Tabi's bill includes $248.94 in charges and $34.99 in interest.
Let x be the amount of interest that Tabi was charged, in dollars.
According to the problem, the new charges are $213.95 more than the interest, so the amount of new charges is x + $213.95.
The total bill, which includes the charges and interest, is $283.93.
Therefore, we can write an equation:
x + (x + $213.95) = $283.93
Simplifying and solving for x, we get:
2x + $213.95 = $283.93
2x = $69.98
x = $34.99
So the amount of interest charged is $34.99.
To find the amount of charges, we can use the equation for new charges:
x + $213.95 = $34.99 + $213.95 = $248.94
So the amount of charges is $248.94.
Therefore, Tabi's bill includes $248.94 in charges and $34.99 in interest.
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Each of the following functions f,g,h, and h represents the amount of money in a bank account in dollars as a function of time x, in years they are each written in form m(x)= a•b
Answer:
f(x) : exponential growth
g(x); exponential growth
h(x): exponential growth
j(x): exponential decay
Step-by-step explanation:
In an exponential function such as
[tex]m(x) = a \cdot b^x[/tex]
the factor that determines whether it is a growth or decay function depends entirely on the value of b since x cannot be negative
If b > 1, it is a growth function
If b < 1 then it is a decay function
If b = 1 neither growth or decay function values are constant
In this context
f(x) has b = 2 > 1 . Hence it is a growth function
g(x) has b = 3 > 1 hence growth function
h(x) has be = 3/2 > 1; hence growth function
j(x) has be = 0.5 < 1 hence decay function
Answer:
O f(x) : exponential growth
O g(x); exponential growth
O h(x): exponential growth
O j(x): exponential decay
Step-by-step explanation: I used to do this before :)
Consider the following function.
h(x)=(x−4)2−1
Step 2 of 4 : Find the x-intercepts, if any. Express the intercept(s) as ordered pair(s).
PLEASE HELP WILL GIVE BRAINLISET AND 60 PTS !
Answer:13)2,4,6,8
14)x=3
Step-by-step explanation:
13) you should make it equal to numbers inside bracket {}.
for example,
1.-6x+11=-37
-6x=-37-11=-48
x=8
2.-6x+11=-25
-6x=-36
x=6
3.-6x+11=-13
-6x=-24
x=4
4.-6x+11=-1
-6x=-12
x=2
14)f(x)=13
f(x)=3x+4=13
3x=9
x=3
timmy has 3,000 miles on his car. he drives 38 miles each day. write a linear model to represent the situation
Answer:
38
Step-by-step explanation:
Let x represent the number of days Timmy has been driving his car since he had 3,000 miles on it. Then, his total mileage can be represented as:
Total mileage = 3,000 + (38 × x)
This is a linear model, because the relationship between the total mileage and the number of days driven is a straight line with a constant slope of 38. The y-intercept of this line is 3,000, which represents the initial mileage on Timmy's car. The slope of 38 indicates that the car is being driven 38 miles further each day, which corresponds to the rate of change in the total mileage.
Solve the system
0.2y=4.6x+1.2
-2.3x=-0.1y+0.6
will the signs be reversed each time in algebraic expansion?
That note about "both signs have been reversed" only applies to the example on the right side, where –4 was distributed into the expression in parentheses.
Notice on the left example, the signs were not reversed.
When you distribute a negative number, that's when the signs will reverse. Since you're distributing a negative number, you'll be multiplying each term in parentheses by a negative number and that negative is what reverses the sign on every term.
So, yes all of the signs will be reversed each time you distribute a negative number into the parentheses, but not if you distribute a positive number.
The graph of f ( x ) = − 1 /2 ( 1 /2 ) ^x − 3 + 5 is shifted downwards 5 units, and then shifted left 3 units, stretched vertically by a factor of 4 , and then reflected about the x -axis. a . What is the equation of the new function, g ( x ) ? g ( x ) = b . What is the y -intercept? ( , ) c . What is the domain? d . What is the range?
Answer: a. To shift the graph downwards 5 units, we subtract 5 from the function, to shift it left 3 units, we add 3 to the input (the x-value), to stretch the graph vertically by a factor of 4, we multiply the function by 4, and to reflect it about the x-axis, we multiply the entire function by -1. Thus, the new function is:
g(x) = -4(1/2)^(x+3) - 5
b. To find the y-intercept, we set x=0 in the equation and solve for y:
g(0) = -4(1/2)^(0+3) - 5 = -9
Thus, the y-intercept is (0, -9).
c. The domain of the function g(x) is all real numbers, since there are no restrictions on the input x.
d. The range of the function g(x) is (-∞, -5], since the function is shifted downwards 5 units and stretched vertically by a factor of 4, which means that the maximum value of the function is -5, and it can take any value less than or equal to -5. The reflection about the x-axis does not change the range.
Step-by-step explanation:
rolling a number greater than 0 but less than 7
Probability of rolling a number greater than 0 but less than 7 is 1.
Define probability?The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. Probability is the ability to happen. The subject of this area of mathematics is the occurrence of random events. From 0 to 1 is used to express the value. To forecast how likely occurrences are to occur, probability has also been introduced in mathematics.The probability formula is as follows:
Probability = Favourable outcomes / Total outcomes
Sample space of rolling a dice:
S = {1, 2, 3, 4, 5, 6}
Total outcomes = 6
Favourable outcomes: number greater than 0 but less than 7
Favourable outcomes: 6
Then, probability of rolling a number greater than 0 but less than 7
Probability = Favourable outcomes / Total outcomes
Probability = 6/6
Probability = 1
Thus, probability of rolling a number greater than 0 but less than 7 is 1.
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The complete question is-
A dice is being rolled. Find the probability of rolling a number greater than 0 but less than 7
You need a 35% alcohol solution. On hand, you have a 245 mL of a 10% alcohol mixture. You also have 70% alcohol mixture. How much of the 70% mixture will you need to add to obtain the desired solution?
You will need mL of the 70% solution
to obtain mL of the desired 35% solution.
Using percentage, we can get that 7ml of the 70% solution will be needed.
What do you mean by percentage?A percentage's denominator, often referred to as a ratio's or a fraction's, is always 100. Sam, for instance, would have gotten 30 out of a potential 100 points if his math test score had been 30%. It is written as 30:100 in ratio form and 30/100 in fraction form.
In this context, "%" is read as "percent" or "percentage" to represent a percentage. By "division by 100," the percent symbol can always be changed to a fraction or decimal equivalent.
In the given question we get the equation,
35(245) + 0.75x = 0.4(245+x) = 98 + 0.4x
85.75 + 0.75x = 98 + 0.4x
0.35x = 98-85.75 = 12.25
x = 12.25/.35 = 35 mL of 75% solution
mixed with 245 mL of 35% it yields 280 mL of 40% so,
35 is within 5 of 40
75 is within 35 of 40
35/5 = 7
245/35 = 7
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If x = 11 degrees, how many degrees is Angle y? (Include only numerals in your response.)
Answer:
79 degrees
Step-by-step explanation:
[tex]x + y = 90 \: degrees \\ 11 + y = 90 \\ y = 90 - 11 \\ y = 79 \: degrees[/tex]
You've just finished making 3 batches of plastic tumblers: a red batch, a yellow batch, and a purple batch. There are 500 tumblers in each batch. You are now making sets of 3 tumblers that contain 1 tumbler of each color. How many sets can you make?
Answer: Since there are 500 tumblers in each batch, there are a total of:
500 tumblers/batch × 3 batches = 1500 tumblers
To make a set of 3 tumblers with one tumbler of each color, we can choose one tumbler from each batch. There are 500 choices for the tumbler from the red batch, 500 choices for the tumbler from the yellow batch, and 500 choices for the tumbler from the purple batch. Therefore, there are:
500 choices for the first tumbler × 500 choices for the second tumbler × 500 choices for the third tumbler = 500^3 = 125,000,000 possible sets of 3 tumblers.
However, we are interested in the number of sets that can be made from the available tumblers. Each set requires one tumbler from each batch, and since there are 500 tumblers in each batch, we can make:
500 sets/batch = 500 sets/batch × 3 batches = 1500 sets
Therefore, we can make a total of 1500 sets of 3 tumblers from the available tumblers.
Step-by-step explanation:
Given △
PQR, drag the correct side lengths to complete the table.
Right triangle P Q R has R as its right angle. A segment is drawn from R to S on side P Q. Angle P S R is a right angle.
PQ and PSPS and QSQR and QSPQ and QSPR and QS
Side Lengths Geometric Mean
RS
PR
QR
The correct side lengths to complete the table are RS: Geometric mean of PR and QR, PR: Geometric mean of RS and QR and QR: Geometric mean of PR and RS.
What is Geometric?Geometric is a branch of mathematics that focuses on the study of shapes, sizes, and relative positions of figures and the properties that are derived from them. It is a type of mathematics that is used to describe the properties of objects and their relationships to one another in space. Geometry is also used to describe the movement of objects in space.
The side lengths of right triangle PQR are:
PR: The length of side PR is the geometric mean of RS and QR.
QR: The length of side QR is the geometric mean of PR and RS.
RS: The length of side RS is the geometric mean of PR and QR.
PQ: The length of side PQ is the hypotenuse of the right triangle PQR.
PS: The length of side PS is the hypotenuse of the right triangle PSR.
QS: The length of side QS is the hypotenuse of the right triangle QSR.
Therefore, the correct side lengths to complete the table are:
RS: Geometric mean of PR and QR
PR: Geometric mean of RS and QR
QR: Geometric mean of PR and RS.
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please help!! i have no idea how to do this.
hi!
first, you have to graph the piecewise function. a piecewise function is basically where there are multiple different lines, but they all have different sections on the graph that they are applicable.
on the graph, graph the first equation, in the piecewise function, which is y= -3x + 2.
then, you have to erase all parts except the segment between x=-1 and x=1. at the endpoints, place a filled in dot to mark the point.
do the same with y = x - 2, however, this time, the restraints are at x=1 and x=3. you'll see that the endpoint at x=1 coincides with the previous equation! for the endpoint on the side of x=3, you should place another filled in dot to mark that it includes x=3.
i've attatched a screenshot below (scroll down a bit!) of what the graph should look like, in case that was confusing :)
next, you can fill in the table by finding what the function outputs for the given x. for the first one, x = -3. first, look at the function. is x between -1 and 1, or between 1 and 3? neither. that means that it is no solution for that point.
continue down the table. it is the same with x=-2.
next, x = -1. this is in the interval of -1<=x<=1, so you should look at the first equation in the piecewise function, which is 2-3x. if we plug in -1 for x, we get 2 - 3(-1) = 2+3 = 5. this means that the point is (-1, 5). you should make sure that this is a point that you plotted on the graph, and if not, the graph is wrong :(
continue down the table and keep doing that!
next question is if there is a min or max. there is! as you can see, the piecewise function only goes from x=-1 through x=3, and all other values give a no solution output. so, the minimum is -1 and the maximum is 3.
next: turning point or vertex. this would be at the point when x = 1, since that would be where the graph changes direction. the vertex is at (1, -1).
the zeroes of the function is where the graph crosses the x-axis. this means that y=0. we can see that this happens when x=2/3 and when x=2.
i hope this was helpful! :)
Lloyd is a divorce attorney who practices law in Florida. He wants to join the American Divorce Lawyers Association (ADLA), a professional organization for divorce attorneys. The membership dues for the ADLA are $550 per year and must be paid at the beginning of each year. For instance, membership dues for the first year are paid today, and dues for the second year are payable one year from today. However, the ADLA also has an option for members to buy a lifetime membership today for $5,000 and never have to pay annual membership dues.
Obviously, the lifetime membership isn’t a good deal if you only remain a member for a couple of years, but if you remain a member for 40 years, it’s a great deal. Suppose that the appropriate annual interest rate is 7.5%. What is the minimum number of years that Lloyd must remain a member of the ADLA so that the lifetime membership is cheaper (on a present value basis) than paying $550 in annual membership dues? (Note: Round your answer up to the nearest year.)
21 years
18 years
14 years
12 years
In 1626, Dutchman Peter Minuit purchased Manhattan Island from a local Native American tribe. Historians estimate that the price he paid for the island was about $24 worth of goods, including beads, trinkets, cloth, kettles, and axe heads. Many people find it laughable that Manhattan Island would be sold for $24, but you need to consider the future value (FV) of that price in more current times. If the $24 purchase price could have been invested at a 4.5% annual interest rate, what is its value as of 2018 (392 years later)?
$987,122,447.84
$635,647,030.80
$859,993,041.68
$747,820,036.24
Answer:
For the lifetime membership to be cheaper than paying $550 in annual membership dues, we need to calculate the present value of the lifetime membership and compare it to the present value of the stream of annual payments.
The present value of the lifetime membership can be calculated using the formula for the present value of a lump sum:
PV = FV / (1 + r)^n
where FV is the future value (which is the cost of the lifetime membership today, $5,000), r is the annual interest rate (7.5%), and n is the number of years for which we want to calculate the present value.
The present value of the stream of annual payments can be calculated using the formula for the present value of an annuity:
PV = A * [(1 - (1 + r)^-n) / r]
where A is the annual payment ($550), r is the annual interest rate (7.5%), and n is the number of years for which we want to calculate the present value.
We need to find the minimum number of years for which the present value of the lifetime membership is less than the present value of the stream of annual payments. We can do this by setting the two present values equal to each other and solving for n:
5000 / (1 + 0.075)^n = 550 * [(1 - (1 + 0.075)^-n) / 0.075]
Solving this equation gives n ≈ 18.7 years. Rounded up to the nearest year, this means that Lloyd must remain a member of the ADLA for at least 19 years for the lifetime membership to be cheaper than paying $550 in annual membership dues.
Therefore, the answer is 19 years.
For the second question, we can use the formula for the future value of a lump sum:
FV = PV * (1 + r)^n
where PV is the present value ($24), r is the annual interest rate (4.5%), and n is the number of years (392).
Substituting the given values, we get:
FV = 24 * (1 + 0.045)^392
FV ≈ $859,993,041.68
Therefore, the value of the $24 purchase price as of 2018 is approximately $859,993,041.68.
There are 140 cars in a parking lot bob looks at 15 cars and finds out that 2 of those cars in the parking lot are gray colored?
Answer:
Step-by-step explanation:
about 18.7
Answer:
18.7
Step-by-step explanation:
2 gray cars / 15 cars = x gray cars / 140 cars
Solving for x, we get:
x = 2 gray cars * 140 cars / 15 cars
x = 18.67 gray cars
EASY MATH POINTS!
Answer from the screenshot.
Therefore, the option D is correct [tex]\frac{4dollar}{1lb}[/tex]
What is rate of change of linear function?The rate of change of a linear function is the slope of the line, which represents the rate at which the output (dependent variable) changes with respect to the input (independent variable).
A line's slope is calculated by dividing the difference in y-coordinates between any two locations on the line by the difference in x-coordinates. Geometrically, the slope is the tangent of the angle that the line makes with the x-axis.
Here in the graph we have x and y values find out the slope,
To calculate the slope of a line from two points (x1, y1) and (x2, y2), we use the formula:
[tex]Slope =\frac{(y2 - y1)}{(x2 - x1)}[/tex] = 4 (for every two points)
So, the line is linear and the rate of change of this linear function is 4/1, which means that for every 1 lb increase in the x-coordinate, the y-coordinate (the output) increases by $4.
Therefor the option D is correct [tex]\frac{4dollar}{1lb}[/tex]
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Arun has x pennies and y nickels. He has no less than 20 coins worth a maximum of $0.40 combined. Solve this system of inequalities graphically and determine one possible solution.
One possible solution of this system is Arun has 5 nickels and 15 pennies.
Define system of linear inequalitiesOne or more linear inequalities in each of the same two variables make up a system of linear inequalities in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system.
From the question;x+y≥20
0.05x+0.01y≤0.40
x≥0
y≥0
Inequality: y≥20-x
Inequality: y≥5x-40
x≥0
y≥0
The solution set satisfying the inequality is shown in black area above when x=5 and y=15
So, Arun has 5 nickels and 15 pennies.
Graph of the system of inequalities is attached below.
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A cereal box advertises that it contains 20% more. It now contains 18.48 ounces. What was the original cereal box amount?
Answer:
If the new cereal box contains 20% more than the original cereal box, then the original cereal box contained 100% - 20% = 80% of the new cereal box.
Let X be the original cereal box amount in ounces, then we can set up the following equation:
X + 0.20X = 18.48
Simplifying and solving for X:
1.20X = 18.48
X = 15.40
Therefore, the original cereal box amount was 15.40 ounces.
Osprey Cycles, Inc. projected sales of 67,577 bicycles for the year. The estimated January 1 inventory is 6,048 units, and the desired December 31 inventory is 7,558 units.
What is the budgeted production (in units) for the year?
units
Therefore, the budgeted production for the year is 69,087 units.
factors
given by the question.
To determine the budgeted production for the year, we need to consider the following factors:
Projected sales for the year: 67,577 bicycles
Estimated January 1 inventory: 6,048 units.
Desired December 31 inventory: 7,558 units
The formula to calculate the budgeted production is:
Budgeted Production = Projected Sales + Desired Ending Inventory - Beginning Inventory
Using the values given in the problem, we can calculate the budgeted production as follows:
Budgeted Production = 67,577 + 7,558 - 6,048
Budgeted Production = 69,087 units
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Find the length of the missing side for this
right triangle.
12
9
Step-by-step explanation:
therefore 9 x 9+12
81+144
225/2
15
For which quotient is x=7
an excluded value?
Answer:
x=3
Step-by-step explanation
x=7 is an excluded value for the quotient x=3 because 3 is not an integer.
What is you answer and how many solutions for the following 3r- 9=3(r + 3)
Answer:
0
Step-by-step explanation:
3r-9=3(r+3)
3r-9=3r+9
collect like terms
3r-3r=9-9
r=0
Answer:
[tex]\large\boxed{\textsf{No Solutions.}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to identify how many solutions are possible for r.}[/tex]
[tex]\textsf{First, we should simplify the given equation.}[/tex]
[tex]\textsf{For one part of the equation, we have to use the \underline{Distributive Property}.}[/tex]
[tex]\Large\underline{\textsf{What is the Distributive Property?}}[/tex]
[tex]\textsf{The \underline{Distributive Property} is a property used to distribute the \underline{multiplier} into}[/tex]
[tex]\textsf{values \underline{inside} the parentheses.}[/tex]
[tex]\textsf{Let's begin simplifying the equation.}[/tex]
[tex]\large\underline{\textsf{Simplify.}}[/tex]
[tex]\mathtt{3r-9=3(r+3)}[/tex]
[tex]\large\underline{\textsf{Distribute:}}[/tex]
[tex]\mathtt{3r-9=(3 \times r)+(3 \times 3)}[/tex]
[tex]\mathtt{3r-9=3r+9}[/tex]
[tex]\large\boxed{\textsf{No Solutions.}}[/tex]
[tex]\large\underline{\textsf{Why?:}}[/tex]
[tex]\textsf{Any value that is substituted into r will \underline{never} make the equation true.}[/tex]
What is the value of x in a triangle with one side being (4x-4) and the other side being 30
The value for the x in the triangle with sides (4x - 4) and 30 is obtained as x > 6.8.
What are triangles?
Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.
In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Assume that the side length 30 is the greatest of the 3 sides.
Using this fact, we can write an inequality based on the lengths of the sides in the given triangle -
(4x - 4) + x > 30
Simplifying this inequality, we get -
4x + x - 4 > 30
Adding x on LHS, we get -
5x > 34
Dividing both sides by 5, we get -
x > 6.8
Therefore, the value of x is greater than 6.8.
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The polynomial 32x^2+12x-57 has two real roots.
True, The polynomial 32x^2+12x-57 has two real roots.
What is a polynomial, exactly?
A polynomial in mathematics is an expression that consists of variables (also known as indeterminates) and coefficients and uses only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
The polynomial x2 4x + 7 is an illustration of one with a single indeterminate x.
It is an absolutely true statement that the polynomial 32x^2+12x-57 has two real roots. The correct option among all the options that are given in the question is the first option or option "A".
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The complete question is -
The polynomial 32x^2+12x-57 has two real roots.
A. True
B. False The polynomial 32x^2+12x-57 has two real roots.
Two positive charges on the y axis has a charge of 3.8 X 10^-9 are located at y
The electric field at the origin due to two positive charges on the y axis with a charge of 3.8 X 10⁻⁹ located at y = 4.0 cm and y = -4.0 cm is 1.05 X 10⁷ N/C.
What is an electric field?
An electric field is a region in which an electric charge experiences a force. It is created by an electric charge or a changing magnetic field. Electric fields exist everywhere in nature and are vital to the functioning of many electronic devices. Electric fields are also used to describe the motion of electrons in a conductor and the behavior of electric currents.
The electric field at the origin (x=0, y=0) can be calculated using the equation of electric field,
E = k(q1/r1² + q2/r2²)
Where k is the Coulomb's constant, q1 and q2 are the charges and r1 and r2 are the distances from the charges to the origin.
The electric field at the origin can be calculated by substituting the given values in the equation.
The distance from the charge at y = 4.0 cm to the origin is 5 cm and the distance from the charge at y = -4.0 cm to the origin is also 5 cm.
E = 8.988 X 10⁹ (3.8 X 10⁻⁹/25 + 3.8 X 10⁻⁹/25)
E = 8.99 X 10⁹ (3.8 X 10⁻⁹/25)
E = 1.05 X 10⁷ N/C
Therefore, the electric field at the origin due to two positive charges on the y axis with a charge of 3.8 X 10⁻⁹ located at y = 4.0 cm and y = -4.0 cm is 1.05 X 10⁷ N/C.
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Right Question:-
Two positive charges on the y axis has a charge of 3.8 X 10^-9 are located at y, Find electric field at the origin due to two positive charges on the y axis with a charge of 3.8 X 10⁻⁹ located at y = 4.0 cm and y = -4.0 cm?
Use the graphs of f and g to find (f+g)(−2).
Using the graph the value of the function (f + g)(-2) = 5
What are graphs?A graph is a diagrammatic representation of a function
Since we have the graphs of the function f(x) and g(x), we desire to find (f + g)(-2). We proceed as follows.
First, we note that (f + g)(x) = f(x) + g(x)
Now, we need to find (f + g)(-2) = f(-2) + g(-2)
So, we use the graph to find these values.
From the graph
f(-2) = 2 and g(-2) = 3
So, substituting the values of the variables into the equation, we have that
(f + g)(-2) = f(-2) + g(-2)
= 2 + 3
= 5
So, (f + g)(-2) = 5
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4.586 to the nearest cm
Answer:
See below.
Step-by-step explanation:
We are asked to round 4.586 cm to the nearest cm.
What is Rounding?
Rounding is a simple method used to change a number, and all of the numbers behind it to 0. Rounding is similar to an approximation, in order to show you how I should give you an example.
Example:
Round 459 to the hundreds place.
The hundreds place is where the 4 is. We should look at the 5.
Requirements necessary are that 5 needs to be greater than [tex]4.\bar{9}.[/tex]
Because 5 is greater, we can round up to 500.
Rounding is an approximation because it's close to the actual number, in other words, inexact.
Let's use the example as a guide for our problem now.
4.586 to the nearest cm (ones place)
The ones place is the 4. We should look at the 5.
5 is greater than [tex]4.\bar{9}.[/tex]
Because 5 is greater, we can round up to 5.000 cm.
Our final answer is 5.000 cm.
Help pleaseee can you tell me the the answers in order please
A car was valued at $45,000 in the year 1991. The value depreciated to $12,000 by the year 2000.
A) What was the annual rate of change between 1991 and 2000?
r=-------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2003 ?
value = $----------------Round to the nearest 50 dollars.
the car depreciated at an annual rate of 13.56% between 1991 and 2000, and would be worth around $6,044.48 in 2003 assuming the same rate of depreciation continued
The answer if subpart are as follows :-
A) To find the annual rate of change between 1991 and 2000, we need to use the formula for exponential decay, which is:
V(t) = V(0) * e raise to the power (-rt)
Where V(t) is the value of the car at time t, V(0) is the initial value of the car, r is the annual rate of change (as a decimal), and e is the mathematical constant 2.71828...
Plugging in the values we have:
V(2000) = $12,000
V(1991) = $45,000
t = 9 years
$12,000 = $45,000 * e raise to the power (-r * 9)
Dividing both sides by $45,000 and taking the natural logarithm of both sides gives:
ln(0.26667) = -9r
Solving for r:
r = ln(0.26667) / (-9) = 0.1356
So the annual rate of change between 1991 and 2000 is 0.1356, which represents a decrease in value of 13.56% per year.
B) To express the answer from part A in percentage form, we need to multiply by 100 and round to two decimal places:
r = 0.1356 * 100 = 13.56%
C) If we assume that the car value continues to drop by the same percentage as it did between 1991 and 2000, we can use the same formula as before to find the value of the car in 2003:
V(2003) = V(2000) * e raise to the power (-r * 3)
Plugging in the values we have:
r = 0.1356
V(2000) = $12,000
V(2003) = $12,000 * e raise to the power (-0.1356 * 3) = $6,044.48
So the value of the car in 2003 would be approximately $6,044.48, rounded to the nearest 50 dollars as requested.
In summary, the car depreciated at an annual rate of 13.56% between 1991 and 2000, and would be worth around $6,044.48 in 2003 assuming the same rate of depreciation continued. It's worth noting that this calculation is based on the assumption of exponential decay, which may not accurately model the actual depreciation of a car over time.
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CAN SOMEONE HELP WITH THIS QUESTION?✨
(a) The derivative of the function, dy/dx = (-399x⁶ - 380x³⁷y) / (9y⁸)
(b) The equation of the tangent line to the curve at (1, 1) is y = (-779/9)x + 778/9.
What is the derivative of the function?To find dy/dx, we differentiate both sides of the equation with respect to x using the chain rule and product rule as necessary:
d/dx (57x⁷) + d/dx (10x³⁸y) + d/dx (y⁹) = d/dx (68)
Simplifying each term using the power rule and the chain rule where appropriate, we get:
399x⁶ + 380x³⁷y + 9y⁸(dy/dx) = 0
Now, solving for dy/dx, we get:
dy/dx = (-399x⁶ - 380x³⁷y) / (9y⁸)
To find the equation of the tangent line to the curve at (1, 1), we first need to evaluate dy/dx at that point. Plugging in x = 1 and y = 1 into the expression for dy/dx, we get:
dy/dx = (-399 - 380) / 9 = -779/9
Now we can use the point-slope form of the equation of a line to find the tangent line. The point-slope form is:
y - y1 = m(x - x1)
where;
m is the slope and (x1, y1) is the point.Plugging in m = -779/9, x1 = 1, and y1 = 1, we get:
y - 1 = (-779/9)(x - 1)
Simplifying, we get:
y = (-779/9)x + 778/9
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Find the equation for the ellipse
Using the data points given, the equation is [tex]\frac{\Big(\frac{(x - 4)^2}{25}+ (y + 2)^2\Big)}{25} = 1[/tex].
What is an ellipse?
An ellipse is a locus of a point that moves in such a way that its perpendicular distance from a fixed straight line (directrix) and its distance from a set point (focus) remain constant. which is smaller than unity, i.e. eccentricity(e).
We are given that the center of the ellipse is at (4,-2), and a vertex is at (9,-2).
We know that the distance from the center to a vertex is a, where a is the length of the semi-major axis.
Therefore, we have -
a = 9 - 4 = 5
Since the point (4,3) is on the ellipse, we can use the distance formula to find the length of the semi-minor axis -
c = distance from (4,-2) to (4,3)
c = [tex]\sqrt{((4-4)^2 + (3-(-2))^2}[/tex]
c = 5
Now, we can use the equation of an ellipse -
[tex]\frac{\Big(\frac{(x - h)^2}{a^2}+ (y - k)^2\Big)}{b^2} = 1[/tex]
where (h,k) is the center of the ellipse, a is the length of the semi-major axis, and b is the length of the semi-minor axis.
Plugging in the values we have found, we get -
[tex]\frac{\Big(\frac{(x - 4)^2}{25}+ (y + 2)^2\Big)}{25} = 1[/tex]
Therefore, the equation for the ellipse is [tex]\frac{\Big(\frac{(x - 4)^2}{25}+ (y + 2)^2\Big)}{25} = 1[/tex].
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