We can infer that the function y = 2 + log2(x - 1) has the following final behaviour:
Y gets closer to infinity as x gets closer to positive infinity.Y moves closer to negative infinity as x moves in the proper direction towards 1.what is a function?A function is a relationship between a number of inputs and outputs. Simply described, a function is an association between inputs in which each input is coupled to exactly one output. There is a range, codomain, and domain for every function. A function is typically referred to as f(x), where x is the input. Y = f is a common way to represent a function (x).
A function in mathematics is a certain configuration of the inputs (also known as the domain) and their outputs (also known as the codomain), where each input has precisely one output and the output can be connected to its input.
from the question;
We may look at what happens to the function as x gets closer to positive and negative infinity to figure out the final behaviour of the function
y = 2 + log2(x - 1).
The formulas (x - 1) and log2(x - 1) also approach infinity as x gets closer to positive infinity. As a result, y increases as x moves closer to positive infinity. The following can be written:
lim x→∞ 2 + log2(x - 1) = ∞
Expression (x - 1) moves closer to zero and log2(x - 1) moves closer to negative infinity as x moves towards 1 from the right. So, as x moves closer to 1 from the right, y moves closer to negative infinity. The following can be written:
lim x→1+ 2 + log2(x - 1) = -∞
This leads us to the following conclusion about the final behaviour of the function y = 2 + log2(x - 1):
Y gets closer to infinity as x gets closer to positive infinity.Y moves closer to negative infinity as x moves in the proper direction towards 1.to know more about the function visit:
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A company that uses job order costing reports the following information. Overhead is applied at the rate of 60% of direct materials. The company has no beginning Work in Process or Finished Goods inventories. Jobs 1 and 3 are not finished by the end of March, and Job 2 is finished but not sold by the end of March. Determine the total dollar amount of Finished Goods Inventory at the end of March.
Answer: To determine the total dollar amount of Finished Goods Inventory at the end of March, we need to calculate the total cost of the jobs that have been completed during March and have been transferred to the Finished Goods Inventory.
From the information given, we know that the company has no beginning Work in Process or Finished Goods inventories, so all the costs incurred during March are related to the jobs started during the month.
Let's start by calculating the total cost of Job 2, which is finished but not sold by the end of March. We will then use this cost to calculate the total cost of the jobs that have been completed during March and transferred to the Finished Goods Inventory.
Job 2:
Direct materials: Rs. 10,000
Direct labor: Rs. 8,000
Overhead applied: 60% x Rs. 10,000 = Rs. 6,000
Total cost of Job 2: Rs. 24,000
Now, let's calculate the total cost of the jobs that have been completed during March:
Job 1:
Direct materials: Rs. 6,000
Direct labor: Rs. 4,000
Overhead applied: 60% x Rs. 6,000 = Rs. 3,600
Total cost of Job 1: Rs. 13,600
Job 3:
Direct materials: Rs. 8,000
Direct labor: Rs. 5,000
Overhead applied: 60% x Rs. 8,000 = Rs. 4,800
Total cost of Job 3: Rs. 17,800
Total cost of jobs completed during March: Rs. 13,600 + Rs. 17,800 = Rs. 31,400
Since the company has no beginning Finished Goods Inventory, the total cost of the jobs completed during March and transferred to the Finished Goods Inventory is equal to the total cost of the Finished Goods Inventory at the end of March.
Therefore, the total dollar amount of Finished Goods Inventory at the end of March is Rs. 31,400.
Step-by-step explanation:
Name the reference angle for -300°
The reference angle for A = -300° is given by R = 60°
What is Reference Angle?Every angle is measured from the positive part of the x-axis to its terminal line (the line that determines the end of the angle) traveling counterclockwise. For angles in the first quadrant, i.e., angles less than or equal to 90 degrees, the reference angle is equal to the original angle.
The reference angle is always positive
0° to 90°: reference angle = angle
90° to 180°: reference angle = 180° - angle
180° to 270°: reference angle = angle - 180°
270° to 360°: reference angle = 360° - angle
Given data ,
Let the reference angle be represented as R
Now , let the given angle be A
A = -300°
And , for 270° to 360°: reference angle = 360° - angle
when the angle is negative and less than -270°
The reference angle is given by adding 360° to it and the angle lies in the first quadrant
So , the reference angle R = A + 360°
R = -300 + 360
R = 60°
Hence , the reference angle is 60°
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349 visitors purchased no costume. 71 visitors purchased exactly one costume. 12 visitors purchased more than one costume. Based on these results, express the probability that the next person will purchase no costume as a percent to the nearest whole number.
The probability that the next person will purchase no costume is 80%.
What is the difference between a probability and an odds?
The possibility of an event occurring can be expressed using odds and probability, but they are computed and understood in different ways.
Probability, which is stated as a number between 0 and 1 (or between 0% and 100%), is the possibility that an event will occur. By dividing the number of positive possibilities by the total number of potential outcomes, the probability of an event happening is determined.
The possibility of an event happening is expressed differently by odds, which are expressed as a ratio of the number of favourable events to the number of negative outcomes. It is possible to state odds as "odds for" or "odds against."
Now,
The total number of visitors who purchased costumes is:
71 (exactly one) + 12 (more than one) = 83
The total number of visitors who did not purchase a costume is: 349
The probability that the next person will purchase no costume is:
349 / (349 + 83) = 349 / 432 ≈ 0.8079
Hence, the probability that the next person will purchase no costume is 80%.
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1) Write an algebraic expression, The quotient of g and 4 added to 15
2) Write an algebraic expression, 6 minus the difference of y and 3
3) Write an algebraic expression, the product of a number d and 8
The algebraic expressions for the given questions are found as:
1) g/4 + 15.
2) 6 - y + 3
3) d * 8
What are algebraic expressions?
A mathematical expression made up of variables, constant algebraic numbers, and algebraic operations are known as an algebraic expression. Everything with a variable value is anything whose value changes over time. Variables in expressions are often represented by letters of the alphabet. Finding the simplified term of the given expression is the goal of simplifying the algebraic expression. We must first understand how to join like terms, factor a number, and the order of operations before we can factorise or simplify the expression. When like terms are combined, the constant terms are divided for the purpose of simplicity and the variables with the same degree are grouped together.
1) The quotient of g and 4 is given by g/4.
Now, this is added to 15.
So the algebraic expression is g/4 + 15.
2) The difference between y and 3 is y - 3.
Now from 6, this difference is subtracted.
So the expression becomes,
6 - (y-3) = 6 - y + 3
3) The product of two numbers is found by multiplying the numbers.
So the expression is :
d * 8
Therefore the algebraic expressions for the given questions are found according to the given statements.
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Use the 2021 marginal tax rates in the table to compute the tax owed by the person with the given filing status and
taxable income.
single with a taxable income of $62,000
Click the icon to view the 2021 marginal tax rates.
The tax owed is $.
The tax owed by a person in 2021 who had a single filling status with a taxable income of $ 62, 000 is $ 9, 388. 50.
How to find the tax owed ?In 2021, the Internal Revenue Service issued rates such that a person with a single filling status and earning $ 62, 000 per year would be subject to tax of ;
= 4, 664 + 22 % of the amount over $ 40, 525
This means that the tax owed by this taxpayer with a $ 62, 000 gross income is :
= 4, 664 + ( 22 % x ( 62, 000 - 40, 525 ) )
= 4, 664 + ( 22 % x 21, 475 )
= 4, 664 + 4, 724. 50
= $ 9, 388. 50
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NEED THIS DUE BY TODAY!!
1) The volume of the first rectangular prism is 175 ft³
2) The volume of the second rectangular prism is 60ft³
3) The volume of the third rectangular prism 140ft³
4) The volume of the Fourth rectangular prism 216ft³
What is the rationale for the above response?Note that in order to find the volume of area of a complex figure, you must deconstruct it into manageable proportions.
Shape 1 above, we deconstructed the rectangular prism into two 3 dimensional shapes with the following metrics:
a)
Length = 7ft
Height = 2ft
widht = 2ft
Volume = Volume = 7ft x 2ft x 2ft
Volume = 28 ft³
b)
Length = 7ft
Height = 3ft
width = 7ft
Volume = 147 ft³
Total Volume = 28 ft³ + 147 ft³
Volume for Shape 1 = 175 ft³
Shape 2 above, we deconstructed the rectangular prism into two 3-dimensional shapes with the following metrics:
a) Length = 3ft
Height = 2ft
width = 1ft
Volume = 6 ft³
b) Length = 6ft
Height = 3ft
width = 3ft
Volume = 54 ft³
Thus, total volume for shape 2 is:
Volume = 6 + 54
Volume = 40 ft³
Shape 3, above, we deconstructed the rectangular prism into two 3-dimensional shapes with the following metrics:
a) Length = 7ft
Height = 1ft
width = 2ft
Volume = 14ft³
b)
Length = 7ft
Height = 3ft
width = 6ft
Volume = 126ft³
Thus, the total volume fior shape 3, =
Volume = 14ft³ + 126ft³
Volume = 140ft³
Shape 4, above, we deconstructed the rectangular prism into two 3-dimensional shapes with the following metrics:
a) Length = 4ft
Height = 3ft
width = 2ft
Volume = 24 ft³
b) Length = 4ft
Height = 12ft
width = 4ft
Volume = 192 ft³
Thus, the total volume for Shape 4:
Volume = 24 ft³+ 192 ft³
Volume = 216ft³
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Use the same values for t and q and your inspection from part b to determine the number of sides that should be contained in your envelope and your partner's envelope combined
Answer: From part b, we know that the number of sides in my envelope is t + q = 10 + 6 = 16, and the number of sides in my partner's envelope is 2t - q = 20 - 6 = 14.
To determine the number of sides in both envelopes combined, we add these values: 16 + 14 = 30.
Therefore, the combined number of sides in both envelopes is 30.
Step-by-step explanation:
line n passes through the points (-3, -7.5) and (2, -5). tahlia determined that the equation of line n is y = 0.5x. explain the error tahlia made while determining her equation. be sure to include the correct equation in your explanation
Answer:
Tahlia was correct in remembering that you can find the slope of a line using the slope formula.
She was also correct that the slope is 0.5.
However, if you use the slope-intercept formula y = mx + b, you still have to find b (the y-intercept) by plugging in one of the two points and the slope.
So, if we plug in the first point and the slope into the line, we can find b and thus the full equation of the line:
[tex]-7.5=0.5(-3)+b\\-7.5=-1.5+b\\b=-6\\\\y=0.5x-6[/tex]
what is the greatest common factor of 4x^3 y^2 and 12x^2 y?
The greatest common factor of 4x³y² and 12x²y is: 4x²y.
What do you mean by greatest common factor?The GCF is a term used to refer to the largest common factor between any two or more numbers (Greatest Common Factor). The GCF of two natural integers, x and y, is the largest possible number that equally and completely divides both x and y. GCF is typically calculated using the following three techniques: division, multiplication, and prime factorization.
Now in the given question,
4x³y² can be written as = 2×2×x×x×x×y×y
12x²y can be written as = 2×2×3×x×x×y
The common factors among them are:
2×2×x×x×y = 4x²y.
Therefore, the greatest common factor of 4x³y² and 12x²y is: 4x²y.
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8. Kelli runs 2 1/4miles on Monday.
Each day after she runs the same 1 1/3 mile route every morning. Her goal is to run at least 4 miles by the
end of the week.
Part A: Which inequality represents the
least number of days that Kelli
needs to run to reach her goal?
Part B: What is the least number of
days after Monday that Kelli needs
to run to reach her goal?
The inequality which represents the least number of days that Kelli needs to run to reach her goal is
2 1/4 + 1/3d ≥ 4.
The least number of days after Monday that Kelli needs to run to reach her goal is 5.25 days
Which inequality represents the least number of days that Kelli needs to run to reach her goal?Monday= 2 1/4 miles
Other days of the week = 1/3 miles
Her goal =™4 miles
Number of days = d
2 1/4 + 1/3d ≥ 4
subtract 2 1/4 from both sides
1/3d = 4 - 2 1/4
1/3d = 4 - 9/4
1/3d = 16-9 /4
1/3d = 7/4
divide both sides by 1/3
d = 7/4 ÷ 1/3
d = 7/4 × 3/1
= 21/4
d = 5.25 days
Hence, Kelli will reach her goal in at least 5.25 days.
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QUESTION 18
Consider the following argument: If Shaun eats popping candy while drinking a can of soda, soda streams out of Shaun's
nose and he gets embarrassed. It isn't the case that soda streams out of Shaun's nose and he gets embarrassed. So, it
isn't the case that Shaun eats popping candy while drinking a can of soda. What is the logical form of this argument?
O a. Affirming a disjunct
b. Denying the antecedent
O c. Affirming the consequent
d. Modus Tollens
Oe. Modus Ponens
If Shaun eats popping candy while drinking a can of soda, soda streams out of Shaun's nose and he gets embarrassed. It isn't the case that soda streams out of Shaun's nose and he gets embarrassed. So, it isn't the case that Shaun eats popping candy while drinking a can of soda. The logical form of this argument is denying the antecedent. The Option B is correct.
How is "denying the antecedent" a logical form in the statement?If we represent the argument in logical symbols, it would look like this:
P: Soda streams out of Shaun's nose when he eat candy Q: Soda does not streams out of Shaun's nose when he doesnt eat candyThe argument can be summarized as follows:
If P, then Q.
Not P.
Therefore, not Q.
This is the form of denying the antecedent, where the argument asserts that if P is true, then Q must also be true. However, the argument then proceeds to deny the antecedent by claiming that P is not true, and therefore, Q must not be true either.
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Divide Katrina's number line into
eighths. Divide Eric's number line into
fourths. Show a point on Katrina's
number line that is less than 1. Show
a point on Eric's number line that is
greater than 1. Write fractions to label
the points you picked.
1. A point less than 1 in Katrina's number line is [tex]\frac{3}{8}[/tex]
2. A point greater than 1 in Eric's number line is 1[tex]\frac{1}{4}[/tex]
What is a number line and how do you identify point less or greater than 1?A number line is a straight line with numbers placed at equal distances from each other.
To identify a line less than 1 in a number line divided into 8, we need to know the value of what each point would be
Each values in Katrina's number line should be 0, [tex]\frac{1}{8}[/tex], [tex]\frac{2}{8}[/tex] , [tex]\frac{3}{8}[/tex], [tex]\frac{4}{8}[/tex], [tex]\frac{5}{8}[/tex], [tex]\frac{6}{8}[/tex], [tex]\frac{7}{8}[/tex] 1
To identify the line greater than 1 in a number line divided into 4, we need to know the values of what each points would be
Each values in Eric's number line should be 1, 1[tex]\frac{1}{4}[/tex], 1[tex]\frac{2}{4}[/tex], 1[tex]\frac{3}{4}[/tex], 2
Check the images below to get a proper view of how your number line should look like.
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m=1 b=4 what does y=
Answer:
Find the value of b using the formula for the equation of a line.
y = mx+b
Replace the known value of m in the slope y-intercept form of the equation.
y=(1)x+b
Replace the known value of b in the slope y-intercept form of the equation.
y=(1)x+4
Simplify the slope y-intercept form of the equation.
Remove parentheses.
y=(1)x+4
Multiply 1 by x
y=1x+4
Remove parentheses.
y=(1)x+4
Multiply x by 1
this is the answer : y=x+4
i hope this helps.
Find x.
X
17
45°
Simplify answer to the simplest form of radical. No decimal.
Check the picture below.
Find the difference. Write your answer in scientific notation. ( 8.4 × 1 0 3 ) − ( 6.4 × 1 0 2 ) (8.4×10 3 )−(6.4×10 2 )
The difference is 7.76 × 10³ in scientific notation.
What is scientific notation?
Scientific notation is a way of expressing a number as a number between 1 and to multiplied by a power of 10.
We can perform the subtraction in the usual way, using the fact that the numbers are already in scientific notation:
(8.4 × 10³) − (6.4 × 10²) = 8.4 × 1000 − 6.4 × 100
= 8400 − 640
= 7760
To write this in scientific notation, we can express the result as a number between 1 and 10 multiplied by an appropriate power of 10. In this case, we can write:
7760 = 7.76 × 10³
Therefore, the difference is 7.76 × 10³ in scientific notation.
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Select ALL the true equations.
(a) 5 + 0 = 0
(b) 15 ⋅ 0 = 0
(c) 1.4 + 2.7 = 4.1
(d) 2/3 ⋅ 5/9 = 7/12
(e) 4 & 2/3 = 5 − 1/3
Answer:
b,c,e
Step-by-step explanation: a: 5+0=5
b:15x0 =0
c: 1.4+2.7=4.1
d:2/3 x 5/9
e:4& 2/3 =5-1/3
General Sherman, a tree located in Sequoia National Park, stands 275 feet tall. To see the top of the tree, Carlos looks up at a 15° angle of elevation. If Carlos is 6 feet tall, how far is he from the base of the tree to the nearest foot?General Sherman, a tree located in Sequoia National Park, stands 275 feet tall. To see the top of the tree, Carlos looks up at a 15° angle of elevation. If Carlos is 6 feet tall, how far is he from the base of the tree to the nearest foot?
We may calculate the distance from Carlos and the tree as [tex]D = 781.23[/tex] ft using trigonometric relationships.
Is calculus more difficult than trigonometry?Many functions in trigonometry offer excellent illustrations of how calculus may be used in practical situations. By the way, basic trigonometry primarily deals with the algebraic features of circular functions, therefore basic calculus is not always simpler than basic trigonometry. On the other hand, calculus is fundamentally non-algebraic in nature.
Trigonometry: SOH CAH TOA or not?The mnemonic SOHCAHTOA makes it simple for us to recall the three primary trigonometric ratios.
Then one of the cathetus of the triangle is equal to:
[tex]275ft - 6ft = 269ft[/tex]
That cathetus is the opposite cathetus to the angle of 19° (the elevation angle). And the adjacent cathetus is the distance between Carlos and the tree.
Then we can use the relation:
Where:
[tex]a=19^{0}[/tex]
opposite cathetus [tex]=269ft[/tex]
adjacent cathetus [tex]=D[/tex]
Replacing that, we get
[tex]tan(19^{0} ) = 269ft/D[/tex]
Solving for D, we get:
[tex]D = 269ft/tan(19^{0} ) = 781.2ft[/tex]
So we conclude that Carlos is at [tex]781.23[/tex] ft of the tree.
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simplify:
tan² θ cos² - sin² θ
can anyone write the steps? many thanks!
Answer:
The given expression simplifies to zero.
Step-by-step explanation:
Tangent Trigonometric Identity:
[tex]\boxed{\tan \theta=\dfrac{\sin \theta}{\cos \theta}}[/tex]
Given expression:
[tex]\tan^2 \theta \cos^2 \theta - \sin^2 \theta[/tex]
To simplify the given expression, rewrite tan²θ using the tan trigonometric identity:
[tex]\implies \dfrac{\sin^2 \theta}{\cos^2 \theta} \cdot \cos^2 \theta - \sin^2 \theta[/tex]
[tex]\implies \dfrac{\sin^2 \theta \cos^2 \theta}{\cos^2 \theta} - \sin^2 \theta[/tex]
Cancel the common factor cos²θ:
[tex]\implies \sin^2 \theta - \sin^2 \theta[/tex]
Add similar elements:
[tex]\implies \sin^2 \theta - \sin^2 \theta=0[/tex]
Therefore, the given expression simplifies to zero.
Transposition solve for v S= 1/2 (u+v) t
The equation can be converted as: 2 (S - 1/2 u t) / t.
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
Let's start by simplifying the equation using the distributive property of multiplication:
S = 1/2 u t + 1/2 v t
Next, we can isolate the variable v by subtracting 1/2 u t from both sides of the equation:
S - 1/2 u t = 1/2 v t
Now we can multiply both sides of the equation by 2 to eliminate the fraction:
2 (S - 1/2 u t) = v t
Finally, we can solve for v by dividing both sides of the equation by t:
v = 2 (S - 1/2 u t) / t
Therefore, the solution for v is v = 2 (S - 1/2 u t) / t.
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Please help! Easy geometry question!
a) If the slant range of the plane in the image is 14.5 km, and the ground range is 10.15 km, find the altitude of the plane to the nearest meter. Show your work and explain your thinking.
b) If this plane loses power and descends suddenly at a rate of 750 meters per minute, how much time will the pilot have before he has to land?
The altitude of the plane to the nearest meter is 9210 meters and if the plane descends at a rate of 750 meters per minute, the pilot will have 12.28 minutes.
What is right angled triangle ?
A right-angled triangle is a triangle that has one angle that measures 90 degrees (a right angle). This means that the other two angles must add up to 90 degrees as well. The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs. The Pythagorean theorem, which states that the sum of the squares of the legs of a right-angled triangle is equal to the square of the hypotenuse, is a fundamental concept in mathematics and has many practical applications. Right-angled triangles are used in fields such as engineering, architecture, and physics to calculate distances, heights, and angles.
a) Let's use the Pythagorean theorem to find the altitude of the plane. We have a right triangle with the slant range as the hypotenuse, the ground range as one leg, and the altitude as the other leg. So, we can use:
altitude² + ground range² = slant range²
altitude² + 10.15² = 14.5²
altitude² = 14.5² - 10.15²
altitude² = 84.9025
altitude ≈ 9.21 km or 9210 meters (rounded to the nearest meter)
b) If the plane descends at a rate of 750 meters per minute, the pilot will have:
time = altitude / descent rate
time = 9210 / 750
time ≈ 12.28 minutes (rounded to two decimal places).
Therefore, the altitude of the plane to the nearest meter is 9210 meters and if the plane descends at a rate of 750 meters per minute, the pilot will have 12.28 minutes.
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How do you solve problems with integers?
first, you must identify which operation you need to fo first.
then, you need to think about which ______ _____ you need to use.
To solve problems with integers, first, you must identify which operation you need to first then, you need to think about which mathematical operations you need to use.
What is integers ?
Integers are a set of whole numbers that include both positive and negative numbers, as well as zero. Integers can be represented on a number line that extends infinitely in both directions.
To solve problems with integers, you need to understand the basic operations such as addition, subtraction, multiplication, and division. You also need to know the rules and properties of integers, such as the commutative, associative, and distributive properties, as well as the rules for adding, subtracting, multiplying, and dividing positive and negative integers.
When solving a problem with integers, you should first identify which operation you need to perform first based on the order of operations. This order is typically remembered with the acronym PEMDAS (parentheses, exponents, multiplication and division, and addition and subtraction). Once you have identified the operation, you can use the appropriate mathematical technique to solve the problem.
Therefore, to solve problems with integers, first, you must identify which operation you need to first then, you need to think about which mathematical operations you need to use.
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Compare the function g(x) = 3/x-2 +5 to the parent function f(x)= 1/x please describe how the function has been transformed from the parent function.
The function g(x) = 3/(x-2) + 5 is a transformation of the parent function f(x) = 1/x with a horizontal shift of 2 units to the right, a vertical stretch by a factor of 3, and a vertical shift of 5 units up.
What is the transformation of the functionThe function g(x) = 3/(x-2) + 5 is a transformation of the parent function f(x) = 1/x.
Here are the transformations that were applied to f(x) to obtain g(x):
1. Horizontal shift: The denominator of f(x) is x, which means that the vertical asymptote is at x = 0. By subtracting 2 from x in the denominator of g(x), we are shifting the vertical asymptote to x = 2. This is a horizontal shift of 2 units to the right.
2. Vertical stretch: The coefficient 3 in front of the fraction means that the function is stretched vertically by a factor of 3 compared to f(x). This means that the distance between the horizontal asymptotes (which are at y = 0 for f(x) and y = 5 for g(x)) is three times larger for g(x) than for f(x).
3. Vertical shift: The constant 5 added to the fraction means that the entire function is shifted vertically by 5 units compared to f(x). This means that the horizontal asymptote of g(x) is at y = 5 instead of y = 0.
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amy and Brian want to fence in a circular portion of there backyard for a play space for their children. determine the area of the largest portion of the yard they can with 90 feet of fencing
The largest portion of the yard they can fence in with 90 feet of fencing has an area of 2025/π feet².
Explain area of circular portion?
The area of a circular portion is the amount of space within the boundary of the circular shape. It is given by the formula A = πr², where r is the radius of the circle.
Now,
To determine the area of the largest portion of the yard, we need to find the radius of the circular portion.
The circumference of a circle is 2πr. Since they have 90 feet of fencing, we can write:
90 = 2πr
Solving for r, we get:
r = 45/π
The area of the circular portion is given by the formula A = πr². Substituting r, we get:
A = π(45/π)² = 2025/π feet²
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20 men working 6 hours a day can finish a work during 10 days. 4 men got seek and didn't work How many hours a day should work other 16 men to finish the work during (a) 10 days? (b) during 15 days?
Answer:
B) 15 days
Step-by-step explanation:
Total Work = (Number of men) x (Hours worked per day) x (Number of days)
Using this formula, we can find the total amount of work to be done in the scenario given in the question:
Total Work = (20 men) x (6 hours per day) x (10 days) = 1200 hours
(a) To find out how many hours a day the remaining 16 men should work to finish the work in 10 days, we need to subtract the work that was not done due to the absence of the 4 men:
Remaining Work = Total Work - Work not done by 4 men
Remaining Work = 1200 - (4 men) x (6 hours per day) x (10 days)
Remaining Work = 840 hours
To finish the remaining work in 10 days, the 16 men would need to work:
Hours per day = Remaining Work / (Number of men) x (Number of days)
Hours per day = 840 / (16 men) x (10 days)
Hours per day = 5.25 hours
Therefore, the 16 men would need to work 5.25 hours per day to finish the work in 10 days.
(b) To find out how many hours a day the remaining 16 men should work to finish the work in 15 days, we need to calculate the total amount of work that needs to be done each day:
Daily Work = Total Work / Number of days
Daily Work = 1200 / 15
Daily Work = 80 hours
To finish the daily work of 80 hours, the 16 men would need to work:
Hours per day = Daily Work / Number of men
Hours per day = 80 / 16
Hours per day = 5 hours
Therefore, the 16 men would need to work 5 hours per day to finish the work in 15 days.
Step-by-step explanation:
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Write an expression for the shaded region.
The expression for the given Venn Diagrams are:
(AпB) U (BпC)(AUC) - (AnB) +(AnBnC)(AUC) - [(AnC) + (BnC)] + (AnBnC)What is a Venn Diagram?A Venn diagram employs circles or other shapes that overlap to show the logical connections between two or more groups of objects.
They frequently serve to visually group objects while highlighting how they differ and how they are similar.
The union of two sets A and B is a new set that contains all the elements that are in A or in B or in both. It is denoted by A ∪ B.
Example: Let A = {1, 2, 3} and B = {3, 4, 5}, then A ∪ B = {1, 2, 3, 4, 5}.
The intersection of two sets A and B is a new set that contains all the elements that are in both A and B. It is denoted by A ∩ B.
Example: Let A = {1, 2, 3} and B = {3, 4, 5}, then A ∩ B = {3}.
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Work out the equation of a line that has a gradient of -2 and passes through (1,7)
With the infοrmatiοn prοvided, the sοlutiοn is 2x + y = 9.
What are equatiοns used fοr?A mathematical equatiοn, including such 6 x 4 = 12 x 2, states that twο numbers οr values are equivalent. a meaningful nοun. An equatiοn is used when twο οr even mοre factοrs must be cοnsidered jοintly in οrder tο understand οr explain the whοle situatiοn.
Given:
Slοpe οr gradient οf line = -2
The lοcatiοn where the line passes = (1,7)
Equatiοn οf a line thrοugh (h,k) with a slοpe οf m:
(y - k) = (x -h) m
Equatiοn οf a line thrοugh (1,7) with a slοpe οf (-2): -
⇒ (y - 7) = (x - 1)(-2)
⇒ y - 7 = - 2x + 2
⇒ y = -2x + 2 + 7
⇒ y = -2x + 9
οr
⇒2x + y = 9
Verificatiοn οf respοnse:
We may check οur respοnse by substituting (1,7) in the fοrmula 2x+y=9.
⟹ LHS = (2×1)+7
⟹ LHS = 2+7
⟹ LHS = 9
Therefοre , LHS = RHS.
Alsο, yοu can use the equatiοn tο determine the gradient οr slοpe and cοnfirm yοur sοlutiοn.
⟹ Slοpe is equal tο -(cοefficient οf x)/ (cοefficient οf y)
⟹ Slοpe = - 2 /1
⟹ slοpe = -2
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1. Given that
lim
x → a f(x) = 2, lim
x → a g(x) = −4, lim
x → a h(x) = 0
find the limits.
(a) lim
x → a [ f(x) + 2g(x)]
(b) lim
x → a [h(x) − 3g(x) + 1]
(c) lim
x → a [ f(x)g(x)] (d) lim
x → a [g(x)]2
(e) lim
x → a
3
√6 + f(x) (f ) lim
x → a
2
g(x)
The answers to all limits are:
(a) lim x → a [ f(x) + 2g(x)] = -6,
(b) lim x → a [h(x) − 3g(x) + 1] = 13
(c) lim x → a [ f(x)g(x)] = -8
(d) lim x → a [g (x)]² = 16
(e) lim x → a 3√6 + f(x) / 2g(x)
What is the algebraic limit theorem?The central limit theorem states that if you take sufficiently large samples from a population, the samples' means will be normally distributed, even if the population isn't normally distributed.
(a) lim x → a [ f(x) + 2g(x)]
= lim x → a f(x) + 2 lim x → a g(x) (using algebraic limit theorem)
= 2 + 2(-4)
= -6
(b) lim x → a [h(x) − 3g(x) + 1]
= lim x → a h(x) - 3 lim x → a g(x) + lim x → a 1 (using algebraic limit theorem)
= 0 - 3(-4) + 1
= 13
(c) lim x → a [ f(x)g(x)]
= lim x → a f(x) * lim x → a g(x) (using algebraic limit theorem)
= 2 * (-4)
= -8
(d) lim x → a [g(x)]²
= [lim x → a g(x)]^2 (using algebraic limit theorem)
= (-4)^2
= 16
(e) lim x → a 3√6 + f(x) / 2g(x)
= [3√6 + lim x → a f(x)] / [2 lim x → a g(x)] (using algebraic limit theorem)
= [3√6 + 2] / [2(-4)]
= (-3√6 - 2) / 8
Therefore, the answers to all limits are:
(a) lim x → a [ f(x) + 2g(x)] = -6,
(b) lim x → a [h(x) − 3g(x) + 1] = 13
(c) lim x → a [ f(x)g(x)] = -8
(d) lim x → a [g (x)]² = 16
(e) lim x → a 3√6 + f(x) / 2g(x)
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For part b, both answers I got come up as incorrect so I need help figuring out what the correct answers are. Im not sure why they’re wrong, this is a Elementary Statistics homework problem
For the new height requirements, this branch of the military requires women's heights to be at least 2.52 in and at most 6.96in.
How to get the z scores?If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.
If we have
[tex]X \sim N(\mu, \sigma)[/tex]
(X is following normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] )
then it can be converted to standard normal distribution as
[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]
(Know the fact that in continuous distribution, probability of a single point is 0, so we can write
[tex]P(Z \leq z) = P(Z < z) )[/tex]
Also, know that if we look for Z = z in z tables, the p value we get is
[tex]P(Z \leq z) = \rm p \: value[/tex]
We are given that;
Mean= 63.8 in
Standard deviation= 2.3 in
Requirement of women height= 58in - 80in.
Now,
To find the minimum and maximum height requirements for this branch of the military, we need to use the standard normal distribution formula, which converts any normal distribution to a standard normal distribution with a mean of 0 and a standard deviation of 1.
We can find the z-scores for the minimum and maximum heights as follows:
For the minimum height requirement:
z = (58 - 63.8) / 2.3 = -2.52
For the maximum height requirement:
z = (80 - 63.8) / 2.3 = 6.96
Using a standard normal distribution table or calculator, we can find the corresponding probabilities for these z-scores:
For a z-score of -2.52, the probability is 0.0059 or 0.59%
For a z-score of 6.96, the probability is very close to 1, or 100%
Therefore, the new height requirements for this branch of the military are:
At least 58 inches, which corresponds to a z-score of -2.52
At most 80 inches, which corresponds to a z-score of 6.96
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Drag the descriptions of each investment in order from which will earn the least simple interest to which will earn the most simple interest of 2000
1) investment of 2000 at 10% simple interest for 9 years
2) investment of 2000 at 3% simple interest for 20 years
3) investment of 2000 at 10% simple interest for 3 years
The response to the given question would be that Because it has a interest higher interest rate and a longer term than option 3, option 1 would generate the greatest interest.
what is interest ?By dividing the principal by the interest rate, the passage of time, and other factors, simple interest is determined. Simple return equals principle plus interest plus hours is the formula used in marketing. The easiest way to compute interest is by using this method. The most typical method for calculating interest is as a portion of the principle amount. For example, if he borrows $100 from a buddy and agrees to pay back the loan at 5% interest, he will only pay his share of the 100% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and you must charge interest when you lend it. Typically, interest is determined as an annual percentage of the loan total. The interest rate of the loan is defined as this ratio.
The following would be the order of 2000 simple interest generated on an investment, from least to most:
2000 invested for 20 years at 3% simple interest
2000 invested for three years at 10% simple interest
2000 invested at 10% simple interest for nine years
Because of its longer length and lower interest rate than the other two alternatives, Option 2 would yield the least amount of interest.
Due to its higher interest rate and longer period, option 3 would generate more interest than option 2.
Because it has a higher interest rate and a longer term than option 3, option 1 would generate the greatest interest.
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Please help on this fast
Answer:
21 miles per gallon
Step-by-step explanation:
find the gradient of the line:
change in y = 105 - 21 = 84
change in x = 5 - 1 = 4
gradient is change in y/ change in x
= 84/4 = 21
