPP PLEASEE!
A) Step 3
B) Step 2
C) No flaws
D) Step 1
The step with the proof that has a flaw is Step 2, AB ≅ BC, Symmetric Property.
How to prove flaw?Step 2 is the flaw in the proof. The symmetric property states that if AB = BC, then BC = AB. It does not justify that AB = BC in the first place.
Therefore, the proof needs additional steps to justify that AB and BC are congruent. One possible way to do this is to use the definition of a midpoint and the segment addition postulate as follows:
Step 1 | B is the midpoint of AC | Given
Step 2 | AB + BC = AC | Segment Addition Postulate
Step 3 | AB + AB = AC | Definition of midpoint (since B is the midpoint of AC)
Step 4 | 2AB = AC | Simplification
Step 5 | AB = AC/2 | Division Property of Equality
Step 6 | AB = BC | Substitution Property of Equality
Step 7 | _____ | Q.E.D.
Step 6 follows from the fact that B is the midpoint of AC, so AC = 2AB. Substituting AC/2 for AB in Step 2 gives AB + BC = AC/2 + BC, which simplifies to AB = BC. Therefore, Step 6 uses the transitive property of equality, which is a valid property of equality.
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Find f(-3) for the piecewise function:
The half-time performance of a marching band includes a performance in which the band members form a circle with
point J at the center. This formation can be modeled by the equation x^2 + y^2 + 10x - 12y - 83 = 0.
What are the coordinates for the point J?
The coordinates for the point J are (-5, 6).
The radius 12 represents the center of the circle from each band member to the edge of the circle.
The domain of the circle is -17 ≤ x ≤ 7.
The range of the circle is -6 ≤ y ≤ 18.
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is modeled by this mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represent the coordinates at the center of a circle.r represent the radius of a circle.From the information provided above, we have the following equation of a circle:
x² + y² + 10x - 12y - 83 = 0
x² + 10x + y² - 12y = 83
x² + 10x + (10/2)² + y² - 12y + (-12/2)² = 83 + (10/2)² + (-12/2)²
x² + 10x + 25 + y² - 12y + 36 = 83 + 25 + 36
(x + 5)² + (y - 6)² = 144
(x + 5)² + (y - 6)² = 12²
Therefore, the center (h, k) is (-5, 6) and the radius is equal to 12 units.
By critically observing the graph shown in the image attached below, we can reasonably and logically deduce the following domain and range:
Domain = [-17, 7] or -17 ≤ x ≤ 7.
Range = [-6, 18] or -6 ≤ y ≤ 18.
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What is the sum of 2/9 + 4/9
Jess purchases a $6,815 dining room set. She can’t afford to pay cash, so she uses the
installment plan, which requires an 20% down payment. How much is the down payment?
The down payment would be 20% of the total cost of the dining room set, which is $6,815. So, the down payment would be $1,363.
To calculate the down payment, we'll use the following steps:
1. Determine the total cost of the dining room set, which is $6,815.
2. Find the percentage of the down payment, which is 20%.
3. Multiply the total cost by the percentage to find the down payment amount.
Using these steps, we can calculate the down payment:
Down payment = Total cost × Down payment percentage
Down payment = $6,815 × 0.20
Down payment = $1,363
So, Jess's down payment for the dining room set is $1,363.
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b. The sum of two consecutive integers is 109. Determine the integers in 4 steps.
Step 1:
Step 2:
Step 3:
Step 4:
The value of the first and second integers are 54 and 55 respectively.
What are the consecutive integers?Let
First integer = x
Second integer = x + 1
Sum of the integers = 109
So,
First integer + Second integer = Sum of the integers
x + (x + 1) = 109
x + x + 1 = 109
2x + 1 = 109
Subtract 1 from both sides
2x = 109 - 1
2x = 108
divide both sides by 2
x = 108/2
x = 54
Ultimately,
First integer = x
= 54
Second integer = x + 1
= 54 + 1
= 55
Therefore, the solution in 4 steps are;
Step 1: x + (x + 1) = 109
Step 2: 2x + 1 = 109
Step 3: 2x = 108
Step 4: x = 54
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A bag of tokens contains 9 red, 4 green, and 6 blue tokens. What is the probability that a randomly selected token is red and green? Enter your answer as a fraction.
The probability that a randomly selected token is red and green is 27/200.
What is probability that the randomly selected token is red and green?The total token = 9 red + 6 green + 5 blue
The total token = 9 + 6 + 5
The total token = 20
There are 9 red and 6 green.
So, 9 out of 20 is red and 6 out of 20 is green
Let set up an equation:
9/20 × 6/20
= 54/400
= 27/200.
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write an equation to represent A, the area in square feet, as a function of w, the width in feet
The equation to represent A, the area in square feet, as a function of w, the width in feet, would be A = w x L
To represent the area (A) in square feet as a function of the width (w) in feet, you will also need to consider the length (l) of the rectangle. The formula for the area of a rectangle is:
A = l * w
However, since you want A to be a function of w, we can rewrite the equation as:
A(w) = l * w
In this equation, A(w) represents the area as a function of the width, and l is a constant value representing the length of the rectangle in feet.
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Help asap 50pts !!!!
Answer:
h (-2) = -2.6 (repeating)
h(2) =2
h(5) = 4.3 (repeating)
Step-by-step explanation:
for h(-2)
= [tex]\frac{1}{3} (-2^{2} )-4\\\\\frac{1}{3} *4-4\\\\\frac{4}{3} -4=-2.6[/tex]
for h(2)
x = 2, so h(2) = 2
for h(5)
[tex]\frac{1}{3} (5^{2} )-4\\\\\frac{1}{3} *25-4\\\\\frac{25}{3} -4\\\\=4.3[/tex]
The pyramid at right has a volume of 312 cubic
feet. If the prism next to it has the same base area
and height, what is its volume? Explain how you
know.
Answer:
936 cubic feet
(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)
Step-by-step explanation:
To find the volume of the prism next to the pyramid, we need to determine its height. Since the prism has the same base area as the pyramid, we can infer that its height is also the same as the height of the pyramid.
Given that the volume of the pyramid is 312 cubic feet, we can use the formula for the volume of a pyramid:
Volume = (1/3) * Base Area * Height
Let's assume the base area of both the pyramid and the prism is represented by "A" and the height is represented by "h".
For the pyramid:
Volume of pyramid = (1/3) * A * h_p
Given that the volume of the pyramid is 312 cubic feet:
312 = (1/3) * A * h_p
Simplifying the equation, we have:
936 = A * h_p
Now, since the prism has the same base area and height, we can use the same values for "A" and "h_p" to find the volume of the prism.
Volume of prism = A * h_p
Substituting the known values, we have:
Volume of prism = 936 cubic feet
Therefore, the volume of the prism next to the pyramid is 936 cubic feet. This is because the prism has the same base area and height as the pyramid, so their volumes will be equal.
How are conditional probability and independent events related? Select the correct phrase or notation from each drop-down menu to complete the explanation. The notation P(The lights go out|There is a thunderstorm outside) reads the probability Choose... . If two events are Choose... , then the probability of one doesn't affect the other. The two events are independent if the probability Choose... is equal to the probability that the lights go out and the probability Choose... is equal to the probability that there is a thunderstorm outside.
The notation P(The lights go out|There is a thunderstorm outside) reads the probability of "The lights go out" given "There is a thunderstorm outside."If two events are independent, then the probability of one doesn't affect the other.
The two events are independent if the probability P(The lights go out) is equal to the probability that the lights go out and the probability P(There is a thunderstorm outside) is equal to the probability that there is a thunderstorm outside.
Conditional probability and independent events are related in the sense that if two events are independent, then the conditional probability of one event occurring given the other event is simply the probability of the first event happening. In other words, if events A and B are independent, then P(A|B) = P(A).
On the other hand, if two events are dependent, then the conditional probability of one event occurring given the other event is different from the probability of the first event happening. The conditional probability takes into account the additional information provided by the occurrence of the second event.
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the triangle below has an area of 12 units. Find the missing length
Answer:
Step-by-step explanation:
Find the derivative guys pls help
[tex] \qquad\longrightarrow \sf f(x) = sin^{-1} \bigg(\dfrac{x}{2}\bigg)\\[/tex]
The Derivative of f(x) with respect to x-
[tex] \qquad\longrightarrow \sf \dfrac{d}{dx} \:sin^{-1} \bigg(\dfrac{x}{2}\bigg)\\[/tex]
[tex] \qquad\longrightarrow \sf \dfrac{1}{\sqrt{1-\bigg(\dfrac{x}{2}\bigg)^2}}\;\times \dfrac{d}{dx}\:\dfrac{x}{2}\\[/tex]
[tex]\qquad\sf\because\boxed{\sf{ \: \dfrac{d}{dx} sin^{-1}x = \dfrac{1}{\sqrt{1-x^2}}}}\\[/tex]
[tex] \qquad\longrightarrow \sf \dfrac{1}{\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}\;\times\dfrac{1}{2} \:x^{1-1}\\[/tex]
[tex]\qquad \sf\because\boxed{\sf{ \dfrac{d}{dx }x^n = nx^{n-1}}}\\[/tex]
[tex] \qquad\longrightarrow \sf \dfrac{1}{\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}\;\times\dfrac{1}{2} \times 1\\[/tex]
[tex] \qquad\longrightarrow \sf \dfrac{1}{\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}\;\times\dfrac{1}{2} \\[/tex]
[tex] \qquad\longrightarrow \sf\dfrac{1}{2}\: \dfrac{1}{\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}\\[/tex]
[tex] \qquad\longrightarrow \underline{\sf\: \dfrac{1}{2\:\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}}\\[/tex]
Henceforth, Option C) is the correct answer.
Linear Equations-Need help on this problem
(4, -2) is the solution of the given system of equations
The given system of linear equations are
2x-12y=16
4x-19y=22
The missing number in 1st step is 1/2
The missing number in 2nd step is -4
The missing number in 3rd step is 1/5
The missing number in 4th step is 6
The solution of the equation is 4 and -2
Hence, (4, -2) is the solution of the given system of equations
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If a 6-sided die is rolled 30 times, how many times can you expect to get a 6
if its constant rate or unit rate its just multiple 6 until u get 30
What is minus+minus =
Answer:
plus (+)
Step-by-step explanation:
Assume there is a number such as 1 after the minus:
[tex] - 1 + ( - 1) = - 2[/tex]
Thus - (+) - = +, since they add the minuses.
find the median and mean of the data set below: 37 , 27 , 1, 31 ,27 ,40, 47
Answer:
Mean and Median 30 and 31 respectively.
Step-by-step explanation:
Mean refers to average of all the observations.
Mean = Sum of all the observations/ Total no. of observations
Mean = 37 + 27 + 1 + 31 + 27 + 40 + 47/ 7
= 210 / 7
= 30
Median refers to middle most value of the series.
In order to find median we need to arrange the given data in ascending order i.e. smallest to largest.
We get,
1, 27, 27, 31, 37, 40, 47
When the no. of observations is odd: (n + 1/ 2)th term
= 7 + 1/ 2
= 4th term
Therefore, Median is 31.
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!! WILL GIVE BRAINLIST !!
Look at the picture and name the term that BEST describes the notation:
Common internal tangent
point of tangency
Center
chord
secant
diameter
common external tangent
radius
semi-cirele
Major arc
Minor arc
Answer:
1. diameter
2. semi-circle
3. point of tangency
4. common internal tangent
5. major arc
6. radius
7. center
8. common external tangent
9. secant
10. chord
11. minor arc
Step-by-step explanation:
You want to identify the elements of the diagram by name.
Common internal tangent — HJ, the line through the point of tangency where two circles touch each other, where neither center is in the other circle.
point of tangency — G (or K or F), a single point where an external geometry touches a circle.
Center — A (or B), the point equidistant from all those on a circle.
chord — GK, a line segment whose endpoints lie on the same circle.
secant — CD, a line that has two points of intersection with a circle.
diameter — EF, a chord that passes through the center of the circle.
common external tangent — KF, a line that is tangent to two circles that are external to each other. It does not cross the line segment between the circle centers.
radius — BF (or BE), a line segment from the circle center to a point on the circle.
semi-circle — arc EGF, an arc whose measure is 180°.
Major arc — arc CDK (or CKD, or GCK, or DCG), an arc whose measure is more than 180°.
Minor arc — CK (or CD, or GD, or GK, or GE, or GF), an arc whose measure is less than 180°.
#95141404393
The decimal number corresponding to the number [2001]11 is
The decimal number that corresponds with the number [ 2001 ] 11 would be A. 2663
How to find the decimal number ?To convert the number [2001]11 to a decimal number, we can use the formula:
Decimal number = a0 + a1 x b¹ + a2 x b ² + ... + an x b ⁿ
Given the number, [ 2001 ] 11, we would have :
a0 = 1
a1 = 0
a2 = 0
a3 = 2
b = 11
With the formula, the decimal number corresponding to the number would be:
Decimal number = 1 + 0 x 11 ¹ + 0 x 11 ² + 2 x 11 ³
Decimal number = 2663
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circle the correct choice. Identify n and k, and substitute these
into the correct formula. You do not need to simplify.
3. There are 100 people at a basketball game. 10 winners are chosen. Each winner wins an identical team T-shirt. To find the number of ways to choose the winners, you use (permutations/combinations).
There are 30 students in a club. The club chooses a president, Vice president, and secretary. To find the number of ways to choose the officers, you use (permutations/combinations)
(-help I don’t get it)
3. To find the number of ways to choose the winners, you use combinations.
n = 100 (total number of people)
k = 10 (number of winners to be chosen)
The formula for combinations is:
C(n,k) = n! / (k! * (n-k)!)
Substituting n and k into the formula, we get:
C(100,10) = 100! / (10! * (100-10)!)
We do not need to simplify this expression.
For the club with 30 students, the number of ways to choose the officers is given by permutations because the order in which the officers are chosen matters.
n = 30 (total number of students)
k = 3 (number of officers to be chosen)
The formula for permutations is:
P(n,k) = n! / (n-k)!
Substituting n and k into the formula, we get:
P(30,3) = 30! / (30-3)!
We do not need to simplify this expression.
