Using the definition of the derivative, we have:
f'(a) = lim (h -> 0) [(f(a+h) - f(a)) / h]
We're asked to use the definition of the derivative, which includes the terms:
limit, h, f(a+h), f(a), and the fraction f(a+h) - f(a) / h.
The definition of the derivative of a function f(x) at a specific point x=a is given by:
f'(a) = lim (h -> 0) [(f(a+h) - f(a)) / h]
f(a+h) represents the value of the function f(x) at the point (a+h).
f(a) represents the value of the function f(x) at the point a.
f(a+h) - f(a) calculates the difference in the function values at these two points.
h is the small change in the x-coordinate (x-axis) between these two points, and we let h approach 0 to ensure we're finding the instantaneous rate of change.
(f(a+h) - f(a)) / h represents the average rate of change between the points (a, f(a)) and (a+h, f(a+h)).
By taking the limit as h approaches 0, we find the instantaneous rate of change at the point x=a, which is the derivative of the function f(x) at x=a.
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Clare bought her first home for $135,000 in 2001. In 2006, the value of real estate in her area had increased by 18%. Based on this, how much was Clare's home worth in 2006?
Answer:
To find the value of Clare's home in 2006 after an 18% increase, we can use the following formula:
Value in 2006 = Value in 2001 x (1 + Percent Increase)
Plugging in the values given in the problem, we get:
Value in 2006 = $135,000 x (1 + 0.18)
Simplifying this expression, we get:
Value in 2006 = $135,000 x 1.18
Value in 2006 = $159,300
Therefore, Clare's home was worth $159,300 in 2006 after an 18% increase in value from its original price of $135,000 in 2001.
You spend $124.54 at Walmart but have to pay the addition 8.5% sales tax. How much sales tax do you owe?
The sales tax owed on a $124.54 purchase at Walmart with an 8.5% sales tax rate is $10.59.
Suppose you spent $124.54 at Walmart and the sales tax rate is 8.5%. To calculate how much sales tax you owe, we first need to convert the sales tax rate from a percentage to a decimal. We do this by dividing the percentage by 100. So, the sales tax rate in decimal form is:
8.5% ÷ 100 = 0.085
Next, we multiply the purchase price by the sales tax rate in decimal form to calculate the amount of sales tax owed:
$124.54 × 0.085 = $10.59
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Satir Corp. reported the following information for 2013 and 2014.Salaries payable, December 31, 2013 $ 3,700Salaries payable, December 31, 2014 1,800Salaries expense--2014 57,000How much cash was paid for salaries during 2014?A. $55,100B. $55,200C. $57,000D. $58,900
Cash was paid for salaries during 2014 was $55,100. These are the formulas for calculating the cash salary received in 2014:
Salary paid in cash = Salary expense in 2014 - Reduction in salary payable
The difference between the balance due for salaries at the end of each year—that is, at December 31, 2013 and December 31, 2014—can be used to determine the decline in salaries payable:
Salaries payable at December 31, 2013, compared to salaries payable at December 31, 2014, are $3,700, $1,800, and $1,900, respectively.
The drop in the balance of salaries payable from 2013 to 2014 indicates that the business paid more compensation than it incurred for the year. As a result, the 2014 salary payments in cash are:
Cash paid for salaries equals salaries paid in 2014 less salaries payable, or $57,000 minus $1,900, or $55,100.
Hence, (A) $55,100 is the correct response.
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Given a quadratic equation in vertex form, find the vertex, axis of symmetry, whether the graph
opens up or down, the maximum or minimum, and the y-intercept. Graph it!
16. y = -2(x + 2)² +4
Vertex:
Axis of symmetry:
Opens: up
Maximum
down
Minimum
X=h A must write
x=
Max/Min Value:
The key features of the given quadratic equation include the following:
Vertex = (-2, 4)
Axis of symmetry: x = -2.
Direction of opening: downward.
There is a maximum (max) at 4.
y-intercept = (0, 0).
roots: x = -4 and x = 0.
What is the vertex form of a quadratic equation?In Mathematics and Geometry, the vertex form of a quadratic equation is modeled by this formula:
f(x) = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided about the graph of this quadratic equation, we can reasonably infer and logically deduce that its vertex can be determined as follows:
y = -2(x + 2)² +4
Vertex, (h, k) = (-2, 4)
Axis of symmetry, Xmax = -2.
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A salesman and 30% commission on all merchandise that he sells last month. He sold $700 worth of merchandise how much commission in dollars did he earn last month
Jennifer is flying a kite. She is looking up at the kite at an angle of elevation of 39°. If the
hand that is holding the kite string is 5.5 feet above the ground, what is the kite’s vertical
distance from the ground?
It is 36 inches from the top of her head to the kite (its the triangle hypotenuse)
The kite's vertical distance from the ground, with an angel of elevation 39° from the line of sight of Jennifer is equal to 7.4 feet.
What is an angle of elevationThe angle of elevation is the angle between the horizontal line and the line of sight which is above the horizontal line.
The kite's vertical distance from the ground is the sum of its vertical height from Jennifer's hand and the distance from the ground to the hand
we shall represent the vertical height of the kite from Jennifer's hand with the letter x so that;
x = 36 inches × sin 39°
x = 3 feet × sin 39° {36 inches = 3 feet}
x = 1.8880 feet
kite's vertical distance from the ground = 1.9 ft + 5.5 ft = 7.4 feet
Therefore, the kite's vertical distance from the ground, with an angel of elevation 39° from the line of sight of Jennifer is equal to 7.4 feet.
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Solve the differential equation.
dy/dx = 9x2y2
for y\neq0
The general solution to the differential equation is y = -1/(3x³ + C)
Where C is an arbitrary constant.
Solving the differential equation:
The concept used to solve this differential equation is the separation of variables. Separated the variables on either side of the equation and then integrated both sides to get the general solution with a constant of integration.
Note that, the solution is valid only for y ≠ 0 as the differential equation is undefined for y = 0.
Here we have
dy/dx = 9x²y²
Solve the differential equation using the separation of variables.
=> dy/dx = 9x² y²
Let's separate the variables by dividing both sides by y² and dx:
=> 1/(y²) dy = 9x² dx
Now we can integrate both sides:
=> ∫1/(y²) dy = ∫9x² dx
Using the power rule of integration, we get:
=> -1/y = 3x³ + C
Where C is the constant of integration.
To solve for y, we can multiply both sides by -1:
=> y = -1/(3x³ + C)
Therefore,
The general solution to the differential equation is y = -1/(3x³ + C)
Where C is an arbitrary constant.
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Mark Twain once said, "The secret of getting started is breaking your complex overwhelming task into small manageable tasks, and then starting on the first one. " How does this quote connect to the process you can use as a writer?
A. Divide the task into pieces and then chose just one to complete in order to write a good story. B. Find the steps a famous writer takes and follow them exactly. C. A well-written story relies on only one step and that is all you need to do as a writer. D. Breaking the story into pieces and then tackling them one at a time can help you as a writer
Mark Twain's quote about breaking down overwhelming tasks into manageable pieces is a valuable lesson for high school students, particularly when it comes to writing. (option d)
In the context of writing, this quote can be particularly helpful. Writing a story or essay can seem like a daunting task, but if you break it down into smaller pieces, it becomes much more manageable. This is where the process of outlining comes in. An outline is essentially a roadmap of your writing, breaking it down into smaller components that you can tackle one at a time.
In mathematical terms, you can think of this process as a series of equations. Each equation represents a small, manageable piece of the overall problem.
By breaking down the problem into smaller equations, you can solve each one individually, which ultimately leads to solving the larger problem. This is similar to how breaking down a writing project into smaller pieces can help you write a well-structured and coherent piece.
Hence the correct option is (d).
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what can be the maximum number of digits in the repeating block of digits in the decimal expansion 5/7
Answer: To find the decimal expansion of 5/7, we can perform long division as follows:
0.7│5.0
4 2
────
8 │ 30
28
───
20 │ 200
196
────
4
Hence, 5/7 = 0.714285... where the digits 714285 repeat indefinitely. To find the maximum number of digits in the repeating block of digits, we can observe that the repeating block will be at most 6 digits long because 7 has a factor of 2 and 5, and therefore 7 divides 10^6 - 1 = 999999.
In fact, we can see that the repeating block in this case has 6 digits, since the digits 714285 repeat indefinitely, and there are 6 digits in this repeating block. Therefore, the maximum number of digits in the repeating block of digits in the decimal expansion of 5/7 is 6.
Step-by-step explanation:
about how much money
The cost of the car with 60,000 miles would be = $13,000 approximately.
How to determine the cost of cars according to mileage?To calculate the cost of the car form the given graph above is to draw a straight line that connects most of the points of interception.
From the graph, the most appropriate point of interception would be on $13,000 since each line in y-axis represents a thousand dollars.
Therefore, the cost of the car with 60,000 miles would be = $13,000 approximately.
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A recent conference had 750 people in attendance. In one exhibit room of 70 people, there were 18 teachers and 52 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 193 principals in attendance.
There were about 260 principals in attendance.
There were about 557 principals in attendance.
There were about 680 principals in attendance.
There were about 557 principals in attendance based on the prediction
Predicting the number of principals in attendance at the conference?To make a prediction about the number of principals in attendance at the conference, we can assume that the proportion of principals in the exhibit room is similar to the proportion of principals in the whole conference.
In the exhibit room, out of 70 people, 52 were principals.
So, the proportion of principals in the exhibit room was 52/70
We can predict the number of principals in attendance at the conference as follows:
Number of principals = proportion of principals x total number of attendees
If we plug in the values, we get:
number of principals = 52/70 x 750 = 557
So, based on this prediction, we can say that there were 557 principals in attendance at the conference.
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If the mRP = 130 , what is the measure of RSP
Answer:
230°
Step-by-step explanation:
Because Arc RSP had three letters that means its a major arc or greater than 180°
Arc RP is the portion of the circle not intercepted by the angle so 360 minus the measure of RP is RSP
360 - 130 = 230
A couple gets financing for 80% of the $150,000 purchase price of a house at the rate of 6% on the monthly unpaid balance. Use the table provided to find the total amount paid to the finance company if the loan is repaid in 40 years. A 5-column table with 4 rows titled Monthly Payments per 1000 dollars of mortgage. Column 1 is labeled Interest Rate (percent) with entries 5, 5.5, 6, 6.5. Column 2 is labeled 10 Years with entries 10.61, 10.86, 11.11, 11.36. Column 3 is labeled 20 years with entries 6.60, 6.88, 7.17, 7.46. Column 4 is labeled 30 years with entries 5.37, 5.68, 6.00, 6.33. Column 5 is labeled 40 years with entries 4.83, 5.16, 5.51, 5.86. a. $231,948.00 c. $317,376.00 b. $289,005.00 d. $141,509.00
The total amount paid to the finance company if the loan is repaid in 40 years is $317,376.00 (option c).
First, we need to find out how much money the couple borrowed. Since they got financing for 80% of the $150,000 purchase price, they borrowed $120,000 ($150,000 x 0.8 = $120,000).
Next, we need to find the monthly interest rate. Since the interest rate is 6% per year, the monthly interest rate is 0.06/12 = 0.005.
Now we can use the table to find the monthly payment per $1000 of mortgage for a 40-year loan with a 6% interest rate. Looking at the fifth column of the table, we find the entry that corresponds to a 6% interest rate and a 40-year loan, which is 5.86. This means that for each $1000 borrowed, the monthly payment is $5.86.
To find the monthly payment for the couple's $120,000 loan, we multiply the monthly payment per $1000 by 120 (since they borrowed $120,000). So the monthly payment is 5.86 x 120 = $703.20.
Finally, we need to calculate the total amount paid to the finance company over the 40-year period. Since the couple will make 12 payments per year for 40 years, the total number of payments will be 12 x 40 = 480. So the total amount paid will be the monthly payment ($703.20) multiplied by the total number of payments (480). This gives us a total of $317,376.
Therefore, the correct option is (c).
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29°
82°
18m
18 m
Find the perimeter
The perimeter of the figure is 38.52.
We have,
The perimeter of the figure:
Side + 18 + 18
From the figure,
82 + 90 + x = 180
172 + x = 180
x = 180 - 172
x = 8
Now,
Using trigonometric identities Sin.
Sin 8 = Side/18
0.14 = side/18
side = 0.14 x 18
side = 2.52
Now,
The perimeter of the figure.
= Side + 18 + 18
= 2.52 + 18 + 18
= 38.52
Thus,
The perimeter of the figure is 38.52.
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True or False?
When Samantha includes more batteries in her project, the current in her project increases. Current is the independent variable in this situation
Answer:
true
Step-by-step explanation:
You rolled a number cube 20 times, you get three 14 times. What is the experimental probability that you will roll a three on your next roll?
The experimental probability that you will roll a three on your next roll is 70%.
To calculate the experimental probability of rolling a number three on the next roll, we need to use the data given in the problem. Out of the 20 rolls that were performed, the number three was rolled 14 times.
The experimental probability is calculated by dividing the number of times the event occurred (in this case, rolling a number three) by the total number of trials.
So, the experimental probability of rolling a number three on the next roll is:
14/20 or 7/10
This means that based on the data from the previous 20 rolls, there is a 70% chance of rolling a number three on the next roll.
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MAKE THE FOLLOWING STATEMENTS ABOUT EXPONENTS TRUE.
--- When multiplying polynomials with the same base,
[Select]
the coefficients.
---
When dividing polynomials with the same base, [Select]
[Select]
[Select]
✓the coefficients.
--- When raising a power to a power, distribute the exponent by [Select]
and applying the exponent to the coefficient.
--- When raising anything to the Zero power, the answer will be [Select]
-- When raising anything to the 1st power, the answer will be [Select]
exponents and
exponents and
exponents
--- When trying to leave a variable without a negative exponent, you should flip the position of the variable
to the reciprocal and [Select]
✓the negative exponent.
Need help with this question!
Answer:
[tex]r = \sqrt{ {3}^{2} + {( - 7)}^{2} } = \sqrt{9 + 49} = \sqrt{58} [/tex]
[tex] {x}^{2} + {y}^{2} = 58[/tex]
-x² + 2x + x - 3x = -9 + 2 + 6
The solution for the equation -x² + 2x + x - 3x = -9 + 2 + 6 is derived to be x = 1
How to solve for the value of x in the equationWe shall solve for x by simplifying the equation and making x the subject as follows:
-x² + 2x + x - 3x = -9 + 2 + 6
-x² + 3x - 3x = 8 - 9
-x² = -1
multiply both sides by -1 we have;
x² = 1
take square root of both sides
x = √1
x = 1
Therefore, the equation -x² + 2x + x - 3x = -9 + 2 + 6 will have a solution for the value of x = 1
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50 *1,967 also solve this 50* 1,000
Do not use a calculator.
Answer: 50 * 1,967 = 98,350
50 * 1,000 = 50,000
Step-by-step explanation: 50 * 1,967 = 50 * 1,000 + 50 * 967 = 50,000 + 48,350 = 98,350.
What do all products of the square of binomial have in common?
The square of binomial have in common is x² - 14x + 49
The first two products you have given, (x + 9)(x + 9) and (x - 7)(x - 7), are examples of the square of a binomial. To find the product of two binomials, we use what's called the FOIL method. FOIL stands for First, Outer, Inner, Last, and it's a way to remember the steps involved in multiplying two binomials.
When we multiply (x + 9)(x + 9), we first multiply the first terms in each binomial: x * x = x². Then we multiply the outer terms: x * 9 = 9x. Next, we multiply the inner terms: 9 * x = 9x. Finally, we multiply the last terms in each binomial: 9 * 9 = 81. So, putting it all together, we get:
(x + 9)(x + 9) = x² + 9x + 9x + 81
= x² + 18x + 81
Similarly, when we multiply (x - 7)(x - 7), we get:
(x - 7)(x - 7) = x² - 7x - 7x + 49
= x² - 14x + 49
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Complete Question:
Find each product. (x + 9) (x + 9) , (x - 7)(x - 7) (2x - 1 )²
a. What do all products of the square of a binomial have in common?
calculate the z-score for a data value of 80 in a data set with a mean of 52 and a standard deviation of 9. round your answer to the nearest tenth.
The z-score for a data value of 80 in a data set with a mean of 52 and a standard deviation of 9 is approximately 3.1.
The formula for calculating the z-score is:
z = (x - μ) / σ
where x is the data value, μ is the mean, and σ is the standard deviation.
Substituting the given values, we get:
z = (80 - 52) / 9 = 3.11 (rounded to two decimal places)
Therefore, the z-score for a data value of 80 in a data set with a mean of 52 and a standard deviation of 9 is approximately 3.1.
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The z-score for a data value of 80 in this data set is approximately 3.1.
Calculate the z-score for a data value of 80 in a data set with a mean of 52 and a standard deviation of 9.
To find the z-score, follow these steps:
Identify the data value (x), mean (µ), and standard deviation (σ).
In this case, x = 80, µ = 52, and σ = 9.
Use the z-score formula:
z = (x - µ) / σ
Plug in the values:
z = (80 - 52) / 9
Perform the calculations:
z = 28 / 9
Round the answer to the nearest tenth: z ≈ 3.1
So, the z-score for a data value of 80 in this data set is approximately 3.1.
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s
Glossary
Calculators Graph Paper
The graph of a linear function is shown on the grid.
Translate
g(x) =
Speak
I+
Line Reader Strikethrough Highlight Sticky Notes
A four quadrant graph with a line that slants down from left to right. The line passes through the points ordered pair (0, 2)
and ordered pair (6, 0).
Which function is best represented by this graph?
Complete the function by selecting the correct answers from the drop-down menus.
Review
Help
The linear function going through the points (0,2) and (6,0) is given as follows:
y = -x/3 + 2.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.When x = 0, y = 2, hence the intercept b is given as follows:
b = 2.
When x increases by 6, y decays by 2, hence the slope m is given as follows:
m = -2/6
m = -1/3.
Thus the equation of the line is given as follows:
y = -x/3 + 2.
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A building contains for offices square force the side length of the office is 18 feet which is a total area of the four offices
The total area of the four offices in the building is 1296 square feet.
When we talk about the area of a shape, we are referring to the amount of space that it occupies. In this case, since the offices are squares, we can find the area of each office by multiplying the length of one side by itself. This is represented by the formula A = s², where A is the area and s is the length of one side.
So, if each office has a side length of 18 feet, we can find the area of one office by plugging that value into the formula: A = 18² = 324 square feet.
Since there are four offices, we can find the total area of all four offices by multiplying the area of one office by 4: 324 square feet x 4 = 1296 square feet.
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If events X and Y are independent, then find P(X and Y). P(X)= 2/3 and
P(Y) = 3/4
O 17/12
O 5/7
O 1/2
O 1/4
Answer:
1/2
Step-by-step explanation:
Since the events are independent, P(A and B) = P(A) * P(B)
P(X and Y) = P(X) * P(Y)
= 2/3 * 3/4
= 2/4
= 1/2
Lines a and bare perpendicular. The equation of line a is y=x+3. What is the
equation of line b?
lines a and b are perlendicularr and the equation of line a is y=x+3.Therefore, after calculation, the equation of line b is y = -x + 3.
What is Perpendicular?Perpendicular refers to a line, ray, or segment that intersects another line or segment at a right angle, or 90-degree angle. The point of intersection is called the point of perpendicularity and is equidistant from the endpoints of the segment.
What is equation of line?An equation of a line is a mathematical representation of a straight line. It can be written in various forms, including slope-intercept form, point-slope form, and standard form, and relates the variables x and y.
According to the given information:
If line a has the equation y = x + 3 and line a is perpendicular to line b, then the slope of line b is the negative reciprocal of the slope of line a.
The slope of line a is 1, so the slope of line b is -1/1, which simplifies to -1.
To find the equation of line b, we need to find the y-intercept (b) using the point-slope form of a linear equation. We can choose any point on line b, but since we don't have any specific point given, we can use the y-intercept of line a, which is 3.
So, the equation of line b is y = -x + 3.
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14. The dimensions of a concrete basketball court and
163
the volume of the concrete pad?
31/
yards. The thickness of the concrete pad is
9
48 yd.
58 yd."
497 yd
522-y
yd?
yards by
yard. What is
The thickness of the concrete pad is 58 and 2/81 yd³. So correct option B.
Describe Volume?Volume is the measure of the amount of space occupied by a three-dimensional object or substance. It is typically measured in units such as cubic meters, cubic feet, liters, or gallons. The formula for calculating the volume of a simple shape like a cube, rectangular prism, or cylinder involves multiplying its length, width, and height or its base area and height. More complex shapes may require more advanced formulas or techniques for determining their volume. Volume is an important concept in many fields, including physics, engineering, architecture, and chemistry, and is often used to measure quantities such as liquids, gases, and solids.
To find the volume of the concrete pad, we need to multiply the length, width, and thickness of the pad.
First, we need to convert the dimensions to yards by dividing by 3 since there are 3 feet in a yard:
Length: 31 and 1/3 yards = 94/3 yards
Width: 16 and 2/3 yards = 50/3 yards
Thickness: 1/9 yard
Now we can calculate the volume:
V = (94/3) * (50/3) * (1/9)
V = 4700/81 cubic yards
V ≈ 58.02 cubic yards
Therefore, the answer is B. 58 and 2/81 yd³.
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The complete question is:
system of equations find the cost each treat please
The costs of each treat are
cookies = 6.48, ice cream 1 = 8.98 and ice cream 2 = 10.25cookies = 1.19, ice cream 1 = 2.99 and ice cream 2 = 4.99Finding the cost of each treat using system of equationsTo solve this, we use the followign representations
x = cookies
y = ice cream 1
z = ice cream 2
Treat 1
Using the columns to generate the system of equations, we have
x + y + z = 25.71
z + 2x = 23.21
3y = 26.94
So, we have
y = 8.98
The other equations become:
x + 8.98 + z = 25.71
z + 2x = 23.21
When solved, we have
x = 6.48
z = 10.25
Treat 2
Using the rows to generate the system of equations, we have
x + 2y = 7.17
y + 2x = 5.37
3z = 14.97
So, we have
z = 4.99
The other equations when solved, we have
x = 1.19
y = 2.99
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Which equation shows how to find p, the price mrs. Mersin paid for the car
An equation which shows how to find p, the price Mrs. Merson paid for the car include the following: B) 5500/p = 55/100.
What is price?In Mathematics and Science, a price can be defined as an amount of money which is primarily set by the seller of a product, and it must be paid by a buyer to the seller, so as to enable the acquisition of this product.
Based on the information provided about the amount of money that Mersin paid for the car, an equation which shows how to find the price (p) is given by;
55% of p = 5500
55/100 × p = 5500
5500/p = 55/100
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Complete Question:
Mrs. Merson is selling her car. Her research shows that the car has a current value of $5,500,
which is 55% of the amount Mrs. Merson paid for the car. A buyer wants to know the price
Mrs. Merson paid for the car.
• Which equation shows how to find p, the price Mrs. Merson paid for the car?
A) 55/p = 5500/100
B) 5500/p = 55/100
C) p/5500 = 55/100
D) p/5 = 5500/100
Identify the unit rate shown in the graph. A graph is shown.
A. $7 per hour B. $9 per hour C. 7 hours per $1 D. 9 hours per $1
Answer:
A
Step-by-step explanation:
it cant be 9 per hour cuz it is a smaller amount and A is the only one that makes sens