NEED HELP WILL GIVE BRAINLIEST AND 5 STARS I HAVE 20 MINUTES PLEASE HELP!
For this rational function, using proper limit notation, explain what happens to m(x) near x=-3
Answers
Answer: as x approaches -3, the rational function m(x) approaches infinity from one side and negative infinity from the other side, and it has a vertical asymptote at x = -3.
Step-by-step explanation: The mathematical expression denoted by m(x) is represented as 4(x-5)(x+8)/(x^2-2x-15) in this context.
When x approaches -3, the limit of the function m(x) is evaluated from both the left and right sides.
In accordance with established convention, it is feasible to express the aforementioned concept as follows:
As x tends towards negative three from the left, the value of m(x) can be expressed as the limit of the function [4(x-5)(x+8)/(x^2-2x-15)] evaluated at x approaching negative three from the left, symbolically represented as lim x → -3⁻.
In the context of contemporary society, the issues of environmental sustainability and conservation are of utmost importance. These concerns have arisen from the impact of human activities on the planet and the need to prevent further harm. Various strategies have been proposed and implemented to address this challenge, and stakeholders from different sectors have been involved in the efforts. Despite this, progress has been slow, and much more needs to be done to achieve the overarching goal of achieving a sustainable future for the earth and its inhabitants. Additionally, the challenges we face in this area are highly complex and multifaceted and require interdisciplinary approaches that can engage different perspectives and knowledge domains. The academic community, as a key player in this domain, has a crucial role to play in advancing knowledge, developing innovative solutions, and disseminating best practices to relevant stakeholders for maximum impact.
The limit as x approaches negative three from the right-hand side of the function m(x) is equivalent to the limit as x approaches negative three from the right-hand side of the function [4(x-5)(x+8)/(x^2-2x-15)].
The determination of the behavior of the function m(x) as it approaches -3 from the left-hand side (values of x less than -3) is denoted by the left-hand limit, lim x → -3⁻ m(x), while the right-hand limit, lim x → -3⁺ m(x), signifies the behavior of m(x) as it approaches -3 from the right-hand side (values of x greater than -3).
In order to assess these limits, the substitution of x = -3 in the m(x) expression may be pursued, however, such an endeavor would culminate in division by zero, a mathematically undefined operation.
The denominator of the expression for m(x) can be factored as stated below.
The given expression x^2 - 2x - 15 can be factored into the product of two binomials (x - 5) and (x + 3).
Consequently, it is possible to rephrase the equation for m(x) in the following manner:
The function m(x) can be expressed as 4(x - 5)(x + 8) / (x - 5)(x + 3) in the academic way of writing.
The expression may be simplified by factoring out the common factor of (x - 5) in both the numerator and denominator, resulting in:
The function m(x) can be expressed as 4(x + 8) / (x + 3), where x is the independent variable.
The limits as x approaches -3 from both the left and right sides can now be assessed.
In the context of mathematical analysis, it can be observed that the left-hand limit of the function m(x) as x approaches -3, denoted as lim x → -3⁻ m(x), can be established as the limit of the function [4(x + 8) / (x + 3)] as x approaches -3 from the left-hand side, denoted as lim x → -3⁻ [4(x + 8) / (x + 3)]. Upon applying mathematical calculations, it can be determined that this limit evaluates to -16/0, which in the realm of mathematics is regarded as undefined.
The mathematical statement "lim x → -3⁺ m(x) = lim x → -3⁺ [4(x + 8) / (x + 3)] = 20/6 = 10/3" may be expressed in a more formal and scholarly manner. Specifically, one may depict the aforementioned equation using mathematical symbols and terminology deemed appropriate within scholarly discourse. As such, one may denote that the limit, as x approaches negative three from the positive direction, of the function m(x) is equivalent to the limit, as x approaches negative three from the positive direction, of the quotient formed by four multiplied by the sum of x and eight, divided by the sum of x and three. Upon evaluating these limits, one arrives at the quotient 20/6, which reduces to the rational number 10/3.
Due to the inequality between the left-hand and right-hand limits, it is deduced that the limit of the function m(x) is not present at x = -3. Consequently, it can be stated that the function m(x) possesses a vertical asymptote at x = -3.
Related Questions
Step by step how to get the answer
Answers
Answer:
(xyz + 1)
Step-by-step explanation:
We can use the identity:
[tex]a^2 - b^2 = (a + b)(a - b)[/tex]
to solve for the blank in this equation.
On the left side, we can identify a difference of two squares (a² - b²).
the first square (a) is xyzthe second square (b) is 1We can see that there is already an (a - b) term on the right, so in the blank, we just have to construct an (a + b) term:
(xyz + 1)
This satisfies the equation:
(xyz)² - 1 = (xyz + 1) · (xyz - 1)
The sugar sweet company will choose from two companies to transport as sugar to market. The first company charges 4500 to rent trucks plus an additional fee of 175.25 for each third of sugar per second copy charges 3995 to rent trucks plus an additional fee of 200.50for each total of sugar.
Answers
The two companies charge the same when the amount of sugar is 20 thirds per second and the cost when the two companies charge the same is $8,125.
What is amount?
Amount is a term used to describe the quantity or size of something. It can refer to a specific quantity of a substance, such as an amount of money or an amount of a particular material, or it can refer to a more abstract concept, such as an amount of time or effort.
To find the amount of sugar for which the two companies charge the same, we need to set the two costs equal to each other and solve for the amount of sugar.
Let x be the amount of sugar in third per second. Then, the cost C1 charged by the first company is:
C1 = 4500 + 175.25x
And the cost C2 charged by the second company is:
C2 = 3995 + 200.50x
To find the amount of sugar for which the two companies charge the same, we set C1 equal to C2:
4500 + 175.25x = 3995 + 200.50x
Solving for x, we get:
25.25x = 505
x = 20
Therefore, the two companies charge the same when the amount of sugar is 20 thirds per second.
To find the cost when the two companies charge the same, we can substitute x = 20 into either of the cost equations. Let's use C1:
C1 = 4500 + 175.25x
C1 = 4500 + 175.25(20)
C1 = 8125
Therefore, the cost when the two companies charge the same is $8,125.
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Twenty horses ran in the 2016 Kentucky Derby. The Exacta bet involves picking the first two finishers in order. Determine the number of outcomes for two horses finishing in the first two spots and the probability of winning the Exacta bet if you pick the horses at random.
Answers
The probability of winning the Exacta bet if you pick the horses at random is given by P ( A ) = 0.26 %
Given data ,
The Kentucky Derby had 20 horses running in the race in 2016. The number of ways to pick the first horse is 20, as any of the 20 horses could finish in the first spot. Once the first horse is picked, there are 19 remaining horses that could finish in the second spot.
Therefore, the total number of outcomes for two horses finishing in the first two spots (i.e., the Exacta bet) is 20 multiplied by 19, which is 380.
Since there is only one winning Exacta combination out of the 380 possible outcomes, the probability of winning the Exacta bet by randomly picking two horses is 1/380, which is approximately 0.0026, or 0.26%.
Hence , the probability is 0.26 %
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The bar graph shows the number of Asturian households, in thousands, living in poverty from 1999 to 2004. The table holds a quadratic function for the data, where y is the number of households, in thousand living in poverty × years after 1999. 10. 10 1999 2000 2001 2002 2003 2004 QuadReg y = ax2 + bx + c a = 0.2299729818 b = - 0.4599459636 c = 7.5426446323 a. Use the table to express the model in function notation, with numbers rounded to two decimal places #(x) = 0.23x2 + - 0.46x + 7.54 b. According to the function in part (a), in which year was the number of households living in poverty at a minimum? 2000 (Round to the nearest year as needed.) c. Use the model to find the number of households, in thousands, for that year. 7400 (Round to one decimal place as needed.)
Answers
Step-by-step explanation:
a. #(x) = 0.23x^2 - 0.46x + 7.54 (numbers rounded to two decimal places)
b. To find the year at which the number of households living in poverty is at a minimum, we need to find the vertex of the quadratic function. The x-value of the vertex is given by -b/2a. Plugging in the values for a and b from the function in part (a), we get:
x = -(-0.46)/(2*0.23) = 1
So the minimum occurs in the year 1999 + 1 = 2000 (rounded to the nearest year).
c. To find the number of households living in poverty in 2000, we need to evaluate the function at x = 1 (since 2000 is 1 year after 1999). Plugging in x = 1 into the function from part (a), we get:
#(1) = 0.23(1)^2 - 0.46(1) + 7.54 = 7.40
So there were approximately 7400 households living in poverty in Asturias in 2000 (rounded to one decimal place).
Express the ratio, 5 1⁄2 : 2 3⁄4 in simplest form
Answers
The ratio 5 1⁄2 : 2 3⁄4 can be expressed in simplest form as 11 : 7.
What is ratio?Ratio is a mathematical comparison between two numbers, usually expressed as a fraction. It is used to compare quantities or measurements, and is a useful tool for understanding relationships between different values. Ratios can be used to solve problems and make decisions, as well as to measure and compare proportions in different situations.
This can be derived by multiplying the numerators and denominators of the two ratios by the same number, in this case 2. The resulting fractions are 11⁄2 and 5⁄2, which can then be simplified to 11 : 7.
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Find the volume of the composite solid. Round your answer to the nearest hundredth.
T
5 cm
8 cm
t
5 cm
The volume is about
cubic centimeters.
Answers
The volume of the composite solid, rounded to the nearest hundredth, is: 213.33 cubic centimeters.
How to Find the Volume of the Composite Solid?The solid given is composed of two square pyramids. Therefore, to find the volume of the composite solid, apply the formula below:
Volume of composite solid = 2(1/3 * length * width * height)
Given the following dimensions:
Length = 8 cm
Width = 8 cm
Height = 5 cm
Plug in the values:
Volume of composite solid = 2(1/3 * 8 * 8 * 5)
≈ 213.33 cubic centimeters (to the nearest hundredth).
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PLEASE HELP!!!! PLEASE HELP...I NEED THE AREA!
Answers
The area of the composite figure that is composed of triangles and a rectangle is: 154 mm².
How to Find the Area of a Composite Figure?The composite figure given comprises two different triangles and one rectangle. Therefore, to find the area of the composite figure, we need to calculate the area of each shape in the figure.
Area of rectangle = length * width = (7 + 7) * 4
= 14 * 4
Area of rectangle = 56 mm²
Area of the larger triangle = 1/2 * base * height
= 1/2 * 14 * 11
= 77 mm²
Area of the smaller triangle = 1/2 * 14 * 3
= 21 mm²
Therefore, area of the composite figure = 56 + 77 + 21
= 154 mm²
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Find the volume of each cylinder. Use 3.14 for Pi
Round your answer to the nearest tenth.
7 mm
Your answer
8 mm
Answers
Answer: 5 mm 6 mm
Step-by-step explanation:
LAB1 Exp 3
Prescription number
Prescription #1
Prescription #2
Prescription #3
mLs needed of soda
mLs needed of solution
Answers
1. Difference between ointment and cream -
Generally, Creams tend to have lighter texture and consistency. They are mostly formulated with a blend of two components, that is water and oil.
What is Ointment?
Ointments are essentially greasy and have thicker consistency. They contain more oil content as compared to creams. Creams are absorbed faster via the skin than ointments. While ointments are absorbed slower through the skin than creams.
2. The label may instruct you to shake a liquid medicine before using so that the active ingredients are evenly distributed throughout it. The important thing to remember is that you have to shake a suspension before giving each dose so that the medicine particles are evenly distributed throughout the liquid.
3. Emulsions are stabilized by adding an emulsifier or emulsifying agents. These agents have both a hydrophilic and a lipophilic part in their chemical structure. In addition to this protective barrier, emulsifiers stabilize the emulsion by reducing the interfacial tension of the system.
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Which expression in the result of factoring the expression below by taking out its greatest common factor?
8x^2-24=?
Answers
Quadratic Expression: is an expression with the variable with the highest exponent being 2
General form: ax^2 + bx + c
Greatest common factor (GCF): the largest whole number that divides evenly into a set of numbers
When factoring out the GCF of this expression we must look at the "a" term and "c" term
the greatest common factor of the terms a and c is 8we can that factor out the 8 from the original expression, putting it outside the brackets and dividing the original terms by the GCF8/8 =1 and -24/8= -3[tex]8(x^2-3)[/tex] which is the expression factored.
The trapezoid is composed of a rectangle and two triangles. What is the area of the rectangle? What is the total area of the triangles? What is the area of the trapezoid?
Responses 'ILL GIVE BRAINLY'
Answers
Answer:
B) 108 cm²; 27 cm²; 135 cm²--------------------
Area of the rectangle:
A(rectangle) = lw = 12*9 = 108 cm²Area of the two triangles:
A(triangles) = 2*(bh/2) = bh = 3*9 = 27 cm²Area of trapezoid is the sum of the areas we found above:
A(trapezoid) = 108 + 27 = 135 cm²The matching answer choice is B.
What is the area of ΔABC given m∠B = 83°, a = 25 feet, and c = 40 feet?
561.46 feet2
496.27 feet2
186.23 feet2
128.51 feet2
Answers
The area of a triangle ABC is 496.25 square feet. Therefore, option B is the correct answer.
Given that, in the triangle ABC, m∠B = 83°, a = 25 feet, and c = 40 feet.
The area of a triangle can be expressed using the lengths of two sides and the sine of the included angle. Area of a triangle = ½ ab sin C.
Here, area of a triangle = 1/2 ×25×40 sin83°
= 25×20×0.9925
= 496.25 square feet
Therefore, option B is the correct answer.
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what is the selling price of a shoe when the cost price is K80 and there is a profit of 65% on it
Answers
Assuming that the cost price in the question is 80K with a 65% profit percentage on cost price, the selling price of the shoe is 132K.
Given, Cost Price (CP) of the shoe = 80K or 80,000
Profit % = 65%
From the formula, we know,
Profit % = (Profit / Cost Price) * 100
Inserting given values in the formula, we get,
==> 65 = (Profit / 80,000) *100
or, 65 = Profit / 800
Therefore, Profit = 65 * 800
= 52,000
In the case of Profit, Selling Price = Cost Price + Profit
Hence, the Selling Price of the shoe is = 80,000 + 52,000
= 132,000 or 132K (Answer)
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which of the following shows an equivalent expression to [(5 * 3) * 12] if only the associative property was used to trasnform the expression
Answers
The equivalent expression using associative property is; 5×(3×12).
Given expression is; [(5 × 3) × 12]
The associative property is a property of addition and multiplication that allows the grouping of numbers or variables without changing the result.
For addition: (a + b)+c = a+(b + c)
For multiplication: (a × b) ×c = a × (b × c)
In simpler terms, it means that you can add or multiply a set of numbers in any order, and still get the same result.
Therefore, the equivalent expression to [(5 × 3) × 12] using only the associative property would have the same operands but a different grouping. One possibility would be;
[(5 × 3) × 12] = [5 × (3 × 12]
Both expressions simplify to 180.
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Casey is going to deposit $500 in an account that earns 6% interest for 10 years. How much more interest will he earn if the account earns annual compound interest rather than annual simple interest?
Answers
Casey will earn $595.42 more interest with annual compound interest compared to annual simple interest over 10 years.
What is simple and compound interest?Simple interest is paid just on the initial amount deposited or borrowed and is computed as a percentage of the principal amount. In other words, interest earned or charged is calculated purely on the principal amount, without taking into consideration interest from prior periods. On the other hand, compound interest adds the principal amount to the interest earned or charged in prior periods to determine the interest earned or charged in the current period. In comparison to simple interest, compound interest results in higher overall interest payments or earnings since the interest generated or charged climbs exponentially over time. Compound interest is more prevalent and beneficial for long-term investments in general.
The compound interest is given as:
[tex]A = P(1 + r/n)^{(nt)}[/tex]
Substituting the values of P = 500, n = 1, r = 0.06 and t = 10 we have:
[tex]A = P(1 + r/n)^{(nt)} = 500 * (1 + 0.06/1)^{(1*10)} = $895.42[/tex]
Now, simple interest is given as:
SI = Prt = 500 * 0.06 * 10 = $300
Now, the difference is:
895.42 - 300 = $595.42
Hence, Casey will earn $595.42 more interest with annual compound interest compared to annual simple interest over 10 years.
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Part A: Create your own experiment with 5 or more possible outcomes.
Part B: Create the sample space for your experiment in Part A. Explain how you determined the sample space.
HELP ME IM SO CUNFUSED!!!
Answers
Answer:
Part A: Experiment: Rolling a fair six-sided die.
Part B: Sample space: {1, 2, 3, 4, 5, 6}. This sample space was determined by listing all possible outcomes of rolling a fair six-sided die.
I hope that's what you are looking for.
In Data Collection, accuracy may be determined O a. O b. O c. None of the responses are correct By counting the number of values to each other By how close repeated measurements are, to the true value of the attribute being measured O d. By how close repeated measurements of an attribute are, to each other Oe. By how much deviation there is between the measured values and the true value
Answers
It is essential to determine accuracy to ensure that the collected data is reliable and can be used to make informed decisions.
How to solve the question?
Data collection is an essential aspect of research and analysis, as it involves gathering information from various sources to make informed decisions. Inaccurate data can lead to incorrect conclusions and flawed decision-making, which can have significant consequences. Therefore, it is crucial to determine the accuracy of the collected data.
Accuracy can be determined in several ways. One way is by how close repeated measurements of an attribute are to each other. This method is known as precision. If repeated measurements are consistent with one another, it indicates that the data is precise. However, precision does not necessarily imply accuracy, as the measured values could be consistently wrong.
Another way to determine accuracy is by how close repeated measurements are to the true value of the attribute being measured. This method is known as validity. Validity ensures that the collected data accurately reflects the attribute being measured. This method is often used in experiments to test the effectiveness of a treatment or intervention. The results of an experiment are valid if they accurately reflect the effects of the treatment or intervention being tested.
Accuracy can also be determined by how much deviation there is between the measured values and the true value. This method is known as error. An error is the difference between the measured value and the true value. The smaller the error, the more accurate the data.
In conclusion, accuracy in data collection is determined by how close the measured values are to the true value, how close repeated measurements are to each other, and how much deviation there is between the measured values and the true value. It is essential to determine accuracy to ensure that the collected data is reliable and can be used to make informed decisions.
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Use PMT=
to determine the regular payment amount, rounded to the nearest dollar. In terms of paying less in interest, which is more economical for a $210,000
HT
mortgage: a 30-year foxed-rate at 10% or a 20-year fixed-rate at 9.5%? How much is saved in interest?
Select the correct choice below and fill in the answer box within your choice.
(Do not round until the final answer. Then round to the nearest thousand dollars.)
OA. The 30-year 10% loan is more economical. The buyer will save approximately $ in interest
OB. The 20-year 9.5% loan is more economical. The buyer will save approximately Sin interest.
Answers
For the 30-year fixed-rate mortgage at 10%:
PMT(10%/12, 30*12, $210,000) = $1,847.23
For the 20-year fixed-rate mortgage at 9.5%:
PMT(9.5%/12, 20*12, $210,000) = $1,836.49
Rounding to the nearest dollar, the regular payment amount for the 30-year mortgage is $1,847, and for the 20-year mortgage is $1,836.
To determine which mortgage is more economical in terms of paying less in interest, we need to calculate the total interest paid over the life of each mortgage.
For the 30-year mortgage, the total interest paid is:
$1,847.23 x 30 x 12 - $210,000 = $576,202.80
For the 20-year mortgage, the total interest paid is:
$1,836.49 x 20 x 12 - $210,000 = $342,477.60
The difference in interest paid is:
$576,202.80 - $342,477.60 = $233,725.20
Rounding to the nearest thousand dollars, the buyer will save approximately $234,000 in interest by choosing the 20-year fixed-rate mortgage at 9.5%. Therefore, the correct choice is:
OB. The 20-year 9.5% loan is more economical. The buyer will save approximately $234,000 in interest
Which of the following is a point-slope equation of a line that passes through
the points (5, 2) and (-1,-6)?
A. y-2-(x-5)
B. y-2--(x-5)
C. y-2-(x-5)
D. y-2--(x-5)
Answers
The point-slope equation of a line that passes through the points (5, 2) and (-1,-6) include the following: B. y - 2 = 4/3(x - 5).
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-6 - 2)/(-1 - 5)
Slope (m) = -8/-6
Slope (m) = 4/3.
At data point (5, 2) and a slope of 4/3, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 2 = 4/3(x - 5)
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
What is the equation of a line that goes through the point (0,−4) and has a slope of 2 ?
Hint: Use the formula sheet to determine the formula(s) needed to solve the problem.
Answers
The equation of the line that goes through the point (0, -4) and has a slope of 2 is y = 2x - 4.
What is equation of line?The relationship between the coordinates of each point (x, y) on a line is represented by the equation of a line, which is linear in the variables x and y. All of the points on the line satisfy the equation, in other words.
We can use the point-slope form of the equation of a line to find the equation of the line that goes through the point (0, -4) and has a slope of 2.
The point-slope form of the equation of a line is:
y - y₁ = m(x - x₁)
where (x₁, y₁) is a point on the line and m is the slope of the line.
Plugging in the values, we get:
y - (-4) = 2(x - 0)
Simplifying, we get:
y + 4 = 2x
Subtracting 4 from both sides, we get:
y = 2x - 4
Therefore, the equation of the line that goes through the point (0, -4) and has a slope of 2 is y = 2x - 4.
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please provide the answer along with proof.
Answers
Note that where the above conditions are given, the probability of A ∩ B is 1/20 and the probability of the union of A and B P( A∪B) = 2/5. See the explanation below.
How were the above probabilities derived?We are given that A and B are events that are independent, P(A∩B), we can rightly state that:
P(A∩B ) = P(A) x P (B)
(1/5) x (1/4)
= 1/20
For P(A∪B)
⇒ P( A ∪B) = P (A ) + P(B) - P(A ∩B)
We can substitute the probabilities to derive:
P(A∪B) = (1/5) + (1/4) - (120)
We can write the above as:
⇒ 4/20 + 5/20 - 1/20
= 8/20
Simplifying , we get:
P(A∪B) = 2/5
Hence it is correct to state that the P(A ∩ B) = 1/20, while P(A∪B) = 2/5.
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NO LINKS!! URGENT HELP PLEASE!!!
1. Find an exponential function of the form f(x) = ba^-1 + c that has the given horizontal asymptote and y-intercept and passes through P
y = 33; y-intercept 408; P(2, 93)
Answers
Answer:
[tex]\bold{f(x) = 375(2.5)^{-x}+ 33}[/tex]
Step-by-step explanation:
An exponential function of form f(x) = ba^(-x) + c has a horizontal asymptote of y = c as x approaches infinity, and a y-intercept of (0, b + c). We can use the given information to set up a system of equations and solve for the unknowns.
The horizontal asymptote is given as y = 33, so we have:
c = 33
The y-intercept is given as (0, 408), so we have:
b + c = 408
Substituting c = 33, we get:
b + 33 = 408
b = 375
So the function we're looking for is of the form:
[tex]\bold{f(x) = 375a^{-x}+ 33}[/tex]
To find a, we use the fact that the function passes through P(2, 93):
93 = 375a^(-2) + 33
60 = 375a^(-2)
a^2 = 375/60
a^2 = 6.25
a = [tex]\sqrt{6.25 } =2.5[/tex]
Therefore, the exponential function that satisfies the given conditions is:
[tex]\bold{f(x) = 375(2.5)^{-x}+ 33}[/tex]
Select the correct answer. The graph of function f is shown. An exponential function passes through (minus 4, 9), (0, 1), (1, 0), and (5, minus 2). Function g is represented by the table. x -1 0 1 2 3 4 g(x) 24 6 0 -2 Which statement correctly compares the two functions? A. They have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞. B. They have different end behavior as x approaches -∞ and different end behavior as x approaches ∞. C. They have the same end behavior as x approaches -∞ and the same end behavior as x approaches ∞. D. They have different end behavior as x approaches -∞ but the same end behavior as x approaches ∞.
Answers
They have different end behavior as x approaches -∞ but the same end behavior as x approaches ∞.
The correct option is D.
From the given points, we can write an exponential function in the form of f(x) = abˣ, where a and b are constants.
Using the point (-4, 9): 9 = ab⁻⁴
Using the point (0, 1): 1 = ab⁰ = a
Using the point (1, 0): 0 = ab¹
Using the point (5, -2): -2 = ab⁵
Solving these equations, we get a = 1 and b = 1/3. So, the function f(x) = 1(1/3)ˣ = (1/3)ˣ.
For function g(x), we can see that as x approaches -∞, g(x) approaches ∞ , and as x approaches ∞, g(x) approaches 0.
This is because as x gets more negative, 24 times 2⁻ˣ becomes a larger positive number, and as x gets larger, 2ˣ becomes a larger positive number causing the product to approach zero.
Therefore, the two functions have different end behavior as x approaches -∞ but the same end behavior as x approaches ∞, making option D the correct answer.
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In a competition, the contestants are being judged on creativity, worth 50%, execution, worth 30%, and style, worth 20%
Alisha received the following scores.
Creativity: 18, 16, 15, 16
Execution: 20, 19, 20, 18
Style: 12, 15, 14, 13
What is Alisha's final score?
Enter your answer, as a decimal, in the box
Answers
First, let's calculate the average score for each category:
Average creativity score = (18 + 16 + 15 + 16)/4 = 16.25
Average execution score = (20 + 19 + 20 + 18)/4 = 19.25
Average style score = (12 + 15 + 14 + 13)/4 = 13.5
Next, we can calculate the weighted average of her scores using the given weights:
Weighted average = (0.5 * average creativity score) + (0.3 * average execution score) + (0.2 * average style score)
= (0.5 * 16.25) + (0.3 * 19.25) + (0.2 * 13.5)
= 8.125 + 5.775 + 2.7
= 16.6
Therefore, Alisha's final score is 16.6.
three men and three women are waiting to be interviewed for a job if they are all selected in random order find the probability that all men will be interview first
Answers
The probability that all men will be interview first is 0.05.
What does probability means?Probability helps with finding out the likelihood of the occurrence of an event and measures chance of an event happening.
Given data:
Men = 3
Women = 3
Total people:
= 3 + 3
= 6
Probabilities of men:
P(first man) = 3/6 = 1/2
P(second man) = 2/5
P(third man) = 1/4
Required probability is:
P(first 3 men) = 1/2 * 2/5 * 1/4
P(first 3 men) = 0.05
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PLEASE HELP!
The profit P (in dollars) made by a cinema from selling x bags of popcorn can be molded by P=2.36x-(x^2/25000)-3500, 0<=x<=50,000.
a) On what intervals is P increasing and decreasing?
b) How many bags of popcorn must the cinema sell in order to maximize profit and what is the maximum profit per bag?
Answers
The maximum profit is given as $31,310
How to solvea. In order to determine the intervals in which profitability P increases and decreases, we need to analyze the first derivative of its respective function, P(x).
Given the profit equation: P(x) = 2.36x - (x^2 / 25000) - 3500, the process begins by articulating its derivative, P'(x):
P'(x) = d(2.36x) - d(x^2 / 25000) - d(3500)
P'(x) = 2.36 - (2x / 25000)
P'(x) = 2.36 - x / 12500
Seeing that P'(x) > 0 implies a rising P while P'(x) < 0 portrays a decreasing P, those values must be determined. Subsequently, the critical points may be found by setting P'(x) = 0:
2.36 - x / 12500 = 0
x / 12500 = 2.36
x = 2.36 * 12500
x = 29500
To adequately evaluate the intervals (0, 29500) and (29500, 50000), we must gauge whether P'(x) is positive or negative:
For x greater than zero & less than 29500:
P'(x) = 2.36 - x / 12500 > 0
For x higher than 29500 but falling beneath 50000:
P'(x) = 2.36 - x / 12500 < 0
Hence, P is augmented on the interval from 0 until 29500, whereas it diminishes from 29500 to 50000.
b. Differentiate again the profit function we get
P'(x)= -1/12,500 <0
Therefore the profit will be maximum.
Hence 29500 bags of popcorn must cinema sell in order to maximize profit.
The maximum profit = $31,310
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Help. Came up with 3 different answers.
Answers
Carlo works at a factory thaat makes potato chips. He works 6 hours a day loading boxes onto trucks. The factory can produce one box filled with bags of potato chips every 4 minutes. How many boxes filled with chips does the factory make in 20 minutes
Answers
Answer:
mark me brilliant
Step-by-step explanation:
The factory produces one box of potato chips every 4 minutes, which means in one minute, it produces 1/4 boxes.
So, in 20 minutes, the factory would produce:
(1/4) x 20 = 5 boxes
Therefore, the factory would make 5 boxes filled with potato chips in 20 minutes.
The principal P is borrowed at a simple interest rate r for a period of time t. Find the simple interest owed for the use of
the money. Assume 365 days in a year.
P = $2000, r = 6%, t = 1 year
Answers
120 is the simple interest owed for the use of the money.
What does the phrase "simple interest" mean?
From the time when money was first lent until the time that it should be paid back with interest, this time frame is considered the borrowing period. The term or deadline for this is also an option. A percentage of the principle is how interest is most commonly computed.
P = $2000, r = 6%, t = 1 year
simple interest = P * r * t/100
= 2000 * 6 * 1/100
= 120
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The simple interest owed for the use of the money is $120.
What is simple interest?Simple interest is the interest charge on a loan calculated using only the original principal amount and a fixed interest rate. It does not use compounding, which causes borrowers to pay interest on principal and interest that accumulates over numerous payment periods.
The simple interest formula is as follows:
SI = P * r * t
where I denotes simple interest, P denotes principal, r denotes interest rate (in decimal), and t denotes time period (in years).
When we substitute the provided values, we get:
SI = $2000 * 0.06 * 1
SI = $120
As a result, the simple interest for the usage of the money is $120.
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