The CDF of Y evaluated at y = 0.72 is 0.1296.
Since X1 and X2 are independent and uniformly distributed over [0, 2], their joint density function is:
f(x1, x2) = 1/4, for 0 ≤ x1 ≤ 2 and 0 ≤ x2 ≤ 2
To find the CDF of Y, we can use the fact that:
Fy(y) = P(Y ≤ y) = P(max(X1, X2) ≤ y)
This event can be split into two cases:
X1 and X2 are both less than or equal to y:
In this case, Y will be less than or equal to y.
The probability of this occurring can be calculated using the joint density function:
P(X1 ≤ y, X2 ≤ y) = ∫0y ∫0y f(x1, x2) dx1 dx2
= ∫0y ∫0y 1/4 dx1 dx2
\(= (y/2)^2\)
\(= y^2/4\)
One of X1 or X2 is greater than y:
In this case, Y will be equal to the maximum of X1 and X2.
The probability of this occurring can be calculated as the complement of the probability that both X1 and X2 are less than or equal to y:
P(X1 > y or X2 > y) = 1 - P(X1 ≤ y, X2 ≤ y)
\(= 1 - y^2/4\)
Therefore, the CDF of Y is:
Fy(y) = P(Y ≤ y) = P(max(X1, X2) ≤ y)
= P(X1 ≤ y, X2 ≤ y) + P(X1 > y or X2 > y)
\(= y^2/4 + 1 - y^2/4\)
= 1, for y ≥ 2
\(= y^2/4,\)for 0 ≤ y ≤ 2
To find Fy(0.72), we simply substitute y = 0.72 into the expression for Fy(y):
\(Fy(0.72) = (0.72)^2/4 = 0.1296\)
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Since X1 and X2 are uniformly distributed over [0, 2], their probability density functions (PDFs) are:
fX1(x) = fX2(x) = 1/2, for 0 <= x <= 2
To find the CDF of Y = max(X1, X2), we need to consider two cases:
1. If y <= 0, then Fy(y) = P(Y <= y) = 0
2. If 0 < y <= 2, then Fy(y) = P(Y <= y) = P(max(X1, X2) <= y)
We can find this probability by considering the complementary event, i.e., the probability that both X1 and X2 are less than or equal to y. Since X1 and X2 are independent, this probability is:
P(X1 <= y, X2 <= y) = P(X1 <= y) * P(X2 <= y) = (y/2) * (y/2) = y^2/4
Therefore, the CDF of Y is:
Fy(y) = P(Y <= y) =
0, y <= 0
y^2/4, 0 < y <= 2
1, y > 2
To find Fy(0.72), we substitute y = 0.72 into the CDF:
Fy(0.72) = 0.72^2/4 = 0.1296
Therefore, the value of Fy(y) at y = 0.72 is 0.1296.
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Frank opened up a café. On the first day, he had no customers. On the second day however, he had five customers. On the third day, there were 10 customers, and on the fourth day there were 15 customers. He also ran a lunch giveaway, whereby if you left a business card, he would enter it in a drawing for a free lunch. On the first day, no one left a card (since there were no customers), on the second day, three people left business cards, and each following day, three more people left business cards than on the previous day. If this pattern continues for a full year (365 days), what is the difference between the total number of customers he would have and the total number of business cards?
In summary, the difference between the total number of customers and the total number of business cards is 109,500.
What is the net disparity between the cumulative customers and business cards?If we examine the pattern established in the initial days, we observe that the number of customers increases by 5 each day, starting from 0. Simultaneously, the number of business cards left increases by 3 more than the previous day's count. To determine the total number of customers over the course of a year, we can sum the arithmetic series, with the first term as 5, the common difference as 5, and the number of terms as 365. This yields a sum of 66,725 customers.
Next, we need to calculate the total number of business cards left. Using the same approach, we have a first term of 3, a common difference of 3, and 364 terms (since no business cards were left on the first day). The sum of this arithmetic series is 66,220 business cards.
Finally, to find the difference between the total number of customers and business cards, we subtract the sum of business cards from the sum of customers: 66,725 - 66,220 = 505. Therefore, the difference between the total number of customers and business cards is 505.
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DETAILS PREVIOUS ANSWERS LARAPCALC10 5.4.012.MI.SA. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receiv points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise Find the area of the region y=3/√x
The area of the region bounded by the curve y = 3/√x from x = 0 to x = a is 6√a.\(y = 3/√x from x = 0 to x = a is 6√a.\)
To find the area of the region bounded by the curve y = 3/√x, we can set up an integral and evaluate it.
First, let's determine the limits of integration. The curve y = 3/√x is defined for x > 0. To find the bounds, we set the denominator equal to zero:
√x = 0
x = 0
So, we need to find the area of the region between the curve and the x-axis from x = 0 to some upper limit x = a.
Now, we can set up the integral for the area A:
A = ∫[0, a] y dx
Substituting the given curve equation, we have:
A = ∫[0, a] (3/√x) dx
To solve this integral, we can rewrite the expression as:
\(A = 3∫[0, a] x^(-1/2) dx\)
Integrating, we get:
A = 3[2√x] evaluated from 0 to a
A = 6√a - 6√0
A = 6√a
Note: Please provide the specific value of 'a' if you want a numerical answer.
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what is the solution of the follow inequality-3x+3> or equal to 9
Answer:
x ≤ - 2
Step-by-step explanation:
Given
- 3x + 3 ≥ 9 ( subtract 3 from both sides )
- 3x ≥ 6
Divide both sides by - 3, reversing the symbol as a result of dividing by a negative quantity.
x ≤ - 2
Answer:
x<or equal to -2
Step-by-step explanation:
-3x>or equal to 9-3
-3x>or equal to 6(dividing both of them by -3)
x<or equal to -2
3. Explain why * =
61
g choose the best apa style report for the t-test using cohen's d. you may choose to ignore the negative signs for the t-statistic or d. note: when interpreting you need only choose one index of effect size.
When reporting the results of a t-test using Cohen's d as the index of effect size in APA style, the report should include the following components: the descriptive statistics, the results of the t-test, and the effect size estimate.
The descriptive statistics should include the mean and standard deviation for each group being compared, as well as the sample size for each group. The t-test results should include the t-statistic, degrees of freedom, and p-value. The effect size estimate using Cohen's d should also be reported.
One example of an APA style report for a t-test using Cohen's d could be as follows:
"A t-test was conducted to compare the mean score on (insert variable name) between (insert group 1 name) and (insert group 2 name). Descriptive statistics showed that the mean score for (insert group 1 name) was (insert mean) with a standard deviation of (insert SD), while the mean score for (insert group 2 name) was (insert mean) with a standard deviation of (insert SD).
Results of the t-test indicated a significant difference between the groups, t(df) = (insert t-statistic), p = (insert p-value). The effect size estimate using Cohen's d was (insert effect size), indicating a (insert interpretation of effect size)."
It is important to note that when interpreting the effect size estimate, researchers should choose only one index of effect size (i.e. either d or the t-statistic, but not both) to avoid redundancy in the report. Additionally, it is important to adhere to the specific APA style guidelines for reporting statistical analyses to ensure clarity and accuracy in the reporting of results.
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What is 1/3÷5 not being a decimal
Answer:
Hello! answer: 1/15
Step-by-step explanation:
1/3 ÷ 5 = 1/15 Hope that helps!
Vicky is a computer programmer. last week she wrote 6,013 lines of code. this week she wrote about half as much.
Vicky, a computer programmer, wrote 6,013 lines of code last week. This week, she wrote approximately half that amount, which is around 3,007 lines of code.
Last week, Vicky's productivity as a programmer resulted in the creation of 6,013 lines of code. However, this week she worked at a slightly slower pace, producing approximately half as much. By dividing last week's count of lines of code by 2, we estimate that she wrote about 3,006.5 lines of code. Since lines of code cannot be expressed as fractions or decimals, we round the number to the nearest whole value, resulting in approximately 3,007 lines of code written this week.
This estimation indicates that Vicky's output decreased by approximately half compared to the previous week. It could be due to various factors such as reduced workload, increased complexity of the code, time constraints, or other factors influencing her productivity. Nonetheless, Vicky's ability to consistently write a substantial number of lines of code showcases her proficiency as a computer programmer.
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A large rectangle has an area of 5x^2 + 3x - 2. If I place a smaller rectangle, with an area of 2x^2 + x + 6, over the larger rectangle. What area of the larger rectangle will still be visible?
Answer:
(5x^2 + 3x - 2) - (2x^2 + x + 6) = 3x^2 + 2x - 8
Step-by-step explanation:
a piece of equipment has a first cost of $150,000, a maximum useful life of 7 years, and a market (salvage) value described by the relation s
The economic service life of the equipment is 1 year, as it has the lowest total cost of $306,956.52 compared to the costs in subsequent years.
Let's calculate the total cost (TC) for each year using the following formula:
TC = FC + AOC + PC
Where:
FC = First cost
AOC = Annual operating cost
PC = Present cost (the present value of the salvage value at each year)
Given:
First cost (FC) = $150,000
Maximum useful life = 7 years
Salvage value (S) = 120,000 - 20,000k (where k is the number of years since it was purchased)
AOC = 60,000 + 10,000k (where k is the number of years since it was purchased)
Interest rate = 15% per year
TC = FC + AOC + PC
\(PC = S / (1 + interest rate)^k\)
Year 1:
TC = $150,000 + ($60,000 + $10,000(1)) + [(120,000 - 20,000(1)) / (1 + 0.15)¹]
TC = $306,956.52
Year 2:
TC = $150,000 + ($60,000 + $10,000(2)) + [(120,000 - 20,000(2)) / (1 + 0.15)²]
TC = $312,417.58
Year 3:
TC = $150,000 + ($60,000 + $10,000(3)) + [(120,000 - 20,000(3)) / (1 + 0.15)³]
TC = $318,508.06
Year 4:
TC = $150,000 + ($60,000 + $10,000(4)) + [(120,000 - 20,000(4)) / (1 + 0.15)⁴]
TC = $324,204.29
Year 5:
TC = $150,000 + ($60,000 + $10,000(5)) + [(120,000 - 20,000(5)) / (1 + 0.15)⁵]
TC = $329,482.80
Year 6:
TC = $150,000 + ($60,000 + $10,000(6)) + [(120,000 - 20,000(6)) / (1 + 0.15)⁶]
TC = $334,319.36
Year 7:
TC = $150,000 + ($60,000 + $10,000(7)) + [(120,000 - 20,000(7)) / (1 + 0.15)⁷]
TC = $338,689.53
We can see that the total costs increase over the 7-year period.
The economic service life is determined by the year where the total cost is minimized.
Hence, the economic service life of the equipment is 1 year, as it has the lowest total cost of $306,956.52 compared to the costs in subsequent years.
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A piece of equipment has a first cost of $150,000, a maximum useful life of 7 years and a salvage value described by the relationship S=120,000-20,000k, where k is the number of years since it was purchased. The salvage value cannot go below zero. The AOC series is estimated using AOC=60,000+10,000k. The interest rate is 15% per year. Determine the Economic Service Life
If y=x+2 changed to y=x-1 how would it change
Which expression is a difference of squares with a factor of 2x+5
Answer:
4x^2 – 25
Step-by-step explanation:
i'vegot your back :))
a fair bet is a: wager entered into with honesty and concern for the welfare of the other party. gamble that provides net gains to all participants so there is no loser. wager entered into when the rules are clear to all participants. gamble that, on average, will leave a person with the same amount of money.
Answer:gamble that,on average,will leave a person with the same amount of money.
Step-by-step explanation:
-1 /-26 simplified
Answer:
0.038
Step-by-step explanation:
I really hope this helps I'm sorry if its wrong
Brainliest please if its right.
Which relation in the below table(s) represents a function?
The relation 2 represents a function.
In order to determine which relation in the below table represents a function, we need to first understand what a function is.A function is a relationship in which each input value corresponds to exactly one output value.
To put it another way, each x-value has one and only one y-value. The most typical method to determine whether a relation is a function is to use the vertical line test.
The vertical line test is a way to determine if a relation is a function graphically. To test if a graph is a function, we draw a vertical line through each x-value on the graph. If a vertical line crosses the graph more than once, it is not a function.
If, on the other hand, the graph passes the vertical line test and no vertical line crosses the graph more than once, it is a function.Now let's look at the table below to determine which relation is a function.
We will first plot the x and y values of each relation on a coordinate system and then apply the vertical line test to each relation.
Relation 1: x | y0 | 10 | 11 | 22 | 23 | 34 | 35 | 4Relation 1 does not represent a function since we can draw a vertical line through x = 3 and the line will cross the graph more than once.
Relation 2: x | y2 | 33 | 34 | 45 | 46 | 57 | 5Relation 2 represents a function since we can draw a vertical line through each x-value on the graph and it will only cross the graph once.
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Write FIVE (5) major learnings of yours in media and current event
course. Explain each learning briefly
Throughout my studies in media and current events, I have gained several major learnings that have shaped my understanding of the subject matter.
These include the importance of media literacy and critical thinking, the power and influence of social media, the role of bias in news reporting, the significance of ethical journalism, and the impact of media on shaping public opinion.
1. Media Literacy and Critical Thinking: One of the most crucial learnings is the importance of media literacy and critical thinking skills. It is essential to analyze and evaluate the information presented by media sources, considering their credibility, bias, and potential agenda. Developing these skills enables individuals to make informed judgments and avoid misinformation or manipulation.
2. Power and Influence of Social Media: Another significant learning is recognizing the power and influence of social media in shaping public opinion and disseminating news. Social media platforms have become prominent sources of information, but they also pose challenges such as the spread of fake news and echo chambers. Understanding the impact of social media is crucial for both media consumers and producers.
3. Role of Bias in News Reporting: Media bias is an important factor to consider when consuming news. I have learned that media outlets may have inherent biases, influenced by their ownership, political affiliations, or target audience. Recognizing these biases allows for a more balanced and critical understanding of news content, and encourages seeking diverse perspectives.
4. Significance of Ethical Journalism: Ethics play a fundamental role in responsible journalism. I have learned about the importance of principles such as accuracy, fairness, and accountability in reporting news. Ethical journalism promotes transparency and ensures the public's trust in the media, contributing to a well-informed society.
5. Impact of Media on Shaping Public Opinion: Lastly, I have learned that the media holds a significant role in shaping public opinion and influencing societal attitudes. Through various forms of media, such as news coverage, documentaries, or entertainment, narratives are constructed that can sway public perception on issues ranging from politics to social matters. Recognizing this influence is crucial for media consumers to engage critically with the information they receive and understand the potential impact it can have on society.
These five major learnings have provided me with a comprehensive understanding of media and current events, enabling me to navigate the vast landscape of information and make more informed judgments about the media I consume. They highlight the importance of media literacy, critical thinking, understanding bias, ethical journalism, and the impact media has on public opinion, ultimately contributing to a more well-rounded and discerning approach to media consumption.
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Can anyone help me with this?
Answer:
a=30°; b=40°;c=40°; d=40°; e=110°: f=110°; g=30°; h=140°; i=70°; j=70°
Amy will be using a t-chart to find 3 points for this linear function: f(x)= 3x -2. Which chart below is the correct answer for this function. WILL GIVE BRAINLIEST
The points for a linear function are (0, -2), (1, 1) and (2, 4)
Linear equation
A linear equation is in the form:
y = mx + b
where y, x are variables, m is the rate of change (slope) and b is the y intercept.
Given that the relationship between f(x) and x is given by:
f(x) = 3x - 2
When x = 0: f(0) = 3(0) - 2 = -2
When x = 1: f(1) = 3(1) - 2 = 1
When x = 2: f(2) = 3(2) - 2 = 4
The points for a linear function are (0, -2), (1, 1) and (2, 4)
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Answer:
(0, -2) (1, 1) (-3, -11)
Step-by-step explanation:
a =
a. 6
b. 9
c. 4
Please find a in the triangle its on my attached file plss
Answer:
Step-by-step explanation:
\(c^{2}+b^{2} = (4+a)^2 \\c = \sqrt{6^2+4^2}\\ c = \sqrt{36+16}\\ c = \sqrt{52} \\c^2 = 52\\a^2 + 6^2 = b^2\\\\52 + a^2 + 36 = 16 + a^2 + 8a\\ 8a = 72\\a = 9\)
Please mark my answer as brainliest .
an outfielder throws a ball to home plate. the balls path is modeled by the graph of y=x/5-x^2/1000 where x represents the horizontal distance of the ball from the outfield and y represents the balls vertical distance above the ground. what are the coordinates of vertex of the ball's path?
Answer:
(100,10)
Step-by-step explanation:
Please help me with this
Answer:
x = 23
Step-by-step explanation:
if line j is parallel to line k then
5x + 9 + 33 + x = 180 add like terms
6x + 42 = 180 subtract 42 from both sides
6x = 138 divide both sides by 6
x = 23
help please :))))))))))))
Answer:
220
Step-by-step explanation: You just do inverse operation 55x4=220, check 220/4=55.
Answer:
x=220
Step-by-step explanation:
x /4 =55
Step 1: Multiply both sides by 4.
x/ 4 =55 ( x 4 )*(4)=(55)*(4)
x=220
The first Epistle of John was written about A.D is :
45
60-65
90-95
97
The first Epistle of John was written about AD of between 95 and 110 . So, by this our option should be 97 AD, which is true.
The Fourth of the Catholic Epistles, The First Epistle of John[a] is the first of the Johannine epistles in the New Testament. The authorship of the Johannine writings is disputed among academics. The First Epistle's author is identified as John the Evangelist, who most scholars do not consider to be the same person as John the Apostle. The three Johannine epistles are thought to have been written by the same person by the majority of scholars, however it is unclear if the same person wrote the Gospel of John.
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Please answer quickly, due soon!
Answer:
Its A
explanation:
The greater than or equal to is usually coloured and normal is not coloured
TRUE/FALSE When inserting a value into a partially-filled array, in descending order, the insertion position is the index of the first value smaller than the value.
The given statement When inserting a value into a partially-filled array in descending order, the insertion position is indeed the index of the first value smaller than the value being inserted is true.
What is partially filled array?
A partially filled array, also known as a sparse array, is an array data structure where not all elements are populated with values. In other words, it is an array that contains empty or uninitialized elements.
When inserting a new value into this sorted array, we start from the beginning and compare the value with each existing element until we find the first element that is smaller. The insertion position for the new value is the index of this first smaller element.
For example, if we have a partially-filled array [10, 8, 5, 3] and we want to insert the value 6 into the array in descending order, we compare 6 with each element from left to right. The first element smaller than 6 is 5, and its index is 2. Therefore, the insertion position for the value 6 would be index 2, resulting in the updated array [10, 8, 6, 5, 3].
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i have a photo can someone solve it
Answer:
I think the answer is B.6.4ft
Step-by-step explanation:
can anyone help me with this
Answer:
ohh i don't know the answer
For a certain population of penguins, the distribution of weight is approximately normal with mean 15. 1 kilograms (kg ) and standard deviation 2. 2 kg. Approximately what percent of the penguins from the population have a weight between 13. 0 kg and 16. 5 kg ?.
56.78% of the penguins in the population have a weight between 13.0 kg and 16.5 kg, according to the usual distribution.
Given,
The mean of the population, μ = 15.1 kg
Standard deviation, σ = 2.2 kg
We have to find the percent of the penguins from the population have a weight between 13. 0 kg and 16. 5 kg;
Here,
z score = x - μ / σ
The z-score calculates how far the measure deviates from the mean by standard deviation.The p-value for this z-score, which is the percentile of X, can be obtained by looking at the z-score table.The ratio of the p-value of Z when X = 16.5 minus the p-value of Z when X = 13 indicates the percentage of penguins in the population whose weight is between 13.0 kg and 16.5 kg.
x = 16.5
z score = x - μ / σ
z = (16.5 - 15.1) / 2.2 = 0.64
Z = 0.64 has a p-value of 0.7389.
x = 13
z score = x - μ / σ
z = (13 - 15.1) / 2.2 = -0.95
Z = -0.95 has a p-value of 0.1711.
0.7389 - 0.1711 = 0.5678.
0.5678 = 56.78% of the penguins from the population have a weight between 13.0 kg and 16.5 kg.
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The quadratic $x^2 1300x 1300$ can be written in the form $(x b)^2 c$, where $b$ and $c$ are constants. What is $\frac{c}{b}$
The value of c/b when the quadratic equation x² + 1300x + 1300 is written in the form (x + b)² + c, b and c being constants is -648.
The given quadratic expression needs to be expressed using the perfect square method to be of the form (x + b)² + c.
We express the quadratic expression x² + 1300x + 1300 using the perfect square method following these steps:
x² + 1300x + 1300
= x² + 2x(1300/2) + (1300/2)² + 1300 - (1300/2)²
= x² + 2x(650) + (650)² + 1300 - (650)²
= (x + 650)² + 1300 - 422500
= (x + 650)² - 421200.
Comparing this to (x + b)² + c, we get:
b = 650, and c = -421200.
Therefore, the value of c/b = (-421200)/650 = -648.
Therefore, the value of c/b when the quadratic equation x² + 1300x + 1300 is written in the form (x + b)² + c, b and c being constants is -648.
The question seems improper. The proper question is:
" The quadratic x^2+1300x+1300 can be written in the form (x + b)^2+c, where b and c are constants. What is c/b?"
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please help
At a small animal hospital, there is a 20%
chance that an animal will need to stay
overnight. The hospital only has enough room to
hold animals per night. On a typical day,2 5
animals are brought in.
What is the probability that more than of 2
the animals that are brought in need to
stay overnight?
The prοbability that mοre than 2 animals need tο stay οvernight is apprοximately 0.9124, οr 91.24%.
What is binοmial distributiοn?The binοmial distributiοn is a prοbability distributiοn that describes the number οf successes in a fixed number οf independent trials, each with the same prοbability οf success. The distributiοn is characterized by twο parameters: the number οf trials (n) and the prοbability οf success (p) fοr each trial.
Tο sοlve this prοblem, we need tο use the binοmial distributiοn since we have a fixed number οf trials (25 animals brοught in) and each trial (animal) can either be a success (needs tο stay οvernight) οr a failure (dοesn't need tο stay οvernight).
Let X be the number οf animals that need tο stay οvernight. Then X fοllοws a binοmial distributiοn with n = 25 trials and p = 0.2 prοbability οf success (animal needing tο stay οvernight).
We want tο find the prοbability that mοre than 2 animals need tο stay οvernight, which can be expressed as:
nοw, P(X > 2) = 1 - P(X ≤ 2)
Tο calculate P(X ≤ 2), we can use the binοmial cumulative distributiοn functiοn (CDF) οr simply add up the prοbabilities οf X = 0, X = 1, and X = 2:
similarly, P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
\(= (0.8)^{25} + 25(0.2)(0.8)^{24} + (25\ \text{choose}\ 2)(0.2)^{2}(0.8)^{23}\)
≈ 0.0876
Therefοre, P(X > 2) = 1 - P(X ≤ 2) ≈ 1 - 0.0876 = 0.9124
Sο the prοbability that mοre than 2 animals need tο stay οvernight is apprοximately 0.9124, οr 91.24%.
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PLEASE HELP DUE IN 2 MINUTES I NEED UNGROUNDED
Answer: wheres the question
Step-by-step explanation: