(a) The amount in the account at the end of 1 year is $3330
(b) The amount in the account at the end of 2 year is $3696.3
Compound interest is interest calculated on the principal and the interest accrued in previous periods. General formula for the number of annual interest on the principal. If the interest is compounded annually, the amounts is given by [tex]A=P(1+\frac{R}{100} )^t[/tex] where "A" represents the new principal sum or the total amount of money after compounding period , "P" represents the original amount or initial amount , "r" is the annual interest rate , "t" represents the number of years .It is given that Deon deposit $3000 that pays 11% interest compounded each year .
(a) Putting P = $3000, R = 11% , T = 1 year in equation (1) , we get
[tex]A=3000(1+\frac{11}{100} )^1\\\\A=3000(1+0.11)\\A=3000(1.11)\\A=3330[/tex]
(b) Putting P = $3000, R = 11% , T = 2 year in equation (1) , we get
[tex]A=3000(1+\frac{11}{100} )^2\\\\A=3000(1+0.11)^2\\A=3000(1.11)^2\\A=3000\times1.23\\A=3696.3[/tex]
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What is the quotient of the following division problem?
14624÷181 = ?
OA. 80 r145
OB. 80 r144
OC. 79 r144
OD. 82 r143
Answer:
b is the correct answer
80r144
Step-by-step explanation:
20. BUSINESS Ramón usually gets one of the routine maintenance options at Annie's Garage. Today, however, he needs a different combination of work than what is listed. + a. Assume that the price of an option is the same price as purchasing each item. separately. Find the prices for an oil change, a radiator flush, and a brake pad replacement. b. If Ramón wants his brake pads replaced and his radiator flushed, how much should he plan to spend? Pls include work
a) The cost of an oil change, brake pads and radiator flush are $59.99, $40 and $10 respectively
b) He can expect to pay $50
The different combinations available are:
Oil change and radiator flush = $69.99
Brake pads and oil change = $99.99
Oil change, radiator flush and brake pads = $139.99
So, equating the above equations we get the individual prices of the items:
Oil change = $59.99
Brake pads = $40
Radiator flush = $10
Part a:
The price of an oil change is $59.99
The cost of brake pads replacement is $40
The price of a radiator flush is $10
Part b:
Brake pads replacement costs $40
Radiator flush costs $10
So, he can expect to pay $50 for the work
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If QK Bisects ∠MQR, QN ⊥ LM and m∠MQK = 34º, find each missing measure
Angle of <RQK=34
Angle of<MQN=90
Angle of<MQK=34
Angle of<PQL=68
Angle of<RQL=112
Angle of<PQN=22
An angle may be a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are within the plane where the rays are located. The meeting of two planes also creates angles. We ask for these as dihedral angles. The angle formed by the rays lying perpendicular to the 2 crossing curves at the point of junction is another property of intersecting curves.
Angle also can refer to the length of a rotation or an angle. This metric represents the connection between a circular arc's length and radius. When a geometrical angle is involved
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Change the following statement into coordinate points
a)f(-1)=1
b)f(2)=7
c)f(1)=1
d)f(3)=0
Changing [f(-1) = 1] into coordinate points, we get (x₁, y₁) = (-1, 1),
Changing [f(2) = 7] into coordinate points, we get (x₂, y₂) = (2, 7),
Also, changing [f(1) = 1] into coordinate points, we get (x₃, y₃) = (1, 1),
And finally, changing [f(3) = 0] into coordinate points,
We get (x₄, y₄) = (3, 0).
As per question statement, we are provided with Four separate functions, as follows, [f(-1) = 1], [f(2) = 7], [f(1) = 1] and [f(3) = 0].
We are required to convert the above mentioned functions into coordinate points.
To solve this question, we need to know the standard form of conversion of functions into coordinate points, which goes as [y = f(x)], i.e., the ordinate is a function of the abscissa.
Thus comparing [y = f(x)] to [1 = f(-1)], we get (x, y) = (-1, 1).
Similarly, comparing [y = f(x)] to [7 = f(2)], we get (x, y) = (2, 7),
Comparing [y = f(x)] to [1 = f(-1)], we get (x, y) = (-1, 1),
And finally, comparing [y = f(x)] to [0 = f(3)], we get (x, y) = (3, 0).
Function: In Mathematics, a function is an operator which when provided with a input, gives a certain output.Coordinate Points: The coordinates of a point are a pair of numbers that define its exact location on a two-dimensional plane by using the horizontal and vertical distances from the two reference axes.To learn more about Coordinate Points, click on the link below.
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X-3 5X-3X-12-4x + 18X-7
Answer:
Algebraic Expressions- An algebraic expression (or) a variable expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc. For example, let us have a look at the expression 2x + 4. Thus, we can say that 2x + 4 is an example of an algebraic expression.
Here are more examples:
• 5x + 4y + 10
• 2x2y - 3xy2
• (-a + 4b)2 + 6ab
To simplify an algebraic expression, we just combine the like terms. Hence, the like variables will be combined together. Now, out of the like variables, the same powers will be combined together
Multiply the numbers
x - 3 . 5x – 3x -12 - 4x + 18x - 7
= x – 15x - 3x – 12 – 4x + 18x – 7
Subtract the numbers
= x – 15x – 3x – 12 – 4x + 18x - 7
= x – 15x – 3x – 19 - 4x + 18x
Combining the like terms
= - 2x – 19
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The sum of two numbers is twenty-one. one number is eighteen less than two times the other. find the numbers.
Answer:
The sum of two numbers is twenty-one. one number is eighteen less than two times the other =
8 and 13
NEED THIS ASAP PLEASE HELP
Bob's Gift Shop sold 200 cards for Mother's Day. One salesman, Bao, sold 2% of the cards sold for Mother's Day. How many cards did Bao sell?
charlies mom just had a baby. he notices that they use an average of 9 dipers per day. At this rate, how many total dipers will they use during June and july this year?
We get that the total dipers that Charlie's mom will use in the month of June and July will be 549 dipers.
Charlie's mom uses an average of 9 diapers a day.
Average = 9
Average means a number that is calculated by adding quantities together and dividing the total by the number of quantities.
Average = Sum of observations / number of observations
A = S / N
We know that:
June has = 30 days
July has = 31 days.
Total days = 30 days + 31 days = 61 days
N = 61
Let the sum = S be x.
Substituting the values in the formula, we get that:
9 = S / 61
S = 9 × 61
S = 549
Therefore, we get that the total dipers that Charlie's mom will use in the month of June and July will be 549 dipers.
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What are the x- and y-intercepts of the function f(x) = -² + 4x − 4?
Select all correct answers.
The point (0,2) is an x-intercept of the function.
The point (2,0) is an x-intercept of the function.
The point (0,-4) is a y-intercept of the function.
The point (-2,0) is an x-intercept of the function.
The point (-4,0) is a y-intercept of the function.
Answer:
x-intercept(s): (2,0)
y-intercept(s): (0,-4)
Step-by-step explanation:
Ann is 4 years older than Julie. 4 years ago, ann was twice as old as julie. find their present ages
Answer: Julie is 8 years old, Ann is 12 years old
Step-by-step explanation:
A=Ann's age. J=Julie's age
A=J+4
A-4=(J-4)*2
A-4=2(J-4)
A=2(J-4)+4
2(J-4)+4=J+4
2J-8+4=J+4
2J-4=J+4
2J=J+8
J=8
A=J+4
A=8+4
A=12
Julie is 8 years old. Ann is 12 years old. :) hope this wasnt too late
Simplify: 35-(15-(19+5)÷3)
Answer:
38
Step-by-step explanation:
35 - {15 - (19 + 5)} ÷ 3
35 - {15 - (24)} ÷ 3
35 - {15 - 24} ÷ 3
35 - {-9} ÷ 3
35 + 9 ÷ 3
35 + 3
38
Answer:
28
Step-by-step explanation:
35 - (15 - (19 + 5) ÷ 3 ) ← evaluate inner parenthesis
= 35 - (15 - 24 ÷ 3) ← evaluate division before subtraction
= 35 - (15 - 8)
= 35 - 7
= 28
A betta fish tank is in shape of a cube. The volume of the fish tank is 216 cubic inches. What is the edge length, in inches, of the fish tank?
Considering the definition of volume and volume of a cube, the edge length of the fish tank is 6 inches.
Definition of volumeAll matter occupies a space that can vary depending on its size. This space can be defined by volume, which is defined as the extension of an object in its three dimensions. That is, the volume corresponds to the measure of the space that a body occupies.
Volume of a cubeThe cube is a polyhedron or three-dimensional geometric figure, with six equal sides, each of which is a regular polygon, that is, a square. In other words, a cube is a body made up of six faces that are square.
The volume of a cube is equal to the measure of its side to the cube:
Volume = side x side x side = side³
Edge length of the fish tankIn this case, you know that:
The volume of the fish tank is 216 cubic inches.The fish tank is in shape of a cube.Replacing in the definition of volume of a cube:
216 cubic inches = side³
Solving:
∛216 cubic inches= side
6 inches= side
Finally, the edge length of the fish tank is 6 inches.
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Find the length of AC if PQ is a segment bisector.
Show work.
Answer:
AC = 135 units
Step-by-step explanation:
since PQ bisects AB , then
BC = AC , that is
12x - 21 = 9x + 18 ( subtract 9x from both sides )
3x - 21 = 18 ( add 21 to both sides )
3x = 39 ( divide both sides by 3 )
x = 13
Then
AC = 9x + 18 = 9(13) + 18 = 117 + 18 = 135
Two cards are selected from a standard deck of 52 playing cards. the first card is not replaced before the second card is selected. find the probability of selecting and then selecting .
The probability of a given event gives a result of 0.00037. It is generated by applying the basic concepts of probability to the assigned problem.
What is probability?
Probability depicts the number of possibilities of how many times an event can occur. The probability of happening of an event invariably lies between 0 and 1. For a sure event, it is always 1. Its formula is given as P(E) = No. of favourable outcomes / Total no. of outcomes
Calculation of finding the probability according to the conditions specified
The entire number of cards in a standard deck = 52
Total number of favourable outcomes = 1
The probability of selecting two cards is given by P(E1) which is equal to 1 / 52
P(E1) = 1 / 52
Another card is selected without replacing the first card, so the total number of cards in the deck becomes 51. The probability of selecting a card from these 51 cards is given by P(E) i.e. (1 / 52) × (1 / 51)
P(E) = 1 / 2652
P(E) = 0.00037
Hence, the required probability is given by 0.00037.
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1. Provide all the details necessary to map △XYZ to △JLK in the picture below. Show your work AND type your explanation.
The transformation to map triangle XYZ to triangle JLK is a reflection over the y axis, that is (x, y) ⇒ (-x, y)
What is a transformation?Transformation is the change of the location of a point or figure on the coordinate plane. Types of transformations are reflection, translation, rotation and dilation.
Reflection, translation, rotation are rigid transformation since they maintain the shape and size of the figure, where as dilation is not a rigid transformation as it changes the size.
The transformation to map triangle XYZ to triangle JLK is a reflection over the y axis, that is (x, y) ⇒ (-x, y)
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Stephanie attempted to solve the equation 5−3k=2(k−5). Her work is shown below. Step 1: 5−3k=2k−10 Step 2: 5=5k−10 Step 3: −5=5k Step 4: −1=k Based on the information provided, which statement justifies why her solution is incorrect? She did not distribute correctly in Step 1. She did not add to/subtract from both sides of the equation equally in Step 2. She did not add to/subtract from both sides of the equation equally in Step 3. She did not multiply/divide both sides of the equation equally in Step 4.
Stephanie did Step 3 wrong as instead of adding 10, she subtracted it.
We are given that Stephanie attempted to solve the equation 5 − 3 k = 2 ( k − 5 ).
5 - 3 k = 2 ( k - 5)
5 - 3 k = 2 k - 10
5 = 2 k + 3 k - 10
5 = 5 k - 10
5 + 10 = 5 k
15 = 5 k
15 / 5 = k
3 = k
We can see that she did Step 3 wrong as instead of adding 10, she subtracted it.
Therefore, she did Step 3 wrong as instead of adding 10, she subtracted it.
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Someone please help me
The type of reasoning utilized in each of the given sentences are;
1) Inductive reasoning
2) deductive reasoning
3) Inductive reasoning
4) Deductive reasoning
5) Deductive reasoning
What is Inductive and Deductive Reasoning?
Inductive reasoning aims at developing a theory while deductive reasoning aims at testing an existing theory.
1) This statement depicts inductive reasoning because it is trying to develop a theory that that studying for a test earns you good grades.
2) This statement depicts deductive reasoning because you are testing an existing theory that red meat has iron in it to draw a conclusion that the steak on your plate has iron in it.
3) This statement depicts inductive reasoning because you are trying to develop a theory that sum of all angles in a triangle is 180 degrees.
4) This statement depicts deductive reasoning because you are testing an existing theory that parallelograms have two pairs of parallel sides to conclude that rectangles also have two pairs of parallel sides.
5) This is deductive reasoning.
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6.7 more than 5 times n
Answer:
5n+6.7
or
n= -1.34
Step-by-step explanation:
For the first answer is base on writing the problem while the second is to solve it
The Second answer
5n+6.7=0
-6.7 on both side
5n= -6.7
divide by 5
n= -6.7/5
if you want the answer to be in decimal than your answer is -1.34
But if you want your answer to be a faction than it -6.7/5
hope this help
translate and solve: 6 fewer than s is no less than −78. (write your solution in interval notation.)
When 6 fewer than s is no less than −78, the solution in interval notation is (84,∞)
Interval notation is a way of writing subsets of the real number line
Given,
6 fewer than s is no less than -78
6-s < -78
Move 6 to right hand side
-s < -78-6
-s < -84
s > 84
Then the interval notation is (84,∞)
Hence, when 6 fewer than s is no less than −78, the solution in interval notation is (84,∞)
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Which rational number equals 0.5?
What is the mean absolute deviation of this data set, rounded to the nearest tenth?
0.7
1.4
3
2
The mean absolute deviation of this data set is 0.2
What is the mean absolute deviation of this data set?The dataset is given as
0.7, 1.4, 3 and 2
Calculate the mean using
m(x) = Sum/Count
So, we have
m(x) = (0.7 + 1.4 + 3 + 2)/4
Evaluate
m(x) = 1.775
The mean absolute deviation is calculated as
Deviation = 1/n∑|(x - m(x))|
So, we have
Deviation = 1/4 * (|0.7 - 1.775| + |1.4 - 1.775| + |3 - 1.775| + |2 - 1.775|)
This gives
Deviation = 1/4 * (-1.075 + 0.375 + 1.225 + 0.225)
Evaluate
Deviation = 0.1875
Approximate
Deviation = 0.2
Hence, the mean absolute deviation of this data set is 0.2
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Given m ∥ n m∥n, find the value of x. m n t (x+9)° (2x+6)°
Can you please help
4x^2-11x+7
Near the surface of Jupiter, the distance d that an object falls in t seconds is given by d = 1/2 gt², where g = 84.48 ft/sec². Find the distance an object falls in 3 seconds.
The distance an object falls in 3 seconds is 380.16 ft.
According to the question we have been given an equation of the distance that an object falls in t seconds, which is
d = [tex]\frac{1}{2} g t^{2}[/tex]
where, d = distance
g = 84.48 ft/sec²
t = time.
We need to find the distance an object falls in 3 seconds. That is we have to find d when t = 3 seconds
Putting the required values in the above formula we get
d = [tex]\frac{1}{2} (84.48) (3)^{2}[/tex]
d = 760.32/2
d = 380.16 ft
hence the distance an object falls in 3 seconds is 380.16 ft.
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Determine the truth value of each conditional statement. If true, explain your reasoning. If false, give a counterexample.If two angles are congruent, then they are vertical angles.
The truth value of the conditional statement is false, and the counterexample of this statement is corresponding angles
How to determine the truth value of the conditional statement?The conditional statement is given as:
If two angles are congruent, then they are vertical angles.
The above statement is false because not all congruent angles are vertical angles
A counterexample of this statement is a corresponding angle
i.e. corresponding angles are congruent angles, but they are not vertical angles
Hence, the truth value of the conditional statement is false, and the counterexample of this statement is a corresponding angle
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A KLM has coordinates K(4, -2), L(6, -1), and M(5, 5). What
would be the coordinates of the vertices of the image after a reflection
in the x-axis?
OA) K'(-4,-2), L'(-6, -1) and M'(-5, 5)
OB) K'(-4, 2), L'(-6, -1) and M'(-5,-5)
● c) K'(4, 2), L'(6, 1) and M'(5,-5)
OD) K'(-2, 4), L'(-1, 6) and M'(5, 5)
The coordinates of the vertices of the image after a reflection
in the x-axis is K(4, 2) , L(6, 1) and M(5, 5).
What are transformations?
A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation.
Given:
A KLM has coordinates K(4, -2), L(6, -1), and M(5, 5).
According to given question we have
When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the x-axis is (x, -y).
So,
K(4, -2) can changed to K(4, 2) .
L(6, -1) can changed to L(6, 1).
M(5, 5) can changed to M(5, 5).
Therefore, the coordinates of the vertices of the image after a reflection
in the x-axis is K(4, 2) , L(6, 1) and M(5, 5).
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Evaluating Functions → Finding the
->
Output
f(x) = 5x + 6
Find f(3)
21 is the value of function f(3) .
What is function?
A function is a type of rule that produces one output for a single input. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.Four main categories can be used to classify different sorts of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element.f(x) = 5x + 6
f(3) = 5(3) + 6 = 15 + 6 = 21
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Kai has 4 bags of marbles .there are 3 red,5 green,2 yellow,and 6 black marbles in each bag. How many marbles does kai have? Show how you found the answer
Answer:
The correct answer is 64 marbles.
Step-by-step explanation:
Let's analyze the information we have:
Jill has 4 bags of marbles.
In each bag she has 16 marbles (in each one she has 3red, 5green, 2 yellow, and 6black)
If each bag has 16 marbles, and she has 4 bags, then we must multiply the contents of each bag by 4.
And we do it as follows:
16 x 4 = 64
Therefore, we can say that Jill has 64 marbles.
Answer:
There is 16 in each bag so there is 64 marbles in total.
Step-by-step explanation:
3 + 2 = 5
5 + 5 = 10
10 + 6 = 16
16 x 4 (16 + 16+ 16+ 16) = 64
Jeff place is a pineapple with a mass of 890 g on a balance scale he balances the scale by placing two oranges an apple and a lemon on the other side each orange weighs 280 g the lemon weighs 195 g less than each orange what is the mass of the apple
use the distributive property to find the quotient 628/2
Answer:
314
Step-by-step explanation: