Yes the product of two perfect squares is always a perfect square, But the quotient of two perfect squares is not always a perfect square.
What is perfect square?A perfect square is a number that can be expressed as the product of an integer multiplied by itself.
Examples of perfect squares include 4 (2*2), 9 (3*3), and 25 (5*5).
What is quotient of a number?The quotient is the result obtained after performing division of one number by another. It is the number of times that the divisor can be subtracted from the dividend until the remainder is smaller than the divisor.
The product of two perfect squares is always a perfect square because the root of the products is equal to the product of roots as shown below,
let us take the two perfect squares 4 and 9, so the square root of 4*9 is,
[tex]\sqrt{4*9} =\sqrt{4} *\sqrt{9} \ =2*3=6[/tex]
But , the quotient of two perfect squares is a perfect square,
When we divide two perfect squares we are not always going to get a quotient that can be represented as the square of an integer. For example, (36/16) = 9/4 which is not a perfect square.
However, if the numerator and denominator in the quotient are the same perfect square then the quotient will be 1 which is a perfect square.
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A number, x, rounded down to 1 significant figure is 40
Write down the error interval for x.
Please explain How you got the answer and thanks so much in advance
Error interval is 35 ≤ x < 45.
Error intervals working?
Error intervals work by providing a range of values within which the true population value is likely to fall, with a certain level of confidence. The most common level of confidence used is 95%, which means that if the survey or experiment were conducted multiple times, the true population value would fall within the error interval 95% of the time.
We are looking at a rounded value when we employ error intervals. The range of values that were possible before the number was rounded is described by an error interval.
Given: A number x becomes 40 if it is rounded to 1 significant figure
To find: error interval for x
In the given question, an error interval is the range of values that a number x can be equal to before it is rounded to 1 significant figure.
As a number x becomes 40 if it is rounded to 1 significant figure, error interval is 35 ≤ x < 45.
A number x in this interval becomes equal to 40 if it is rounded to 1 significant figure.
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Solve the system of equations by the addition method.
4x-5y=22
3x +2y = - 18
Using the provided equations, Applying the addition method in the system of equations, The answer is x=-2 and y =-6.
What do you mean by equation?An equation is a statement of equality between two expressions, usually containing one or more variables. Equations can be used to express mathematical relationships and can be solved to find the value of the variables. Equations can take many forms, such as linear equations, quadratic equations, and differential equations. They can also be represented graphically.
What is the addition method to solve system of equations?The addition method to solve a system of equations is a way to solve a system of two linear equations by adding them together. The goal is to eliminate one variable by adding or subtracting the equations. We can eliminate one variable by adding the equations together. To do this, we'll add the left-hand side of the first equation to the left-hand side of the second equation and add the right-hand side of the first equation to the right-hand side of the second equation. It is important to note that the addition method works only when the coefficients of the variable you want to eliminate are opposite in sign.
4x-5y=22
3x+2y=-18
multiplying first equation with 3 and second equation with 4 and subtracting them , we eliminate x and solve for y,
y=-6
put y=-6 in first equation , we get x,
x=-2
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A restaurant manager believes that a majority of customers who dine at his restaurant would rate the food as excellent. To investigate this belief, he sends an email survey to a random sample of 50 customers from the large list of customers who have signed up for his frequent diner club. To encourage the customers to complete the survey, he offers a $10 gift card upon completion of the survey. He receives 22 responses, of which 20 rated the food as excellent. He would like to know if these data provide convincing evidence that more than 50% of customers who dine at his restaurant would rate the food as excellent. Are the conditions for inference met
The conditions for inference are: The customers who are surveyed are chosen independently at random, so we can assume that the survey results are independent.
What do you mean by normalcy?The amount of grams or mole equivalents of solute present in a solution that contains one liter is what is referred to as normalcy according to the accepted definition. The amount of moles of reactive units in a compound is what we mean when we say it is equal.
Sample size: The manager is surveying 50 customers, which is a moderate-sized sample.Normality: Since the manager is only looking at the proportion of customers who rated the food as excellent, we can assume that the data are approximately normally distributed.Randomness: The manager is using a random sample from the list of customers who have signed up for his frequent diner club, so we can assume that the sample is random.The conditions for inference are met.
However, to conclude that more than 50% of customers who dine at his restaurant would rate the food as excellent, we need to conduct a statistical test such as a one-sample proportion test or a confidence interval. The manager would need to compare the proportion of the customers who rated the food as excellent from the survey with the proportion of customers who would rate the food as excellent. This would allow to see if the data provides convincing evidence that more than 50% of customers who dine at his restaurant would rate the food as excellent.
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Samera placed the congruent sides of these two triangles together to form a quadrilateral.
2 triangles are connected at one side. One triangle has angles 25 degrees, 125 degrees, 30 degrees. The other triangle has angles 30 degrees, 60 degrees, and 90 degrees.
Which statements are true of the quadrilateral she constructed? Select three options.
It is a rectangle.
It is a trapezoid.
It has only one right angle.
It has two right angles.
It has two sides that are parallel.
The correct statements are It is a trapezoid, It has only one right angle, It has two sides that are parallel.
What is a trapezoid?A quadrilateral with at least one pair of parallel sides is called a trapezoid.
Given that, Samara placed the congruent sides of these two triangles together to form a quadrilateral.
2 triangles are connected at one side. One triangle has angles 25 degrees, 125 degrees, 30 degrees. The other triangle has angles 30 degrees, 60 degrees, and 90 degrees.
If we construct such quadrilateral, we will get a trapezoid with one angle a right angle.
Hence, the correct statements are It is a trapezoid, It has only one right angle, It has two sides that are parallel.
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Answers:
1. B its a trapezoid
2. D it has two right angles
3. E it has 2 sides that are parallel
Step-by-step explanation:
Is 2x3 is a polynomial?
In 2x^3, 3 is the greatest degree of the exponent. 2x^3 is a cubic polynomial as a result.
A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.
An example of a polynomial of a single indeterminate x is x² − 4x + 7.
An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials.
For instance, the polynomial 3x+2x-5.
By noticing which formulas only contain the operations of addition, subtraction, multiplication, and non-negative integer exponents, the polynomials may be located. Expressions with additional operations are considered non-polynomial expressions.
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put this equation in Slope-Intercept form
Y + 2 = -5 ( X + 3 )
Answer: y=-5x-17
Step-by-step explanation:
Slope-intercept form follows the formula y-mx+b, where m is slope and b is y-intercept. All we have to do is to manipulate the equation to look like y=mx+b.
[tex]y+2=-5(x+3)[/tex] [distribute right side]
[tex]y+2=-5x-15[/tex] [subtract both sides by 2]
[tex]y=-5x-17[/tex]
Now, our equation matches y=mx+b with m=-5 and b=-17.
Which functions have an axis of symmetry of x = –2? Check all that apply.
f(x) = x2 + 4x + 3
f(x) = x2 – 4x – 5
f(x) = x2 + 6x + 2
f(x) = –2x2 – 8x + 1
f(x) = –2x2 + 8x – 2
The quadratic functions that have an axis of symmetry at x = -2 are given as follows:
f(x) = x² + 4x + 3.f(x) = -2x² - 8x + 1.How to obtain the axis of symmetry of a quadratic function?The standard definition of a quadratic function is given by the rule presented as follows:
y = ax² + bx + c, in which a is different of zero.
The axis of symmetry is given by the x-coordinate of the vertex, hence it's equation is defined as follows:
x = -b/2a.
Meaning that the correct options are given by the first and by the fourth options in this problem.
For the first function, we have that:
a = 1, b = 4.
Hence the axis of symmetry is obtained as follows:
x = -4/2 = -2.
For the fourth function, we have that:
a = -2, b = -8.
Hence:
x = -8/4 = -2.
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What is the maximum number of students among whom 135 pens, 180 pencils and 300 books can be equally divided.
Answer:
Step-by-step explanation: You can add all of these numbers with a calculator. but be sure what are the numbers telling you what to do. So always focus on the words that are going to mention about the numbers.
In the figure shown, EF is tangent to the circle at F, and EG is
tangent to the circle at G. Line segments HF, PG, HJ, and PJ
are also tangent segments.
When mEF = 10 units, what is the perimeter of triangle EHP?
Explain your reasoning.
Answer:
The perimeter is 20 units----------------------------------
According to the two-tangent theorem, two tangent segments drawn to one circle from the same external point are congruent.
That is:
EF = EG,HF = HJ,PJ = PG.We have EF = 10 units, it means EG is also 10 units.
The perimeter of triangle EHP is:
P = EH + HP + EPWe can substitute:
HP = HJ + PJ, segment addition,HJ = HF, stated above,PJ = PG, stated above.Then the perimeter is:
P = (EH + HF) + (EP + PJ) = EF + EG = 10 + 10 = 20 unitsWhy is the sine of an acute angle less than one?
The sine of an acute angle is less than one because it is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. Since the side opposite the angle is shorter than the hypotenuse, the ratio is always less than one.
To what does sin equate?
In contrast to the cosine of an angle, which corresponds to the ratio of the nearby side to the hypotenuse, the sine of an angle is the ratio of the opposite side to the hypotenuse.
It's also the same reason why the cosine of an acute angle is always less than one because it is the ratio of the adjacent side of the angle to the hypotenuse.
It's important to note that this is only true for acute angles, angles smaller than 90 degrees.
For obtuse angles, greater than 90 degrees, the sine and cosine values are greater than one.
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For Drew’s week 1 classes identify the domain and range is the relation a function? Explain
From the table for Drew's week 1 classes:
Domain = {English, Math, History, Biology, Biology Lab}
Range = {60. 90, 45, 0}
What is domain and range?A function's domain is the set of values that can be plugged into it. This set contains the x values in a function such as f. (x). A function's range is the set of values that it can take. This is the set of values that the function returns when we enter an x value. They are the y values.
A function can be thought of as a machine on an assembly line. On one end of the assembly line, there are a few screws and bolts, and on the other end, there is a car. The function is represented by the machine in the middle. The domain consists of the screws and bolts that we insert into the machine (our function).
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3x -y=-2y solve for y pls help me
Answer:
-x
Step-by-step explanation:
3x - y = -2y
add y to both sides
3x = -3y
divide both sides by -3
-x = y
A line passes through 3,1 and 0,-3 whats the equation
Answer:
y=(this is a fraction) 4/3 times x-3
Step-by-step explanation:
According to a Harris poll, 5% of U.S. adults admitted to having spent money gambling online. If a U.S. adult is selected at random, what is the probability that he or she has never spent any money gambling online
If a U.S. adult is selected at random, the probability that he or she has never spent any money gambling online is 95.
What is gambling?Gambling, the betting or staking of something of value, with consciousness of risk and hope of gain, on the outcome of a game, a contest, or an uncertain event whose result may be determined by chance or accident or have an unexpected result by reason of the bettor’s miscalculation.
Given that there was a 5 probability of U.S. adults admitted to having spent money gambling online.
We have to find the probability of a U.S. adult selected randomly that he or she has never spent any money gambling online.
We will assume the probability of the outcome which is known as P(E) and the probability of the outcome which we need to know as , P(E) since both are the complement of each other. Then we will substitute the value of P(E) in the formula compliment of P(E)= 1-P(E) so as to obtain compliment of P(E)
Given that there was a 5 probability of U.S. adults admitted to having spent money gambling online, therefore
P(E) =5
P(E)= 5/100
=0.05
The probability of a U.S. adult selected randomly that he or she has never spent any money gambling online will be given as compliment of P(E) , such that
compliment of P(E)= 1-P(E)
=0.95
= 0.95/100
=95
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What does a 30 60 90 triangle look like?
The 30-60-90 triangle is shaped like half of an equilateral triangle.
A special right triangle with angles 30°, 60°, and 90° is called a 30-60-90 triangle. Since 30° is the smallest angle in the triangle, the side opposite to the 30° angle is always the smallest.
The side opposite to the 60° angle is the longer leg, and finally, the side opposite to the 90° angle is the largest side of the right triangle, also known as the hypotenuse.
30°-60°-90° Triangle Rule:
In a 30-60-90 triangle, we can find the measure of any of the three sides by knowing the measure of at least one side in the triangle. This is known as the 30-60-90 triangle rule.
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Use the quadratic formula to find both solutions to the quadratic equation
given below.
4x² + 5x+1=0
A. X=-
-3-√√-7
8
□ B. x=-3-√7
8
C. x=
E. x=
-3+√√-7
8
D. x=-¹
+3+√7
8
F. x= -1
Answer: x=-1/4 and x=-1
Step-by-step explanation:
The answer choices you give are extremely hard to figure out, so I hope my explanations and answers help.
The quadratic formula is [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]. Once we figure out a, b, c, we can plug them into the formula and solve for x.
The standard form equation is ax²+bx+c=0. The equation given matches this so we know that:
a=4
b=5
c=1
Plug them into the formula. There is a [tex]\pm[/tex] symbol, which stands for "plus or minus". This means we solve the formula with addition and subtractions separately. We should have 2 solutions at the end. Let's do them separately to show work.
Solution 1: addition
[tex]x_1=\frac{-5+\sqrt{5^2-4(4)(1)} }{2(4)}[/tex] [exponents]
[tex]x_1=\frac{-5+\sqrt{25-4(4)(1)} }{2(4)}[/tex] [multiply]
[tex]x_1=\frac{-5+\sqrt{25-16} }{8}[/tex] [inside square root]
[tex]x_1=\frac{-5+\sqrt{9} }{8}[/tex] [square root]
[tex]x_1=\frac{-5+3}{8}[/tex] [add]
[tex]x_1=\frac{-2}{8}[/tex] [divide top and bottom by 2]
[tex]x_1=-\frac{1}{4}[/tex]
Solution 2: subtraction
[tex]x_2=\frac{-5-\sqrt{5^2-4(4)(1)} }{2(4)}[/tex] [exponents]
[tex]x_2=\frac{-5-\sqrt{25-4(4)(1)} }{2(4)}[/tex] [multiply]
[tex]x_2=\frac{-5-\sqrt{25-16} }{8}[/tex] [inside square root]
[tex]x_2=\frac{-5-\sqrt{9} }{8}[/tex] [square root]
[tex]x_2=\frac{-5-3}{8}[/tex] [subtract]
[tex]x_2=\frac{-8}{8}[/tex] [divide]
[tex]x_2=-1[/tex]
I am not able to find the answer choices, but we know that x=-1/4 and x=-1.
WILL GIVE BRAINLIEST PLEASE HELP
The following triangular prism has a base that is a right triangle.
A. Draw or describe the net of this triangular prism. Make sure to include the dimensions of each part of the net.
B. Use your net to calculate the surface area of the prism.
A. The net of a triangular prism is a flattened version of the prism that shows all the faces of the prism.
The prism's base is a right triangle with a base of 3 units and a height of 4 units. The prism is six units tall. The net of the triangular prism would look like a rectangle with a length of 3 units and a width of 4 units. On top of this rectangle, there would be two smaller triangles, each with a base of 3 units and a height of 6 units.
B. To calculate the surface area of the prism, we need to add the area of all the faces.
The base of the prism is a right triangle with an area of (1/2) (3 units) (4 units) = 6 square units.
The two triangular faces have an area of (1/2) (3 units) (6 units) = 9 square units each.
The rectangular face has an area of (3 units) (6 units) = 18 square units.
So, the total surface area of the prism is:
6 square units (base) + 9 square units (triangular face) + 9 square units (triangular face) + 18 square units (rectangular face) = 42 square units.
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How do you find third side of triangle if two sides are given and angle is given?
The Third side of a triangle if the two sides are given and one angle is given can be found by using the Cosine Law .
What is Cosine Law ?
The Cosine Law states that the square of any one side of the triangle is equal to difference between sum of squares of the other two sides and double of product of other sides and cosine of the angle included between them.
In mathematical terms it means that ;
let a , b be the the know sides and "c" be the unknown side of the triangle ABC , and the known angle be = angle C ;
So , the side c will be ⇒ [tex]c^{2}= a^{2} +b^{2} - 2ab\times Cos(C)[/tex] ;
Therefore , the Cosine Law helps in finding the missing third side .
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Suppose y varies directly with x, and y = 6.5 when x = 1.3. What direct variation equation relates x and y ?
Select one:
a.
y = − 5x
b.
y = x / 5
c.
y = 5x
d.
y = 1.5x
Answer:
c
Step-by-step explanation:
given y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
to find k use the condition y = 6.5 when x = 1.3
6.5 = 1.3k ( divide both sides by 1.3 )
5 = k
y = 5x ← equation of variation
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Quetion
Suppoe a plane flie 48 mile in 12 minute. The relationhip between mile flown, x, and minute flown, y, by the plane can repreented by the equation y = 14x. How far will the plane fly in 28 minute?
Repone
A 120 mile120 mile
B 116 mile116 mile
C 112 mile112 mile
D 124 mile
The plane will fly 392 miles in 28 minutes. Therefore, the answer is D) 124 miles.
What is the relationship between distance and time?
The important thing is that speed is always the ratio of the distance traveled to the time needed to travel that distance: distance/time.
To find out how far the plane will fly in 28 minutes, we need to substitute x = 28 into the equation y = 14x.
y = 14x represents the relationship between the distance flown (y) and time flown (x).
Substituting x = 28 into the equation:
y = 14 * 28 = 392
Hence, the plane will fly 392 miles in 28 minutes.
Therefore, the answer is D) 124 miles.
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Peter owns a total of one hundred and forty four prized baseball cards. If he were to add 7 more American League players and three more national league players, his collection of American to national would be in a ratio of nine five. Find out how many cards of each league he has currently.
Answer:
24
Step-by-step explanation:
Wanda has 5 different fish in a small, crowded tank. She decides to randomly scoop up individual fish and transfer them to a new tank until a total of 4 fish have been moved. How many sequences of 4 fish are possible?
Answer:
64 sequences of 4 fish are possible.
Triangle DEF was dilated according to the rule DO,One-third(x,y)(one-third x, one-third y) to create similar triangle D'E'F'.
On a coordinate plane, (0, 0) is the center of dilation. Triangle F D E is dilated to create smaller triangle F prime D prime E prime. Triangle F D E has points (negative 9, 3), (negative 9, 9), (negative 6, 6). Triangle F prime D prime E prime has points (negative 3, 1), (negative 3, 3), and (negative 2, 2).
Which statements are true? Select three options.
∠F corresponds to ∠F'.
Segment EE' is parallel to segment FF'.
The distance from point D' to the origin is One-third the distance of point D to the origin.
The measure of ∠E' is One-third the measure of ∠E.
△DEF △D'E'F'
A. ∠F corresponds to ∠F' is True.
B. Segment EE' is parallel to segment FF' is False.
C. The distance from point D' to the origin is One-third the distance of point D to the origin is True.
D. The measure of ∠E' is One-third the measure of ∠E is False.
E. △DEF ~ △D'E'F' is True.
What is Dilation?Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.
Given:
As triangle DEF was dilated according to the rule DO, One-third(x, y)(one-third x, one-third y) to create similar triangle D'E'F'.
and, The center of dilation = (0, 0)
Also, Triangle FDE has points: (- 9, 3), (- 9, 9), (- 6, 6).
Triangle F'D'E' has points : (- 3, 1), (- 3, 3), (- 2, 2)
A) ∠F corresponds to ∠F'. ( True)
B) Segment EE' is parallel to segment FF'. (False)
As they intersect each other at the origin.
C) The distance from point D' to the origin is One-third the distance of point D to the origin. ( True)
Now, the length of DE
D = √(-9-0)² + (-9-0)²
D = 9√2
and, length of D'E'
D = √(-3-0)² + (-3-0)²
D = 3√2
Thus, DE / D'E' = 3√2/ 9√2 = 1/3
D) The measure of ∠E' is One-third the measure of ∠E. ( False)
E) △DEF ~ △D'E'F'. ( True)
As they are similar triangles.
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Answer:
A. ∠F corresponds to ∠F'.
C. The distance from point D' to the origin is 1/3 the distance of point D to the origin.
E. △DEF ~△D'E'F'
Step-by-step explanation:
got it right on edge 23
3. (a) How many 0.32kg portions of minced beef can be made from 15.36kg of beef? (b) If beef is sold at $25.16 per kilogram, what is the cost of six and a quarter 0.32kg portions?
Answer:
a) 48 portions
b) $157.25
Step-by-step explanation:
1) 15.36/.32 to get 48 portions
2) Since it's asking for 6.25 0.32kg portions, multiply 6.25 by $25.16 to get $157.25
Is (- 2 4 a solution to the system?
yes, (-2,4) is the solution of the system of equation 4x² - 4y = 0.
To check whether the given points are the solution of the given system of equation 4x² - 4y = 0. We have to put the values of x = -2 and y = 4 in the given equation. If we get the result equals zero then (-2, 4) is the solution of 4x² - 4y = 0 and if the result is a non-zero number then (-2, 4) is not the solution of 4x² - 4y = 0.
⇒4x² - 4y = 0
⇒4(-2)² - 4 × 4 = 0
⇒4 × 4 - 4 × 4 = 0
⇒0 = 0
Here we get the result equal to zero, hence (-2,4) is the solution of the system of equation 4x² - 4y = 0.
--This question is incomplete, the complete question is
''Is (-2,4) a solution of the system of equation 4x² - 4y = 0?''--
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How do you find the legs of a 45 45 90 triangle given the hypotenuse?
The value of the legs of the triangle would be hypotenuse/√2.
You can use basic trigonometry to solve this problem. We know that the sine of the angle made by the hypotenuse and the base is equal to the ratio of perpendicular height and the hypotenuse, given that the angle is 45° the perpendicular will be equal to ⇒ hypotenuse × sin(45°).
That is perpendicular=hypotenuse/√2
Similarly, the cosine of the angle made by the hypotenuse and the base is equal to the ratio of base length and the hypotenuse, given that the angle is 45° the base will be equal to ⇒ hypotenuse × cos(45°)
That is base=hypotenuse/√2
Therefore, the value of the legs of the 45°-45°-90° triangle would be hypotenuse/√2.
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What is the value of f in a function?
A function is generally indicated by f.
What is function?A mathematical expression that indicates a relationship between an independent variable and a dependent variable.
In other word, a function shows a relation between a set of input values to a set of output values in where each input value is connected to only a particular output value.
What is the value of f in a function?A function is generally, expressed by letters such as f, g and h and so on.
It is said that f(x) is a function of x or g(x) and h(x) are a function of x when functions are denoted by g or h.
For an input value of an independent variable x, the output value is denoted by f(x) that is equal to a dependent variable such as y. We can write, y = f(x)
The set of x value are the domain of function, and the set of f(x) value are the ranges of a function.
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Complete question is: What is the value of f in a function?
TRANSLATE EACH PHRASE INTO AN ALGEBRAIC EXPRESSION
1) 4 times a number,increased by 11.
2) 8 times the sum of a number and 7.
3) 1 less than twice a number.
4) the sum of a number and 3 times that number.
5) 12 more than 5 times a number.
6) 16 increased by 1 more than a number.
7) 20 decreased by 5 less than a number.
8) 6 less than a number increased by 15.
Answer:
Step-by-step explanation:
Let the number be x then,
1) 4 * x + 11
2) 8 * (x + 7)
3) 2x - 1
4) x+ 3x
5) 5x + 12
6) 16 + 1 + x = 17 + x
7) 20 - ( x - 5) = 20 - x + 5 = 25 - x
8) x - 6 + 15 = x +9
In AAEC, G is the centroid.
A
B.
If EG = 6, find GB.
O 2
03
06
09
B) The length of GB is 3 in the given triangle.
The centroid of a triangle is the point at which the three medians of the triangle intersect. A median of a triangle is a line segment that connects a vertex of the triangle to the midpoint of the opposite side. The three medians divide the triangle into six smaller triangles, each with a vertex at the centroid.
The ratio in which the centroid divides a median of a triangle is 2:1. That is, the distance from the centroid to the vertex is twice the distance from the centroid to the midpoint of the opposite side.
So, if G is the centroid and B is the midpoint of the side opposite to point A, the ratio of EG: GB is 2:1.
so the length of GB = EG/2
so the length of GB = 3
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Complete question:
In ΔAEC, G is the centroid , as shown in the figure .
if EG = 6 ,find GB
A) 2
B) 3
C) 6
D) 9
at a certain high school, the distribution of backpack weight is approximately normal with mean 19.7 pounds and standard deviation 3.1 pounds. a random sample of 5 backpacks will be selected, and the weight, in pounds, of each backpack will be recorded. For samples of size 5, which of the following is the best interpretation of P\left(\overline{x}>22\right)\approx0.05P(x>22)≈0.05?
The Normal probability for all sample of 5 that the sample mean will be greater than 22 pounds is approximately 0.05. In this Question The normal probability distribution and the central limit theorem were used.
What is Normal probability distribution?The most prevalent continuous probability distribution is the Normal (or Gaussian) distribution. As the curve becomes closer to zero on either side of the mean, the function calculates the likelihood that a given event will fall between any two real number limits. The area under the normal curve is always one.
Central limit theorem
The central limit theorem implies that the distribution of the sample means will be roughly normally distributed if you have a population with mean and standard deviation and take sufficiently enough random samples from the population with replacement.
Normal probability distribution, ; Problems of normally distributed samples are solved using the z-score formula.
Mean standard deviation , the z-score of a measure X is given by:
Z = x-μ/σ
Given ,
The distribution of backpack with mean deviation = 19.7 pounds
And the standard deviation = 3.1 pounds
The number of standard deviations is measured by the Z-score. The average is used as the measure.
We glance at the z-score table after determining the Z-score to determine the p-value connected to it.
The likelihood that the measure's value is less than X, or the percentile of X, is represented by this p-value.
1 is subtracted from the p value.
We calculate the likelihood that the measure exceeds X.
P(ä > 22) is the probability of the sample means being above 22.
For all samples of size 5, the probability that the sample mean will be greater than 22 pounds is approximately 0.05.
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