Debts, or other outstanding bills or loans that must be repaid are called option B: Liabilities.
What is Debt?
Debt can be defined as the sum that the borrower owes the lender. A debt is an amount of money that has been borrowed for a set period of time and must be repaid, plus interest.
A liability is a debt that a person or business has, typically in the form of money. Through the transmission of economic benefits like money, products, or services, liabilities are eventually satisfied.
Liabilities are items that are listed on the balance sheet's right side and consist of debts including loans, accounts payable, mortgages, deferred income, bonds, warranties, and accumulated expenses.
Therefore, debts are a form of liability.
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olve item carefully.
1. rm rode 4 kilometer on hi bike.hi iter matina rode 3,000 meter on her bike.who rode the farthet and how much farther did he/he ride?? anwer in term of km.
He rode 1 kilometer farther than her, which is equal to 1,000 meters.
He rode the farthest as he rode 4 kilometers and she rode 3,000 meters. To calculate how much farther he rode, we need to convert 3,000 meters into kilometers. 1 kilometer is equal to 1,000 meters. So, 3,000 meters is equal to 3 kilometers. Therefore, he rode 1 kilometer farther than her, which is equal to 1,000 meters.
To calculate the difference between the two distances, we can use the following formula:
Difference = km1 - km2
In this example, km1 is 4 kilometers and km2 is 3 kilometers.
Difference = 4 - 3
Difference = 1
Therefore, he rode 1 kilometer farther than her, which is equal to 1,000 meters.
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Which polynomial is NOT equivalent to (5x – 2)(-2x + 4)?
The polynomial which is not equivalent to (5x – 2)(-2x + 4) is -10x + 20x + 4x – 8 and is therefore denoted as option A.
What is a Polynomial?This is referred to as a type of algebraic expression in which the exponents of all variables should be a whole number.
(5x – 2)(-2x + 4) when expanded will give:
-10x² + 20x + 4x – 8 which can be rewritten as the following below:
-8 + 24x – 10x² -10x² + 24x – 8This is therefore the reason why -10x + 20x + 4x – 8 was chosen as the correct choice.
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The options are:
A) -10x + 20x + 4x – 8
B) 4x + 20x – 10x2 – 8
C) -8 + 24x – 10x2
D) -10x2 + 24x – 8
the subjects in this dataset answered a call for volunteers to participate in this study. assuming every subject who volunteered has a recorded response for every variable, what type of bias could possible result from this sampling design?
The individuals in this dataset consented to participate in this study after receiving a request for volunteers. This sampling design may be biased in favor of volunteers, given that every volunteer has recorded responses for each variable.
At any point during the trial—from recruitment to retention to follow-up—volunteer bias may manifest itself. Volunteers and the target community differ not only in terms of sociodemographic characteristics but also in terms of views about the experiment and the institutions involved.
Volunteer bias may also be related to the illnesses or conditions being investigated, as volunteers may be less likely to volunteer for research on illnesses or behaviors that are viewed as less acceptable by society, such as ailments linked to drug usage.
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After being asked for volunteers, the people in this dataset agreed to take part in the study. Given that each volunteer has recorded responses for each variable, this sample design may be skewed in favour of the volunteers.
Volunteer bias may appear at any time during the experiment, from recruitment to retention to follow-up. The target community and volunteers have different sociodemographic features, as well as different perspectives on the experiment and the participating institutions.
As volunteers may be less likely to volunteer for research on illnesses or behaviours that are perceived as less acceptable by society, such as conditions associated to drug use, bias may also be related to the illnesses or conditions being examined.
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Over which interval is this function continually increasing?
f(x) = 2/3|x - 3| + 2
A. (3, ∞)
B. (-∞, 2)
C. (-∞, 3)
D. (2, ∞)
The given function is continually increasing at an interval (3, ∞)
What is an interval of a function?An interval is a set of (real) numbers with the property that for every pair of numbers y and z that it contains, it contains also every number between y and z.
Given that, a function f(x) = 2/3|x - 3| + 2
Plot the graph for the function. we get that, the graph is continuously decreasing from ∞ to -3 and continuously increasing in 3 to ∞
Hence, the given function is continually increasing at an interval (3, ∞)
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oh my god please someone help
1) Note the line of best fit is indicated in the attached graph.
2) Based on the line, the total score (on the y-axis) for the person who didn't study for the test (that is whose hours of homework are zero) is 38.
3) The y-intercept of the line of best fit in graph two is 8
4) The slope of the line of best fit for the scatter plot in graph 2 is -1/2
5) the equation of the line of best fit is given as y = -0.5x + 8
What is a line of best fit?A straight line with the best fit is one that minimizes the distance between it and certain data. In a scatter plot of multiple data points, the line of best fit is used to express a connection.
It is a result of regression analysis and may be used to forecast indicators and price changes.
Note that most of the answers above are self-explanatory.
1) When drawing a line of best fit, you try to keep the line in such a way that it captures as many points as possible while balancing the number of points to the left and to the right of the line as much as possible.
2) Note that the person who didn't study is the person with zero hours of homework. Thus identifying the corresponding grade
3) to determine the y-intercept, just look at the point on the y-axis where the line is touching. The total score that corresponds with zero on the y-axis is 38.
4) the formula for slope is ΔY/ΔX
Since we have the two corresponding points each on the y-axis and on the x-axis, that is:
X1 = 0
X2 = 2
Y1 = 8
Y2 = 7
ΔX = 2 – 0 = 2
ΔY = 7 – 8 = -1
Thus,
Slope (m) = ΔY/ΔX
= -1/2
=-0.5
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A. 60 degrees
B. 150 degrees
C. 120 degrees
D. 240 degrees
Answer:
D
Step-by-step explanation:
please helppp
Examine the two news headlines from real observational studies and determine at least one plausible lurking variable that could explain the cause and effect. Remember, do not argue about the link expressed in the headline, but rather accept the association as true. Your task is to determine the other variable(s) that could be the actual cause(s).
b. “Is Gluten the Culprit in Our Fight Against Obesity?”
A plausible lurking variable that could explain the cause and effect in the headline "Is Gluten the Culprit in Our Fight Against Obesity?" is overall diet.
It's possible that individuals who consume a diet high in gluten also consume a diet high in overall calories and processed foods, leading to weight gain and obesity. This would mean that it is not specifically gluten causing the obesity, but rather a combination of factors in the individual's diet.
What is a lurking variable?A lurking variable is a variable that has a connection (e.g., may be correlated) with the response and the explanatory variable but is neither the explanatory variable nor the response variable.
Although it is not taken into account in the study, it might affect how the variables are related.
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3x - 4y = 6
6x - 8y = 10
The system shown has _____ solution(s).
one
infinite
no
Answer:
no solution
Step-by-step explanation:
6x - 8y = 10
Divide by 2,
6x/2 - 8y/2 = 10/2
3x - 4y = 5
3x - 4y = 6
3x - 4y = 5 = 6
But actually, 5 ≠ 6
The system shown has no solution. The answer is obtained by solving the linear equations.
What is a linear equation?
The equation with the highest degree of one is a linear equation. This demonstrates that there are no variables in a linear equation with an exponent bigger than one. Such an equation yields a straight line on the graph.
We are given 6x - 8y = 10
On dividing both sides by 2, we get
⇒6x/2 - 8y/2 = 10/2
⇒3x - 4y = 5
But, we are given that 3x - 4y = 6
This shows that 5 must be equal to 6
But, 5 ≠ 6
Hence, the system shown has no solution.
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Someone help me do further maths ‘transformations of graphs and functions’ question
Answer:
see attached
Step-by-step explanation:
just draw a narrower one, about 1/2 of the x value.
Identify the interval (–8, 3) as open, closed, half-open, or unbounded.
A.
open
B.
closed
C.
half-open
D.
unbounded
Answer:
it should be
Step-by-step explanation:
no.c half - open
Greta, an elderly investor, has a degree of risk aversion of A = 3 when applied to return on wealth over a one-year horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of one-year strategies. (All rates are annual and continuously compounded. ) The S&P 500 risk premium is estimated at 5. 6% per year, with a SD of 20. 6%. The hedge fund risk premium is estimated at 10. 6% with a SD of 35. 6%. The returns on both of these portfolios in any particular year are uncorrelated with its own returns in other years. They are also uncorrelated with the returns of the other portfolio in other years. The hedge fund claims the correlation coefficient between the annual returns on the S&P 500 and the hedge fund in the same year is zero, but Greta is not fully convinced by this claim.
Calculate Greta’s capital allocation using an annual correlation of 0. 3. (Do not round your intermediate calculations. Round your answers to 2 decimal places. )
Greta’s capital allocation is 0.37 for the S& P 500 and whereas for the hedge fund the captial allocation is 0.63. it is done using the Capital Allocation formula.
The calculation was done using the Capital Allocation formula, which is Risk Aversion multiplied by Risk Premium divided by the sum of the squared standard deviations of the two portfolios plus the correlation between the two portfolios multiplied by the standard deviation of portfolio 1 times the standard deviation of portfolio 2.
for S& P 500 : Capital Allocation = Risk Aversion x Risk Premium / (SD^2 + (Correlation x SD1 x SD2)) = 3 x 5.6% / (20.6^2 + (0.3 x 20.6 x 35.6)) = 0.37 .
whereas Hedge Fund: Capital Allocation = Risk Aversion x Risk Premium / (SD^2 + (Correlation x SD1 x SD2)) = 3 x 10.6% / (35.6^2 + (0.3 x 20.6 x 35.6)) = 0.63
The Risk Aversion was given as 3, the Risk Premiums of the S& P 500 and the Hedge Fund were given as 5.6% and 10.6% respectively, and the standard deviations of the S& P 500 and the Hedge Fund were given as 20.6% and 35.6% respectively. The correlation between the two portfolios was given as 0.3. The calculation yielded a capital allocation of 0.37 for the S& P 500 and 0.63 for the Hedge Fund.
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The side lengths of quadrilateral WXYZ are 8, 10, 12, and 16 units. Quadrilateral EFGH is a reduction of Quad WXYZ by a ratio of. What are the side lengths for Quad EFGH?
The side lengths for Quadrilateral EFGH are 4, 5, 6, and 8 units.
Quadrilateral EFGH is a reduction of Quad WXYZ by a ratio of 1:2. To find the side lengths for Quad EFGH, divide the side lengths of Quad WXYZ by 2. Therefore, the side lengths of Quad EFGH will be 4, 5, 6, and 8 units.
There are four sides, four vertices, and four angles in a closed quadrilateral. It is a form of polygon. Quadrilaterals' inner angles add up to 360 degrees in total. The English word quadrilateral is derived from the Latin words quadra, which means four, and latus, which means sides.
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A game piece used in a math game is shaped like a right trapezoid. The drawing is not to scale. What is the area of the game piece? Enter your answer in the box. in² A square with sides measuring 3 inches is attached to a triangle, giving a total combined length on one side of 10 inches.
Answer: The game piece is a right trapezoid and its area can be calculated by using the formula:
Area = (b1 + b2) * h / 2
Where b1 and b2 are the lengths of the bases (the parallel sides of the trapezoid) and h is the height.
We can use the information given to find the area of the game piece:
A square with sides measuring 3 inches is attached to a triangle, giving a total combined length on one side of 10 inches.
So, the length of the base of the triangle is 7 inches (10 inches - 3 inches) and the height of the trapezoid is 3 inches.
Now we can substitute these values into the formula:
Area = (3 + 7) * 3 / 2
Area = 10 * 3 / 2
Area = 15 in²
So the area of the game piece is 15 square inches.
Step-by-step explanation:
An online recruiting website offers listings for a fixed fee of $30+ $0.42 per word. Your listing has 43 words. How much
will you pay?
Answer:
You will need to pay $48.06.
Solution:
Given that,
The fixed fee of online recruiting website offers listings is $30,
and $0.42 per word.
Your listing has 43 words,
so,
No.of words*Cost per word = 43*0.42
=$18.06
Total fee for 43 listings =$30 + $18.06
=$ 48.06
Total fee for listing 43 words on an online recruiting website=$48.06
Select the correct answer. Sides of three square rooms measure 13 feet each, and sides of two square rooms measure 15 feet each. Which expression shows the total area of these five rooms? A. (3 × 13^2) + (2 × 15^2) B. (2 × 13^3) + (2 × 15^2) C. (3 × 15^2) + (2 × 13^2) D. (3 × 13^2) × (2 × 15^2)
The correct answer i.e. the total area is A. (3 × 13^2) + (2 × 15^2).
What is the area formula?The edge of a shape's area is measured. You must divide the length and breadth of a rectangles or square in order to determine its area. A is x times y in size.
How do you calculate a square's area?The area of a square is composed of (Side) (Side) square units. Once the diagonally, d, is known, the surface of a square is equal to d22 square units. For instance, 8 8, or 64 sq ft is the size of a cube with sides that are each 8 feet long (ft2).
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How many different roots does the polynomial function,
y = (x − 2)(x + 3)² have?
-
A. 1
B. 3
C. 2
D. 4
The polynomial function is the product of two different linear factors, (x-2) and (x+3)^2, which means that we have two different roots, x=2 and x=-3
What are the roots the given polynomial function have?A polynomial function is a function that can be written as constants and n is the degree of the polynomial. The polynomial function y = (x − 2)(x + 3)² is a quadratic function because it has an [tex]x^{2}[/tex] term.
The roots of a polynomial function are the values of x that make the function equal to zero. In other words, they are the solutions to the equation y = 0.
The polynomial function y = (x − 2)(x + 3)² can be factored as (x-2)(x+3)(x+3), which means that we have three different linear factors, (x-2), (x+3), and (x+3) . Each linear factor corresponds to one root of the polynomial.
So the polynomial function y = (x − 2)(x + 3)² has 2 distinct roots. The correct answer is C.
Alternatively, we can also see that the polynomial function is the product of two different linear factors, (x-2) and [tex](x+3)^{2}[/tex], which means that we have two different roots, x=2 and x=-3.
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A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 15 ft by 5 ft by 10 ft. If the container is entirely full and, on average, its contents weigh 0.09 pounds per cubic foot, find the total weight of the contents. Round your answer to the nearest pound if necessary.
In a case whhereby container built for transatlantic shipping is constructed in the shape of a right rectangular prism and Its dimensions are 15 ft by 5 ft by 10 ft the total weight of the contents is 68 pounds.
How can the Volume of right rectangular prism be calculated?The concept that will be usd here is rectangular prism.
Then to calculate the volume of a rectangular prism, we will need to to make the multiplication with 3 dimensions:( length×width×height).
the dimensions of the container built are 7.5 ft by 11.5 ft by 3 ft.
the container is entirely full and, on average, its contents weigh 0.15 pounds per cubic foot.
So, the volume of the container is calculated as:
The dimensions of the container built are 15 ft by 5 ft by 10 ft. since the container is entirely full , considering the average, its contents weigh 0.09 pounds per cubic foot.
we can calculate the volume of the container as:15 ft * 5 ft * 10 ft= 750ft^3
Then, the total weight of the contents can be found as :
750 ft³× 0.09 pounds per cubic foot= 67.5 pounds = 68 pounds.
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I really need help on this question
Answer: NOT Parallel because 98 /= 82 (Alternate angles are equal)
cool beans is a locally owned coffee shop that competes with two large coffee chains, planeteuro and frothies. alicia, the owner, hired two students to count the number of customers that entered each of the coffee shops to estimate what percent of people who are interested in coffee are visiting each shop. after a week, the students found the following results: 606 visited cool beans, 810 visited planeteuro, and 1,160 visited frothies. the students were surprised that cool beans had 148 visits on monday which represented 60% of all people who visited one of the three coffee shops on mondays. how many people visited one of the three coffee shops on monday?
48.15% people visited one of the three coffee shops on monday
The scholars discovered that;
518 people went to Cool Beans, 974 to Planet Euro, and 1,160 to Frothies.
Assume that x% of Monday's customers at each of the three coffee shops were x.
One hundred thirty-five people went to Cool Beans on Monday.
Of the total number of customers who went to one of the three coffee shops on Monday, 52% went to Cool Beans.
Consequently, 52/100 * x = 135
The calculation for x is (135*100)/52.
x = 260 individuals
On Monday, the following number of visitors visited either PlanetEuro or Frothies:
260-135 =125
Calculating the percentage of Monday visitors to either PlanetEuro or Frothies;
135= 52%
125=?
Cross-product as you
(125*52)/135 =48.15%
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the difference between a positive number X and 3 is 21 what is a number stepsssss
Answer:
Solution:
Let another number be x.
Then positive number = 5x
According to the question,
5
�
+
21
=
2
(
�
+
21
)
5x+21=2(x+21)
⇒
5
�
+
21
=
2
�
+
42
⇒5x+21=2x+42
⇒
5
�
−
2
�
=
42
−
21
⇒5x−2x=42−21
⇒
3
�
=
21
⇒3x=21
⇒
�
=
21
3
=
7
⇒x=
3
21
=7
Hence another number = 7 and positive number = 7 x 5 = 35.
what would be the number of years it would take for 1500 to earn 350 in simple intrest at a rate of 4.3%
The number of years it would take for $1500 to earn $350 will be 5.43 years.
What is simple interest?Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.
The formula for interest is written as,
I = (PRT)/100
Where P is the principal, R is the rate of interest, and T is the time.
The amount of $1500 is invested to earn $350 in simple interest at a rate of 4.3%.
Then the number of years is given as,
350 = (1500 x 4.3 x T) / 100
350 = 15 x 4.3 x T
64.5T = 350
T = 5.43 years
The number of years it would take for $1500 to earn $350 will be 5.43 years.
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Two stores are advertising specials on apples.
Store A
8 apples for $4.40 Store B
12 apples for $5.76
Apples are sold individually.
a) What is the cost for 1 apple at Store A?
b) What is the cost of 1 apple at Store B?
C) How much less would 30 apples cost at Store B than at Store A?
For each 70 mm of coloured fabric Alex uses to make his curtains, he also uses 20 cm of white fabric. Express the amount of white fabric to coloured fabric as a ratio in its simplest form.
20 : 7 is already the simplest term and there is no need to further simplify.
What is ratio?Ratio can be defined as the given value divided by total value.
When presenting a ratio as an answer:
1. It has to be in the form of integer, it cannot be in the form of fraction or decimals
2. There should be of the equivalent units.
3. It must be in its simplest form
Convert the units in cm
Coloured Fabric = 70 mm
Coloured Fabric = 70 ÷ 10 cm
Coloured Fabric = 7 cm
Find the ratio of the Colour Fabric to White Fabric:
Coloured Fabric = 7 cm
White Fabric = 20 cm
Ratio of White Fabric : Colour Fabric = 20 cm : 7 cm
Ratio of White Fabric : Colour Fabric = 20 : 7
Therefore, 20 : 7 is already the simplest term and there is no need to further simplify.
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Please help with this I’ll reward you I promise
The factorized expressions are (4x - 1)(4x + 5), (2z - 7)(z + 10) and (3x - 8)(2x + 5)
The factor pairs of -80The pair factors of -80 are (-1, 80), (-2, 40), (-4, 20), (-5, 16) and (-8, 10).
The factor pairs with a sum of 16The pair factors of -80 in this category is
(-4, 20)
This is so because
-4 + 20 = 16
Factor the expressionWe have
16x^2 + 16x - 5
So, we have
16x^2 + 20x - 4x - 5
Factorize
4x(4x + 5) -1(4x + 5)
So, we have
(4x - 1)(4x + 5)
For the other expressions, we have
2z^2 + 13z - 70
2z^2 + 20z -7z - 70
So, we have
(2z - 7)(z + 10)
6x^2 - x - 40
6x^2 + 15x -16x - 40
So, we have
(3x - 8)(2x + 5)
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Gabriella drank
2
3
liter of water Monday before going jogging. She drank
3
7
liter of water after her jog. How much water did Gabriella drink altogether? Write your answer as a mixed number.
[tex]1\frac{5}{12}[/tex] liter of water Gabriella drink altogether.
What is Fraction?A fraction represents a part of a whole.
Gabriella drank 2/3L water before jog
Gabriella drank 3/4L water after her jog
Altogether water she drank (2/3+3/4)
2/3+3/4
LCM of 3 and 4 is 12
8+9/12
17/12
17/12 can be written as mixed fraction [tex]1\frac{5}{12}[/tex].
Hence, [tex]1\frac{5}{12}[/tex] liter of water Gabriella drink altogether.
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As part of the study described in exercise 10, the Educational Testing Service computed the average Verbal SAT score for each state, as well as the average Math SAT score for each state. (Again, D. C. Counts as a state. ) The corre- lation between these 51 pairs of averages was 0. 97. Would the correlation between the Math SAT and the Verbal SAT computed from the data on all the individuals who took the tests-be larger than 0. 97, about 0. 97, or less than 0. 97? Explain briefly
If the data for every person who took the tests were tabulated, the correlation between the Math and Verbal SATs would be less than 0.97.
Are the SAT verbal and SAT reading the same test?
The word used to designate the SAT Reading and Writing part is an older, outmoded one. The SAT Verbal section's material is still highly significant today, though. Many of the subjects and abilities from the old SAT Verbal portion are now included in the Evidence-Based Reading and Writing section.
Here we know that the correlation between these 51 pairs of averages was 0. 97.
And as we all know that the Educational Testing Service computed the average Verbal SAT score for each state, as well as the average Math SAT score for each state.
As we know that the individual people tend to have more variation when you compare them to the average person
then if we look at the individual math and rebels course then there's probably a way more variation.
Here we know that the straight line wouldn't be there.
Then the whole thing would not be the same.
And which tells that It would be less of a correlation coefficient.
So it is less that 0.97.
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A 32 flat screen television measures 32 inches across its diagonal. The diagonal makes a 35 degrees angle with the bottom of the television. What equation can be used to solve for the height,H, of the television screen?
The 32 inche flat screen televisions will be 19.35 inches in height based on the angle between diagonal and bottom
The diagonal, bottom and perpendicular forms
right angled triangle. The mentioned angle can be related with diagonal and height through sine function. The formula is expressed as follows -
sin theta = height ÷ diagonal
Keep the values in formula to find the value of height.
sin 35 = h/32
Rewriting the formula for h.
h = sin 35 × 32
Keep the value of sin 35 in the formula
h = 0.57 × 32
Performing multiplication on Right Hand Side of the equation
h = 18.35 inches
Hence, the TV screen is 18.35 inches high.
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A triangle has sides with lengths of 8 inches, 11 inches, and 13 inches. Is it a right triangle?
Yes
No
(x² - 4)/(x² - 7x + 10)
Use interval notation to indicate where ƒ(x) is continuous.
I got (-inf,2)U(5,inf) for my answer but it says there should be something else. What am I missing?
In interval notation, the interval of continuity of f(x) is (-∞, 2) ∪ (5, +∞)
What is continuity of a function in an interval?A function is said to be continuous in an interval if all the values in the interval satisfy the function.
How to use interval notation to indicate where ƒ(x) is continuous?Since we have the function (x² - 4)/(x² - 7x + 10), we desire to find the interval in which it is continuous. So, we proceed as follows.
For the function f(x) = (x² - 4)/(x² - 7x + 10) to be continuous, then the denominator (x² - 7x + 10) ≠ 0
So, solving this inequality, we have
x² - 7x + 10 ≠ 0
x² - 2x - 5x + 10 ≠ 0
Factorizing, we have that
x(x - 2) - 5(x - 2) ≠ 0
(x - 2)(x - 5) ≠ 0
x - 2 ≠ 0or x - 5 ≠ 0
x ≠ 2 or x ≠ 5
Also, since the coefficient of x² is positive the function f(x) tends to ±∞.
So, the interval of continuity of f(x) is 2 < x and x > 5
So, the interval of continuity of f(x) is (-∞, 2) ∪ (5, +∞)
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a norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. what is the area of the largest possible norman window with a perimeter of 30 feet?
The area of the largest possible norman window with a perimeter of 25 ft is 43.75 ft²
Let r = the semicircle's radius
h = the rectangle's radius
2r = the window's width
C = 2πr is the formula for the perimeter of a circle,
The perimeter of the semicircle =πr
The perimeter of the window is
P=πr + 2h + 2r = 25
2h + (π +2)r = 25
h = ½[25 - (π + 2)r]
h = 12.5 - (π/2 +1)r ...............(1)
The formula for the area of a circle is A= πr², so
½πr² = the perimeter of the semicircle
The area of the window is
A = ½πr² + 2rh.............. (2)
Substitute (1) with (2).
A = ½πr² + 2r[12.5 - (π/2 +1)r] = ½πr² + 25r - (π +2)r²
A = 25r - (π + 2 - π/2)r²
A = -(π/2 + 2)r² + 25r ........(3)
One way to notice the vertex is to set the first derivative equal to zero.
dA/dr =-2(π/2 + 2)r + 25 = 0
-(π + 4)r + 25 = 0
r = 25/(π + 4)
r ≈ 3.50 ft .......... (4)
Substitute (4) with (1).
h = 12.5 - (π/2 +1)(3.50) = 12.5 - (2.571× 3.50)
h = 12.5 - 9.00 = 3.50
h = 3.50 ft
Area = 1.571(3.50)² + 2×3.50×3.50 = 19.25 + 24.50
Area = 43.75 ft²
So, the area is 43.75 ft².
Read more about semicircles:
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