The value of sin -1(square root 2/2) is π/4 or 45 degrees.
Describe Inverse Sine?Inverse sine, also known as arcsine, is a trigonometric function that is the inverse of the sine function. It is denoted as sin^-1(x), where x is a number between -1 and 1.
The inverse sine function is used to find the angle in a right triangle that has a given sine value. In other words, if we know the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle, we can use the inverse sine function to find the measure of that angle.
The inverse sine function returns an angle in radians, which can be converted to degrees if needed. It has a domain of -1 ≤ x ≤ 1 and a range of -π/2 ≤ sin^-1(x) ≤ π/2.
Like other inverse trigonometric functions, the inverse sine function is a multivalued function. This means that for a given value of x, there can be multiple angles that satisfy sinθ = x. To address this, the principal value of the inverse sine function is defined as the angle between -π/2 and π/2 that satisfies sinθ = x.
The inverse sine function has many applications in mathematics, physics, engineering, and other fields. It is used in the calculation of angles in a variety of contexts, such as in the design of structures and in the analysis of wave phenomena. It is also used in calculus and other advanced mathematics courses to solve integrals and differential equations.
To see why, we can use the definition of the inverse sine function, which gives us the angle whose sine is equal to the input value. In this case, we have:
sin -1(square root 2/2) = θ
where sin(θ) = square root 2/2.
We know that the sine of 45 degrees (or π/4 radians) is also equal to square root 2/2. Therefore, we have:
sin(45 degrees) = square root 2/2
Taking the inverse sine of both sides gives us:
sin -1(square root 2/2) = 45 degrees = π/4
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A right triangle has a base, b
, that is 6
inches. The area of the triangle, with h
representing the height, is given by the expression
The height of the triangle is h = 2A/6.
What is height?Height is the measure of vertical distance, either how "tall" something or someone is, or how "high" the point is. For example, a person's height is typically measured using a stadiometer and is recorded in centimeters or feet and inches. The height of a mountain is usually measured in meters or feet. In aviation, height is measured from the surface of the earth, either above ground level (AGL) or above mean sea level (AMSL).
To find the height of a right triangle given the base, we can use the area formula A = 1/2bh. Rearranging this equation gives us the height: h = 2A/b. In this case, the base is 6 inches and the area is given as A. Therefore, the height of the triangle is h = 2A/6.
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Determine whether the following statement describes a population or a sample. The amount of money each person in your world history class spends renting movies in a week.
The statement describes a sample. Specifically, it is referring to the amount of money each person in your world history class spends renting movies in a week. The class is a subset of a larger population, and the statement is only referring to the sample within that population.
How can you tell if a sample is representative of the whole?By incorporating members of all demographic categories (gender, rural/urban, economic levels, etc.) and having them in the same proportions as the entire population, your sample must be representative of the general population. If there are excessive numbers of participants from rural areas, men, etc., it is not truly representative.
Is money a sampling or a population?Response and justification: A population is the sum of money each student in your global history class spends each week on movie rentals. Because each member of the group is included in the study, this is a population.
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What is the equivalent expression to 4(9+3)
Answer:
4(9+3) = 48
Step-by-step explanation:
To simplify the expression 4(9+3), we need to perform the addition inside the parentheses first and then multiply the result by 4.
9+3 = 12, so we can substitute this into the expression as follows:
4(9+3) = 4(12)
Now we can perform the multiplication:
4(12) = 48
Therefore, the equivalent expression to 4(9+3) is simply 48.
One of your friends who is self- employed starters buying, indicional heath Insurance ll years ago at a cost of $579 per quarte.
Kenny need to buy 4 quarts.
It cost $14.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
The mailbox is splitted into two shapes.
One is rectangle and the other is hemisphere.
Length of the rectangle = 2.4 ft
Width of the rectangle = 1.5 ft
Height of the rectangle = 3 ft
Surface area of the given rectangle
= 2(lw + wh + lh) – lw
= 2(2.4 × 1.5 + 1.5 × 3 + 2.4 × 3) – (2.4 × 1.5)
= 2(3.6 + 4.5 + 7.2) – 3.6
= 2(15.3) – 3.6
= 27
Surface area of the given rectangle = 27 square feet
Radius of the hemisphere = 1.2 ft
Curved surface area of hemisphere
= 2*pi*r^2
= 9.0432 square feet
Curved surface area of hemisphere = 9.0432 square feet
Total surface area of the mailbox = 27 + 9.0432
= 36.0432 square feet
To find how many quarts are needed to cover the mailbox.
1 Quart covers = 10 square feet
36.0432 sq. ft = 36.0432 ÷ 10
= 3.60432 quarts
≈ 4 quarts (approximately)
Hence Kenny need to buy 4 quarts.
Cost of 1 quart = $3.50
Cost of 4 quart = 4 × 3.50
= 14
Hence it cost $14.
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The multiplicative inverse of a number is also called its _______________.
Answer:
Step-by-step explanation:
In formally proving that lim (x² + x) = 42, let e > 0 be arbitrary.
In formally proving that lim (x² + x) = 42
m = ⌈√ε⌉ - 1
How do we calculate?It is shown that for any ε > 0, there exists a δ > 0 such that if 0 < |x - c| < δ, then |(x^2 + x) - 42| < ε.
|(x^2 + x) - 42| = |x^2 + x - 42| = |(x - 6)(x + 7)|
Since |x - c| < δ, we have:
|x - 6| < δ + 6 < δ(m+2)
|x + 7| < δ + 7 < δ(m+2)
Since δ = ε/(m+1), we can solve for m:
m+1 = ε/δ
m+1 = ε/ (ε/(m+1) )
(m+1)^2 = ε
m^2 + 2m + 1 = ε
m^2 + 2m + (1-ε) = 0
Using the quadratic formula, we get:
m = (-2 ± ⌈√ε⌉ - 1 (4 - 4(1-ε)))/2 = -1 ± √(ε)
Therefore, in conclusion m = ⌈√ε⌉ - 1
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A circular grassy plot of land of diameter 42 metre has a path wide 3.5 m running around it on outside find the cost of gravelling the path ₹ 4 per square metre
Answer:
₹ 2,001.20
Step-by-step explanation:
We can consider the grassy plot as a circle with radius = 42/2 = 21 m
The grassy plot and the path together form another circle with radius = 21 + 3.5 = 24.5 m
Area of a circle = πr² where r is the radius
Area of grassy plot = π x 21² = 441π m²
Area of outer circle (grassy plot + path) = π x (24.5)² = 600.25π m²
Area of the outer path alone = 600.25π - 441π = 159.25π = 500.30 sq meters
Cost of paving 1 square meter = ₹ 4
Cost of paving 500.3 sq m = 500.3 x 4 = ₹ 2,001.20
The diameter of a circle is 22 feet. What is the circle's area?
Use 3.14 for .
Answer: 3.14 ft
Step-by-step explanation:
★Given,→ Diameter = 2 feet → Circumference = 2/2 = 1 feet
★Now,→Area of a circle = πr²→ = 3.14 × 1 × 1→ = 3.14 feet
Hence , the circumference is 3.14 ft.
Round 10.468 to the nearest hundredth
Answer:
Step-by-step explanation:
10.468 rounded to the nearest hundredth would be 10.47
4 = tenths place
6 = hundredths place
8 = thousandths place
8 >= 0.5 so 10.468 --> 10.47
Answer: 10.47
Step-by-step explanation: After the decimal, it goes tenths, hundredths, thousandths. So we're looking at the second place after the decimal, which is a 6, and the next number is 8. Think of it like 68, rounding up to the next ten, or 70. So that turns it into 10.470, and you get to drop the zero to make it 10.47.
given that f(x) =x^2 - 13x + 36 and g (x) = x -4, find f (x) -g (x) and express the result as a polynomial in simplest form.
Answer:
f(x)-g(x)
= [tex](x^{2} - 13x + 36) - ( x -4)[/tex]
= [tex]x^{2} -13x+36-x+4[/tex]
= [tex]x^{2} -14x-40[/tex]
Suppose that the quadratic function:
f (x) = (x − 3)² + 5
is transformed
into:
g(x) = (x − 6)² + 3.
How is the graph of the original function transformed?
A: left 2 units and down 3 units
B: right 3 units and down 2 units
C: right 3 units and up 2 units
D: right 2 units and down 3 units
E: left 3 units and up 2 units
F: left 3 units and down 2 units
Answer:B
Step-by-step explanation: I took the test
trust me :p
If the discriminant is negative, there are nο real sοlutiοns, but there are twο cοmplex sοlutiοns in the fοrm οf cοmplex cοnjugates.
What is the quadratic equatiοn?In algebra, a quadratic equatiοn is any equatiοn that can be rearranged in standard fοrm as where x represents an unknοwn value, and a, b, and c represent knοwn numbers, where a ≠ 0.
A quadratic equatiοn is a secοnd-degree pοlynοmial equatiοn in οne variable οf the fοrm:
ax² + bx + c = 0
where a, b, and c are cοnstants, and x is the variable. The quadratic equatiοn is used tο sοlve prοblems that can be represented by a secοnd-degree pοlynοmial functiοn.
The general fοrm οf the quadratic equatiοn can be sοlved using the quadratic fοrmula:
x = (-b ± √(b² - 4ac)) / 2a
where the "±" sign means that there are twο pοssible sοlutiοns, οne with the pοsitive square rοοt and the οther with the negative square rοοt.
The quadratic equatiοn can have οne, twο, οr nο real sοlutiοns depending οn the value οf the discriminant b² - 4ac. If the discriminant is pοsitive, there are twο distinct real sοlutiοns. If the discriminant is zerο, there is οne real sοlutiοn with a multiplicity οf 2.
If the discriminant is negative, there are nο real sοlutiοns, but there are twο cοmplex sοlutiοns in the fοrm οf cοmplex cοnjugates.
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What is 5/8 equative to
Answer chooses
0.48
0.6
0.675
Answer: C
Step-by-step explanation:
Yesterday, a movie theater sold 289 bags of popcorn. A large bag of popcorn costs $4. A small bag of popcorn costs $1. In all, the movie theater made $544 from popcorn sales. Write and solve a system of equations to find how many bags of each side of popcorn were sold.
The movie theater sold __ large bags of popcorn.
The movie theater sold __ small bags of popcorn.
(MARKING BRAINLIEST FOR RIGHT ANSWER)
Answer:
The movie theater sold 85 large bags of popcorn and 204 small bags of popcorn.
Step-by-step explanation:
Let's use the following variables to represent the number of large and small bags of popcorn sold:
L: the number of large bags of popcorn sold
S: the number of small bags of popcorn sold
We can then write a system of equations based on the information given in the problem:
L + S = 289 (the total number of bags sold is 289)
4L + S = 544 (the total revenue from popcorn sales is $544)
To solve for L and S, we can use the method of substitution. Rearrange the first equation to solve for one variable in terms of the other:
L = 289 - S
Substitute this expression for L in the second equation and solve for S:
4(289 - S) + S = 544
1156 - 4S + S = 544
3S = 612
S = 204
Now that we know that 204 small bags of popcorn were sold, we can use the first equation to solve for L:
L + S = 289
L + 204 = 289
L = 85
Therefore, the movie theater sold 85 large bags of popcorn and 204 small bags of popcorn.
Least Common Denominator
The required least common denominator for the given expression is 4x³(x + 3). Option C is correct.
What is a rational fraction?A rational expression is a mathematical expression that is the ratio of two polynomial expressions. That is, a rational expression is formed by dividing one polynomial expression by another polynomial expression.
Here,
The given rational expression,
= 1/x² - 1/4x² + 12x
In the question, we have been asked to determine the least common denominator for the given rational expression.
Since least common denominator is given expression,
= x² (4x² + 12x)
= 4x³(x + 3)
Thus, the required least common denominator for the given expression is 4x³(x + 3). Option C is correct.
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What is the frequency of the function f(x)? f(x)=14cos(2x)+5 express the answer in fraction form. Enter your answer in the box.
The frequency of the function f(x) is 1/π.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable. In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
We need to find the frequency of given function;
f(x)=1/4 cos(2x)+5
To finding the period and then use the general relation frequency
frequency = 1/period
In the given function f(x)=1/4 cos(2x)+5 here, only the constant 2 which will multiply with x effects the period.
As we know that 2π is the period of cosx then the period of cos(2x) is
2x=2π
x=π
So, the period of cos(2x) is π
Now the frequency is F=1/π
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use the multiplier method to increase £258 by 43%
Answer:
43% * 258 = 110.94 (£110.94 is 43% of £258) 258 + 110.94 = 368.94
Step-by-step explanation:
jo needs to estimate the cost, icluding tax, of a pair of jeans originally priced at $30, they are on sale for 40% off.
which is the best plan for determining the sale price ?
Therefore , the solution of the given problem of percentage comes out to be $18 is the original price.
What is a percentage?In mathematics, a percentage is any value that can be represented as a fraction of 100. There are also sporadic uses of the abbreviations "pct.," "pct," or "pc." Nonetheless, it is typically denoted by the "%" symbol. The proportional amount is flat and lacks any dimensions. As percentages have a numerator of 100, they can be thought of as fractions. The percent symbol (%) must come after a number to denote that it is a percentage.
Here,
To determine the sale price of the jeans including tax, Jo should follow these steps:
Find the sale price of the jeans before tax:
Sale price = Original price - Discount
= $30 - 40%($30)
= $30 - $12
= $18
Find the tax amount by multiplying the sale price by the tax rate (which varies depending on the location):
Tax amount = Sale price x Tax rate
Add the sale price and the tax amount to get the total cost:
Total cost = Sale price + Tax amount
So the best plan for Jo to determine the sale price including tax would be to follow the above steps using the applicable tax rate in their location.
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In your first semester of college you took 13 credit hours and earned a GPA of 2.13. In your second semester your Gpa of 2.34 was based on 12 credit hours. Your third semester GPA was 3.00 Based on 17 hours. Calculate overall GPA for the three semesters.
Answer:
below
Step-by-step explanation:
[ 2.13 * 13 + 2.34 * 12 + 3.00 * 17 ] / ( 13 + 12 + 17) = 2.54 GPA
What is the volume of a cube with a side length of 1/4 inch?
Answer: 1/64 cubic inch
Step-by-step explanation:
Side of cube = 1/4
Volume = s^3 = 1/4^3
= 1/64
Hope this helps!!
A 4-yard dumpster cost $95.00 monthly how much would it cost for the year?
Answer options:
A) 190.00
B) 180.00
C) 170.00
D) 160.00
If a 4-yard dumpster cost $95.00 monthly, the total cost for the year is $1,140.
How is the total cost determined?The total cost for the year of the dumpster is the product of the multiplication of the monthly cost and 12.
Multiplication is one of the four basic mathematical operations, including addition, subtraction, and division.
In any multiplication, there must be the multiplicand (the number being multiplied), the multiplier (the number multiplying the multiplicand), and the product (or the result).
The monthly cost of the 4-yard dumpster = $95.00
1 year = 12 months
The total annual cost = $1,140 ($95 x 12)
Thus, using the multiplication operation, we can find that none of the options is correct as the total annual cost but $1,140.
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Plot the points (-3, 8) and (5, -8) on the plane below. Determine the slope-intercept form of the equation of the line
through these points.
A graph of the points (-3, 8) and (5, -8) is shown on the plane below.
The slope-intercept form of the equation of the line through these points is y = -2x + 2.
How to determine an equation of this line?In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.At data point (-3, 8), a linear equation in standard form for this line can be calculated by using the point-slope form as follows:
y - 8 = (-8 - 8)/(5 + 3)(x + 3)
y - 8 = -16/8(x + 3)
y = -2(x + 3) + 8
y = -2x - 6 + 8
y = -2x + 2
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Regina and Abby both want to buy new shoes for their shoe collection.
Regina only has 500 dollars the shoes she wants is 600 dollars.
Her mom makes her work for 5 hours and she gets 120 dollars per hour.
Abby has 600 dollars and the shoes she wants is $870
Her mom makes her work for 5 hours and gets $320
Is the relationship between hours worked and money proportional? Who would buy their shoes first?
The relationship between hours worked and money is not proportional.
Regina would be able to buy her shoes first after working an additional 50 minutes.
What is proportion?
In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. According to the definition of proportion, two ratios are in proportion when they are equal.
To determine if the relationship between hours worked and money is proportional, we need to calculate the hourly rate for each person and see if it is the same.
For Regina, she earned $120 per hour and worked for 5 hours, so she earned a total of 5 x 120 = $600.
This means her hourly rate is $120.
For Abby, she earned $320 for 5 hours of work, so her hourly rate is 320/5 = $64.
Since the hourly rates are different, the relationship between hours worked and money is not proportional.
Now let's see who would be able to buy their shoes first.
Regina needs $100 more to be able to buy her shoes, and she earned $600 from working 5 hours.
Therefore, she can buy the shoes after working for an additional $100/$120 = 0.83 hours, which is approximately 50 minutes.
On the other hand, Abby needs $270 more to buy her shoes, and she earned $320 from working 5 hours.
Therefore, she can buy the shoes after working for an additional $270/$64 = 4.22 hours, which is approximately 4 hours and 13 minutes.
Therefore, Regina would buy her shoes first.
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show how the damping ratio for a mass-spring-damper system is defined by the ode for a mass-spring-damper system in terms of mass, m, stiffness, k, and damping, b?
The equation that shows the damping ratio for a mass-spring-damper system which is defined in terms of the mass, m, stiffness, k, and damping, b is ζ = b / (2sqrt(mk)).
What is damping ratio?The damping ratio ζ is defined as the ratio of the damping coefficient b to the critical damping coefficient b_c, which is the minimum damping required to prevent the system from oscillating.
The damping ratio is a dimensionless quantity that represents the amount of damping in the system relative to the critical damping needed to prevent oscillations. A higher damping ratio indicates a more heavily damped system, while a lower damping ratio indicates a less damped system that may oscillate more.
The motion of a mass-spring-damper system can be described by a second-order linear ordinary differential equation (ODE) of the form:
md²x/dt² + bdx/dt + kx = F(t)
where m is the mass of the system, b is the damping coefficient, k is the spring constant, x is the displacement of the mass from its equilibrium position, and the external force applied to the system is F(t).
The critical equation will be -
b_c = 2√(mk)
Therefore, the damping ratio can be expressed as:
ζ = b / b_c
Substituting the expression for b_c into the above equation, we get:
ζ = b / (2√(mk))
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Examine the coordinate grid below. What are the coordinates of the point A’ when point A is reflected across the x-axis?
Answer:
The rule for reflection along the x axis (x;y) to (x; -y)
A' (x ; -(y) )
A' (4 ; -(5) )
A' (4 ; -5 )
Determine whether descriptive or inferential statistics were used in the statement. in 2008, the average credit card debt for college students was $3173. (source: newser)
The collection, description, analysis, and drawing of conclusions from quantitative data are all included in the area of statistics, which is a branch of applied mathematics. Probability theory, linear algebra, and calculus of differential and integrals are some of the core mathematical concepts in statistics.
Descriptive statistics were used in the statement.
Descriptive statistics is a branch of statistics that deals with the collection, presentation, and summary of data. It is used to describe and summarize the main features of a data set, such as measures of central tendency (e.g., mean, median, mode) and measures of dispersion (e.g., range, variance, standard deviation).
In this case, the statement is simply reporting a single value, the average credit card debt for college students in 2008. This is an example of a descriptive statistic because it is a summary measure that describes a characteristic of the population or sample under study.
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Descriptive statistics were used in the statement.
What is descriptive statistics?Descriptive statistics is a branch οf statistics that deals with the analysis, descriptiοn, and summarizatiοn οf data. It invοlves the use οf variοus statistical measures, such as measures οf central tendency (mean, median, and mοde), measures οf dispersiοn (standard deviatiοn, variance, range), and graphical representatiοns (histοgrams, bοx plοts, scatter plοts, etc.) tο describe the features οf a dataset.
Descriptive statistics were used in the statement. The statement is simply describing the average credit card debt fοr cοllege students in 2008. Descriptive statistics are used tο describe οr summarize a dataset οr pοpulatiοn, while inferential statistics are used tο draw cοnclusiοns οr make predictiοns abοut a larger pοpulatiοn based οn a sample οf data. Since the statement οnly prοvides infοrmatiοn abοut a specific grοup οf cοllege students in 2008, it dοes nοt invοlve making any inferences οr predictiοns beyοnd this grοup.
Hence, Descriptive statistics were used in the statement.
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The vertices of a rectangle are at (-4,2),(3,2),(3,-2), and (-4,-2). What is the length of the longer side of the rectangle?
The longer side of the rectangle is the side that connects the points (-4,2) and (3,2), which have the same y-coordinate, so it is a horizontal line.
The length of this side is the distance between the x-coordinates of these two points, which is:
3 - (-4) = 7
Therefore, the length of the longer side of the rectangle is 7 units.
I'll give brainliest
(-7, 4).
Step-by-step explanation:1. Write the given equations.[tex]x=-2y+1\\ \\3x+8y=11[/tex]
2. Solve one of the equations for one of the variables.Most of the times you solve a systems of equations, you'll have to solve one of the equations for one of the variables (x or y), since the first equation is already solved for "x", we may use that and skip this first solving step.
[tex]x=-2y+1[/tex]
3. Substitute the value of "x" on the second equation by the argument of "x" in the first equation.[tex]3(-2y+1)+8y=11[/tex]
4. Distribute and multiply on the left side of the equation.Chech attached image 1.
[tex](3)(-2y)+(3)(1)+8y=11\\ \\(-6y)+(3)+8y=11\\ \\-6y+3+8y=11[/tex]
5. Subtract "3" from both sides of the equation.[tex]-6y+3+8y-3=11-3\\ \\-6y+8y=8[/tex]
6. Work out like terms at the left hand side.[tex]2y=8[/tex]
7. Divide by "2" on both sides.[tex]\frac{2y}{2} =\frac{8}{2} \\ \\y=4[/tex]
8. Substitute "y" by the calculated value (4) on any of the equations to find the value of "x".[tex]x=-2(4)+1\\ \\x=-8+1\\ \\x=-7[/tex]
9. Express the final answer.Now that weëve found a value for both "x" and "y", write the solution as an ordered pair:
(x, y)
(-7, 4).
10. Verify your answer.To algebraically verify your answer, you must use the value of either "x" or "y" on both of the equations and it should return the other value of the missing variable.
Since we already checked with the first equation, go ahead and plug in any of the values on the second equation and check if it returns the correct value.
For example, if we use y=4 in equation 2, it should return an "x" value of -7. Let's test it!
[tex]3x+8(4)=11\\ \\3x+32=11\\ \\3x=11-32\\ \\3x=-21\\ \\\frac{3x}{3} =\frac{-21}{3} \\ \\x=-7[/tex]
That's correct! Answer is (-7, 4).
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A researcher calculated sample proportions from two independent random samples. Assuming all conditions for inference are met, which of the following is the best method for the researcher to use to estimate the true difference between the population proportions?Construct a two-sample z-interval for the difference between population proportions.Answer A: Construct a two-sample z -interval for the difference between population proportions.AConstruct a two-sample z-interval for the difference between sample proportions.Answer B: Construct a two-sample z -interval for the difference between sample proportions.BPerform a z-test for the difference in sample proportions.Answer C: Perform a z -test for the difference in sample proportions.CSubtract the proportions and construct a one-sample z-interval for a single population proportion.Answer D: Subtract the proportions and construct a one-sample z -interval for a single population proportion.DSubtract the proportions and construct a z-interval for a single sample proportion.
Answer A: Construct a two-sample z-interval for the difference between population proportions.
What is fraction?
A fraction is a mathematical expression that represents a part of a whole or a ratio between two quantities. It is written as a/b, where a is called the numerator and b is called the denominator. The numerator represents the number of parts or units being considered, while the denominator represents the total number of parts or units in the whole.
According to given conditions:
The best method for the researcher to use to estimate the true difference between the population proportions would be to:
Answer A: Construct a two-sample z-interval for the difference between population proportions.
This is the most appropriate method for estimating the difference between population proportions, as it takes into account the variability of the sample proportions and provides a confidence interval for the true difference between the two populations. The formula for calculating the two-sample z-interval for the difference between population proportions is:
(p₁−p₂) ± z x √[(p₁(1−p₁))/₁ + (p₂(1−p₂))/₂]
Therefore, Answer A: Construct a two-sample z-interval for the difference between population proportions.
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Find domain Range Y-intercept X- intercept Vertical asymptote Horizontal asymptote Pic attached below note write domain and range in interval notation Find domain Range Y-intercept X intercept Vertical asymptote Horizontal asymptote Pic attached below
The domain of the function is (-∞, -2) ∪(-2, ∞) and it's range is (-∞, 1) ∪ (1, ∞). The function has vertical and horizontal asymptotes as x = -2 and y = 1
What is the domain and range of a functionIn mathematics, the domain of a function is the set of all possible input values (also known as the independent variable) for which the function is defined. The range of a function is the set of all possible output values (also known as the dependent variable) that the function can produce.
To determine the domain and range of a function, it's important to consider the nature of the function, its graph or formula, and any restrictions that may apply.
The function f(x) = - (2/ x + 2) + 1
The domain of the function is (-∞, -2) ∪(-2, ∞)
The range of the function is (-∞, 1) ∪ (1, ∞)
The vertical asymptote is x = -2
The horizontal asymptotes y = 1
The y-intercept is (0, 0)
The x - intercept is (0, 0)
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As an oil well is drilled, each new section of drill pipe supports its own weight and that of the pipe and drill bit beneath it. Calculate the stretch in a new 6.00 m length of steel pipe that supports 3.00 km of pipe having a mass of 20.0 kg/m and a 100-kg drill bit. The pipe is equivalent in stiffness to a solid cylinder 5.00 cm in diameter.
Therefore, the cylinder stretch in the new 6.00 m length of steel pipe is 0.094% of its original length, or about 5.64 mm.
What is a cylinder?The cylinder, which is frequently a three-dimensional solid, is one of the most primitive curved geometric forms. In simple geometry, it is known as a prismatic with a circular as its basis. The term "cylinder" is also used to refer to an infinitely curved surface in a number of modern domains of geometry and topology. A "cylinder" is a three-dimensional object made up of curved surfaces with round tops and bottoms.
Here,
The total weight supported by the new 6.00 m length of pipe is the weight of the pipe and drill bit beneath it, which is:
W = (20.0 kg/m)(3.00 km) + 100 kg
W = 60,100 kg
The equivalent diameter of the solid cylinder is 5.00 cm, or 0.05 m, so its radius is 0.025 m. The cross-sectional area of the steel pipe is therefore:
A = πr^2 = π(0.025 m)^2 = 0.0019635 m^2
The modulus of elasticity for steel is typically around 200 GPa (gigapascals), or 200,000,000 N/m^2. Using the formula for the stretch of a rod under tension, which is:
ΔL/L = F/(AE)
ΔL/L = (Wg)/(AE)
where g is the acceleration due to gravity (9.81 m/s^2).
Substituting the values we have calculated, we get:
ΔL/L = [(60,100 kg)(9.81 m/s^2)]/[(0.0019635 m^2)(200,000,000 N/m^2)]
ΔL/L = 0.0009397 or 0.094%
Therefore, the stretch in the new 6.00 m length of steel pipe is 0.094% of its original length, or about 5.64 mm.
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