3. Explain without using taking derivatives why f(12)(t) = 0 if f(t) = 5t10 (4 points). 4. Find g(0)(a) if g(x) = -1024 cos ) (6 points) 10)) a
Answers
1] Without taking derivatives, we can use the knowledge that the 12th derivative of tn equals n!/(n-12) to obtain the 12th derivative of f(t) = 5t10! t(n-12), where n! stands for n factorial (i.e., the product of all positive integers up to n). Hence, f(t) = 5t10's 12th derivative is given by \(f(12)(t) = 5*10!/(-2)! * t^(-2) (-2)\)
When we condense this expression, we get:
\(f(12)(t) = 30240 * t^(-2) (-2)\)
We cannot evaluate f(12)(t) at t=0 since t(-2) is undefined at that time. Nonetheless, it is clear that f(12)(t) approaches infinity as t approaches 0 on either side. We can therefore not state that f(12)(t) = 0 for every t, but we may state that f(12)(t) is undefined at t=0.
2] finding g(0) (a) We must calculate the derivative of g(x) with respect to x and evaluate it at x=0 if g(x) = -1024 cos(10a). We obtain the following by using the chain rule to differentiation:\(g'(x) = -1024 * (-sin(10a)) * 10 = 10240 sin (10a)\)
As a result, when g(0)(a) = g'(0)(a) = 10240 sin(10a), and x=0, it results in:
g(0)(a) = 10240 sin(0) = 0
Hence, g(0)(a) = 0.
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Related Questions
Question 1(Multiple Choice Worth 2 points)
(Comparing Data MC)
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru typically has more wait time, and why?
Burger Quick, because it has a larger median
Burger Quick, because it has a larger mean
Super Fast Food, because it has a larger median
Super Fast Food, because it has a larger mean
Answers
We may infer from the box plots that Super Fast Food, with its smaller IQR, is better equipped to predict wait times than Burger Quick.answer is option (a).
What is median?When values are sorted in order of magnitude, the median, a measure of central tendency, is the middle value in the collection.
BX charts are a common approach to visually depict a distribution of data, such as wait times at a drive-through restaurant. The bx in a bx plot depicts the interquartile range (IQR), or the middle 50% of the data, with the bttm and tp of the bx standing in for the first quartile (25th percentile) and third quartile (75th percentile), respectively. A line inside the box represents the median, or the value that splits the data into equal halves.
Although the range, which is the difference between the data's highest and minimum values, can also be used as a consistency indicator, its accuracy is lower than that of the IQR due to its sensitivity to extreme values and outliers. In this instance, Burger Quick's range is 30 - 2 = 28 minutes, while Super Fast Food's range is 27 - 3 = 24 minutes. Despite the fact that the range for Super Fast Food is narrower, it is still unreliable as a measure of consistency since it is significantly impacted by the outlier at 27 minutes, which is considerably outside the range of the data.
We may therefore deduce from the box plots that Super Fast Food, due to its smaller IQR, is able to estimate their wait time more reliably than Burger Quick.
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The complete question is,
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru is able to estimate their wait time more consistently and why?
Burger Quick, because it has a smaller IQR
Burger Quick, because it has a smaller range
Super Fast Food, because it has a smaller IQR
Super Fast Food, because it has a smaller range
Please help me with help please please 6 to 9 please
Answers
Answer with Step-by-step explanation:
$20.04-$16.44
$3.6
7. 6*$11.99=$71.4
24*$15.99=$383.76
30*$17.29=$518.7
8.
110.13 Canadian dollars
9.
a.36*$25.99
$935.64
b.$699+$935.64
$1634.64
c.No hidden fee
While rock climbing, Farrell starts at 20 feet above sea level and climbs upward at a rate of 3 feet per minute. Theresa starts at 200 feet above sea level and climbs down at a rate of 2 feet per minute. Write and solve an equation that can be used to find the time t in minutes it takes for the two climbers to reach the same height.
Use the Equation editor to write your equation and final answer. You do not need to show all steps, but you may if you choose to.
Answers
Answer:24 feet
Step-by-step explanation:
Find the measure of angles 1,2 and 3
Answers
Answer:
??
Step-by-step explanation:
where is the question
Suppose a normal distribution has a mean of 266 and a standard deviation of
12. What is P(x >= 242)
Answers
If we standarize the variable x, we get:
\(z=\frac{x-\mu}{\sigma}=\frac{x-266}{12}\)doing this inside the probability, we get the following:
\(\begin{gathered} P(x\ge242)=P(\frac{x-\mu}{\sigma}\ge\frac{242-266}{12})=P(z\ge-2) \\ By\text{ the property of the complement, we have:} \\ P(z\ge-2)=1-P(z<-2)=1-0.0228=0.9772 \\ \Rightarrow P(x\ge242)=0.97 \end{gathered}\)therefore, the probability is 0.97
Write an example from daily life that uses each type of real number.
rational numbers
Answers
Write an example from daily life that uses rational numbers .
Real numbers that may be expressed as p/q, where p, q are integers, and q 0, are rational numbers. The money we have is a rational number. If we spend some sum out of it, it is subtraction of rational number.The running race involves rational numbers if you're an athlete.Rational numbers include the following:the distance runthe time needed to complete the distance,the number of competitors placing first, second, or thirdthe number of heartbeats you take per minute.We use fractions to represent taxes.If you split a pizza or any other food.When you finish a piece of your work, you indicate that you have done half, or 50%.Loan and mortgage interest rates.Savings account interest.To learn more about rational numbers, refer:
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Which equation represents the vertical asymptote of the graph?
x= -8
y= -8
x= 0
y= 0
Answers
Answer: x= -8
Step-by-step explanation:
A vertical asymptote is a line cut in the middle of both graphs!
It can't be x= 0 or y= 0 because it is not the middle of both graphs!
It can't be y= -8 because it is not cut in the middle.
So x=-8 is the right answer!
If Mikal uses all his money to buy one type of flour, he has exactly enough money to buy either 12 pounds of wheat flour, or 6 pounds of rice flour, or 4 pounds of almond flour. If Mikal uses all his money to buy an equal number of pounds of all three types of flour, what is the total number of pounds of flour that he can buy?
Answers
The total number of pounds of flour he can buy is 7 pounds of flour
Let's assume that Mikal has $1 to spend on flour. According to the problem, he can buy:
- 12 pounds of wheat flour for $1, which means that the price of wheat flour is 1/12 = $0.0833 per pound.
- 6 pounds of rice flour for $1, which means that the price of rice flour is 1/6 = $0.1667 per pound.
- 4 pounds of almond flour for $1, which means that the price of almond flour is 1/4 = $0.25 per pound.
If Mikal spends $1 on an equal amount of all three types of flour, he will spend $1/3 = $0.3333 on each type of flour. To determine how many pounds of each type of flour he can buy, we need to divide $0.3333 by the respective price per pound of each type of flour:
- Wheat flour: $0.3333 / $0.0833 per pound = 3.9996 pounds (rounded to 4 pounds)
- Rice flour: $0.3333 / $0.1667 per pound = 1.9998 pounds (rounded to 2 pounds)
- Almond flour: $0.3333 / $0.25 per pound = 1.3332 pounds (rounded to 1 pound)
Therefore, Mikal can buy 4 pounds of wheat flour, 2 pounds of rice flour, and 1 pound of almond flour with $1. The total number of pounds of flour he can buy is:
4 + 2 + 1 = 7 pounds of flour.
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Consider the cylinder, given in the figure {r=1.5, h=3}. The potential V within the cylinder is given in cylindrical coordinates as: V = 5r + 4 cos Ø Calculate the total charge within the cylinder.
Answers
To calculate the total charge within the cylinder with dimensions r=1.5 and h=3, we use the potential function V = 5r + 4 cos Ø in cylindrical coordinates.
The total charge can be obtained by integrating the charge density over the volume of the cylinder.
The potential V within the cylinder is given by V = 5r + 4 cos Ø, where r represents the radial distance from the axis of the cylinder and Ø represents the angle in the cylindrical coordinate system. To calculate the total charge within the cylinder, we need to integrate the charge density over its volume.
The charge density ρ can be related to the potential by ρ = -∇²V, where ∇² is the Laplacian operator. In cylindrical coordinates, the Laplacian operator takes the form:
∇² = (1/r) ∂/∂r (r ∂/∂r) + (1/r²) ∂²/∂ز + ∂²/∂z²
Since the potential function V does not depend on the z coordinate, the Laplacian reduces to:
∇² = (1/r) ∂/∂r (r ∂/∂r) + (1/r²) ∂²/∂ز
Applying this operator to the potential function V, we find:
∇²V = (1/r) ∂/∂r (r ∂V/∂r) + (1/r²) ∂²V/∂ز
To find the charge density, we substitute this expression into ρ = -∇²V:
ρ = -(1/r) ∂/∂r (r ∂V/∂r) - (1/r²) ∂²V/∂ز
To calculate the total charge, we integrate the charge density ρ over the volume of the cylinder:
Q = ∫∫∫ ρ dV = ∫∫∫ -(1/r) ∂/∂r (r ∂V/∂r) - (1/r²) ∂²V/∂ز dV
The integration is performed over the cylindrical coordinates r, Ø, and z, with appropriate limits. Evaluating this integral will give us the total charge within the cylinder.
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Explain the process and the properties you have to use to solve the logarithmic equation: log(3)x + log(3)4 - 2 log(3)3 = 2
Answers
81/4
Step-by-step explanation:
\( log_{3}( \frac{4x}{{3}^{2} } ) = 2\)
\( {3}^{2} = \frac{4x}{ {3 }^{2} } \)
9=4x/9
81=4×
x=81/4
adding logs means elements are multiplied, subtracting means divide. number in front of log is raised to power
base of log is raised to power of element after =
element in log is then equal to log base raised to power
solve resulting equation
Heather purchased a new $1,500 laptop by using a credit card with a 17% interest rate. She will pay off the balance in 2 years by paying monthly payments of $74.16. Calculate Heather’s total cost of repayment.
Answers
12 months in a year
2 years
2x12=24
74.16x24=1779.84
Heather's total cost of repayment is $1,779.84.
What exactly is a monthly payment?A monthly payment is a payment made every month to pay off loans or advances. It's similar to EMI.
Given,
Principal = $1,500
Rate = 17% per year (or 0.17 as a decimal)
Time = 2 years
Total interest = (principal × rate × time) / 12
Substitute the given values, and we get:
Total interest = (1500 × 0.17 × 2) / 12 = $51
So, Heather will pay a total of $51 in interest over the two years.
Total repayment = monthly payment × number of months
Here,
Monthly payment = $74.16
Number of months = 2 years × 12 months/year = 24 months
Substitute these values, and we get:
Total repayment = $74.16 × 24 = $1,779.84
Therefore, Heather's total cost of repayment is $1,779.84.
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Find the area of the circle pictured above.
Round your answer to the nearest tenth
Answers
Answer:
~201.1\(u^2\)
Step-by-step explanation:
Formula for area of a circle:
\(\pi r^2\)
The diameter is any straight line that passes through the circle and endpoints lie on the perimeter of the circle.
We are given the diameter: 16. The diameter is twice the radius (for all circles) Divide the diameter, 16 by 2 to get the radius. If the problem gives you the radius, which is a line from the center of the circle, do not divide by 2 and directly plug into formula.
16/2 = 8
Plug into formula.
\(\pi r^2\)
\(\pi 8^2\)
Using PEMDAS, the standard order of operations order for math, we firsty do 8^2 before multiplying by pi.
8^2 = 8 x 8 = 64
\(64*\pi\) = ~201.1
A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola. What are the dimensions of such a rectangle with the greatest possible area?.
Answers
The dimensions of the rectangle such that the rectangle have the greatest area is length = 8 and width = 4 .
In the question ,
it is given that ,
a rectangle is inscribed with its base on the x axis , and its upper corner on the parabola y = 12 − x² ,
let the coordinate of the upper right corner be P(x,y) ,
and A be the area of the rectangle .
the point P lies on the parabola , given y = 12 − x² ,
So, P = P(x,12−x²)
Due to symmetry of the rectangle, the width of rectangle is half the distance between P and the y axis ,
that means width = 2x and length = y .
Area of the rectangle = width × Length
= 2x * y
= 2x (12 − x²)
= 24x - 2x³
To maximize the area we differentiate Area with respect to x ,
we get ,
dA/dx = 24 - 6x²
for critical point dA/dx = 0 ,
24 - 6x² = 0
6x² = 24
x² = 4
x = ±2 ,
since length cannot be negative ,
So , x = 2 .
to check for maximum and minimum ,we differentiate Area with respect to x,
we get
d²A/dx² = -12x
substituting , x = 2 ,
we get -12 < 0, So , the area is maximum .
hence the width = 2*2 = 4
and length = 12 - 4 = 8
and the maximum area is 32 .
Therefore , The dimensions of the rectangle such that the rectangle have the greatest area is length = 8 and width = 4 .
The given question is incomplete , the complete question is
A rectangle is inscribed with its base on the x axis and its upper corners on the parabola y = 12 − x² . What are the dimensions of such a rectangle with the greatest possible area ?
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A man is now twice as old as his son. Fifteen years ago he was three times as old as his son was then. How old is the son now?
Answers
Answer:
20 is the answer to that question
Does anybody know the answer to this question I need help please?!
Answers
Answer:
Answer is C
Step-by-step explanation:
When u plug in the values in C u get the ranges
Correct each of the following errors by circling the error, describing what is wrong, entering what should be there instead, and entering the correct answer.
1. (3x²)(-2x⁴)=3(-2)x²•⁴=6x⁸
2. 4a²•3a⁵=(4+3)a²+⁵=7a⁷
3. x⁶•x•x³=x⁶+³=x⁹
4. 3⁴•2³=6⁴+³
Answers
Answer:The error in #1 is that it should read "3x²•(-2x⁴)=3•(-2)•x²⁴=6x⁸". The error in #2 is that it should read "4a²•3a⁵=4•a²•3•a⁵=12a⁷". The error in #3 is that it should read "x⁶•x³=x⁶•x³=x⁹". The error in #4 is that it should read "3⁴•2³=3⁴•2³=24".
Step-by-step explanation:
easy
Between which two numbers is √8 located on a number line?
Answers
Answer:
√8 is between 2 and 3.
Step-by-step explanation:
♡ im sorry if its wrong ♡
Solve fort.
-t = 9(t – 10)
t=
Answers
Answer:
t = 9
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
-t = 9(t - 10)
Step 2: Solve for t
[Distributive Property] Distribute 9: -t = 9t - 90[Subtraction Property of Equality] Subtract 9t on both sides; -10t = -90[Division Property of Equality] Divide -10 on both sides: t = 9Answer:
Step-by-step explanation:
-t=9(t-10)
-t=9t-90
90=9t+t
90=10t
90/10=t
9=t
The volunteer firemen in a small town had a breakfast fund-raiser to raise money for new equipment. Each meal of pancakes, sausage, orange juice, and coffee (or tea) cost $6.00. If the firemen took in $1,470, how many meals did they sell?
Answers
The volunteer firemen sold 245 meals at their breakfast fund-raiser to raise $1,470 for new equipment.
Let's assume that the number of meals sold is "x". Then, the total amount of money raised from the fund-raiser is given by:
Total amount = Number of meals sold x Cost per meal
We know that the cost per meal is $6.00, so we can write:
Total amount = 6x
We also know that the total amount raised was $1,470, so we can set up an equation:
6x = 1,470
Solving for x, we get:
x = 245
Therefore, the firemen sold 245 meals at the fund-raiser.
Revenue refers to the total amount of money that a business or organization earns through its operations or sales over a particular period. It is the income generated from the sale of goods or services or any other business activity that brings in money.
Revenue is an essential financial metric for businesses as it represents the amount of money a company has available to cover its expenses, invest in new opportunities, and ultimately generate profit. A company's revenue can be calculated by multiplying the price of its goods or services by the number of units sold, or by adding up all the sources of income the company has earned over a specific period.
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Write the equation of the line fully simplified slope-intercept form.
Answers
Answer:
y=-x+3
Step-by-step explanation:
Josiah plants vegetable seeds in rows. Each row has the same number of seeds in it. He plants more than one row of seeds. What could be the total number of seeds he plants?
Answers
The total number of seeds that Josiah would plant would be = nR×S
How to determine the total number of seeds that Josiah will plant?To determine the total number of seeds that Josiah will plant will be to add the seeds in the total number of rooms he planted.
Let each row be represented as = nR
Where n represents the number of rows planted by him.
Let the seed be represented as = S
The total number of seeds he planted = nR×S
Therefore, the total number of seeds that was planted Josiah would be = nR×S.
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A surveyor is 3 miles from a mountain The angle of elevation from the ground to the top of the mountain is 15°. What is the height of the mountain?
Answers
What is the speed of 240 km in 3 hours?
Answers
The speed of the moving body that is being referred to here is 80 kilometer per hour.
The given problem is a straightforward one based on the idea of the universal law of motion. According to the universal law of motion, any uniformly traveling body's distance traveled is determined by the product of its speed and the time elapsed. Distance is calculated as speed * time. Therefore the body is going at a speed of 80 kilometers per hour, according to the same relation as above, assuming that it is moving at a constant speed.
\(Distance = speed * time\)
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Which expression is equivalent to
(5^-2)(5^-1)
-1/125
-1/5
1/125
1/5
Answers
Answer:
it will be 1/125 if I am wrong please tell me
An artist can sell 20 copies of a painting at $100 each, but for each additional copy he makes, the value of each painting will go down by a dollar. Thus, if 22 copies are made, each will sell for $98. How many copies should he make to maximize his sales?
Answers
Answer:
60 copies
Step-by-step explanation:
Answer: 60 copies
Step-by-step explanation:
What is the value of k?
Answers
Answer:k=2.4
Step-by-step explanation:
The weights for newborn babies is approximately normally distributed with a mean of 6. 9 pounds and a standard deviation of 2 pounds. Consider a group of 1500 newborn babies:
1. How many would you expect to weigh between 5 and 9 pounds?
2. How many would you expect to weigh less than 8 pounds?
3. How many would you expect to weigh more than 7 pounds?
4. How many would you expect to weigh between 6. 9 and 10 pounds?
Answers
We would expect about 979 babies to weigh between 5 and 9 pounds.
We would expect about 1063 babies to weigh less than 8 pounds.
We would expect about 720 babies to weigh more than 7 pounds.
We would expect about 692 babies to weigh between 6.9 and 10 pounds.
We have,
We can use the normal distribution to answer these questions.
1)
To find the number of babies expected to weigh between 5 and 9 pounds, we need to find the area under the normal curve between these two values.
The z-scores for the lower and upper bounds are:
z1 = (5 - 6.9) / 2 = -0.95
z2 = (9 - 6.9) / 2 = 1.05
The area between these z-scores is approximately 0.653.
Now,
= 0.653 x 1500
= 979.5
So we would expect about 979 babies to weigh between 5 and 9 pounds.
2)
To find the number of babies expected to weigh less than 8 pounds, we need to find the area under the normal curve to the left of this value.
The z-score for 8 pounds.
z = (8 - 6.9) / 2 = 0.55
The area to the left of this z-score is approximately 0.7088.
To get the actual number of babies, we need to multiply this proportion by the total number of babies:
= 0.7088 x 1500
= 1063.2
So we would expect about 1063 babies to weigh less than 8 pounds.
3)
To find the number of babies expected to weigh more than 7 pounds, we need to find the area under the normal curve to the right of this value.
The z-score for 7 pounds.
z = (7 - 6.9) / 2 = 0.05
The area to the right of this z-score is approximately 0.4801.
So,
= 0.4801 x 1500
= 720.15
So we would expect about 720 babies to weigh more than 7 pounds.
4)
To find the number of babies expected to weigh between 6.9 and 10 pounds, we can use the z-scores for these values:
z1 = (6.9 - 6.9) / 2 = 0
z2 = (10 - 6.9) / 2 = 1.55
The area between these z-scores is approximately 0.4616.
So,
0.4616 x 1500 = 692.4
So we would expect about 692 babies to weigh between 6.9 and 10 pounds.
Thus,
We would expect about 979 babies to weigh between 5 and 9 pounds.
We would expect about 1063 babies to weigh less than 8 pounds.
We would expect about 720 babies to weigh more than 7 pounds.
We would expect about 692 babies to weigh between 6.9 and 10 pounds.
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Use the algebra tiles to help you solve the equation 4x - 5 = 7
Answers
Add five to both sides
4x=12
Divide both sides by 4
X=3
You have a rectangular prism cake with dimensions of 16 inches long, 12 inches wide and 3 inches tall. If we keep the height of 3 inches, what does the width of a round cake need to be to keep the same volume
Answers
The width of the round cake needs to be approximately 15.63 inches to keep the same volume as the rectangular prism cake.
To keep the same volume when changing the shape of the cake from a rectangular prism to a round cake with a fixed height of 3 inches, we need to find the width of the round cake.
The volume of the rectangular prism cake is given by:
Volume = Length * Width * Height
Substituting the given values:
Volume = 16 inches * 12 inches * 3 inches
The volume of a round cake can be calculated using the formula for the volume of a cylinder:
Volume = π * radius^2 * Height
We want to keep the height at 3 inches, so the equation becomes:
Volume = π * radius^2 * 3 inches
To keep the same volume as the rectangular prism cake, we can equate the two volume expressions:
16 inches * 12 inches * 3 inches = π * radius^2 * 3 inches
Simplifying, we can cancel out the common terms:
16 inches * 12 inches = π * radius^2
Dividing both sides by π:
(16 inches * 12 inches) / π = radius^2
Taking the square root of both sides to solve for the radius:
radius = √[(16 inches * 12 inches) / π]
Now, to obtain the width of the round cake, we can double the radius since the radius represents half the width:
Width of round cake = 2 * radius
Width of round cake = 2 * √[(16 inches * 12 inches) / π]
Width of round cake ≈ 2 * √[(192 inches^2) / π]
Width of round cake ≈ 2 * √(61.211)
Width of round cake ≈ 2 * 7.815
Width of round cake ≈ 15.63 inches (rounded to two decimal places)
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Suppose that you made three purchases using your credit card during the month of January. - The first purchase was on January 8th for $492. - The second purchase was on January 19th for $292. - The third purchase was on January 24ti . If your average daily balance for January was $695, what was the dollar amount of your last purchase? Remember: - There are 31 days in January. - You made no purchases between January 1 st and January 7 th. - This question is not asking for the card's final January balance. Round your answer to the nearest dollar. Question 4 A $14,513 par value bond whose coupon rate is 4.9% is purchased. If the investment represents a current yield of 3.1%, compute the bond's market price at the time of the purchase. Round your answer to the nearest dollar.
Answers
Average Daily Balance:It is defined as the average balance for a day or a month in a credit account. The balance is calculated by adding the unpaid balance at the end of each day and dividing the total by the number of days in a month.
According to the question, the average daily balance for January was $695. Therefore, the total balance for January was:$695 x 31 = $21,545.Let x be the last purchase amount. So, the balance after two transactions:$21,545 – $492 – $292 = $20,761.The third transaction would have made the balance equal to x + $20,761 as there are 31 days in January. Therefore, we can represent the equation as: x + $20,761 = $695 x 31.Since x is the last purchase amount, we must isolate it to find it: x + $20,761 = $21,545.Dividing both sides by 1, we get: x = $784. The question asks us to determine the amount of the last purchase, given three transactions and the average daily balance for January 2021. We begin by calculating the average daily balance for January 2021, which is $695. This is calculated by taking the balance at the end of each day and dividing it by the number of days in January 2021, which is 31. Therefore, the total balance for January 2021 is $695 x 31 = $21,545. We are given that the first purchase was $492 and the second purchase was $292, which means that the remaining balance after the second purchase is $20,761. We are asked to find the amount of the third purchase, which means that we need to add this amount to the remaining balance to get the total balance at the end of January 2021. We can set up an equation to solve for the third purchase amount. Let x be the amount of the third purchase. Therefore, x + $20,761 = $695 x 31. Solving for x, we get x = $784. Therefore, the amount of the last purchase was $784.
Therefore, the amount of the last purchase was $784, which was obtained by adding the remaining balance of $20,761 to the third purchase.
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