Measurements taken in a different frame of reference reveal a decrease in their dimensions—the only component that is parallel to the motion—and a delay in time—commonly referred to as "Length Contraction" and "Time Dilation"
when the objects are moving at a speed that is comparable to the speed of light and is in the order of C. The following is a discussion of the given relativistic issue.
The length AC is the only length that observers using the platform frame of reference would perceive as being shorter (the length).
What is change in measurement?
Estimation of progress alludes to the evaluation of fluctuation from one viewpoint, and to the appraisal of progress in a smaller sense then again. Short-term and reversible fluctuations (such as mood state variability) are characteristics of variability.
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the birth weight of newborns, measured in grams, is an example of . a. quantitative data b. either categorical or quantitative data c. neither categorical nor quantitative data d. categorical data
The birth weight of newborns, measured in grams, is an example of quantitative data. So the option a is correct.
In the given question,
The birth weight of newborns, measured in grams, is an example of .
a. quantitative data
b. either categorical or quantitative data
c. neither categorical nor quantitative data
d. categorical data
The quantitative data means data that is explain in the subjective ways. It is also explain quantity, amount and range.
Categorical data is a body of knowledge that is organised into categories. For instance, the data obtained when an organisation or agency tries to collect the biodata of its employees is referred to as categorical data.
The birth weight of newborns measured in grams, is an example of quantitative data.
Birth weight is quantitative because it can take on multiple numerical values. So the option a is correct.
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2 of 8
The angle marked a = 109⁰.
Work out the angle marked x.
Answer:
x = 71 degrees
Step-by-step explanation:
Answer:
Step-by-step explanation:
180-109
x=71
The two polygons are similar, find the missing length. (the ?)
4 is the length of missing length of polygon.
What are Polygons?Polygon, in geometry, any closed curve consisting of a set of line segments (sides) connected such that no two segments cross. The simplest polygons are triangles (three sides), quadrilaterals (four sides), and pentagons (five sides)
Similar polygons are two polygons with the same shape, but not the same size. Similar polygons have corresponding angles that are congruent, and corresponding sides that are proportional.
16/2=8
15.4/2=7.7
16/2=8
8/2=4
Hence, 4 is the length of missing length.
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How do you know what is ABC on a triangle?.
The three angles of the triangle ABC are ∠ABC, ∠BCA, and ∠CAB. These angles are also called ∠B, ∠C, and ∠A, respectively.
What does ABC mean in a triangle?
In triangle ABC, the sides are AB, BC, and CA. The angle formed by any two sides of a triangle is the angle of the triangle, denoted by the symbol ∠. A triangle has three angles. The three angles of the triangle ABC are ∠ABC, ∠BCA, and ∠CAB. These angles are also called ∠B, ∠C, and ∠A, respectively.
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The pumped-storage hydroelectricity pumps water from the lower elevation reservoir to a higher elevation to store electricity. Suppose that the water is pumped out
from the upper elevation which is h meters above the top to the lower reservoir. The
lower reservoir has the shape of half ball with radius r meters. The lower reservoir is
full at the beginning. How much work should be done given the density of water is ρ
kg/m3? You do not need to replace the acceleration g as 9.8m/sec2. Just leave g in
the expression.
The work done by the water from the reservoir, traveling a distance, h, meters, can be found using the expression; (2/3)·π·r³×ρ×g×h
What is the relationship between work energy and power?Energy is the ability to do work, and power is the rate at which work is done.
The work done is the product of the force applied and the distance traveled in the direction of the force.
Radius of the reservoir = r
Density of the water = ρ
Height of the upper elevation = h
Gravitational acceleration = g
The force is the weight of the water pumped
Weight = Mass × Gravity
Mass = Density × Volume
Therefore;
Volume of the water = (2/3)·π·r³
Mass of the water = (2/3)·π·r³ × ρ
Weight of the water = (2/3)·π·r³ × ρ × g
The work done by the water is therefore;
The work that should be done is, W = (2/3)·π·r³ × ρ × g × h
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Airlines typically accept more reservations for flight than the number of seats on the plane. Suppose that for certain route an airline accepts 40 reservations on plane that carries 38 passengers Based on experience the probability distribution of Y = the number of passengers who actually show up for randomly selected flight is given in the following table You can check that Hlr 37.4 and "- 1.24 Number of passengers Yi 35 36 37 38 39 40 Probability pi 0.10 0.10 0.30 0.35 0.10 0.05 There is also crew of two flight attendants and two pilots on each flight Let X = the total number of people (passengers plus crew) on randomly selected flight
The probability that there are not enough seats left is given by:
0.15 = 15%.
How to obtain the probability?The probabilities in this problem are given from the discrete probability table, as follows:
P(X = 35) = 0.1 -> exactly 0.1 = 10% probability that exactly 35 passengers show up.P(X = 36) = 0.1 -> exactly 0.1 = 10% probability that exactly 36 passengers show up.P(X = 37) = 0.3 -> exactly 0.3 = 30% probability that exactly 37 passengers show up.P(X = 38) = 0.35 -> exactly 0.35 = 35% probability that exactly 38 passengers show up.P(X = 39) = 0.1 -> exactly 0.1 = 10% probability that exactly 39 passengers show up.P(X = 40) = 0.05 -> exactly 0.05 = 5% probability that exactly 40 passengers show up.There will not be enough seats if:
Exactly 39 or 40 passengers show up.
Hence the probability is given as follows:
p = P(X = 39) + P(X = 40) = 0.1 + 0.05 = 0.15.
Missing InformationThe problem asks for the probability that there are not enough sets left.
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Write an equation for a parabola with x-intercept (-3,0) and (2,0) which pae through the point (1,-20)
An equation for a parabola with x-intercept (-3,0) and (2,0) which pass through the point (1,-20) is "[tex]5x^2+5x-30[/tex]".
parabola is a major conic section that has wide applications in science and technology. know according to the condition by following intercepts we begin with an equation
[tex]y=a(x+3)(x-2)[/tex]
where a is any number that restricts the parabola to pass through (1,-20)
know we have to choose a for what the above equation got its require achievements. substitute (1,-20) in [tex]y=a(x+3)(x-2)[/tex] we get
[tex]-20=a(1+3)(1-2)\\\\-20=a(4)(-1)\\\\a=5[/tex]
substituting a back in the first equation we get the equation of the parabola. so, the parabola has an equation y= f(x)=[tex]5x^2+5x-30[/tex].
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The triangles below are similar.
What does y equal to?
The value of y after solving the pair of similar triangle is 15.
What is similar triangle?Similar shapes are enlargements of each other using a scale factor.
To find the value of y from the similar triangle below, we use the formula below.
Note: The ratio of the corresponding sides of two similar triangle are equal
Formula:
22/10 = 33/ymake y the subject of the equation above
y = 33×10/22y = 15Hence, the value of y is 15
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How do you state congruent triangles?.
If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.
Given,
We have to state that the triangles are congruent;
Here,
Congruent state;-
In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
Conditions for congruent triangles;-
If two triangles satisfy one of the following conditions, they are congruent:
The three corresponding side pairings are all equal. The comparable angles between two pairs of corresponding sides are equal. The corresponding sides between two pairs of corresponding angles are equal.That is,
If each of the three corresponding sides and each of the three corresponding angles in two triangles equals one another, then the two triangles are said to be congruent.
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How do you make a function table?.
These are the following steps you should follow to create a function table:
Function - A function is a mathematical concept that describes the relationship between an input and an output. A function can be expressed in four different ways. They can be communicated in a variety of methods, including spoken language, math, pictures, and function tables. Function table - A visual griddled table with input and output cells arranged in rows and columns is referred to as a function table. When students first learn function tables, they are sometimes referred to as function machines. The input value is subjected to the special rule of the table to produce the result.Rules of function tableThe rules of the function table can be used to comprehend the relationship between the input and the output. The rule of the table must be followed for all inputs and outputs. Function tables are helpful in this application. The rule must work if it is applied to one input/output and then verified with other sets to make sure it holds true.Another question that the rules subtly raises is the relationship between the input and the result. The question varies based on the table variable. What input value would result in the desired outcome when exposed to the known rule?, What outcome will result from using the known rule with the known input?, What mathematical technique—also referred to as a rule—can be used to generate the desired output from a known input?, Writing the input, output, and rule as a single line equation, solving it, and then figuring out the variable is commonly preferred.The third important item to note about the rule governing the relationship between the input and the output is that the mathematical operation will be constrained dependent on the input and output values. If the input is less than the result, the rule will be an operation that raises values, such as addition, multiplication, or exponents. If the input is more than the output, an operation such as subtraction, division, or square roots reduces the values. Example: If a cell contained the number 10 and another contained the number 12, what would be the logical conclusion? In plain English, what could be done to the 10 to get 12? The function's rule is to add two because adding two to ten results in seven. In a function table, there would have been more inputs and outputs than just 10 and 12, but the function would still have been the same. As a result, if the next input cell contained the number 16, the output would be 18 because the rule is add 2, which adds twoBy rule since [tex]X^{2} = Y[/tex] or square of input = output
By output since [tex]\frac{x}{5}[/tex] = output
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A random sample of 50 suspension helmets used by motorcycle riders and automobile race-car drivers was subjected to an impact test, and on 18 of these helmets some damage was observed. (a) Test the hypotheses H_0: p = 0.3H 0:p=0.3 versus H_{1} : p \neq 0.3H 1 :p
=0.3 with \alpha = 0.05.α=0.05. (b) Find the P-value for this test. (c) Find a 95% two-sided traditional CI on the true proportion of helmets of this type that would show damage from this test. Explain how this confidence interval can be used to test the hypothesis in part (a). (d) Using the point estimate of p obtained from the preliminary sample of 50 helmets, how many helmets must be tested to be 95% confident that the error in estimating the true value of p is less than 0.02? (e) How large must the sample be if we wish to be at least 95% confident that the error in estimating p is less than 0.02, regardless of the true value of p?
On testing the hypothesis , We fail to reject the null hypothesis at 5% level of significance.
In the question ,
it is given that ,
sample size (n) is = 50 ,
sample proportion(â) = 18/50 = 0.36
The null hypothesis is given as H₀ : p = 0.3
and the alternate hypothesis is [tex]H_{\alpha }[/tex] : p ≠ 0.3
The z - test statistics can be calculated using the formula
z = (â - p) / √(p(1-p)/n)
Substituting the value â = 0.36 , p = 0.3 and n = 50 ,
we get ,
z = (0.36 - 0.3) / √(0.3(1-0.3)/50)
On simplifying ,
we get ,
z = 0.93
the excel function for the critical value ,
=NORMINV(0.05/2,0,1)
we get , the critical value as 1.96
we can see that the critical value is greater than test statistic value ,
So , we fail to reject null hypothesis at 5% level of significance .
Therefore , On testing given hypothesis , We fail to reject the null hypothesis at 5% level of significance.
The given question is incomplete , the complete question is
A random sample of 50 suspension helmets used by motorcycle riders and automobile race-car drivers was subjected to an impact test, and on 18 of these helmets some damage was observed.
Test the hypotheses H₀ : p = 0.3 versus H₁ : p ≠ 0.3 with α = 0.05 .
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The sides of a triangle with positive area have lengths 4, 6 and x . The sides of a second triangle with positive area have length 4, 6 and y. The smallest positive number that is not the positive number that is not the possible value of | x - y | is ( x and y are integer ) a. 2 b. 4 c. 6 d. 8
The value of |x - y| which is not possible is 8.
Here we have to find the value of | x - y| which is not possible.
Given data:
The sides of a triangle are 4,6 and x and the other sides of a triangle are 4, 6, and y.
We know the fact that the sum of the lengths of two sides of a triangle is always greater than the third side.
Let us take the minimum and maximum values of the third side as x and y.
Minimum value is ≥ 6 - 4 that is ≥ 2
Maximum value is ≤ 6 + 4 that is ≤ 10
So, | x - y | ≤ | 10 - 2| that is ≤ 8.
The smallest positive number that is not the possible value of | x - y| is 8.
Therefore the value of | x-y| which is not possible is 8.
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generate a scatterplot of the variables. describe the relationship between gre scores and the chance of admission.
"Scatterplot is a quality controle tool",which shows us the increase or decrease of the function.Obviously it called the "Scatter Diagram".
It's totaly depand upon XY corelation.
In scatterplot the two variables are very important that are :
1. Indipendent
2. Dependent
To depict the values for two different numerical variables, dots are used in a scatter plot (also known as a scatter chart or scatter graph). Values for each data point are shown by the location of each dot on the horizontal and vertical axes. The relationships between variables are visualized using scatter plots.
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What if the base of an exponent is a 1?.
Answer:
The answer will always be 1
Step-by-step explanation:
The exponent is how many times the base number is multiplied by itself
For example 2^4 means 2 multiplied by itself 4 times or 2*2*2*2
But it doesn't matter how many times you multiply 1 by itself and it will always be 1
For example 1^5 is 1*1*1*1*1 which is equal to 1. you can even have 1^16 which is 1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1 but the answer is still 1 so the answer will always be 1
In a recent year, an author wrote 177 checks. Use the Poisson distribution to find the probability that, on a randomly selected day, he wrote at least one check.
The probability that on a randomly selected day, he wrote at least one check is 0.3843
How to solve for the Poisson distributionA year is made up of 365 days
The number of checks written = 177
λ = 177 / 365
= 0.4849
P(x ≥ 1) = 1 - p(x < 1)
p(x < 1) is going to be 0
so we would have 1 - p(x = 0)
the Poisson distribution is given as
P = e^-λ (λκ) / κ!
This is written as
1 - e^-0.485 x 0.485⁰ / 0!
1 - 0.6157
= 0.3843
The probability that on a randomly selected day, he wrote at least one check is 0.3843
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20. Every day Isabel swims 10 to 20 laps in a 50-meter pool. She tracks the numbers of laps she swims and how long it takes her to complete the lap, in
minutes.
All integers higher than or equal to 10 and less than or equal to 20 are included in the domain.
What is meant by domain?The domain of a function is the set of all possible inputs. The set of all potential values that can be used as inputs, or alternatively, the entire range of possible values for independent variables, constitutes the domain of a function.
As, The domain of a function is the set of all values that can be put into it while assuring that it exists and accepts a real number as a value.
The domain of a function is understood to be the set of values that we are permitted to enter into our function.
This set consists of the x values for a function like f(x).
Hence, the correct answer is the domain consists of all integers greater than or equal to 10 and less than or equal to 20.
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The Complete Question is:
Every day Isabel swims 10 to 20 laps in a 50-meter pool. She tracks the numbers of laps she swims and how long it takes her to complete the laps, in
minutes
Choose the correct answer below.
O A. The domain consists of all integers greater than or equal to 0.
OB. The domain consists of all integers greater than 0 and less than or equal to 20.
OC. The domain consists of all integers greater than or equal to 0 and less than or equal to 20
D. The domain consists of all integers greater than or equal to 10 and less than or equal to 20.
E. The domain consists of all integers less than or equal to 20.
uniform thin rod of length 0.500 m and mass 4.00 kg can rotate in a horizontal plane about a vertical axis through its centre. The rod is at rest when a 3.00 g bullet travelling in the rotation plane is fired into one end of the rod. In the view from above, the bullet's path makes angle θ=60.0o with the rod. If the bullet lodges in the rod and the angular velocity of the rod is 10 rad/s immediately after the collision, what is the bullet's speed just before impact?
The speed of bullet just before the impact would be 1.28 x 10^3 meter per second.
Let the speed of the bullet before impact be 'V₀.'
According to the question, we are given the mass of the rod 'M' = 4 kg. Length of the rod 'l' = 0.5 meter. The angle of the bullet's path 'Θ' = 60 degree and the angular velocity 'ω' = 10 rad/s.
For bullet, the mass 'M' = 3 g = 3 x 10^3 kg. and the velocity is V₀.
According to the law of conservation of momentum, we get
L(bullet) = l (bullet + rod)
mV₀ (l/2 sinΘ) = Iω
mV₀ x (l/2 sinΘ) = [ ml²/ 12 + m (l/2) ²] x ω
By cancelling the like terms, we get the equation as,
V₀ = (m +3m) x l/6m sin Θ
By calculating the above equation, we get,
V₀ = 1.28 x 10^3 meter per second.
Therefore, the speed of bullet before the impact is 1.28 x 10^3 meter per second.
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Let f be a twice-differentiable function on R such that f′′ is continuous. Prove that f(x)f′′(x)<0 cannot hold for all x. I have been able to think of specific examples of f(x) in which f(x)f′′(x)<0 does not hold, but I have not been able to come up with specific values of x for which f(x)f′′(x)<0 does not hold. Any help is greatly appreciated!
Must assume positive values
f is above this line outside [a, b]
So, f(x)f′′(x)<0 cannot hold for all x.
Given,
In the question:
Let f be a twice-differentiable function on R such that f′′ is continuous. Prove that f(x)f′′(x)<0 cannot hold for all x.
Now, According to the question:
Assume that :
f"(0) > 0
Then, f(0) < 0 and as neither factor can change sign.
f"(x) > 0 > f(x) for all x ∈ R and f is strictly convex.
Pick a < b with f(a) ≠ f(b).
Then the line through (a f(b)) and (b f(b)) intersect the x - axis.
By convexity, f is above this line outside [a, b],
Hence, Must assume positive values
f is above this line outside [a, b],
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What i 1 and 3 over 4 time 2 and 2 over 3? 2 and 1 over 2 3 and 5 over 12 4 and 2 over 3 4 and 6 over 7
a)If if 1 and 3 over 4 time 2 and 2 over 3 then our answer is 14/3 and
b) If 2 and 1 over 2 3 and 5 over 12 4 and 2 over 3 4 and 6 over 7,then our answer is 647/42
a)We have 1 and 3 over 4 or in other word if we convert this in improper fraction it is 7/4
Similarly, we have 2 and 2 over 3,in improper fraction it is 8/3
Now ,we multiply both the number to find the required answer =(7/4)×(8/3)=14/3
B) In b part we need to follow the same procedure which we followed in part a.
We have,2 and 1 over 2 3 and 5 over 12 4 and 2 over 3 4 and 6 over 7
On Converting all the mixed fraction into improper fraction
5/2, 41/12, 14/3 , 34/7
Take LCM of 2,12,3,7
LCM = 84
Convert all the fraction into proper fraction
(5×42)/(2×42)=210/84--------(eq1)
(41 × 7)/(12×7) =287/84----------(eq2)
(14 × 28)/(3×28)= 292/84--------(eq3)
(34 ×12 )(7×12) =408/84----------(eq4)
Now add all equations
(210+287+ 392+408)/84
= 1294/84=647/42
Hence, our answers are a)14/3 and b)647/42
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Given the number of rows and the number of columns, write nested loops to print a rectangle.
Answer:
You need to use a nested for loop. Use the range() builtin to produce an iterable sequence. The outer for loop should iterate over the number of rows.
Step-by-step explanation:
Use the range() builtin to produce an iterable sequence. The outer for loop should iterate over the number of rows overtime.
are the following statements true or false? ? 1. if the columns of an matrix are orthonormal, then is the orthogonal projection of onto the column space of ? 2. for each and each subspace , the vector is orthogonal to . ? 3. if is orthogonal to and and if , then must be in . ? 4. the orthogonal projection of onto a subspace can sometimes depend on the orthogonal basis for used to compute ? 5. if is in a subspace , then the orthogonal projection of onto is itself.
The given statements are true or false as following:
TrueTrueTrueFalse TrueWe have given some statements about matrix and subspace and we have to check whether the statements are true or false .
1. True
The columns of U are linearly independent and thus form an orthonormal basis for Col U. So, projcolU y = UU^T*y for all y in R^n.
2. True
The statement is true because y can be written uniquely in the form y = projw y+z where y − projw y is in W and Z is in W⊥ and it follows that Z = projw y
3. True
since z is orthogonal to u1 and to u2 it is orthogonal to every vector in W = Span{u1, u2}, a set that spans W.
4. False
The uniqueness property of the orthogonal decomposition y = y^ + z indicates that, no matter the basis used to find it, it will always be the same.
5. True
For an orthogonal basis of W, B = u1, ..., uP y and projw y can be written as linear combinations of vectors in B with equal weights.
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Each possible outcome of the number cube has the same theoretical probability. what is that probability?
It is possible to determine the theoretical probability of an occurrence without doing the event itself. A number cube has 6 alternative outcomes, giving each one a theoretical probability of 1 out of 6.
For example, the likelihood of drawing an ace at random is 4 out of 52 since there are 4 aces in a deck of cards. The probability of hitting a double bullseye on a regular dartboard is roughly 78 out of 100,000 because the area of the double bullseye in the center is 0.078% of the dartboard's overall area.
The likelihoods of potential possibilities are instead calculated using the frequencies of past outcomes in empirical probability. They are merely projections. The empirical chance of rolling a 4 or a 5 on the following roll is 58 out of 96 since you rolled 4s and 5s more often than any other number when you rolled the number cube.
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Answer: 1/6 is the probability
Which of factors has a product of 96?.
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
1 x 96 = 96 (1, 96)
2 x 48 = 96 (2, 48)
3 x 32 = 96 (3, 32)
4 x 24 = 96 (4, 24)
6 x 16 = 96 (6, 16)
8 x 12= 96 (8, 18)
How do you prove that SAS is congruent?.
By defining the SAS theorem of congruency, we have proved that SAS is congruent.
Congruency;-
Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.
Here,
We have to prove that SAS is congruent.
For that, lets consider the SAS theorem of congruence,
According to the side-angle-side (SAS) theorem of congruence, two triangles are congruent if their corresponding two sides and their included angles are precisely equivalent to those of the first triangle.
That is,
We proved by the definition SAS is congruent
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during a recent soccer season, the starting forward made 10 out of 27 shots on goal. at this rate, how many goals would the forward make next season if 35 shots on goal were taken? explain how you determined your answer.
Step-by-step explanation:
10 goals out of 27 attempts gives a ratio of
10/27 = 0.37037037... goals per shot.
now, for 35 shots we expect
35 × 10/27 = 350/27 = 12.96296296... ≈ 13 goals
The population of a town i 3808000. What i the value of the digit 3 in 3808000?
(a) 3 million (b) 3 hundred thouand
(c) 3 thouand (d) 3 hundred
The value of the digit 3 in 3808000 is 3 million.
What are population digits?
A population is a distinct group of individuals, animals, or objects that can be distinguished from one another for the purposes of data collection and analysis in statistics and other branches of mathematics. Data is typically collected from a sample in order to learn more about a large population.
Here, we have
The population of the town is 3808000.
We have to find the value of the digit 3 in 3808000.
We concluded from the given statement is the value of the digit 3 in 3808000 is 3 million.
Hence, the value of the digit 3 in 3808000 is 3 million.
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How is the tax base of an area calculated?.
The total market value of all the assets, properties, and income in a given region or jurisdiction is what is referred to as the tax base. The tax base must be multiplied by the tax rate to determine the overall tax obligation: Tax Base x Tax Rate equals Tax Liability.
Describe the tax base?
The whole amount of income, property, assets, consumption, transactions, or other economic activity that a tax authority is allowed to tax is known as the tax base.
What is tax base formula?
Multiplying the tax base by the tax rate yields the tax obligation. The tax liability divided by the tax rate would be the result. Tax Liability/Tax Rate in the Tax Base Formula.Learn more about tax base
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What is the formula of obtuse angle triangle?.
The Formula of Area of Obtuse Triangle is equal to ½ × b× h .
and by using Heron's formula,
A = √(S(S-a)(S-b)(S-c)) ; S = (a+b+c)/2
A closed two-dimensional figure with three sides of equal or unequal length and three corners of equal or unequal angles is called a triangle.
Obtuse triangle: A type of triangle with the following properties:
One of the angles of the triangle is greater than the other two angles (>90 degrees). One of the angles is obtuse, this triangle is known as obtuse triangleThe sum of interior angles of a triangle is always 180 degrees. Therefore, the other two angles of an obtuse triangle are acute.The sum of the squares of the shortest sides of an obtuse triangle is equal to the square of the largest side of the triangle.Area formula of obtuse triangle :
Area of obtuse triangle = ½ × b × h
where b --> base of triangle
h ---> height of triangle.
The area of a triangle can also be found using Heron's formula.
A = √(S(S-a)(S-b)(S-c)),
where s is half the perimeter of the triangle and a, b, c are the three sides of the triangle.
the perimeter of the triangle = a + b + c cm then
S = (a + b + c)/2
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A test of writing ability is given to a random sample of students before and after they completed a formal writing course. The results are given below. Construct a 99% confidence interval for the mean difference between the before and after scores. Round the limits to the nearest tenth. Before 70 80 92 99 93 97 76 63 68 71 74 After 69 79 90 96 91 95 75 64 62 64 76
-0.5 < µd< 4.5 are the limits of the given data.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given,
The results are given below. Construct a 99% confidence interval for the mean difference between the before and after scores
Before 70 80 92 99 93 97 76 63 68 71 74
After 69 79 90 96 91 95 75 64 62 64 76
Mean SD SEM N
80.27 12.76 3.85 11
78.27 12.92 3.89 11
df = 10
standard error of difference = 0.798
The mean of Before minus After equals 2.00
Given a=0.01, |t(0.005, df=10)|=3.17 (check student t table)
So 99% confidence interval is 2±ts
2±3.17(0.798)
-0.5 < µd< 4.5
Hence, -0.5 < µd< 4.5 are the limits of the given data.
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a square with a side length of 2 units is drawn on the coordinate plane with a vertex at the origin. Which shows a dilation of the square by a scale factor of 2
the dilation factor will change the square of the side 2 units.
What is square?
Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognised by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.
A square with a side length of 2 units is drawn on the coordinate plane with a vertex at the origin.
If a scale factor of 2 is applied to the given square, with point D serving as the centre of dilation
A point is enlarged by a scale factor k according to the following rule:
(x, y) → (kx, ky)
According to this rule, k =2
A(-2, 0) → A'(-4, 0)
B(-2, 2) → B'(-4, 4)
C(0, 2) → C'(0, 4)
D(0, 0) → D'(0, 0)
Hence the dilation factor will change the square of the side 2 units.
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