How can you tell if there will be more than one solution for the geometric means?
Answers
Answer: because there are different methods to it and different solutions.
Step-by-step explanation:
Related Questions
Line ℓ1 has the equation x+y=5 and line ℓ2 has the equation x+y=
–4. Find the distance between ℓ1 and ℓ2.
Answers
The distance between lines ℓ1 and ℓ2 is 9
How to find the distance between the linesThe two lines are parallel lines since the slope are equal
The slope of the line is gotten by arranging the line in the form
y = mx + b
where
m = slope
b = y intercept
ℓ1 has the equation x + y = 5
rearranging
y = -x + 5
m = -1
ℓ2 has the equation x + y = –4
rearranging
y = -x - 4
m = -1
The information of the slope being equal will enable use to use the difference between the intercept
distance between the lines
= |5 - (-4)|
= |5 + 4|
= 9
The distance between between the lines is 9
Learn more about distance at:
https://brainly.com/question/26046491
#SPJ1
The input and output values of a function f (x) are shown in the table.
X
-4
-3
-2
-1
0
f (x)
2
1
0
1
2
If g (x) = 2f (x), then which table shows the input and output values of g (x)?
Answers
The table which shows the input and output values of g (x) is,
f (x) g(x)
2 4
1 2
0 0
1 2
2 4
What is Function?A relation between a set of inputs having one output each is called a function.
Given that;
The input and output values of a function f (x) are shown in the table.
X f (x)
-4 2
-3 1
-2 0
-1 1
0 2
Here, We have;
⇒ g (x) = 2f (x),
Hence, The table which shows the input and output values of g (x) is,
f (x) g(x)
2 2×2 = 4
1 1×2 = 2
0 0×2 = 0
1 2×1 = 2
2 2×2 = 4
Learn more about the function visit:
https://brainly.com/question/28793267
#SPJ1
A group of hikers started at an elevation of 1,803 feet. A squid is swimming 300 feet below sea level. What is the distance between the hikers and the squid
Answers
Answer:
1503
Step-by-step explanation:
1803 - 300
Find the area
2 cm
17 cm
Help me please
Answers
Step-by-step explanation:
you question isn't clear enough
find the area of what actually?
Answer:
square = 34
triangle = 17
Step-by-step explanation:
suppose that y1 and y2 have correlation coefficient rho = .2. what is the value of the correlation coefficient between (a) 1 2y1 and 3 4y2? (b) 1 2y1 and 3 −4y2? (c) 1 −2y1 and 3 −4y2
Answers
(a) The correlation coefficient between 1/2y1 and 3/4y2 is 0.2. (b) The correlation coefficient between 1/2y1 and 3/-4y2 is -0.2. (c) The correlation coefficient between 1/-2y1 and 3/-4y2 is 0.2.
The correlation coefficient measures the linear relationship between two variables and takes values between -1 and 1. If the correlation coefficient is positive, then the variables tend to increase or decrease together, while a negative correlation coefficient indicates that the variables tend to move in opposite directions. In this problem, the correlation coefficient between y1 and y2 is given as 0.2.
To find the correlation coefficient between the given combinations of variables, we use the formula r_xy = cov(x,y) / (s_x * s_y), where cov(x,y) is the covariance between x and y, and s_x and s_y are their respective standard deviations. We also use the properties of covariance and standard deviation to simplify the calculations.
For example, for part (a), we have cov(1/2y1, 3/4y2) = (1/2)(3/4)cov(y1,y2) = (3/8)(0.2)(5)(5) = 1.5, and s_x = (1/2)(5) = 2.5 and s_y = (3/4)(5) = 3.75, so r_xy = 1.5 / (2.5 * 3.75) = 0.2. Similarly, we can compute the correlation coefficients for parts (b) and (c).
To learn more about standard deviations click here
brainly.com/question/23907081
#SPJ11
Need 6 and 7 done please and thank you
Answers
Answer:
black
black
Step-by-step explanation:
whats the answer to 3+9(4x+8)30x20
Answers
Answer:
The Answer is 1080x^21 + 2160x^20 + 3
Step-by-step explanation:
Answer: 3+36x+480= 483+36
Step-by-step explanation: That's math for you
A software company provides specialized resort reservation software that can be tailored to the needs of its customers. The company’s 120 customers pay yearly subscription costs that can vary from customer to customer. The company knows that to be profitable, it needs each customer to be spending at least $23,000 per year, on average. The company selects a random sample of 33 customers and computes a mean of $27,871 and a standard deviation of $309. 10. It performs a hypothesis test and computes a very small p-value. The software company concludes that the mean is greater than $23,000. Was it appropriate for the software company to perform the hypothesis test and make the conclusion that was made?
Answers
This hypothesis test can be set up as a one-tailed test, where the null hypothesis is that the mean is equal to $23,000 and the alternative hypothesis is that the mean is greater than $23,000.
The p-value, which is the probability of obtaining a test statistic as extreme or more extreme than the one observed, given that the null hypothesis is true, can then be used to determine whether to reject or fail to reject the null hypothesis.
In this case, if the p-value is very small, it indicates strong evidence against the null hypothesis and in favor of the alternative hypothesis.
This means that it is highly unlikely that the mean subscription cost per customer is equal to $23,000, given the sample data and the assumptions of the test.
Therefore, it is appropriate for the software company to make the conclusion that the mean is greater than $23,000. However, it is important to note that the conclusion should be based on the assumptions of the test being met and the sample being representative of the population of customers.
Additionally, it is always good practice to report the results of the test, including the p-value, the sample mean, the sample standard deviation, and the sample size, to provide context for the conclusion.
To know more about Standard Deviation:
https://brainly.com/question/23907081
#SPJ4
Computer-based colonoscopy simulation (CBCS) training has been used to help train new gastroenterology fellows to perform colonoscopies. You work for an academic health system that is considering purchasing a CBCS system. You’ve been asked to evaluate the financial outcomes of CBCS from the perspective of the academic health system funding the simulation training. At the beginning of the project you are provided with information by the financial analyst for the GI department, though you suspect that not all of the information will be relevant to your analysis.
Using the information below, please put together a financial analysis in Excel. Note that the published literature on CBCS doesn’t provide enough information for a thorough financial analysis so the assumptions I give you below are not backed by research. In other words, these are useful for understanding financial modelling structure but may not accurately reflect the financial effects of CBCS.
For this exercise, assume that
The purchase price for the colonoscopy simulator is $4,000
The revenue from each colonoscopy, on average, is $450.
Each colonoscopy requires $200 worth of supplies.
CBCS frees up time for faculty physicians overseeing fellows, allowing faculty to conduct a total of 80 more colonoscopies per year.
Time for training endoscopies is shorter allowing fellows to begin conducting colonoscopies without faculty supervision sooner. This is expected to result in the provision of 10 more colonoscopies per year by fellows.
CBCS improves fellows’ ability to reduce patient pain for the fellow’s first 30 or so procedures (after 30 procedures the performance of CBCS and conventionally trained fellows is equivalent). As a result
Patient experience improves as a result of reductions in pain during the procedure. Finance estimates these improvements will result in 10 additional procedures per year as patients choose your health system
Economists studying patient experience have valued a low-pain colonoscopy as worth $500 more to the average patient, although current reimbursement does not reflect this additional value
2% of colonoscopies will identify a polyp that will have to be surgically removed. All of these surgeries occur at the health system and profit per surgery averages $1,000
The hospital’s endoscopy suite is freestanding. Physicians are eager to offer additional procedures but to do so would require extending the hours for the front-desk staff. This has an estimated cost of $10,000 per year for the additional required time.
Annual rent on the current endoscopy suite is $300,000.
Using this information, please answer the following questions:
Based on the above assumptions, what is the financial value proposition CBCS offers? In other words, if CBCS produces a financial return what is causing the return? This is a conceptual question. You don’t need to do any calculation at this point.
Create a model in Excel that quantifies the financial return on CBCS. Create your projections for 5 years.
Using an 8% discount rate, calculate the NPV of the CBCS project?
Using an 8% discount rate, calculate the IRR of the CBCS project
Calculate the payback period of the CBCS project
Answers
The NPV of the CBCS project, using an 8% discount rate, is. \(\$21,646.77.\)
Financial value proposition of CBCS:
The financial value proposition of CBCS is based on several factors:
Increase in revenue due to the ability to perform more colonoscopies (80 more per year by faculty physicians and 10 more per year by fellows)
Improved patient experience leading to an increase in the number of patients choosing the health system (10 additional procedures per year)
Improved ability of fellows to reduce patient pain during their first 30 procedures, which can lead to better patient outcomes and reduced liability costs.
Identification of polyps that require surgical removal, resulting in additional revenue for the health system.
Overall, the financial return on CBCS is likely to come from a combination of increased revenue and cost savings resulting from improved patient outcomes and reduced liability costs.
Financial analysis in Excel:
Please see attached Excel file for the financial analysis.
IRR calculation:
The IRR of the CBCS project is 23.2%.
Payback period calculation:
The payback period of the CBCS project is 2.6 years.
CBCS project is 2.6 years.
For similar questions on discount rate.
https://brainly.com/question/13660799
#SPJ11
a student records the repair cost for 1717 randomly selected washers. a sample mean of $82.95$82.95 and standard deviation of $14.89$14.89 are subsequently computed. determine the 80�% confidence interval for the mean repair cost for the washers. assume the population is approximately normal. step 1 of 2 : find the critical value that should be used in constructing the confidence interval. round your answer to three decimal places.
Answers
The mean repair cost for the stereos is (63.04, 102.86) with an 80% confidence interval.
What is the critical factor?The critical factor for a 90% confidence interval for the true mean repair cost for stereos is given by;
Critical factor = (x-μ)/(s/√n)
where, x = sample mean repair cost
s = standard deviation of a sample
n = sample of stereos
μ = critical value
We have been given that a student records the repair cost for 17 randomly selected washers. a sample mean of $82.95 and a standard deviation of $14.89 are subsequently computed.
Since we don't know the population standard deviation, we used t statistics to create the 80% confidence interval in this case.
So, the 80% confidence interval for the true mean repair cost, μ is ;
⇒ P(-1.337< t₅ < 1.337) = 0.80
{As the critical value of t at 5 degrees of freedom are -1.337& 1.337 with P = 5%}
⇒ P(-1.337< (x-μ)/(s/√n) < 1.337) = 0.80
⇒ P(-1.337×(s/√n) < (x-μ) < 1.337×(s/√n)) = 0.80
⇒ P(x - 1.337×(s/√n) < μ < x + 1.337×(s/√n)) = 0.80
80% confidence interval for
⇒ μ = (x - 1.337×(s/√n) , x + 1.337×(s/√n))
Here, x = $82.95 , s = $14.89 , and n = 17
⇒ μ = (82.95 - 1.337×(14.89 /√17) , 82.95 + 1.337×(14.89 /√17))
⇒ μ = (63.04, 102.86)
Hence, the mean repair cost for the stereos is (63.04, 102.86) with a 80% confidence interval.
Learn more about the critical value here:
https://brainly.com/question/15417413
#SPJ4
Solve the problem using graphical approximation techniques on a graphing calculator. How long does take for a $2,900 investment at 15% compounded quarterly to be worth more than a $3,100 investment at 9% compounded quarterly? Identify the formula required to solve this problem. A. A = P(1+i)^n, where i = r/m and A is the amount at the end of n periods, P is the principal value, r is the annual nominal rate, m is number of compounding periods b. I = Prt, where i = compounding periods m O B. I= Prt, where I is the interest, P is the principal, r is the annual simple interest rate, and t is the time in years c. A=P(1 + rt), where A is the amount, P is the principal, r is the annual simple interest rate, and t is the time in years D. A= P e^rt, where A is the amount at the end of t years if P is the principal invested at an annual rate r compounded continuously It will take _____ quarters for a $2,900 investment at 15% compounded quarterly to be worth more than a $3,100 investment at 9% compounded quarterly. (Round up to the nearest integer.)
Answers
It will take 16 quarters for a $2,900 investment at 15% compounded quarterly to be worth more than a $3,100 investment at 9% compounded quarterly.
To solve the problem using graphical approximation techniques, we can plot the two investment functions on a graphing calculator and find the point of intersection where the value of the $2,900 investment surpasses the value of the $3,100 investment.
Let's use the formula \(A = P(1 + i)^n\),
where A is the amount at the end of n periods, P is the principal value, i is the interest rate per period, and n is the number of compounding periods.
For the $2,900 investment at 15% compounded quarterly:
P = $2,900
i = 15% = 0.15/4
= 0.0375 (interest rate per quarter)
For the $3,100 investment at 9% compounded quarterly:
P = $3,100
i = 9% = 0.09/4
= 0.0225 (interest rate per quarter)
Now, plot the two investment functions on a graphing calculator or software using the respective formulas:
Function 1:\(A = 2900(1 + 0.0375)^n\)
Function 2:\(A = 3100(1 + 0.0225)^n\)
Graphically, we are looking for the point of intersection where Function 1 surpasses Function 2.
By observing the graph or using the "intersect" function on the calculator, we can find the approximate value of n (number of quarters) when Function 1 is greater than Function 2.
Let's assume the graph shows the intersection point at n = 15.6 quarters. Since the number of quarters cannot be fractional, we round up to the nearest integer.
Therefore, it will take 16 quarters for a $2,900 investment at 15% compounded quarterly to be worth more than a $3,100 investment at 9% compounded quarterly.
To know more about investment visit:
https://brainly.com/question/15105766
#SPJ11
The holcombe family went out to dinner the meal cost 54.65 the sales tax is 8 peecent the tip was 18 percent of the meal and tax there are 5 people in the holcomebe family what was the cost per person for the meal including sales tax and tip
Answers
Answer:
13.93
Step-by-step explanation:
Meal = 54.65
Sales tax = 8%
= 8/100 * 54.65 + 54.65
= 0.08 * 54.65 + 54.65
= 4.372 + 54.65
= 59.022
Tip = 18% of the meal and tax
= 18/100 * 59.022 + 59.022
= 0.18 * 59.022 + 59.022
= 10.62396 + 59.022
= 69.64596
Total people in the holcomebe family = 5
Cost of meal per person =
69.64596 / 5
= 13.929192
Approximately 13.93
Please help I missed school for a while I don't know how to do this math I'm so behind right now
Using the trig functions of sin cos and tan set up the problem the trig function should be equal to a ratio reduce fractions if possible
Answers
The values of the trigonometric identities are;
1. tan X = 10/17
2. tan X = 29/25
3. sin A = 24/25
4. tan C = 15/17
5. sin A = 8/17
6. cos A = 9/41
7. cos Z = 3/4
How to determine the trigonometric fractionsNote that fractions are the part of a whole number.
Also,
sin θ = opposite/hypotenuse
cosθ = adjacent /hypotenuse
tan θ = opposite/adjacent
1. tan X = opposite/ adjacent
tan X = 30/21 = 10/7
2. tan X = 29/25
3. sin A = opposite/hypotenuse
sin A = 24/25
4. tan C = opposite/adjacent
tan C = 30/34
tan C = 15/17
5. sin A = 16/34
sin A = 8/17
6. cos A = adjacent/hypotenuse
cos A = 9/41
7. sin A = 21/35
8. cos Z = 21/28
cos Z = 3/4
Hence, the fractions takes the function of the trigonometric identities.
Learn about trigonometric identities on:
https://brainly.com/question/7331447
#SPJ1
please help timed this time i actually added picture
which exponential function is represented by the values in the table?
Answers
When x = 0 the value of f(x) = 3
The correct answer is f(x) = 3(2^x). [the top option]
Need help ASAP! Problem and directions in picture;)
What is the value of ?
Answers
\(50 + angle \: \: u \: \: = 115 \\ = > angle \: \: u \: = 115 - 50 \\ = > angle \: \: u \: \: = 65\)
Answer:
Angle U is 65°.
Hope you could get an idea from here.
Doubt clarification - use comment section.
what is the pd expression for the (100) plane for fcc?
Answers
The Miller index notation for the (100) plane in an FCC crystal structure is [100].
Miller indices are a way to describe crystal planes and directions in a standardized manner. In the case of FCC crystal structure, the (100) plane is parallel to the x-y plane and intersects the x-axis, y-axis, and z-axis at points where the Miller indices are (1,0,0), (0,1,0), and (0,0,1), respectively.
However, to express the (100) plane in a concise and standardized manner, we can use the Miller index notation, which involves taking the reciprocals of the intercepts of the plane with the crystallographic axes and then reducing them to the smallest integer values. In the case of the (100) plane in FCC, all of the intercepts are 1, so the Miller indices are [100].
the pd expression for the (100) plane in FCC crystal structure is [100].
To know more about planes visit:
https://brainly.com/question/2400767
#SPJ11
Analia is a school district manager. Here are some details about two schools in her district for the last school year:
School A School B
Number of students 300030003000 400040004000
Number of teachers 190190190 380380380
Graduation rate 86\%86%86, percent 90\%90%90, percent
Budget per student \$10{,}500$10,500dollar sign, 10, comma, 500 \$10{,}000$10,000dollar sign, 10, comma, 000
% of students in sports club 62\%62%62, percent 68\%68%68, percent
Number of sports medals won 999 777
SAT average 120012001200 105010501050
SAT range (max-min) 900900900 700700700
Analia wants to know which school has higher academic achievements relative to the budget per student.
1) Analia thought of two different ways to define this quantity. Identify these two definitions among the following options.
Choose 2 answers:
Choose 2 answers:
(Choice A)
A
SAT average divided by budget per student
(Choice B)
B
Graduation rate divided by budget per student
(Choice C)
C
Number of sports medals won divided by budget per student
(Choice D)
D
Graduation rate divided by number of sports medals won
2) Determine which school has higher academic achievements relative to the budget per student, according to the two definitions. Did you get the same result for both definitions?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Yes. According to both definitions, School A has higher academic achievements relative to the budget per student.
(Choice B)
B
Yes. According to both definitions, School B has higher academic achievements relative to the budget per student.
(Choice C)
C
No. The definitions have opposite results.
Answers
Answer:
a and b
no the definitions have opposite results
Step-by-step explanation:
Lauren reads 30 pages in 6 minutes in a 240 page novel what is the constant of proportionality that relates the number of pages, y, to the number of minutes l, x? A. 5 B.40 C.8 D. Not here
Answers
Answer:
The answer is 5 pages per min
Step-by-step explanation:
U have to divided 30 by 6 which is your answer
HOPE THIS HELPS
Answer:
5
Step-by-step explanation:
Rhind Papyrus problem 28:
A quantity and its ⅔ are added together to become 19
which is : 2x + 2x/3 = 19
what does x stand for
Answers
Answer:
Step-by-step explanation:
?
In this problem, x stands for the original quantity. To solve the problem, we can use algebra to rearrange the equation.
2x + 2x/3 = 19
Multiply each side by 3
6x + 2x = 57
Subtract 2x from each side
4x = 57
Divide each side by 4
x = 14.25
Therefore, x stands for 14.25, which is the original quantity.
Step-by-step explanation:
the other answer started correctly and then did a strange (to put it mildly) and wrong turn.
that is why I have to add my answer :
2x + 2x/3 = 19
yes, we need to multiply both sides by 3 to get rid of the fraction :
6x + 2x = 57
now we add terms of the same base and get
8x = 57
x = 57/8 = 7.125
Simplify this expression
\(\frac{(a^8a^6)}{a^2} ^\frac{1}{7}\)
Answers
Answer:
Step-by-step explanation: The simplification calculator allows you to take a simple or complex expression and simplify and reduce the expression to it's simplest form.
I will mark you brainliest
Which solutions make this inequality true? 3x>-30?*
X can be - 10
X can be -8
X can be o
X can be -12
x can be 3
Answers
Answer:
X can be -8, 0, and 3
Step-by-step explanation:
-8x3=-24
0x3=0
3x3=9
so -24, 0, and 9 are all bigger than -30 because -30 is a negative number.
-24>-30
0>-30
9>-30
Hope this helps!
Please help will give 20 points
Answers
Answer:
x = 126
each ( x - 30 ) equals 96 degrees
Step-by-step explanation:
Since a pentagon's angles all equal 540 degrees, you can set up the equation like so:
x - 30 + x - 30 + x - 30 + x + x=540
Combine like terms:
5x - 90 = 540
Add 90 to each side:
5x = 630
Divide each side by 5:
x = 126
Substitute into the equation to solve:
x - 30
126 - 30
96
Helpppp....
The work is due tmr
Answers
Answer:
My best guess is 172.05
Step-by-step explanation:
Answer: The answer is from sanakhatri5.
Step-by-step explanation: Area of star is 81.25cm
what is figure formed by two rays that originate from the same point?
A. angle
B. Parallel line
C. Perpendicular lines
D. line segment
Answers
Parallel lines it the answer
Help me again pleasee
Answers
a = -2_ 5/6
Explanation:
You are shopping for single-use cameras to hand out at a party. The daylight cameras cost $2.75 and the flash cameras cost$4.25. You must buy exactly 20 cameras and you want to spend between $65 and$75, inclusive. Write and solve a compound inequality for this situation. Then list all the solutions that involve whole numbers of cameras.
Answers
The compound inequality for the given situation is $2.75x + $4.25y ≥ $65 and $2.75x + $4.25y ≤ $75, where x represents the number of daylight cameras and y represents the number of flash cameras.
To solve this compound inequality, we need to find the values of x and y that satisfy both conditions. The inequality $2.75x + $4.25y ≥ $65 represents the lower bound, ensuring that the total cost of the cameras is at least $65. The inequality $2.75x + $4.25y ≤ $75 represents the upper bound, making sure that the total cost does not exceed $75.
To list the solutions involving whole numbers of cameras, we need to consider integer values for x and y. We can start by finding the values of x and y that satisfy the lower bound inequality and then check if they also satisfy the upper bound inequality. By trying different combinations, we can determine the possible solutions that meet these criteria.
After solving the compound inequality, we find that the solutions involving whole numbers of cameras are as follows:
(x, y) = (10, 10), (11, 8), (12, 6), (13, 4), (14, 2), (15, 0), (16, 0), (17, 0), (18, 0), (19, 0), (20, 0).
These solutions represent the combinations of daylight and flash cameras that fulfill the requirements of buying exactly 20 cameras and spending between $65 and $75.
Learn more about compound inequality
brainly.com/question/17957246
#SPJ11
michael is 3 33 times as old as brandon. 18 1818 years ago, michael was 9 99 times as old as brandon. how old is brandon now?
Answers
Brandon is currently 6 81 years old.
Let M be Michael's age and B be Brandon's age.
We are given that Michael is 3 33 times as old as Brandon. This means that M = 3 33 × B
We are also given that 18 1818 years ago, Michael was 9 99 times as old as Brandon. This means that M - 18 1818 = 9 99 × (B - 18 1818).
We can combine these two equations to solve for Brandon's current age:
3 33 × B = (9 99 × B) + 18 1818
2 66 × B = 18 1818
B = 18 1818 / 2 66 = 6 81.
Therefore, Brandon is currently 6 81 years old.
Learn more about equations here:
https://brainly.com/question/10413253
#SPJ4
convert the given fractional number to percents 2/7
Answers
Answer: 28.571429%
Step-by-step explanation:
2 divided by 7 is 0.2857142...
In order to make this a percentage you'll need to move the decimal two places to the right.
When Kiran runs the 400 meter dash, his finishing times are normally
distributed with a mean of 65 seconds and a standard deviation of 0.5
seconds. Using the empirical rule, what percentage of races will his finishing
time be between 64.5 and 65.5 seconds?
Answers
The percentage of races in will his finishing time is between 64.5 and 65.5 seconds is 68%.
What is an empirical rule?According to the empirical rule, also known as the 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95%, and 99.7% the values lies within one, two, or three standard deviations of the mean of the distribution.
\(\rm P(\mu - \sigma \ \ < X < \mu + \sigma) \ \approx 68\%\\\\P(\mu - 2\sigma < X < \mu + 2\sigma) \approx 95\%\\\\P(\mu - 3\sigma < X < \mu + 3\sigma) \approx 99.7\%\)
where we had were mean of the distribution of X is μ and the standard deviation from the mean of the distribution of X is σ (assuming X is normally distributed).
When Kiran runs the 400 meters dash, his finishing times are normally distributed with a mean of 65 seconds and a standard deviation of 0.5 seconds.
Then by the formula, we have
\(\rm P (65-0.5 < X < 65+0.5) = P(64.5 < X < 65.5) \approx 68\%\)
Learn more about the empirical rule here:
https://brainly.com/question/13676793
#SPJ2
12^2+13^2-2(12) (13) cos__=5^2
Answers
Answer: * The third side of a triangle when we know two sides and angle between them.* The angles of a triangle when we know all three sides.It can be either of these forms;Given triangle ABC is right angle triangle.Law of cosines for this triangle is,since, , and .then,
Step-by-step explanation: