[tex]1/4\\[/tex]
Explanation:
To subtract 2/3 from 11/12, we need to find a common denominator for the two fractions. The least common multiple (LCM) of 3 and 12 is 12. We can rewrite each fraction with a denominator of 12:
11/12 - 2/3 = (11/12) - (2/3) * (4/4) (Multiplying the denominator and numerator of 2/3 by 4 to get a denominator of 12)
11/12 - 8/12 = 3/12
Now that both fractions have a common denominator of 12, we can subtract the numerators:
11/12 - 2/3 = (11 - 8)/12 = 3/12
Simplifying this fraction by dividing both the numerator and denominator by 3, we get:
3/12 = 1/4
Therefore, 11/12 - 2/3 = 1/4.
The prime factorization of 6. Use exponents when appropriate and order the factors from least to greatest
The prime factorization of 6 is the expression of 6 as a product of its prime factors.
A prime factor is a prime number that is a factor of the given number. To find the prime factorization of 6, we need to express 6 as a product of its prime factors. Since 6 can be evenly divided by 2 and 3, which are both prime numbers, the prime factorization of 6 is 2 x 3. We can also write this as 2^1 x 3^1, using exponents to show that there is only one 2 and one 3 in the prime factorization of 6. Finally, since 2 and 3 are both prime, we order the factors from least to greatest as 2 x 3.
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For the following exercises, find the domain, vertical asymptotes, and horizontal asymptotes of the functions. 10. f(x)=x−14 11. f(x)=5x+22 12. f(x)=x2−9x 13. f(x)=x2+5x−36x 14. f(x)=x3−273+x 15. f(x)=x3−16x3x−4 16. f(x)=x3+9x2+14xx2−1 17. f(x)=x2−25x+5 18. f(x)=x−6x−4 19. f(x)=3x−14−2x For the following exercises, find the x - and y-intercepts for the functions. 20. f(x)=x2+4x+5 21. f(x)=x2−xx 22. f(x)=x2+11x+30x2+8x+7 23. f(x)=x2−10x+24x2+x+6 24. f(x)=3x2−1294−2x2
10. Domain: all real numbers; Vertical Asymptotes: x=14; Horizontal Asymptotes: none
11. Domain: all real numbers; Vertical Asymptotes: none; Horizontal Asymptotes: y=5x+22
12. Domain: all real numbers; Vertical Asymptotes: x=0 and x=9; Horizontal Asymptotes: none
13. Domain: all real numbers; Vertical Asymptotes: x=-5; Horizontal Asymptotes: y=0
14. Domain: all real numbers; Vertical Asymptotes: none; Horizontal Asymptotes: y=x3
15. Domain: all real numbers; Vertical Asymptotes: none; Horizontal Asymptotes: y=x3-16x3
16. Domain: all real numbers; Vertical Asymptotes: none; Horizontal Asymptotes: y=x2-1
17. Domain: all real numbers; Vertical Asymptotes: none; Horizontal Asymptotes: y=0
18. Domain: all real numbers; Vertical Asymptotes: x=-6; Horizontal Asymptotes: y=0
19. Domain: all real numbers; Vertical Asymptotes: none; Horizontal Asymptotes: y=3x-14
20. x-intercepts: -4 and 1; y-intercepts: 5
21. x-intercepts: 0 and 1; y-intercepts: 0
22. x-intercepts: -8 and -3; y-intercepts: 7
23. x-intercepts: -1 and 6; y-intercepts: 0
24. x-intercepts: -2 and 0; y-intercepts: -1294
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Suppose X and Y are independent and X∼Bernoulli(1/2) and Y∼Bernoulli(1/3). Determine a) the PMF of X+Y b) the CDF of X+Y c) the range of X+Y d) the expectation of X+Y e) the variance of X+Y f) the expectation of X⋅Y
The PMF of X+Y is given byP(X + Y = k) = P(X = 0,Y = k) + P(X = 1,Y = k-1) + P(X = 1,Y = k) = (1/2)(1/3)^k + (1/2)(1/3)^(k-1) + (1/2)(1/3)^(k-1)for k = 0, 1, 2.
The CDF of X+Y can be determined as below:P(X + Y = 0) = (1/2)(1/3)^0 = 1/2P(X + Y ≤ 1) = P(X = 0,Y = 0) + P(X = 1,Y = 0) + P(X = 0,Y = 1) = 1/2 + (1/2)(1/3) + (1/2)(1/3) = 5/6P(X + Y ≤ 2) = P(X = 0,Y = 0) + P(X = 1,Y = 0) + P(X = 0,Y = 1) + P(X = 1,Y = 1) + P(X = 0,Y = 2) = 1/2 + (1/2)(1/3) + (1/2)(1/3) + (1/2)(1/3)(2/3) + (1/2)(1/3)^2 = 11/18P(X + Y ≤ 3) = 1, as the range of X+Y is 0, 1, 2.
The expectation of X+Y can be determined asE(X + Y) = E(X) + E(Y) = 1/2 + 1/3 = 5/6
The variance of X+Y can be determined asVar(X + Y) = Var(X) + Var(Y) = (1/2)(1/2) + (1/3)(2/3) = 7/18
The expectation of X⋅Y can be determined as below: E(X⋅Y) = P(X = 1,Y = 1) = (1/2)(1/3) = 1/6
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Jim takes out a mortgage for 30 years at an interest rate of 2. 49% and his monthly repayments are $986. 50. What is the principal loan amount? Round your answer to the nearest ten thousand dollars. Do NOT round until you have calculated the final answer
The principal mortgage amount is $220,000.
To compute the principal loan amount, we need to apply the compound interest formulation for a loan:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
Where M is the monthly reimbursement, P is the primary mortgage amount, i is the month-to-month interest charge, and n is the range of months.
First, we need to calculate the month-to-month interest charge:
i = 2.49% / 12 = 0.02075
Subsequent, we want to calculate the range of months:
n = 30 years x 12 months/year = 360 months
Now we are able to plug in the given values:
$986.50 = P [ 0.02075(1 + 0.02075)^360 ] / [ (1 + 0.02075)^360 – 1]
Solving for P, we get:
P = $221,114.07
Rounding to the nearest ten thousand dollars, the principal mortgage amount is $220,000.
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Can someone help with this fast!?!
Solve the equation 2(4x - 1) = -10(x - 3) + 4. Show each step in the solving process separately, please. Also in order what would this be in like properties wise? Been trying to get better at this I just need a little help so I can get better.
Answer:
x=2
Step-by-step explanation:
2(4x - 1) = -10(x - 3) + 4
First, we distribute the 2 on the left side and -10 on the right side using the distributive property of equality:
8x - 2 = -10x + 30 + 4
Next, we combine like terms on the right side:
8x - 2 = -10x + 34
We add 10x to both sides using the addition property of equality:
8x - 2 + 10x = -10x + 34 + 10x
Simplifying:
18x - 2 = 34
We add 2 to both sides:
18x - 2 + 2 = 34 + 2
Simplifying:
18x = 36
Finally, we divide both sides by 18:
18x / 18 = 36 / 18
Simplifying:
x = 2
In each step, we used a different property of equality:
Distributive property of equalityCombining like termsAddition property of equalitySimplifyingAddition property of equalitySimplifyingDivision property of equalityPlease hit brainliest if this helped! Comment if you have a question.
Alex had an income of $7,000. He got 9% of his income from tips. How much of his income
was not from tips?
well, Not from tips that'd be 100% - 9% = 91%, so 91% of $7000.
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{91\% of 7000}}{\left( \cfrac{91}{100} \right)7000}\implies \text{\LARGE 6370}[/tex]
Rewrite x/√16+x^2 by using x= 4 tan θ The answer should not include a radical.
The equation x/√16+x² can be rewritten by using x= 4 tan θ as x/4.
The given expression is x/√16+x^2 and we need to rewrite it by using x= 4 tan θ.
We know that 1 + tan2θ = sec2θ ⇒ 1 = sec2θ − tan2θ ... (1)
x = 4tanθ⇒ x/4 = tanθ ... (2)
Let's substitute (2) in (1) and get:
sec2θ − tan2θ = sec2θ − x²/16 ... (3)
Now, let's simplify the denominator and numerator of x/√16+x² using trigonometry.
We have:
x/√16+x²= x/[4sec2θ]
Using (2), we know that x = 4 tanθ, so substituting this in (3) we get:
sec2θ − x²/16 = sec2θ − (4tanθ)2/16= sec2θ − tan2θ= 1 (from equation (1))
Therefore,
x/√16+x²= x/[4sec2θ] = x/[4√(sec2θ − tan2θ)] (from equation (3))= x/[4√1]= x/4
Hence, x= 4 tan as x/4 can be used to rewrite x/16+x².
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The school library has 35 biology books, 17 chemistry books, and 33 physics books. What is the ratio of chemistry books to the number of books in the library written in the simplest form
Answer:
17:85
Step-by-step explanation:
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
We can say that after answering the offered question The terms in the equation given equation can be streamlined and rearranged to produce the following equation: 23p – 101 = 64p – 40
What is equation?An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.
Using the equality properties, we can rewrite the preceding equation as follows:
2.3p – 10.1 = 6.5p – 4 – 0.01p
2.3p – 10.1 = 6.49p – 4
We can alter the equations using the equality characteristics to look for equations that have the same solution. The answers to the next two equations are the same as those for the previous one:
2.3p – 10.1 = 6.4p – 4
The following equation can be created by adding 0.09p to both sides of the given equation:
2.3p - 10.1 + 0.09p = 6.5p - 4 - 0.01p + 0.09p
2.39p – 10.1 = 6.4p – 4
23p – 101 = 65p – 40 – p
The terms in the given equation can be streamlined and rearranged to produce the following equation:
23p – 101 = 64p – 40
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if a = 2.4 units, b = 4 units, c = 6 units, and d = 8 units, what is the volume of the figure above?
A) 162.56
B) 111.36
C) 256
D) 130.56
I neeeeeed help, this is due tomorrow!!!!
10 points to whoever gives the correct answer!
A rental car company charges $37. 93 per day to rent a car and $0. 11 for every mile driven. Taylor wants to rent a car, knowing that:
She plans to drive 50 miles.
She has at most $300 to spend.
Which inequality can be used to determine dd, the maximum number of days Taylor can afford to rent for while staying within her budget?
The inequality 5.5+37.93d ≤ 300 should be used to calculate the number of days.
The relationship between two non-equal expressions, denoted by a symbol such as 'not equal to, 'greater than' or 'less than' is known as inequality.
She drives 50 miles and per mile, it costs $0.11.
So, for 50 miles, cost = 50 x $0.11 = $5.5
and per day cost = $37.93
Thus, the inequality that must be used to calculate the number of days is
5.5+37.93d ≤ 300 .
the complete question is-
A rental car company charges $37.93 per day to rent a car and $0.11 for every mile driven. Taylor wants to rent a car, knowing that:
She plans to drive 50 miles.
She has at most $300 to spend.
Which inequality can be used to determine dd, the maximum number of days Taylor can afford to rent for while staying within her budget?
5.5d + 37.93 ≥ 300
5.5 + 37.93d ≤300
5.5 + 37.93d ≥ 300
5.5d + 37.93 ≤ 300
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What is the area of a sector with a central angle of 30° and a radius of 12.5 cm?
Use 3.14 for pi and round your final answer to the nearest hundredth.
Enter your answer as a decimal in the box.
Therefore , the solution of the given problem of area comes out to be section has a size of about 164.07 square centimetres.
What exactly is area?Calculating how much space would be needed to fully cover the outside will reveal its overall size. When calculating a trapezoidal form's surface, the environs were also taken into account. The surface area of something determines its overall measurements. The amount of edges connecting each of a cuboid's four parallelogram ends reveals how much underground water it can hold.
Here,
The following algorithm determines a sector's area:
=> A = (θ/360°) * π * r²
where is the mathematical constant pi, r is the radius, and is the centre angle (approximately 3.14).
If we substitute the numbers provided, we get:
=> A = (30/360) * 3.14 * (12.5)^2
By condensing and computing, we arrive at:
=> A ≈ 164.06
To the closest hundredth, we have the following:
=> A ≈ 164.06 ≈ 164.07
Consequently, the section has a size of about 164.07 square centimetres.
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The ministry of health was interested in the relationship between office habits of workers and health issues. Each year, they distributed a survey to all workers in the public sector that contained various questions on work habits as well as a standard health questionnaire. After 555 years they gathered and analyzed the entire data
The data collected by the ministry of health denotes C) Observational Study
The degree of movement along or opposite that may occur in one of the data values when another data value is increased or lowered, respectively, is shown by the correlation of two pairs of data values. An observational study selects participants from a sample of the community, but the independent variable is not controlled due to moral considerations, outside influence, and occasionally, restrictions.
To gather data on office employment and worker health concerns, the health ministry only provides questionnaires to employees every five years. They are only keeping an eye on the employees, and the survey enables them to evaluate and draw a connection between working in an office and health issues among employees. This makes the study an observational one.
Complete Question:
The ministry of health was interested in the relationship between the office habits of workers and health issues. Each year, they distributed a survey to all workers in the public sector that contained various questions on work habits as well as a standard health questionnaire. After 5 years they gathered and analyzed the entire data.
A) Sample study
B)Experiment
C) Observational Study
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A bronze statue has a volume of 36 cm³ and a mass of 311.4g. Work out the density of the statue. Give your answer to 2 d.p.
Answer:
8.65 g/cm³
Step-by-step explanation:
You want the density of a bronze statue with a volume of 36 cm³ and a mass of 311.4 g.
DensityDensity is the ratio of mass to volume:
ρ = mass/volume = (311.4 g)/(36 cm³) ≈ 8.65 g/cm³
The density of the statue is about 8.65 g/cm³.
write 150ml as a percentage of 2litres
Answer:
7.5%
Step-by-step explanation:
1 L = 1000 ML2 L = 2000 MLWhat is a percentage?A percentage is a ratio or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.
In order to express 150 mL as a percentage of 2 liters (2000 mL), you need to divide 150 by 2000 and then multiply the result by 100 to get the percentage.
(150 ÷ 2000) × 100 = 7.5%.Therefore, 150 mL is 7.5% of 2 liters.
ABCD is a trapezium.
EBC is a straight line.
F is the point on AB so that DFE is a straight line.
Angle BEF = 45°
Angle FBC = 100°
Work out the value of angle ADF.
Give a reason on the same line of each
stage of your working.
+
F
Answer: angle ADF =
E
45°
100°
B
Diagram not drawn to scale
C
Total marks: 4
Answer:
35 Degrees
Step-by-step explanation:
Given in figure.
Happy to help :)
The solution is, the value of the angle ADF = 35° .
Here, we have,
from the given diagram, we get,
ABCD is a trapezium.
EBC is a straight line.
F is the point on AB so that DFE is a straight line.
Angle BEF = 45°
Angle FBC = 100°
now, we have,
angle FBE = 180 - 100
= 80 degrees
now, from triangle BEF , we get,
Angle EFB = 55 degrees
again, as AFB is vertically opposite angle,
so, angle AFB = Angle EFB = 55 degrees
finally from triangle ADF , we get,
Angle ADF = 180 - 90 - 55
= 90 - 55
= 35 degrees
so, the value of the angle ADF = 35° .
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350=(4/3)πr2^2
Find r
Answer:
see below
Step-by-step explanation:
350=[tex]\frac{4}{3}[/tex][tex]\pi[/tex]r[tex]2^{2}[/tex]
^ is this correct. i will edit my answer to be the solution.
NO EXPLANATION JUST ANSWER!
The surface area of a cube with a volume of 4913 cubic yards is 972 square yards.
What is surface area?Surface area is the measurement of the total area of a 3D object. It is the sum of all the individual faces of a 3D object, including the area of each side of the object. It is a way to measure the total exposed area of an object, including any protrusions or indentations.
The surface area of a cube is the sum of the areas of the six faces of the cube. The formula for the surface area of a cube is 6 × s2, where s is the length of the side of the cube.
In this case, the volume of the cube is 4913 cubic yards, so the length of the side of the cube is ∛4913 = 17. Therefore, the surface area of the cube is 6 × 172 = 972 square yards.
To find the surface area of a cube, the first step is to determine the length of the side of the cube. This is done by finding the cube root of the volume (in this case, 4913). Once the length of the side is known, the surface area of the cube is simply 6 times the length of the side squared.
In conclusion, the surface area of a cube with a volume of 4913 cubic yards is 972 square yards.
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what is (3-4i)+(3+4i)
Answer:
6
Step-by-step explanation:
.
Answer:
6
Step-by-step explanation:
look above
Oliver earns $25.50 per hour and saves 25% of his income. Oliver wants to save at least $160
a. Write this situation as an inequality.
b. What is the minimum number of hours Oliver needs to work?
Answer: a. 25.50(h)(25%) >= 160
b. 26
Step-by-step explanation:
a. Let the number of hours Oliver works be h hours.
25.50(h)(25%) >= 160
b. 25.50(h)(25%) >= 160
h >= 25.1 (cor. to 3 sig. fig)
The minimum number of hours Oliver needs to work is 26 hours.
Muffy ordered 3 muffins and 2 lattes for $7. Sammy ordered 4 muffins and a latte for $6. Create a system of equations.
The system of equations created from the statements is 3m + 2l = 7 and 4m + l = 6
Creating the system of equations. Let's define the variables:
m = cost of one muffinl = cost of one latteUsing these variables, we can create the following system of equations to represent the given information:
Equation 1: 3m + 2l = 7
Muffy ordered 3 muffins and 2 lattes for $7.
Equation 2: 4m + l = 6
Sammy ordered 4 muffins and a latte for $6.
Hence, the system is 3m + 2l = 7 and 4m + l = 6
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Pleaseeeee hurryyyyy
Julia had a bag filled with gumballs. There were 1 watermelon, 2 lemon-lime, and 3 grape gumballs. What is the correct sample space for the gumballs in her bag?
A. Sample space = watermelon, lemon-lime, lemon-lime, grape, grape, grape
B. Sample space = lemon-lime, watermelon, grape
C. Sample space = 1, 2, 3, 4, 5, 6
D. Sample space = 1, 2, 3
Answer:
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
dudjeisosidheis9sjdhxisjdgskkjehud
let f(x)=6x-2 and g(x)=5x-kx+15. if k=3, what is the value of f(g(10))?
Answer:
We need to find the value of f(g(10)) when k = 3, where f(x) = 6x - 2 and g(x) = 5x - kx + 15.
First, we need to evaluate g(10) when k = 3:
g(x) = 5x - kx + 15
g(10) = 5(10) - 3(10) + 15
g(10) = 50 - 30 + 15
g(10) = 35
Now that we know g(10) = 35, we can evaluate f(g(10)):
f(x) = 6x - 2
f(g(10)) = 6(35) - 2
f(g(10)) = 208
Therefore, when k = 3, f(g(10)) = 208.
Two boats depart from a port located at (–8, 1) in a coordinate system measured in kilometers and travel in a positive x-direction. The first boat follows a path that can be modeled by a quadratic function with a vertex at (1, 10), whereas the second boat follows a path that can be modeled by a quadratic function with a vertex at (0, –7). Which system of equations can be used to determine whether the paths of the boats cross?
StartLayout Enlarged Left-Brace 1st Row y = negative one-ninth (x minus 1) squared + 10 2nd Row y = one-eighth x squared minus 7 EndLayout
StartLayout Enlarged Left-Brace 1st Row y = one-ninth (x + 8) squared + 1 2nd Row y = Negative one-eighth (x + 8) squared + 1 EndLayout
StartLayout Enlarged Left-Brace 1st Row y = negative StartFraction 9 Over 49 EndFraction (x + 1) squared + 10 2nd Row y = one-eighth x squared minus 7 EndLayout
StartLayout Enlarged Left-Brace 1st Row y = negative 17 (x minus 1) squared + 10 2nd Row y = 17 x squared minus 7 EndLayout
A system of equations can be used to determine whether the paths of the boats cross include the following:
A. y = -1/9(x - 1)² + 10.
y = 1/8x² - 7
How to determine the required system of equations?Based on the information provided about the first boat, the x-coordinate of the vertex can be determined as follows;
x = -b/2a
1 = -b/2a
b = -2a
Additionally, the standard form of the equation of a parabola (quadratic function) is given by;
y = a(x - h)² + k.
y = ax² - 2ax + c.
Therefore, the y-coordinate of the vertex is given by:
y = ax² - 2ax + c
10 = a(1)² - 2a(1) + c
c - a = 10 .......equation 1.
Since the parabola passes through the point (-8, 1), we have:
y = ax² - 2ax + c
1 = a(-8)² - 2a(-8) + c
80a + c = 1 .......equation 1.
Solving equations 1 and 2 simultaneously, we have:
81a = -9
a = -9/81 = -1/9
b = -2a = -2(-1/9) = 2/9
c = 10 + a = 10 - 1/9 = 89/9
Rewriting the equation for the first boat, we have:
y = -1/9x² + 2/9x + 89/9
y = -1/9(x - 1)² + 10.
For the second boat, the x-coordinate of the vertex can be determined as follows:
y = ax² + bx + c
x = -b/2a
0 = -b/2a
b = 0
Additionally, the y-coordinate of the vertex is given by:
y = ax² + c
-7 = a(0)² + c
c = -7
Since the parabola passes through the point (-8, 1), we have:
y = ax² + c
1 = a(-8)² - 7
a = -1/8
b = 0
c = -7
Rewriting the equation for the second boat, we have:
y = ax² + c
y = 1/8x² - 7
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Answer: A
Step-by-step explanation:
edge 2023
A rectangle has a height of 555 and a width of 4x^2-2x-64x
2
−2x−64, x, squared, minus, 2, x, minus, 6.
Express the area of the entire rectangle.
Expression should be expanded.
The area of the entire rectangle is 20x^2 - 10x - 30
How to determine the area of the entire rectangleFrom the question, we have the following parameters that can be used in our computation:
Height = 5
Width = 4x^2 - 2x - 6
Using the above as a guide, we have the following:
The area of a rectangle is the product of its dimension
So, we have
Area = Height * Width
Substitute the known values in the above equation, so, we have the following representation
Area = 5 * (4x^2 - 2x - 6)
Evaluate
Area = 20x^2 - 10x - 30
Hence, the area is 20x^2 - 10x - 30
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Tammy’s water bill is automatically deducting $160 from her bank account every other month. How
much will the deductions total for two years?
Step-by-step explanation:
Every-other-month for two years ( 24 months) is 12 deductions
12 * $ 160 = $ 1920
Helphelphelphelphelphelp
Answer: -1
Step-by-step explanation:
An easy way to figure out the slop of a linear graph is the formula:
(y1-y2)/(x1-x2)
In order to use this, find two spots on the line that run exactly through a point, in this example (0,20) and (20,0).
Plug in the xs and ys into the formula, which gets you
(20-0) / (0-20)
When simplified, the result is -1 and that is your slope
khomo and Peter bought a house for R575 000 as an investment. khomo payed R245 000 and Peter payed the rest . they sold the house 5 years later and made a profit of R 234 500 if they share the profit in the same ratio as their respective investment, how much profit will Peter receive
Peter will receive R134,417.50 of the profit.
What is Investment ?
Investment refers to the purchase of goods that are not consumed today but are used in the future to create wealth. In financial terms, investment typically involves buying assets such as stocks, bonds, real estate or other financial instruments with the expectation of earning a profit or income from them.
Khomo paid R245,000 for the house, so his investment ratio is:
245,000 / 575,000 = 0.426
Peter's investment ratio is:
1 - 0.426 = 0.574
If they share the profit in the same ratio as their respective investment, then Peter will receive:
0.574 x 234,500 = 134,417.5
Therefore, Peter will receive R134,417.50 of the profit.
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Publishing scientific papers online is fast, and the papers can be long. Publishing in a paper journal means that the paper will forever in libraries. The British Medical Journal combines the two: it prints short and readable versions, with longer versions available online. The journal asked a random sample of 104 of its recent authors several questions. One question was "Should the journal continue using this system?" In the sample, 72 said "yes." Do the data give good evidence that more than 67% of authors support continuing this system? Interpret the p-value in the context of the problem. If an error has been committed, explain which type of error could it be.
There is no significant evidence that more than two-thirds (67%) of authors support continuing this system.
Define null hypothesis?This hypothesis is either rejected or accepted, depending on whether the population or sample under investigation is viable.
In other words, the null hypothesis is an assertion that the sample observations are the result of chance. It is asserted that surveyors who are interested in the data have made this allegation. It has the prefix H0.
Let p be the proportion of authors who support continuing the system.
Then hypotheses are:
H0: p=0.67
Ha: p>0.67
For calculating the test statistic:
z = p(s)-p/√ [p0(1-p)/N]
where, p(s) = 72/104 ≈ 0.692, p is 0.67 and N is the sample size =104
Then Z ≈ 0.477
The test statistic's p-value is 0.317.
Since 0.317>0.05 and we're assuming a significance level of 0.05, we are unable to reject the null hypothesis.
p-value 0.317 is the likelihood that the sample is chosen from the distribution assumed under null hypothesis, that is where the fraction of authors favouring the new publication scheme is at most 0.67.
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