The statement "If point (x, y) is rotated 90 degrees about the origin, the resulting point is (-y, -x)." is incorrect.
The origin of the coordinate plane is the point (0, 0), and it is the center of rotation for many geometric transformations.
When a point (x, y) is rotated 90 degrees about the origin, the resulting point is (-y, x). This is because rotation by 90 degrees counterclockwise causes the x-coordinate to become the negative of the original y-coordinate and the y-coordinate to become the original x-coordinate.
To see this, imagine the point (x, y) on the coordinate plane and draw a line segment connecting the point to the origin. The length of this line segment is given by the Pythagorean theorem as the square root of x² + y². After rotating the point 90 degrees about the origin, the line segment will be perpendicular to the original line segment and have a length equal to y and -x.
In summary, rotating a point (x, y) at 90 degrees about the origin results in the point (-y, x) due to the change in the direction and length of the line segment connecting the point to the origin.
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Help!!! I need help I don't know how to do it
In the year 2000, the population of Mexico was about 100 million, and was growing by approximately 1.53% per year. At this growth rate, the function f(x)=100(1.0153)^x
gives the population, in millions, x
years after 2000. Using this model and a graph of the function, in what year would the population reach 111 million? Round your answer to the nearest year.
The solution is, The population would reach 111 million in next 7 years
What is an exponent in math?An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.
here, we have,
given that,
The initial population of Mexico was 100 million
The growth rate of the population is 1.53 %per year
Then the future population of Mexico is given by
P = P_0(1+r)^t
Where P = future population after t years
P_0= initial population
t = time period in years
Substituting the given vales in above equation we get
(1+ 0.0153)^t = 1.11
Taking log on both sides we get
t* log (1.0153) = log(1.11)
solving we get,
t = 6.87
≈ 7 years
The population would reach 111 million in next 7 years.
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Ted jogged a total of 11.2 miles in 4 days. He jogged the same distance each day.
Part A
How far did he jog each day? Enter your answer in the box.
2.8
miles
Part B
How many total miles would Ted jog if he continued to jog the same number of miles each day for 6 days? Enter your answer in the box.
miles? put answer bellow for part b
Answer: 16.8 miles
Step-by-step explanation:
Multiply 2.8 miles by 6 to find the number of miles jogged after 6 days.
Answer:
16.8 miles!
Step-by-step explanation:
What is the definition of covariance
Answer:
indicates the relationship of two variables whenever one variable changes.
Step-by-step explanation:
in the xy-plane, the lines y=3x-5 and y=-2x+10 intersect at a point (h,k). what is the value of k?
Answer:
(3,4)
k is 4
Step-by-step explanation:
See attached graph.
the longer diagonal of a field in the shape of a quadrilateral is 120 m and the length of the perpendiculars from the opposite vertex upon a longer diagonal is 20 m and 30 m find the area of the field Step by Step Explaination class 8 lesson no 11 mensuration
The area of the field is 900√10 m².
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
Quadrilateral ABCD.
The longer diagonal connects vertices A and C, and let E and F be the feet of the perpendiculars from vertices B and D to the longer diagonal AC.
From the figure,
BE = 20 m
DF = 30 m
AE = EC = 120/2 = 60 m
Now,
The area of the quadrilateral.
The area of a trapezoid.
= (sum of parallel sides) x (height) / 2
Using the Pythagorean theorem,
AB² = AE² + BE²
60² + 20² = 4000
AB = √(4000)
AB = 20 √10
And,
CD² = CE² + DF²
CD² = 60² + 30²
CD² = 4500
CD = √(4500)
CD = 15 √20
Now,
Area = AB + CD x 1/2 x AC
= 20√10 + 15√20 x 1/2 x 120
= 900√10
Therefore,
The area of the field is 900√10 m².
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f(x) = − ³/2 x and g(x) = (½)² – 1
-
Graph the functions on the same coordinate plane.
Let
What are the solutions to the equation
?
f(x) = g(x) ₂
The solution to the equations have the coordinates of (-6.61, 9.91) and (0.61, -0.91)
How to determine the solution to the system of equationFrom the question, we have the following parameters that can be used in our computation:
f(x) = − ³/2 x and g(x) = (½)² – 1
Express the equation properly
So, we have
f(x) = -3/2x
g(x) = (1/2x)^2 - 1
Next, we make a plot of the system to determine the solution
The point of intersection in the plot represent the solution to the equations
In this case, the point of intersection has a coordinate of (-6.61, 9.91) and (0.61, -0.91)
Hence, the solution is (-6.61, 9.91) and (0.61, -0.91)
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How do I solve this?
The given triangles are similar by SSS theorem
Similarity property of a triangleThe given figures are similar triangles with 3 sides and angles. There are several ways triangles can be proved to be similar such as the AAS, SSS, SAS etc theorems.
For the given triangles, if the ratio of their similar sides is equivalent to the same constant, then the triangles are similar.
AC/HF = AB/HG = CB/GF = k
84/14 = 72/12 = 48/8
84/14 = 6
72/12 = 6
48/8 = 6
Since the ratios are all equal, hence the triangles are similar
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The cost of putting on a play is $500 for the theater rental, $500 for the actors, and $750 for set decorations and costumes. If tickets are sold for $25 each, how many tickets need to be sold to reach the break-even point?
Answer:
The total cost of putting on the play is $500 for theater rental + $500 for actors + $750 for set decorations and costumes = $1750.
To reach the break-even point, the revenue from ticket sales needs to equal the total cost, so $1750 = $25 x (number of tickets sold).
Solving for the number of tickets sold, we can divide both sides by $25: $1750 / $25 = (number of tickets sold).
This gives us: 70 = number of tickets sold.
Therefore, Mr. Curry needs to sell 70 tickets to reach the break-even point.
Step-by-step explanation:
whats is 5.2r-2.4=8.7
The value of r is 2.134
in the equation, we would first
add 2.4
to both sides:
5.2r - 2.4 + 2.4 = 8.7+ 2.4
5.2r = 11.1
now we will
divide both sides by 5.2
to isolate the variable "r"
[tex]\frac{5.2r}{5.2} = \frac{11.1}{5.2}[/tex]
1r = 2.13461538
thus, the value of r = 2.134 approximately
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A company is designing a new cylindrical package. The volume of the package is 87.92 in.3. The radius is 2 inches. Use the formula V = Bh and 3.14 to approximate π
to answer the questions.
Part A
To the nearest inch, how many inches is the height of the cylindrical package?
Part B
The company decides to keep the radius the same and double the height. Rounded to the nearest hundredth, how many cubic inches is the new volume of the package?
The height of the cylindrical package is 6 inches.
The new volume of the package is 88.26 cubic inches.
What is a cylinder?A cylinder is a 3-D figure that has a radius and a height.
The volume of a cylinder is given as πr²h.
Example:
The volume of a cup with a height of 5 cm and a radius of 2 cm is
Volume.
= 3.14 x 2 x 2 x 5
= 62.8 cm³
We have,
Part A:
The formula for the volume of a cylinder is V = Bh, where B is the area of the base of the cylinder and h is its height.
For a cylinder with radius r and height h, the base area B is given by
B = πr².
Substituting the given values, we have:
V = Bh
87.92 = π(2²)h
h = 87.92 / (4π)
h ≈ 5.57
Rounding to the nearest inch, the height of the cylindrical package is 6 inches.
Part B:
If the company doubles the height of the cylinder while keeping the radius the same, the new height will be 2h = 2(5.57) = 11.14 inches.
The new volume can be calculated using the same formula:
V = Bh
V = π(2²)(11.14)
V ≈ 88.26 cubic inches
Rounding to the nearest hundredth, the new volume of the package is 88.26 cubic inches.
Thus,
The height of the cylindrical package is 6 inches.
The new volume of the package is 88.26 cubic inches.
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How do you calculate the arc length of a circle?
To calculate the arc length of a circle, you need to use the formula: arc length = (central angle in radians) x (radius)
where the central angle is measured in radians and the radius is the distance from the center of the circle to the edge. To use this formula, first convert the central angle from degrees to radians by multiplying it by π/180. Then, multiply the result by the radius to find the arc length. For example, if you have a circle with a radius of 5 units and a central angle of 45 degrees, you can calculate the arc length as follows: Convert the central angle to radians: 45 x π/180 = 0.7854 radians. Multiply the central angle in radians by the radius: 0.7854 x 5 = 3.927 unit. Therefore, the arc length of a circle with a radius of 5 units and a central angle of 45 degrees is 3.927 units.
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Urgent! Can you help me solve these 3 numbers with detailed steps please!
d) whenther there the limit is going to infinity like that
take the large term on the top and the largest one on the bottom
so;
4x^5/12x^2 =
basically if you continued to plug it in it would give you
4x^5/12x^2
eventually 12x^2 would = 24 because you would get 12x^2 to 24x^1, take the dervative = 24
for the top it would go from 4x^5; 20x^4; 80x^3
then you would have 80x^3/24
plug in infinity for x
infinity/24
What is the linear equation represented by the graph?
The linear equation represented by the graph is y = 8x.
Describe Linear equation?A linear equation is a mathematical equation that describes a straight line in a two-dimensional space. It can be written in the form of:
y = mx + b
where y and x are variables, m is the slope of the line, and b is the y-intercept of the line (the point where the line crosses the y-axis).
The slope, represented by "m", describes the steepness of the line, while the y-intercept, represented by "b", is the point where the line intersects with the y-axis.
Linear equations can also be written in other forms, such as the standard form:
Ax + By = C
where A, B, and C are constants, and x and y are variables. In this form, the equation describes a line in terms of its x and y intercepts.
Linear equations are used in a variety of fields, including mathematics, physics, engineering, economics, and more. They are useful for describing and predicting relationships between variables that exhibit a linear pattern.
The equation represented by the graph is a linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept.
To find the slope, we can use the formula:
m = (y2 - y1)/(x2 - x1)
Let's choose the first two points (0.5, 4) and (1, 8):
m = (8 - 4)/(1 - 0.5) = 8
So, the slope is 8.
To find the y-intercept, we can use the point-slope form of the equation:
y - y1 = m(x - x1)
Let's choose the point (0.5, 4) and the slope we just found:
y - 4 = 8(x - 0.5)
y - 4 = 8x - 4
y = 8x
So, the linear equation represented by the graph is y = 8x.
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The sum of deviations of the individual observations from their sample mean isO sometimes greater than and sometimes less than zero, depending on the observations O always less than zero O always greater than zero O We do not have enough info to answer this questionO always equal to zero
The sum of deviations of the individual observations from their sample mean is always equal to zero.
The sum of deviations of the individual observations from their sample mean is always equal to zero. This is because the sum of all the deviations is the sum of a positive and a negative value. When we add the negative value to the positive value, the net result is always zero.To illustrate this, let's take an example. Suppose we have a sample of 5 observations: 2, 4, 6, 8, 10. The mean of the sample is 6. The deviations of the individual observations from the sample mean can be calculated as follows:
2-6=-4
4-6=-2
6-6= 0
8-6= 2
10-6=4
When we add the deviations, we get: -4+(-2)+0+2+4=0. The sum of all the deviations is always equal to zero.
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Suppose the cumulative distribution function of the random variable X is F(x) = 0 when x<-2 , F(x) = .25x + .5 when -2 <= x < 2 and F(x) = 1 when 2<=x (<= means greater than or equal). Determine the following a. P(X<1.8) b. P(X>-1.5) c. P(X<-2) d. P(-1
the probability P(X<-2), we use the cumulative distribution function F(x) = 0 for x < -2. We plug in -2 for x in the function to get F(-2) = 0.
a. P(X<1.8) = .25(1.8) + .5 = .95
b. P(X>-1.5) = .25(-1.5) + .5 = .375
c. P(X<-2) = 0
d. P(-1.5<X<2) = .25(2) + .5 - (.25(-1.5) + .5) = .875
a. For the probability P(X<1.8), we use the cumulative distribution function F(x) = 0.25x + 0.5 for -2 <= x < 2. We plug in 1.8 for x in the function to get F(1.8) = 0.25(1.8) + 0.5 = 0.95. Therefore, P(X<1.8) = 0.95.
b. For the probability P(X>-1.5), we use the cumulative distribution function F(x) = 0.25x + 0.5 for -2 <= x < 2. We plug in -1.5 for x in the function to get F(-1.5) = 0.25(-1.5) + 0.5 = 0.375. Therefore, P(X>-1.5) = 0.375.
c. For the probability P(X<-2), we use the cumulative distribution function F(x) = 0 for x < -2. We plug in -2 for x in the function to get F(-2) = 0. Therefore, P(X<-2) = 0.
d. For the probability P(-1.5<X<2), we use the cumulative distribution function F(x) = 0.25x + 0.5 for -2 <= x < 2. We plug in -1.5 and 2 for x in the function to get F(-1.5) = 0.25(-1.5) + 0.5 = 0.375 and F(2) = 0.25(2) + 0.5 = 0.95. Therefore, P(-1.5<X<2) = 0.95 - 0.375 = 0.875.
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Find the range, IQR, and MAD of the data set.
15, 22, 16, 13, 14, 20, 40, 44
IQR = 16.5
The range = 31
Mean absolute deviation = 9.5
What is the median?The median is the value that splits the mathematical numbers or expressions in the half. The median value is the middle number of data points. to find the median first arrange the data points in ascending order.
Given:
A data set:
15, 22, 16, 13, 14, 20, 40, 44.
The lower half of median Q1 = (14 + 15)/2 = 14.5
The upper half of median Q3 = (40 + 22)/2 = 31
So IQR = Q3 - Q1 = 31 - 14.5 = 16.5
The range = 44 - 13 = 31
Mean absolute deviation = 9.5
Therefore, MAD = 9.5.
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PLEASE HELPPP
WILL GIVE BRAINLIEST!!!!!!
Julie is correct. If n=0 then you would get the fraction [tex]\frac{0}{0}[/tex] which is indeterminant (or undefined) since a zero is present in the denominator.
Suppose you translate the graph of y = 3/4 so that the new graph has asymptotes at x = -5 and y = 14. What is the equation for the
new graph?
Answer: The graph of y = 3/4 is a horizontal line with y-intercept at 3/4. When this graph is translated, its y-intercept changes, while its slope remains the same.
Since the new graph has asymptotes at x = -5 and y = 14, the new equation must be of the form y = m(x + 5) + 14, where m is the slope of the original line, which is 3/4. Substituting the values, we get:
y = (3/4)(x + 5) + 14
So the equation of the translated graph is y = (3/4)(x + 5) + 14.
Step-by-step explanation:
Pls help 23736 x 2858=?
Answer:
23736 x 2858
= 67837488
Step-by-step explanation:
You're welcome.
Answer:
67837488
Step-by-step explanation:
24 X 3 X 23 X 43 X 1429
How to Write 9 in Roman Numerals?
To write 9 in Roman Numerals, you would use the symbols "IX".
The symbol "I" represents the number 1 and the symbol "X" represents the number 10. When a smaller symbol is placed before a larger symbol, it means that the smaller symbol is subtracted from the larger symbol.
In this case, "I" is placed before "X", so it is subtracted from 10, giving us the value of 9.
Here is a step-by-step explanation:
1. Identify the symbols for 1 and 10: "I" and "X"
2. Place the smaller symbol before the larger symbol: "IX"
3. Subtract the smaller symbol from the larger symbol: 10 - 1 = 9
4. The result is the value of the Roman Numeral: "IX" = 9
Therefore, the Roman Numeral for 9 is "IX".
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Give three solutions to the equation y=1/2x+1
Answers:
(12, 7)
(20, 11)
(32, 17)
There are infinitely many possible answers.
=======================================================
Explanation:
The equation given to us is the same as y = 0.5x+1 because 1/2 = 0.5
If we replace x with even numbers, then we'll get whole number outputs for y.
Example: if x = 12, then y = 0.5x+1 = 0.5*12+1 = 7
This leads to (12,7) as one solution to this equation. A solution is a point that is on the line. Use graphing software like Desmos or GeoGebra to confirm.
Another example: if x = 20, then y = 0.5x+1 = 0.5*20+1 = 11. Therefore, another solution point is (20, 11)
Final example: If x = 32, then y = 0.5x+1 = 0.5*32+1 = 17. This gives the point (32,17)
There are infinitely many possible answers since we can replace x with infinitely many real numbers.
What is 10 percent of 20000?
To find 10 percent of 20000, you can multiply 20000 by 0.1, which gives you the answer of 2000.
0.1 × 20000 = 2000.
Here's the explanation of the calculation: When we want to find a certain percentage of a number, we can convert the percentage into a decimal by dividing it by 100. In this case, 10% is equivalent to 10/100, which simplifies to 0.1. Then, we can multiply 20000 by 0.1 to find the answer, which is 2000. In summary, to find 10% of a number, we can convert the percentage into a decimal by dividing it by 100, and then multiply the decimal by the original number.
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3.In an online quiz, positive points are awarded for a correct answer, and negative
points are awarded for an incorrect answer. Elena answers 10 questions correctly and
4 incorrectly and scores 42 points. Kiran answers 6 questions correctly and 8 incorrectly and scores 14 points.
a. Write a system of equations that describes Elena's and Kiran's scores. Usex to
represent the number of points for a correct answer and y to represent the
number of points for an incorrect answer.
that
X represents number of points and y represents incorrect answer
The system of equations can be written as:-
10x + 4y = 42
6x + 8y = 14
What is a system of equations?A system of equations, also known as a set of simultaneous equations or an equation system, is a finite set of equations for which we sought common solutions in mathematics. A system of equations can be classified in the same way that a single equation can.
Given that in an online quiz, positive points are awarded for a correct answer, and negative points are awarded for an incorrect answer. Elena answers 10 questions correctly and 4 incorrectly and scores 42 points. Kiran answers 6 questions correctly and 8 incorrectly and scores 14 points.
The system of equations can be written as:-
10x + 4y = 42
6x + 8y = 14
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Jayden measured a desk to be 4 feet. The actual measurement is 3.2 feet. What is Jayden's percent error?
The percentage error made by the person is 25%.
What is percentage error?To get the percentage error, multiply the relative error by 100%. In other words, first, calculate the difference between the true value and the measured value. Then, divide the obtained difference by the true value. Then take the absolute value of the obtained result and multiply it by 100%.
The measured value is 4 feet.
The true value is 3.2 feet.
So, the difference between the true value and the measured value is (4 feet - 3.2 feet), that is, 0.8 feet.
Now, divide the obtained difference by the true value.
(0.8 feet)/(3.2 feet) = 1/4
= 0.25
To get the percentage error, take the absolute value of the obtained result and multiply it by 100%.
|0.25|×100% = 0.25×100%
= 25%
Therefore, the obtained answer is 25%.
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PLEASE HELP! A horse's weight decreases by 1/2 pound per week. At this rate, how many weeks will it take for the horse to lose a total of 5 1/2 pounds? Write an expression that could be used to model the situation. State what strategy you will use to answer the question, explain your choice, then find the answer.
A) An algebraic expression that could be used to model the situation where a horse's weight decreases by ¹/₂ pounds weekly is w/r, where w is the total weight lost and r is the constant rate of weight loss.
B) Using division operation and decreasing rate, if a horse's weight decreases by ¹/₂ pounds weekly, it will take the horse 11 weeks to lose a total of 5¹/₂ pounds.
What is an algebraic expression?An algebraic expression combines constants, variables, and mathematical operations (+, -, ×, ÷) without the equal sign (=) found in equations.
While equations show the equality of expressions, algebraic expressions merely state values.
Division operation is one of the four basic mathematical expressions, including addition, subtraction, and multiplication.
Division operations involve the dividend, the divisor, the equal sign (=), the division operand (÷), and the result called the quotient.
The total weight loss over time = 5¹/₂ pounds
The constant rate of weight loss = ¹/₂ pounds per week
The number of weeks for the horse to lose 5¹/₂ pounds = 11 weeks (5¹/₂ ÷ ¹/₂).
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What does alpha 0.05 mean in stats?
An alpha value of 0.05 means that there is a 5% chance of incorrectly rejecting the null hypothesis.
In statistics, "alpha" is used to represent the significance level in a hypothesis test. The significance level, denoted by α, is the probability of rejecting the null hypothesis when it is actually true.
In other words, if the p-value in a hypothesis test is less than or equal to 0.05, we can reject the null hypothesis and conclude that there is a statistically significant difference between the groups or variables being tested.
An alpha value of 0.05 is commonly used in research studies, but other values such as 0.01 or 0.10 may also be used depending on the desired level of significance.
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An air navigation system spots two planes converging to a point at right angles and at colliding speeds. The planes are flying at 560 mph and 900 mph and are at 280 miles and 450 miles from the point, respectively. At what rate, in mph, is the distance between the planes decreasing?
The distance is decreasing at a rate of 1028.30 miles/hour.
What is Rate of Change?An indicator of how one quantity changes in proportion to another is called a rate of change. If x and y are the independent and dependent variables, respectively, then rate of change is equal to y-to-x conversions. Positive or negative change rates are possible.
Plane X: The first plane is due west of you, or at x = -280
traveling towards you at 560 mph
Plane Y: The second plane is due south of you, or at y = -450
traveling towards you at 900 mph.
D = Distance between the two planes.
D = √( x² + y² )
d/dt [ D ] = d/dt [ √( x² + y² ) ]
dD/dt = 1 / 2√( x² + y² ) (2XX' + 2YY')
dD/ dt = 1/2 √(-280)² + (-450)² (2 (-280)(560) + 2(-450)(900)
dD/ dt = 1/2 √(-280)² + (-450)² (2 (-280)(560) + 2(-450)(900))
dD/ dt = 1/ 530 (-140,000 - 405, 000)
dD/ dt = -1028.30
Thus, The distance is decreasing at a rate of 500 miles/hour
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Emily parents put $1,500 in her bank account for college tuition. At an interest rate of 8.25% compounded annually. What will be the total balance after 2 years?
Responses
$3,273.50
$3,273.50
$1,757.71
$1,757.71
$2,385.72
$2,385.72
$1,314.08
Answer:
B
Step-by-step explanation:
Using the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = final amount
P = principal (starting amount)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = time (in years)
We can plug in the given values:
P = $1,500
r = 0.0825 (8.25% expressed as a decimal)
n = 1 (compounded annually)
t = 2
A = $1,500(1 + 0.0825/1)^(1*2)
A = $1,500(1.0825)^2
A = $1,757.71
Therefore, the total balance after 2 years will be $1,757.71. Answer choice B is correct.
Marcy has 20$ she wants to buy a book that is marked down 30% from its original price of 28$ if the sales tax is 2.5% does marcy have enough money to buy the book
Answer:
yes
Step-by-step explanation:
if i did the math right marcy should have enough