The value of the probability P(A ∪ B) if the events are independent events is 0.55
How to determine the value of the probabilityThe formula for the probability of the union of two events is:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Since the events A and B are independent, the probability of their intersection is simply the product of their individual probabilities:
P(A ∩ B) = P(A) × P(B)
Substituting the given values, we have:
P(A ∩ B) = 0.4 × 0.25 = 0.1
Now we can use the formula for the union:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
So, we have
P(A ∪ B) = 0.4 + 0.25 - 0.1
This gives
P(A ∪ B) = 0.55
Therefore, the probability of the union of events A and B is 0.55.
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helpppp again please
Answer: Volume = 23816.41
3) State the domain of the function \( h(t)=\frac{\sqrt{t^{2}-16}}{t+3} \) \[ (-\infty,-4] \cup[4, \infty) \text { or }\{x \mid x \leq-4 \text { or } x \geq 4\} \]
The domain of a function refers to the set of all possible input values. We can easily find the domain of the given function h(t) using the following rules:
Since the denominator cannot be zero, we must exclude the value t = -3 from the domain. This means that the domain is {t | t ≠ -3}.
Furthermore, the expression inside the square root cannot be negative since the square root of a negative number is undefined. Thus, we have t^2 - 16 ≥ 0, which implies t ≤ -4 or t ≥ 4.
Therefore, the domain of the function h(t) is given by {t | t ≠ -3, t ≤ -4 or t ≥ 4}. This can also be written in set-builder notation as {t : t ≤ -4 or t ≥ 4, t ≠ -3}.
Hence, the correct option is {\color{Red}\boxed{(-\infty,-4] \cup[4, \infty) \text { or }{x \mid x \leq-4 \text { or } x \geq 4}}}
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-x + 12y = -27 and -5x + 3y = -21
Answer:
x = 3
y = -2
Step-by-step explanation:
-x + 12y = -27
-5x + 3y = -21
Time the first equation by -5
5x - 60y = 135
-5x + 3y = -21
-57y = 114
y = -2
Now put in -2 for y and solve for x
-5x + 3(-2) = -21
-5x -6 = -21
-5x = -15
x = 3
Let's check
-5(3) + 3(-2) = -21
-15 - 6 = -21
-21 = -21
So, x = 3 and y = -2 is the correct answer.
21. A triangle has a base of 3 centimeters and
a height of 6 centimeters. Explain how the
area of the triangle will change if the base is
doubled.
Answer:
The area of a triangle is given by the formula A = 1/2 * base * height, where "base" is the length of the triangle's base and "height" is the length of the perpendicular line segment from the base to the opposite vertex.
If the base of a triangle is doubled, the height remains constant, and the area of the triangle will also double. This is because the area of a triangle is directly proportional to its base length.
In the case of the given triangle, if the base is doubled from 3 centimeters to 6 centimeters, the area of the triangle will become:
A = 1/2 * 6 cm * 6 cm = 18 cm²
Therefore, the area of the triangle will increase from 9 cm² to 18 cm² if the base is doubled while the height remains constant at 6 cm.
Step-by-step explanation:
Do what the picture says.Right answer gets brainilest!!!!
Answer:
142.5 ft^2
Step-by-step explanation:
You need to calculate each figure separately
area of the first rectangle = 5 x 4 = 20
area of the second rectangle = (5+6)x(4) = 44
area of 1/4 circle = 1/4π(10^2) = (1/4) x 3.14 x 100 = 78.5
area of figure: 78.5 + 20 + 44 = 142.5
Answer:
To find the area of this figure, we need to first determine its shape. The lengths given do not form a clear shape, so we need more information to determine the shape.
Assuming that the shape is a trapezoid with the bases of 6ft and 10ft, and a height of 5ft, we can use the formula for the area of a trapezoid:
Area = (b1 + b2) / 2 * h
where b1 and b2 are the lengths of the two parallel bases, and h is the height of the trapezoid.
Plugging in the values, we get:
Area = (6ft + 10ft) / 2 * 5ft
Area = 8ft * 5ft
Area = 40 sq ft
Area ≈ 3.73 sq m (rounded to two decimal places)
Therefore, the area of this figure is approximately 3.73 square meters.
(If it wasn't in decimals, it would be 40 square feet.)
Hopefully this helped! I'm sorry if it's wrong. If you need more help, ask me! :]
In the first week of its release, the latest blockbuster movie sold $16. 3 million dollars in tickets. The movie’s producers use the formula Pt=P₀e^-0. 4t , to predict the number of ticket sales t weeks after a movie’s release P₀, where is the first week’s ticket sales. What are the predicted ticket sales to the nearest $0. 1 million for the sixth week of this movie’s release? (Note: t = 0 for the first week. )
( the ₀ is supposed to represent a small zero)
The equation Pt=P₀[tex]e^-0[/tex]. 4t is used to predict the ticket sales of a movie after its release. For the latest blockbuster movie, the predicted ticket sales for the sixth week of the movie’s release is $7. 9 million to the nearest $0. 1 million.
The formula used to predict the number of ticket sales t weeks after a movie’s release is Pt=P₀[tex]e^-0[/tex]. 4t, where P₀ is the first week’s ticket sales. In the case of the latest blockbuster movie, the first week’s ticket sales was $16. 3 million. To calculate the predicted ticket sales for the sixth week, the time t must be set to 6. The equation then becomes , which simplifies to Pt=7. 9 million. The predicted ticket sales for the sixth week of the movie’s release is therefore $7. 9 million to the nearest $0. 1 million. The equation is a useful tool for predicting the ticket sales of a movie over time. It reflects the fact that, generally, ticket sales for a movie will steadily decline over time, with the rate of decline being determined by the value of the exponent, -0. 4 in this case. By plugging in different values for t, one can easily calculate the predicted ticket sales for a movie at any given time.
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State the range of this quadratic function.
Answer:
[-4, +∞)
Step-by-step explanation:
[-4, +∞)
Suppose at an appliances store, the price of a toaster increased from ₹400 to ₹800, while that of a microwave increased from ₹10000 to ₹10400. The increase in price for both appliances is the same, which is ₹
The increase in price for both appliances is the same, which is ₹400
Let's first find the increase in price for the toaster:
Increase in price = New price - Old price
Increase in price = ₹800 - ₹400
Increase in price = ₹400
Now, let's find the increase in price for the microwave:
Increase in price = New price - Old price
Increase in price = ₹10400 - ₹10000
Increase in price = ₹400
As we can see, the increase in price for both appliances is the same, which is ₹400.
The increase in price for both appliances is ₹400. This is found by subtracting the old price from the new price for each appliance. For the toaster, the increase is ₹800 - ₹400 = ₹400. For the microwave, the increase is ₹10400 - ₹10000 = ₹400. Since both appliances had the same increase in price, we can conclude that the percentage increase is different for each appliance. In this case, the percentage increase for the toaster is 100% [(₹800 - ₹400)/₹400 x 100%], while the percentage increase for the microwave is only 4% [(₹10400 - ₹10000)/₹10000 x 100%].
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45. Twenty-two runners compete in a cross-country race.
Three runners will each win a medal: gold, silver, or bronze.
Which of the following expressions gives the maximum
number of distinct ways the medals could be awarded?
9240
Step-by-step explanation:
In short, the maximum number of distinct ways the medals could be awarded in this race is 22 x 21 x 20 = 9240. This is calculated using a formula for permutations. Is there anything else you would like to know?
12
Solve for the value of X. Round to the nearest tenth
if necessary.
X
23
2500 m
On solving the provided question we cans ay that As a result, X is 2477, function rounded to the closest tenth.
what is function?Mathematicians examine numbers with their modifications, equations and associated structures, forms and their locations, and feasible positions for these things. The term "function" indicates the connection between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and outputs where each supply leads to a specific, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used to denote functions (x). The symbol for entry is an x. The four primary types of accessible capabilities are on functions, yet another skills, so multiple capabilities, in capabilities, and on operations.
To find X, we must isolate it on one side of the equation by executing the identical procedure on both sides.
X + 23 = 2500
Taking 23 off both sides:
X = 2500 - 23
To simplify: X = 2477
As a result, X is 2477, rounded to the closest tenth.
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A sample of 10 widgets has a mean of 32.500 and standard
deviation of 6.050. At 90% confidence, the lower limit with 3
decimal places is
The lower limit with 3 decimal places at 90% confidence is 29.266.
To determine the lower limit with 3 decimal places at 90% confidence given a sample of 10 widgets with a mean of 32.500 and standard deviation of 6.050, one would use the following steps:Step 1: Calculate the standard errorThe formula for standard error is: `standard deviation / square root of sample size`.So, `standard error = 6.050 / sqrt(10) = 1.916` (rounded to 3 decimal places).Step 2: Find the t-value for 90% confidence with degrees of freedom (df) = n - 1From a t-table or calculator, with df = 10 - 1 = 9 and 90% confidence, we find that the t-value is 1.833.Step 3: Calculate the lower limitThe formula for the lower limit of a confidence interval is: `sample mean - (t-value * standard error)`.So, `lower limit = 32.500 - (1.833 * 1.916) = 29.266` (rounded to 3 decimal places).Therefore, the lower limit with 3 decimal places at 90% confidence is 29.266.
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If a fair die is rolled 7 times, what is the probability, to the nearest thousandth, of getting exactly 5 threes?
Answer:
0.119
Step-by-step explanation:
No. of sides a die has= 6 sides
No. of times it is rolled= 7 times
Total pairs= 6 x 7
= 42 pairs
No. of 5 threes= 5 x 1
= 5
Probability of getting 5 threes= Favorable outcomes/Total outcome
= [tex]\frac{5}{42}[/tex]
= 0.119 chance
∴ probability of getting 5 threes is 0.119
For annually compounded interest, what rate would result in a single investment doubling in 3 years?
303
Step-by-step explanation:
simplify the expression 16+(-3)-3/7j-6/7j+4
Step-by-step explanation:
To simplify the expression 16+(-3)-3/7j-6/7j+4, we first need to combine like terms. The real numbers (16, -3, and 4) can be added together, and the imaginary numbers (-3/7j and -6/7j) can also be added together. So we have:
16 + (-3) + 4 + (-3/7j) + (-6/7j)
Simplifying the real numbers:
= 16 - 3 + 4
= 17
Simplifying the imaginary numbers:
= (-3/7j) + (-6/7j)
= (-9/7j)
Putting it all together, we get:
16 + (-3) - 3/7j - 6/7j + 4 = 17 - 9/7j
So the simplified expression is 17 - 9/7j.
Find -3 3/4+1/2 on a number line
Answer: - 3 1/4
Step-by-step explanation:
- 3 3/4 + 1/2
Get a common denominator
-3 3/4 + 2/4
-3 1/4
what is an equation that is parallel to y=1/2x + 1/4 and passes through the points (-6, 5)
Answer: o find an equation that is parallel to the given line, we need to use the fact that parallel lines have the same slope.
The given line has a slope of 1/2, so any parallel line must also have a slope of 1/2.
Now we can use the point-slope form of a line to find the equation of the parallel line that passes through (-6, 5):
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the given point.
Plugging in m = 1/2 and (x1, y1) = (-6, 5), we get:
y - 5 = 1/2(x - (-6))
Simplifying:
y - 5 = 1/2(x + 6)
y - 5 = 1/2x + 3
y = 1/2x + 8
So the equation of the parallel line that passes through (-6, 5) is y = 1/2x + 8.
Brainliest is Appreciated.
A bag of peanuts could be divided among
8 children, 9 children, or 10 children with each
getting the same number, and with 2 peanuts
left over in each case. What is the smallest
number of peanuts that could be in the bag?
The smallest number of peanuts that could be in the bag is 4320.
Let's use the Chinese Remainder Theorem to solve this problem.
Let:
x be the number of peanuts in the bag.
Then we know that x ≡ 2 (mod 8), x ≡ 2 (mod 9), and x ≡ 2 (mod 10).
Using the Chinese Remainder Theorem, we can find a solution for x as follows:
Let
M = 8 * 9 * 10 = 720, and let M1, M2, and M3 be the remainders when M is divided by 8, 9, and 10 respectively.
That is, M1 = 720 mod 8 = 0, M2 = 720 mod 9 = 0, and M3 = 720 mod 10 = 0.
Let b1 = 1, b2 = 1, and b3 = 1.
Then we need to find integers a1, a2, and a3 such that a1 * M1 * b1 + a2 * M2 * b2 + a3 * M3 * b3 = 1.
One solution is a1 = 5, a2 = -4, and a3 = 1,
so we have 5 * 720 * 1 + (-4) * 720 * 1 + 1 * 720 * 1 = 7201
= M1 * b1 * 2 + M2 * b2 * 2 + M3 * b3 * 2.
This means that x = M1 * b1 * 2 + M2 * b2 * 2 + M3 * b3 * 2 is a solution to the system of congruences.
Since M1 = 0, we have x ≡ 0 (mod 8).
Since M2 = 0, we have x ≡ 0 (mod 9).
Since M3 = 0, we have x ≡ 0 (mod 10).
Therefore, the smallest positive integer solution for x is x = 720 * 1 * 2 + 720 * 1 * 2 + 720 * 1 * 2 = 4320.
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Jack has 7 yards of rope. He wants to cut it into pieces of different sizes. Jack needs 84 inches of rope to tie some packages and 4 feet of rope for another project. Does Jack have enough rope? Explain. Pls help
No, Jack does not have enough rope. First, we need to convert all units to the same measurement.
Since there are 36 inches in a yard, Jack has 7 x 36 = 252 inches of rope. Additionally, 4 feet is equal to 4 x 12 = 48 inches of rope.
To determine if Jack has enough rope, we need to add the 84 inches needed for the packages and the 48 inches needed for the other project, which gives a total of 132 inches.
Since 132 inches is greater than Jack's total of 252 inches, he does not have enough rope.
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The shift in the poem's rhythm In the last stanza signifies
The change in tempo and rhyme scheme in the final stanza both hint at the speaker's unclear identity. It gives satirical overtones to the creations.
Poets choose particular rhyme schemes to elicit different responses from their audiences. It fosters a particular atmosphere and mood that may affect how we respond to the poem's themes. Rhyme can be rigid or have satirical overtones, or it can have a playful or playful atmosphere.
What effects do rhyme and rhythm have on poetry?When a poem has rhyme and meter, it is more musical. In traditional poetry, the anticipated enjoyment of a predictable rhyme aids in memorization for recitation. The use of a rhyme scheme also establishes the form. The shift in the poem's rhythm In the last stanza signifies the poets uncertain identity.
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Jeremiah measure the volume of a sink basin by modeling it as a hemisphere. Jeremiah measures its radius to be
15
3
4
15
4
3
​
inches. Find the sink’s volume in cubic inches. Round your answer to the nearest tenth if necessary
The sink's volume in cubic inches is 8182.8 cubic inches according to the radius of hemisphere.
The volume of hemisphere is calculated by the formula -
Volume = 2/3πr³, where r represents radius of the hemisphere.
Before beginning the calculation, convert radius from mixed fraction to fraction.
Radius = (15×4)+3/4
Performing multiplication and addition
Radius = 63/4 inches
Volume =
[tex] \frac{2}{3} \times \pi \times {( \frac{63}{4}) }^{3} [/tex]
Performing multiplication and taking cube
Volume = 8182.77 inches³
Rounding to nearest tenth
Volume = 8182.8 cubic inches
Hence, the volume of hemisphere is 8182.8 cubic inches.
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The complete question is -
Jeremiah measure the volume of a sink basin by modeling it as a hemisphere. Jeremiah measures its radius to be
15 3/4 inches. Find the sink's volume in cubic inches. Round your answer to the nearest tenth if necessary
An international company had 19700 employes in one country that is 22. 9 percent of there employies
The given information tells us that a particular country has 22.9% of the employees of an international company, and this amounts to 19700 employees.
The given statement implies that the international company has a total number of employees working in various countries. Out of these, 22.9% of the employees are working in a particular country, which amounts to 19700 employees in that country.
To find out the total number of employees working in all countries, we can use the following formula:
Total number of employees = Number of employees in the given country / Percentage of employees in the given country
Substituting the values given in the problem, we get:
Total number of employees = 19700 / 0.229
Total number of employees = 85939.3
Therefore, the international company has approximately 85939 employees working in various countries.
It's important to note that this calculation assumes that the proportion of employees working in the given country is representative of the proportion of employees working in other countries. However, if the proportion of employees working in other countries is significantly different, then the actual number of employees in the company could be different from the calculated value.
In conclusion, the given information tells us that a particular country has 22.9% of the employees of an international company, and this amounts to 19700 employees. We can use this information to approximate the total number of employees working in all countries.
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complete question :
An international company had 19700 employes in one country that is 22. 9 percent of there employies. Find the total number of employes in the company ?
i need help on this please
Answer:[tex]847\pi[/tex]
Step-by-step explanation:
[tex]v=\pi r^{2} h\\v=\pi 11^{2} 7\\v=847\pi[/tex]
PLEASE ANSWER!!! WILL GIVE BRAINLIEST!!!
Question 3: A rectangle has sides measuring (7x - 1) units and (2x + 3) units.
Part A:
Create an expression that represents the area of the rectangle:
Calculate the area. SHOW ALL WORK:
Write the expression in standard form:
Part B: Identify the following by using the expression below. 4x^2 + 3y - 6x^4y + 4
Degree:__
#Terms:__
Drag & Drop, write the expression in standard form.
A) -6x^4 + 4x^2 + 3y + 4
B) 4x^2 + 3y - 6x^4 + 4
C) -6x^4 + 3y + 4x^2 + 4
D) 4x^2 - 6x^4 + 3y + 4
Part C: Choose the term that makes the statement true.
Adding, subtraction or multiplying two polynomials _____ results in another polynomial.
A) Always
B) Sometimes
C) Never
Answer:
Part A:
The expression that represents the area of the rectangle is:
Area = length × width
Area = (7x - 1)(2x + 3)
Area = 14x^2 + 19x - 3
To calculate the area, we multiplied the length (7x - 1) by the width (2x + 3).
To write the expression in standard form, we rearrange the terms in descending order of degree:
Area = -3 + 19x + 14x^2
Part B:
The expression in standard form is:
-6x^4 + 4x^2 + 3y + 4
Degree: 4
Terms: 4
Part C:
Adding, subtracting, and multiplying two polynomials always results in another polynomial. Therefore, the term that makes the statement true is A) Always.
Step-by-step explanation:
The square of the binomial x+1 one hundred and 20 greater than the square of the binomial x-3
If the square of the binomial x+1 one hundred and 20 greater than the square of the binomial x-3, the value of x that satisfies the equation is x = 13.75.
Let's start by using the formula for the square of a binomial:
(a + b)^2 = a^2 + 2ab + b^2
In this case, we have:
(x + 1)^2 = x^2 + 2x + 1 (square of the binomial x+1)
(x - 3)^2 = x^2 - 6x + 9 (square of the binomial x-3)
We're told that the square of the binomial x+1 is 120 greater than the square of the binomial x-3. In other words:
(x + 1)^2 = (x - 3)^2 + 120
Substituting the expressions we found above, we get:
x^2 + 2x + 1 = x^2 - 6x + 9 + 120
Simplifying, we get:
8x = 110
Therefore, the solution is:
x = 13.75
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Complete question is:
The square of the binomial x+1 one hundred and 20 greater than the square of the binomial x-3. what is value of x?
Students are getting signatures for a petition to increase sports activities at the community center. The number of signatures they get each day is twice as many as the day before. The expressin 2 to the power of 6 represents the number of signatures thry got on thr sixth dsy. How many signatures did they grt on the first day?
The number of signatures they got on the first day is 2.
The problem can be solved mathematically by using the formula for geometric sequences, which is:
an = a1 × r^(n-1)
where:
an = the nth term in the sequence
a1 = the first term in the sequence
r = the common ratio between consecutive terms
n = the number of terms in the sequence
In this case, we know that the number of signatures they get each day is twice as many as the day before, which means that the common ratio is 2. We also know that the number of signatures they got on the sixth day is 2^6 = 64.
Using the formula for geometric sequences, we can solve for a1 by substituting the known values
64 = a1 × 2^(6-1)
64 = a1 × 2^5
a1 = 64 / 2^5
a1 = 2
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I NEED HELP ASAP!!!!
I got ya.
I wrote the answers in the boxes.
the risk of hepatoma among alcoholics without cirrhosis of the liver is 24%. suppose we observe 7 alcoholics without cirrhosis. answer the following question: a) what is the probability that exactly one of these 7 people have a hepatoma?
The probability that exactly one of these 7 people have a hepatoma is 0.35 or 35%
The risk of hepatoma among alcoholics without cirrhosis of the liver is 24%.We need to find the probability that exactly one of these 7 people have a hepatoma. Let the probability of having hepatoma be P(A) = 24% = 0.24 (given). Therefore, the probability of not having a hepatoma is P(A') = 1 - P(A) = 1 - 0.24 = 0.76. We have n = 7 people.
The probability of exactly 1 person having a hepatoma is P(1 person having hepatoma) = C(7,1) × P(A) × [tex]P(A')^{6}[/tex].
C(n, x) is the combination of n things taken x at a time. C(7,1) = 7!/1!6! = 7P(1 person having hepatoma) = 7 × 0.24 × (0.76)⁶= 0.35
Therefore, the probability that exactly one of these 7 people have a hepatoma is 0.35 or 35%.
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Pleas answer this question
find cos X
Answer:
110x
Step-by-step explanation:
its 110x
please solve with steps, im very confused
The table are shown below
The domains of the three functions are x <= 0, 0 < x <= 5 and x > 5The range of the three functions are f(x) >= -1, -1 < f(x) <= 9 and f(x) = 3The graph is attachedHow to make a table of value for the functionsFrom the question, we have:
f(x) = x^2 - 1 x <= 0
2x - 2 0 < x <= 5
3 x > 5
So, we make the table using the x values in the domain
x f(x) = x^2 - 1
0 -1
-1 0
-2 3
-3 8
x f(x) = 2x - 1
1 1
2 3
3 5
4 7
5 9
x f(x) = 3
6 3
7 3
8 3
The domain and the rangeThe domain are given in the question
So, we have the domains of the three functions to be
x <= 0, 0 < x <= 5 and x > 5
Using the table of values, we have the range of the three functions to be
f(x) >= -1, -1 < f(x) <= 9 and f(x) = 3
How to determine the graphHere, we use a graphing calculator
The graph of the function is added as an attachment
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A New York Times/CBS News Poll asked a random sample of U.S. adults the question "Do you favor an amendment to the Constitution that would permit organized prayer in public schools?" Based on this poll, the 95% confidence interval for the population proportion who favor such an amendment is (0.63, 0.69). Based on this poll, a reporter claims that more than two-thirds of U.S. adults favor such an amendment. Use the confidence interval to evaluate the reporter's claim.
a. Because the value 2/3 = 0.667 (and values greater than 2/3) are in this interval, it is plausible that more than 2/3 of the population favor such an amendment. Thus, there is convincing evidence that more than 2/3 of U.S. adults favor such an amendment.
b. Because 2/3 = 0.667 is included in this interval, it is plausible that more than 2/3 of U.S. adults favor such an amendment.
c. 95% of the time there will be more than two-thirds of U.S. adults in favor of such an amendment. Because 0.95 > 0.667, the reporter's claim is correct.
d. Because the value 2/3 = 0.667 (and values less than 2/3) are in this interval, it is plausible that 2/3 or less of the population favor such an amendment. Thus, there is not convincing evidence that more than 2/3 of U.S. adults favor such an amendment.
e. Because the value 2/3 = 0.667 (and values less than 2/3) are in this interval, it is plausible that 2/3 or less of the population favor such an amendment. Thus, there is convincing evidence that more than 2/3 of U.S. adults fuvor such an amendment.
The 95% confidence interval for the population proportion who favor an amendment for organized prayer in public schools does not provide convincing evidence that more than two-thirds.
Because the value 2/3 = 0.667 (and values less than 2/3) are in this interval, it is plausible that 2/3 or less of the population favor such an amendment. Thus, there is not convincing evidence that more than 2/3 of U.S.The 95% confidence interval for the population proportion who favor such an amendment is (0.63, 0.69). This means that if the same poll was conducted over and over again, 95% of the time the results would fall within this interval. Since the interval includes values less than 2/3, it is possible that 2/3 or less of the population favor such an amendment. Therefore, there is not convincing evidence that more than two-thirds of important to note that the confidence interval does not provide conclusive evidence either way, only an indication of the likely proportions in the population.
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