The credit card holder paid $720.27 in interest over the 12 months. Answer choice A, $720.27, is the correct answer.
What is simple interest?
Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.
First, let's calculate the monthly interest rate by dividing the APR by 12:
11.99% / 12 = 0.99917%
Next, let's calculate the interest paid on the monthly balance for each of the 11 months before the final payment:
Month 1:
Interest = $7,568.19 x 0.99917% = $75.59
Month 2:
Balance = $7,568.19 - $350 - $75.59 = $7,142.60
Interest = $7,142.60 x 0.99917% = $71.38
Month 3:
Balance = $7,142.60 - $350 - $71.38 = $6,721.82
Interest = $6,721.82 x 0.99917% = $67.11
Month 4-11: (follow the same process as above)
Interest for Month 4: $63.82
Interest for Month 5: $60.51
Interest for Month 6: $57.17
Interest for Month 7: $53.80
Interest for Month 8: $50.41
Interest for Month 9: $47.00
Interest for Month 10: $43.56
Interest for Month 11: $40.11
Now, at the end of month 11, the cardholder has a balance of:
$7,568.19 - ($350 x 11) - $75.59 - $71.38 - $67.11 - $63.82 - $60.51 - $57.17 - $53.80 - $50.41 - $47.00 - $43.56 - $40.11 = $1,225.74
Finally, the cardholder pays off the remaining balance of $1,225.74 at the end of month 12. The interest charged for this month would be:
Interest = $1,225.74 x 0.99917% = $12.25
So the total interest paid by the cardholder over the 12 months is:
$75.59 + $71.38 + $67.11 + $63.82 + $60.51 + $57.17 + $53.80 + $50.41 + $47.00 + $43.56 + $40.11 + $12.25 = $720.27
Therefore, the credit card holder paid $720.27 in interest over the 12 months. Answer choice A, $720.27, is the correct answer.
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What is the base of the exponent in the function f(x)=3(8√3) 2x when the function is written using only rational numbers and is in simplest form?
Answer:
We can rewrite the function as:
f(x) = 3(8√3)^(2x) = 3(2^3√3)^(2x)
Using the properties of exponents, we can rewrite this as:
f(x) = 3(2^(3*2x)√3^(2x)) = 3(2^(6x)√(3^(2x)))
Therefore, the base of the exponent is 2.
Researchers comparing the effectiveness of two pain medications randomly selected a group of patients who had been complaining of a certain kind of joint pain. They randomly divided these people into two groups, then administered the pain killers. Of the 112 people in the group who received medication A, 84 said this pain reliever was effective. Of the 108 people in the other group, 66 reported that pain reliever B was effective.
(a)Find a 95% confidence interval for the difference in the proportions of people who may find these medications effective. Interpret your interval.
(b) Does this interval contain zero? What does that mean for the hypothesis test of the difference in proportions?
(a) The 95% confidence interval for the difference in proportions of people who may find these medications effective is 0.029 to 0.231, which suggests that medication A is more effective than medication B in relieving joint pain.
(b) No, the interval does not contain zero, which means that the difference in proportions is statistically significant and supports the hypothesis that medication A is more effective than medication B.
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What is the value of x in the figure below
A) 4.5
B) 10
C) 5
D) None of the choices are correct
Answer:
I will not show you the process it is easy the answer is 4.5 or 6 ≈
can y’all show that a x - 4 is a factor of the function f(x) = 2x^3 - 5x^2 - 11х - 4.
Answer:
To show that a x - 4 is a factor of the function f(x) = 2x^3 - 5x^2 - 11x - 4, we need to show that f(a x - 4) = 0 for all values of x.
We can use polynomial long division or synthetic division to divide f(x) by (a x - 4) and check if the remainder is zero. Here, we will use synthetic division:
4/a | 2 -5 -11 -4
| 8a 12a 4a-16
+------------------
2 8a-5 a-11 4a-20
The last term in the bottom row of the table is the remainder, which is 4a - 20. We can see that this remainder is equal to zero if a = 5.
Therefore, if we substitute x = (5/ax - 4) into the function f(x), we get:
f(a x - 4) = 2(5/ax - 4)^3 - 5(5/ax - 4)^2 - 11(5/ax - 4) - 4
Simplifying this expression, we get:
f(a x - 4) = 0
This means that a x - 4 is indeed a factor of the function f(x) = 2x^3 - 5x^2 - 11x - 4 when a = 5.
A cone has a radius of 6 centimeters and a height of 10 centimeters. What is the volume of the cone in cubic centimeters?
centimeters?
A 480π cm³
B 120π cm³
C 360π cm³
D 60π cm³
The volume of the cone in cubic centimeters in terms of π = 120π cm³. That is option B.
How to calculate the volume of a cone?To calculate the volume of a cone, the formula that is to be used;
Volume = 1/3 πr²h
Where;
Height = 10 centimetres
Radius = 6 centimetres
Volume = 1/3 × π × 6²× 10
= 360π/3
= 120π cm³
Therefore the volume of the cone whose dimensions are given = 120π cm³.
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eight different names were put into a hat. A name is chosen 124 times and the name fred is chosen 17 times. What is the experimental probability of the name fred being chosen? What is the theoretical probability of the namedred being chosen? Use pencil and paper. Explain how each probability would change if the number of names in the hat were different.
The answer of given Theoretical Probability Question is 0.1379 , 0.125
Experimental probability of the name Fred being chosen = number of times Fred is chosen / total number of trials
= 17/124
= 0.1379 (rounded to four decimal places)
Theoretical probability of the name Fred being chosen = number of outcomes in which Fred is chosen / total number of possible outcomes
Since there are eight different names in the hat, the total number of possible outcomes is 8. The number of outcomes in which Fred is chosen is 1 (since there is only one Fred in the hat).
Therefore, the theoretical probability of Fred being chosen is:
1/8 = 0.125 (rounded to three decimal places)
If the number of names in the hat were different, both the experimental and theoretical probabilities would change.
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Alen has read 60% of a book. He has 32 more pages to finish. How many pages are there in the book?
Alen has read 60% of a book in which there are 80 pages in the book.
What is total number?The term "total number" typically refers to the complete quantity or count of something. It can refer to the number of items in a set, the number of people in a population, the total sales of a company, or any other numerical quantity that represents a whole.
According to question:Let's say the total number of pages in the book is "x".
According to the problem, Alen has read 60% of the book, which means he has completed 0.6x pages.
He still has 32 more pages to finish, so the number of pages he has left to read is (x - 0.6x) = 0.4x.
We can set up an equation:
0.4x = 32
Solving for x:
x = 80
Therefore, there are 80 pages in the book.
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Ken bought 3 3/4 pounds of apples at the farmers market Abby bought 2 1/8 pounds of apples how many pounds of apples did ken buy
Answer:Ken 3 3\4 pounds of apples
Step-by-step explanation:
PLEASE HELP Area of Cross Sections
For the given pyramid the area of the cross section is 1,307.63 mm² (option D).
What is pyramid?
A pyramid is a geometrical shape that has a polygonal base and triangular faces that meet at a common vertex, called the apex.
We can use the formula for the area of a trapezoid to find the area of the cross section. Since the slice is perpendicular to the base of the pyramid, the cross section will be a trapezoid.
The length of the top side of the trapezoid is the same as the length of one of the sides of the rectangular base of the pyramid, which is 37.8mm. The length of the bottom side of the trapezoid can be found using similar triangles:
(49.3 / 37.8) = (bottom side / height)
Simplifying, we get:
bottom side = (height x 49.3) / 37.8 = (42.1 x 49.3) / 37.8 = 54.94 mm
The height of the trapezoid is the same as the height of the pyramid, which is 42.1mm.
Using the formula for the area of a trapezoid:
area = [(top side + bottom side) x height] / 2
area = [(37.8 + 54.94) x 42.1] / 2
area = 1,307.63 mm²
Therefore, the area of the cross section is 1,307.63 mm² (option D).
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during a sale, all shirts cost $35 and all pants cost $50. jonathan is buying new clothes for school and planes to spend at least $350
The minimum purchase Jonathan can make to meet his spending requirement is 7 pants and 0 shirts, which will cost him $350.
What is equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".
Assuming Jonathan only wants to buy shirts and pants, let's represent the number of shirts he buys as "s" and the number of pants as "p". Then we have two equations:
1. The total cost of Jonathan's purchase:
35s + 50p >= 350
2. Jonathan wants to spend at least $350:
s, p >= 0
To solve this problem, we can start by finding the minimum number of pants Jonathan needs to buy to meet his spending requirement.
When s = 0, 50p >= 350, so p >= 7.
Therefore, Jonathan needs to buy at least 7 pants.
If Jonathan buys 7 pants, the total cost of his purchase is 35s + 50(7) = 35s + 350. To spend at least $350, he needs to buy enough shirts to make the total cost of his purchase at least $350.
35s + 350 >= 350
35s >= 0
s >= 0
Since s must be a non-negative integer (you can't buy a fractional part of a shirt), Jonathan needs to buy at least 0 shirts.
So the minimum purchase Jonathan can make to meet his spending requirement is 7 pants and 0 shirts, which will cost him $350.
Of course, Jonathan can buy more than 7 pants and/or some shirts to meet his spending requirement. For example, he could buy 5 pants and 4 shirts, which would cost him $375.
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The gasoline gauge on a van initially read
1/4 full. When 12 gallons were added to the tank, the gauge read 3/4 full. How many more gallons are needed to fill the tank?
Initially, 1/4 of the tank was filled.
After adding 12 gallons, it was 3/4 full.
Increase in fuel filled portion =
[tex]\dfrac{3}{4} -\dfrac{1}{4} =\dfrac{3-1}{4} =\dfrac{2}{4}[/tex]
So 2/4 of the tank = 12 gallons
1/4 of tank [tex]= 12 \div 2 = 6[/tex] gallons
4/4 of tank [tex]= 6\times4 = 24[/tex] gallons
____________________
Portion remaining to be filled =
[tex]1-\dfrac{3}{4} =\dfrac{4-3}{4} =\dfrac{1}{4}[/tex]
Fuel needed [tex]= \dfrac{1}{4} \times 24 = 6[/tex] gallons
So you need 6 more gallons to fill the tank
A rectangular prism is 4 inches long, 3 inches wide, and 8 inches tall. Eli packs the prism with unit cubes to find the volume. Abby uses a formula to find the volume.
Part A]
Answer:
The volume of this rectangular prism is
4 × 3 × 8 = 96 square inches. So Eli would need 96 unit cubes.
A block of metal with volume 15 m³ 3 and density 8,800 kg/m³ is combined with another metal of 3 mass 850 kg and volume 6.2 m³ to form an alloy. What is the density of the alloy to the nearest integer?
Answer:
Step-by-step explanation:
The total mass of the alloy is the sum of the masses of the two metals:
mass = density x volume = (8800 kg/m³ x 15 m³) + 850 kg = 132,000 kg + 850 kg = 132,850 kg
The total volume of the alloy is the sum of the volumes of the two metals:
volume = 15 m³ + 6.2 m³ = 21.2 m³
Therefore, the density of the alloy is:
density = mass / volume = 132,850 kg / 21.2 m³ ≈ 6266 kg/m³
Rounding to the nearest integer, the density of the alloy is 6266 kg/m³.
Circle Project 1. Draw a point at (1, -2) 2. Draw an 8-unit long radius 3. Using a compass, Draw a circle with your point from step one as your center and the point from step two as the side. 4. Using a protractor, draw a 70 degree arc 5. Draw a central angle which intercepts your arc 6. Draw an inscribed angle which intercepts a 40 degree arc 7. Draw a tangent line 8. Draw a secant line 9. Write the equation of your circle.
Answer:
I can explain how to complete each of the steps you have provided.
1. Draw a point at (1, -2)
This is a simple step. Just mark a dot on your paper at the coordinates (1, -2).
2.
Draw an 8-unit long radius
Using your compass, set the radius to 8 units. Place the compass on the point you drew in step 1 and draw a circle around it, making sure that the radius is 8 units long.
3. Using a compass
Draw a circle with your point from step one as your center and the point from step two as the side: This step is already completed in step 2.
4. Using a protractor draw a 70 degree arc
Place your protractor on the center of the circle (the point you drew in step 1) and draw a 70 degree arc on the circle.
5. Draw a central angle which intercepts your arc
Use a straight edge to draw a line from the center of the circle to each endpoint of the arc you drew in step 4. This creates a central angle, which is an angle whose vertex is at the center of the circle and whose sides intercept the circle.
6. Draw an inscribed angle which intercepts a 40 degree arc
Use a straight edge to draw a line from one endpoint of the 70 degree arc to the other endpoint. Then, draw a perpendicular bisector of this line, which intersects the center of the circle. This creates a 40 degree arc on the circle. Draw a line from the center of the circle to one endpoint of the 40 degree arc, and draw a line from that endpoint to the other endpoint of the 40 degree arc. This creates an inscribed angle, which is an angle whose vertex is on the circle and whose sides intercept the circle.
7. Draw a tangent line
Choose a point on the circle that is not on the 70 degree arc. Draw a line from that point tangent to the circle.
8. Draw a secant line
Choose two points on the circle that are not on the 70 degree arc. Draw a line through those points, which intersects the circle at two points.
9. Equation of your circle
The equation of a circle with center (a,b) and radius r is (x-a)^2 + (y-b)^2 = r^2. Using the coordinates of the center from step 1 and the radius from step 2, the equation of the circle is (x-1)^2 + (y+2)^2 = 64.
anna uses $25 to open a savings account. The function a(t) models the amount of money, a in her account, where t is the number of years since the account was opened. which function models the situation if her account earns 2.5% interest per year
The formula can also be written as: a(n) = 25(1.025)ⁿ where 1.025 is the factor by which the initial amount is multiplied after each year of interest.
What is function?In mathematics, a function is a rule that assigns each input (or element of the domain) a unique output (or element of the range). It is a mathematical object that takes an input and produces an output based on a specified rule or set of rules. A function can be represented in different ways, such as by an equation, a graph, or a table of values. The most common notation for a function is f(x), where x is the input and f(x) is the corresponding output. Functions are used to describe relationships between quantities in various fields of mathematics and science, such as in calculus, linear algebra, statistics, physics, and engineering. They are also used in modeling real-world situations and solving problems in many areas, including finance, economics, and computer science.
Here,
The formula for calculating the amount of money in Anna's savings account with an initial deposit of $25 and 2.5% annual interest rate, compounded annually, is:
a(n) = 25(1 + 0.025)ⁿ
where t is the number of years since the account was opened.
This is the formula for calculating the future value of a present sum using compound interest formula.
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Complete question:
anna uses $25 to open a savings account. The function a(t) models the amount of money, a in her account, where t is the number of years since the account was opened. create a function that models the situation if her account earns 2.5% interest per year.
1/2 + 3/9 = The first time a team is
Answer:
Step-by-step explanation:
To get the LCM in the denominator:
1/2 x 9/9 = 9/18
3/9 x 2/2 = 6/18
9/9 and 2/2 both equal 1, so multiplying these fractions by ny number will result in the same number since any number times 1 is the same number.
9/18 - 6/18 = 3/18
Simplifying this answer:
3/18 = 1/6 because both the numerator and denominator are both multiples of three and are divisible by three.
The answer is 1/6.
Answer: 7/9 or 0.83333333333
Step-by-step explanation:
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Lamonte was driving down a road and after 4 hours he had traveled 62 miles. At this speed, how many hours would it take Lamonte to drive 93 miles?
The time taken by the Lamonte would be 6 hours to drive 93 miles at a speed of 15.5 miles per hour.
How to calculate the time ?We can use the following formula to answer this question:
rate x time = distance
We know Lamonte drove 62 miles in four hours, so we can use that to calculate his speed:
62 miles = rate multiplied by 4 hours
When we solve for the rate, we get:
rate = 62 miles divided by 4 hours equals 15.5 miles per hour
We can now use this rate to calculate how long it would take Lamonte to drive 93 miles:
93 miles = time x rate
Substituting the recently discovered rate yields:
93 miles = 15.5 miles per hour multiplied by time
When we solve for time, we get:
time = 93 miles / 15.5 miles per hour = 6 hours
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Evaluate when a=1/2 and b=7 b*2 - 16a + 5
Answer:
46
Step-by-step explanation:
b*2 - 16a + 5 a = 1/2 b = 7
= (7)² - 16(1/2) + 5
= 49 - 8 + 5
= 41 + 5
= 46
79 Points!!! Algebra question. A biologist plotted the data from his latest experiment and connected the points to form the graph shown. He recognizes that the graph is a translation of y=x^2. Write a function f(x) to represent the graph of his data. Photo attached. Thank you!
I need help anyone wants to help me with this to write it out :) thank you<3!!!
Answer:
Dip your finger in both whichever one is salty don't give to your plant
Step-by-step explanation:
How much water can a cylindrical bottle hold that is 5 cm in diameter and 10 cm tall?
a. 196.35 cm^3
b. 785.4 cm^3
c. 735 cm^3
d. 215 cm ^3
In response to the stated question, we may state that As a result, the cylindrical container can carry around 196.35 cm3 of water. As a result, (a) 196.35 cm cubic is the right answer.
what is cylinder?A cylinder seems to be a three-dimensional geometric shape made up of two parallel congruent circular bottoms and a curving surface linking the two bases. The bases of a cylinder are always perpendicular from its axis, which is an artificial straight line passing through the centre both of bases. The volume of a cylinder is equal to the product among its base area and height. A cylinder's volume is computed as V = r2h, within which "V" represents the volume, "r" represent the circle of the base, and "h" represents the height of the cylinder.
The volume of a cylinder is determined by the formula V = r2h, where r is the radius of the base, h is the cylinder's height, and is a mathematical constant close to 3.14.
In this situation, the radius is 2.5 cm since the base is 5 cm in diameter. The cylinder stands 10 cm tall. As a result, the volume of the cylinder is:
[tex]V = \pi(2.5 cm)^2(10 cm) (10 cm)\\V = 196.35 cm^3[/tex]
As a result, the cylindrical container can carry around 196.35 cm3 of water. As a result, (a) 196.35 cm cubic is the right answer.
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(URGENT)!!!!!!!
Write one sentence that addresses the issue of globalization from the text and one sentence on how the absence of plantation owners perpetuated cruel treatment of slaves by overseers
Answer:
Step-by-step explanation:
One sentence on globalization from the text: The process of globalization has brought significant changes to the world economy, including the emergence of new trade patterns and the increasing interconnectedness of markets.
One sentence on how the absence of plantation owners perpetuated cruel treatment of slaves by overseers: In the absence of plantation owners, overseers were left with unchecked power over the enslaved population, often resulting in brutal treatment and violence
which continent do you think I live in
Suppose 50 rabbits are on Groff Farm… DOUBLING every SIX MONTHS…
How many rabbits after 5 years?
How many rabbits after 10 years?
Using geometric progression Rabbits after 5 years will be 5120. Rabbits after 10 years will be 52,428,800.
What is geometric progression?When each term is varied by another by a common ratio, the series is referred to as a geometric progression or sequence. When we multiply the previous term by a constant (which is non-zero), we get the following term in the series. It should be mentioned that the common ratio is obtained by dividing any succeeding term by its preceding term.
What is ratio?Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate organizations or groups.
In this question,
The number of rabbits initially=50=a
rabbits after 6 months=100
common ratio=r= 100/50=2
Since it is a geometric progression, the 11th term will give us the number of rabbits after 5 years.
a₁₁=a₁(r)¹¹⁻¹
=50(2)¹⁰=5120
the 21th term will give us the number of rabbits after 10 years.
a₂₁=a₁(r)²¹⁻¹
=50(2)²⁰=52,428,800
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I need to know the z score of 2,-2 and also the mean and standard deviation
Answer: two standard deviations below the average value.
Step-by-step explanation: The z score tells you how far below the average value that person or group is, on a scale from -2 to 2. The higher the z score, the more abnormal or anomalous the data being compared is. A z score of 1 indicates that the data is exactly average, while a z score of -2 indicates that the data is two standard deviations below the average value.
Solve 2^x=32, and rewrite this equation in a logarithmic form.
Answer:
To solve 2^x = 32, we need to find the value of x that satisfies the equation.
We can rewrite 32 as a power of 2 by noting that 2^5 = 32. Therefore, we have:
2^x = 2^5
Since the bases of the powers are equal, we can equate the exponents:
x = 5
So the solution to 2^x = 32 is x = 5.
To rewrite this equation in a logarithmic form, we can use the definition of logarithms:
log(base 2)32 = x
Here, the logarithm with base 2 of 32 is equal to x.
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Question 29 Which expression represents the distance between points J and K on the number line?
On the number line, there are five spaces between the points J and K.
What does a number line exactly mean?A number line is a horizontal line with consistently spaced numerical increments. How you respond to the number on the line will depend on the numbers on the line. Depending on the question that goes with it, a number can be used in a variety of ways, such as when graphing a point.
The absolute value of the difference in the coordinates between points J and K on the number line can be used to calculate the distance between them.
Points J and K in this instance have coordinates of -4 and 1, respectively. As a result, the following formula may be used to indicate the distance between locations J and K:
|1 - (-4)|
If we condense this expression, we get:
|1 + 4|
= |5|
= 5
Hence, the distance on the number line between points J and K is 5.
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A rectangular sheet of paper 72 cm x 48 cm is rolled along its length and a cylinder is formed. Find the volume of the cylinder.
Answer:
5
Step-by-step explanation:
this is wrong
for each situation, determine taxable income, assuming pretax accounting income is $100 million
Answer:
Temporary Differences Reported First on: The Income Statement The Tax Return Revenue Expense Revenue Expense1) $272) $273) $274) $275) $22 $276) $27 $227) $22 $27 $178) $22 $27 $12 $17Taxable Income assuming pretax accounting income is $100 million1) Pretax Income - Revenue = $100m - $27m = $73m2) Pretax Income + Expense = $100m + $27m = $127m3) Pretax Income + Revenue Return = $100m + $27m = $127m4) Pretax Income - Expense Return = $100m - $27m = $73m5) Pretax Income - Revenue + Expense = $100m - $22m + $27m = $105m6) Pretax Income + Expense + Revenue Return = $100m + $27m + $22m = $149m7) Pretax Income - Revenue + Expense - Expense Return = $100m - $22m + $27m - $17m = $88m8) Pretax Income - Revenue + Expense + Revenue Return - Expense Return = $100m - $22m + $27m + $12m- $17m = $100m
Step-by-step explanation:
First, return is added to differentiate revenue and expense from the tax return from that of the income statement.Temporary difference is defined as the difference between the tax and financial reporting bases of assets and liabilities. These differences can result in taxable or deductible amounts in future years (deferred tax assets or liabilities).For each scenario, temporal difference of revenue reported first in the income statement is deducted from the pretax accounting income while expenses are added back to the pretax accounting income.For temporal differences from the tax return, the revenue is added to the pretax accounting income while expenses are deducted.
Graph the solution set to this inequality.
-2(x + 6) > -4x
Drawing Tools
Select
Point
Open Point
Ray
Click on a tool to begin drawing.
-10
+
-8
-6
-2
Delete
Undo
Answer:
Step-by-step explanation: