Answer:
its 5
Step-by-step explanation:
I did this question
A parent donated 36 fruit cups and 24 bananas to fifth grade. The teacher wanted to make field trip snack bags with the donated food and wondered about the ways snacks could be packed. To be fair the teacher wants to make sure that all bags are exactly the same.
A) What is the greatest number of snack bags that the teacher can make, if each bag is identical? How do you know ?
B) What other numbers of snack bags could she make? How do you know?
2) Another parent also donated 24 bananas, so there are 48 bananas total. Now what is the greatest number of snack bags can that can be made?
3) The teacher realized that she miscounted and had only 30 fruit cups. How many snack bags can she make with 48 bananas and fruit cups?
4) What do the different numbers of snack bags that can be made have to do with the number of fruit cups and number of bananas?
When two unequal forces act on an object, it causes the object to move.
These forces are called:
Answer:
resultant force
Step-by-step explanation:
the body will move to the direction where greater force is applied
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Since ∠1 ≅ ∠3 and ∠3 ≅ ∠7, then:
A) ∠6 ≅ ∠7
B) ∠7 ≅ ∠8
C) ∠1 ≅ ∠7
Answer:
C) ∠1 ≅ ∠7
Step-by-step explanation:
If ∠1 = ∠3, then ∠3 = ∠7, behind there is written ∠1 = ∠3, so it's A) ∠1 = ∠7.
find a polynomial function with the following zeros: double zero at -4 simple zero at 3.
f(x) = (x+4)^2(x-3) has polynomial function with the following zeros: double zero at -4 simple zero at 3.
If a polynomial has a double zero at -4, it means that it can be factored as (x+4)^2.
If it also has a simple zero at 3, then the factorization must include (x-3).
Therefore, the polynomial function with these zeros is :-
f(x) = (x+4)^2(x-3)
This polynomial has a double zero at -4, because $(x+4)^2$ has a zero of order 2 at -4, and a simple zero at 3, because $(x-3)$ has a zero of order 1 at 3.
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PLEASE HELP!!! 40 points.
Answer:
D. 7/5
Step-by-step explanation:
In right triangle ABC with right angle C,
sinA = 4/5 = cosB
cosA = 3/5 = sinB
sinB + cosB = 3/5 + 4/5 = 7/5
If A =12 and 120% of A equal to 80% of B, then what is A+B
So,
120% is the same as 1.2 or 6/5. 80% is the same as 0.8 or 4/5.
We are given the value of a, which is 12.
6/5 of a, or 1.2 times a, is equal to 4/5 of b, or 4/5 times b.
[tex]\dfrac{6}{5} (12)=\dfrac{4}{5} b[/tex]
Simplify.
[tex]\dfrac{72}{5} =\dfrac{4}{5} b[/tex]
Multiply both sides by 5/4.
[tex]\dfrac{72}{4} \ \text{or} \ 18=b[/tex]
Therefore, the sum of a and b is 12 + 18 = 30.
true/false. when the population variance is not known (i.e., must be estimated from data), we use a z-statistic instead of a t-statistic for our hypothesis tests.
The given statement " when the population variance is not known (i.e., must be estimated from data), we use a z-statistic instead of a t-statistic for our hypothesis tests. " is false. Because in distribution of sample means, population variance is unknown.
When the population variance is not known and must be estimated from the data, we use a t-statistic instead of a z-statistic for our hypothesis tests.
This is because the distribution of the sample means follows a t-distribution when the population variance is unknown, whereas it follows a standard normal distribution (z-distribution) when the population variance is known.
The t-distribution has fatter tails than the z-distribution to account for the extra uncertainty introduced by estimating the population variance from the sample.
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Can someone help quick i have 6 questions left
Step-by-step explanation:
remember the trigonometric triangle inside a circle.
sine is the up/down leg, cosine is the left/right leg.
the Hypotenuse (baseline) of the right-angled triangle is the angle-defining radius of the circle.
this is the basic definition inside the norm-circle with radius = 1.
for any other size sine and cosine need to be multiplied by the actual radius for the actual triangle side lengths.
I think you need the answer in simplified fraction and square root notification (you cut that off), but I give you also the decimal result, just in case.
so,
78 = cos(30)×y
78 = (sqrt(3)/2) × y
y = 78 / (sqrt(3)/2) = 2×78/sqrt(3) = 156/sqrt(3) =
= 90.06664199...
x = sin(30) × y = 0.5 × 156/sqrt(3) = 78/sqrt(3) =
= 45.033321...
AGENT X IS IN DANGER
Question #1 (70 points)
- Create the matrix M and encode the message using the product of matrices A and M.
Question #2 (30 points)
The agents decided to make it harder to decode the message if intercepted by the enemies. The message
was initially encoded by a 2-letter circular shift to the right (Letter A was replaced with C, letter B was
replaced with D, etc.). The spaces remained zeros.
- Create the matrix M and encode the message using the product of matrices A and M.
Must show work.
The evaluation of the matrix multiplication can be presented as follows;
Question #1
The matrix M and A are;
[tex]M=\begin{bmatrix}1 &14 &24 &19 &14 &1&5 \\7 &20 &0 &0 &0 &14 &18\\5 &0 &9 &9 &4 &7 &0 \\\end{bmatrix}[/tex]
[tex]A = \begin{bmatrix} 1& 2 &3 \\3 & 1 & 2 \\ 2 & 3& 1 \\\end{bmatrix}[/tex]
The encoded message in matrix form is therefore;
[tex]A\times M=\begin{bmatrix}30 &54 &51 &46 &26 &50&41 \\20 &62 &90 &75 &50 &31&33 \\28 & 88 &57 &47 &32 &51&64 \\\end{bmatrix}[/tex]
The encoded message is; 30 20 28 54 62 88 51 90 57 46 75 47 26 50 31 51 41 33 64
Question #2
The matrices M and A × M are;
[tex]M=\begin{bmatrix}3 &16 &26 &21 &16 &3 &7\\9 & 22 & 0 &0 &0 &16&20 \\7 &0 &11 &11 &6 &9 &0\\\end{bmatrix}[/tex]
[tex]A\times M=\begin{bmatrix}42 &60 &59 &54 &34 &62&47 \\32 & 70 & 100 &85 &60 &43&41 \\40 & 98 & 63 &53 &38 &63 &74\\\end{bmatrix}[/tex]
The encoded message is; [tex]{}[/tex]42 32 40 60 70 98 59 100 63 54 85 53 34 60 38 62 43 63 47 41 74
What is the rule for matrix multiplication?The rule for matrix multiplication is that the number of columns in the first matrix should be the same as the number of rows in the second matrix
A m by n matrix can only multiply a n by p matrix to produce a m by p matrix
The matrix M for the message can be presented as follows;
The letters are replaced with the corresponding numbers to get;
[tex]{}[/tex]1 7 5 14 20 0 24 0 9 19 0 9 14 0 4 1 14 7 5 18 0
M = [tex]\begin{bmatrix}1 &14 &24 &19&14&1 &5 \\7 & 20 &0 &0 &0&14&18\\5 & 0& 9 & 9&4&7&0\\\end{bmatrix}[/tex]
The matrix A is presented as follows;
[tex]A=\begin{bmatrix}1 & 2 & 3 \\3 & 1 & 2 \\ 2& 3 &1 \\\end{bmatrix}[/tex]
Therefore;
[tex]A \times M = \begin{bmatrix}30 &54 &51 &46&26&50 &41 \\20 & 62 &90 &75 &50&31&33\\28 & 88& 57 & 47&32&51&64\\\end{bmatrix}[/tex]
The encoded message is therefore;
[tex]{}[/tex]30 20 28 54 62 88 51 90 57 46 75 47 26 50 32 50 31 51 41 33 64Question #2
The 2-letter circular shift indicates that the message becomes;
AGENT X IS IN DANGER
The above message becomes;
CIGPV Z KU KO FCOIGT
The numbers comes;
[tex]{}[/tex]3 9 7 16 22 0 26 0 11 21 0 11 15 0 6 3 15 9 7 20
The Matrix Mis therefore;
[tex]M = \begin{bmatrix}3 &16 &26 &21&16&3 &7 \\9 & 22 &0 &0 &0&16&20\\7 & 0& 11 & 11&6&9&0\\\end{bmatrix}[/tex]
The message becomes;
[tex]A \times M = \begin{bmatrix}42 &60 &59 &54&34&62 &47 \\32 & 70 &100 &85 &60&43&41\\40 & 98& 63 & 53&38&63&74\\\end{bmatrix}[/tex]
The encoded message is; [tex]{}[/tex] 42 32 40 60 70 98 59 100 63 54 85 53 34 60 38 62 43 63 47 41 74
The information in the attached file related to the question includes;
Two agents are to send a confidential message which is to be encoded using a 3 × 3 invertible matrix A that consists of natural number elements. The coding strategy consists of replacing each letter by the number representing the letter in the alphabet, after which the numbers representing the letters are placed in columns of 3 elements, completing the missing elements in the last column and blanks with zero in the matrix M. See above.
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CAN SOMEONE HELP WITH THIS QUESTION?✨
The rate at which the water level is rising in the pyramid is 5 cm/s when the water level is 3 cm.
What is a pyramid?A pyramid is a three-dimensional object with triangle faces that meet at a shared vertex and a base that is a polygon. The perpendicular distance between a pyramid's base and apex determines the structure's height. The base form of a pyramid can be used to categorise them. A square pyramid, for instance, has a square base, a triangle-shaped pyramid, a triangle-shaped base, and so on. From the ancient Egyptian pyramids to the contemporary pyramids found in cities all over the world, pyramids have been employed in architecture and art for thousands of years.
Given that, sides of length 3 cm and the height is 5cm.
The volume of a pyramid is given by:
V = (1/3) * A * h
where A is the area of the base.
The base of the pyramid is a square thus,
Area = (3)(3) = 9 sq. cm.
Substitute the value of A and h in volume:
V = (1/3) * 9 * 5 = 15
Now, water is being filled at a constant rate of 45 cubic cm per second.
The rising level can thus be calculated as:
r - 45/9 = 5 cm/s
Hence, the rate at which the water level is rising is 5 cm/s when the water level is 3 cm.
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What is the measure of angle R?
A) 17 degrees
B) 25 degrees
C) 34 degrees
D) 65 degrees
Answer: D) Angle R is 65 degrees
Step-by-step explanation:
In the given figure, we have a right-angled triangle PQR.
Using the property of angles in a triangle, we know that the sum of angles in a triangle is 180 degrees. Therefore,
∠QRP + ∠QPR + ∠PRQ = 180 degrees
Since ∠PRQ is a right angle (90 degrees), we have:
∠QRP + ∠QPR = 90 degrees
Now, we are given that ∠QPR is 25 degrees. Substituting this in the above equation, we get:
∠QRP + 25 = 90 degrees
Solving for ∠QRP, we get:
∠QRP = 90 - 25 = 65 degrees
Therefore, the measure of angle R is 65 degrees, which is option (D).
Answer:
Answer is D
Step-by-step explanation:
SPiDerMom is so hot bTw
A block of mass 2kg is attached to the spring of spring constant 50Nm −1. The block is pulled to a distance of 5 cm from its equilibrium position at x=0 on a horizontal frictionless surface from rest at t = 0. The displacement of the block at any time t is thenA. x= 0.05sin5tmB. x= 0.05cos5tmC. x= 0.5sin5tmD. x= 5sin5tm
The displacement of the block at any time t is then x= 0.05cos5tm. (option b).
Now, when the block is released, it starts oscillating back and forth about its equilibrium position due to the force exerted by the spring. This motion is described by the equation of motion for a simple harmonic oscillator:
x = Acos(ωt + φ)
The angular frequency ω of the oscillation is given by:
ω = √(k/m)
where k is the spring constant and m is the mass of the block.
Substituting the given values of k and m, we get:
ω = √(50/2) = 5 rad/s
The phase angle φ depends on the initial conditions of the system, i.e., the initial displacement and velocity of the block. Since the block is initially at rest, its initial velocity is zero and the phase angle is zero as well.
Therefore, the equation of motion for the displacement of the block is:
x = 0.05cos(5t)
Hence, option B, x = 0.05cos(5t), is the correct answer.
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valuate the
expression
12 - 3y
2
+
√²v=4] for y = 3.
2y -
The result of the formula [tex]12 - 3y2 + (v=4) / (2y - 2)[/tex] for y = 3 is [tex]-29/2[/tex] .
What are the ways to analyse an algebraic expression?When [tex]y = 3[/tex] is used, the value of the expression [tex]12 - 3y2 + (v=4) / (2y - 2)[/tex] has a value of [tex]-29/2[/tex] .
To analyse an algebraic expression is to determine its value when a certain number is used in lieu of the variable. To evaluate the expression, we first replace the variable with the given number, then we use the order of operations to simplify the expression.
If [tex]y = 3[/tex] , we can insert it into the expression & simplify as follows to evaluate [tex]12 - 3y2 + (v=4) / (2y - 2)[/tex] for [tex]y = 3[/tex] .
[tex]12 - 3(3)^2 + (√4) / (2(3) - 2)[/tex] (y = 3 replacement)
[tex]12 - 27 + 2 / 4\s-15 + 1/2\s-29/2[/tex]
Therefore, The result of the formula [tex]12 - 3y2 + (v=4) / (2y - 2)[/tex] for y = 3 is [tex]-29/2[/tex] .
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If z=x+y ;where x varies p Square and y varies 1/p, find the equation connecting z and p . If z=5 when p=2 ,and z=6 when p=4 find z when p=6
The equation connecting z and p is:
z = x + (1/p)
To find z when p = 6, we can use the values of x and y when p = 2 and p = 4 to calculate the corresponding value of z when p = 6.
When p = 2, x = 4 and y = 1, so z = 5
When p = 4, x = 16 and y = 0.25, so z = 16.25
Therefore, when p = 6, x = 36 and y = 0.167, so z = 36.167
TRUE OR FALSE to calculate the average of the numeric values in a list, the first step is to get the total of values in the list.
The given statement 'to calculate the average of the numeric values in a list the first step is to get the sum of all the given values ' is a true.
Average of the numeric values in a list,
First step is to get the sum of values in the list.
It is not the total number of values.
Once we have the sum, we can divide it by the number of values to get the average.
Here is an example,
Suppose we have a list of numeric values are as follow,
[2, 4, 6, 8, 10].
To calculate the average of these values, we first find their sum,
2 + 4 + 6 + 8 + 10 = 30
Next,
divide the sum by the number of values in the list
Number of values = 5
30 / 5 = 6
This implies,
The average of the values in the list is 6.
Therefore, to get the average first step is to get the total of all values is true statement.
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Next > Pretest: Essential Learning 13 Select the correct answer. What is the simplified form of this expression? (5x² + 2x + 11) − (7 + 4x - 2x²)
Answer:
7x² - 2x + 4
Explanation:
(5x² + 2x + 11) − (7 + 4x - 2x²)
= 5x² + 2x + 11 - 7 - 4x + 2x²
= 7x² + 2x + 11 - 7 - 4x
= 7x² - 2x + 11 - 7
= 7x² - 2x + 4
So, the answer is 7x² - 2x + 4
PLEASE I NEED HELP, what is the equivalent of 7/tan b+7tan b
In response to the stated question, we may state that The equivalent trigonometry expression of 7/tan b + 7tan b is (7 - 7tan b cot b)/sin b.
what is trigonometry?The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.
tan(A + B) = (tan A + tan B)/(1 - tan A tan B)
Set A = 90 degrees and B = b degrees:
tan(90 + b) = (tan 90 + tan b)/(1 - tan 90 tan b)
tan(90 + b) = (undefined + tan b)/(1 - undefined tan b)
tan(90 + b) = -cot b
7/tan b + 7tan b
= 7/(tan b) + 7(tan(90 + b) - 1)
= 7/(tan b) + 7(-cot b - 1)
= (7 - 7tan b cot b)/sin b
The equivalent expression of 7/tan b + 7tan b is (7 - 7tan b cot b)/sin b.
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HELP ASAP PLEASE! A yard plan includes a rectangular garden that is surrounded by bricks. In the drawing, the garden is 7 inches by 4 inches. The length and width of the actual garden will be 35 times larger than the length and width in the drawing.
What is the perimeter of the drawing? Show your work.
What is the perimeter of the actual garden? Show your work.
What is the effect on the perimeter of the garden with the dimensions are multiplied by 35? Show your work.
The perimeter of the garden in the drawing is 22 inches and the perimeter of the actual garden is 770 inches
The perimeter of the drawingThe perimeter of the garden in the drawing is calculated as
Perimeter of garden in drawing = 2(length + width)
So, we have
Perimeter of garden in drawing = 2(7 inches + 4 inches)
Evaluate
Perimeter of garden in drawing = 22 inches
So the perimeter of the garden in the drawing is 22 inches.
The perimeter of the actual gardenFor the perimeter of the actual garden, we have
Perimeter of actual garden = 22 inches * 35
Perimeter of actual garden = 770 inches
The effect on the perimeterWe can see that the perimeter of the actual garden is 35 times larger than the perimeter of the garden in the drawing.
This makes sense since the length and width of the actual garden are 35 times larger than the length and width in the drawing, so the perimeter (which is the sum of the lengths of all four sides) would also be 35 times larger.
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For a standard normal distribution, find:
P(-2.11 < z < -0.85)
Answer:
Step-by-step explanation:
Using a standard normal table, we can find the area under the curve between -2.11 and -0.85.
P(-2.11 < z < -0.85) = P(z < -0.85) - P(z < -2.11)
Using the table, we find:
P(z < -0.85) = 0.1977
P(z < -2.11) = 0.0174
Therefore,
P(-2.11 < z < -0.85) = 0.1977 - 0.0174 = 0.1803
So the probability that a standard normal random variable falls between -2.11 and -0.85 is 0.1803.
In the diagram of right triangle ABC shown below, AB= 14 and AC = 9.
What is the measure of ZA, to the nearest degree?
1) 33
2) 40
3) 50
4) 57
The measure of the angle A is 49.99 degrees or 50 degrees if the length of AB = 14 and AC = 9.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have a given a right angle triangle in the picture
It is required to find the measure of angle A
Applying cos ratio to find the measure of the angle A:
cosA = 9/14
cosA = 0.642
A = 49.99 ≈ 50 degree
Thus, the measure of the angle A is 49.99 degrees or 50 degrees if the length of AB = 14 and AC = 9.
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Can someone please tell me what 5 divided by 1/3 is?
Answer:
15.
The trick to working out 5 divided by 1/3 is similar to the method we use to work out dividing a fraction by a whole number.All we need to do here is multiply the whole number by the numerator and make that number the new numerator. The old numerator then becomes the new denominator.
So, the answer to the question "what is 5 divided by 1/3?" is
15!
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Consider the line segment AB
shown. Which of the following
locations for point C makes ABC a right triangle with hypotenuse AB?
A - C(7,9)
B - C(1,4)
C - C(2,3)
D - C(8,7)
Consider the line segment AB shown the locations for point C makes ABC a right triangle with hypotenuse AB
C - C(2,3)How to find point C with hypotenuse ABIn a coordinate pair the points are as represented as (x, y).
The point that forms the right triangle is located by tracing the point on the x axis of of the point A and the point on the y axis of the point B. This is done below
A (2, 1) point on x axis here is 2B (9, 3) point on y axis here is 3therefore we can say that the point C that forms the right triangle is
C (2, 3)
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Solve for x algebraically, given the domain.
4sin x+2=0, 0≤ x<2π
Answer:
x = [tex]\frac{7\pi }{6}[/tex], [tex]\frac{11\pi }{6}[/tex] or x = 210°, 330°
Step-by-step explanation:
4sin(x) + 2 = 0
4sin(x) = -2
sin(x) = -1/2
x = [tex]\frac{7\pi }{6}[/tex], [tex]\frac{11\pi }{6}[/tex]
I’m having a hard time understanding how to get the Domain and Range. If you help please
Answer:
[-1,inf) and [-2,inf)
Step-by-step explanation:
Domain is all the X coordinates that the function will pass through. it starts at -1 and goes to inf so [-1,inf) is the domain. The range is all the Y coordinates the function will pass through. It starts at -2 and goes up to inf so [-2,inf) and that is your answer
a water park sold 1679 tickets for total of 44,620 on a wa summer day..each adult tocket is $35 and each child ticket is $20. how many of each type of tixkwt were sold?
Therefore , the solution of the given problem of unitary method comes out to be the attraction sold 943 child tickets and 736 adult tickets on that particular day.
What is an unitary method?It is possible to accomplish the objective by using previously recognized variables, this common convenience, or all essential components from a prior malleable study that adhered to a specific methodology. If the expression assertion result occurs, it will be able to get in touch with the entity again; if it does not, both crucial systems will undoubtedly miss the statement.
Here,
Assume the attraction sold x tickets for adults and y tickets for kids.
Based on the supplied data, we can construct the following two equations:
=> x + y = 1679 (equation 1, representing the total number of tickets sold)
=> 35x + 20y = 44620 (equation 2, representing the total revenue generated)
Using the elimination technique, we can find the values of x and y.
When we divide equation 1 by 20, we obtain:
=> 20x + 20y = 33580 (equation 3)
Equation 3 is obtained by subtracting equation 2 to yield:
=> 15x = 11040
=> x = 736
When we enter x = 736 into equation 1, we obtain:
=> 736 + y = 1679
=> y = 943
As a result, the attraction sold 943 child tickets and 736 adult tickets on that particular day.
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use the equation that you wrote in excerise 21 to find the number of vertices of a cube, which has 12 edges and 6 faces
The cube has 8 vertices. Exercise 21 states that for a polyhedron with V vertices, E edges, and F faces, the following equation holds:
V - E + F = 2
To use this equation to find the number of vertices of a cube with 12 edges and 6 faces, we first need to identify the values of E and F.
A cube has 12 edges, as given in the problem statement, and it has 6 faces since a cube has 6 square faces.
Substituting these values into the equation, we get:
V - 12 + 6 = 2
Simplifying this equation, we have:
V - 6 = 2
Adding 6 to both sides, we get:
V = 8
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Sorry if photo is side ways or upside down
Consider the following algebraic statements and determine the values of x for which each statement is true. On a number line, show the set of all points corresponding to the values of x.
4=|-2x|
Your question is incomplete. The complete question is: Consider the following algebraic statements and determine the values of x for which each statement is true. On a number line, show the set of all points corresponding to the values of x.
|x| = 7
4=|-2x|
The values of x for which each statement is true are:
|x| = 7: x = -7 or x = 7
4 = |-2x|: x = -2 or x = 2
How to determine the values of x for which each statement is true?a) |x| = 7
-x = 7 or x = 7
x = -7 or x = 7
This statement is true for two values of x:
x = -7 and x = 7.
b) 4 = |-2x|
4 = -2x or 4 = 2x
x = -2 or x = 2
This statement is true for two values of x:
x = -2 and x = 2.
The number line is shown in the image attached.
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The figure to the right shows the results of a survey in which 1007 adults from Country A, 1005 adults from
Country B, 1016 adults from Country C, 1016 adults from Country D, and 1000 adults from Country E were
asked whether national identity is strongly tied to birthplace.
National Identity and Birthplace
People from different countries who believe national
identity is strongly tied to birthplace
Country A
Country B
Country C
Country D
Country E
34%
22%
29%
50%
14%
Construct a 99% confidence interval for the population proportion of adults who say national identity is strongly tied to birthplace for each country listed.
99% confidence interval is that the true population proportion of adults who say national identity is strongly tied to birthplace in Country A is between 30.7% and 37.3%.
What is confidence interval?The confidence interval is a set of values that, with a given level of certainty, contains the real population parameter. The likelihood that the genuine population parameter falls inside the interval is represented by the degree of confidence. In this instance, we created 99% confidence intervals for the percentage of individuals in each demographic who claim that national identity is highly correlated with birthplace. This indicates that 99% of the intervals we build would include the genuine population percentage if the survey were to be repeated numerous times.
The confidence interval is given using the formula:
CI = p ± z*(√((p*(1-p))/n))
Using the given values for different intervals the 99% for different countries are:
For Country A we have:
p = 0.34
n = 1007
z = 2.58 (based on a 99% confidence level)
CI = 0.34 ± 2.58*(√((0.34*(1-0.34))/1007)) = 0.307 to 0.373
For Country B we have:
p = 0.22
n = 1005
z = 2.58
CI = 0.22 ± 2.58*(√((0.22*(1-0.22))/1005)) = 0.187 to 0.253
For Country C we have:
p = 0.29
n = 1016
z = 2.58
CI = 0.29 ± 2.58*(√((0.29*(1-0.29))/1016)) = 0.259 to 0.321
For Country D we have:
p = 0.5
n = 1016
z = 2.58
CI = 0.5 ± 2.58*(√((0.5*(1-0.5))/1016)) = 0.469 to 0.531
For Country E we have:
p = 0.14
n = 1000
z = 2.58
CI = 0.14 ± 2.58*(√((0.14*(1-0.14))/1000)) = 0.108 to 0.172.
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could anyone help me out with this? thank you much in advance
Once we have this data, we can substitute the values into the formula to find the empirical probability that a person prefers apple pie given that they prefer whipped cream. Therefore, the missing probability is 1/12, and we know this because it is the value that makes the sum of all probabilities equal to 1.
What is probability?Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an event that is impossible, and 1 represents an event that is certain to occur. For example, if the probability of winning a coin toss is 1/2, this means that there is an equal chance of the coin landing heads or tails. Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This is known as the classical probability approach. Another approach is empirical probability, where probabilities are calculated based on observed data or experiments. Lastly, subjective probability involves making an informed guess or estimate about the likelihood of an event occurring based on subjective factors such as experience, intuition, or expert opinion. Probability is a fundamental concept in statistics and is used in many application
Here,
1. The formula needed to calculate the empirical probability that a person prefers apple pie given that they prefer whipped cream is:
P(Apple Pie | Whipped Cream) = P(Apple Pie and Whipped Cream) / P(Whipped Cream)
where P(Apple Pie and Whipped Cream) is the probability that a person prefers both apple pie and whipped cream, and P(Whipped Cream) is the probability that a person prefers whipped cream.
This formula is used because it is a conditional probability, which is a measure of the probability of an event occurring given that another event has occurred. In this case, we want to find the probability that a person prefers apple pie given that they already prefer whipped cream.
To calculate P(Apple Pie and Whipped Cream), we would need to gather data on the number of people who prefer both apple pie and whipped cream. Similarly, to calculate P(Whipped Cream), we would need to gather data on the number of people who prefer whipped cream.
2. To find the missing probability, we need to use the fact that the sum of all probabilities in a probability distribution must be equal to 1. Therefore, we can set up an equation to solve for the missing probability:
1/6 + 1/3 + x + 5/12 = 1
Simplifying the equation by finding a common denominator gives:
2/12 + 4/12 + x + 5/12 = 1
Combining like terms gives:
11/12 + x = 1
Subtracting 11/12 from both sides gives:
x = 1 - 11/12
x = 1/12
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