Yes, if you have minimums and maximums that are several standard deviations away from the rest of the data observations, medians would be the best measure of central tendency.
Having minimums and maximums that are far away (several standard deviations away from the mean) from the rest of the data observations, medians would be the best measure of central tendency. This is because, when there are outliers or extreme values in a dataset, the mean can be influenced and it may not be an accurate representation of the central tendency.
However, the median is not affected by extreme values or outliers since it only depends on the middle value of the dataset. Therefore, if the dataset has outliers, it is better to use the median as a measure of central tendency to provide a more accurate representation of the data.
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PLEASE HELP FAST (giving brainliest)
First one is 6
second one is 12
third one is -8
hope this helps
Answer:
Step-by-step explanation:
x=6
x=12
x=-8
how many driving lessons do you need to do with a professioanl instructor before my parents could teach me
The number of driving lessons you need to take with a professional instructor before your parents can teach you varies depending on the regulations in your area. In some regions, a specific number of driving lessons is required by law before you can apply for your driver's license. As a result, you should check with your local Department of Motor Vehicles (DMV) or other regulatory agency to learn more about the specific requirements in your area.
In general, however, it is usually beneficial to take as many driving lessons as possible with a professional instructor. Professional driving instructors have been educated in how to teach driving skills safely and effectively. They have also assisted many other people in learning how to drive, and as a result, they have a wealth of knowledge and expertise to draw on.
The more driving lessons you take with a professional instructor, the more chances you'll have to learn and improve your driving abilities. You may be able to practice with your parents after only a few lessons, but it's generally a good idea to take as many as possible with an instructor before doing so. This will give you the best chance of success while you learn to drive safely and confidently.
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PLEASE HELP ME SOLVING THIS CHART PLEASEEE I TRIED BUT I DON'T FEEL IT RIGHT
assume that you want to construct a 95% ci for the mean of a normal distribution with population variance 30. the sample average is 10 and the sample size is 20. what is the lower limit of the ci? approximate your answer using only one decimal.
By using the formula for the confidence interval and the standard error, we were able to calculate the lower limit of the interval as 7.59.
To construct a 95% CI for the population mean of a normal distribution, we can use the formula:
CI = sample mean ± z* (standard error)
Where z* is the critical value from the standard normal distribution that corresponds to a 95% confidence level (i.e., 1.96), and the standard error is calculated as:
standard error = population standard deviation / √sample size
In this case, we are given that the population variance is 30, so the population standard deviation is √30 = 5.48 (rounded to two decimal places). The sample size is 20, so the standard error is:
standard error = 5.48 / √20 = 1.226
Now, we can use the formula for the CI:
CI = 10 ± 1.96 x 1.22
Simplifying this expression gives us:
CI = (7.59, 12.41)
This means that we are 95% confident that the true population mean lies within the interval from 7.59 to 12.41. The lower limit of the CI is 7.59, rounded to one decimal place.
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HELP ME PLEASE PLEASE!!! URGENT
This equation fits the given data: Oy = -2x + 10. The equation creates a linear relationship between the x and y values, with each x value increasing by 1 resulting in a decrease in the y value by 2.
What is linear ?Linear refers to a type of relationship between two or more variables. It is a straight line relationship where the output is directly proportional to the input. Linear relationships can be observed in the natural world such as in the relationship between distance and time. They can also be observed in mathematical equations and models, where the output is directly related to the input. Linear relationships are also used to represent real-world problems in the form of linear equations and models.
The equation satisfies the data points, as plugging in each x value will result in the corresponding y value. For example, when x = 0, the equation produces y = 10, which is the given data point. Similarly, when x = 2, the equation produces y = 6, which is also the given data point.
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This equation fits the given data: y = 1/3x + 2. The equation creates a linear relationship between the x and y values. Hence the correct option is b.
What is linear relationship?Linear refers to a type of relationship between two or more variables. It is a straight line relationship where the output is directly proportional to the input. Linear relationships can be observed in the natural world such as in the relationship between distance and time. They can also be observed in mathematical equations and models, where the output is directly related to the input. Linear relationships are also used to represent real-world problems in the form of linear equations and models.
The equation satisfies the data points, as plugging in each x value will result in the corresponding y value. For example, when x = 0, the equation produces y = 10, which is the given data point. Similarly, when x = 2, the equation produces y = 6, which is also the given data point.
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an apple falls from a tree 100 km to the ground. if the acceleration due to gravity is 9,8 m/s² and the mass of the apple is 0,2 gram. what is the potential energy of the apple?
Answer: 196 Joules (J)
Step-by-step explanation:
To calculate the potential energy of the apple, we can use the formula:
Potential Energy = Mass x Gravity x Height
First, let's convert the height from kilometers to meters:
100 km = 100,000 meters
Now, let's convert the mass of the apple from grams to kilograms:
0.2 gram = 0.0002 kilograms
Using these values, we can calculate the potential energy:
Potential Energy = 0.0002 kg x 9.8 m/s^2 x 100,000 m
Potential Energy = 196 Joules (J)
Therefore, the potential energy of the apple is 196 Joules (J).
planets x, y and z take $360$, $450$ and $540$ days, respectively, to rotate around the same sun. if the three planets are lined up in a ray having the sun as its endpoint, what is the minimum positive number of days before they are all in the exact same locations again?
By using LCM, we find that the three planets x, y and z will be in the exact same locations again after $5400$ days.
To find the minimum positive number of days before the planets are all in the exact same locations again, we need to find the least common multiple (LCM) of the three given periods of rotation.
The prime factorization of each of the given periods of rotation is as follows
$360 =[tex]2^3 \cdot 3^2 \cdot 5$[/tex]
$450 =[tex]2 \cdot 3^2 \cdot 5^2$[/tex]
$540 =[tex]2^2 \cdot 3^3 \cdot 5$[/tex]
To find the LCM, we need to take the highest power of each prime factor that appears in any of the three factorizations. So the LCM is:
[tex]$LCM = 2^3 \cdot 3^3 \cdot 5^2 = 2^3 \cdot 27 \cdot 25 = 5400$[/tex]
Therefore, the three planets will be in the exact same locations again after $5400$ days.
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Pls help answer with good detailed explanation
Evaluate. 547+233×5−142 whats this answer
The answer to the expression 547 + 233 × 5 - 142 is 1752. To solve the expression, we must follow the order of operations, which is PEMDAS: Parentheses, Exponents, Multiplication, and Division (performed left to right), and Addition and Subtraction (performed left to right).
Since there are no parentheses or exponents in this expression, we start with multiplication and division. In this case, we have to multiply 233 by 5, which gives us 1165. Then, we add 547 to 1165, which gives us 1712. Finally, we subtract 142 from 1712, which gives us the final answer of 1752. Therefore, the result of the expression 547 + 233 × 5 - 142 is 1752, which can be obtained by following the order of operations and performing the arithmetic operations in the correct order.
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calculate the amount of heat produced, in kj, when 52.40 g of methane, ch4, burns in an excess of air, according to the following equation.
Therefore, the amount of heat produced when 52.40 g of methane, CH4, burns in an excess of air is -39568.2 kJ
The amount of heat produced when 52.40 g of methane, CH4, burns in an excess of air can be calculated using the following equation:
[tex]Q = mcΔT[/tex]
Where Q is the amount of heat produced (in kJ), m is the mass of the methane (in g), and ΔT is the change in temperature (in K).
Using the equation, the amount of heat produced can be calculated as follows:
Q = [tex](52.40 g)(-753.15 K) = -39568.2 kJ[/tex]
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The sum of two numbers is 18. Their difference is -8. Find the two numbers.
Part A
Write a system of equations that represents the situation.
x + y =
x-y =
Part B
Solve the system of equations. Express the coordinates as decimals if necessary.
The two numbers in the system of equation is 5 and 13.
What is system of equation?A group of multiple-variable equations that must all be solved concurrently make up a system of equations. Finding values for the variables that satisfy every equation in a system of equations is the objective. Each equation in the system reflects a connection between the variables. In order to find a singular solution or a group of solutions, systems of equations can be solved using a variety of methods, such as substitution or elimination. In many disciplines, including mathematics, physics, engineering, and economics, systems of equations can occur.
Let us suppose the two numbers as x and y.
x + y = 18
x - y = -8
The second equation can be written as:
x + 8 = y
Substitute the value of y in equation 1:
x + x + 8 = 18
2x = 10
x = 5
Substitute the value of x to get y:
x + y = 18
5 + y = 18
y = 13
Hence, the two numbers in the system of equation is 5 and 13.
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Rotate the figure 180 degrees
The coordinates of the image after rotating the figure 180 degrees about the origin are T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)
Calculating the coordinates of the imageGiven that
T'(-4, 3). V'(-5, 5), W'(-2, 5). X(-1, 3)
Rotating a figure by 180 degrees is equivalent to flipping it over the horizontal and vertical axes simultaneously.
This means that the x-coordinate of each point will be negated, and the y-coordinate will be negated as well.
Therefore, to find the coordinates of the image of a point after rotating it by 180 degrees, you can use the following formula:
(x', y') = (-x, -y)
Using the above, the image is
T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)
Hence, the image is T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)
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Complete question
Rotate the figure 180 degrees about the origin
T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)
T'(3, 4). V'(5, 5), W'(5, 2), X '(3. 1) (Th
T'(-3, 4) V(-5. 5), W'(-5, 2). X'(-3, 1)
T'(-3, -4), V'(-5, -5). W(-5, -2), X '(-3, -1)
Peter bought 100 shares of stock for $6.35 per share last year. He paid his broker a 2% commission. He sold the stock this week for $12.57 per share and paid his broker a $15 flat fee. What were Luis’s net proceeds?
The net proceeds for Luis would be amount $1,169.50. This is calculated by subtracting the cost of the stock (100 x $6.35 = $635) and the commission (2% of $635 = $12.70) from the sale of the stock (100 x $12.57 = $1,257) and subtracting the flat fee of $15. ($1,257 - $635 - $12.70 - $15 = $1,169.50).
The net proceeds for Luis from the sale of the stock were calculated by subtracting the cost of the stock, the commission fee, and the flat fee from the proceeds of the sale. The cost of the stock was 100 shares at $6.35 per share, which totaled amount $635. The commission fee was 2% of the cost of the stock, which was $12.70. The flat fee was a set fee of $15. The proceeds from the sale of the stock was 100 shares at $12.57 per share, which totaled $1,257. The net proceeds for Luis was calculated by subtracting the cost of the stock, the commission fee, and the flat fee from the proceeds of the sale, which was $1,257 - $635 - $12.70 - $15 = $1,169.50.
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Kendrick bought a calculator priced at $71. Shipping and handling cost an additional 25% of the price. What was the total cost of the calculator, including shipping and handling?
Answer:
The answer to our problem is, $17.75
Step-by-step explanation:
First we need to find out what is 25% of 71
25% of 71 is 17.75. Or [tex]17\frac{3}{4}[/tex] We would need to stick to the term in decimals because of we are using money. Have you ever heard of a fraction in money my guess is no. So let’s stay with decimals. 17.75
How I got it:
25 percent * 71
= (25:100)* 71
= (25* 71):100
= 1775:100
= 17.75
Percentage solution with steps:
Step 1: Our output value is 71.Step 2: We represent the unknown value with x.Step 3: From step 1 above, 71 = 100%.Step 4: Similarly, x = 25%.Step 5: This results in a pair of simple equations:71 = 100% (1)
X = 25% (2)
Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of bothequations have the same unit (%); we have
[tex]\frac{71}{x} = \frac{25}{100}[/tex]
X = 17.75
Thus the answer to your problem is, $17.75
valencia theater sold 487 tickets for a play. tickets cost $14 per student with valid valencia identification and $25 per non-student. if total receipts were $8391, how many valencia student tickets and non-student tickets were sold?
354 Valencia student tickets and 133 non-student tickets were sold.
Let's use algebra to solve the problem. Let
x be the number of Valencia student tickets sold
y be the number of non-student tickets sold
We know that
x + y = 487 (the total number of tickets sold is 487)
14x + 25y = 8391 (the total receipts from ticket sales is $8391)
We can use the first equation to express one of the variables in terms of the other. For example, we can solve for y
y = 487 - x
Here we have to use the substitution method, we can then substitute this expression for y into the second equation
14x + 25(487 - x) = 8391
Simplifying and solving for x
14x + 12275 - 25x = 8391
-11x = -3884
x = 354
So, 354 Valencia student tickets were sold. We can use the first equation to find y
x + y = 487
354 + y = 487
y = 133
So, 133 non-student tickets were sold.
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Could someone help me? Please.
The solution of the system of equations is (2, 1).
How to solve the system of equations graphically?Here we have the system of equations:
y = 2x - 3
y = -x + 3
To solve the system of equations graphically, we need to graph both of these lines in the same coordinate axis and then find the point where the lines intersect.
That point will be the solution of the system.
On the image at the end you can see the graph of the system of equations, there we can see that the solution is (2, 1).
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in square units, what is the largest possible area a rectangle inscribed in the triangle shown here can have?
For the triangle shown, the area is (1/2) * 5 * 4 = 10 square units. The largest possible area of a rectangle inscribed in a triangle is equal to the area of the triangle.
The area of the triangle can be calculated using the formula: Area = (1/2) * Base * Height.
Note that the rectangle must be completely within the triangle and all of its sides must be parallel to the sides of the triangle. To calculate the area, the base and height of the triangle must be known. The base is the length of any one side, while the height is the perpendicular distance from the base to the opposite vertex.
In this case, the triangle is 5 units along the base and 4 units in height. The area can then be calculated as (1/2) * 5 * 4 = 10 square units.
It is also important to note that the rectangle can have sides of different lengths and will still have an area of 10 square units.
To summarize, the largest possible area a rectangle inscribed in the triangle shown can have is 10 square units. This can be calculated using the formula (1/2) * Base * Height. The rectangle can have sides of different lengths, but the area will remain the same.
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i need help ASAP
Calculate the amount of interest on $2,000.00 for 4 years, compounding daily at 2.25 % APR.
From the Monthly Interest Table use $1.094171 in interest for each $1.00 invested
A $2,088.34
B $2188.34
C $2,288.34
D $2,388.34
Answer:
Step-by-step explanation:
First, we need to calculate the annual interest rate from the given APR.
APR = 2.25%
Daily interest rate = 2.25% / 365 = 0.00616438
Now, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = time in years
In this case, P = $2,000, r = 0.00616438, n = 365 (daily compounding), and t = 4.
A = 2000(1 + 0.00616438/365)^(365*4)
A = 2000(1.00616438)^1460
A = $2,388.34 (rounded to the nearest cent)
Therefore, the answer is option D) $2,388.34.
^-AB IS THE MID SEGMENT of triangle CDE what is the value of x? Show all work please
In response to the stated question, we may state that As a result, the trigonometry value of x is 11/4.
what is trigonometry?The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.
Because AB is the midpoint of triangle CDE, it is parallel to CD and equal to half of CD.
As a result, we have:
AB = 1/2 CD
We also know that AD has a length of 3x - 1 and DB has a length of x + 4.
Given that AB is the mid-segment, we may write:
1/2 (AD + DB) = AB
In place of the values we have:
3x - 1 + x + 4 = 2AB
4x + 3 = 2AB
We also know that AB = 7, therefore we may use this number instead:
4x + 3 = 2(7) (7)
4x + 3 = 14
4x = 11
x = 11/4
As a result, the value of x is 11/4.
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The angle turns through 5/6 of the circle The angle measures of 5/6 of the circle the answer is?
Answer:
A circle has 360 degrees, so 5/6 of the circle can be found by multiplying 360 by 5/6:
5/6 of 360 = (5/6) × 360 = 300
Therefore, the angle measures of 5/6 of the circle is 300 degrees.
find the amount due on the loan round to the nearest cent.
principal= $4,000
rate =7 1/2 %
time in months = 3
Answer:
The first step is to calculate the interest that accrues over the 3-month period:
Interest = Principal x Rate x Time
= $4,000 x 0.075 x (3/12)
= $75
The amount due on the loan is the sum of the principal and interest:
Amount due = Principal + Interest
= $4,000 + $75
= $4,075
Rounding to the nearest cent gives: $4,075.00
what is the area of the trapizoid. not draw to scale
a. 8 cm2
b. 62 cm2
c. 84 cm2
d. 125 cm2
The area of a rectangular pool is 5056 m². If the width of the pool is 64 m, what is its length?
Answer:
79
Step-by-step explanation:
Using the formula
A=wl
Solving forl
l=A
w=5056
64=79m
To find area, you multiply the width by the length [tex]( \text{A} = \text{L} \times \text{W})[/tex]. Here, it is asking for the length, giving the area of the pool and the width. With this information, you can inverse operation ( division) to find the length of the pool. So:
[tex]5056 \div 64 = 79[/tex]
This tells us that the length of the pool is 79 meters. To check this answer, multiply 64 and 79. If it's equivalent to 5056, the given area, then 79 is indeed the length of the pool.
[tex]64 \times79 = 5056[/tex].
Thus, the length of the pool is 79 m.
Find the slope of the line that passes through the points A( 2, -4 ) and B( 3, 4 ).
The slope of AB =
Answer: slope=4
Step-by-step explanation:
[tex]Slope=\frac{y2-y1}{x2-x1}[/tex]
[tex]Slope=\frac{4- - 4}{3-2}[/tex]
[tex]Slope=\frac{4+4}{3-2}[/tex]
[tex]Slope=4[/tex]
is the number of linearly independent columns in a matrix a equal to the number of linearly independent rows in a? why?
Yes, the number of linearly independent columns in a matrix A is equal to the number of linearly independent rows in A.
This is because the definition of linear independence states that no linear combination of a set of vectors can equal the zero vector, so if one set of vectors is linearly independent, the other set of vectors must also be linearly independent.
To explain further, the number of linearly independent vectors in a matrix A is determined by the rank of the matrix. The rank of a matrix is the number of linearly independent rows and columns in the matrix.
So if the rank of A is n, then the number of linearly independent columns and rows of A must be n. This is because if there are n linearly independent columns in the matrix, the number of linearly independent rows must also be n.
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Rewrite the following equation in slope-intercept form. Y + 5 = 1 7 ( x + 7 )
Answer: y = 17x + 114
Step-by-step explanation:
The equation for the slope-intercept form is y = mx + b.
Arrange the equation so that it resembles y = mx + b.
You will do this by multiplying and subtracting so y is on the left side of the equation and mx + b is on the right side of the equation.
y + 5 = 17(x + 7)
y + 5 = 17x + 119
y + 5 - 5 = 17x + 119 - 5
y = 17x + 114
Answer:
Y = 17x + 114
Step-by-step explanation:
1. Y + 5 = 17 (x+7)
2. Y + 5 = 17x + 119 [Multiply the numbers in parenthesis by 17.]
3. Y = 17x + 114. [To keep the balance and move the 5 over, subtract it from 119.]
If $4,323 was withheld during the year and taxes owed were $4,576:
a. Would the person owe an additional amount or receive a refund?
b. What is the amount? [Make sure to show your work]
Answer:
a. Since taxes owed ($4,576) are greater than the amount withheld ($4,323), the person would owe an additional amount.
b. The additional amount owed can be calculated by subtracting the amount withheld from the taxes owed:
Additional amount owed = Taxes owed - Amount withheld
= $4,576 - $4,323
= $253
Therefore, the person would owe an additional $253.
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Write the equation of the parabola which has its vertex at (0, 5) and passes through the point (1, 0)
y = -5x² + 5 is the equation of the parabola which has its vertex at (0, 5) and passes through the point (1, 0)
We know that the vertex of the parabola is (0, 5), which means that the equation for the parabola has the form:
y = a(x - 0)² + 5
where 'a' is a constant that determines the shape of the parabola. Since the parabola passes through the point (1, 0), we can substitute these values into the equation and solve for 'a':
0 = a(1 - 0)² + 5
0 = a + 5
a = -5
Therefore, the equation of the parabola is: y = -5x² + 5
This equation represents a parabola that opens downwards (since the coefficient of x² is negative), has a vertex at (0, 5), and passes through the point (1, 0).
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the probability is approximately 0.6 that in a randomly selected week, they will make a combined total less than what amount?
There is a probability of around 60% that during a week picked randomly, the combined sum of their earnings will be below $0.2533.
The given probability is a measure of the chances that the occurrence of an event will happen. In the context of the question, we want to calculate the combined total of earnings that are less than a certain amount. We know that the probability is approximately 0.6. Therefore, the answer is given by the value that satisfies this condition.
That is, P(X < a) = 0.6where X represents the combined total earnings of a randomly selected week, and a is the required amount.
To solve for a, we can use the cumulative distribution function (CDF) of X. The CDF gives the probability that X is less than or equal to a. Therefore, CDF(a) = P(X ≤ a)
The complement of this probability isP(X > a) = 1 - CDF(a)
We know that P(X < a) = 0.6, which is equivalent to (X ≤ a) = P(X < a) + P(X = a) = 0.6 + 0 = 0.6
Therefore, P(X > a) = 1 - CDF(a) = 1 - P(X ≤ a) = 1 - 0.6 = 0.4
Now we can use a calculator to find the value of a that corresponds to P(X > a) = 0.4.
For example, if we use a calculator, we get a value of a = 0.2533 (rounded to four decimal places).
Therefore, the probability is approximately 0.6 that in a randomly selected week, they will make a combined total of less than $0.2533.
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50 POINTS!!
1. Find a polynomial that represents volume of the fish tank. Explain how you used the
properties of exponents to determine your expression.
HINT: The formula for the volume of a rectangular prism is = ℎ.
2. The volume of each hemisphere is represented by the polynomial 3 − 702 + 360 − 1800.
Explain how to rewrite your answer for question 1 to reflect the volume of the fish tank after the
hemispheres are installed. Then carry out your plan. Show your work.
3. Show that the binomial that represents the length of the fish tank is a factor of the polynomial
you wrote in question 1.
4. Is the binomial that represents the length of the fish tank a factor of the polynomial that
represents the volume of the fish tank after the hemispheres are installed? Support your answer
mathematically.
5. The sanctuary currently has 125 exotic fish. The average amount of the tank allotted for each fish is represented by the binomial (22 − 1). Are the dimensions of the new habitat adequate
for these 125 fish? Explain.
To ensure that the dimensions of the fish tank are adequate, we need to ensure that the volume of the fish tank is greater than or equal to 2625. Since we do not have any information about the dimensions of the fish tank,
What ensures dimensions of the fish tank are adequate?1. Let the dimensions of the fish tank be length, width, and height, represented by l, w, and h, respectively. V = l^1 × w^1 × h^1 = lwh. Therefore, the polynomial that represents the volume of the fish tank is V = lwh.
2. Then the volume of each hemisphere is (4/3)πr^3. Since there are two hemispheres, the total volume they take up is 2(4/3)πr^3 = (8/3)πr^3.
Therefore, the new volume of the fish tank after the hemispheres are installed is V - (8/3)πr^3, where V is the original volume of the fish tank. Substituting V = lwh, we get:
[tex]V_new = lwh - (8/3)πr^3[/tex]
3.The binomial that represents the length of the fish tank is l. To show that it is a factor of the polynomial V = lwh, we need to show that V is divisible by l, which means there exists a polynomial q such that V = lq. We can see that:
[tex]V = lwh = l(wh) = l(q)[/tex], where q = wh.
Therefore, l is a factor of V.
4. To determine if the binomial l is a factor of the polynomial V_new = lwh - (8/3)πr^3, we need to check if V_new is divisible by l. We can use polynomial long division to divide V_new by l:
Let the dimensions of the fish tank be length, width, and height, represented by l, w, and h, respectively.
Then the volume of the fish tank is V = lwh. We can use the properties of exponents to simplify this expression by multiplying the powers of the variables: [tex]V = l^1 × w^1 × h^1 = lwh[/tex] . Therefore, the polynomial that represents the volume of the fish tank is V = lwh.
The volume of each hemisphere is [tex](4/3)πr^3[/tex] . Since there are two hemispheres, the total volume they take up is [tex]2(4/3)πr^3 = (8/3)πr^3.[/tex]
Therefore, the new volume of the fish tank after the hemispheres are installed is V - (8/3)πr^3, where V is the original volume of the fish tank. Substituting V = lwh, we get:
V_new = l [tex]wh - (8/3)πr^3[/tex]
The binomial that represents the length of the fish tank is l. To show that it is a factor of the polynomial V = lwh, we need to show that V is divisible by l, which means there exists a polynomial q such that V = lq. We can see that:
V = lwh = l(wh) = l(q), where q = wh.
Therefore, l is a factor of V.
To determine if the binomial l is a factor of the polynomial V_new = lwh - (8/3)πr^3, we need to check if V_new is divisible by l. We can use polynomial long division to divide V_new by l:
Since there is a remainder of [tex]- (8/3)πr^3[/tex] , we can see that l is not a factor of V_new.
5. The average amount of tank allotted for each fish is represented by the binomial [tex](22 − 1)[/tex] . To determine if the dimensions of the new habitat are adequate for 125 fish, we need to check if the volume of the fish tank is greater than or equal to the space required for 125 fish.
Let the required space for each fish be v, then the total space required for [tex]125[/tex] fish is [tex]125v[/tex] . Substituting the given binomial, we have:
[tex]v = (22 - 1) = 21[/tex]
Therefore, the total space required for 125 fish is [tex]125v = 125(21) = 2625[/tex] . We cannot determine if it is adequate for the given number of fish.
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