Answer:
(a) Let X be the number of boxes that do not have any balls. We can calculate the probability that a particular box is empty, which is (1-p)^10, where p is the probability that a ball is put into that box. The expected number of boxes that are empty is then:
E(X) = 5(1-p)^10 (since each box has the same probability of being empty)
Substituting ∑(i = 1 to 5) p = 1, we get p = 1/5. Therefore,
E(X) = 5(1-1/5)^10 = 5(4/5)^10 ≈ 0.328
So, the expected number of boxes that do not have any balls is approximately 0.328.
(b) Let Y be the number of boxes that have exactly one ball. The probability that a particular box has exactly one ball is given by:
P(exactly one ball in a box) = 10p(1-p)^4
where p is the probability that a ball is put into that box. The expected number of boxes that have exactly one ball is then:
E(Y) = 5(10p(1-p)^4)
Substituting p = 1/5, we get:
E(Y) = 5(10/5^5) = 1/25
So, the expected number of boxes that have exactly one ball is 1/25.
Answer this question please
Answer:
Translation of three units to the right (on the x-axis) and one unit down (on the y-axis).
If you want, this can be represented in vector form (3 1).
Step-by-step explanation:
This was done by translating the shape three units to the right and one unit down
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What identity can be used to rewrite the expression 8x³ +243?
A. Difference of Cubes
B. Pythagorean Triples
C. Difference of Squares
D. Sum of Cubes
Here the option is (D): Sum of Cubes.
The Given expression can be written as:
a³ + b³ = (a + b)(a² - ab + b²)
we can write 8x³ as (2x)³ and 243 as 3³.
we have,
8x³ + 243 = (2x)³ + 3³
we can rewrite the above equation
(2x + 3)(4x² - 6x + 9)
Therefore, the identity that can be used to rewrite the given expression is an option (D): Sum of Cubes
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Need help with this, can anyone give me the answer?!
In ALMN, LM || OP. Given that NL= 33, NM= 44, and NP = 24, find NO.
L
M
NO =
Answer:
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f(x)=3x^2-7x-4 determine el valor de f(0)
The numeric value of f(x) = 3x² - 7x - 4 at x = 0 is given as follows:
f(0) = -4.
How to obtain the numeric value of a function or of an expression?To obtain the numeric value of a function or of an expression, we substitute each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The function for this problem is defined as follows:
f(x) = 3x² - 7x - 4
We want to find the numeric value of the function at x = 0, hence both instances of x in the definition of the function are replaced by zero and then we add the terms, as follows:
f(0) = 3(0)² - 7(0) - 4
f(0) = -4.
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help me pleaseeee!!!
Answer: -5/6
Step-by-step explanation:
Hopefully this helps, my friend, best of luck to you :)
Farmer Ed has 1,000 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the river, what is the largest area that can be enclosed?
Answer:
Step-by-step explanation:
Farmer Ed has 1,000 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the river, what is the largest area that can be enclosed?
15. Find the missing side lengths. Answers are in simplest radical form with the denominator rationalized.
60°
2√6
Oz=4√6.y=6√2
Oz= 8√3,y=6
= 4√6, y=6
Oz=6√2y = 8√3
Thus, the length of the missing side for the given Right triangles using the Trigonometric Ratios is found as :x = 18.47 units.
What is meant by Trigonometric Ratios?In order to examine the sides of both a right triangle, which will depend on an acute angle, trigonometric ratios are used. Right triangles what about those produced by the intersection of the legs, which have an internal angle of 90 degrees. We can determine the right triangle's missing sides or sharp angles using trigonometric ratios.The leg, denoted as, that is next to the 30 degree angle θ is represented by Side BC. To get the length of side BD, the hypotenuse of triangle BCD, we use the cosine ratio.
cos θ = Adjacent leg / Hypotenuse = BC/BD
cos 30° = 8√2 / BD
Now, we know.
cos 30° = √3/2
√3/2 = 8√2 / BD
BD = 8√2 / √3/2
BD = 16√2 / √3
On rationalising;
BD = 16√2*√3 / √3*√3
BD = 16√6 / 3
Sin A = Opposite leg /Hypotenuse = BD / x
Sin 45° = (16√6 / 3) / x = 16√6 / 3x
We know that:
Sin 45° = 1/√2
(1/√2) = 16√6 / 3x
(1/√2) * x = 16√6 /3
Or,
√2/2 * x = (16√6 /3) * (2/√2)
x = 32√3 / 3
x = 18.47
Thus, the length of the missing side for the given Right triangles using the Trigonometric Ratios is found as :x = 18.47 units.
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The correct question is-
Find the missing side length. Give the answer as radicals in simplest form.
Consider the following function.
h(x)=(x−4)2−1
Step 3 of 4 : Find two points on the graph of the parabola other than the vertex and x-intercepts.
Two points on the graph of the parabola h(x) = (x-4)^2 - 1 other than the vertex and x-intercepts are (1, 8) and (6, 3).
How to determine the points on the functionTo find two points on the graph of the parabola other than the vertex and x-intercepts
We can simply choose two values of x and find their corresponding y values using the function h(x).
Let's choose x = 1:
h(1) = (1-4)^2 - 1 = 9 - 1 = 8
So one point on the graph is (1, 8).
Now let's choose x = 6:
h(6) = (6-4)^2 - 1 = 4 - 1 = 3
So another point on the graph is (6, 3).
Hence, the two points are (1, 8) and (6, 3)
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-3-(-2)(5)-(-4)³ show your calculations
Answer:71
Step-by-step explanation:
-3-(-10)-(-64)=-3+10+64=71
Ball Bearings, Inc., faces costs of production as follows:
Quantity
Total Fixed Costs
Total Variable Costs
(Dollars)
(Dollars)
0 120 0
1 120 60
2 120 80
3 120 100
4 120 140
5 120 200
6 120 320
Complete the following table by calculating the company's total cost, marginal cost, average fixed cost, average variable cost, and average total cost at each level of production.
Quantity
Total Cost
Marginal Cost
Average Fixed Cost
Average Variable Cost
Average Total Cost
(Dollars)
(Dollars)
(Dollars)
(Dollars)
(Dollars)
0
1
2
3
4
5
6
The price of a case of ball bearings is $60. Seeing that the company can't make a profit, the company's chief executive officer (CEO) decides to shut down operations.
The firm's profit in this case is
$
. (Note: If the firm suffers a loss, enter a negative number in this cell.)
True or False: This was a wise decision.
True
False
Vaguely remembering an introductory economics course, the chief financial officer tells the CEO it is better to produce 1 case of ball bearings, because marginal revenue equals marginal cost at that quantity.
At this level of production, the firm's profit is
$
. (Note: If the firm suffers a loss, enter a negative number in this cell.).
True or False: This is the best decision the firm can make.
True
False
The firm's profit in this case is = $360.
What is the total cost?
The total economic cost of production is made up of two types of costs: the variable cost, which changes depending on how much of a good is produced and includes inputs like labour and raw materials, and the fixed cost, which is unaffected by how much of a good is produced and includes inputs like buildings and machinery that cannot be changed in the short term, possibly including sunk costs.
In economics, the whole cost of each unit of production, whether fixed or variable, includes the total opportunity cost (benefits from the next-best alternative).
Example:
Q Fixed Variable Total Marginal Aver. Aver. Aver.
Costs Costs Cost Cost FC VC TC
0 100 0 100 - - - -
1 100 50 150 150 100 50 150
2 100 70 170 20 50 35 85
3 100 90 190 20 33.33 30 63.33
4 100 140 240 50 25 35 60
5 100 200 300 60 20 40 60
6 100 360 460 160 16.67 60 76.67
The firm's profit in this case is = $360.
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Which of the following characteristics would best describe a sample that enables you to draw accurate inferences from the sample? A. The sample is biased, but not random or representative. B. The sample is random, but not biased or representative. C. The sample is random and representative, but not biased. D. The sample is random, representative, and biased.
Answer:
The best option that describes a sample that enables you to draw accurate inferences from the sample is option C: "The sample is random and representative, but not biased."
A random sample is one in which every member of the population has an equal chance of being selected. This helps to ensure that the sample is not influenced by any outside factors that could skew the results.
A representative sample is one that accurately reflects the characteristics of the population it is drawn from. This ensures that the results obtained from the sample can be generalized to the larger population.
However, if the sample is biased, it may not accurately represent the population. This could lead to inaccurate inferences and conclusions.
Therefore, a random and representative sample that is not biased is the best option for drawing accurate inferences from the sample.
Step-by-step explanation:
Need help with this problem 5
The values of h1 and h2 for which v3 is a linear combination of v1 and v2 is given as follows:
h1 = 1.h2 = -4.What is a linear combination?Vector v3 being a linear combination of v1 and v2 means that the following system of equations is used to relate the three vectors:
xv1 + yv2 = v3.
From each line of each vector, the system of equations relating these amounts is given as follows:
x = 1.-y = h1.-x + 3y = h2.From the second equation, considering h1 = 1, the value of y is given as follows:
1 = -y
y = -1.
Hence, from the third equation, the value of h2 is obtained as follows:
-1 + 3(-1) = h2
-1 - 3 = h2
h2 = -4.
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If we take the values are h₁ = -1, h₂ = 2, then the last vector is a linaer combination of the first two.
How to see if v₃ is a linear combination of the other two?Here we want to find the values of h₂ and h₃ such that the last vector is a linear combination of the first one, that means that we can write:
a*v₁ + b*v₂ = v₃
For each of the components we can write:
a*1 + b*0 = 1
a*0 + b*-1 = h₁
a*-1 + b*3 = h₂
With the first equation we conclude that a = 1, then:
1*0 + b*-1 = h₁
1*-1 + b*3 = h₂
If we also take b = 1 we will get:
0 - 1= h₂
-1 + 3 = h₃
Then the values are h₁= -1, h₂ = 2.
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Find a 5th degree polynomial with real coefficients that has zeros 0, -7i, and 2-i. show work
Answer:
f(x) = x^5 - 4x^4 + 54x^3 - 196x^2 + 245x.
Step-by-step explanation:
If a polynomial has a complex root, then its conjugate is also a root. Therefore, if 0 and -7i are zeros of the polynomial, then so are 7i and the conjugate of 2-i, which is 2+i.
The factors of the polynomial are then:
(x-0)(x-7i)(x+7i)(x-(2-i))(x-(2+i))
Simplifying the factors, we get:
x(x^2+49)(x^2-4x+5)
Expanding the last factor, we get:
x^5 - 4x^4 + 5x^3 + 49x^3 - 196x^2 + 245x
Finally, we have the 5th degree polynomial:
f(x) = x^5 - 4x^4 + 54x^3 - 196x^2 + 245x
Therefore, the polynomial with zeros 0, -7i, and 2-i and 5th degree with real coefficients is f(x) = x^5 - 4x^4 + 54x^3 - 196x^2 + 245x.
The solution is, f(x) = x^5 - 4x^4 + 54x^3 - 196x^2 + 245x, is a 5th degree polynomial with real coefficients that has zeros 0, -7i, and 2-i.
What are Polynomials?Polynomials are sums of k-xⁿ terms, where k can be any number and n can be any positive integer.
here, we have,
If a polynomial has a complex root, then its conjugate is also a root. Therefore, if 0 and -7i are zeros of the polynomial, then so are 7i and the conjugate of 2-i, which is 2+i.
The factors of the polynomial are then:
(x-0)(x-7i)(x+7i)(x-(2-i))(x-(2+i))
Simplifying the factors, we get:
x(x^2+49)(x^2-4x+5)
Expanding the last factor, we get:
x^5 - 4x^4 + 5x^3 + 49x^3 - 196x^2 + 245x
Finally, we have the 5th degree polynomial:
f(x) = x^5 - 4x^4 + 54x^3 - 196x^2 + 245x
Therefore, the polynomial with zeros 0, -7i, and 2-i and 5th degree with real coefficients is f(x) = x^5 - 4x^4 + 54x^3 - 196x^2 + 245x.
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Anybody It's easy!! if correct answered, will give crown.. I'm stuck at this for sooo long.. Anyone please helpppppppp.
What kind of transformation converts the graph of f(x)=2|x|+4 into the graph of g(x)=|x|+2?
reflection across the y-axis
reflection across the x-axis
Vertical stretch
Vertical Shrink
Answer:
The transformation that converts the graph of f(x)=2|x|+4 into the graph of g(x)=|x|+2 is a Vertical Shrink.
To see this, note that the 2 in f(x) causes a vertical stretch of the absolute value graph. Removing the 2 in g(x) results in a Vertical Shrink of the absolute value graph. The +4 and +2 only cause a vertical shift of the graph.
Answer: Vertical Shrink
Step-by-step explanation:
The transformation that converts the graph of f(x)=2|x|+4 into the graph of g(x)=|x|+2 is a vertical shrink.
To see why, let's examine each function separately:
The function f(x) = 2|x| + 4 has an absolute value in its equation, which means it has a "V" shape. The coefficient 2 in front of the absolute value means that the "V" is stretched vertically by a factor of 2. The constant 4 added to the end of the function moves the entire graph up by 4 units.The function g(x) = |x| + 2 also has an absolute value in its equation, but without a coefficient in front of it. This means that the "V" shape is not stretched or shrunk vertically. The constant 2 added to the end of the function moves the entire graph up by 2 units.Therefore, the transformation from f(x) to g(x) involves removing the vertical stretch by dividing the absolute value term by 2. This results in a smaller "V" shape for the graph of g(x), or a vertical shrink.
The answer is:
[tex]$\boxed{\text{Vertical Shrink}}$[/tex]
How do I solve for the answer please?
The value of the 5 measurements according to the given function is 66.
What is summation of values?When a group of numbers, known as addends or summands, are added together in mathematics, the outcome is their sum or total. Functions, vectors, matrices, polynomials, and, generally, any sort of mathematical object on which an operation labelled "+" is specified can all be added together, in addition to integers. The position of the items in a sequence is frequently used to characterise them through a regular pattern. Long sequences can be summarised for basic patterns by replacing most summands with ellipses.
The function is given as:
[tex]\sum_{i = 1}^5 (x_i^2)\\\\\sum_{i = 1}^5 = x_1 + x_2 + x_3 +x_4 + x_5\\\\\sum_{i = 1}^5 (x_i^2) = 12 + 14 + 16 + 7 + 17 = 66[/tex]
Hence, the value of the 5 measurements according to the given function is 66.
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What is the slope of the line
m=?
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
graph the equation f(x)=4x-3
Answer:
Step-by-step explanation:
SEE THE GRAPH
I need this , to solve ,
Thank you
b) The mean and standard deviatiοn οf the data is 8.022 and 0.335 respectively.
What is Mean?In statistics, mean is measure οf central tendency that represents average value οf set οf numbers. It is calculated by adding up all values in set and dividing sum by the tοtal number οf values in set.
b) Tο determine the mean and standard deviatiοn οf the data, we can input the given values intο a calculatοr οr a spreadsheet prοgram and use the apprοpriate fοrmulas. Here are the calculatiοns:
Mean = (7.96 + 8.54 + 7.92 + 8.40 + 8.02 + 7.91 + 8.12 + 7.85 + 8.27 + 7.67) / 10
= 8.022
Standard deviatiοn = sqrt([(7.96 - 8.022)² + (8.54 - 8.022)² + ... + (7.67 - 8.022)²] / 9)
= 0.335 (rοunded tο 3 decimal places)
Therefοre, the mean petrοl price is 8.022 and the standard deviatiοn is 0.335.
c) The histοgram appears tο be slightly skewed tο the right, as the tail οf the histοgram extends further tο the right than tο the left.
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i need help with question 6
Which of the following represent a linear inequality in open-sentence form? (Select all that apply.) 2x + 8 = 10y 2x - 7y > 10 8 + x > 5 3 < 5
The linear inequality in open-sentence form are
2x - 7y > 10 8 + x > 5 What are open sentences?An open sentence is a mathematical statement that contains at least one blank or unknown and that becomes true or false when the blank is filled or a quantity is substituted for the unknown.
Now, since we have the expressions,
2x + 8 = 10y 2x - 7y > 10 8 + x > 5 and3 < 5First, we note that there are 3 open sentences and only two of them are inequalities.
The 3 open sentences are
2x + 8 = 10y 2x - 7y > 10 8 + x > 5The two inequalities are
2x - 7y > 10 8 + x > 5So, the linear inequality in open-sentence form are
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From the sum of 8a-2b+8 and -2a+6b,subtract 5b-6a ?
Therefore , the solution of the given problem of expressions comes out to be b + 8 when 8a-2b+8 and -2a+6b are added together.
Expression : what is it ?There is a need for calculations like joining, random variable division, variable multiplication, and removal. If they were united, the following would happen: A mathematical equation, some data, and a formula. A statement of truth is composed of numerical data, formulae, components, and mathematical operations like additions, subtractions, errors, and segmentations. One can assess and analyse words and sentences.
Here,
The formula is as follows:
=> 8a - 2b + 8 - 2a + 6b - (5b - 6a)
By combining similar words to make the expression shorter, we get:
=> (0a - b + 8 = -b + 8)
=> (8a - 2a - 6a) + (-2b + 6b - 5b)
Therefore, the answer is b + 8 when 8a-2b+8 and -2a+6b are added together.
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You and your five friends run for political office. Assuming three offices are available (president, secretary, treasurer), how many different election outcomes are possible?
Please help god bless you!
There are 20 different election outcomes are possible.
What is outcomes?An outcome is a possible result of a random experiment or event. It is a specific occurrence that may or may not happen, but that could happen under certain conditions. Outcomes are often associated with probabilities, which are measures of the likelihood that a particular outcome will occur.
This is a problem of counting the number of ways to choose 3 people out of 6 for 3 distinct positions. We can solve this using the combination formula:
ⁿCr = C(n, r) = n! / (r! * (n-r)!)
C(6, 3) = 6! / (3! * (6-3)!) = 20
Therefore, there are 20 different election outcomes possible for the president, secretary, and treasurer positions among a group of 6 people.
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Solve the equation 3* = 8 for x.
Answer:
x = log(3) (8)
or log 8 base 3
Step-by-step explanation:
some number^x = another number
some number = base (the lower case number)
another number = the big number next to it.
put log infront in these situations.
Revise the suggested questionnaire so that it is more suitable. Include 5 reasons for taking a GAP YEAR. Submit a copy of a new revised questionnaire
The revised questionnaire that is more suitable that includes reasons for taking a GAP year is given below:
The QuestionnaireThe new questionnaire includes four questions aimed at gaining insight into the participant's motivations, goals, and timeframe for taking a gap year:
Have you considered taking a gap year before starting your next academic or professional endeavor?
What are your top 5 reasons for considering a gap year? (Please list in order of importance)
What are your goals for your gap year? (e.g., travel, volunteer work, internships, personal development, etc.)
How long do you plan to take for your gap year?
Reasons for taking a gap year may vary from person to person, but here are five common motivations for doing so:
To gain life experience and personal growth
To travel and explore new cultures
To gain work experience or internships in a desired field
To take a break from academic or professional responsibilities
To pursue passions or hobbies that may not be feasible during a regular academic or work schedule.
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Revise the suggested questionnaire so that it is more suitable. Include 5 reasons for taking a GAP YEAR. Submit a copy of a new revised questionnaire
Have you considered taking a gap year before starting your next academic or professional endeavor?
What are your reasons for considering a gap year?
What are your goals for your gap year?
How long do you plan to take for your gap year?
i need help pleaseee
The dataset is evenly distributed, so the appropriate measure of variability is the range
The dataset is evenly has no outliers, so the appropriate measure of center is the mean
How to determine the appropriate measuresMeasure of variability
When the data set is evenly distributed, a measure of variability appropriate for stem and leaf plot would be the range
The range is simply the difference between the largest and smallest value in the data set.
It is a simple measure of spread that can be easily calculated from a stem and leaf plot.
Measure of center
When there are no outliers in a dataset, the appropriate measure of center to use in a stem and leaf plot is the mean
The mean, also known as the average, is calculated by summing all the values in the dataset and then dividing by the total number of values.
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penny would love to open a coffee shop at her local shopping centre, so she decides to hand out a questionnaire at the shopping center's entrance in order to do market research. draw up a questionnaire that penny could use to gather the information she requires
Penny plans to distribute a questionnaire at the entrance to the coffee shopping center in order to do market research because she would love to build a coffee shop there which are explained.
Explain about the term questionnaire?Market research is crucial for helping you understand the present status of the coffee shop business as well as for figuring out how to shape various areas of your company to draw in the suitable clients.
Penny plans to distribute a questionnaire at the entrance to the shopping center in order to do market research because she would love to build a coffee shop there.
Penny may utilize a questionnaire to collect the data she needs, which would include the following:
What are the current consumption patterns of customers at coffee shops? Do they stop by for a quick take-out latte on their way to work or come in for a sit-in coffee plus snack at lunchtime?What qualities define a normal coffee shop patron? Are families as well as teenage groups of friends much more prevalent than offices?What is the typical client budget?What are the best-selling products? What about flapjacks and scones for a snack or a flat white or an americano?know more about the questionnaire
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find the domain of the function f(x)=7x+5/3x-1
The domain of the function f(x)=7x+5/3x-1 is all real numbers except x = 1/3. This means that the function will produce a real number for any value of x except for x = 1/3.
What is a function?Function in mathematics is a relation which assigns each element of a set (called the domain) to exactly one element of another set (called the codomain). It can also be thought of as a type of mapping from one set to another. Functions are used to model real-world problems and to simplify the expression of a certain problem. They are widely used in algebra, trigonometry and other areas of mathematics.
The domain of a function is the set of all possible inputs for the function. In other to determine the domain of a function, we must first identify the independent variable (x) and then determine which values of x can be used in the function.
In the given function, f(x)=7x+5/3x-1, the independent variable is x. To find the domain of this function, we must identify the values of x that will produce results that are real numbers. To do this, we must set the denominator (3x-1) equal to zero and solve for x.
We can solve this equation by factoring and setting each factor equal to zero:
3x - 1 = 0
3x = 1
x = 1/3
Therefore, the domain of the function f(x)=7x+5/3x-1 is all real numbers except x = 1/3. This means that the function will produce a real number for any value of x except for x = 1/3.
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Find a formula for the linear function depicted in the following graph.
The equation of the line passing through the points (0, 7) and (2, -5) is y = -6x + 7
What is an equation?An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.
The standard form of a linear equation is:
y = mx + b
where m is the slope(rate of change) and b is the y intercept
As shown in the graph, the line passes through the points (0, 7) and (2, -5). Hence:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-7=\frac{-5-7}{2-0} (x-0)\\\\y=-6x+7[/tex]
The equation of the line is y = -6x + 7
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PLEASE HELP ASAP!! i really really need it
Answer:
The number of hamburgers is 136.
Step-by-step explanation:
What we know:
We got cheeseburgers and hamburgers
The total: 408
The number of cheese burgers was 2 times the number of hamburgers
This is pretty much all the info we need to know.
Lets define our variables:
x = hamburgers
y = cheeseburgers
Now, we need our two equations to make a system.
[tex]x+y=408[/tex]
[tex]y=2x[/tex]
To find hamburgers, x, we plug the value of y into our first equation.
[tex]x+2x=408[/tex]
Add like terms
[tex]3x=408[/tex]
Divide by 3
[tex]x=136[/tex]
The number of hamburgers is 136.
Just to check our work, lets find the cheeseburgers.
[tex]y=2(136)[/tex]
[tex]y=272[/tex]
[tex]272+136=408[/tex]
Use the graph of the rational function to complete the following statement. As x → −∞, f(x) →
For the graph of the rational function the as x → −∞, f(x) → −∞.
What are rational functions?A rational function is the ratio of two polynomial functions with a non-zero denominator polynomial. R(x) = P(x)/Q(x), where P(x) and Q(x) are polynomial functions, is the standard representation of this relationship. We studied the rational number idea in previous grades. When the denominator is not equal to zero, it is the quotient or ratio of two integers. Rational, then, is a name that comes from the term ratio.
From the given graph we observe that as the value of x tends to - ∞, the value of f(x), that is, the value of y constantly goes upwards and leftwards.
Thus,
As x → −∞, f(x) → −∞.
Hence, for the graph of the rational function the as x → −∞, f(x) → −∞.
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