The correct option is (C) I and III only. Let's see how:
I. True. In a t-test for a single population mean, increasing the sample size (while everything else remains the same) changes the number of degrees of freedom used in the test. The degrees of freedom for a single population mean t-test is calculated as (sample size - 1), so when the sample size increases, the degrees of freedom also increase.
II. False. In a chi-square test for independence, increasing the sample size (while everything else remains the same) does not change the number of degrees of freedom used in the test. The degrees of freedom in a chi-square test for independence are calculated as (number of rows - 1) x (number of columns - 1), which is not affected by the sample size.
III. True. In a t-test for the slope of the population regression line, increasing the number of observations (while leaving everything else the same) changes the number of degrees of freedom used in the test. The degrees of freedom for a regression slope t-test is calculated as (number of observations - 2), so when the number of observations increases, the degrees of freedom also increase.
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Prove that, cosecA/(tanA + cot A) =cosA
The proof is given below
We can start by using the definition of the trigonometric functions cosec(A), tan(A), and cot(A):
cosec(A) = 1/sin(A)
tan(A) = sin(A)/cos(A)
cot(A) = 1/tan(A) = cos(A)/sin(A)
Now, we can substitute these definitions into the equation:
cosec(A)/(tan(A) + cot(A)) = 1/sin(A) / (sin(A)/cos(A) + cos(A)/sin(A))
Simplifying the right-hand side gives us:
1/sin(A) / (sin(A)(1/cos(A) + 1/sin(A))) =
1/sin(A) / (sin(A)/sin(A)cos(A) + sin(A)) =
1/sin(A) / (1 + sin(A))
Finally,
multiplying both sides by sin(A) (which is not 0 because A is not a multiple of pi/2)
cosec(A)/(tan(A) + cot(A)) * sin(A) = 1/sin(A) / (1 + sin(A)) * sin(A) = 1 / (1 + sin(A)) * sin^2(A) = cos(A)
Therefore, cosec(A)/(tan(A) + cot(A)) = cos(A)
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Why is the exponent 0 1?
The exponent 0 refers to the number being raised to the power of 0.
When any number, except 0, is raised to the power of 0, the result is always 1. This is known as the "zero power property" and it is true for any non-zero number a. The mathematical statement can be represented as:
a^0 = 1
For example, 2^0 = 1, 5^0 = 1 and so on. This property holds true for any base a, including real numbers, complex numbers, and even matrices.
The exponent 1 refers to the number being raised to the power of 1. When any number is raised to the power of 1, the result is always the same as the number itself. This is known as the "identity property" and it is true for any non-zero number a. The mathematical statement can be represented as:
a^1 = a
For example, 2^1 = 2, 5^1 = 5 and so on. This property holds true for any base a, including real numbers, complex numbers, and even matrices.
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A 14-foot ladder is set up 4 feet from the base of a building. How far up the building does the ladder reach? Round your answer to the nearest tenth of a foot.
The distance up the building that the ladder would reach, given the ladder height and the base of the building, is 13.4 ft.
How to find the height ?To find out how far up the building the ladder reaches, we can use the Pythagorean theorem. The theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse).
Assuming the height that the ladder reaches is x, the formula would be:
x ² + 4 ² = 14 ²
x ² = 14 ² - 4 ²
x ² = 196 - 16
x = √ 180
x = 13. 4 ft
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How do you solve 3 variable equations with 3 variables?
The linear combination method will be used to resolve a system of three equations in three variables.
What is equation ?Consider the equation 3x + 5 = 14, in which the terms 3x + 5 and 14 are separated by the word "equal." The slope-intercept form, standard form, and point-slope form are the three primary formats for linear equations. A mathematical expression known as an equation has an equals sign. Many equations contain algebra. When you don't know the exact number to compute in math, algebra is used.
given
The linear combination method will be used to resolve a system of three equations in three variables.
This time, we will consider two equations at a time, eliminate one variable using the resulting equations in two variables, then solve for the third variable. with respect to this instance.
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19/2-1/3-9/6=?????????
Answer:
[tex] \frac{23}{3} ....in \: fraction \: or \\ 7.666666...in \: decimal[/tex]
Step-by-step explanation:
Greetings!!!
look at the image attached
Hope it helps!!!
given the function f(x)=-2x+3 complete the table
Answer:
Outputs are-
f(-2) = 7
f(-1) = 5
f(0) = 3
f(3) = -3
Step-by-step explanation:
Given, f(x) = -2x+3
To find, 1) f(-2)
2) f(-1)
3) f(0)
4) f(3)
Solution,
1) Substituting x for -2,
f(-2) = -2 x -2 + 3 = 7
2) Substituting x for -1,
f(-1) = -2 x -1 + 3 = 5
3) Substituting x for 0,
f(0) = -2 x 0 + 3 = 3
4) Substituting x for 3,
f(3) = -2 x 3 + 3 = -3
Who is the father of geometry?
Euclid is the father of geometry
Euclid and René Descartes was often called the father of modern mathematics because he created analytic geometry and the Cartesian coordinate system.
What is modern mathematics?
Different methodologies have been used in contemporary mathematics. It focuses mostly on entities, whereby interconnections follow themes and patterns.
René Descartes was a person who was very famous for his philosophy of science and mathematics. He was considered a person who evaluate and made various new development in the field of math as well as time in separate fields like geometry and algebra with new properties that is developed by him.
He had the main idea of having finite and infinite particles or numbers in geometry. And also used various scientific methods to prove that.
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Tim's book has 50 pages.
Lisa's book has 2 1 2 times as many pages.
Which shows how many pages (y) Lisa's book has?
Lisa's book has 10,600 pages.
What is multiplication?Multiplication is an operation that represents repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication is the product of those numbers. Multiplication is used to simplify the task of repeated addition of the same number.
Tim's book has 50 pages, if Lisa's book has 212 times as many pages, therefore;
Lisa's book has 212 x 50 pages
Lisa's book has 10,600 pages.
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What is a real image for Class 7?
In optics, an image is defined as the group of focus points of light rays coming from an object. A real image is a collection of focus points actually made by converging rays, while a virtual image is a collection of focus points made by extensions of diverging rays.
The real image is produced by the intersection of light rays. It can be obtained on a screen. Hence, projectors form real images.
The virtual image is formed when the light rays appear to be originating from a point but do not actually meet. It can be seen by human eyes.
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Can someone help me and show the work
ans is 90 and 30
Step-by-step explanation:
LN=90° (right angle)
MN=30°(DO THE MATH)
PLease help me find the distance between AB BC and CA please help
The distance of AB is 42.04 units, BC is 35.77 units and CA is 34.5 units.
What is Distance?The length along a line or line segment between two points on the line or line segment.
The coordinates of A are (-18, -18)
coordinates of B are (20, 0)
coordinates of C are (-12, 16)
The formula for distance is Distance=√(x₂-x₁)²+(y₂-y₁)²
Distance AB=√(20-(-18))²+(0-18)²
=√(20+18))²+(0-18)²=√38²+18²
AB=√1444+324=√1768=42.04 units
Distance BC=√(-12-20)²+(16)²
=√(-32)²+(16)²=√1024+256
=√1280
=35.77
Distance CA=√(-12-(-18))²+(16+18)²
=√(6)²+(34)²
=√36+1156=34.5
Hence, the distance of AB is 42.04 units, BC is 35.77 units and CA is 34.5 units.
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given that 2x + 3y divideby 3x+4y ,find the ratio y : x
Although part of your question is missing, you might be referring to the question :
Given that 2x+3y / 3x+4y = 5, find the ratio of y:x
Given : 2x+3y / 3x+4y =5
To find : y : x
Solution :
(2x+3y) / (3x+4y) = 5, or
2x + 3y = 15x + 20y, or
-15x + 2x = 20y - 3y, or
-13x = 17y
Therefore, x/y = -17/13
Hence, y/x = -13/17
y : x = -13 : 17.
The answer is -13 : 17.
Use the information about four different waves to answer the question.
Which wave contains the lowest energy?
-wave 2
-wave 1
-wave 3
-wave 4
^
(screenshot is for this one)
X-ray technicians wear protective gear to keep them safe from the X-rays. Why are X-rays dangerous?
They have short wavelengths that can penetrate materials, and their low energy can damage matter.
They have short wavelengths that can penetrate materials, and their high energy can damage matter.
They have long wavelengths that can penetrate materials, and their low energy can damage matter.
They have long wavelengths that can penetrate materials, and their high energy can damage matter.
1) X-Rays are dangerous because: "They have short wavelengths that can penetrate materials, and their high energy can damage matter." (Option B)
2) From the table given, the wave that has the lowest energy is Wave 4.
What is the relationship between Frequency and wavelength?The relationship between frequency and wavelength is inverse. The wavelength of the wave with the highest frequency is the shortest. One-half the wavelength equals twice the frequency. As a result, the wavelength ratio is inverse to the frequency ratio.
To summarize, waves transport energy. The quantity of energy carried by them is proportional to their frequency and amplitude. The greater the frequency, the greater the energy, and the greater the amplitude, the greater the energy.
Also, the lower the frequency, the lower the energy, and the lower the amplitude, the lower the energy. Thus, the wave with the lowest energy is Wave 4.
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Somebody help please I don’t understand!!
The unit rate of the 76th player is [tex]1\frac{1}{3}[/tex] miles per hour.
The unit rate of the 91st player is [tex]1\frac{1}{9}[/tex] miles per hour.
The unit rate of the 44th player is [tex]1\frac{1}{2}[/tex] miles per hour.
What is an improper fraction?
An improper fraction is one in which the denominator is greater than or equal to the numerator. 5/2 and 8/5, for example, are incorrect fractions. Every fraction is made up of two parts: the numerator and the denominator. Proper fractions and improper fractions are the two main types of fractions in mathematics based on the numerator and denominator values.
For 76 number of players:
In 1/4 hour he can run 1/3 mile
In 1 hour he can run (1/3)/(1/4)mile
=4/3 miles
Convert it into a mixed number:
= [tex]1\frac{1}{3}[/tex] miles per hour
For 91 number of players:
In 3/4 hour he can run 5/6 mile
In 1 hour he can run (5/6)/(3/4)mile
=10/9 miles
Convert it into a mixed number:
= [tex]1\frac{1}{9}[/tex] miles per hour
For 44 number of players:
In 1/2 hour he can run 3/4 mile
In 1 hour he can run (3/4)/(1/2)mile
=6/4 miles
=3/2 miles
Convert it into a mixed number:
= [tex]1\frac{1}{2}[/tex] miles per hour
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In the of 76th player's unit rate is 1 1/3 miles per hour , 91st player's unit rate is 1 1/9miles per hour and the 44th player's unit rate is 1 1/2miles per hour.
What is meant by an unit rate?When expressed as a fraction, a unit rate has a denominator of one unit. To write a rate as a unit rate, divide the rate's numerator and denominator by the rate's denominator.
For a total of 76 players:
He can run 1/3 mile in 1/4 hour.
He can run (1/3)/(1/4) mile in 1 hour.
= 4/3 miles
Change it to a mixed number:
= 1 1/3 miles per second.
For a total of 91 players:
He can run 5/6 mile in 3/4 hour.
He can run (5/6)/(3/4) mile in an hour.
= 10/9 miles
Change it to a mixed number:
= 1 1/9 miles per hour.
For a total of 44 players:
He can run 3/4 mile in half an hour.
He can run (3/4)/(1/2) mile in 1 hour.
=6/4 miles
=3/2 miles
Change it to a mixed number:
= 1 1/2 miles per hour.
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Solve for x= 2 11/12x-5/6(x-2/5)
The value of the equation on x = 2 is 0.5
Given Quadratic equation,
[tex]= \frac{11}{12} x - \frac{5}{6}( x - \frac{2}{5})[/tex]
Put the value of x = 2 in the above equation and we get
[tex]= \frac{11}{12} *2 - \frac{5}{6}( 2 - \frac{2}{5})[/tex]
[tex]= \frac{11}{6} - \frac{5}{6} * \frac{8}{5}[/tex]
[tex]= \frac{11}{6} - \frac{4}{3}[/tex]
[tex]= \frac{1}{2}[/tex]
= 0.5
Therefore, the value of the equation on x = 2 is 0.5
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A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 447 gram setting. Based on a 24 bag sample where the mean is 444 grams and the standard deviation is 10, is there sufficient evidence at the 0.1 level that the bags are underfilled or overfilled? Assume the population distribution is approximately normal.
Step 3 of 5: Specify if the test is one-tailed or two-tailed.
The test that we have here is the one tailed test.
How do we know that the test is one tailed?From the direction of change of the parameter, we would be able to tell if the test is a one tailed test or not. That is, if the parameter is increasing or decreasing.
This test is looking to determine if the bags are underfilled (decreased) or if they are overfilled (increased).
The test's alternative hypothesis is written in a way that it predicts the direction of the difference between two groups. The test is one-tailed if the alternative hypothesis predicts a direction of change
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Pleaseeee help me thx
When the length of JK is 9.5 feet and the angle L is 61 degrees trigonometric ratio of the tangent, solving yields: KL=9.5ft/1.804 KL=5.27 ft.
what is trigonometry ?The relationship between triangle side lengths and angles is investigated in the branch of mathematics known as trigonometry. The application of geometry in astronomical study gave rise to the area's first appearance during the Hellenistic era, roughly in the third century BC. Exact methods mathematics focuses on certain trigonometric functions and how they might be applied to calculations. In trigonometry, there are six widely used trigonometric functions. Their respective names and acronyms are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of the properties of triangles, especially of right triangles. The features of all geometric shapes are studied in geometry, though.
given
△JKL
JK=9.5ft
∠L=61∘
Find:KL
We may determine the outcome using the tangent's trigonometric ratio.
Tan = JK/KL = 61
When we separate KL, we get KL=9.5ft/tan61.
When the length of JK is 9.5 feet and the angle L is 61 degrees trigonometric ratio of the tangent, solving yields: KL=9.5ft/1.804 KL=5.27 ft.
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The correct question is :-
Given triangle JKL, find the length of KL. The length of JK is 9.5 ft and the angle L is 61 degrees.
What is the relationship between <4 and <15? *
The Least Common Factor of 4 and 15 is 1. The factors of 4 are 1, 2 and 4, and the factors of 15 are 1, 3, 5 and 15. Hence, 1 is the Least Common Factor of 4 and 15.
What's meant by Factor?A factor is a number that fully divides another number.
To put it another way, if adding two whole figures results in a product, also the figures we're adding are factors of the product because the product is separable by them.
Factor simply translates to" doer" in Latin. therefore, a" factor" in English is a" actor,"" element," or" element" in a situation or number.
Success can depend on charm, and having a terrible constitution can affect from inadequate exercise.
Variable factors are those whose employment varies in proportion to affair; further are employed when product rises and smaller when product falls.
Labor, energy, and raw accoutrements employed directly in product are exemplifications of typical variable rudiments.
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Does 2 dilated mean?
2 dilated means that the measurement of an area has increased or expanded in size.
This can be a linear measurement such as the diameter of a circle, or the area of a square or rectangle. The formula for the area of a circle is A=πr2 where r is the radius of the circle. A 2 dilated measurement would mean that the radius has doubled, so the formula would be A=π(2r)2 A=4πr2. This would mean that the area of the circle has increased by a factor of 4. Similarly, if the length and width of a rectangle were 2 dilated, the area would be A=2L2W, which would be four times the original area.
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NEED ANSWER PLS!
WORTH 60 POINTS!
Select the correct answer.
Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g.
A.
g(0) = 2
B.
g(-13) = 20
C.
g(7) = -1
D.
g(-4) = -11
Answer:
7
Step-by-step explanation:
7
Please help! Running out of time!
We can use some rules for exponents to simplify the expression, we will get:
7⁵/7¹ = 7⁴
How to simplify the expression?Here we need to use two properties about exponents, these are:
The exponent of 1 bassically does nothing:
x¹ =x
The rule for divisions is:
xᵃ/xᵇ = x⁽ᵃ ⁻ ᵇ ⁾
Now we have the expression:
7⁵/7
We can rewrite that as:
7⁵/7¹
Now we can use the second property to get:
7⁵/7¹ = 7⁵ ⁻ ¹ = 7⁴
That is the simplified expression.
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What is an R value that tells you how well a line of best fit fits the data?
Correlation Coefficient (r) o A model is deemed to be "excellent fit" if r is near to 1 (or -1). o The model is "not a good match" if r is close to 0. o The model has a "perfect fit" if r = 1, with all data points falling on the line. o The two variables do not have a linear connection if r = 0.
What is Correlation Coefficient?The strength of the linear link between two separate variables, x and y, is shown by correlation coefficients.
A positive relationship is shown by a linear correlation coefficient greater than zero.
Indicating a negative association is a value less than zero. The two variables x and y do not have any relationship when their values are 0, to sum up.
The correlation coefficient (r2) is a statistic that expresses how closely two variables' movements are related to one another.
To determine the linear relationship between two variables, the Pearson product-moment correlation, the most popular correlation coefficient, is used.
However, this correlation value might not necessarily be a reliable indicator of reliance in a non-linear connection.
Hence, Correlation Coefficient (r) o A model is deemed to be "excellent fit" if r is near to 1 (or -1).
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If m = −72 is slope, y - intercept is 12 and the point ( x, 5 ) lies on the line. What is the value of x ?
A line can be represented in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
Given that m = −72 and the y-intercept is 12, we can represent the line as y = −72x + 12
We are also given that the point (x, 5) lies on the line. So we can substitute the x and y values of the point into the equation of the line to find the value of x.
y = −72x + 12
5 = −72x + 12
-7 = -72x
x = 7/72
So the value of x is 7/72.
We can also get this by solving the equation of the line for x.
y = -72x + 12
y - 12 = -72x
(y - 12)/-72 = x
x = (y - 12)/-72
So for any point (x, y) on the line, the value of x can be obtained by substituting y and the slope-intercept form equation.
my square orchid garden abuts my house so that the house itself forms the northern boundary. the fencing for the southern boundary costs $5 per foot, and the fencing for the east and west sides costs $3 per foot. find the total cost of the fencing as a function of the length (in feet) of a side x.
The total cost of the fencing as a function of the length of the x side is 11x
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
To solve this problem we must perform the following algebraic operations with the given information
Information about the problem:
southern = 5$east = 3$west = 3$side = xTotal cost = ?Calculating the total cost:
Total cost = (southern + east + west) * side
Total cost = (5 + 3 + 3)*x
Total cost = 11x
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Conider the problem, in 3/4 cup of oatmeal, there i no 1/10 of the recommended daily value of iron. What fraction of the daily recommended value of iron i in 1 cup of oatmeal. (1 multiplication and diviion equation)
The fraction which is recommended as value of iron in 1 cup of oatmeal as per the given relation is equal to 2/15.
As given in the question,
Daily recommended value of iron in the given cup of oatmeal
3 / 4 cup of oatmeal gives 1/10 daily value of iron.
Fraction recommended as daily value of iron is given by :
⇒ 3 /4 cup of oatmeal = 1 /10 value of iron
⇒ 1 cup of oatmeal = ( 1 × 4 ) / ( 3 × 10 ) value of iron
⇒ 1 cup of oatmeal = ( 4 ) / ( 30 ) value of iron
⇒ 1 cup of oatmeal = ( 2 ) / ( 15 ) value of iron
Therefore, the fraction recommended as daily value of iron is equal to
( 2/15 ).
The above question is incomplete, the complete question is :
In 3/4 cup of oatmeal, there is 1/10 of the recommended daily value of iron. What fraction of the daily recommended value of iron is in 1 cup of oatmeal? ( multiplication and division equation)
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Evaluate.
33 + (23)2 I will probally give u brainlest
A.27 4/9
B.9 2/3
C.9 4/9
D.27 2/3
Answer:
69
Step-by-step explanation:
33 + (23)2 =
= 33 + 46
= 69
This is the correct answer to the problem you posted. If you meant something else, you should have written it differently.
Use / for fractions and ^ for exponents.
Which is a correct solution for the following system of Inequalities
HELPP DUE IN 30MIN
Answer:
I think the answer is A
1,2
Marshall divides his money into four categories. He saves of his money. He gives of his money to a charity. He uses of his money to buy snacks at school, and he spends of his money on fun. What fraction of his money does he save and spend on fun?
Answer:
Marshall saves 1/4 of his money and spends 1/4 of his money on fun. Therefore, he saves and spends 1/4 + 1/4 = 1/2 or 50% of his money on those two categories.
Step-by-step explanation:
Heidi has made a sequence of patterns using tiles. use the rule to find out how many tiles there are in the 7th pattern.
Answer:
29 is the correct answer
Sydney is playing a game. She draws a fraction card labeled, Then she rolls a number cube labeled 1 through 6. sydney mutuplles the fraction b. the number rolled. If her score is greater than 1. she gets another turn. If her score is less than or equal to 1. her turn is over. What is the lowest number that Sydney can roll to get another turn? Enter the answer in the box.
Answer: To get another turn, Sydney's score must be greater than 1. Therefore, to find the lowest number that Sydney can roll to get another turn, we need to find the smallest number that, when multiplied by the fraction on the card, will give a result greater than 1.
It's not mentioned which fraction card Sydney drew, so we can assume any fraction.
Let's assume the fraction card is labeled 1/4.
To get another turn, Sydney's score must be greater than 1. Therefore, we need to find the smallest number that, when multiplied by 1/4, will give a result greater than 1.
1/4 * x >1
x > 4
so the smallest number that Sydney can roll to get another turn is 5.
It should be noted that this is assuming that the fraction card is labeled 1/4 , if the fraction card is labeled with any other fraction the answer would be different.
Step-by-step explanation: