After Julia has driven for a quarter of an hour, she was 170 miles east from Denver. After driving for 3 hours, she was only 100 miles east from Denver. Assume that Julia drove at a constant speed during the trip. Let be a function that gives Julia’s position east from Denver (measured in miles) after having driven for hours.
a) Determine a rule for the function .
b) Interpret the meaning of ^−1(16) and then find its value if it exists.
c) Interpret the meaning of ^−1(-141) and then find its value if it exists.
d) Determine a rule for ^−1 .
e) Construct a graph for ^−1 .
Answers
The rule for the function is P(t) = 170 + 680t
The time t after which Julia is 16 miles east from DenverThe time t after which Julia is -141 miles east from DenverThe inverse is P^-1(t) = (t - 170) / 680a) Determine a rule for the functionLet's call Julia's final position after t hours as P.
If she drove at a constant speed v (in miles per hour), then the distance traveled can be given as:
P - P0 = vt
Given that she was 170 miles east from Denver after driving for a quarter of an hour (0.25 hours), we can write the first equation:
170 = v * 0.25
v = 680
This means that her speed was 680 miles per hour.
Using this speed, we can write the second equation:
P = 680 * t
100 = 680 * t
t = 100 / 680 = 0.147
Combining the two equations, we can find the function that gives Julia's position east from Denver after t hours as:
P(t) = P0 + v * t ----- P0 = 170 i.e. her initial position
P(t) = 170 + 680 * t
So, the rule for the function P(t) is:
P(t) = 170 + 680t
The meaning of P^-1(16)P^-1(16) is the inverse of the function P(t) at the value 16.
In other words, it gives us the time t after which Julia is 16 miles east from Denver.
To find its value, we can use the equation of the function P(t):
P(t) = 170 + 680 * t
16 = 170 + 680 * t
-154 = 680 * t
t = -154 / 680
Time cannot be negative.
So, it does not exist
The meaning of P^-1(-141)P^-1(-141) is the inverse of the function P(t) at the value -141.
In other words, it gives us the time t after which Julia is 16 miles east from Denver.
So, we have
-141 = 170 + 680 * t
-311 = 680 * t
t = -311 / 680
Time cannot be negative.
So, it does not exist
Determine a rule for ^−1 .We simply make t the subject in P(t)
So, we have
P^-1(t) = (t - 170) / 680
The graph is attached
Read more about inverse function at
https://brainly.com/question/14796161
#SPJ1
Related Questions
What is a number that when you multiply it by 7 and add 2 to the product, you get 30?
Answers
Answer:
4
7 * 4 = 28
28 + 2 = 30
Step-by-step explanation:
Hope it helps! =D
Solution is in the attachment!!
Assume an exponential function has a starting value of 14 and a decay rate of 42%. Write an equation to model the situation.
The equation is y=
Answers
The equation to model the situation will be written as y = 14 × (0.58)ˣ.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
y = a (1 ± r)ˣ
Assume an exponential function has a starting value of 14 and a decay rate of 42%. Then the equation is given as,
y = 14 × (1 - 0.42)ˣ
y = 14 × (0.58)ˣ
The equation to model the situation will be written as y = 14 × (0.58)ˣ.
More about the exponent link is given below.
https://brainly.com/question/5497425
#SPJ1
A person who is exercising should not exceed his or her maximum heart
rate, which is determined on the basis of that person's gender, age, and
resting heart rate. The table relates resting heart rate and maximum heart
rate for a 20-year-old man.
a) Use a graphing calculator to model the data with a linear function.
b) Estimate the maximum heart rate if the resting heart rate is 40, 60, 72,
and 80.
c) What is the correlation coefficient? How confident are you about using
the regression line to estimate function values?
Answers
Answer:5 star would be greatly aprreciated
For b) Estimating the maximum heart rate, a common formula used to calculate maximum heart rate is:
Max HR = 220 - Age
Since the person is 20 years old, the maximum heart rate can be estimated as:
Max HR = 220 - 20 = 200 beats per minute.
To estimate the maximum heart rate given a resting heart rate, we can use the formula:
Max HR = Resting HR + (Max HR - Resting HR) * Percentage of Max HR
Assuming a typical range of 70-85% of maximum heart rate during exercise, the estimated maximum heart rate for a resting heart rate of 40, 60, 72, and 80 beats per minute would be:
Resting HR = 40: Max HR = 140 + (200 - 140) * 0.85 = 170 beats per minute
Resting HR = 60: Max HR = 140 + (200 - 140) * 0.80 = 176 beats per minute
Resting HR = 72: Max HR = 140 + (200 - 140) * 0.75 = 182 beats per minute
Resting HR = 80: Max HR = 140 + (200 - 140) * 0.70 = 188 beats per minute
For c) the correlation coefficient, the coefficient measures the strength and direction of the linear relationship between two variables. A value close to 1 indicates a strong positive correlation, a value close to -1 indicates a strong negative correlation, and a value close to 0 indicates no correlation.
Step-by-step explanation:
For b) Estimating the maximum heart rate, a common formula used to calculate maximum heart rate is:
Max HR = 220 - Age
Since the person is 20 years old, the maximum heart rate can be estimated as:
Max HR = 220 - 20 = 200 beats per minute.
To estimate the maximum heart rate given a resting heart rate, we can use the formula:
Max HR = Resting HR + (Max HR - Resting HR) * Percentage of Max HR
Assuming a typical range of 70-85% of maximum heart rate during exercise, the estimated maximum heart rate for a resting heart rate of 40, 60, 72, and 80 beats per minute would be:
Resting HR = 40: Max HR = 140 + (200 - 140) * 0.85 = 170 beats per minute
Resting HR = 60: Max HR = 140 + (200 - 140) * 0.80 = 176 beats per minute
Resting HR = 72: Max HR = 140 + (200 - 140) * 0.75 = 182 beats per minute
Resting HR = 80: Max HR = 140 + (200 - 140) * 0.70 = 188 beats per minute
For c) the correlation coefficient, the coefficient measures the strength and direction of the linear relationship between two variables. A value close to 1 indicates a strong positive correlation, a value close to -1 indicates a strong negative correlation, and a value close to 0 indicates no correlation.
To model the data with a linear function, find the slope using two points from the table, and use the slope-intercept form of the equation to find the y-intercept. To estimate the maximum heart rate for different resting heart rates, substitute the values into the equation. The correlation coefficient cannot be determined based on the given table of data.
Explanation:To model the data with a linear function, we can use the formula for the equation of a line, y = mx + b, where m is the slope and b is the y-intercept.
First, we need to find the slope (m). The slope is given by the formula: m = (y2 - y1) / (x2 - x1). We can choose any two points from the table to calculate the slope. Let's choose (60, 200) and (70, 180) as our two points.
Using the formula, we have m = (180 - 200) / (70 - 60) = -20 / 10 = -2.
Now, we can use the slope-intercept form of the equation to find the y-intercept (b). Let's substitute one of the points into the equation: 200 = -2(60) + b. Solving for b, we get b = 320.
Therefore, the equation of the linear function that models the data is y = -2x + 320.
To estimate the maximum heart rate for different resting heart rates, we can substitute the given values into the equation:
If the resting heart rate is 40: y = -2(40) + 320 = 240.
If the resting heart rate is 60: y = -2(60) + 320 = 200.
If the resting heart rate is 72: y = -2(72) + 320 = 176.
If the resting heart rate is 80: y = -2(80) + 320 = 160.
The correlation coefficient measures the strength and direction of the relationship between two variables. In this case, it represents the correlation between resting heart rate and maximum heart rate. The closer the correlation coefficient is to 1 or -1, the stronger the correlation. However, since we are given a table of data and not actual data points, we cannot calculate the correlation coefficient. We can only estimate it visually based on the scatter plot of the data points.
Therefore, the correlation coefficient cannot be determined and our confidence in using the regression line to estimate function values is limited.
Learn more about a linear function here:https://brainly.com/question/31874188
#SPJ2
The area of the circular base of a cone is 25π cm², and the slant height of the cone is four times the radius of the cone.
What is the approximate lateral area of the cone?
Use π≈3.14.
Enter your answer rounded to the nearest whole number in the box.
Answers
The approximate lateral area of the cone is equal to 314 cm².
How to calculate the lateral area of the cone?Mathematically, the lateral area of a cone can be calculated by using this mathematical expression:
Lateral surface area of a cone, LSA = πrl or πr√(r^2 + h^2)
Where
l represents the slant height of the cone.r represents the radius of the cone.h represents the height of the cone.How to calculate the area of a circle?Mathematically, the area of a circle can be calculated by using this formula:
Area of a circular base = πr²
25π = πr²
Radius, r = √25
Radius, r = 5 cm.
Substituting the given parameters into the lateral area of a cone formula, we have the following;
Lateral surface area of a cone, LSA = πrl = πr4(r)
Lateral surface area of a cone, LSA = 3.14 × 5 × 20
Lateral surface area of a cone, LSA = 314 cm².
Read more on area of circle here: brainly.com/question/15531597
#SPJ1
The area of the circular base of a cone is 16π cm², and the slant height of the cone is 4 times the radius of the cone.
What is the approximate lateral area of the cone?
Answers
The approximate lateral area of the cone is equal to 200.96 cm².
How to calculate the lateral area of the cone?Mathematically, the lateral area of a cone can be calculated by using this mathematical expression:
Lateral surface area of a cone, LSA = πrl or πr√(r^2 + h^2)
Where
l represents the slant height of the cone.r represents the radius of the cone.h represents the height of the cone.How to calculate the area of a circle?Mathematically, the area of a circle can be calculated by using this formula:
Area of a circular base = πr²
16π = πr²
Radius, r = √16
Radius, r = 4 cm.
Substituting the given parameters into the lateral area of a cone formula, we have the following;
Lateral surface area of a cone, LSA = πrl = πr4(r)
Lateral surface area of a cone, LSA = 3.14 × 4 × 16
Lateral surface area of a cone, LSA = 200.96 cm².
Read more on surface area here: https://brainly.com/question/27812847
#SPJ1
Answer:
201 beause you are rounding to the nearest whole number
Step-by-step explanation:
over the course of an 18 year research project, the height of an oceanside cliff actually dropped due to soil erosion. At the end of this period, its height was measured as -3 inches compared to what it had been at the beginning of the research project. What was the average amount that the cliff's height changed each year?
Answers
The average amount of cliff's height that decreased each year is 1/6 inches.
What is unit rate?The rate at which one value changes with respect to per unit change in the other value is called the unit rate. Mathematically -
{ r } = y/x .... Eq { 1 }
Given is that over the course of an 18 year research project, the height of an oceanside cliff actually dropped due to soil erosion. At the end of this period, its height was measured as -3 inches compared to what it had been at the beginning of the research project.
We can write the the average amount of cliff's height that changed each year as -
{r} = |h|/|t|
{r} = 3/18
{r} = 1/6
Therefore, the average amount of cliff's height that decreased each year is 1/6 inches.
To solve more questions on unit rate, visit the link below -
https://brainly.com/question/29781084
#SPJ1
Question 9 find the height of the building
Answers
were going to need a lil more than that to answer :(
Please help! The question is in the image.
Answers
Answer:
Step-by-step explanation:
Sam is moving bags of soil from a loading dock into a storeroom. The topsoil
weighs 40 pounds per bag, and the mulch weighs 20 pounds per bag. The
cart Sam uses to move the bags can only carry up to 480 pounds.
Which graph represents the number of topsoil bags and mulch bags that Sam
can move in a single trip? Graphed
Answers
The inequality that can be used to represent the number of topsoil and mulch Sam can carry is, 40x + 20y ≤ 480
And, The graph which represents the number of topsoil bags and mulch bags that Sam can move in a single trip is shown in figure.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that:
Weight of top soil = 40 pounds
Weight of mulch = 20 pounds
Total weight Sam can carry = 480 pounds
Now, Let number of bags of top but soil = x
And, The number of weight of mulch = y
Hence, The inequality is,
⇒ 40x + 20y ≤ 480
Therefore, the inequality that can be used to represent the number of topsoil and mulch Sam can carry is 40x + 20y ≤ 480
And, The graph which represents the number of topsoil bags and mulch bags that Sam can move in a single trip is shown in figure.
Learn more about inequality visit:
brainly.com/question/18881247
#SPJ1
At a football game, 43% were supporting the visiting team. If total number of people attending the game was 2800, how many people were supporters of the home team?
Answers
Therefore, the number of people supporting the home team was 2800 - 1204 = 1596 people
In your biology class, your final grade is based on several things: a lab score, scores on two major tests, and your score on the final exam. There are 100 points available for each score. However, the lab score is worth 23% of your total grade, each major test is worth 21.5%, and the final exam is worth 34%. Compute the weighted average for the following scores: 94 on the lab, 89 on the first major test, 63 on the second major test, and 73 on the final exam. Enter your answer as a whole number.
Answers
Answer: 79
Step-by-step explanation: The weighted average for the scores can be calculated as follows:
Lab score: 94 x 0.23 = 21.62
First major test: 89 x 0.215 = 19.135
Second major test: 63 x 0.215 = 13.495
Final exam: 73 x 0.34 = 24.82
Total weighted average: 21.62 + 19.135 + 13.495 + 24.82 = 78.976
Rounding to the nearest whole number, the weighted average is 79.
How many degrees is the peripheral angle above the circular arc that represents 4/9 of the circle
Answers
The peripheral angle above the arc would be:
160 / 2 = 80 degrees.
Solution
The peripheral angle above a circular arc is equal to the central angle subtended by the arc divided by 2.
The central angle of a circle is 360 degrees, so if the arc represents 4/9 of the circle, the central angle subtended by the arc would be:
360 * (4/9) = 160 degrees
The peripheral angle above the arc would be:
160 / 2 = 80 degrees.
Learn more about peripheral angle here: brainly.com/question/29293987
#SPJ1
PLEASE HELP ASAP DONT IGNORE:(((
Answers
Answer:
Step-by-step explanation:
Notebooks Total Cost
0 0.00
1 3.00
2 6.00
3 9.00
If a fair die is rolled 5 times what is the probability of rolling 3 sixes to the nearest thousandth
Answers
The probability of rolling 3 sixes to the nearest thousandth is 0.556.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Using binomial distribution.
[tex]^nC_r P^cQ^{n - r}[/tex]
Now,
Probability of getting a six = 1/6
P = 1/6
Probability of not getting a six = 5/6
Q = 5/6
Now,
n = 5 and r = 3
So,
[tex]^nC_r P^rQ^{n - r}[/tex]
= [tex]^5C_3(1/2)^3(5/6)^2[/tex]
= (5 x 4)/2 x (1/2) x (1/2) x (1/2) x (5/6) x (5/6)
= 10 x 1/8 x 25/36
= 5/9
= 0.556
Thus,
The probability of rolling 3 sixes is 0.556.
Learn more about probability here:
https://brainly.com/question/14099682
#SPJ1
Question in image, PLEASE HELP
Answers
The value of ST = 10 for the given rectangle.
What is a rectangle?A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.
Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.
In the given triangle PQRS, the diagonals bisect each other, that is they divide each other in equal halves.
Thus. PT = TR
Since, PT = 10 we have TR = 10,
The diagonals of the rectangle are equal, hence we also have:
TR = ST
Since, the value of TR = 10, then the value of ST = 10.
Hence, the value of ST = 10 for the given rectangle.
Learn more about rectangle here:
https://brainly.com/question/29123947
#SPJ1
Which of the following numbers is probably an irrational number? 0 1.6490221... 3/4 -5
Answers
The number that probably is an irrational number is 1.6490221...
How to determine the irrational numberAn irrational number is a number that cannot be expressed as a finite decimal or a fraction.
The number 0 is not irrational.
The number 1.6490221... is an example of a decimal that goes on forever, which is the characteristic of an irrational number.
The number 3/4 can be expressed as a fraction and is therefore not irrational.
The number -5 is not irrational.
Therefore, the answer is 1.6490221..., which is probably an irrational number.
Read more about rational numbers at
https://brainly.com/question/22221295
#SPJ1
Write 23.224 as a rational number
Answers
Answer:
Step-by-step explanation:
0.10267857142000002
x=√40-3x can someone help solve
Answers
The solution of the given equation is x= 5 and x = -8.
What is quadratic equation?An algebraic equation of the second degree in x is a quadratic equation. First, there must be a term other than zero in the coefficient of x^2 for an equation to be a quadratic equation. The x^2 term is written first when constructing a quadratic equation in standard form, then the x term, and finally the constant term.
The given equation is x = √40 - 3x.
Square on both sides of the equation:
x^2 = (√40 - 3x)²
x² = 40 - 3x
Regroup to one side of the equation:
x² + 3x - 40 = 0
x² + 8x - 5x - 40 = 0
x(x + 8) - 5 (x+8) = 0
(x - 5)(x + 8) = 0
Equate each term to 0:
x - 5 = 0
x= 5
x+ 8 = 0
x = -8
Hence, the solution of the given equation is x= 5 and x = -8.
Learn more about quadratic equations here:
https://brainly.com/question/30098550
#SPJ1
hello teacher can u help me with this
Answers
The problem states:
How many groups of 3/4 are in each of the following quantities.
So it sounds like it’s asking how many 3/4’s can go into 11/4 and 6 1/2. So we’ll use division.
First, let’s do 11/4.
11/4 divided by 3/4
When dividing by fractions, remember this tip: “keep, change, flip.” So keep the first fraction as it is, change the division sign to a multiplication sign, and flip the second fraction. So:
11/4 x 4/3
44/12
Simplify:
11/3 or 3 2/3 or 3.6666…
So the answer for 5a is above.
Now let’s do 5b.
6 1/2 divided by 3/4
First, convert mixed fraction to improper fraction to do the keep, change, flip:
13/2 divided by 3/4
Now, keep, change, flip:
13/2 x 4/3
52/6
Simply:
26/3 or 8 2/3 or 8.6666…
And above is your answer for 5b!
Hope this helped!
The graph of a parent function is shown. Which function belongs to the same function family as the graphed function?
Answers
Answer:
I doubt I'm wrong but it's D
I'll give you brainliest and extra points if it's right! :)
Answers
Answer:
see explanation
Step-by-step explanation:
given the ratio of 2 similar figures is [tex]\frac{a}{b}[/tex]
then the ratio of perimeters is also [tex]\frac{a}{b}[/tex]
and the ratio of areas is ( [tex]\frac{a}{b}[/tex] )² = [tex]\frac{a^2}{b^2}[/tex]
the ratio of side lengths, yellow to green is
[tex]\frac{36}{60}[/tex] = [tex]\frac{3}{5}[/tex] ( cancelling 36 and 60 by 12 )
the ratio of perimeters is equal to ratio of sides, that is [tex]\frac{3}{5}[/tex]
the ratio of areas = [tex]\frac{3^2}{5^2}[/tex] = [tex]\frac{9}{25}[/tex]
let x be the area of the green figure, then by proportion
[tex]\frac{45}{x}[/tex] = [tex]\frac{9}{25}[/tex] ( cross- multiply )
9x = 1125 ( divide both sides by 9 )
x = 125
that is the area of the green figure is 125 units²
Look at the figure. Find the value of CG.
VIEW THE IMAGE ATTACHED BELOW.
Answers
Answer:
CG = 8
Step-by-step explanation:
Given CG = 4x-16 is congruent to AG = 2x -4, you want the value of CG.
SetupThe congruent segments are equal length:
CG = AG
4x -16 = 2x -4
Solution2x = 12 . . . . . . . . . . add 16 -2x
Substitute into the expression for AG:
2x -4 = 12 -4 = 8
AG is congruent to CG, so ...
CG = 8
__
Additional comment
You know triangles GBC and GBA are congruent by the HA theorem, since GB bisects angle ABG. Corresponding parts of congruent triangles are congruent, so CG ≅ AG.
A teacher is placing a border around the classroom bulletin board which measures 28 7/8 inches long by 22 one fourths inches wide what is the length of the border
Answers
On solving the provided question we cans ay that area of bulletin board would be 22*10 = 220 cm sq.
What is area?The size of an area on a surface can be expressed as an area. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a planar region or planar region refers to the area of a form or planar layer. The total amount of space filled by a planar (2-D) surface or shape of an object is known as its area. Draw a square on a piece of paper using a pencil. a character with two dimensions. The area of a shape on paper is the space it takes up. Imagine that the square is composed of more compact unit squares.
This question depends on how thick you would want the border to be.
One simple way to find this is finding the perimeter of the bulletin board. You can do this by using the formula: 2(L) + 2(W)
(L) Represents Length
(W) Represents Width
In this situation, it would be 2(4) + 2(6)
that would turn into 8 + 12
which turns into 20 feet.
area of bulletin board would be 22*10 = 220 cm sq.
To know more about area visit:
https://brainly.com/question/13194650
#SPJ1
Please helppp I've been stuck on this for sooo long
Answers
The relation between a and c can be written as:
a = c + 24
Which is the relationship between a and c?First we know two equations:
a = b + 12
b = c + 12
So we have relations between a and b, and between b and c, and we want a relation between a and c.
If we replace the b of the first equation with the second equation, then we will get:
a = (c + 12) + 12
a = c + 24
That is the relation between a and c.
Learn more about equations at:
https://brainly.com/question/13729904
#SPJ1
Samantha mixes some amount of 25% sugar syrup with x grams of 10% sugar syrup. The result is 120 grams of 15% sugar syrup. How many grams of 25% sugar syrup did Samantha use?
Answers
Answer:
40 grams
Step-by-step explanation:
Answer: 120-x
Step-by-step explanation:
The scale on a 1:50 000 ordnance survey map indicates that 2cm on the map = 1km on the ground. How many centimetres would 1km be represented by on a 1:25 000 scale map
Answers
1km would be represented by 4cm on a 1 : 25000 scale map.
What is a scale factor?The scale factor defines a variable in a ratio of two different measurements.
Sometimes drawings of large models are represented in a scale factor of a smaller unit.
Given, The scale on a 1 : 50000 ordnance survey map indicates that 2cm on the map = 1km on the ground.
We know 1 km = 1×100000 = 100000 cm.
So, If 2 cm represents 100000 cm it has a scale factor of 100000/2 = 50000.
Now, Again 1 km = 100000 cm,
So, 1km will be represented by 100000/25000 = 4 cm.
learn more about scale factors here :
https://brainly.com/question/29047298
#SPJ1
Find the ordered pair that is a member of both -6x + 3y = 84 and
-6x - 3y = 24 or indicate if it does not exist or there are infinite
possibilities.
Answers
Answer:
(- 9, 10 )
Step-by-step explanation:
Solve the equations simultaneously to find solution to both
- 6x + 3y = 84 → (1)
- 6x - 3y = 24 → (2)
add (1) and (2) term by term to eliminate y
- 12x + 0 = 108
- 12x = 108 ( divide both sides by - 12 )
x = - 9
substitute x = - 9 into either of the 2 equations and solve for y
substituting into (1)
- 6(- 9) + 3y = 84
54 + 3y = 84 ( subtract 54 from both sides )
3y = 30 ( divide both sides by 3 )
y = 10
solution is (- 9, 10 )
A mallard duck has 13 ducklings. Five of the ducklings are male. What
is the ratio of male to female ducklings?
Answers
Answer: 13 ducklings 5 male 7 female so the answer is 5:7
Step-by-step explanation:
Ms. Pesko pulled 5 candy bars out of a bag. She pulled the following candies: Twix, Kit-Kat, Milky Way, Twix, Twix. What is the experimental probablity of getting a Twix?
Answers
Answer:
Step-by-step explanation:
The experimental probability of getting a Twix is 3/5 or 60%.
A savings account with simple annual interest rate of 3.92% and an initial deposit of $5,460.75 yields a final account balance of $6,370.51 after 51 months. - Part A: Using the rate and term as the simple interest account, calculate the final account balance if the initial deposit is invested for the same number of months, with interest compounded semiannually. Show all work.- Part B: Compare that simple interest final account balance with the compound interest final account balance.
Answers
The final account balance with compound interest is $6,440.30.
The final account balance when compounded semiannually is higher.
How to calculate the final account balance?
The formula for compound interest is:
A = P (1 + r/n)^(nt)
where:
A = the future value of the investment, including interest
P = the principal investment amount
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested/borrowed for
Part A:
r = 3.92% = 0.0392, P = $5,460.75, n = 2 (semiannually means twice a year), t = 51 months = 4.25 years
A = P (1 + r/n)^(nt)
A = 5,460.75 (1 + 0.0392/2)^(2*4.25)
A = 5,460.75 (1 .0196)^(8.5)
A = $6,440.30
Thus, the final account balance is $6,440.30
Part B:
difference = 6,440.30 - $5,460.75 = $975.55
When the initial deposit is invested with interest compounded semiannually, the final account balance is higher.
Learn more about compound interest on:
brainly.com/question/24274034
#SPJ1