==================================================
Method #1
Multiply the two values to get 12*16 = 192
Then divide over the GCF 4 getting 192/4 = 48
------------------
Method #2
List out the multiples of each and see what they have in common
Multiples of 12 = {12, 24, 36, 48, 60, 72, 84, 96, ...}
Multiples of 16 = {16, 32, 48, 64, 80, 96, ...}
We see that 48 is the smallest common multiple.
-------------------
Method #3
Find the prime factorization for each
12 = 2*2*3
16 = 2*2*2*2
The unique prime factors are 2 and 3
The prime 2 shows up at most 4 times, so 2^4 = 16 is one factor of the LCM
The prime 3 shows up at most 1 time, so 3^1 = 3 is the other factor of the LCM
The LCM is 3*16 = 48.
The least common multiple (LCM) of 12 and 16 is 48.
To find the LCM, you can use the following steps:
List the multiples of each number until you find a common multiple.
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, ...
Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, ...
The least common multiple (LCM) is the smallest number that appears in both lists.
The smallest number that appears in both lists is 48.
So, the least common multiple (LCM) of 12 and 16 is 48.
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The weights of bags of chips are normally distributed with a mean of 180 grams and a standard deviation of 4 grams.
What percent of the bags of chips weigh less than 176 grams?
2.5%
16%
32%
34%
The percent of the bags of chips weigh less than 176 grams is b 16%
What percent of the bags of chips weigh less than 176 grams?From the question, we have the following parameters that can be used in our computation:
Mean = 180
Standard deviation = 4
Bags of chips weigh less than 176 grams
This means that
x = 176
So, the z-score is
z = (176 - 180)/4
Evaluate
z = -1
The percent of the bags of chips weigh less than 176 grams is represented as
P = P(z < -1)
Using a graphing calculator, we have
Percentage = 0.15866
So, we have
Percentage = 16%
Hence , the percentage is 16%
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for what value of k will the relation not be a function
R={(k-8.3+2.4k,-5),(3/4k,4)}
Step-by-step explanation:
hope you can understand
Find the perimeter of each figure
The hexagon with sides of length 5 inches, 4 inches, 4 inches, 5 inches, 3 inches, and 3 inches has a perimeter of 24 inches.
What is a hexagon?A hexagon is a regular polygon, meaning all sides and angles are equal in size. It is a symmetrical shape, which means it can be divided into two equal halves.
To calculate the perimeter of this hexagon, we must first identify the length of each side.
All sides of the hexagon have a length of either 5 inches, 4 inches, or 3 inches, as there are two sides of each length.
The perimeter of the hexagon is the sum of the length of all its sides. Adding the length of all the sides, we get
5 + 4 + 4 + 5 + 3 + 3 = 24.
Thus, the perimeter of the hexagon is 24 inches.
Hence, the sum of the length of the sides of a hexagon is always greater than the length of any one of its sides.
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What is the scale factor for this dilation? How do you
know?
Look at the left-most part of the blue diagram. It is 1 unit high. The corresponding left-most part of the red diagram is 2 units high, which is twice as high as the blue portion it corresponds to.
The scale factor tells us how to enlarge or shrink the object. In this case, the red figure is twice as tall and wide compared to the blue figure.
You can pick any pair of corresponding sides to get the scale factor.
(2.5*10^3)*3.4*10^2 (in scientific notation)
Answer:
8.5 × 10^5
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
\(\\ \rm\Rrightarrow (2.5\times 10^3)^3\times 4\times 10^2\)
\(\\ \rm\Rrightarrow 2.5\times 3.4 10^3 \times 10^2\)
\(\\ \rm\Rrightarrow 8.5\times 10^{3+2}\)
\(\\ \rm\Rrightarrow 8.5\times 10^5\)
Express the first quantity as percentage of the second of 45g and 75g
The first quantity (45g) as 60 percentage of second (75g).
What do you mean by Percentage?A part of whole expressed in Hundredth. Percentage is a fraction of a number out of 100%. It can be in fraction or in decimal.
To convert the given percentage value in decimal, divide the given value by 100.
For example:
1. 50% in decimal or fraction will be 50/100 = 0.5.
2. 20% in decimal or fraction will be 20/100 = 0.2.
How to calculate Percentage?1. Finding the total amount from which we need to find the percent.
2. Dividing the required amount to find the percentage by total amount.
3. Multiply it by 100.
For example:
1. It rained 10 of the 30 days in April.
Percentage will be 10/30 = (1/3) x 100
Percentage = 33.33%
Here, we have given that:
Total amount = 75g
Required amount for percent = 45g
Now, to find the percentage:
Percentage = 45/75
Percentage = 0.6 x 100
Percentage = 60%
Hence,
The first quantity (45g) as 60 percentage of second (75g).
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Please answer this question !! Thank you !! Will give brainliest !!
Find missing probability
The value of missing probability is,
⇒ P (A or B) = 131/200
We have to given that;
P (A) = 9/20
P (B) = 1/4
P (A and B) = 9/200
Now, We know that;
P (A or B) = P (A) + P (B) - P (A and B)
P (A or B) = 9/20 + 1/4 - 9/200
P (A or B) = 9/20 + 5/20 - 9/200
P (A or B) = 14/20 - 9/200
P (A or B) = 140/200 - 9/200
P (A or B) = 131/200
Thus, The value of missing probability is,
⇒ P (A or B) = 131/200
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Expand and simplify x(3x + 5)-5(2x - 1)
PLEASE HELP ME AND ANSWER THIS QUESTION !! I need this for my assessment revision
The simplified expression of x(3x + 5)-5(2x - 1) is 3x² - 5x + 5
How to expand and simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
x(3x + 5)-5(2x - 1)
Open the brackets
So, we have
3x² + 5x - 10x + 5
Evaluate the like terms
So, we have
3x² - 5x + 5
Hence, the simplified expression is 3x² - 5x + 5
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name the quadrilateral with 2 pairs of consecutive congruent sides with diagonals that meet at a right angle
The quadrilateral you're describing is a Kite. A kite is a quadrilateral with two pairs of consecutive congruent sides, and its diagonals meet at a right angle.
please help!!!
maths functions
Answer:
Point A: (2, 10)
Point B: (-3, 0)
Point C: (-5, -4)
Point D: (-5, -32)
Step-by-step explanation:
Part (a)Points A and B are the points of intersection between the two graphs.
Therefore, to find the x-values of the points of intersection, substitute one equation into the other and solve for x:
\(\implies 2x+6=-2x^2+18\)
\(\implies 2x^2+2x-12=0\)
\(\implies 2(x^2+x-6)=0\)
\(\implies x^2+x-6=0\)
\(\implies x^2+3x-2x-6=0\)
\(\implies x(x+3)-2(x+3)=0\)
\(\implies (x-2)(x+3)=0\)
\(\implies x=2, -3\)
From inspection of the graph:
The x-value of point A is positive ⇒ x = 2The x-value of point B is negative ⇒ x = -3To find the y-values, substitute the found x-values into either of the equations:
\(\begin{aligned} \textsf{Point A}: \quad 2x+6 & =y\\2(2)+6 & =10\\ \implies & (2, 10)\end{aligned}\)
\(\begin{aligned} \textsf{Point B}: \quad -2x^2+18 & =y\\-2(-3)^2+18 & =0\\ \implies & (-3,0)\end{aligned}\)
Therefore, point A is (2, 10) and point B is (-3, 0).
Part (b)If the distance between points C and D is 28 units, the y-value of point D will be 28 less than the y-value of point C. The x-values of the two points are the same.
Therefore:
\(\textsf{Equation 1}: \quad y=2x+6\)
\(\textsf{Equation 2}: \quad y-28=-2x^2+18\)
As the x-values are the same, substitute the first equation into the second equation and solve for x to find the x-value of points C and D:
\(\implies 2x+6-28=-2x^2+18\)
\(\implies 2x^2+2x-40=0\)
\(\implies 2(x^2+x-20)=0\)
\(\implies x^2+x-20=0\)
\(\implies x^2+5x-4x-20=0\)
\(\implies x(x+5)-4(x+5)=0\)
\(\implies (x-4)(x+5)=0\)
\(\implies x=4,-5\)
From inspection of the given graph, the x-value of points C and D is negative, therefore x = -5.
To find the y-value of points C and D, substitute the found value of x into the two original equations of the lines:
\(\begin{aligned} \textsf{Point C}: \quad 2x+6 & =y\\2(-5)+6 & =-4\\ \implies & (-5,-4)\end{aligned}\)
\(\begin{aligned} \textsf{Point D}: \quad -2x^2+18 & = y \\ -2(-5)^2+18 & =-32\\ \implies & (-5, -32)\end{aligned}\)
Therefore, point C is (-5, -4) and point D is (-5, -32).
Answer:
a) A = (2, 10) and B = (-3, 0)
b) C = (-5, -4) and D = (-5, -32)
Explanation:
a) To determine the coordinates of A and B, find the intersection points of the line "y = 2x + 6" and curve "y = -2x² + 18".
Solve the equation's simultaneously:
y = y
⇒ 2x + 6 = -2x² + 18
⇒ 2x² + 2x + 6 - 18 = 0
⇒ 2x² + 2x - 12= 0
⇒ 2x² + 6x - 4x - 12 = 0
⇒ 2x(x + 3) - 4(x + 3) = 0
⇒ (2x - 4)(x + 3) = 0
⇒ 2x - 4 = 0, x + 3 = 0
⇒ x = 2, x = -3
Then find value of y at this x points,
at x = 2, y = 2(2) + 6 = 10
at x = -3, y = 2(-3) + 6 = 0
Intersection points: A(2, 10) and B(-3, 0)
b) Given that CD = 28 units. Also stated parallel to y axis so x coordinates for both will be same but differ in y coordinate.
\(2x + 6 = -2x^2 + 18 + 28\)
\(-2x^2 + 18 + 28-2x - 6 = 0\)
\(-2x^2-2x+40=0\)
\(-2x^2-10x+8x+40=0\)
\(-2(x+5)+8(x+5)=0\)
\((-2x+8)(x+5)=0\)
\(x = -5, 4\)
\(\leftrightarrow \sf C(-5, y_2), \ D(-5, y_2)\)
Find y value for Point C : 2x + 6 = 2(-5) + 6 = -4
Find y value for Point D : -2x² + 18 = -2(-5)² + 18 = -32
\(\sf \rightarrow Point \ C = (-5, -4)\\ \\\rightarrow Point \ D = (-5, -32)\)
The sum of two numbers is −45. One number is 9 more than the other. Find the numbers
Answer:
-18 and -27 ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
Anyone can solve this question for me??
its john because 14.7/2 is 7.35 and 19.5/3 is 6.5 so it would have to be john
pls mark brainliest
Please help! 15 points!!
Answer:
none of the answers are correct because 2 and 5 are across
( don't know how to explain it) and they have to be the same
6.
5. ¿Qué número tiene el mismo
valor que l centena, 7 decenas?
Answer:
7 Decenas = 70 Unidades espero que te ayude
Step-by-step explanation:
An inner city revitalization zone is a rectangle that is twice as long as it is wide. The width of the region is growing at a rate of 34 m per year at a time when the region is 450 m wide. How fast is the area changing at that point in time?
Answer:
The area is changing at the point of \(\mathbf{61200 m^2/year}\)
Step-by-step explanation:
From the given information:
Let's recall from our previous knowledge that the formula for finding the area of a rectangle = L × w
where;
L = length and w = width of the rectangle
Suppose the Length L is twice the width w
Then L = 2w --- (1)
From The area of a rectangle
A = L × w
A = 2w × w
A = 2w²
Taking the above differentiating with respect to time
\(\dfrac{dA}{dt }= 4w \times \dfrac{dw}{dt} --- (2)\)
At the time t
\(\dfrac{dw}{dt}= 34 m \ per \ year ; w = 450 \ m\)
Replacing the values back into equation 2, we get:
\(\dfrac{dA}{dt }= 4 \times 450 \times 34\)
\(\mathbf{\dfrac{dA}{dt }= 61200 m^2/year}\)
A cylinder has volume 727 and radius 3. What is its height?
Answer:
height = 25.71
Step-by-step explanation:
HELPP!!
Ryan collects rainwater in a barrel for his garden. The barrel is filled with 15 gallons of water. Ryan used 6.8 gallons to water his garden in June and 5 and one-eighth gallons in July. How much water is left in the barrel?
1.) 3.075 gallons
2.) 5.125 gallons
3.) 5.178 gallons
4.) 16.675 gallons
Subtracting the initial amount of water from the amount used, the remaining amount of water is given by:
1.) 3.075 gallons.
How to find the remaining amount of water in the barrel?
To find the remaining amount of water in the barrel, we have to subtract the initial amount by the amount used.
We have that:
The initial amount was of 15 gallons.The amount used was of: 6.8 + 5 + 1/8(relative to the one-eight) = 11.925 gallons.Hence the remaining amount is:
15 - 11.925 = 3.075 gallons.
Which means that option 1 is correct.
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Answer: 3.075 gallons
Step-by-step explanation:
A bowl contained 59.16 grams of salt. Then, Omar poured in another 13.2 grams. How much salt does the bowl contain now?
Answer: 72.36
Step-by-step explanation:
To find the total amount of salt in the bowl after Omar poured 13.2 grams, we need to add the initial amount of salt in the bowl to the amount of salt Omar added.
The initial amount of salt in the bowl was 59.16 grams.
Omar added 13.2 grams of salt to the bowl.
To find the total amount of salt in the bowl now, we add these two amounts: 59.16 + 13.2 = 72.36
Therefore, the bowl contains 72.36 grams of salt now.
Consider this equationx^2+1=2x-3Which expression correctly sets up the quadratic formula?
we have the equation
\(x^2+1=2x-3\)Rewrite the given equation
\(\begin{gathered} x^2+1-2x+3=0 \\ x^2-2x+4=0 \end{gathered}\)where
a=1
b=-2
c=4
substitute in the formula
\(x=\frac{-(-2)\pm\sqrt{-2^2-4(1)(4)}}{2(1)}\)The answer is the option AFind the sum of whole number that are less than 100 and leave reminder 2 when divided by 5
Answer:
99
Step-by-step explanation:
2+5, ∈ℤ
=2+7+12+⋯+97
This is AP with =2,=5,
th term is given by =+(−1)
97=2+(−1)5⟹=20
So sum of such integers,
20=202(2+97)=990
The sum of whole number that are less than 100 and leave reminder 2 when divided by 5 is 990.
What is Arithmetic Progression?A series in which the differences between each pair of following terms are the same is known as an arithmetic progression.
An arithmetic progression is a sequence in which every phrase—aside from the initial term—is created by multiplying the previous term by a predetermined amount.
Given:
We have to find the sum of number that are less than 100 and leave reminder 2 when divided by 5
So, we get the sequence
2, 7, 12, ................97
=2+7+12+⋯+97
This is AP with =2,=5,
So, l= a+( n-1)
97= 2+ (n-1)(5)
95 = 5(n-1)
n-1 = 95/5
n-1 = 19
n= 19 + 1
n=20
Now, the sum is
\(S_{20}\) = 20/2( 2 x 2+ (20 - 1 )(5))
= 10( 4 + 19(5)
= 10 (99)
= 990
Hence, the sum is 990.
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1. 18x^3-2x^2+4x-1
1.1 How many terms are in 18x^3-2x^2+4x-1
The polynomial 18x³ - 2x² + 4x - 1 consists of four terms.
The number of terms in a polynomial helps when performing operations like simplification, factoring, or evaluating expressions.
The polynomial 18x³ - 2x² + 4x - 1 consists of four terms.
In order to determine the number of terms in a polynomial, we count the number of distinct algebraic expressions separated by addition or subtraction operations.
In this polynomial, we have:
Term 1: 18x³ (This is the term with the highest degree, which is 3 in this case, and it includes the coefficient 18.)
Term 2: -2x² (This term has a degree of 2 and a coefficient of -2.)
Term 3: 4x (This term has a degree of 1 and a coefficient of 4.)
Term 4: -1 (This is a constant term with a degree of 0.)
We can see that there are four distinct terms separated by addition and subtraction operations:
18x³, -2x², 4x, and -1.
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the 7th-grade class wants to collect empty soda pop cans to earn $50.00. If pop cans earn $0.25 per pound how many cans will they need to collect to earn the $50.00?
200 pounds need to collect to earn the $50.00. Divide the cost per pound from the total amount needed, \(\frac{50.00}{0.25}\)= 200 pounds.
Is the British pound?The official money of the U.k. and its regions is the GBP, or British pound sterling. The Pound is the earliest currency that is still accepted as legal tender in the entire world. The GBP, represented by pound sign (£), has one of the greatest trade volumes worldwide.
What makes something a "pound"?The development of the pounds sterling -The Latin word "libra," which means balance and weight, is where the name "pound sterling" comes from. During the years, the pound banknotes underwent various revisions before being initially printed by the Bank of England and over 300 years ago.
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A company has a 20-person grievance committee. When a grievance is filed, three of these 20 people are chosen at random to serve on a hearing panel. Suppose that two committees are formed. What is the probability that these committees have at least one member in common?
Answer:
the probability that the two committees have at least one member in common is approximately 0.3622.
Step-by-step explanation:
To find the probability that two committees have at least one member in common, we can use the complement rule, which states that the probability of an event happening is 1 minus the probability of the event not happening.
Let A be the event that the two committees have no members in common. To calculate the probability of A, we can first find the number of ways to choose three people out of 20 without any overlap, and then use this to find the total number of ways to choose two committees of three people each without any overlap:
Number of ways to choose 3 people out of 20 without overlap:
C(20,3) = (201918)/(321) = 1140
Number of ways to choose 3 people out of 20 with overlap:
C(20,3) - C(2,1)C(17,2) = 1140 - 2(2*136) = 680
The first term is the total number of ways to choose 3 people out of 20, and the second term is the number of ways to choose 3 people out of 20 such that one particular person is included. We multiply by 2 because there are two committees.
The total number of ways to choose two committees of three people each without any overlap is:
C(20,3) * C(17,3) = (1140*680) = 775200
Therefore, the probability that the two committees have no members in common is:
P(A) = 775200 / (C(20,3)*C(17,3)) = 0.6378
So the probability that the two committees have at least one member in common is:
P(at least one member in common) = 1 - P(A) = 1 - 0.6378 = 0.3622
Therefore, the probability that the two committees have at least one member in common is approximately 0.3622.
Falling objects can be modeled with quadratic functions. One student was thinking about this
and wondered what might happen in a few different situations.
They wondered if they could get on top of a 126 foot tall building and throw a tennis ball
straight up in the air as hard as they could, how long would it take for the ball to hit the ground.
Based on their knowledge of gravity and how fast they can throw a ball, they created the
following equation, which relates time, t, in seconds to height, h(t), in feet.
h(t) = -14t² + 56t+126
a. Find the vertex of the equation and explain what it means in this context.
b. Find the x-intercepts and y-intercept and explain what they mean in this context.
This student also wonders how long it will take the ball to reach the 6th floor, which
they measured to be 72 feet from the ground. Find the time it will take for the ball to reach 72 feet.
a. The x-coordinate of the vertex (2) represents the time it takes for the ball to reach its maximum height, and the y-coordinate (182) represents the maximum height itself.
b. The tennis ball is initially at a height of 126 feet above the ground.
How to calculate the valuea. The x-coordinate of the vertex is 2. To find the y-coordinate, we substitute this value back into the equation:
h(2) = -14(2)² + 56(2) + 126
h(2) = -14(4) + 112 + 126
h(2) = -56 + 112 + 126
h(2) = 182
Therefore, the vertex of the equation is (2, 182). In this context, the vertex represents the highest point reached by the tennis ball during its trajectory. The x-coordinate of the vertex (2) represents the time it takes for the ball to reach its maximum height, and the y-coordinate (182) represents the maximum height itself.
b. In order to find the y-intercept, we set t equal to zero and evaluate h(t):
h(0) = -14(0)² + 56(0) + 126
h(0) = 126
The y-intercept is 126. In this context, the y-intercept represents the initial height of the ball when it is thrown. Therefore, the tennis ball is initially at a height of 126 feet above the ground.
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What is the meaning of "The usual notation makes this identification transparent by writing every sequence (x1, x2, ..., xn) as a product or word x1x2· · · xn in the alphabet X"?
The statement refers to the way that symbols are represented in sequences, a common practice in formal language theory, by employing a notation that makes symbols a part of the sequence.
How is sequence notation and language related?In formal language theory, a language is often defined as a set of strings over an alphabet. By representing any alphabetic sequence of symbols as a single string using the notation outlined in the statement, we are able to recognise the language that comprises that sequence as a collection of strings. A subset of the language having all possible strings over the alphabet (a, b, and c) is the set of strings abc, which may be used to represent the language including the sequence (a, b, and c). So, this notation offers an easy approach to discuss languages and the sequences that make up such languages.
Hence, the statement relates the symbols and sequences.
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A car is traveling at a rate of 108 kilometers per hour. What is the cars rate in meters per second? How many meters will the car travel in 20 seconds?
Answer:
\(\frac{30meters}{second}\)
600meters
Step-by-step explanation:
Use conversion factors that represent 1. You can cross cancel wods just like numbers.
\(\frac{108km}{1hour}\) · \(\frac{1hour}{60 minutes}\) · \(\frac{1minute}{60seconds}\) ·\(\frac{1000meters}{1 km}\)
\(\frac{108000meters}{3600seconds}\)
\(\frac{30meters}{second}\)
\(\frac{30meters}{second}\) ·\(\frac{20seconds}{1}\)
600 meters
Helping in the name of Jesus.
(02.02 MC)
If trapezoid ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°, where would point A′′′ lie?
Trapezoid formed by ordered pairs A at negative 4, 1, B at negative 3, 2, C at negative 1, 2, D at 0, 1.
(1, −1)
(−4, 1)
(1, 1)
(−4, −1)
The location of point A''' after the three transformations would be (-4, 1).
To determine the location of point A''', we need to apply the three transformations (reflection over the y-axis, reflection over the x-axis, and rotation of 180°) to point A.
When a point is reflected over the y-axis, the x-coordinate is negated while the y-coordinate remains the same.
So, the reflection of point A (-4, 1) over the y-axis would be (4, 1).
When a point is reflected over the x-axis, the y-coordinate is negated while the x-coordinate remains the same. So, the reflection of point (4, 1) over the x-axis would be (4, -1).
When a point is rotated 180°, the x-coordinate and y-coordinate are both negated. So, the rotation of point (4, -1) by 180° would be (-4, 1).
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1. You decide to buy a guitar for $1257. With tax the total comes to $1357.56. You'll have to charge it on your credit card. If your monthly Interest rate is 1.7%, and you make a payment of $150 per month, what will your new balance be by the end of the 3rd month? Fill in the
chart below completely. Each box should be filled.
Here's the complete chart:
Month Balance Interest Payment New Balance
0 $1,357.56 - - $1,357.56
1 $1,383.54 $23.98 $150 $1,257.52
2 $1,409.62 $26.08 $150 $1,266.06
3 $1,435.81 $27.19 $150 $1,473.61
What is percent?Percent is a way of expressing a fraction or a ratio as a number out of 100. The word "percent" comes from the Latin per centum, which means "per hundred." Percentages are commonly used in many areas, including finance, economics, and statistics. For instance, interest rates, inflation rates, and stock market returns are often expressed as percentages. In addition, percentages are used to calculate discounts, markups, and taxes.
Here,
To calculate the new balance by the end of the 3rd month, we need to use the formula for the balance after n months with monthly payments:
B(n) = (1 + r)ⁿ * B(0) - (PMT/r) * [(1 + r)ⁿ-1]
where B(0) is the initial balance, r is the monthly interest rate, PMT is the monthly payment, and n is the number of months.
In this case, we have:
B(0) = $1357.56
r = 1.7% per month = 0.017
PMT = $150
n = 3 months
Plugging these values into the formula, we get:
B(3) = (1 + 0.017)³ * $1357.56 - ($150/0.017) * [(1 + 0.017)³ - 1]
= $1473.61
Therefore, the new balance by the end of the 3rd month is $1473.61.
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5 + 2
6 6
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Answer:
271
Step-by-step explanation: