The method of least squares of residuals is commonly used to get the best fit with linear regression. The reason why the absolute value of residual's (|y- ypred|) is not used is as follows :
Although least squares purposefully square the error in the belief that it will respond better when values deviate from your projected value, you could run something similar if you so desired.
Consider the following scenario: You plot your data's real values on a graph, and you observe a straight line of numbers with a few outliers that have greater values than you would expect. You could be tempted to believe that the best fit is a straight line along the values. Because the real pattern must take into account all the values that occurred, least squares adapt more to the outliers than other values and purposefully squares values, sort of assuming that the straight line of actual values was a coincidence.
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Paint is being applied to a rectangular wall. A diagram of the wall is shown below.
The cost of the paint is $3.45 per square foot. What will it cost in total to paint the wall?
( 12.5ft , 18ft.)
It will cost $776.25 to paint the area of the rectangular wall
Area of a RectangleThe area can be defined as the amount of space covered by a flat surface of a particular shape. It is measured in terms of the "number of" square units (square centimeters, square inches, square feet, etc.) The area of a rectangle is the number of unit squares that can fit into a rectangle. Some examples of rectangular shapes are the flat surfaces of laptop monitors, blackboards, painting canvas, etc.
The formula of area of a rectangle is given as;
A = L * W
l = lengthw = widthImputing the values and calculate the area of the rectangular wall;
A = 12.5 * 18
A = 225ft²
But in the question, the cost of painting the wall is $3.45 per square feet.
1ft² = 3.45
225 = x
x = 3.45 * 225
x = 776.25
The cost of painting the wall is $776.25
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at the start of 2014 tims house was worth £100,000
the value of the house increased by 10% every year
work out the value of his house at the start of 2018
The value of Tim's house at the start of 2018 is £146410
How to determine the value of his house at the start of 2018?From the question, we have the following parameters that can be used in our computation:
Initial value = 100,000
Rate of increase = 10%
The value of the house x years after 2014 can be represented as the following exponential function
Value = Initial value * (1 + rate)ˣ
So, we have
Value = 100000 * (1 + 10%)ˣ
2018 is 4 years after 2014
This means that x = 4
So, we have
Value = 100000 * (1 + 10%)⁴
Evaluate
Value = 146410
Hence, the value is #146410
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PLEASE HELP
which of the following equations represents a linear function?
x = 1
y equals one third times x squared
y equals one fourth times x minus 1
4x − 2 = 6
Answer:
the third opinion: [tex]y = \frac{1}{4}x - 1[/tex] (or as you put it, y equals one fourth times x minus 1)
This is because it's written in slope-intercept form: y = mx + b . m is the slope, which is 1/4, and b is the y-intercept, -1
In order to package products for her business class, Jessica needs to determine the size of a
box in which they would fit. To meet shipping specifications, the volume of the box should be
6x215x-36. The box is in the shape of a rectangular prism. The width of the box must be
3, and the length of the box must be x - 4. What expression can represent the height of the
box?
According to the volume of the box, the height of the box is (2x + 3)
Volume:
Volume is defied as the space occupied within the boundaries of an object in three-dimensional space.
Given,
In order to package products for her business class, Jessica needs to determine the size of a box in which they would fit. To meet shipping specifications, the volume of the box should be 6x² - 15x-36. The box is in the shape of a rectangular prism. The width of the box must be 3, and the length of the box must be x - 4.
Now, we have to find the expression or the height of the box.
From the given details, we know that,
Volume of the box = 6x² - 15x-36
Width of the box = 3
length of the box = x - 4
Let us consider the height of the box is h.
By using the volume of the box formula, we have calculated the height of the box as,
=> 6x² - 15x-36 = (3) × (x-4) × h
Here we need the value of h,
The given expression is rewritten as,
=> (6x² + 15x-36) / 3(x - 4) = h
When we factorize the numerator, then we get,
=> 3(2x + 3)(x - 4)/3(x-4) = h
Therefore, the expression for h is 2x + 3.
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true or false: of all possible samples of 100 stores taken from the population of 1,000 stores, 95% of the confidence intervals developed will contain the true population mean within the interval.
For all possible samples of 100 stores taken from the population of 1,000 stores, 95% of the confidence intervals developed will contain the true population means is true or false depending on the points shown below.
A. Referring to the problem statement, if the population had consisted of 10,000 stores, the confidence interval estimate of the mean would have been wider in the range is false since increasing sample size will decrease the width of the confidence interval
B. Referring to the problem statement, of all possible samples of 100 stores drawn from the population of 1,000 stores, 95% of the sample means will fall between 5.623 and 6.377 lawnmowers is false since the interval is for the population mean and not the sample mean.
C. Referring to the problem statement, of all possible samples of 100 stores taken from the population of 1,000 stores, 95% of the confidence intervals developed will contain the true population mean within the interval is true.
D. Referring to the problem statement, 95% of the stores have sold between 5.623 and 6.377 lawnmowers is false.
E. Referring to the problem statement, we do not know for sure whether the true population means between 5.623 and 6.377 lawnmowers sold is true since this is a confidence interval that has only 95% confidence to contain the true population means.
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cleveland cove enterprises is evaluating the purchase of a lift system for all of its locations to use for boat repair. information on the b14 model, one of the options is listed below:
The net present value formula helps us to determine the net present value of boat repair model B14 model by Cleveland Cove enterprises.
so, the net present value is 384,285.714.
Net present value: The net present value is applied to a series of cash flows occurring at different times. The present value of a cash flow always depends on the interval of time between now and the cash flow.
NPV = Rt /(1+i)^t
where , Rt --> net cash flow at time t
i --> discount rate
t --> time of cash flow
We have given that , A company has narrowed their choices down to two: the B14 Model and the F54 Model.
F54 Model :
Residual value , = 18,000
Annual net cash inflow = 30,000
investment = 230,000
time , t = 10
rate of return,r = 12%
B14 Model :
Residual value , = 10,000
Annual net cash inflow = 80,000
investment = 330,000
time , t = 10
rate of return,r = 8%
we have to calculate the net present value for model B14.
so, Net present Value = present value of annually cash - investment
present value of annually cash
= 80000/1.12 = 71,428.571
Net present value =71,428.571 ×10 - 330000
= 714,285.71 - 330,000 = 384,285.714
hence, net present value for model B14 is 384,285.714
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Complete question:
Cleveland Cove Enterprises is evaluating the purchase of an elaborate hydraulic lift system for all of its locations to use for the boats brought in for repair. The company has narrowed their choices down to two: the B14 Model and the F54 Model. Financial data about the two choices follows. B14 Model investment 330,000 useful life (yr) 10 , estimated annual cash inflow 80,000
F54 Model Investment 230 comma 000 Useful life (years) 10 10 Estimated annual net cash inflows for useful life 33 comma 000 Residual value 18 comma 000 Depreciation method Straightminusline Straightminusline Required rate of return 12% 8% What is the net present value of the B14 Model?
Order the numbers from least to greatest.
Put the lowest number on the left.
A) 2. 95 B) 2. 509 C) 2. 925
The orders numbers from least to greatest are 2.509, 2.925, and 2.95 respectively.
What is ascending order?
When numbers are arranged in ascending order, they are done so from least to greatest.
Ordering Decimal from Least to Greatest.
Compare each decimal's whole number component first. The smallest number is the one with the smallest entire number.
Compare the decimal parts in the same way as we compare the whole numbers if the whole number parts are the same.
Given, 2. 95, 2. 509, 2. 925
Arranging numbers from least to greatest, we get
2.509, 2.925, 2.95
Hence, the order numbers from least to greatest are 2.509, 2.925, and 2.95 respectively.
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the following are six observations collected from treatment 1, four observations collected from treatment 2, and five observations collected from treatment 3. test the hypothesis at the 0.05 significance level that the treatment means are equal. treatment 1 treatment 2 treatment 3 9 13 10 7 20 9 11 14 15 9 13 14 12 15 10 required: a. state the null and the alternate hypotheses.
The Null hypothesis:
H₀: μ₁=μ₂=μ₃
Alternative hypothesis:
H₁: Treatment means are all not same.
Given that,
Test the idea that the treatment means are equivalent at the 0.05 level of significance using the following data: six observations gathered from treatment 1, four observations gathered from treatment 2, and five observations gathered from treatment 3. treatment 1 therapy two therapies Required: 3 9 13 10 7 20 9 11 14 15 9 13 14 12 15 10.
We have to find name the null and the alternative hypotheses.
We know that,
For the given scenario, the null and alternative hypotheses are stated as below:
Null hypothesis:
H₀: μ₁=μ₂=μ₃
Alternative hypothesis:
H₁: Treatment means are all not same.
Therefore, The Null hypothesis:
H₀: μ₁=μ₂=μ₃
Alternative hypothesis:
H₁: Treatment means are all not same.
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What is the base of an triangle that has an area of 24 square units and a height of 12 units
Answer:
base is 4 units
Step-by-step explanation:
the formula for a triangle is (b x h)/2= a
So we can fill in what we know
(b x 12)/2=24
Our goal is to solve for b or the base
12b/2=24
X2. x2
12b=48
/12. /12
b=4
Hopes this helps please mark brainliest
Consider the reflection of parallelogram pqrs across the line of reflection, line w y. if rr' = 14, then rz = . if sx = 5, then = 5.
The correct answer is 7XS when RR' = 14, then RZ = 7 when the parallelogram PQRS is reflected across the line of reflection.
Given that,
If RR' = 14, then RZ = 7 when the parallelogram PQRS is reflected across the line of reflection.
SX = 5 if Y = 5.
What is parallelogram?In Euclidean geometry, a parallelogram is a straightforward (non-self-intersecting) quadrilateral with two sets of parallel sides.
A parallelogram has equal-length opposing angles and facing or opposing sides.
The Euclidean parallel postulate or one of its equivalent formulations must be used in order to demonstrate the congruence of opposite sides and angles because both requirements flow naturally from this postulate.
A quadrilateral with only one pair of parallel sides, on the other hand, is referred to in British or American English as a trapezoid or trapezium.
We get,
The parallelepiped is a three-dimensional representation of a parallelogram.
So, 7 XS is the right response to the question.
Therefore, The correct answer is 7XS when RR' = 14, then RZ = 7 when the parallelogram PQRS is reflected across the line of reflection.
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Answer:
1. 7
2. XS
Step-by-step explanation:
find the 10th nth term of 2n²
Answer:
Step-by-step explanation:
Their food and beverage cot $25. 30 and there i an 8% meal tax After adding a tip, the total lunch cot wa $32. 24. What percentage tip did they give? Enter your anwer to the nearet percentage
A tip of 18% was given to the restaurant after the meal and tax to the nearest percentage.
Cost of the food = $25.30
Tax on the food cost = 8%
Tax amount
= 8% of 25.30
= 0.08 × 25.30
= 2.204
Total cost of food before tip = 25.30 + 2.204 = $27.504
Tip given = 32.24 - 27.504 = 5.036
Tip percentage
= 5.036 / 27.504 × 100%
= 18.31%
≈ 18%
Hence a tip of 18% was given to the restaurant after the meal and tax to the nearest percentage.
Percentage increases and decreases are calculated by computing the difference between two numbers or by comparing that difference to the starting value.
One can calculate how significantly the initial value has changed mathematically by dividing the result by the starting value and using the absolute value of the difference between the two values.
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What is the equation of the given line in slope-intercept form?.
The equation of given line in slope-intercept form is 5x – 4y + 20 = 0 if the line makes intercepts –4 and 5 on the x- and y-axes respectively.
The diagram of the straight condition y = mx + c is a line with m as incline, m and c as the y-block. This type of the direct condition is known as the incline block structure, and the upsides of m and c are genuine numbers. The incline, m, addresses the steepness of a line. The incline of the line is additionally named as inclination, in some cases. The y-catch, b, of a line, addresses the y-direction of the place where the chart of the line converges the y-hub.
We have x-intercept as -4 and y-intercept as 5
Equation of the line in intercept form is:
(x/a) + (y/b) = 1
Substituting the values of a and b, we get the equation as:
=>(x/-4) + (y/5) = 1
=>(-5x + 4y)/20 = 1
-=>5x + 4y = 20
=>5x – 4y + 20 = 0
Hence, line equation is 5x – 4y + 20 = 0
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(Complete question) is:
What is the equation of the given line in slope-intercept form if x-intercept is -4 and y intercept is 5?
a juice drink filling machine, when in perfect adjustment, fills the bottles with 14 ounces of drink on an average. a random sample of 41 bottles is selected, and the contents are measured. the sample yielded a mean content of 13.89 ounces with as a standard deviation of 0.3485 ounces.
On using the critical value (13.89 – 0.3485, 13.89 + 0.3485) when, the mean is13.89 the confidence level is 95%.
Given, a juice drink filling machine, when in perfect adjustment, fills the bottles with 14 ounces of drink on an average. a random sample of 41 bottles is selected, and the contents are measured.
as the standard deviation = 0.3485 ounces
mean = 13.89 ounces.
we have to find the confidence level,
The critical value we will use is (13.89 – 0.3485, 13.89 + 0.3485) when, the mean is 13.89.
The confidence interval for a population with a known standard deviation is based on the fact that the sample means follow an approximately normal distribution. Suppose
So, on using the critical value (13.89 – 0.3485, 13.89 + 0.3485) when, the mean is13.89 the confidence level is 95%.
Hence, on using the critical value (13.89 – 0.3485, 13.89 + 0.3485) when, the mean is13.89 the confidence level is 95%.
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can you guys please answer this? its timed so dont take too long!
The simplified expression is - (4z⁴ + 4z³ - 14z² - 47z - 70) / z + 2
Simplification of ExpressionSimplification of an algebraic expression can be defined as the process of writing an expression in the most efficient and compact form without affecting the value of the original expression.
The process entails collecting like terms, which implies adding or subtracting terms in an expression.
In the given expression;
7 - 2z - 4 [z³ - (z³ + 4z² + 11z + 14) / (z + 2) ]
This is simplified to ;
7 - 2z - 4 [z³ - (z³ + 4z² + 11z + 14) / (z + 2) ] = - (4z⁴ + 4z³ - 14z² - 47z - 70) / z + 2
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a 23.0 kg kg bucket of water is suspended by a very light rope wrapped around a solid uniform cylinder 0.300 mm in diameter with mass 13.0 kgkg. the cylinder pivots on a frictionless axle through its center. the bucket is released from rest at the top of a well and falls 10.0 mm to the water.
Total force exerted is 50N.
What is force?
Force is any interaction that, when unopposed, will change the motion of an object.
Main body:
F=Mg-Ma
then implied:
a=(F-Mg)/M
which seems unsound, it should have said:
a = (Mg - F)/M
----------------------
Now, let's begin and use the previous gentleman's notation:
Mass of bucket=M
mass of cylinder=m
Tension force=F
So, regarding the bucket:
F + Ma = Mg
F = Mg - Ma
a = (Mg - F)/M
Also, regarding the cylinder: T = Iα
∴ (By the dot product of torque, radial vector crossed with force, r cross F, which is Frsinθ for θ = 90 degrees)
T = Iα = Fr = (1/2)(mr2)(a/r)
where α = a/r
And T = Fr because that's what torque is, just the radial distance times the force.
So
a = 2F/m
and we also have:
a = (Mg-F)/M
So 2F/m = (Mg-F)/M
2F = mg - mF/M
2F+(mF)/M = mg
F(2+m/M) = mg
F = mg/(2+m/M)
F = (127.4 )/(2+0.56)
F = 49.765 N
That is to say, the tension that the rope induces on the bucket is 50.5 Newtons in the upward direction (positive).
Hence force exerted is approx 50 N.
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Modeling an Equation
Use the algebra tiles to model the equation
2x + 4 = 3x + (−1). Then complete the sentences.
To model 2x + 4, you need:
positive x-tiles to represent 2x.
positive unit tiles to represent 4.
To model 3x + (−1) you’ll need:
3
x-tiles to represent 3x.
1
unit tile to represent –1.
The sentences is completed as follows
To model 2x + 4, you need:
2 positive x-tiles to represent 2x4 positive unit tiles to represent 4To model 3x + (−1) you’ll need:
3 positive x-tiles to represent 3x1 negative unit tile to represent –1What is algebra tile models?An algebra tile model is a graphic representation made out of various arrangements of algebra tiles. A model's function is to depict a polynomial expression or equation.
Algebra tiles it self are shapes of different colors that represents numbers or parts of numbers.
In the question, algebra tiles are used to represent the equations used in the problem. The tiles in the problem will be of 3 types
x-tilespositive unit tiles negative unit tiles2x + 4
In this case, the equation will require the twice the x-tiles then 4 positive unit tiles
3x + (−1)
In this case, the problem is represented using 3 x-tiles and 1 negative unit tile.
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Answer:2,4,positive,negative
Step-by-step explanation:
A random sample of 15 new born babies are taken from a large hospital.
Weight in pounds are given below:
9.2, 6.5, 4.3, 5.5, 7.2, 9.5, 11.2, 8.5, 5.2, 4.7, 11.0, 7.4, 8.2, 6.9, 4.1
Use R to answer the following:
The hospital claims that average weight of all the babies in population is greater than 7.5 lbs.
(a)Write five steps to Test this claim using alpha= 5%. Use critical value method.
(b)Write five steps to Test this claim using alpha= 5%. Use p- value method.
The p-value statistic to test the claim that the average weight of all babies is greater than 7.5 lbs. is 7.293.
a) Data set : 9.2, 6.5, 4.3, 5.5, 7.2, 9.5, 11.2, 8.5, 5.2, 4.7, 11.0, 7.4, 8.2, 6.9, 4.1
mean of the data set = sum / frequency
mean = 7.293.
Standard deviation
= √(871.96-797.98)/14
= 2.3001
Hence the point of estimate = 7.293
b) Using p-value> q(.80)
p> 1.282
And the sample average is just mean(x)
p>7.2933
So our margin of error is
e <- 1.282*(2.3001/sqrt(15))
e<0.7614
The lower and upper bounds are:
= mean(x) - e = 6.5319
= mean(x) + me = 8.0547
Hence the lower and upper bounds for the p-value will be 6.5319 and 8.0547 .
A statistical calculation known as a p-value is employed to assess the applicability of a hypothesis to the data. A p-value establishes the likelihood that the outcomes that were observed would occur if the null hypothesis were true. The found difference becomes statistically more significant as the p-value decreases.
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excel's can be used to construct a crosstabulation. chart tools sum function pivottable report countif function
Excel's PivotReport Table can be used to construct a crosstabulation.
What is Pivot Report Table?
Data summaries are created using pivot tables. Large data sets can be processed automatically, and the resulting report can include groupings of the data as well as count totals, averages, sums, and other calculations. Pivot report tables offer insight that could be challenging to perceive otherwise.Here is a table with sales data in its original format as an illustration. It includes a list of the goods that salespeople offer. However, it is challenging to evaluate the effectiveness of each salesperson or determine which product brings in the most money. A pivot report table can be used to quickly access data and accurately answer these queries.To know more about pivot report table check the below link:
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g a spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.1 cm/min. at what rate is the volume of the snowball decreasing when the radius is 12 cm. (note the answer is a positive number).
Rate at which volume of the snowball decreasing when the radius is 12 cm is 180.864 cm^3/min
Given:
a spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.1 cm/min. at what rate is the volume of the snowball decreasing when the radius is 12 cm.
Let r be the radius of the spherical snowball
Radius is decreasing at rate of 0.1 cm/min.=> dr/dt = -0.1
(negative sign indicates decreasing)
Volume v = 4/3πr^3
dv/dt = 4/3 π 3r^2*dr/dt
= 12π/3*r^2*(-0.1)
= 4π*12^2*(-0.1)
= 4π*144*-1/10
= 4π*(-14.4)
= -57.6π
= 180.864 cm^3/min
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Use a translation rule to describe the translation of x that is 5 units to the left and 7 units up.
Translation of x with 5 units to the left is ( x + 5 ) and 7 units up is ( x + 7 ) .
As given in the question,
The translation represents the movement of the original shape in the coordinate plane.
Translation of x for the given conditions :
5 unit to the left :
Here function shift 5 units to the left by adding 5 in the function.
x → ( x + 5 )
7 units up
Function shift 7 units up by adding 7 in the function.
x → ( x + 7 )
Therefore, translation of the function by 5 units left is x+5 and 7 units up is x + 7.
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What is the equation of the line that passes through the point (5,4) and has a slope of 2
Answer:
y=2x-6
Step-by-step explanation:
y-4=2(x-5)
y-4=2x-10
+4
y=2x-6
Which pair of triangles can be proved congruent by ASA?.
Answer: If any two angles and the side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by ASA rule.
The Angle Side Angle Postulate (ASA) says triangles are congruent if any two angles and their included side are equal in the triangles. An included side is the side between two angles.
Step-by-step explanation:
FILL IN THE BLANK. For a function to have an inverse, it must be ___. to define the inverse sine function, we restrict the__ of the sine function to the interval ___.
As per the concept of inverse function, For a function f: X → Y to have an inverse, it must have the property that for every y in Y, there is exactly one x in X such that f(x) = y.
Inverse function:
Inverse function refers a function that serves to “undo” another function.
Given,
Here we need to find the a function to have an inverse, it must be what type of function.
Based on the explanation of the inverse function, if the function is a inverse function, then it means that for all x values must have the relation in y similarly, for a the y values must have the x values.
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a 12-lb weight is attached both to a vertically suspended spring that it stretches 6 in. and to a dashpot that provides 3 lb of resistance for every foot per second of velocity. if the weight is pulled down 1 ft below its static equilibrium position and then released from rest at time t
The weight is pulled down 1 ft below its static equilibrium position and then released from rest at time t the phase angle is α=π÷16.
The mass in fps gadgets is m = 0.375 and the spring consistent is [tex]k = 12/5 × (lb)/(lt) = 24lb / ft .[/tex]
The round frequency is given through [tex]ω{0} ^ 2 = k/m = 64 , so ω{0} = 8rad / s[/tex] The damping consistent is[tex]c = 3lb - s / ft so p = i/(2m) = 4[/tex], and the machine is consequently underdamped. Then [tex]ω= (ω{0} ^ 2 - p ^ 2) = sqrt(48) = 4^(3)[/tex]so the overall answer is
[tex]x(t) = Ac ^ (- 4t) cos 4 t + B * c ^ (- 4t) * sin 4 ^3t\\v(t) = A * e ^ (- 4t) * (- 4cos 4 ^3 t - 4^3\\sin 4 * ^3 t) + B * e ^ (- 4t) * (- 4sin 4 * 63 t + 4^3 cos 4 ^3* t)[/tex]
We degree the displacement vertically, thinking about a displacement downwards as being positive, because it corresponds to stretching the string further.
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If the original price is 120 and the percent of discount is 80 what’s the new price
Answer:
24
Step-by-step explanation:
120 minus 80% = 120 times 20% (fractions division method)
120 times 20% = 120 times 0.2 (simplify)
120*0.2 = 24, so the answer is 24
how many bytes difference will there be in the amount of memory allocated by the following code on the intel ia 32 versus the intel x86-64?
By using operations on integers, it can be calculated that
Difference between the amount of memory allocated by char*arr[3] on the intel ia 32 versus the intel x86-64 is 12 bytes
What is operation on integers?
At first it is important to know about integers
Integers are those numbers without any fractional part. Integers can be positive or negative and zero is also an integer.
The operation on integers are
Addition
Suppose there are numbers and the sum of those numbers has to be calculated. For this addition is used
Subtraction
To find the difference between two integers, subtraction is used
Multiplication
Repeated addition is called multiplication. Multiplication is used to find the product of two or more integers
Division
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
This problem can be solved using operation on integers
On Intel IA 32, the address is 32 bit or 32 [tex]\div[/tex] 8 = 4 bytes
On Intel x86 - 64, the address is 64 bit or 64 [tex]\div[/tex] 8 = 8 bytes
On an array of size 3,
On Intel IA 32, the address is 4 [tex]\times[/tex] 3 bytes = 12 bytes
On Intel x86 - 64, the address is 8 [tex]\times[/tex] 3 bytes = 24 bytes
Difference between the address = 24 - 12 = 12 bytes
Difference between the amount of memory allocated by char*arr[3] on the intel ia 32 versus the intel x86-64 is 12 bytes
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Complete Question
how many bytes difference will there be in the amount of memory allocated by the following code on the intel ia 32 versus the intel x86-64?
char*arr[3]
A psychologist studied the number of puzzles subjects were able to solve in a 5 minute period while listening to soothing music. Let X be the number of puzzles completed successfully by a subject. The psychologist found that X had the following probability distribution: Value of X Probability 1 0.2 3 0.3 4 0.1 The probability that a randomly chosen subject completes at least three puzzles in the 5-minute period while listening to soothing music is Answer 2 Points I Tables Ke Keyboard She 01.09 0.03 00.4 06
The probability that a randomly chosen subject completes at least three puzzles in the 5 minute period while listening to soothing music is 0.4.
Probability is the branch of discrete mathematics. It is used for calculating how likely an event is to occur or happen. The probability of a random variable can be given by,
⇒ f ( x ) p ( x ) = P ( X = x )
As per the question,
Puzzle subjects can be solved in 5 minsNumber of puzzles completed successfully by a subject = XThe value of X and the probability is as follows:P ( X = 1 ) = 0.2
P ( X = 2 ) = ?
P ( X = 3 ) = 0.3
P ( X = 4 ) = 0.1
⇒ P ( X ≥ 3 ) = P ( X = 3 ) + P ( X = 4 )
= 0.3 + 0.1
P ( X ≥ 3 ) = 0.4
Therefore, 0.4 is the probability that a randomly chosen subject completes at least three puzzles in the 5-minute period while listening to soothing music.
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The complete question is
A local boutique is having a sale on sweaters, but customers are not aware of the sale until they are already in the store. In other words, there is no advertising of the sale other than signs in the back of the store that cannot be seen from the outside. All sweaters are marked as 15% off. Is this price discrimination?
Yes
No
No, there is no price discrimination in the given question
Price discrimination is a marketing strategy where a firm levies its customers variously for a similar commodity based on the standards they have set. It is offering customers various products at various price points based on their purchasing power and demographics.
Since the retailer does not charge different prices for various products, there is no price discrimination in the given question. It cannot be argued that a local boutique owner is engaging in price discrimination if they offer a discount to a customer who is unaware of it without asking them first. Additionally, it is no priced discrimination if the shop owner does not give more than a 15% discount or any incentives for purchasing in bulk.
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is the absolute value of an integral always less than integral of absolute value for lebesgue integrals
YES, the absolute value of an integral is always less than the integral of the absolute value for Lebesgue integrals.
An integral is like a sum, but fancier. So look at a sum 1+(-5)+2+(-3)=-5. Take the absolute value, |1+(-5)+2+(-3)|=5. But, if you take the absolute value of the individual terms and then add them, you get |1|+|-5|+|2|+|-3|=1+5+2+3=11. 11>5
The reason is that when you add them all up and then take the absolute value, the positive and negative terms of the sum get to cancel each other out and make the absolute value of the sum greater overall. When you take the absolute value of individual terms, you force them all to "point in the same direction" (positive) so they are working together and the sum gets higher.
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