The expression for the sum is 2n + 1 and the sum must be an odd number because it will leave 1 as remainder when divided by 2.
What is Euclid division lemma?The Euclid division lemma states that when two positive integers a and b are divided then their are other two integers q and r that represent quotient and remainder. The equation for the lemma can be written as a = bq + r where r < b.
(a) The given consecutive integers are n and n + 1 respectively.
The expression for their sum can be written as,
n + n + 1
⇒ 2n + 1
(b) The general expression for the sum is 2n + 1.
Now, as per the Euclid's division lemma, the number when divide by 2 will leave remainder as 1.
Which implies the number will be an odd number.
Hence, the expression for the sum is 2n + 1 and it will be an odd number.
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Renaldo plans to leave from Atlanta and fly into London (4281 miles). On the return, he will fly back from London to New York City (3470 miles) to visit his aunt. Then Renaldo heads back to Atlanta. Atlanta, New York City, and London do not lie on the same line. Find the range of the total distance Renaldo could travel on his trip.
The total distance Renaldo could travel on his trip when he starts from Atlanta goes to London and Newyork city, and return to Atlanta is 15502 miles.
What is distance?The complete movement of an object, regardless of direction, is referred to as distance. The amount of ground a thing travels from its starting point to its destination is also referred to as distance.
Given:
The distance between Atlanta and London = 4281 miles,
The distance between London to Newyork city = 3470 miles,
Write the trip blue plan as shown below,
Renaldo start from Atlanta → London → Newyork city → London → Atlanta
Calculate the total distance as shown below,
The total distance = 4281 + 3470 + 3470 + 4281
The total distance = 2 (4281 + 3470)
The total distance = 2 × 7751
The total distance = 15502 miles
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from 9 employees at dunder mifflin paper company, michael will choose 3 employees to go on a trip to canada. how many combinations of 3 employees can be chosen from the set of 9?
In 84 ways 3 employees can be chosen from the set of 9.
What is combination?
Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.You can choose the components of combos in any order. Permutations and combinations can be mixed up.Total 9 employees from that 3 employees can be chosen.
Total number of combination = ⁹C₃
= 9! / (9-3)! 3!
= 9 *8 *7/3*2
=3* 4* 7
= 12 * 7
= 84
Hence, in 84 ways 3 employees can be chosen from the set of 9.
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6. Solve for x. Then state the excluded value.
16
3 = 1
x-5
a.
Answer: x=
Excluded Value: x #
Please help someone please!!!!!
Answer: x=9, excluded value x≠5
Step-by-step explanation:
1. add 3 to both sides -> 16/x-5 = 4
2. then multiply both sides by x-5 -> 16=4(x-5) -> 16=4x-20
3. add 20 to both sides -> 36=4x
4. divide both sides by 4 to solve for x -> 9=x
the excluded value is whatever would make the denominator of the fraction equal to 0. You can't divide by 0. Therefore in this case, x can't equal 5 because 5-5=0
an apple chew was selected 53 times a lemon chew was selected 3 times a peach chew was selected 3 times what's the probability
The probability that the next chew that Jamar removes from the bag will be an apple chew is of:
0.9 = 90%.
How to calculate the probability?In the context of an experiment, a probability is calculated as the division of the number of desired outcomes in the context of the problem by the number of total outcomes in the context of the experiment.
In this problem, the outcomes are given from the previous experiments, hence we have an experimental probability.
The outcomes are given as follows:
Desired: apple chew = 53 outcomes.Total: 53 + 3 + 3 = 59 outcomes.Then the probability that the next chew that Jamar removes from the bag will be an apple chew is calculated as follows:
p = 53/59 = 0.9 = 90%.
Missing InformationThe problem is given by the image shown at the end of the answer.
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Select all of the true statements.
A. π is the area of a circle of radius 1
B. π is the area of diameter 1
C. π is the circumfrence of a circle of radius 1
D. π is the circumfrence of a circle of diameter 1
E. π is the constant of proportionality relating the diameter of a circle to its circumfrence
F. π is the constant of proportionality relating the radius of a circle to its area
The statements that are true are:
π is the area of a circle of radius 1.
π is the circumference of a circle of diameter 1.
π is the constant of proportionality relating the diameter of a circle to its circumference.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2 x pi x r.
The area of a circle is given as:
We have,
Circumference of a circle = 2πr
Area of a circle = πr²
π is the area of a circle of radius 1.
Area = πr² = π x 1 = π
π is the area of diameter 1.
2r = 1
r = 1/2
Area = πr² = π x 1/4 = π/4
π is the circumference of a circle of radius 1.
Circumference of a circle = 2πr = 2 x π x 1 = 2π.
π is the circumference of a circle of diameter 1.
Circumference of a circle = 2πr = 2 x π x 1/2 = π.
π is the constant of proportionality relating the diameter of a circle to its circumference.
Diameter ∝ Circumference
2r = 2πr
2r = π (2r)
π is the constant of proportionality relating the radius of a circle to its area.
r = (πr)r
Thus,
π is the area of a circle of radius 1 is true.
π is the circumference of a circle of diameter 1 is true.
π is the constant of proportionality relating the diameter of a circle to its circumference is true.
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factor binomial
x²-36=
Answer: (x - 6)(x + 6)
Step-by-step explanation:
To factor this, recall the difference of squares
[tex]a^{2} - b^{2} = (a-b)(a+b)[/tex]
And because 36 is [tex]6^{2}[/tex], that means
[tex]x^{2} - 36 = x^{2} - 6^{2} = (x-6)(x+6)[/tex]
[tex] \bold{(x-6)(x+6)}[/tex]
To simplify this equation, quadratic factoring patterns should be used. These patterns are the following:
[tex] \bold{a^2-b^2=(a-b)(a+b)}[/tex]
This pattern works because if one distributes the terms in the parentheses by multiplying each term in one of the parentheses by each term in the other, the result is the original equation:
[tex] \bold{36=6^2}[/tex]
So it can be applied to the given equation:
[tex] \bold{x^2-36}[/tex]
[tex] \bold{ \bold{\boxed{(x-6)(x+6)}}}[/tex]
The factored form of the expression is [tex]\bold{(x-6)(x+6)}[/tex]
in a clinical test with 570 subjects, 135 showed improvement from the treatment. find the margin of error for the 95.0 percent confidence interval used to estimate the population proportion that showed improvement.
On solving the provided question, we can say that - Level significance = 0.05, Z = 1.96, Margin of error= 0.0349
What is Null Hypothesis?A well-known statistical theory called the null hypothesis asserts that there is no statistical connection between two sets of observable data and measurable phenomena for a given set of observed variables. A null hypothesis is a kind of statistical hypothesis that asserts that a certain collection of observations has no statistical significance. Using sample data, hypotheses are tested to determine their viability. Sometimes known as "zero" and symbolized by H0. A scientific hypothesis is a prediction of what researchers will discover via their investigation. A statistical hypothesis, however, states what a statistician does not anticipate. The null hypothesis is so named because of this.
Null hypothesis,
Sample size, n = 570
Sample portion, P’ = 135/579 = .2368
At 95% confidence,
Level significance = 0.05
Z = 1.96
Margin of error= 0.0349
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Gabby worked 60 hours in 7 days. determine the rate for a ratio of the two different quantities. a. 60 over 7 hours per day b. 60 over 67 hours per day c. 7 over 60 hours per day d. 7 over 67 hours per day
Answer:
a
Step-by-step explanation:
60 hours in 7 days = 60/7 hours per day
Answer:
A is correct
Step-by-step explanation:
I got it right on my test
Write the following expressions without any radicals and only positive exponents:
[tex]\sqrt[6]{25^{3} }[/tex]
[tex]\frac{1}{\sqrt[3]{5^{4} } }[/tex]
Convert the radicals as follows:
[tex]\sqrt[6]{25^3}= \sqrt[6]{(5^2)^3}= \sqrt[6]{5^6}=5^{6/6}=5^1=5[/tex][tex]\dfrac{1}{\sqrt[3]{5^4} } =\dfrac{1}{5^{4/3}} }[/tex] - can't be further simplifiedThe simplification of the expression are;
[tex]\sqrt[6]{25^3}[/tex] = 5
[tex]\dfrac{1}{\sqrt[3]{5^4} } =\dfrac{1}{5^{4/3}} }[/tex]
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; which can also be used to indicate the logical syntax's order of operations and other features.
We are given the expression as;
[tex]\sqrt[6]{25^3}[/tex]
Convert the radicals as follows:
[tex]\sqrt[6]{25^3}\\\\= \sqrt[6]{(5^2)^3}\\\\= \sqrt[6]{5^6}\\\\=5^{6/6}\\=5^1=5[/tex]
Now,
[tex]\dfrac{1}{\sqrt[3]{5^4} } =\dfrac{1}{5^{4/3}} }[/tex]
Here this cannot be further simplified.
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inverse function
[tex]f(4) = 7 {f}^{ - 1} = ?\ \textless \ br /\ \textgreater \ [/tex]
If f(4) = 7 then the inverse of the function f⁻¹(7) is 4.
What is function?Function is a combination of different types of variable and constants in which for the different values of x the value of function y is unique.
The given function is,
f(4) = 7
According to inverse function property,
if f(x) = y, then f⁻¹(y) = x
The inverse of function,
f⁻¹(7) = 4
The inverse of the function f(4) = 7 is f⁻¹(7) = 4.
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suppose that you are rolling a six sided dice. let a = get a number smaller than 2 what is p(ac)?
Given A = rolling a number lower than 2
A six- sided bones has possible issues and 6. We also note that the only outgrowth lower than 2. probability of both issues is equal i.e. 50 or 1/2.
So, the probability of an event is Favorable issues Total number of issues. It's denoted with the gap i.e. P( Event) The possibility of the result of any arbitrary event is known as probability. This expression refers to determining the liability that any given circumstance will do. What are the chances of entering a head, for case, when we toss a coin in the air? The number of issues that could do is the base for the response to this question. The outgrowth in this case might be either head or tail. thus, there's a 50 chance that the result will be a head. The probability serves as a hand for how probably an event is to do. It gauges how likely an event is. The probability formula is as follows P( E) is equal to the rate of favourable issues to overall issues.
P( E) = n( E)/ n( S)
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4. A circular region has a population of about 44,600
and a population density of 388 people per square
kilometer. Find the radius of the region.
The radius of the given region is calculated as; 19.329 km
How to find the area of a circle?We are told that the region is circular and as such the formula for the area of a circle is;
A = πr²
We are told that the population is 44600
Population density is defined as the average number of individuals in a population per unit are.
In this question, the population density is given as 388 people per sq. km
Thus;
Area = Population/population density
πr² = 44600/388
r² = 44600/388π
r² = 373.595
r = 19.329 km
We conclude that is the radius
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PLS HELP WILL GIVE BRAINLIEST
Harry needs wood pieces to complete a project in woodshop class. He needs three pieces of wood that have a length of two and three fourths feet and six pieces of wood that are one and one third feet. What is the total amount of wood that Harry will need for the project?
four and one twelfth feet
sixteen and one fourth feet
three and four sevenths feet
six and one third feet
Answer:
D) six and one third feet
Step-by-step explanation:
To find the total amount of wood that Harry needs, we need to find the total length of the three pieces of wood that are two and three fourths feet long and the total length of the six pieces of wood that are one and one third feet long.
The three pieces of wood that are two and three fourths feet long have a total length of 3 * 2 and 3/4 = 6 and 1/4 feet.
The six pieces of wood that are one and one third feet long have a total length of 6 * 1 and 1/3 = 8 and 2/3 feet.
To find the total length of all the pieces of wood, we need to add the total length of the three pieces that are two and three fourths feet long and the total length of the six pieces that are one and one third feet long. This gives us a total of 6 and 1/4 + 8 and 2/3 = 14 and 7/12 feet.
Therefore, Harry will need a total of 14 and 7/12 feet of wood for the project. This is equivalent to approximately six and one third feet, so the correct answer is d) six and one third feet.
find the area of the region that lies inside both curves. r^2 = 50 sin(2θ), r = 5
The area under the curve r²=50sin2Θ is (15.71)unit square
How to find the area under the parabola?A parabola is defined as a plane curve that is mirror-symmetrical and approximately U-shaped.
Given:
parabola is r²=50sin 2[tex]\theta[/tex],
where r=5
So, 5²=50 sin 2[tex]\theta[/tex],
Simplifying the equation
25=50 sin 2[tex]\theta[/tex],
sin 2[tex]\theta[/tex] = 1/2
2[tex]\theta[/tex] = [tex]sin^{-1[/tex] 0.5
[tex]\theta[/tex] = 15 degree.
Now, the Area = 22/7 × 5
Area = 15.71 unit²
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In the equation 5x + 9 = 3x, _________ and
__________ are like terms.
Answer: 5x and 3x
Step-by-step explanation:
5x and 3x are like terms because they both have the same variable being multiplied to them which is x.
which one of the numbers does not belong in the following series?1 - 2 - 5 - 10 - 13 - 26 - 29 - 48
48 is the number does not belong in the following series 1, 2, 5, 10, 13, 26, 29, 48
The series is formed by following the sequence that is:
1, 2, 5, 10, 13, 26, 29, 48
What is a number pattern?Number pattern is a pattern or sequence in a series of numbers. This pattern generally establishes a common relationship between all numbers. A recursive pattern rule is a pattern rule that tells you the start number of a pattern and how the pattern continues.
The first number is multiplied by 2 and the next number should be added by 3 to the previous number.
The first number is 1 and it should be multiplied by 2
1 × 2 = 2
Then the next number should be added by 3
2 + 3 = 5
The series will be continued:
5 × 2 = 10
10 + 3 = 13
13 × 2 = 26
26 + 3 = 29
but 29 × 2 = 58 ≠ 48.
Therefore the number 48 does not belongs to the given series.
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complete the table such that a and b represent a proportional relationship
The complete table of values of the proportional relationship is
A= 8, 24, 40
B= 3, 9, 15
How to complete the table of proportional relationship between A and B.From the question, we have the following parameters that can be used in our computation:
A= 8, _, 40
B= 3, 9, _
Calculate the constant of proportion using
constant = B/A
Substitute the known values in the above equation, so, we have the following representation
constant = 3/8
Substitute constant = 3/8 in constant = B/A
3/8 = B/A
So, we have
3A = 8B
When B = 9, we have
3A = 8 * 9
This gives
A = 24
When A = 40, we have
3 * 40 = 8B
This gives
B = 15
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Complete question
Complete the table such that a and b represent a proportional relationship
A= 8, _, 40
B= 3, 9, _
At the beginning of her enior year maria received a $5,000 ubidized loan and a $4,500 unubidized loan with an apr of 5. 5%. If maria begin making payment on her loan 6 month after graduation, how much interet will he oweto the nearet dollar?
The total amount of interest that Maria will owe on her unsubsidized loan = $113.63
In this question we have been given Maria received a $5,000 subsidized loan and a $4,500 unsubsidized loan with an apr of 5.05%
We need to find the total amount of interest that Maria will owe on her unsubsidized loan.
Using simple interest formula,
I = P * t * r
where P - the principal
r - the interest rate,
and t - time period
Maria begins making payments 6 months after graduation, this means there are 12 - 6 = 6 months between graduation and the start of payments.
so, t = 6 months
i.e., t = 0.5 year
Here, R = 5.05%, P = $4500
Now we convert R percent to r a decimal
r = R/100
= 5.05%/100
= 0.0505 per year,
Using the formula of simple interest,
I = 4500 * 0.0505 * 0.5
I = $113.63
Therefore, the interest amount is $113.625
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The complete question is:
At the beginning of her senior year maria received a $5,000 subsidized loan and a $4,500 unsubsidized loan with an apr of 5.05%. if maria begins making payments on her loans 6 months after graduation, how much interest will she owe to the nearest dollar?
find the x- and y- intercepts of the graph of 10x+y=8
Answer:
Step-by-step explanation:
in x intercepts y is equals to 0
10x = 8
x = 8/10
x = 4/5
in y intercepts x is equals to 0
y = 8
You start at (3, 6). You move down 1 unit and up 4 units. Where do you end?
Answer:
(3, 9)
Step-by-step explanation:
You start on (0, 0), and try and remember the term, "you run before you can jump(x before y, (x, y)) when working with coordinates.
X axis: so you "run" 3 units to the right, as it's not a negative number. so now your on (3, 0) (dark blue arrows)
Y axis: now you do the "jumping" portion of this, so you jump up six units as it's a negative, so now your on (3, 6) (red arrows)
Y: axis: but now you have to move down 1 unit, so you essentially "fall" 1 unit down, (3, 5) (pink arrow)
Y axis: you have to "jump" 4 units up now, so now your at (3, 9) (green arrows)
you haven't moved along the X axis so you keep the 3, you only moved the Y axis.
So your asnwer is (3, 9)!
Hope this helped!! (picture help as well!)
I am a mixed number between 2 and 10. I am nearer to 8 than 10. If you eparate my fractional part then I am an odd number. Who am I?
The mixed number between 2 and 10. I am nearer to 8 than 10 is 6 1/9, it is an entire quantity, and a right fraction represented together.
A mixed fraction is an entire quantity, and a right fraction represented together. It commonly represents a range of among any complete numbers. Look on the given image, it represents a fragment this is extra than 1 however much less than 2. It is thus, a mixed fraction. A fraction represented with its quotient and the rest is a combined fraction. For example, 2 1/three is a combined fraction, wherein 2 is the quotient, 1 is the the rest. So, a combined fraction is a aggregate of an entire quantity and a right fraction.
Thus, the mixed number if 6 1/9.
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A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 3 large boxes and 2 small boxes has a total weight of 83 kilograms. A delivery of 5 large boxes and 6 small boxes has a total weight of 175 kilograms. How much does each type of box weigh?
large box:
small box:
Answer:
Large box: 18.5 kg
Small box: 13.75 kg
Step-by-step explanation:
Let L represent a large box, and S represents a small box
We have the equation
3L + 2S = 83 kg
5L + 6S = 175 kg
We time the first equation by -3
-9L - 6S = - 249 kg
5L + 6S = 175 kg
Now Let's find the large box weighs first
Add both equation and we get
-4L = -74 kg
L = 18.5 kg
Now put 18.5 in for the L to find the weight of the small box
5(18.5) + 6S = 175 kg
92.5 + 6S = 175 kg
6S = 82.5 kg
S = 13.75 kg
Answer:
x as large; y as small
3 large + 2 small = 83 (1st equation)
5 large + 6 small = 175 (2nd equation)
3x + 2y = 83 (multiply by -5)
5x + 6y = 175 (multiply by 3)
-15x - 10y = -415
15x + 18y = 525 (simplify)
8y = 110
y = 13.75 (small box weight)
3x + 2y = 83 (substitute the value of y)
3x + 2(13.75) = 83
3x + 27.5 = 83
3x = 55.5
x = 18.5 (large box weight)
CHECKING:
3x + 2y = 83
3(18.5) + 2(13.75) = 83
55.5 + 27.5 = 83
83 = 83 (1st equation is proven right)
5x + 6y = 175
5(18.5) + 6(13.75) = 175
92.5 + 82.5 = 175
175 = 175 (2nd equation is proven right)
therefore, large box weight is 18.5kg and the small box weight is 13.75kg.
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Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Identify the angles shown
A. Corresponding angles
B. Same side interior angles
C. Alternate exterior angles
D. Alternate interior angles
Help!!!
Answer:
B. Same-side interior angles
Step-by-step explanation:
Same Side interior angles are angles that are on the same side and add up to 180 degrees. So, the answer is B
PLS answer i dont understand how to do it
Answer:
answer on the picture. Let me know if I am right!
What i the equation of a line perpendicular to y = - 1/4 x 6 and goe through the point (2, 9) ?
The required equation of the line is y = 4x + 1.
Slope-Intercept form of a line:The Slope-intercept form of a line is given by
y = mx + cWhere m is the slope of the line and c is the y-intercept
Note:
The product of slopes of perpendicular lines = -1
Here we have
y = -1/4x + 6 Line (1)
Here slope of the line m₁ = -1/4
Let y = m₂x + c Line (2)
Assume that Line (2) is the perpendicular line to Line
As we know The product of slope of two perpendicular lines is -1
=> m₁m₂ = -1 [∵ Line (1) and Line (2) perpendicular lines ]
=> -1/4(m₂) = -1 [ ∵ m₁ = -1/4 ]
=> m₂ = 4
The line (2) => y = 4x + c
Given that the line passes through (2, 9)
=> 9 = 4(2) + c
=> c = 9 - 8
=> c = 1
Therefore,
The required equation of the line is y = 4x + 1
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The econd highet mountain on earth ha a peak elevation of 9,417 yard. What i the elevation of thi mountain in feet?
The elevation of this mountain in feet is 28,169 feet. This gives us the original number of 9,417 yards, confirming that our answer is correct.
To convert yards to feet, we simply need to multiply the number of yards by 3. There are 3 feet in a yard, so to convert 9,417 yards to feet, we multiply 9,417 by 3.
This gives us the total of 28,169 feet as the elevation of this mountain. To check our answer, we can also convert 28,169 feet back to yards by dividing 28,169 by 3.
This gives us the original number of 9,417 yards, confirming that our answer is correct.
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on average, for every hour spent on clinical care how much time is spent on the ehr documenting care? one half hour four hours one hour two hours
On average, for every hour spent on clinical care two hours is spent on the EHR documenting care.
According to a new survey, physicians spend slightly over 16 minutes every patient visit examining electronic health records(EHR). For every hour of clinical care two hours are spend on EHR documentation. According to the study published in the Annals of internal medicine this accounts for a large percentage of a physician's day.
An Electronic Health Record (EHR) is an electronic version of a patients medical history, that is maintainrd by the provider over time, and may include all of the key administrative clinical data relevent to that persons care under a particular provider. It helps providers better manage care for patients and provide better health care.
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Which of the following numbers is NOT divisible by 2,5 and 10?
A.17
B.25
C.40
D.70
Answer: 17
Step-by-step explanation: 2 is an even number and 17 is an odd number, therefore it can't be divisible by 2. 17 does not have a 5 or a 0 in it therefore it is not divisible by 5. Any multiple of 5 will always have a 5 or 0 in it. If it doesn't have a zero in it anywhere it is not divisible by 10. A multiple of 10 will always have a zero in it.
If the profit is the difference between the revenue and the cost, what expression represents the profit? 3x – 260 3x 140 5x – 260 5x 140
The profit function for this problem is defined as follows:
P(x) = 5x - 260.
How to obtain the profit function?The profit function is defined as the subtraction of the revenue function by the cost function, as follows:
P(x) = R(x) - C(x).
In which:
R(x) is the revenue function.C(x) is the cost function.From the image given at the end of the answer, the revenue function and the cost function are given as follows:
R(x) = 3x² + 4x - 60.C(x) = 3x² - x + 200.Then the profit function is calculated as follows:
P(x) = R(x) - C(x)
P(x) = 3x² + 4x - 60 - (3x² - x + 200).
Combining the like terms, we have that:
P(x) = (3 - 3)x² + (4 + 1)x - 60 - 200
P(x) = 5x - 250.
Meaning that the third option is correct.
Missing InformationThe problem is given by the image shown at the end of the answer.
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A rod with a length of 63 cm is cut into two pieces.
The lengths of the two pieces are in the ratio 7:2
Work out the length of each piece.
Answer:
The lengths of the two pieces are 7 cm and 14 cm.
Step-by-step explanation:
Let x represent the length of the longer piece of the rod. Since the lengths of the two pieces are in the ratio 7:2, the length of the shorter piece is 2x. The total length of the two pieces is therefore 7x + 2x = 9x. Since the total length of the two pieces is 63 cm, we have:
9x = 63
Dividing both sides by 9, we get:
x = 7
Thus, the length of the longer piece is 7 cm, and the length of the shorter piece is 2 * 7 = 14 cm. Therefore, the lengths of the two pieces are 7 cm and 14 cm.