The longest piece of same size that can be cut from 90 inches and 72 inches pieces of wood using HCF is of length 18 inches.
So, the correct option is (c) 18.
Given that,
Jeremy has two pieces of 90 inches and the other is 72 inches wood. He wants to cut both pieces of wood into smaller pieces of same length and length as long as possible.
Therefore, the Highest Common Factor (H.C.F.) of both the lengths will gives the highest possible length i.e between both the wooden pieces.
To find Highest Common factor,
Prime factorizations of 90 and 72 :
90 = (2 x 3 x 3) x 5
72 = 2 x 2 x (2 x 3 x 3)
2 x 3 x 3 is common factor between 90 and 72
∴ The Highest Common Factor of 90 and 72 = 2 x 3 x 3 = 18
The longest possible length that can be cut out from both the pieces are of length = 18 inches
Number of pieces that can be cut from 90 inches long piece = 90/18 = 5
Number of pieces that can be cut from 72 inches long piece = 72/18 = 4
Therefore, the total number of pieces of lumber = 5+4 = 9 pieces
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Describe the transformations of the parent function for f(x) = -1/2√x+4.
The graph would be narrower.
The graph would shift down 4 units.
The graph would reflect over the y-axis.
The graph would shift up 4 units.
The graph would be wider.
The graph would shift to the left 4 units.
The graph would shift to the right 4 units.
The graph would reflect over the z-axis.
The parent function for f(x) = -1/2√x+4 can be transformed in a variety of ways to create new functions.
Describe the transformations of the parent function for f(x) =-1/2√x+4?The parent function for f(x) = -1/2√x+4 can be transformed by shifting, reflecting, and stretching.Shifting:
f(x) = -1/2√x+4 + c, where c is the amount of the shift on the y-axis
Reflecting:
f(x) = -1/2√-x+4, where the negative sign reflects the graph across the y-axis
Stretching:
f(x) = k(-1/2√x+4), where k is the amount of the stretch on the y-axis.
The most basic transformation is a vertical shift, which can be accomplished by adding or subtracting a constant from the function. When the constant is positive, the function shifts up, and when it is negative, the function shifts down.Horizontal shifts can also be applied by adding or subtracting a constant from the x-value inside the radical. When the constant is positive, the function shifts to the left, and when it is negative, the function shifts to the right.To learn more about The parent function refer to:
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A restaurant customer left $1.65 as a tip. The tax was 6% and the tip was 15% of the cost including tax.
a. Which information is not needed to compute the bill after tax and tip?
b. What was the total bill?
a) The information not required in the tax computation is; the amount of the bill
b) The total bill is calculated as; $12.65
How to solve Percentage Problems?A percentage is defined as a number or ratio that is expressed as a fraction of 100.
The parameters are that a restaurant customer left $1.65 as a tip, the tax was 4 % and the tip was 15% of the after tax cost. Thus;
Let the bill after the tax plus tip will be a and the bill after tax be b,
Therefore,
a = b + $1.65
Since $1.65 = 15% of b, then we have;
b = 1.65*100/15
b = 11
a = 11 + 1.65
a = 12.65
Hence, the total cost after the tip = $12.65
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Kris currently has $190 and plans to earn more money each of the 8 weekends this summer She wants at least $1,625 by the end of the summer Write and solve an inequality for the amount of money Kris needs to earn each weekend Which answer choice best interprets the solution in the context of the problem?
A. Kris needs $179.38 more to meet her goal
B. Kris needs $13.13 each hour to meet her goal
C. Kris needs to earn at least $179.38 each weekend to meet her goal
D. Kris needs to earn $105 more to meet her goal
Kris currently has $190 and wants to have at least $1,625 by the end of the summer. To find out how much money she needs to earn each weekend we need to subtract the money she already has from the money she wants to have and divide that by the number of weekends.
$1,625 - $190 = $1,435
$1,435 ÷ 8 = $179.38
So, Kris needs to earn at least $179.38 each weekend to reach her goal.
Answer choice C. Kris needs to earn at least $179.38 each weekend to meet her goal. is the best interpretation of the solution in the context of the problem.
a machine closes 35 packages per minute
If a machine closes 35 packages per minute. The number of packages the machine can close in 40 minutes is: 1400 packages.
How to find the number of packages?Using this formula to find the number of packages
Number of packages = Packages per minute machine closes × Number of minutes
Let plug in the formula
Number of packages = 35 packages per minute × 40 minutes
Number of packages = 1400 packages
Therefore we can conclude that the number of packages is 1400 packages.
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The complete question is:
A machine closes 35 packages per minute How many packages can the machine close in 40 minutes? Enter your answer in the box. packages?
What is 2015 in Roman numeral
Answer:
MMXV
Step-by-step explanation:
(◕ᴗ◕✿)(◕ᴗ◕✿)(◕ᴗ◕✿)
8. ABC has vertices A(0, 0), B(0, -2), and C(-3, 0). What are the coordinates
of the orthocenter of ABC?
Answer:
(-1,-1)
Step-by-step explanation:
join the mid points of AB, BC & AC ...
you got the orthocenter point, then we can read the coordinates from X-axis and Y-axis.
In a congressional district, 55% of the registered voters are Democrats. Which of the following is closest to the probability of getting less than 50% Democrats in a random sample of size 100?
Using the normal distribution and the central limit theorem, considering that this is a sample proportion, as we are dealing with percentages, it is found that there is a 0.1562 = 15.62% probability of getting less than 50% Democrats in a random sample of size 100.
Normal Probability Distribution
In a normal distribution with mean and standard deviation , the z-score of a measure X
It measures how many standard deviations the measure is from the mean.
After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
By the Central Limit Theorem, the sampling distribution of sample proportions of a proportion p in a sample of size n has mean and standard deviation .
In this problem:
55% of the registered voters are Democrats, hence .
A sample of size 100 is taken, hence
The mean and the standard deviation of the sampling distribution of sample proportions
The probability of getting less than 50% Democrats in a random sample of size 100 is the p-value of Z when X = 0.5, hence:
By the Central Limit Theorem
has a p-value of 0.1562.
0.1562 = 15.62% probability of getting less than 50% Democrats in a random sample of size 100.
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A person wishes to have $21,200 cash for a new car 7 years from now. How much should be placed in an account now, if the account pays 6.4% annual interest rate,
compounded weekly?
Step-by-step explanation:
To calculate how much should be placed in an account now to have $21,200 cash for a new car 7 years from now, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = future value (amount of money after t years)
P = present value (amount of money now)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case, we have:
A = $21,200
r = 0.064 (6.4% as a decimal)
t = 7
n = 1 (the interest is compounded annually)
So, we can solve for P:
P = A / (1 + r/n)^(nt)
P = $21,200 / (1 + 0.064)^(7)
P = $15,093.35
Therefore, the person should place $15,093.35 in an account now to have $21,200 cash for a new car 7 years from now, at an annual interest rate of 6.4%.
F
The volume of a box is 4x3+19x2 + 12x. The height is x
and the length is x +4.
Find the width.
The width is
(Simplify your answer.)
Answer:4x+3
Step-by-step explanation:
Given the following in the question if:
Volume of the box= 4x3+19x2+12z
Height of the box= x
width of the box =?
we have to find the width of the box, so as we know that
box is in the shape of cuboid, so
Volume of the cuboid = length * width * height
4x3+9x2+12x = x+4* width * x
width = 4x3+9x2+2x/x2+4x
we have to use long division method for this algebraic expression to divide and find width of the box.
we get width= 4x+3
Hence, the width of the box which in the shape of cuboid is 4x+3
Differentiation stationary points please help
A stationary point can be found by solving d y d x = 0 , i.e. finding the x coordinate where the gradient is 0.
How do you find the coordinates of a stationary point of a curve?When the derivative of a function, f(x), equals 0, it is said to be stationary. Because the function is neither increasing nor decreasing at these locations, they are referred to be "stationary" points.
This graphically correlates to locations on the graph of f(x) where the horizontal line that forms the tangent to the curve is present.When the derivative of a function, f(x), equals 0, it is said to be stationary. Because the function is neither increasing nor decreasing at these locations, they are referred to be "stationary" points.
Stationary Points Defined. Remember that a stationary point is a value of x0 for x at which f′(x0)=0 f ′ (x 0) = 0 for a univariate function y=f(x) y = f (x).
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Which of the following could represent consecutive even integers, given x =1?
x + 1, x + 2
x+1, 2x + 1
2x, 2x + 2
Answer:
2x, 2x + 2
Step-by-step explanation:
2x is even
2x + 2 = 2(x+1)
x and x+1 are consecutive integers
So multiplying both by 2 makes them consecutive even integers
For example with x = 1
2x = 2, 2(x+1) = 2 . 2 = 4 which is next even consecutive integer
Answer:
2x, 2x + 2
Step-by-step explanation:
Each expression is divisible by 2, so it is even.
An Economist consultant needs to forecast the unit cost of a product for the next year. He notes
that each unit of the product requires 10 labor hours and 5 kg of raw material. In addition, each
unit of the product is assigned an overhead cost of ETB 200. He estimates that the cost of a labor
hour next year will be normally distributed with an expected value of ETB 45 and a standard
de useviation of ETB 2; the cost of raw material will be normally distributed with an expected value
of ETB 60 and a standard deviation of ETB 3.
A. Find the distribution of the unit cost of the product.
B. Find its expected value and variance.
A. The unit cost of the product follows a normal distribution with an expected value of ETB 305 and a standard deviation of ETB 5.
B. The expected value of the unit cost of the product is ETB 305 and the variance is ETB 25.
How do you calculate a standard deviation?In order to calculate the standard deviation, follow the following steps:
1. Calculate the mean (average) of your data set.
2. For each data point, subtract the mean and square the result (the squared difference).
3. Sum all of the squared differences.
4. Divide the sum by the number of data points. This gives you the variance.
5. Take the square root of the variance to get the standard deviation.
Therefore, the correct answer is as given above
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There are three boxes one of them contains gold. In each box, there is amessage
Answer:
Gold is in Box 1
Step-by-step explanation:
There are 3 boxes. One of them contains gold
In each box, there is a message, and one of them is true.
Box 1: "The gold is not in Box 2".
Box 2: "The gold is in this box"
Box 3: "The gold is not in this box".
Which box has the gold?
Answer:
O Box 1
O Box 3
O Box 2
There's not enough info
Assume each statement to be true at a time, and check for contradictions.
Box 1: "The gold is not in Box 2".
Assume True. Gold in 1 or 2.
Box 2: "The gold is in this box"
False. Gold not in 2.
Box 3: "The gold is not in this box".
False. Gold in 3
Contradiction between box1 and box 3 message.
Box 2: "The gold is in this box"
Assume true. Gold in 2.
Box 1: "The gold is not in Box 2".
False. Gold in 2.
Box 3: "The gold is not in this box".
False. Gold in 3.
Contradiction between boxes 2 and 3. Box 2 message cannot be true.
Box 3: "The gold is not in this box".
Assume true. Gold in 1 or 2.
Box 1: "The gold is not in Box 2".
False. Gold in 2.
Box 2: "The gold is in this box"
False. Gold not in 2.
No contradictions.
Gold must be in 1.
Answer: Gold is in Box 1
determine the equation of the circle centered at (3 comma space minus 2 ), with radius 4.
The center of the circle is (3 , -2) and the radius is 4 then the equation of circle is (x)² + (y)²-6x+4y = 3
What is a circle?
The circle is defined as the locus of the point traces around a fixed point called as the center and is equidistant from the outer trace.
All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
The equation of the circle is,
( x - h )² + ( y - k )² = r²
(x-3)² + (y+2)² = 16
(x)² + (y)²-6x+9 +4y+4 = 16
(x)² + (y)²-6x+4y = 3
Compare the equations and find the center and radius,
Center = ( h,k) = ( 3, -2)
Radius = r = 4
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4. Alfonso surveyed several students in his school. He asked them to give the grade that they are in and the number of pets they have at home. The results are shown in the table below.
Survey Results
Grade
5
6
2
1
4
2
4
1
4
3
5
Number of
Pets
0
4
2
3
5
1
2
2
0
5
2
Find the correlation coefficient for the data. Round to the nearest hundredth
EDIT: IT ISNT 0.35 , 0.36 nor 0.37 SOOO PLEASE REFRAIN FROM GIVING ME THISE ANSWERS!!!
Answer: sorry would help ya but i can't because i have no clue what the question is asking me to round...
Mains 10 kilograrA company uses copper and zinc in a ratio of 3:2 to manufacture bronze. How many kilograms of copper is needed to make a bronze sheet that contains 10 kilograms of Zinc?
Using the ratio, if a certain piece of brass requires 10kg of zinc, the weight of the copper required for the same piece is 15 kg.
What is ratio?A ratio expresses the frequency with which one number contains another. If a fruit dish contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six. Similarly, the orange to lemon ratio is 6:8, while the orange to total fruit ratio is 8:14.
Here,
Given that a company uses copper and zinc in a weight-to-weight ratio of 3:2 to make bronze. As a result, the metal ratio can be written as,
3/2 = copper/zinc
Now, because the zinc weighs 10 kilograms.
As a result, the ratio can be depicted as,
3/2 = copper / zinc
3/2 = copper / 10kg
3 x 10 /2 =copper
30/2 = copper
15 = copper
As a result, if 10kg of zinc is required for a specific piece of bronze, the weight of copper required for the same piece is 15kilograms.
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Pls help please pls please
Answer:
x=5/3 0r 1 2/3
Square ABCD has a diagonal AC with the given vertices. Find the coordinates of the remaining vertices.
A(2, 2) and C(6, - 2)
The coordinates are (_,_) and (_,_)
Square ABCD has a diagonal AC with the given vertices. Find the coordinates of the remaining vertices. A(2, 2) and C(6, - 2)
The coordinates are B(4,-2,) and (4,0)
What do you mean by coordinates?Coordinates are two numbers (Cartesian coordinates), or sometimes a letter and a number, that locate a specific point on a grid, known as a coordinate plane. A coordinate plane has four quadrants and two axes: the x axis (horizontal) and y axis (vertical). (One way of helping children to remember which of these is which is to tell them that the x axis goes across because ‘x’ is a cross.)
The Cartesian Coordinate System is the name of the two-dimensional plane that is used in math to calculate points using a set of perpendicular lines and basing the points on the place where the line meet. The plane is called a Cartesian plane and Perpendicular lines are lines that intersect at exactly 90 degrees, which makes a right angle.
If A(2,2) and C(6,-2) are the coordinates of two opposite vertices of the square, then the square is a rectangle with a diagonal AC. The remaining vertices of the square can be determined by using the fact that opposite sides of a square are parallel and congruent.
If A(2,2) is one vertex of the square, then the vertex opposite it is C(6,-2)
If C(6,-2) is one vertex of the square, then the vertex opposite it is A(2,2)
The vertex B(x,y) can be found by moving 2 units left from C(6,-2)
x = 6 - 2 = 4
y = -2
so B(4,-2)
The vertex D(x,y) can be found by moving 2 units up from B(4,-2)
x = 4
y = -2+ 2 = 0
so D(4,0)
Therefore, the coordinates of the remaining vertices of the square are B(4,-2) and D(4,0)
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sam runs a large chain of car repair shops. he pays his employees for 8 hours of work each day. the employees have to log the amount of time they spend working on each job, which results in a number of billable hours for each employee each day. sam would like to estimate the mean number of billable hours for the large number of employees at the company. to do so, he selects a random sample of 10 employees and asks them how many billable hours they tend to have each day. from their responses, he constructs a 95% confidence interval for the true mean number of billable hours for all employees in the company. which of the following may have an impact on the confidence interval, but is not accounted for by the margin of error?
Sampling variation will have more impact on confidence interval but it is not accounted for by the margin of error.
What is Sampling variation?
The term "sampling variance" describes how much a sample estimate (a statistic) is likely to fluctuate from sample to sample due to the unique nature of each sample.
Sample Sizes and Variability are the factors which lead to sampling variation. As and when the sample size is changed i.e. either increased or decreased, the variability of samples fluctuates.
Since, Sam runs a large chain of car repair shops, this means he has large number of employees.
But his sample size is only of 10 employees whom he asks about their billable hours from which he constructs a 95% confidence interval for the true mean number of billable hours for all employees in the company.
Since, sampling variation is greatly affected by the sample size and variability, therefore it will have more impact on confidence interval.
Hence, sampling variation will have more impact on confidence interval but it is not accounted for by the margin of error.
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Since the options are missing in the question, here are the options from which answer is to be chosen
response biasnonresponse biassampling variationundercoverage biasSolve equation 9x-3(x-5)=6x+3
Answer: x= -1
Step-by-step explanation:
9x-3(x-5)=6x+3
9x-3x+15=6x+3
9x+6x-3x= 3-15
15x-3x= -12
12x= -12
x= -1
find the distance between dallas, texas, whose latitude is n, and omaha, nebraska, whose latitude is n. assume that earth is a sphere of radius 4000 miles and that the cities are on the same longitude (omaha is due north of dallas). City Latitude
Dallas, Texas 32° 47' 39'' N.
Omaha, Nebraska 41° 15' 50'' N.
The distance between Dallas, Texas and Omaha, Nebraska is 631.4 miles.
The distance between Dallas, Texas and Omaha, Nebraska can be calculated using the Haversine Formula. This formula calculates the great circle distance between two points on a sphere, taking into account the curvature of the Earth. The formula is as follows:
d = 2r arcsin( sqrt[ sin^2((lat2 - lat1)/2) + cos(lat1)cos(lat2)sin^2((lon2 - lon1)/2)] )
In this case, the latitude of Dallas, Texas is 32° 47' 39'' N and the latitude of Omaha, Nebraska is 41° 15' 50'' N. Since the two cities are on the same longitude, we can assume that the longitude for both cities is 0°.
Plugging these values into the formula, we get:
d = 2(4000 miles) arcsin[ sqrt[ sin^2((41° 15' 50'' N - 32° 47' 39'' N)/2) + cos(32° 47' 39'' N)cos(41° 15' 50'' N)sin^2((0° - 0°)/2)] ]
d = 631.4 miles
Therefore, the distance between Dallas, Texas and Omaha, Nebraska is 631.4 miles.
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Can anyone please tell me the answers to the blue boxes please? Thank you
Answer:
The transaction amount for 3: -155.15
The transaction amount for 4: -223.75
Step-by-step explanation:
In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points is in the same quadrant as the fourth vertex of the square?A. (-5, -3)B. (-5, 3)C. (5, -3)D. (3, -5)E. (3, 5)
The point (-5,3) is in the same quadrant as the fourth vertex of the square.
The given points are representing the points in the quadrant of the cartesian coordinate system. According to this any location on a 2-D plane is represented by 2 numbers, x and y, where x represents the horizontal displacement from the origin of the plane and y represents the vertical displacement from the origin.
Since the given points are the vertices of a square they must be in the form (c, d), (c, -d), (-c, -d), and (-c,d). So, from the given points only the B (-5,3) satisfies the given condition and forms the square.
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out of 200 people sampled, 36 received flu vaccinations this year. based on this, construct a 99% confidence interval for the true population proportion of people who received flu vaccinations this year.
The 99% confidence interval for population proportion p is 0.117 < P < 0.243 for the true population proportion of people who received flu vaccinations this year when out of 200 people sampled, 36 received flu vaccinations this year.
Given that,
n = 200
x = 36
Point estimate = sample proportion
= x/n = 36/200 = 0.18
1 - p = 1 - 0.18 = 0.82
At a 99% level, the z is,
α = 1 - 0.99 = 0.01
α/2 = 0.005
Zα/2 = 0.005Z = 2.576
The margin of error = E = Zα/2 [tex]\sqrt{p(1-p)} /n[/tex]
= 2.576[tex]\sqrt{0.18*0.82} /200[/tex]
E = 0.063
A 99% confidence interval for population proportion p is,
p - E < P < p + E
0.18 - 0.063 < P < 0.18 + 0.063
0.117 < P < 0.243
Therefore, the 99% confidence interval for population proportion p is 0.117 < P < 0.243 for the true population proportion of people who received flu vaccinations this year when out of 200 people sampled, 36 received flu vaccinations this year.
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if there are 5 people and 2 have to sit next to each other and 2 others cant sit next to each other, how many combinations
if there are 5 people and 2 have to sit next to each other and 2 others cant sit next to each other, then 30 combinations possible
What are combinations?
A combination is a calculation that determines the number of possible arrangements in a collection of items in which the order of the selection does not matter. In combinations we can select the items in any order.
nn!/r!(n-r)!
Number of ways=5
=5!/2!2!
=5!/2*2
=5*4*3*2/2*2
=30
=30 ways
if there are 5 people and 2 have to sit next to each other and 2 others cant sit next to each other, then 30 combinations possible
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i need the Quadratic formula answer
a jar holds five lollipops: three red and two yellow. if you remove and replace three lollipops after every draw, find the probability of drawing the same color lollipop twice.
The probability of drawing the same color lollipop twice is 0.72.
According to the given question, 3 lollipops were picked up one by one, but after every draw, the lollipop is kept back in the jar. So it is a case of sampling with replacement.
Thereby, there will be 6 cases when the same color i.e red & yellow lollipops will be picked up 2 times i.e, rry, ryr, yrr, yry, yyr, ryy
(where r & y stand for red and yellow lollipops respectively)
And the corresponding probabilities for these six situations will be
(i) 3/5∗3/5∗2/5=18/125
(ii) 3/5∗2/5∗3/5=18/125
(iii) 2/5∗3/5∗3/5=18/125
(iv) 2/5∗3/5∗2/5=12/125
(v) 2/5∗2/5∗3/5=12/125
(vi) 3/5∗2/5∗2/5=12/125
Hence, the required probability will be the sum of all these probabilities i.e,
(i)+(ii)+(iii)+(iv)+(v)+(vi)
=3∗(18/125)+3∗(12/125)
=90/125
so, the probability that the same color Lollipop will be drawn two times is 90/125 or 0.72.
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BRAINLIEST ANSWER
please help me answer this question
thanks
-Jake
Answer:
I1 ≈ 103.6∠68.7° mA
I2 ≈ 163.7∠50.3° mA
Step-by-step explanation:
Given equations for mesh currents, you want to find their values in polar form.
(2+j6)I1 -(j4)I2 = 0(j1)I1 +(8-j10)I2 = 2SolutionThe coefficients of these equations can be used to fill an augmented matrix, which can then be reduced by a suitable calculator to give the values of the variables.
I1 = (14+j36)/373 ≈ 0.1036∠68.7°
I2 = (39+j47)/373 ≈ 0.1637∠50.3°
__
Additional comment
The equations can be solved "by hand" using any of the usual methods: substitution, elimination, Cramer's Rule, and others. The complex arithmetic makes it tedious, but not significantly more difficult. A suitable calculator reduces the work substantially.
The second attachment shows more working using the "cross multiplication method", similar to Cramer's Rule.
in the hypothesis test, the decision between one sided and a two sided alternative hypothesis is based on..
a) which one gives you a significant result
b) the alternative hypothesis appropariate for the context of the problem
c) how accurate you wish the reults of the test
d) the level of significance of the test
e) the statement of the null hypothesis
The decision between one sided and two sided alternative hypothesis is based on the statement of the null hypothesis and the alternative hypothesis appropriate for the context of the problem.
The hypothesis test is used to check if the observed data is consistent with the expected data or not. To do this, a null hypothesis and an alternative hypothesis are formulated. The decision between one sided and two sided alternative hypothesis is based on the statement of the null hypothesis and the alternative hypothesis appropriate for the context of the problem. The one-sided alternative hypothesis is used when the researcher is mainly interested in testing whether the population mean is either greater than or less than a given value. On the other hand, the two-sided alternative hypothesis is used when the researcher is mainly interested in testing whether the population mean is either different from or not different from a given value. The level of significance chosen for the test should be determined before the decision is made between one sided and two sided alternatives.
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If A and B are independent events of random experiment such that P(A∩B)=1/6 and P(A ∩ B)= 1/3, then P(A)=a. 1/4b. 1/5c. 1/2s. 2/3
C) 1/2 is the value of P(A)
What is independent events?Independent events are events in probability and statistics that have no effect on each other and are not related to each other in any way, so the outcome of one event does not affect the outcome of the other event.
let the value of P(A) be x and the value of P(B) be y given A and B are independent events
so P(A∩B) = P(A) * P(B)
=> x*y=1/6 ---(i)
now P(⁻A) = 1 - P(A) , P(B) = 1 - P(⁻B)
so P( ⁻A ∩ ⁻B ) = (1-x)*(1-y)
=> 1 -x - y +xy = 1/3
=> x +y =1+1/6-1/3
=> x + y = 5/6 ----(ii)
x - y = √(x+y)²-4xy
=> √(5/6)² - 4*1/6
=> √25/36 - 4/6
=> √(25-24)/36
=> √1/36
=> 1/6
so x-y = 1/6 ---(iii)
adding equation (ii) and (iii) we get
2x = 1
=> x = 1/2
so P(A) = 1/2
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Complete question :
If A and B are independent events of random experiment such that P(A∩B)=1/6 and P( ⁻A ∩ ⁻B )=1/3, then P(A)=?
a. 1/4b. 1/5c. 1/2s. 2/3
