1) The interest if it is compounded using simple interest is $240
2) The interest if it is compounded annually is $249.73
3) The interest if it is compounded semiannually is $252.325
4) The interest if it is compounded quarterly is $253.650
5) The interest if it is compounded monthly is $254.543
6) The interest if it is compounded daily is $254.978
7) The interest if it is compounded hourly is $254.993
8) The interest if it is compounded every minute is $254.993
9) The interest if it is compounded continuously is $254.993
10) The difference in interest between simple interest and interest compounded continuously is $14.993
What is meant by compound interest?Compound interest is the addition of interest to the principal sum of a loan or deposit, or interest on interest plus interest.
Given, P=2000
r=4%
r=4/100
r=0.04
t=3 years
1) Simple interest⇒ A=P(1+rt)
=2000(1+3(0.04)
=2000(1+0.12)
=2240
S.I= 2240-2000
S.I=$240
2) Compound interest(yearly)
1st year= 2000(4/100)=80
2nd year=2080(4/100)=83.2
3rd year=(2080+83.2)(4/100)=86.528
P=2163.2+86.528
P=2249.728
C.I=2249.728-2000
C.I=249.728≈$249.73
3) Compounded semiannually
A= P(1+(R/200))²ⁿ
A=2000(1+(4/200))⁶
A=2000(1.12616)
A=2252.325
C.I= 2252.325-2000
C.I=$252.325
4) Compounded quarterly
A=P(1+(R/400))⁴ⁿ
A=2000(1+(4/400))¹²
A=2253.650
C.I=2253.650-2000
C.I=$253.650
5) Compounded monthly
A=P(1+(R/1200))³⁶
A=2000(1+(4/1200))³⁶
A=2254.543
C.I= 2254.543-2000
C.I=$254.543
6) Compounded daily
A=P(1+(R/36500))³⁶⁵ⁿ
A=2000(1+(4/36500))¹⁰⁹⁵
A=2254.978
C.I=2254.978-2000
C.I=$254.978
7) Compounded hourly
A=P(1+(R/876000))²⁶²⁸⁰
A=P(1+(4/876000))²⁶²⁸⁰
A=2254.993
C.I=2254.993-2000
C.I=$254.993
8) Compounded every minute
A=P(1+(R/52560000))¹⁵⁷⁶⁸⁰⁰
A=P(1+(4/52560000))¹⁵⁷⁶⁸⁰⁰
A=2254.993
C.I=2254.993-2000
C.I=$254.993
9) Compounded continuously
A= [tex]Pe^{rt}[/tex]
A=2000([tex]e^{0.04*3}[/tex])
A=2254.993
C.I=2254.993-2000
C.I=$254.993
10) The difference in interest between simple interest and interest compounded continuously is
254.993-$240=$14.993
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Can someone sketch the graph plsss? I rlly need help to sketch it
Answer:
1. Plot x = 0
(A. IF YOU CAN EASILY FIND IT, PLOT Y = 0)
(B. BONUS: PLOT A FEW EASY TO CALCULATE POINTS LIKE X = 1 & X = -1)
2. Figure out what happens when x is really big (in the positive and negative direction)
3. Optional: look for any “significant” x-values
4. Connect the dots and finish!
Step-by-step explanation:
1. Plot x = 0
The first thing we want to do is get some points up on our graph, so we want to pick the ones that will be easy to calculate. For almost any equation, plugging in x = 0 and solving for y is fast and easy to do by eye, and almost always doable without a calculator. For our example equation:
So, the first point we’ll put on our graph is (0, -4).
so many points if dine quickly
WILL GIVE BRAINLIEST !!
A helicopter lifts 75m vertically into the air and then comes back down to the ground.
a) What is the distance of the helicopter’s flight?
b) What is the displacement of the helicopter’s flight? Show your work
Distance is the total length covered by an object.
Displacement is the distance between the final point and the initial point.
The distance of the helicopter's flight is 150 m
The displacement of the helicopter's flight is zero.
What is displacement?Displacement is the distance between the final point and the initial point.
We have,
A helicopter lifts 75m vertically into the air and then comes back down to the ground.
Distance is the total length covered by an object.
Distance of the helicopter's flight.
= 75m + 75m
= 150 m
Displacement of the helicopter's flight.
= Final point - Initial point
= 0 - 0
= 0
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ALGEBRA 1 HW!! PLEASE HELP I WILL GIVE BRAINLYEST
The value of constant C is 50.
Explain linear equation.Equations with a maximum degree of one are referred to as linear equations. According to this rule, a variable in a linear equation cannot have an exponent greater than 1.
A linear equation's graph is always depicted as a straight line. There are linear equations for one variable and two variables, respectively.
Given, the linear equation is 12.5x+5y = C
Here, constant C.
Consider one points from given table x = -2 and y = 15,
Putting the value of x and y,
C = 12.5×(-2) + 5×15
= -25 + 75
= 50
For point, x = 0 and y = 10,
Putting the value of x and y,
C = 12.5×0 + 5×10
= 50
For point, x = 2 and y = 5,
Putting the value of x and y,
C = 12.5×2 + 5×5
= 25 + 25
= 50
Given, x = 4 and y = 0,
Putting the value of x and y,
C = 12.5×4 + 5×0
= 50
Therefore, the value of constant C was found to be 50.
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Convert the height of a person who is 5.2 feet tall to centimeters. Include the inches-centimeter conversion
factor. Use the table given to create conversion factors. Show all conversion factors needed.
Round final answer to 2 decimal places if needed. The setup below should look like the typical dimensional
analysis that you learned.
The height of the 5.2 feet person in centimeters is 158.496 cm.
Explain unit conversion.A conversion factor must be added, subtracted, multiplied, or divided throughout the multi-step process of unit conversion. Additionally, selecting the appropriate number of significant digits and rounding may be necessary.
Different conversion units are used to quantify various measurements. By definition, unit conversion is the process of converting two measures of the same quantity between distinct units by multiplying or dividing them.
In mathematics, conversion is the process of changing a value's form, such as from millimeters to inches or liters to gallons. Units are used for measurements of length, weight, capacity, temperature, and speed.
Given,
Height of a person = 5.2 feet.
The conversion between inches and centimeters must also be included.
First, convert feet to inches.
1 foot = 12 inches
Converting the given height to inches,
Height = 5.2 × 12
= 62.4 inches
Now, we will convert the height into centimeters,
To convert, we will multiply by 2.54
Height = 62.4 × 2.54
= 158.496 cm
Therefore, the height of the person in centimeters is 158.496 cm
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solve for x. "-8+x/4=-4" simplify your answer as much as possible
Answer:
48
Step-by-step explanation:
multiply by 4 to make x whole number
-32+x=16
+32 to isolate x
x=16+32
add for answer
x=48
Linear regression question 8
Use graph below using all the points on the graph to figure out the line of best fit and the estimate of Carter’s weight 15 weeks into his diet.
The linear regression equation from the given scatter plot is:
y = -1.62x + 215.64.
Using this function, the estimate of his weight 15 weeks into the diet is:
191.34 pounds.
How to obtain the linear regression equation?The linear regression equation is obtained inserting the points of the scatter plot of the situation into a linear regression calculator.
From the given scatter plot, the points are given as follows:
(0,216), (1,214), (2,213), (3,210), (4,210), (5,207), (6,206), (7,202), (8,203), (9,202), (10,200)
Inserting these points into a calculator, the line of best fit is given as follows:
y = -1.62x + 215.64.
The estimate weight at the 15th week of the diet is the numeric value of the function when x = 15, that is, the lone instance of x in the function is replaced by 15, as follows:
y = -1.62(15) + 215.64 = 191.34 pounds.
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A ramp goes from a doorway of a building to the ground. The end of the ramp connected to the doorway is 1 foot above the ground. The distance along the ramp to the building is 5 feet. What is the angle of elevation of the ramp to the nearest degree?
A. 11°
B. 0°
C. 12°
D. 1°
Using the trigonometry ratio, he angle of elevation of the ramp to the nearest degree is 11°.
In the given question,
A ramp goes from a doorway of a building to the ground.
The end of the ramp connected to the doorway is 1 foot above the ground.
The distance along the ramp to the building is 5 feet.
We have to find the angle of elevation of the ramp to the nearest degree.
The distance is 5 feet.
The height is 1 foot.
To find the angle of elevation we used the trigonometry ratio.
According the trigonometry ratio, we know that tangent is the ratio between height and distance.
We can write it as
tan A=height/distance
Now putting the value
tan A=1/5
tan A=0.2
So A = arctan(0.2)
A = 11.30°
A ≈ 11°
Hence, the angle of elevation of the ramp to the nearest degree is 11°.
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Red- 5 skittles
Purple- 8 skittles
Yellow- 1 skittle
Orange- 2 skittles
Green- 4 skittles
Tomas reaches in a bowl and pulls out a green skittle. Without replacing the green skittle, what is the probability he picks a yellow skittle.
A. 1/100
B. 1/80
C. 1/95
D. 1/76
Answer:
I think its C. 1/95
Step-by-step explanation:
I am not sure this is the answer, i haven't done this math in ages so I'm a bit rusty so good luck on the test!
Given m=-1/2 and n= -1/3 which is greater
Answer: n is greater than m
Step-by-step explanation:
if m=-1/2 then that means its -.50 and n=-1/3 meaning its -.333(...)
so n is greater (remember its negative so higher numbers are actually lesser in value)
Hope this helped... :)
A store sells grapes for $1.99 per pound, strawberries for $2.50 per pound, and pineapples for
$2.99 each. Jonathan has $25 to buy fruit.
He plans to buy 2 more pounds of strawberries than grapes. He also plans to buy 2 pineapples.
The maximum number of whole pounds of grapes bought by Jonathan is 3 pounds.
What is meant by the term inequality?In mathematics, "inequality" describes the connection between two factors or values that aren't equal to one another.You can cross inequalities when they are connected. A will therefore be greater than c if an is larger than b and b is larger than c.For the given question;
The rate of grapes = $1.99 per pound
The rate of strawberries = $2.50 per pound
The rate of pineapples = $2.99 per pound
Let x be the number of pounds of grapes.
strawberries = x + 2
Total price paid by Jonathan = $25
Thus, the inequality becomes.
2(2.99) + 1.99x + 2.50(x + 2) ≤ 25
Solve the inequality to find the pounds of grapes.
5.98 + 1.99x + 2.5(x + 2) ≤ 25
x ≤ 3.11
x = 3
Thus, the maximum number of whole pounds of grapes bought by Jonathan is 3 pounds.
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The complete question is-
A store sells grapes for $1.99 per pound, strawberries for $2.50 per pound, and pineapples for
$2.99 each. Jonathan has $25 to buy fruit.
He plans to buy 2 more pounds of strawberries than grapes. He also plans to buy 2 pineapples.
If x represents the number of pounds of grapes, write an inequality in one variable that models this
scenario.
Determine algebraically the maximum number of whole pounds of grapes he can buy.
In Ty’s English class 70% of the students completed and essay by the due date there are 30 students in Ty’s English class how many completed the essay by the duet date?
21 students completed the essay by due date
What is unitary method ?In its simplest form, the unitary procedure is used to determine the value of a single unit from a given multiple. How to calculate the value of one pen, for example, if 40 cost Rs. 400. To finish it, using the unitary method. Additionally, after the value of a single unit has been established, we can multiply that value by the quantity of additional units required to establish the value of the additional units. This is typically how the concepts of ratio and proportion are used.
Calculation30 ----------> whole
30 ----------> 100 %
0.3 -----------> 1%
multiplying both sides by 70
21 ----------> 70 %
therefore 21 students completed the essay by due date .
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There are 90 new houses being built in a neighborhood.last month, 1/5 of them were sold. this month,1/3 of the remaining houses were sold. How many houses were left to be sold?
Step-by-step explanation:
1:
1/5 of 90 = 18 hours which are sold.Means are 72 houses left.
2.
1/3 of 72 =24 houses sold again. Sooo means there are 48 houses left to be sold
Approximate the following square root to the nearest integer.
√10~
Which of these types of angles have the same measure after being rotated, reflected, or translated in a coordinate plane?
I. Acute Angles
II. Right Angles
III. Obtuse Angles
a
I. II. and III.
b
I. and II. only
c
II. and III. only
d
I. only
The type of angles have the same measure after being rotated, reflected, or translated in a coordinate plane is a I. II. and III.
What is transformation?Transformation is a term used in mathematics to refer to the movements made by objects.
Transformation is basically of two major divisions
Rigid transformationnon rigid transformationNon rigid transformation are the transformation where the dimension or size of the object will be different from the image, example is dilation
In rigid transformation, the dimensions of the object is maintained through out the transformation examples of rigid transformation are
rotationreflectiontranslationSince the transformation types mentioned are all rigid transformation hence all the angles will remain same
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Consider the equation and the following ordered pairs: (1,y) and (x,−3).
6x+3y=15
Step 1 of 2 : Compute the missing x and y values so that each ordered pair will satisfy the given equation.
Answer
Keyboard Shortcuts
Complete the table below.
x y
row 11 Answer
row 2 Answer
−3
Answer:
(1,3)
(4,-3)
Step-by-step explanation:
To find y, replace x with 1 in the equation and solve for y
6x + 3y = 15
6(1) + 3y = 15
6 + 3y = 15 Subtract 6 from both sides
3y = 9 Divide both sides by 3
y = 3
(1,3)
To find x, replace y with -3 in the equation and solve for x
6x + 3y = 15
6x + 3(-3) = 15
6x - 9 = 15 Add 9 to both sides
6x = 24 Divide both sides by 6
x = 4
(4, -3)
If a circle has an Area of 84.9056, find the radius and the circumference of the circle.
(Use π=3.14 and do not round.)
Radius =
Circumference =
Answer: Radius is estimated to = 5.2
Circumference is estimated to = 32.66
Please Help!!!!
Kim and Tracy are collecting data for their final project in their psychology
class, in which they are conducting a survey about people’s overall job
satisfaction. They decide to go to the local mall to collect their data. To get a
more varied sample, Kim surveys shoppers coming out of store A, a discount
clothing store, while Tracy surveys shoppers coming out of store B, a high-end
boutique.
A. Identify a possible problem with this type of sampling method. (6 points)
B. How might Kim and Tracy improve on their sample design so as to get more
accurate information from the shoppers at the mall?
Answer:
below
Step-by-step explanation:
A problem would be that they are not surveying people from multiple places. They are doing it at 2 opposite stores, at the same times. They should try multiple different stores at other days and times to get more objective data.
Evaluate the given function for f (2).
The value of f(2) is 2.
What is graph function?
The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. We may alternatively say that the graph of f is the graph of y = f. (x). As a result, the graph of an equation is a particular instance of the graph of a function.
All y-coordinates of the graph function are an output of the graph function.
All x-coordinates of the graph function are an input of the graph function.
f(2) is an output of the function.
Here find the y-coordinates of the point on the graph when the value of x is 2.
(2,3) is a point on the graph.
Thus f(2) = 3
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What is the measure of each angle of a regular 22-gon? If necessary, round to the nearest tenth.
The measure of each angle of a regular 22-gon is 163.6 degrees.
How to find the sum of angles of a polygon?In geometry, a polygon can be defined as a flat or plane, two-dimensional closed shape bounded with straight sides.
Polygon can be named base on the number of sides they possess. For example pentagon has 5 sides, hexagon has 6 sides, heptagon has 7 sides, octagon has 8 sides, nonagon has 9 sides and decagon has 10 sides.
Therefore, a regular polygon is one which sides and angles are congruent.
A regular 22-gon has 22 sides.
The measure of each angle of 22-gon can be found as follows;
angle= 180(n - 2) / n
where
n = number of sides
angle = 180 (22 - 2) / 22
each angle = 180(20) / 22
each angle = 3600 / 22
Therefore,
each angle = 163.636363636
each angle = 163.6 degrees.
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Are These acute obtuse or right
What fraction is represented by .8 point is a blank which point represents 56 point blank represents 56
The fraction that represents 0.8 is 4/5 .
Fraction can be defined as a numerical quantity that is part of a whole number . it is written in the form of a/b , where a is called the numerator and b is called the denominator .
For Example , 1/2 , 3/8 4/9 are all fractions .
In the question ,
it is given that the point is 0.8 ,
we need to convert this point in fraction ,
the point 0.8 in fraction can be written as 8/10 ,
= 8/10
simplifying further ,
we get
= 4/5
Therefore ,The fraction that represents 0.8 is 4/5 .
The given question is incomplete , the complete question is
What fraction is represented by 0.8 ?
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8x - 6 = 2(4x-3)
Does the equation have one
none, or infinite solutions?
Explain why.
The given linear equation has only one solution i.e. x = 3/4
What is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
A linear equation in one variable has
(a) Only one solution
(b) Two solutions
(c) More than two solutions
(d) No solution
Here,
On solving we have 8x - 6 = 0 or x = 3/4. The above linear equation is only true if x = 3/4 and
Hence, the given linear equation has only one solution i.e. x = 3/4.
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Current Year Previous Year
Occupied Rooms 1,512 1,458
Total Rooms 1,800 1,800
The proportions of the total rooms that were occupied each year are:
The current year is 84%.The previous year is 81%.What is the proportion?Proportion is the fractional value of a variable when compared to the whole.
Proportions show the ratio or relative relationship between two or more values set as equal.
Like ratios, proportions are depicted in fractions, decimals, or percentages to show how two values compare.
Current Year Previous Year
Occupied Rooms 1,512 1,458
Total Rooms 1,800 1,800
Proportion of occupied rooms = 84% 81%
(1,512/1,800 x 100) (1,458/1,800 x 100)
Thus, on average, room occupancy for the two years is 82.5%, and proportionately for each year, it is 84% for the current year, while the previous year recorded 81%.
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Question Completion:What proportion of the total rooms were occupied each year?
Subtract and simplify.
With the help of subtraction we can say that the answer is =21/15
What is subtraction?The process of subtracting one number from another is called subtraction. The way to calculate the difference between two numbers is by using the basic arithmetic operation of subtraction, which is represented by the symbol (-).The operation of subtraction is used to calculate the difference between two numbers. If you remove a few items from a collection of things, the group will get smaller.Acc to the question-
32/15 - 11/15as the denominator is same21/15more simplifying we get = 1.4Hence,The answer is = 21/15
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Answer:
21/15
Step-by-step explanation:
Given problem,
→ (32/15) - (11/15)
Let's solve the given problem,
→ (32/15) - (11/15)
→ (32 - 11)/15
→ 21/15
Hence, the answer is 21/15.
The formula for distance is expressed as d = rt, where d is distance, r is the rate, and t is time.
How long would it take a car to travel 348 miles if it is traveling at a rate of 60 miles per hour?
hours
Answer:
5.8 hours
Step-by-step explanation:
First, you just plug it the given information.
Turn the equation to t=d/r by dividing the rate by both sides.
Plug it in 348miles/ 60 miles per hour
It'll take 5.8 hours for the car to travel 348 miles at the rate of 60 miles per hour.
Helppp it’s due tomorrow…
The carousel on the national mall has four rings of horses. Kiran is running on the inner ring, which has a radius of 9 feet. Mai is riding on the outer ring, which is 8 feet farther out from the center then the inner ring is. And one rotation of the carousel, how much farther does mai travel from Kiran. One rotation takes 12 seconds. How much faster does mai travel than kiran?
Answer:
50.24
Step-by-step explanation:
so u subtract the distanse not 9-4 u have to find a porportional ratio it was 100 - 50 or something add u get 50.24
tbh i didnt knw i just searched it up and im only in 6th grade so im not the the smartest in the world
i have no clue what the second on is so good luck with that
Which answer choice represents the difference of 20 and 3 times a number?
The difference of 20 and 3 times a number x is represented by 20 - 3x , the correct option is (c) .
In the question ,
it is given that
the number is x ,
we have to find the expression , that represents the difference of 20 and 3 times a number .
three times the number x is denoted by 3x .
and the difference of 20 and three times the number x is 20 - 3x .
the expression is (20 - 3x).
Therefore , The difference of 20 and 3 times a number x is represented by 20 - 3x , the correct option is (c) 20 - 3x .
The given question is incomplete , the complete question is
Which answer choice represents the difference of 20 and 3 times a number x ?
(a) 3x + 20
(b) 20(3x)
(c) 20 – 3x
(d) (20 · 3)x
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A group of 3 students plants 141 seeds. Each student plants the same number of seeds.
How many seeds does each student plant?
Write an expression you can use to solve
the problem.
Answer:
to find the answer you just need to divide 3 out of 141
141÷3=47seeds per each student
3x=141
x=141÷3
x=47
The equation is represented as A = S/3 , where S is the total number of seeds and A is the number of seeds planted by each student and the value of A = 47 seeds
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total number of seeds by each student be A
Now , the equation will be
The total number of seeds be S = 141 seeds
The number of students be n = 3 students
So , the total number of seeds planted by each student A = total number of seeds S / number of students n
A = S / n
Substituting the values in the equation , we get
Total number of seeds planted by each student A = 141 / 3
Total number of seeds planted by each student A = 47 seeds
Therefore , the value of A is 47 seeds
Hence , the number of seeds is 47 seeds
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